https://hdl.handle.net/1721.1/142915 2026-04-05T02:05:31Z https://hdl.handle.net/1721.1/143085 Mathematical Simulation of Tidal Time-averages of Salinity and Velocity Profiles in Estuaries Fisher, John S.; Ditmars, John D.; Ippen, Arthur T. Scanning notes: Disclaimer inserted for illegible graphs and text. 1972-07-01T00:00:00Z https://hdl.handle.net/1721.1/143084 A Mathematical Model for the Prediction of Unsteady Salinity Intrusion in Estuaries Thatcher, M. Llewellyn; Harleman, Donald R. F. The salinity structure of a tidal estuary fed by upstream fresh water sources is an important factor of water quality. In addition, this structure is intimately related to the circulation of the estuary because of density currents induced by the salt-fresh water relation. Previous investigations in two and three dimensions have been limited to extremely simplified geometrical and steady-state assumptions. One dimensional studies have considered the variable area case, but have been limited to descriptive rather than predictive methods because of the difficulty of handling the downstream boundary condition for the one-dimensional salt balance equation and because of the necessity to specify a longitudinal dispersion coefficient based on field data for the estuary being studied. This study presents a predictive numerical model of unsteady salinity intrusion in estuaries by formulating the problem in finite-difference terms using the one-dimensional, tidal time, variable area equations for the conservation of water mass, conservation of momentum and conservation of salt. Tidal time means a time scale of calculation larger than that defining turbulence, but much smaller than a tidal period in order to correctly represent the tidal advection within a tidal period. The tidal dynamic equations are coupled to the conservation of salt equation through a salinity-density relationship, and the ocean boundary condition for salt is formulated in a manner which depends on the direction of flow at the entrance to the estuary. The longitudinal dispersion coefficient has been shown to be proportional to the magnitude of the local, time-varying longitudinal salinity gradient, and this constant of proportionality has been shown to depend on a dimensionless parameter which expresses the degree of vertical stratification of the estuary. This relationship has been established for a wide range of stratification conditions. The mathematical model has been verified using data from the Waterways Experiment Station salinity flume and field data from the Delaware, the Potomac, and the Hudson. By specifying initial conditions, fresh water hydrographs, and tidal elevations at the ocean, it is possible to predict the time-varying salinity using this model. Prepared under the support of the Office of Sea Grant National Oceanic and Atmospheric Administration U. S. Department of Commerce through Coherent Area Project Grant GH-88 2-35150 1972-02-01T00:00:00Z https://hdl.handle.net/1721.1/143083 Simulation of Observed Topography Using a Physically-based Basin Evolution Model Moglen, Glenn E.; Bras, Rafael L. This work presents a model for basin evolution and a procedure for estimating the parameters of this model to reproduce a given topography. The model is calibrated based on three measures: the slope-area relationship, the cumulative area distribution, and the hypsometric curve. We find that these measures quantify fundamentally different characteristics of the drainage basin. We show that spatial variability and structure are inherently necessary to sufficiently reproduce observed statistics of a basin. The presence of uncorrelated spatial variability introduces scatter to the slope-area relationship which is consistent to the scatter observed for an observed system. Uncorrelated spatial variability also influences the cumulative area distribution by causing the drainage aggregation pattern to encompass a greater spread of cumulative drainage areas around the representative hillslope scale. In contrast, a system with no spatial variability exhibits an almost single-valued distribution for the representative hillslope scale. We illustrate how the channel selectively chooses pixels of greater susceptibility to erosion in which to grow. Based on a knowledge of the underlying distribution of spatial heterogeneities, we show that channel extension is limited to effectively three potential growth sites at any location. These results were confirmed for two different distributions: normal and uniform. This channel selectivity has the consequence of reducing the mean channel slope by an analytically determined amount based on the fluvial sediment transport parameters and the distribution of heterogeneities. We analyze the effect of spatially correlated soil heterogeneities on simulated basins. Such correlations cause a shift in the slope-area relationship power-law exponent, 6. Correlated heterogeneities also have a profound influence on the hypsometric curve. We show how correlated erosivity in the horizontal direction leads to smaller mean basin elevations compared to the control or prototypical case. Meanwhile, stratification in heterogeneities may lead to larger or smaller mean basin elevations depending on the stratification pattern. The process for calibrating the basin evolution model to statistically reproduce a given topography is presented. The process entails making initial estimates of model parameters from the observed slope-area relationship and using a numerical optimization package to determine the remaining parameter values. The numerical optimization process employs an off-line version of the evolution model which predicts the cumulative area distribution that would result from a given set of parameter values. The optimization selects the model parameters that will best reproduce the observed cumulative area distribution. The resulting simulation may be subsequently improved to reflect stratification or any other peculiarities that are present in the observed system. Finally, we illustrate how the hydrologic response of a simulated basin is a function of the basin evolution model parameters that created it. Most notably, we show that the distribution of saturated areas is significantly affected by the presence of spatial heterogeneities in erosivity. Results indicate that as heterogeneities increase within a basin, there is a greater spread in saturation indices. Thus, as the degree of heterogeneity in erosivity increases within a basin, the predicted runoff response from the basin becomes decreasingly sensitive to errors in estimation of the degree of saturation. Prepared under the support of the U.S. Army Research Office under agreement DAAL03-92-G-0182 1994-10-01T00:00:00Z https://hdl.handle.net/1721.1/143082 Use and Characterization of Steady-state Soil Moisture Profile in Setting Flux Capacities Prior to Storm and Interstorm Events Salvucci, Guido D.; Entekhabi, Dara Supported by the National Aeronautics and Space Administration. NAS5-31721 NAGW-1696 1993-05-01T00:00:00Z https://hdl.handle.net/1721.1/143081 Climatology of Station Storm Rainfall in the Continental United States: Parameters of the Bartlett-Lewis and Poisson Rectangular Pulses Models Hawk, Kelly Lynn; Eagleson, Peter S. The parameters of two stochastic models of point rainfall, the Bartlett-Lewis model and the Poisson rectangular pulses model, are estimated for each month of the year from the historical records of hourly precipitation at more than seventy first-order stations in the continental United States. The parameters are presented both in tabular form and as isopleths on maps. The Poisson rectangular pulses parameters are useful in implementing models of the land surface water balance (eg. Eagleson, 1978). The Bartlett-Lewis parameters are useful in disaggregating precipitation to a time period shorter than that of existing observations (Rodriguez-Iturbe et al., 1987). Supported by the National Aeronautics and Space Administration. NAS 5-31721 1992-05-01T00:00:00Z https://hdl.handle.net/1721.1/143080 A Test of Ecological Optimality for Semiarid Vegetation Salvucci, Guido D.; Eagleson, Peter S. Three ecological optimality hypotheses (Eagleson, 1978 and 1982) which have utility in parameter reduction and estimation in a climate-soil-vegetation water balance model are reviewed and tested. The first hypothesis involves short term optimization of vegetative canopy density through equilibrium soil moisture maximization. The second hypothesis involves vegetation type selection again through soil moisture maximization, and the third involves soil genesis through plant induced modification of soil hydraulic properties to values which result in a maximum rate of biomass productivity. The first hypothesis is found to be in excellent agreement with data observed at the Beaver Creek watershed in Central Arizona. The utility of this hypothesis in estimating soil properties is supported. The second hypothesis is found to be physically unrealistic and alternatives to the hypothesis are studied. Conditions at Beaver Creek are not appropriate for testing the third hypothesis. While the locus of canopy densities predicted by the short term ecological hypothesis creates a condition of stress free transpiration in typical years, lower than mean annual rainfall may still lead to drought-induced stress. In order to quantify this phenomenon, the expected value of the time spent in stress, and the resulting reduced transpiration, are analytically derived. The results of this analysis are shown to be useful in gaining a quantitative understanding of the water environment of semiarid regions and the drought tolerance required of its local vegetation. Prepared under the support of the National Aeronautics and Space Administration grant no. NAGW 1696 1992-05-01T00:00:00Z https://hdl.handle.net/1721.1/143079 The Implementation and Validation of Improved Landsurface Hydrology in an Atmospheric General Circulation Model Johnson, Kevin D.; Entekhabi, Dara; Eagleson, Peter S. New landsurface hydrological parameterizations are implemented into the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: 1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically-based equations of hydrologic flux at the soil surface, and 2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one-dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three-dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics, is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales. (Key words: Climate modeling, Global hydrology) Supported by the National Aeronautics and Space Administration. NAG 5-743. Supported by the Ralph M. Parson Foundation. 1991-10-01T00:00:00Z https://hdl.handle.net/1721.1/143078 Atmospheric Water Vapor Transport: Estimation of Continental Precipitation Recycling and Parameterization of a Simple Climate Model Brubaker, Kaye L.; Entekhabi, Dara; Eagleson, Peter S. The advective transport of atmospheric water vapor and its role in global hydrology and the water balance of continental regions are discussed and explored. The data set consists of ten years of global wind and humidity observations interpolated onto a regular grid by objective analysis. Atmospheric water vapor fluxes across the boundaries of selected continental regions are displayed graphically. The water vapor flux data are used to investigate the sources of continental precipitation. The total amount of water that precipitates on large continental regions is supplied by two mechanisms: (1) advection from surrounding areas external to the region and (2) evaporation and transpiration from the land surface within the region. The latter supply mechanism is tantamount to the recycling of precipitation over the continental area. The degree to which regional precipitation is supplied by recycled moisture is a potentially significant climate feedback mechanism and land surface-atmosphere interaction, which may contribute to the persistence and intensification of droughts. A simplified model of the atmospheric moisture over continents and simultaneous estimates of regional precipitation are employed to estimate, for several large continental regions, the fraction of precipitation that is locally derived. In a separate, but related, study estimates of ocean-to-land water vapor transport are used to parameterize an existing simple climate model, containing both land and ocean surfaces, that is intended to mimic the dynamics of continental climates. Supported by a National Science Foundation Graduate Fellowship. Supported by the National Aeronautics and Space Administration. NAG 5-743 1991-07-01T00:00:00Z https://hdl.handle.net/1721.1/143077 A Channel Network Evolution Model with Subsurface Saturation Mechanism and Analysis of the Chaotic Behavior of the Model Ijjasz-Vasquez, Ede J.; Bras, Rafael L. Prepared under the support of the National Science Foundation, Army Research Office and National Research Council of Italy. 1990-09-01T00:00:00Z https://hdl.handle.net/1721.1/143076 A Distributed, Physically-based, Rainfall-runoff Model Incorporating Topography for Real-time Flood Forecasting Cabral, Mariza C.; Bras, Rafael L.; Tarboton, David; Entekhabi, Dara We present a distributed, physically-based model of runoff generation in a catchment, for operational use in flood forecasting. The model accounts for both the infiltration-excess and saturation-excess mechanisms of runoff production, and for lateral subsurface flows. The effect of local terrain slope on subsurface flows and the development of areas of saturated soil is accounted for. The model uses spatial discretization into rectangular elements which correspond to the grid of a Digital Elevation Map. Each basin element consists of a soil column in which hydraulic conductivity decreases with depth, in the form of an exponential function. Spatial discretization allows for distributed terrain slope, soil parameters, moisture conditions, and rainfall inputs. Time discretization allows for consideration of time-variable rainfall rates. The model uses the kinematic approximation of infiltration and subsurface flows, which are assumed to occur only within the porous soil matrix. The kinematic model of infiltration is used to show how decreasing conductivity with depth may result in the development of a zone of perched saturation during a rainstorm, and that the flow in the perched saturated zone is diverted laterally if the terrain is inclined. A simplified computational procedure is introduced that allows flow transfer among elements. Inter-element flow transfers are used to predict the position of the permanent water-table in each element at the time of initiation of the rainfall event and the extent of the area of saturated soils. Moisture transfer between elements during the storm is also considered. The model is extended to consider anisotropic soils, and we show that higher lateral than vertical conductivity results in increased lateral diversion of flow. The model was applied to the Sieve catchment in Italy and used to reproduce hydrographs for 12 recorded rainstorms. Given that pre-storm baseflow was not available for any of the 12 storms, three different water-table positions were considered for each storm, low average and high, corresponding to steady-state equilibrium with the baseflow values that have a 90% and 10% probability of being exceeded in the month in question. The observed hydrographs for the various storms were, generally, in the area comprised between the "dry" and "wet predicted hydrographs, or did not fall far from this area. Given the scarcity of data available for the Sieve, we consider model predictions to be quite encouraging. Research partially supported by the Arno Project of the National Research Council of Italy through a cooperative agreement with the University of Florence, Italy and the Ralph M. Parsons Foundation. Research partially supported by the U.S. Army Research Office grant DAAL0-3-89-K-0151. Research partially supported by the National Science Foundation grant CES-8815725. Research partially supported by the National Weather Service cooperative agreement NA86AA-D-HY123. 1990-10-01T00:00:00Z https://hdl.handle.net/1721.1/143075 Chemically Enhanced Wastewater Treatment Morrissey, Shawn P.; Harleman, Donald R. F. Many municipalities are currently under court order to provide secondary-level treatment to their wastewater. Since federal funding is no longer available to build the necessary facilities, the burden of paying for secondary treatment is on the rate-payers. Traditionally, conventional primary treatment followed by a biological process has been used to obtain secondary levels of treatment; however, the capital and operations and maintenance costs for this type of treatment are high. Chemically-enhanced wastewater treatment is a lower-cost alternative. Both jar and full-scale tests using chemicals and polymers have been conducted at South Essex Sewerage District (SESD) to determine the effects of chemically-enhanced wastewater treatment. SESD's plant is unique in that it can be run as two distinct, parallel, and simultaneous processes. This allowed a direct comparison between chemical treatment and conventional primary treatment. The test results indicate a significant improvement in the removal of total suspended solids, biochemical oxygen demand, phosphorus, and fats, oils, and greases without a large accumulation of sludge. The chemically-enhanced wastewater treatment process is extremely promising in terms of reducing the size of any additional treatment facilities needed to meet secondary levels, increasing the performance of overloaded clarifiers, and as a viable alternative to biological secondary treatment especially in environments where nutrient removal is more of a concern than BOD effluent concentrations (such as in the ocean). Supported by MIT's School of Engineering, the Dept. of Civil Engineering and the Ralph M. Parsons Foundation. 1990-09-01T00:00:00Z https://hdl.handle.net/1721.1/143074 Hydraulic Model Study of Seawater Purging for the Boston Wastewater Outfall Adams, E. Eric; Sahoo, Dipak; Liro, Christopher R. A 1:83 hydraulic scale model was built to study the mechanism of seawater purging in the tunneled outfall that will convey effluent from MWRA's Secondary Treatment Plant on Deer Is. out into Massachusetts Bay. Purging generally requires high rates of effluent flow which presents a concern for the Boston system because of the wide range of expected flow rates. Daily average flow rates are expected to range from about 320 mgd to 1270 mgd although instantaneous rates as low as 150 mgd may occur. Model results for the original outfall design (described in the Secondary Treatment Facilities Plan) showed that riser purging would require an effluent flow rate of over 900 mgd, which is slightly less than the theoretical (Munro) criterion. Furthermore, because of the increase in tunnel invert slope beginning at the riser section, tunnel purging would require an effluent flow rate of over 800 mgd. Hence there would be significant periods of time when the effluent flow rate would be insufficient to purge seawater from either the tunnel or the riser sections of the outfall. The resulting unpurged condition would lead to poor distribution of the effluent within the receiving water and possible problems with sediment accumulation and biofouling within the tunnel. However, once purged the outfall would not experience seawater intrusion until flows dropped below the expected low-flow condition. Construction of a tunnel constriction (Venturi section) just upstream from the risers was found to substantially reduce seawater penetration in the tunnel by creating a condition of densimetric critical flow. Theoretical calculations for a section with a 10' throat suggested that penetration could be eliminated for flows greater than about 420 mgd while observations showed elimination for flows greater than about 340 mgd. The lower observed flow is attributed to downstream mixing. The effluent flow rate required for riser purging would remain essentially the same--about 900 mgd. Further tests showed that, in combination with the Venturi section, a short-term increase in effluent flow caused by intermittent dumping of the chlorine-contact tanks would significantly reduce the purging requirement. The release could be made through motorized gates and would require a peak flow of at least 700 mgd over a duration of 10 to 20 minutes. The total excess flow volume would be about 600,000 ft3, which is about one-third of the total volume and about one-half of the active volume of the chlorine-contact tanks. Because of the absence of seawater penetration upstream of the Venturi, this "rapid-purge" procedure would be successful at base flows down to 340 mgd or less, substantially increasing the periods of time when purging is possible. Sponsored by Metcalf and Eddy, Inc., Wakefield, Mass. OSP 72065. Sponsored by the Massachusetts Water Resources Authority, Boston, Mass. 1990-04-01T00:00:00Z https://hdl.handle.net/1721.1/143073 Comparison of Cooling Lake Mathematical Models for Mount Storm Lake Adelaja, Olutoyin M.; Adams, E. Eric Mt. Storm Lake is an impoundment of the Stony River that provides cooling for the three-unit electric generating station which is owned by Virginia Power. The lake is relatively deep and narrow with a submerged intake and a surface discharge. Although the temperature structure in a cooling lake is usually three dimensional, it is often possible to use reduced dimension calculations to make sufficiently accurate predictions by dividing the lake into zones. MITEMP is a time-dependent temperature model for cooling lakes consisting of a 1-D (longitudinal) surface layer overlying a 1-D (vertical) variable-area hypolimnion. This model was adapted to Mt. Storm Lake using available field data for calibration and verification. The initial model predictions, using data from Sept. 1986 - Aug. 1987 and made prior to our calibration, were quite good with average errors ranging from -0.1 to -1.10�C depending on location within the lake. Model calibration consisted of adjustments to the net solar radiation, as well as the entrance dilution coefficient and the surface layer longitudinal dispersion coefficient. The average errors after calibration were reduced to about 0-0.50 C with a standard deviation of 1-1.40 �C. The residual time series of model errors after calibration was shown to be correlated to station generation, indicating that better model performance could be achieved by an improved representation of the heat rejection. As part of a related study, a O-D water and energy balance model was developed to assess water availability at Mount Storm Lake under several different scenarios. This model is very efficient, requiring less than five minutes of CPU time to do over 1000 years of simulation in comparison with about 3 minutes for a 1-year simulation with MITEMP. (Both are for a MicroVax II.) The temperature predictions of the 0-D model were evaluated to assess its accuracy as a screening model. Although the model is steady-state, it was shown theoretically and empirically to have similar thermal inertia to a transient model if 30-day (monthly averaged) data were used as input. Results show that the 0-D model predicts the lake temperature fairly accurately. The mean error varies between 0.35 �C for different averaging intervals between 10 and 40 days, and the standard deviation is 2.50� C using 30-day averaged data. A preliminary comparison was also made between MITEMP and a 2-D (longitudinal and vertical transient model), NARES, to see what changes in thermal structure result from an improved description of the flow field.. There was not time to complete this part of the study, but initial model predictions show reasonable agreement between observed and predicted longitudinal variation in hypolimnetic temperature. However, because the maximum observed longitudinal variation is only about 2.00 �C, the added detail is not critical especially since the 2-D model is quite time consuming to run (about 14 hours of MicroVax II CPU time for an annual simulation). This is two-and-one-half orders of magnitude more expensive than MITEMP. However, there is the potential for this model to provide useful information if a new generating facility were to be added at a different location on the lake. However, it would require more calibration and validation effort. Supported by Virginia Power, Richmond, Virginia. 1990-03-01T00:00:00Z https://hdl.handle.net/1721.1/143072 A Physiological Explanation for Vegetation Ecotones in Eastern North America Arris, L. L.; Eagleson, P. S. Prediction of the vegetative cover of land surfaces as climatic conditions change is an important aspect of general circulation models that has not been adequately explored. In this study, a model is developed for the purpose of predicting the location of two major vegetation ecotones in eastern North America based on the interaction of plant physiological characteristics, climate, and edaphic influences. The model represents the relative competitive ability of different vegetation types by their annual net primary productivity. At any given location, the vegetation type with the highest productivity is predicted to be the dominant type. Ecotones are located where competitive dominance shifts from one vegetation type to another. Productivity is computed as a function of annual evapotranspiration, which is a function of the length of the growing season, photosynthetic capacity, potential evapotranspiration, and soil moisture availability, among other things. When considering the boreal/deciduous forest ecotone, it is found that inherent physiological differences between conifers and deciduous trees lead to differences in productivity which are related primarily to temperature. The model predicts deciduous dominance to a latitude slightly north of the observed ecotone location. However, an absolute physiological limit in the form of low temperature tolerance is apparently preventing the deciduous forest formation from further northward migration. It was necessary to include soil characteristics when considering the deciduous/southern pine ecotone. Water limitations apparently play a role in the determination of this boundary, although the model results indicate that an additional limiting factor is also operating at this ecotone. It is suggested that nutritional limitations may be present as a result of the soil characteristics of the region, and that this may contribute to the dominance of pine in the south. Supported by the NSF grant ECE-8603628. Supported by the MIT Edmund K. Turner Professorship and an Ida M. Green graduate fellowship. 1989-06-01T00:00:00Z https://hdl.handle.net/1721.1/143071 The Analysis of River Basins and Channel Networks Using Digital Terrain Data Tarboton, David G.; Bras, Rafael L.; Rodriguez-Iturbe, Ignacio This work examines patterns of regularity and scale in landform and channel networks. Digital elevation model data sets from throughout the United States are used as a data source. First we consider the two-dimensional planform properties of channel networks. We find that networks as a whole may be regarded as space filling fractals, ie.., with fractal dimension 2. The scaling may be described by Horton's laws and provides a link between Horton length and bifurcation ratios. Second we focus on elevation where the mean slope of rivers is characterized by a power law scaling with area. Investigations have recently used this to suggest that channel slopes are self-similar with magnitude or area as a scaling index. Our data indicates otherwise; in particular the variance of channel slope is larger than that predicted by simple self-similarity. The coefficient of variation of link slopes increases with area contributing to the link. This suggests multi-scaling. The scaling exponent for the standard deviation is approximately half the corresponding exponent in the relationship of the slope mean to magnitude or area. A model for channel slopes based on a point process of elevation drops along the channel is suggested. This model reproduces the observed multi-scaling properties when the density of elevation increments is related to area (or magnitude) as A-0. This scaling cannot hold in the limit of small area and must break at some point. We suggest that this break defines the lower bound scale for which channels exist and can therefore be used to determine the drainage density, the basic horizontal length scale associated with the dissection of the landscape by the channel network. This break in scale can also be detected as a break in the constant drop property, namely the empirical fact that the elevation drop along Strahler streams is on average constant. That the break in scale gives drainage density is justified using a stability analysis of landform development processes and empirical comparison of drainage densities from many DEM data sets. This work provides a rational way to extract channel networks with physically justifiable drainage density from digital elevation models. Prepared under the support of the National Science Foundation ECE-8513556. Prepared under the support of the National Research Council of Italy through a cooperative agreement with the University of Florence. 1989-09-01T00:00:00Z https://hdl.handle.net/1721.1/143070 Landsurface Hydrology Parameterization for Atmospheric General Circulation Models: Inclusion of Subgrid Scale Spatial Variability and Screening with a Simple Climate Model Entekhabi, Dara; Eagleson, Peter S. Parameterizations are developed for the representation of subgrid hydrologic processes in atmospheric general circulation models. Reasonable a priori probability density functions of the spatial variability of soil moisture and of precipitation are introduced. These are used in conjunction with the deterministic equations describing basic soil moisture physics to derive expressions for the hydrologic processes that include subgrid scale variation in parameters. The major model sensitivities to soil type and to climatic forcing are explored offline of the climate model. For more comprehensive sensitivity analyses, a one-dimensional model equipped with GCM physical parameterizations is used. The dynamic heat and moisture convergence are parameterized. The advantages of online sensitivity analyses with this one-dimensional model is that the major model climate landsurface-atmosphere feedbacks are essentially reproduced in this simple GCM analog. The climate model is then used to screen various alternatives and sensitivity simulation experiments. Prepared under the support of the National Aeronautics and Space Administration. NAG 5-743 1989-09-01T00:00:00Z https://hdl.handle.net/1721.1/143069 Physically-based Parameterization of Spatially Variable Soil and Vegetation Using Satellite Multispectral Data Jasinski, Michael F.; Eagleson, Peter S. A stochastic-geometric landsurface reflectance model is formulated and tested for the parameterization of spatially variable vegetation and soil at subpixel scales using satellite multispectral images without ground truth. Landscapes are conceptualized as three-dimensional Lambertian reflecting surfaces consisting of plant canopies, represented by solid geometric figures, superposed on a flat soil background. Multiple scattering among landsurface components is neglected. The model is cast within the framework of an existing theoretical model of upwelling solar radiance for optically-thin atmospheres, as observed by a nadir-viewing satellite. A computer simulation program is developed in order to investigate image characteristics at various spatial aggregations representative of satellite observational scales, or pixels. In particular, the evolution of the shape and structure of the red-infrared space, or scattergram, of typical semi vegetated scenes is investigated by sequentially introducing model variables into the simulation. The correlation between canopy and shadow is identified as a principal mechanism contributing to the frequently observed tasseled cap of red-infrared scattergrams of semivegetated landscapes. A Sampling Scale Ratio is formulated as a quantitative criterion that identifies when that correlation occurs. The analytical moments of the total pixel reflectance, including the mean, variance, spatial covariance, and cross-spectral covariance, are derived in terms of the moments of the individual fractional cover and reflectance components. The moments are applied to the solution of the inverse problem: The estimation of subpixel landscape properties on a pixel-by-pixel basis, given only one multispectral image and limited assumptions on the structure of the landscape. The inverse procedure involves the formulation of conditional moments for subsets of pixels that possess similar properties, and that can be identified through their common orientation in red-infrared scattergrams. The analysis is facilitated by assuming geometric similarity among canopy elements and by assuming a functional relationship between fractional covers in the case of large Sampling Scale Ratios. The landsurface reflectance model and inversion technique are tested using actual aerial radiometric data collected over regularly spaced pecan trees, and using both aerial and Landsat Thematic Mapper data obtained over discontinuous, randomly spaced conifer canopies in a natural forested watershed. For the Landsat case, adjacency effects are neglected by assuming low interpixel contrast. Different amounts of solar backscattered diffuse radiation are assumed and the sensitivity of the estimated landsurface parameters to those amounts is examined. Prepared under the support of the NASA Goddard Space Flight Center NAG 5-510 NAGW-1696 1989-09-01T00:00:00Z https://hdl.handle.net/1721.1/143068 Technology and Policy Issues Involved in the Boston Harbor Cleanup Morrissey, Shawn P.; Harleman, Donald R. F. Introduction: Throughout history, disposing of human wastes has been a problem. In the late 1800's, when communities began to flourish, it was generally believed that human waste was the source of many diseases. The principal method of disposal at this time was to discharge the waste into local waters - rivers, lakes, or the ocean. In the Boston area, the receiving water was the Boston Harbor. In the late-1800's, Boston's waste was combined with water, transported to Deer Island and Moon Island, chlorinated, and discharged into the harbor. In the early- 1900's, Boston's disposal method was considered innovative because wastewater from Moon Island was discharged only on the outgoing tide. By the mid-1900's, Boston realized that its method of wastewater disposal was beginning to adversely effect the water quality and aesthetics of the harbor. Primary treatment of the wastewater did not begin until the late-1960's when the Deer Island and Nut Island facilities were constructed. Due to Boston's rapid population growth, these primary treatment plants were obsolete the moment they began operation. Both plants discharge chlorinated effluent and chlorinated digested sludge into the President Roads area of the Boston Harbor. The sludge is still discharged only on the outgoing tide. Boston and some of its neighboring communities have a combined sewer system. This system transports both wastewater and stormwater to the treatment facilities. During periods of excessive flows, the combined sewers are designed to overflow into nearby waters - such as Boston Harbor and the freshwater rivers that feed the harbor. These discharges occur frequently (more than one hundred times per year) in the Boston area which results in an estimated overflow of 40 billion liters per year of wastewater and stormwater into the harbor. These overflows cause beach and shellfish bed closures throughout the area. The Clean Water Act (CWA), created in 1972 and amended in 1977, required all municipalities to provide uniform (secondary) treatment to the wastewater before releasing it into the receiving water. At this time, the federal government was providing funding for 85% of the construction costs for the secondary treatment facilities. In the amended act, a provision, under section 301(h), allowed municipalities the right to waive the secondary treatment requirements if they were discharging into marine waters through a long outfall. The Metropolitan District Commission (MDC), who at that time was responsible for providing treatment to the greater Boston area wastewater, believed that the benefits of secondary treatment were not justified. This was based on a number of studies that determined the priority of 52 projects related to the Boston Harbor cleanup. Secondary treatment ranked 4 3rd. Based on these findings, MDC applied for the secondary treatment waiver. It was not until nearly eight years after the enactment of the amended CWA that MDC was tentatively denied its waiver. During this time, nothing was done to improve the wastewater treatment facilities because no funding was made available during the waiver application process. Political tensions surrounding the Boston Harbor cleanup issues began to emerge and a new agency, Massachusetts Water Resources Authority (MWRA), was created. MWRA is responsible for providing treatment to the wastewater. When MWRA was established, there was strong political and legal pressure to cleanup the Boston Harbor. Due to this pressure, MWRA gave up its right to appeal the tentative denial of the secondary treatment waiver and began plans for the construction of a secondary treatment facility. The construction schedule consisted of consolidating the treatment process at a single location on Deer Island. The treatment process would provide primary treatment by 1995 and secondary treatment by 1999 of all MWRA wastewater. This schedule also included the construction of an outfall to transport the effluent 14 km off the shore of Deer Island, and to stop ocean disposal of the sludge. The estimated cost of this project is $6.1 billion. At this time, the funding by the federal government for the construction of secondary treatment facilities is no longer available; therefore, the burden of paying for these facilities is on the taxpayers. Ever since the enactment of the CWA, scientists have been questioning the need for disposing secondary treated effluent into deep coastal waters. This question has been the focal point of many debates on Boston Harbor. Although, an even more important question for the taxpayers and MWRA is - whether the $6.1 billion project will cleanup the harbor? This document summarizes the enormous amount of literature available on the technical and political issues related to the Boston Harbor cleanup. Chapter 1 and 2 discuss the physical aspects of the Boston Harbor and the existing treatment facilities. Chapter 3 addresses the technical and political issues that led to the decision to construct secondary treatment facilities. The components of the proposed secondary treatment facilities are discussed in detail in Chapter 4. The management of sludge, which is the residual byproduct of secondary treatment, is discussed in Chapter 5. Controlling the combined sewer overflows - a major source of pollution to the Boston Harbor - are discussed in Chapter 6. Chapter 7 discusses the modeling and monitoring efforts done to date and the efforts recommended for the future. Finally, Chapter 8 discusses alternate ways of approaching the cleanup. Prepared under the support of the S. Technology Center of America, Inc. and M.I.T. Civil Engineering Department. 1989-11-01T00:00:00Z https://hdl.handle.net/1721.1/143067 A Physically Based Channel Network and Catchment Evolution Model Willgoose, Garry; Bras, Rafael L.; Rodriguez-Iturbe, Ignacio A catchment evolution and channel network growth model is presented. Elevations within the catchment are simulated by a sediment transport continuity equation applied over geologic time. Sediment transport may by modelled by both fluvial (e.g. Einstein-Brown) and mass movement (e.g. creep and landsliding) mechanisms. An explicit differentiation between the channel and the hillslope is made with different transport processes in each regime. The growth of the channel network is governed by a physically based threshold, which is nonlinearly dependent on discharge and slope and thus governed by hillslope form. Hillslopes and the growing channel network interact through the different sediment transport processes and the preferred drainage to the channels to produce the long term form of the catchment. General requirements for network formation in physically based models are examined by use of a previously reported leaf vein growth model. Elements of chaos were discovered that result in apparently random networks being generated. It was argued that this is also true for the catchment and connections with topologically random networks were provided. Synthetic catchments were simulated using a numerical implementation of the model and statistics for the catchments are analyzed. Drainage density and elevation characteristics are correlated with nondimensional numbers arising from a nondimensionalization of the governing equations. These nondimensional numbers parameterize rates of tectonic uplift, sediment transport, both in the channel and the hillslope, channel growth, and resistance to channelization. Runoff rate, erodability and flood frequencies arise explicitly in these numbers. A fundamental measure of catchment dissection based on one of the nondimensional numbers is proposed. It follows that drainage density and hillslope length are dependent, in a well defined way, on runoff rate, slopes and catchment erodability. Simulation results are compared with reported field data and small scale experimental catchment evolution studies and found to be consistent. A linear log-log relationship between channel slope and area, observed in the field, is also observed in the simulation data at dynamic equilibrium. An explanation based on model physics is proposed, a central feature being the balance between tectonic uplift and fluvial erosion at dynamic equilibrium. This explanation also accounts for observed deviations from the linear log-log relationship where slopes are reduced for small areas; these small areas are dominated by diffusive transport processes in the hillslope. The channelization threshold based on discharge and slope is compared with recently reported data of hillslope slopes and contributing areas at channel heads; the threshold is consistent with the field data. Observed differences between hypsometric curves, previously attributed to catchment age, are found to result from differences in the tectonic uplift regime. A scheme for landscape classification, based on the nondimensional numbers, is proposed which is more consistent with the governing physical processes than previous work. A one-dimensional advection-diffusion reformulation of the sediment transport equation is proposed that predicts rates of hillslope retreat and hillslope degradation, and provides a link to observed hillslope transport mechanisms. Partly supported by the National Science Foundation grant 8513556-ECE. Partly supported by the National Weather Service Cooperative Research Agreement NA86AA-H-HY123. 1989-06-01T00:00:00Z https://hdl.handle.net/1721.1/143066 Evaluation of Longitudinal Dispersivity from Tracer Test Data Welty, Claire; Gelhar, Lynn W. Introduction: Mathematical modeling of solute transport has become a standard tool for evaluating the movement and spreading of chemical contaminants in the subsurface aquatic environment. Most frequently, numerical techniques such as finite element or finite difference methods are used to solve the governing partial differential equations of flow and solute transport over a large aquifer region, in order to predict the concentration of a chemical contaminant at some future time and at points distant in space from a source. One problem that continues to plague users of these techniques is estimation of mixing or dilution parameters, or more specifically the dispersivity (if the dispersion coefficient is assumed to be the product of dispersivity and mean pore velocity), in the governing equations. Summaries of field observations (e.g., Lallemand-Barres and Peaudecerf, 1978; Anderson, 1979; and Gelhar, et al., 1985) and theoretical studies (e.g., Gelhar and Axness, 1983) both have indicated that dispersivity is a function of the heterogeneity of the geologic formation and that there is a dependence of the value of dispersivity on the solute displacement distance in the aquifer. Typically, then, there is a need to determine a value for dispersivity for the aquifer material and scale of problem at hand. Tracer tests are often attempted as a means of estimating the required dispersivity. Figure 1-1 from Gelhar, et al. (1985), summarizes the information available on longitudinal dispersivity values determined from tracer tests conducted at various length scales and on many type of aquifer materials around the world. Figure 1-2 illustrates the ranking of the relative reliability for these same data, based on judgements about the type of experiment and method of data interpretation. This graphical summary reinforces the fact that modelers indeed face difficulties in determining the proper value of dispersivity for a given problem. It is with this motivation in mind that we explore improved methods for analysis of tracer tests to yield accurate information on dispersivity values. This will contribute to more realistic modeling of the solute transport process in evaluation of groundwater contamination cases. The two overall goals of this study are: 1) to develop and demonstrate improved methods of analyzing existing tracer test data; and 2) to use this information and experience to better define the reliability of existing data and to provide an improved basis for selecting, designing, and analyzing tracer tests. Scanning notes: Missing innner title page. Page 32 contains text that runs off edge of page. Disclaimer scanned.; Prepared with the support of U.S. Environmental Protection Agency and National Science Foundation. 1989-03-01T00:00:00Z https://hdl.handle.net/1721.1/143065 Three-dimensional Flow in Random Porous Media Ababou, Rachid; Gelhar, Lynn W.; McLaughlin, Dennis Supported by the Nuclear Regulatory Commission. NRC-04-83-174. Supported by the National Science Foundation. ECE-8311786. 1988-03-01T00:00:00Z https://hdl.handle.net/1721.1/143064 Numerical Simulation of Solute Transport in Randomly Heterogeneous Porous Media: Motivation, Model Development, and Application Tompson, Andrew F. B.; Vomvoris, Efstratios G.; Gelhar, Lynn W. A particle tracking, or "random walk" solute transport model is developed to study detailed contaminant movements through large, synthetic heterogeneous flow systems in porous media. Such simulations can be used to examine the large time and spatial effects of the variable flow field on the expanding solute plumes. More specifically, the large scale experimental dispersive behavior can be compared with theoretical predictions based upon stochastic analyses. The particle tracking model is developed from first principles and is shown to be the most computationally efficient model for this type of application. Computational issues regarding the model's implementation are discussed, including the choice of time steps, boundary and initial conditions, and conversion of solutions to concentration fields. The model is applied to some simple test problems and then to two large, three-dimensional, heterogeneous, saturated flow systems. The results of these preliminary investigations are analyzed and compared with results of stochastic theories. They are also used to plan more comprensive simulations to be carried out in the future. Supported by the Nuclear Regulatory Commission, contract NRC-04-83-174. Supported by the National Science Foundation grant ECE-8311786. 1988-12-01T00:00:00Z https://hdl.handle.net/1721.1/143063 Large-scale Dispersive Transport in Aquifers: Field Experiments and Reactive Transport Theory Garabedian, Stephen P.; Gelhar, Lynn W.; Celia, Michael A. A large-scale natural-gradient tracer test was conducted to examine the transport of reactive and nonreactive tracers in a sand and gravel aquifer on Cape Cod, Massachusetts. The movement and spreading of bromide, a nonreactive tracer, and lithium, a reactive tracer, were monitored over time using a three-dimensional sampling network and analyzed using spatial moments. Calculated total mass of bromide for each sampling date varied between 86 to 105 percent of the total injected mass. The lack of any trend in the calculated mass over time confirms conservative transport of the bromide ion. The horizontal displacement of the bromide center of mass followed a predicted velocity of 0.43 meters per day. During the early part of the test the bromide cloud sank rapidly due to the density difference between the native ground water and the bromide cloud. The bromide cloud moved more slowly downward during the later part of the test due to the accretion of recharge. A nonlinear trend in the bromide longitudinal variance with travel distance was observed during the first 40 meters of distance traveled, indicating the dispersion process was non-Fickian in the early part of the test. After 40 meters the longitudinal variance followed a linear trend, apparently reaching a Fickian limit. The longitudinal dispersivity, given by one-half the change in variance with travel distance, is about 0.96 meters. Transverse horizontal dispersivity is much smaller, about 1.8 centimeters, and transverse vertical dispersivity is even smaller, about 0.15 centimeters. The distribution and movement of the reactive solute, lithium, was strongly affected by adsorption to the aquifer sediments. The mass of lithium in solution showed a large decrease during the first 300 days of transport until about 10 percent of the injected mass remained in solution. The velocity of the lithium in solution was initially the same as bromide velocity (0.43 m/d) and then decreased to about 0.05 m/d after 300 days. The distribution coefficient for the lithium adsorption was estimated to be about 2.0 mL/g for the later part of the test. The change in longitudinal variance for lithium showed a strong nonlinear trend, concave upward, which in the later part of the test indicated a dispersivity ten times larger than that for bromide. In contrast, the values of the transverse horizontal and vertical dispersivities did not differ greatly from those for bromide. A theoretical analysis of reactive solute macrodispersion was developed to explain, in part, the enhanced spreading of reactive solutes relative to nonreactive solutes. The approach used in this analysis was to postulate correlations between hydraulic conductivity and both porosity and the distribution coefficient. Using a spectral analysis method it was found that longitudinal dispersivity can be significantly increased by a negative correlation of hydraulic conductivity to porosity and the distribution coefficient. It was also found that the effective retardation coefficient is the arithmetic mean. Although the theoretical analysis provides an explanation of the enhanced longitudinal mixing for lithium, the enhanced spreading of lithium could also be caused by a kinetically controlled reaction. Supported by the U.S. Nuclear Regulatory Commission contract NRC-04-83-174. Supported by the National Science Foundation grant ECE-8311786. Supported by the U.S. Geological Survey grant 14-08-0001-A0460 1988-01-01T00:00:00Z https://hdl.handle.net/1721.1/143062 Copper Sulfate Treatment of Lakes and Reservoirs: Chemical and Biological Considerations McKnight, Diane M.; Chisholm, Sallie W.; Morel, Francois M. M. Since 1905, copper sulfate has been widely used as a means of controlling nuisance algae in drinking water reservoirs. Reservoir managers, relying on experience, have developed procedures which are generally successful in combating summer blooms of these algae. In some cases, however, treatment programs fail to prevent blooms or may exacerbate the problem. Furthermore, at least two states have issued regulations which effectively prohibit the use of copper in drinking water reservoirs. This report reviews the recent scientific advances in this laboratory and elsewhere on the subject of interactions between copper and lake organisms. The report concludes that algicide treatments are often a necessary part of water quality management and that copper sulfate is still the safest and most effective algicide in most reservoirs. Alternatives to copper, such as organic algicide, are ecological "unknowns" and have determined effects on human health. By contrast, copper, when properly used, is safe for both humans and the environment, as evidenced by nearly eighty years of experience in the field. Part of the report discusses practical techniques for determining the optimal treatment strategy for a given reservoir. This is especially important in lakes or reservoirs that have experienced difficulties in controlling nuisance algae. Using the procedures developed in this laboratory, reservoir managers can design copper treatment programs that will effectively eliminate undesirable algae, with minimal environmental side effects and with a cost effective dosing of copper sulfate. Sponsored by International Copper Research Association, Inc. 1981-01-01T00:00:00Z https://hdl.handle.net/1721.1/143061 An Interspecific Comparison of Trace Metal Toxicity to Marine Phytoplankton Hughes, David J. Introduction: Over the past few years, the emphasis placed on quantifying the metal speciation in culture media has clarified considerably our understanding of trace metal effects on phytoplankton. For example, it is now generally accepted that copper toxicity is controlled by the activity of the cupric ion (Davey et al., 1974; Sunda, 1975; Sunda and Guillard, 1976; Anderson and Morel, 1978; Morel, N.M.L. et al., 1978). It has also been demonstrated that the availability of metals for nutrition is dependent on their free ion activities (Manahan and Smith, 1973; Anderson et al., 1978; Anderson and Morel, in prep.). While there is no practical analytical method for determining free metal activities in seawater, the availability of convenient computer programs and a suitable range of synthetic chelators make it possible to calculate metal activities for controlled laboratory experiments performed in chemically defined (and buffered) culture media and to relate these results to field conditions, where metals and ligands are generally present at lower concentrations (Sunda and Guillard, 1976; Morel et al., 1979). The limited available data on metal toxicity in phytoplankton cultures demonstrate wide differences in metal sensitivities among species (e.g., compare Anderson and Morel, 1978; and Morel et al., 1978), leading to the hypothesis that trace metals may partially control the composition of species assemblages in natural waters. This hypothesis is supported by the results of in situ experiments. For example, addition of copper in the plastic enclosures of the CEPEX experiments resulted in a shift of dominant algal species from centric diatom and dinoflagellates to pennate diatoms and microflagellates (Goering et al., 1977). In lakes and reservoirs such a shift in algal species is commonly observed upon copper sulfate treatment for control of nuisance algae (McKnight, 1981). In order to begin documenting the possible role of trace metals as natural modulators of phytoplankton species assemblages in marine systems, we need to know a great deal more about what metals, in addition to copper and zinc, may be toxic or limiting in the range of metal activities that prevail in the ocean; we need also to undersand what differences in metal sensitivities there might be among the principal algal species. The toxic effects of metals may be observed in several ways, some of which are not consistent with each other. There are numerous reports of depressed photosynthesis and growth rates under metal stress. Morel et al. (1978) reported a systematic increase in the lag phase of Skeletonema costatum as a function of cupric ion activity. However, the subsequent division rate of the organism during exponential growth was not affected by the copper. Stewart (1977) measured the biomass of batch cultures after eight days incubation in lead-treated media, which would fail to discriminate between a prolonged lag phase and a depressed growth rate. Even a careful study of growth rate sometimes yields ambiguous results. Sunda (1975) reported a delay of up to three days in development of acute copper toxicity. Several of his cultures displayed declining growth rates with time. Other methods of assessing toxicity include loss of motility in dinoflagellates (Anderson and Morel, 1978) and chlorosis in higher plants (Foy et al., 1978). In this report we are reporting data on the toxicity of seven metals (copper, cadmium, zinc, nickel, cobalt, manganese, and lead) to an assortment of clones of marine phytoplankton. The experimental protocol was designed under the assumption--which was subsequently verified--that the free metal ion activities were the critical parameters for all the metals. For example, to study the effect of a given metal we adjusted the total concentrations of all other metals present in the medium so as to maintain constant activities. We have chosen exponential growth rates as our principal measure of the organisms' response to the metals, on the grounds that growth rate is an essential parameter governing diversity in natural populations, and that the requisite time series data might permit us to identify other time-dependent parameters relating to toxicity. Supported in part by NSF Grant OCE-7919549. Supported in part by NOAA Grant NA79AA-D-00077. 1981-12-01T00:00:00Z https://hdl.handle.net/1721.1/143060 The Hydrology of Fractured Rocks: A Literature Review Brown, David M.; Gelhar, Lynn W. Recent literature on the quantitative description of flow in fractured rocks is reviewed with emphasis on modeling approaches and their conceptual framework. The relationships of modeling results to laboratory and field observations is also emphasized. The review is organized in terms of the following three categories: fracture characterization, hydraulics of fractured rocks, and solute transport in fractured media. It is found that there are several probabilistic models which seem to adequately characterize three-dimensional fracture geometry, but it is not clear how well these models represent fracture interconnection. The theory for hydraulic behavior of extensively fractured systems is well established but no workable theory has been developed for non-extensive three-dimensional fracture networks. The question of when the flow in a discrete fracture network can be treated as a hydraulic continuum remains unresolved. Matrix diffusion models of solute transport are conceptually attractive and have been developed extensively. However, it has not been shown by direct field observations that the matrix diffusion mechanism is important in the field. No theoretical approach has been advanced for treating solute transport in three-dimensional fracture networks. This work was supported in part by Sandia National Laboratories under Contract No. NRC-04-83-174. This work was supported in part by the National Science Foundation under Grant No. ECE-8311786 1985-12-01T00:00:00Z https://hdl.handle.net/1721.1/143059 Reliability of Water Distribution Systems Wanger, Janet M.; Shamir, Uri; Marks, David H. Reliability of water distribution systems is becoming of increasing concern to water system designers and operators because of the increasing age of many systems and the decreasing availability of public money for water system construction and repair. This report is concerned with identifying, developing, and applying methods for the calculation of probabilistic reliability measures for water distribution systems. Methods are developed for assessing the reliability of water distribution systems for moderately large systems (10 - 50 nodes) with unreliable elements such as: pipe breaks, malfunctioning pumps, and out-of-service transmission and treatment facilities. A comprehensive literature review of reliability methods and measures from a number of fields is presented. The objective of this review is to understand previously used measures and the methods used to calculate them, to integrate measures and methods from different fields, and to suggest other measures and problems to be addressed in a reliability analysis. The water distribution is modeled as a flow-carrying network, with reliable supply and demand nodes and unreliable links. Link failures are assumed to be statistically independent. Analytical methods are identified and/or developed to assess the following measures on these networks: (1) the probability that all demand points in a system are connected to a source; (2) the probability that a given demand point in a system is connected to a source; and by assigning a capacity limit to each link in the system (3) the probability that a system can meet a specified level of flow at each demand point. Two sample systems are analyzed with these methods. A stochastic simulation program is developed which calculates a number of reliability measures for networks with reliable supply and demand nodes, unreliable links, and water storage tanks of finite volume. Link failures are again assumed to be statistically independent. Different probability distributions are postulated for the distributions of (1) time until failure and (2) time until repair of individual elements. Three sample systems are analyzed with this program. Finally, an overview of a general methodology for the reliability assessment of an existing water distribution is presented. Project was funded by the National Science Foundation by a grant concerning stochastic methods for Water Resources Management, NSF Grant CEE 8408369 1986-06-01T00:00:00Z https://hdl.handle.net/1721.1/143058 A Coupled Heat, Salt and Water Balance Model of Evaporation and Stratification in Saline Terminal Lakes: An Application to the Dead Sea Salhotra, Atul Mohan; Adams, E. Eric; Harleman, Donald R. F. A time varying, one-dimensional, coupled heat, salt and water budget model is developed for a hypersaline water body in which the vertical stability depends on the opposing influences of temperature and salinity stratification. A mixed layer modelling approach is used in which entrainment from the hypolimnion into the epilimnion occurs as a result of mass, heat, salt and momentum fluxes at the water surface. The effect of salinity on evaporation has been discussed in detail using evaporation pan data collected at the Dead Sea. An accurate method to account for this effect based on the dependence of saturation vapor pressure on salinity and ionic composition is suggested and shown to be superior to the commonly used approach based on the ratio of salt water to fresh water evaporation. Also, the negative feedback effect of temperature on salinity has been quantified. A comparison of various formulae to compute atmospheric long wave radiation is presented. Using data collected at the Dead Sea these formulae have been calibrated to account for site specific conditions. The importance of using accurate cloud cover values is indicated. The primary components of the mixing algorithm are wind stirring and penetrative convection. The relative magnitudes of each during different periods in a year are compared. On an annual level, the energy supplied by wind mixing is significantly larger than the penetrative convective mixing energy. The model is calibrated and verified using vertical temperature and salinity data from the Dead Sea over a period of five years. The model has been used to predict the lake levels, annual evaporation and vertical stratification over a period of thirty years with the proposed Mediterranean Dead Sea Hydro Power Project in operation. Prepared under the support of the Water Resources and Environmental Engineering program National Science Foundation and Mediterranean-Dead Sea Co. Ltd. Israel. 1986-04-01T00:00:00Z https://hdl.handle.net/1721.1/143057 Spatial Poisson Models of Stationary Storm Rainfall: Parameterization, Evaluation and Numerical Simulation Fennessey, Neil M.; Qinliang, Wang; Eagleson, Peter S.; Rodriguez-Iturbe, Ignacio Eight years of summer raingage observations are analyzed for a dense, 93 raingage, network operated by the U.S. Department of Agriculture, Agricultural Research Service, in the 150 km2 Walnut Gulch catchment near Tucson, Arizona. Storms are defined by the total depths collected at each raingage during the noon-to-noon period for which there was depth recorded at any of the gages. For each of the resulting 428 storm days, the 93 gage depths are interpolated onto a dense grid and the resulting random field is analyzed to obtain storm depth isohyets, the first three moments of point storm depth, the spatial correlation function, the spatial variance function, and the spatial distribution of total rainstorm depth. The sample is split and half is used to estimate for each storm day the three parameters of each of three conceptual spatial Poisson process models proposed elsewhere [Rodriguez-Iturbe, Cox and Eagleson, 1986]. The distributions of these parameters are estimated and used to evaluate the absolute and relative worth of the three Poisson models in comparison with the second half of the sample. Prepared with the support of the National Science Foundation grant no. ATM8420781 1986-08-01T00:00:00Z https://hdl.handle.net/1721.1/143056 Spatial Analysis of Storm Depths from an Arizona Raingage Network Fennessey, Neil M.; Eagleson, Peter S.; Qinliang, Wang; Rodriguez-Iturbe, Ignacio Eight years of summer rainstorm observations are analyzed by a dense network of 93 raingages operated by the U. S. Department of Agriculture, Agricultural Research Service, in the 150 km Walnut Gulch experimental catchment near Tucson, Arizona. Storms are defined by the total depths collected at each raingage during the noon-to-noon period for which there was depth recorded at any of the gages. For each of the resulting 428 storm days, the 93 gage depths are interpolated onto a dense grid and the resulting random field analyzed to obtain moments, isohyetal plots, spatial correlation function, variance function, and the spatial distribution of storm depth. Prepared with support of the National Aeronautics and Space Administration grant no. NAG 5 388. Prepared with support of the National Science Foundation grant no. ATM 8420781. 1986-08-01T00:00:00Z https://hdl.handle.net/1721.1/143055 Wave Reflection and Transmission in Channels of Gradually Varying Depth Ippen, A. T.; Alam, A. M. Z.; Bourodimos, E. L. This report presents the results of a study on the reflection and transmission of water waves in a rectangular channel with transitions of linearly varying depths. Two channel sections of uniform depths are joined by sections of slopes 1:0.58, 1:2.75 and 1:16 in the three sets of experiments. Wave conditions were systematically varied to cover the range of deep-water to shallow-water waves in the deeper approach channel. The pertinent parameters considered for each slope were relative depth (ratio of upstream to downstream depth), ratio of group velocities and wave steepness. Since a comprehensive theory does not exist, the classical small wave amplitude theory for abrupt transitions was employed to correlate the results of the study. Comparisons with other theories developed recently were made where applicable. Some of the important conclusions are: 1. For short and intermediate waves reflection coefficients become generally larger than predicted as the slope of the transition decreases. 2. For short and intermediate waves transmission coefficients generally agree with predictions for group velocity ratios near unity, but tend to lower values for lower ratios of group velocity as the slope of the transition decreases. 3. For short and intermediate waves wave steepness has a relatively small influence on reflection and transmission coefficients. 4. For shallow water waves the reflection coefficients were found independent of relative depth ratios contrary to prediction but decreased markedly with increasing wave steepness for the smallest slope. 5. For shallow water waves the transmission coefficients followed the predicted trend, but became relatively lower for increasing relative depth ratios. Increasing wave steepness had the effect of increasing the transmission coefficients for the smallest slope. Prepared Under Contract from Fluid Dynamics Branch Office of Naval Research Department of the Navy , Contract no. Nonr-1841(59) 1964-07-01T00:00:00Z https://hdl.handle.net/1721.1/143054 Dispersion of Pollutants in Estuary Type Flows Holley, Jr., Edward R.; Harleman, Donald R. F. Much of the engineering literature has failed to show an understanding of the mechanism of longitudinal dispersion which arises in the one dimensional representation of pollution transport in turbulent shear flows. In the present work, it is shown that the one dimensional form of the mass balance equation may be obtained by spatially averaging the three dimensional mass balance equation. This averaging indicates that the convective transport cannot be represented in a one dimensional equation solely by the average velocity and average concentration at a section since there is a net transport associated with the variations of velocity and concentration from their averages. This net transport (called longitudinal dispersion) is shown to be diffusive in nature for uniform flow, and it is assumed to be diffusive for non-uniform flow. Thus, the mass transport due to dispersion is proportional to the longitudinal gradient of average concentration. The relative importance of dispersion depends on the relative steepness of the concentration gradient. A review is given of the procedures which have been used for modeling dispersion in estuaries. Investigation of the model laws, the dispersive mechanism, and model verification procedures indicates that model results on concentration distributions have been incorrectly transferred to prototype scale in the constant density regions of estuaries. It is shown that in distorted models concentration ratios are not numerically the same at geometrically similar points as has been assumed. This assumption has resulted in predicted concentrations which are an order of magnitude too large in many cases. An analytical method is presented for calculating the dispersion coefficient for uniform oscillating flow of the type found in constant density regions of estuaries. For turbulent estuary type flow in a uniform pipe of radius a, the analytical value of the dispersion coefficient is ... the shear velocity (square root of boundary shear stress divided by fluid density). Since u, is a periodic function of time, so is the dispersion coefficient. It is shown that after one or two periods of dispersal of mass, a sufficiently accurate concentration distribution may be obtained by use of a constant dispersion coefficient (Viz., the time average of the dispersion coefficient during a period of tidal oscillation). A mass balance equation representing conditions at "slack" times in an estuary is commonly used as a mathematical model for the distribution of a pollutant. The results of this investigation may be used to estimate the time averaged dispersion coefficient in this equation for constant density portions of tidal estuaries. Thus, preliminary estimates of concentration distributions may be obtained for known input conditions. Prepared Under Research Grant, Division of Water Supply and Pollution Control Public Health Service Department of Health, Education and Welfare ; WP-00071 1965-01-01T00:00:00Z https://hdl.handle.net/1721.1/143053 Mathematical Models of the Massachusetts Bay Connor, Jerome J.; Wang, John D.; Briggs, Douglas A.; Madsen, Ole S.; Christodoulou, Georgios C.; Leimkuhler, William F.; Ippen, Arthur T. Part 1. The vertically integrated conservation of mass and momentum equations for shallow water bodies are reviewed. The equations used in this study are based on only two assumptions: hydrostatic pressure and squares of surface elevation gradients negligible with respect to unity. The finite element method is applied to reduce the governing equations to a system of ordinary non-linear differential equations in time for which two different numerical integration schemes are described. Model results are compared with analytical solutions. Also, numerical predictions of the tidal response for Massachusetts Bay are presented. Part 2. A need for qualitative information concerning the hydrodynamics of Massachusetts Bay has been seen from recent oceanographic measurements and current studies in the Bay area. In response to this, two analytical models have been derived for a simple rectangular configuration which can be applied to the geometry of Massachusetts Bay. A one layer model has been developed to simulate the conditions found during the winter season when the water column is well mixed. A two layer model represents the stratified case generally observed, with the presence of a strong thermocline, during the summer. Both models are derived from the linearized long wave equations in two dimensions and analytical solutions are obtained by neglecting Coriolis force, bottom friction, and wind stress. The models are depth averaged and the geometry of the Bay is represented by a rectangle. The boundary conditions are specified as zero normal velocity along the walls and a constant surface slope across the opening connecting Massachusetts Bay to the ocean. The results of the two models indicate that the surface elevations at high tide are fairly insensitive of the assumed conditions (one or two layer model). However, for the two layer model, relatively large interfacial waves are predicted as well as velocities which at some locations in the upper layer, are directed shoreward on the ebbing tide, rather than seaward. Comparison of available field observations with these results verify, qualitatively, that these conditions do exist and 'shows that if a model capable of predicting velocities in the Bay is desired, it must incorporate the conditions corresponding to a two layer flow. Part 3. A three-dimensional analytical model is proposed for the description of the dispersion of fine suspended sediments in coastal waters. The model basically predicts the quasi-steady state sediment concentration as a function of space and tidal time and the deposition pattern in the region surrounding a continuous vertical line source. It requires that the sediment settling velocities and the hydrodynamic features of the area, the net drift and the tidal velocities as well as the dispersion coefficients be known. Effects of wave action and vertical stratification are not explicitly considered. A separation of variables technique permits a rather independent treatment of the vertical and horizontal distributions; they are linked primarily through the decay factor, which represents the loss of material to the bottom. The model is applied to a hypothetical dredging situation in Massachusetts Bay. Values for the hydrodynamic parameters were obtained from the analysis of field data collected during the past year. Laboratory experiments were carried out for the determination of settling rates of clays in seawater, in view of unknown flocculation factors. Stoke's law was considered adequate for silt and very fine sand. The model results indicated very long and relatively narrow dispersion patterns, under the assumption of constant drift direction. The net drift and the sediment settling velocity seem to be the most important factors controlling the dispersion of fines in coastal waters. Prepared with the support of Sea Grant Office, National Oceanic and Atmospheric Administration, Department of Commerce, Washington, D.C. 1973-10-01T00:00:00Z https://hdl.handle.net/1721.1/143052 The Diffusion of Two Fluids of Different Density in a Homogeneous Turbulent Field Harleman, D. R. F.; Jordaan, Jr., J. M; Lin, J. D. Introduction: Industrial communities situated near large bodies of water or in drainage systems connected with such bodies dispose their waste water after treatment by dilution. Disposal by irrigation or evaporation after removing the solids by filtering, drying and incineration is justified in circumstances where the necessity outweighs the increased cost. However, comparatively few large industrial communities in the United States are situated away from either ocean, estuary, lake or river, so that the predominant form of ultimate waste water disposal is by dilution. In waste disposal by dilution a certain degree of primary treatment is usually required to reduce the concentrations of constituents that are toxic, odoriferous or otherwise chemically or physically detrimental or objectionable to human, animal or vegetable existence. Industrial and other wastes, varying widely in composition, coming from a diversity of establishments, such as dye or fertilizer factories, paper mills; primary treated sewage and supernatant liquor from digested sewage, radioactive waste products; wastes from hospitals, dairies, slaughter houses, etc., present different treatment problems and different standards for their effective disposal. After a sufficient time interval has elapsed following disposal, harmful chemicals will be oxidized to well below allowable levels, organic material digested by bacterial action, low level radioactive waste products; subjected to decay and a natural balance will be obtained. This can, however, be achieved only if the dilution process is aided by dispersion with currents due to winds and tidal action. Conversely, inadequate primary treatment or initial dilution can lead to widespread contamination by dispersion of harmful constituents endangering life. of property. The disposal of the water-borne waste products should be made in such, a fashion and at such regions in the body of water that tendencies for segregation of the influent will be minimized. The nature of the solution of this problem is twofold: (1) the achievement of optimum mixing characteristics with economical energy input at the disposal point, (2) the location of the disposal area in a region where hydrographic or oceanographic evidence indicates degrees of boundary shear, of wave and wind generated turbulence, and thermal or tidal convection currents that will continue the dispersion of the diluted effluent in order that concentrates would not tend to accumulate with passage of time or segregate into tidal backwaters or be absorbed by vegetation or soil on the shores. Allied problems, which have in most cases direct bearing on the flushing of disposal areas, are the salt water intrusion into river mouths and the fresh and salt water balance in tidal estuaries. Apart from the estuary flushing,there is also the consideration of contamination of public or industrial water supply intakes due to salinity intrusion. All of the problems mentioned above, in general terms, involve the mechanics of mass transfer according to the combined operation of turbulent diffusion and convection. Turbulent diffusion processes thus fall into two general categories. In the first, the turbulent diffusion is due entirely to the momentum of the diffusion which is being introduced into a quiescent diffusing medium: this process being governed by the mechanics of momentum and mass transfer in submerged turbulent jets. In the second category, the turbulent diffusion is due largely to the turbulent energy of the receiving fluid, the diffusion being introduced without materially increasing the turbulent activity at the region of introduction. In practice the ideal dilution process would be a combination of the two processes in the above sequence. The diffusing substance would be discharged with as high a momentum as practical into the receiving medium in the form of submerged jets, and the diffusion process in the vicinity of the disposal points would be entirely governed by the energy of introduction of the diffusion. At sufficiently large distances from its source the momentum of a jet would have decayed to levels comparable to the turbulence level in the receiving body of fluid. Further dispersion will occur according to mechanics of diffusion due to the turbulence in the receiving fluid body itself. (That is, if one considers momentarily turbulence as including all sizes of eddies present and hence also what would be customarily considered convection currents). The analysis will be simplified, however if it is considered that the motion of the fluid body consists of a field of homogeneous turbulence in which a convection pattern may be superimposed. With further simplification, the general problem may be made feasible for mathematical and experimental analysis in particular cases. Thus all of the above-enumerated disposal problems involve ultimately the mechanism of turbulent (eddy) diffusion which can accordingly be treated in two distinct parts. Public Health Service National Institutes of Health Department of Health, Education and Welfare Research grant No. 4815 1959-02-01T00:00:00Z https://hdl.handle.net/1721.1/143051 The Hydroelastic Behavior of Flat Plates as Influenced by Trailing Edge Geometry Ippen, A. T.; Toebes, G. H.; Eagleson, P. S. This report presents the results of a theoretical review and an experimental investigation of the hydroelastic vibration of thin flat plates suspended at zero mean angle of attack in a fluid stream. The review indicated that recognized experimental facts such as the influence of trailing edge geometry and the three-dimensional wake structure were inadequately related to theoretical considerations about the vibration phenomenon. The experimental investigation consisted of a detailed determination of the amplitude and frequency spectra of the vibration on a number of flat test plates which were mounted in the test section of a water tunnel at zero mean angle of attack. The effects on the vibrational behavior of trailing edge geometry, geometric and elastic properties of the plate support, free stream velocity and ambient pressure have been explored experimentally. An equation of motion has been written for the test plate - torsion spring system employed. Results of a qualitative analysis of this non-linear equation are compared with the experimental results obtained. Administered by the David Taylor Model Basin, U.S. Dept. of the Navy, Washington, D.C. and prepared under contract and project Nonr-1841(21) NS 715-102 1960-01-01T00:00:00Z https://hdl.handle.net/1721.1/143050 Measurement and Analysis of Turbulent Flow of Wood Pulp Fiber Suspensions Daily, J. W.; Bugliarello, G.; Troutman, W. W. In a previous report techniques were described for measuring turbulence and velocity profiles in turbulent shear flows of water and dilute fiber suspensions, and some preliminary results presented. The present report describes subsequent experience with the techniques, and the results of their application to an extended range of flow velocities and an additional wood pulp suspension. The report has two areas of emphasis. The first has to do with some basic facts about turbulence, together with relevant theoretical relations among variables and their implications as regards problems of measurement and analysis. The second relates to the specific -measurements and their significance as regards flowing fiber suspensions. The results confirm and extend the previous conclusions regarding the .mechanism of turbulence and the momentum transfer process in dilute fiber suspensions. In particular, the significance of the combined roles of turbulence and fiber entanglement in diffusion and mixing is examined in detail. The necessity of isolating these roles is discussed and recommendations presented. The procedures employed for data measurement and analysis of the statistically turbulent flow are: analyzed and recommendations made. Prepared under contract with the Technical Association of the Pulp and Paper industry. 1959-09-01T00:00:00Z https://hdl.handle.net/1721.1/143049 Model Study of a Flood-control Pumping Station at the Charles River Dam Harleman, D. R. F.; Broughton, R. S.; Huval, C. J.; Partenscky, H. W. This report describes the design, construction and testing of a Froudian model of a proposed 8400-cfs capacity pumping station, Site restrictions require that the flow approach the high specific-speed pumps asymmetrically from an existing ship lock through the Charles River Dam (Boston, Massachusetts). The model included a portion of the Charles River Basin, the existing navigation lock and the pump forebay at the exit of the lock. A single recirculating pump and a suction manifold was used in the model to withdraw water from the forebay through six intakes simulating the prototype pumping station. Flow patterns were obtained by photographs of floating confetti and subsurface streamers. Water surface measurements were made with a point gage read through a surveyor's level. The majority of tests were run with the maximum design discharge and the minimum basin pumping elevation. This provided the most severe forebay conditions of high velocity and low intake submergence. Tests were made to investigate: (1) the improvement of flow conditions at the entrance to the lock; (2) the performance of a single intake in uniform approach flow; and (3) the performance of several forebay and pumping station arrangements. The tests showed that: (1) an 18 ft diameter semi-cylindrical pier was needed at the lock entrance to reduce flow contraction and entrance loss; (2) the intake performed very well when the approach flow was uniform; and (3) the most satisfactory forebay arrangement, within the design restrictions imposed by the site, was with equal lengths of intake chambers. The center line of the pumps and the straight portion of the intake chamber walls were deflected 200 toward the approach flow. The. straight portion of the intake chamber walls were 51 ft in length and thence curved upstream in a circular arc. The circular arc terminated six ft from the lock line and the chord of the are forced an angle of 400 with the line of the lock. Vertical struts placed behind the intakes retarded circulation in the intake chambers and improved the flow into the intakes. Prepared under contract with the Metropolitan District Commission of the Commonwealth of Massachusetts. 1959-06-01T00:00:00Z https://hdl.handle.net/1721.1/143048 Non-linear Standing Waves in a Rectangular Tank Due to Forced Oscillation Lin, J. D.; Howard, L. N. This study is concerned with standing waves generated by a two-dimensional wave maker in a rectangular tank. The theoretical investigation was first based on the well-known linear theory of surface waves. The linearized version of the problem is basically two-dimensional and the solution of forced two-dimensional standing waves of small amplitude was obtained. Then, a system of equations, based on the exact free surface conditions, was derived for solutions of forced two-dimensional standing waves of finite amplitude. A non-linear solution corresponding to any mode of oscillation can in general be obtained by the method of iteration from the system of equations. However, only the fundamental mode was solved here for the velocity potential, free surface elevation and frequency-amplitude relation with the computation carried to the third order of approximation. The frequency amplitude curves for two constant amplitudes of wave maker were found to consist of two non-intersecting branches of oscillation; the range of significant nonlinear effects was also determined for the particular mode. Two profiles of standing waves were computed for the frequencies on each branch of the oscillation. The stability of non-linear forced two-dimensional standing waves was studied by investigating the possibility of excitation of the fundamental mode of cross waves. A system of equations was again derived for solutions of cross waves by extending the method used in the two-dimensional case. The solution corresponding to the first mode of the longitudinal component and the first mode of cross waves was solved by the method of iteration to the second order of approximation, and yields the following results: (1) The half-frequency relation between the cross waves and wave maker, (2) The frequency for excitation of the cross waves, (3) The length/width ratios of the tank at which the cross waves can be excited by an infinitesimal amplitude of wave maker, and (4) The phase relation between the cross waves and the wave maker. The experimental investigation comprises essentially two parts: forced two-dimensional standing waves and cross waves. The experiment of two-dimensional standing waves serves as a verification of the theoretical solutions for both the frequency-amplitude relation and the profile of the standing waves. A satisfactory agreement was indicated in the comparison of the theoretical prediction and of the experimental results. For cross waves, the frequency- amplitude curve was obtained from the experiment in addition to confirming the results of the theoretical analysis above mentioned. Scanning notes: Brittle pages needed to be flatbed scanned.; Support of the Office of Naval Research, United States Department of Navy under Contract from Oct. 1959 to June, 1960 Nonr 1841-12. Support of the Office of Naval Research, United States Department of Navy under Contract from July to October, 1960 Nonr 1841(65) 1960-10-01T00:00:00Z https://hdl.handle.net/1721.1/143047 Linear Programming and Dynamic Programming Application to Water Distribution Network Design Schaake, Jr., John C.; Lai, Dennis The water distribution network design problem is to find the optimal set of investments in pipelines that are needed to satisfy water requirements. The strategy of this study has been first to define an optimality criterion for ranking alternative investment opportunities and then to formulate a mathematical programming model for solving the optimal investment problem. The least cost optimality criterion leads to a non-linear mathematical programming problem for which no computational methods exist that guarantee an optimal solution. Other existing techniques that yield "good" solutions are computationally inefficient. The strategy taken in this study has been to modify the least cost problem so that linear programming could be applied to achieve a solution to the modified form of the problem. Variables were transformed to linearize the non-linear terms in the pipe flow formula. In this way, the non-linear flow phenomenon is represented exactly. The resulting linear programming model may be used to determine the pipe diameters of pipes that must be added to the system to satisfy given sets of water requirements that are expected to occur at a given future time. Water requirements increase with increases in population and economic productivity. To meet these growing requirements, excess capacity must be provided. The problem of deciding how far into the future the system should be planned is known as a capacity expansion problem. The capacity expansion problem has been formulated as a dynamic programming problem and applied to the water distribution network expansion problem. The work upon which this publication is based was supported by funds provided by the New York City Bureau of the Budget and by the MIT Sloan Basic Research Fund. 1969-07-01T00:00:00Z https://hdl.handle.net/1721.1/143046 Design of a Closed Jet, Open Circuit Water Tunnel for the Study of Wake Mechanics Toebes, G. H.; Perkins, F. E.; Eagleson, P. S. This Technical Note describes the design of an open-circuit water tunnel with a 7-1/2 inch by 9 inch closed-jet working section. The maximum velocity obtainable in the empty test section is approximately 50 fps. The water tunnel was built for the purpose of investigating wakes behind objects placed in its test section. In particular, a study is to be made of the relationship between the trailing edge geometry of two-dimensional flat plates, the frequency of vortex shedding from them and the resulting elastic response of the plates when placed at zero angle of attack. Prepared under David Taylor Model Basin, U.S. Dept. of the Navy Nonr-1841(21) 1958-04-01T00:00:00Z https://hdl.handle.net/1721.1/143045 Constrained Stochastic Climate Simulation: Computer Programs and User Manual Curtis, David Carleton Computer programs for Constrained Stochastic Climate Simulation (CSCS) and for preliminary parameter estimation are presented. Many of the parameters required by CSCS, can be estimated by commonly available procedures. The remaining parameters can be estimated with the aid of the programs described in this report. Data input summaries and Fortran program listings are also included. This report is a supplement to: Curtis, David Carleton; and Peter S. Eagleson, Constrained Stochastic Climate Simulation, Report Number 274, Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, May 1982. Prepared with the support of the National Oceanic and Atmospheric Administration, the National Weather Service, and the National Science Foundation. 1983-02-01T00:00:00Z https://hdl.handle.net/1721.1/143044 User's Manual for the MIT Lake Circulation Models (MITLAKE) Shanahan, Peter; Harleman, Donald R. F. Introduction: During the course of research into water quality and hydrodynamic interactions in Lake Balaton in Hungary (Shanahan et al., 1981 and Shanahan and Harleman, 1982) two models of wind-driven lake circulation were employed. The models, which were developed from an earlier model by Nelson (1979), are two-dimensional and three-dimensional versions. The 3-D model employs the Galerkin method to solve for the vertical velocity distribution as a function of time and horizontal space. A linear bottom friction relation is used, thus making the model inappropriate to very shallow lakes. The 2-D model was developed in response to this limitation. The 2-D model determines the depth integrated velocity as a function of time and horizontal space. A non-linear bottom friction law is employed, broadening the model applicability to include very shallow lakes. These notes are a brief description of the computer programs developed to perform the 2-D and 3-D model simulations and to plot the model output. The notes are intended as an aid to potential users; however, no effort has been made to be exhaustive in explaining the implementation of the programs. Prepared under the support of the National Science Foundation Water Resources and Environmental Engineering Program Division of Civil and Environmental Engineering and Eastern European Program Division of International Programs Grant No. CEE-7906125 1982-06-01T00:00:00Z https://hdl.handle.net/1721.1/143043 Subscale Steam Tests of Vapor Supression Pool Mixing and Circulation with Application to the Shoreham Nuclear Power Station Adams, E. Eric; Baker, Richard M. This report addresses the temperature distribution induced within a suppression pool by a steam discharge. The problem is first examined theoretically to identify the dominant zones and to estimate circulation and mixing occurring within each zone. This analysis is then used to justify physical model tests using a 1/17 Froude scale model employing an actual steam source. Results complement earlier sub-scale tests at MIT performed by Soliva (1980) using hot water in place of steam. Experiments were performed to test sensitivity to the number of quencher ports,the fractional area of basin flow resistance, the initial water depth and the quencher orientation and location within the pool. Model results can be used to help understand the physical processes underlying pool mixing and circulation and to help extrapolate prototype temperature measurements from one site to another. This study was sponsored by Stone and Webster Engineering Corporation, Boston, Massachusetts, under Stone and Webster ESSOW No. SHl-474 1981-12-01T00:00:00Z https://hdl.handle.net/1721.1/143042 Entrainment in Diffusive Thermohaline Systems: Application to Salt Gradient Solar Ponds Atkinson, Joseph F.; Adams, E. Eric; Melville, W. Kendall; Harleman, Donald R. F. The development of a numerical model for simulating the temporal evolution of vertical temperature and salinity profiles in a salt gradient solar pond is described. The model uses a mixed-layer approach and a general entrainment relation is derived for predicting the growth of the upper mixed layer. A major part of the research involves an experimental study of the process of mixed-layer deepening in a strongly stratified "diffusive" double-diffusive system. Two different experiments are described. In the first, a vertically oscillating grid was used to drive interfacial mixing in a two-layer system in which the temperature and salinity differences between the layers were varied over a large range of values. Results for single stratification (temperature or salinity) were found to agree with those of earlier researchers, but it was found that for a given ... where g = reduced gravity ... are turbulence length and velocity scale, respectively, an increase in the destabilizing temperature difference would cause an increase in the rate of entrainment over the value for salinity stratification alone. This effect is modeled by defining a velocity scale which includes the buoyancy-induced velocity resulting from the temperature distribution. The second experiment looked at wind-induced mixing in a laboratory wind/wave tank. Tests were done using several different mean wind speeds ranging from 4 m/s to 11 m/s. Two-layer systems were again considered, with either salt or diffusive double-diffusive stratification. Two separate fetch lengths were also considered in an attempt to find a fetch dependence on the entrainment rates. No differences could be seen in the results for the two different kinds of stratification, with the entrainment rate following roughly an inverse Richardson number law. However, the mixed layer deepening was somewhat faster for the longer fetch and this result is explained in terms of an increased return flow along the interface, leading to increased shear-induced mixing. A series of experiments was also conducted in the wind/wave tank to test the effect of placing floating plastic netting or floating plastic pipes on the water surface. This has been suggested as a possible means of helping to reduce wind-induced mixing in solar ponds. The results obtained here indicate that both the nets and pipes can be at least partially effective in reducing wind-mixing, with the nets generally performing better than the pipes. Some increased mixing may be present directly beneath a floating net or pipe, but the a really averaged effect of the nets or pipes is to decrease the turbulence levels in the surface water layer. Experimental data, along with suggested values obtained from previous researchers, are used to define suggested values for the coefficients in the entrainment model which is incorporated into the full numerical simulation model. Sensitivity of the model to several of the parameters is examined and a calibration run is shown, using field data from a small solar pond. Unfortunately, wind-mixing was apparently not very important in this pond and a full calibration test of the wind-mixing model will have to wait until data from a much larger pond becomes available. The research reported here has been supported by the Department of Energy, through the Solar Energy Research Institute subcontract no. XX-3-03066-1. The research reported here has been supported by the National Science Foundation, grant no. CEE-8119384. 1984-12-01T00:00:00Z https://hdl.handle.net/1721.1/143041 Spillway Analysis in Dam Safety Evaluation Langseth, David E.; Perkins, Frank E. This work develops, tests, and applies a non-dimensional flood damage model which includes both overtopping and non-overtopping dam failures. The model represents a catchment, reservoir, dam, channel, and damage site. Peak reservoir flood inflow, initial reservoir stage, and overtopping failure stage are represented as stochastic variables. The model computes the expected value of total flood damage and of the damages attributable to natural floods, overtopping failures, and non-overtopping failures. The model also computes overtopping failure probability. Four dams are used as case studies. Parameters of the catchment, reservoir, and dam are estimated from real data. Channel and damages site parameters are hypothetical. Sensitivity of model results to variations of uncertain model parameters is examined. Channel and damage site parameters are also varied. Estimates of expected damage and failure probability are shown to vary substantially as parameters which are difficult to estimate are varied within reasonable ranges. It is also shown that expected damage can decrease, increase, pass through a minimum, or remain fairly constant as spillway size is increased. The influence of spillway size varies with the initial reservoir stage. Scanning notes: Contains figure pages with illegible text. Disclaimer scanned.; This research was done as part of a research project on "Risk-Based Assessment of the Safety of Dams", sponsored by the National Science Foundation under Grant No. PFR-7815989 1984-12-01T00:00:00Z https://hdl.handle.net/1721.1/143040 Large-scale Models of Transient Unsaturated Flow and Contaminant Transport Using Stochastic Methods Mantoglou, Aristotelis; Gelhar, Lynn W. A new framework for modeling large-scale unsaturated flow and solute transport systems in spatially variable soils is proposed. The largescale model structures are derived by averaging the local governing flow and transport equations over the ensemble of realizations of the underlying soil property random fields. The resulting mean representations are in the form of partial differential equations in which averaged or effective model parameters occur. These effective model parameters, i.e., effective hydraulic conductivity, effective specific moisture capacity and effective macro-dispersivity, are evaluated using a quasi-linearized fluctuation equation and a spectral representation of stationary processes. The large-scale model structures consider the large-scale effects of soil variability and have relatively flw parameters identifiable from a realistic data set. The effective parameters are analytically evaluated in particular cases of practical interest, and generic expressions showing explicitly the dependence of the effective parameters on the different flow, transport and soil property characteristics are derived. General methods for testing the validity of the stochastic theory and application of the large-scale models in practical situations are suggested. The spectral turning bands method developed by Mantoglou and Wilson (1981, 1982) is extended for digital generation of point values or spatial averages of multiple, cross-correlated, stationary random fields. Statistical inference methods are discussed and a new identification method is presented. The most important findings of this study are that spatial variability of the hydraulic soil properties produces significant large-scale effects. In particular, it was found that the effective hydraulic conductivity, the mean soil moisture content and the effective specific soil moisture capacity show significant hysteresis, and that the effective hydraulic conductivity is anisotropic with a degree of anisotropy depending on the mean flow conditions (wetting or drying). It was also found that in the case of unsaturated flow, the effective macrodispersivities depend on the soil moisture content, the type of soil stratification and the direction for the mean flow relative to stratification and the direction for the mean flow relative to stratification. The longitudinal macrodispersivity predicted from the stochastic theory is found to be of the same order of magnitude as observed in large-scale field experiments. The transient unsaturated flow and steady transport results of this study were previously unknown, have important practical implications, and should be considered in field applications such as waste disposal control. The general stochastic modeling framework and the simulation and identification methods developed here are applicable not only to unsaturated flow and transport but also to other distributed parameter systems. This research was supported in part by the U.S. Nuclear Regulatory Commission, Contract No. NRC-04-83-174. This research was supported in part by the National Science Foundation , Grant No. CEE-8311786. 1985-01-01T00:00:00Z https://hdl.handle.net/1721.1/143039 Final Calibration of the Cooling Lake Model for North Anna Power Station Ho, Edmond K.; Adams, E. Eric The North Anna Power Station is a two-unit power plant located on Lake Anna and operated by Virginia Electric and Power Company (VEPCO). A complex cooling lake system, involving a diked-off portion of Lake Anna - known as the Waste Heat Treatment Facility (WHTF) - as well as the main lake, was designed to dissipate the waste heat rejected by the plant. In order to monitor the impacts that the waste heat discharge has on the natural environment and also to assess the efficiency of the cooling lake system, a segmented mathematical model was previously developed (Jirka et al., 1977). Since Unit 1 of North Anna Power Station came on line in summer of 1978 (followed by Unit 2 in autumn of 1980), an extensive data collection network was established by VEPCO. The model was previously calibrated using data from the first three years of operational data (1978 to 1981, primarily one-unit operation). Since then more measurements were available and an independent validation was conducted by comparing model predictions with data for the following two years (1981 to 1983, with more two-unit operation) using the same model calibrations. Surface temperature error analysis was made for four representative diagnostic control points over the cooling lake system. It was noticed that the model results for five years were similar to those for the first three years. However, temperature rise across the plant condenser was consistently over-predicted by an average of about 0.70 �C over all five years. In addition, results of spectral analysis showed that the raw error at DIKE III was periodic at predominantly the annual frequency whereas the rest of the control points showed mild periodicities over a relatively wide range of frequencies. Model recalibration aiming at improving the goodness-of-fit of the five years of measurement data at DISCHARGE and DIKE III was motivated by the results of the surface temperature error analysis. Two possible reasons for the transient errors characterized by annual periodicity of the raw error at DIKE III were identified, namely, errors associated with (1) the forcing function (surface heat transfer) and (2) system response of the model. Two candidates for each of the possible reasons were considered: (la) atmospheric radiation, (1b) evaporation, (2a) spatially-averaged system response, and (2b) longitudinal system response. Regarding the steady state errors at DISCHARGE, a sensitivity analysis of the raw error with respect to changes in the plant operation data was made, and it was noticed that the mean raw error was reduced substantially by a moderate reduction of the waste heat discharged into the WHTF. In all, two changes of the model were made as a result of recalibration: computation of residence times in the WHTF and adjustment of plant operation data. The recalibrated model was validated by comparing predictions with five years (1978-1983) of measurement data in terms of both surface temperatures and vertical temperature profiles. Overall mean errors for the four diagnostic control points ranged (in terms of magnitude) from a minimum of 0.01 �C to a maximum of 0.16 �C while standard deviations ranged from 0.80 �C to 1.37 �C. In comparision with the large peak-to-peak annual variation in water surface temperature of about 23 �C, the mean errors and standard deviations are both acceptably small. Comparisons between measured and predicted vertical temperature profiles in the main lake indicated that the dynamic nature of the data both in space and time was also modelled satisfactorily. In addition to overall averages, monthly averages of the surface temperature raw errors were also computed for each of the diagnostic control points. These monthly error statistics can be applied by VEPCO to increase the accuracy of future model predictions. Prepared under the support of the Virginia Electric and Power Company. 1984-08-01T00:00:00Z https://hdl.handle.net/1721.1/143038 Surface Area Variability of the Bahr el Ghazal Swamp in the Presence of Perimeter Canals Gaudet, Sharron C.; Eagleson, Peter S. Prepared by the Technology Adaptation Program, Massachusetts Institute of Technology and sponsored by United States Agency for International Development. 1984-06-01T00:00:00Z https://hdl.handle.net/1721.1/143037 Eulerian-Lagrangian Analysis of Pollutant Transport in Shallow Water Baptista, Antonio E. de M.; Adams, E. Eric; Stolzenbach, Keith D. A numerical method for the solution of the two-dimensional, unsteady, transport equation is formulated, and its accuracy is tested. The method uses a Eulerian-Lagrangian approach, in which the transport equation is divided into a diffusion equation (solved by a finite element method) and a convection equation (solved by the method of characteristics). This approach leads to results that are free of spurious oscillations and excessive numerical damping, even in the case where advection strongly dominates diffusion. For pure diffusion problems, optimal accuracy is approached as the time-step, At, goes to zero; conversely, for pure-convection problems, accuracy improves with increasing At; for convection-diffusion problems the At leading to optimal accuracy depends on the characteristics of the spatial discretization and on the relative importance of convection and diffusion. The method is cost-effective in modeling pollutant transport in coastal waters, as demonstrated by two prototype applications: hypothetical sludge dumping in Massachusetts Bay and the thermal discharge from Brayton Point Generating Station in Narragansett Bay. Numerical diffusion is eliminated or greatly reduced, raising the need for realistic estimation of dispersion coefficients. Costs (based on CPU time) should not exceed those of conventional Eulerian methods and, in some cases (e.g., problems involving predictions over several tidal cycles), considerable savings may even be achieved. Prepared under the support of Northeast Utilities Service Co., Hartford, Connecticut and New England Power Service Company, Westboro, Massachusetts. 1984-06-01T00:00:00Z https://hdl.handle.net/1721.1/143036 Nonlinear Filtering, Parameter Estimation and Decomposition of Large Rainfall-Runoff Models Angulo, Carlos Enrique Puente; Bras, Rafael L. Three topics related to the real time forecasting of river flows are studied. First, the usefulness of nonlinear filtering procedures in connection with a conceptual rainfall-runoff model is investigated. By means of a case study it is determined that only filters which employ future information to correct the past (smoothers) could potentially improve forecasts over the simpler extended Kalman filter. The quality of the predictions is heavily dependent on the nature of the assigned error of the conceptual rainfall-runoff model. The second topic deals with the estimation of the conceptual model error using the maximum likelihood method and consistency conditions on model residuals. The utility of the procedures is tested in practical applications. It is shown the simplified maximum likelihood procedure gives excellent forecasting results independent on the initial conditions, but raises some questions as to the sensitivity of the soil moisture accounting part of the model. - The third topic deals with the forecasting on a basin composed of several interconnected sub-basins. Decomposition procedures are proposed to forecast on sub-basins separately, using upstream flow predictions as inputs to downstream basins. When tested in practice, these methods provide reliable and inexpensive forecasts. This work was sponsored by the Hydrologic Research Laboratory of the National Weather Service, U.S. Department of Commerce, under Cooperative Agreement NA 80AA-H-00D44 1984-10-01T00:00:00Z https://hdl.handle.net/1721.1/143035 SWAHP: A Soil Water and Heat Parameterization Milly, P. Christopher D. SWAHP is an efficient algorithm for prediction of moisture and heat fluxes across a bare soil surface. Surface moisture flux is calculated using the time compression assumption in conjunction with special solutions of the nonlinear moisture diffusion equation. Effects of water vapor and hysteresis are incorporated. The average moisture concentration near the surface is calculated continuously, and redistribution is considered. Potential evaporation is calculated using the surface temperature given by the force-restore procedure. SWAHP has been programmed in Fortran for computer solution, and the program is documented in detail. Required input consists of soil physical properties and atmospheric forcing data. Based on work supported by the National Science Foundation. Grant numbers ATM-7812327 ATM-8114723 1983-02-01T00:00:00Z https://hdl.handle.net/1721.1/143034 Planning and Design of Agricultural Drainage under Uncertainty: A Dynamic Multi-level Approach Strzepek, Kenneth M.; Wilson, John L.; Marks, David H. Drainage systems are major capital investments for irrigated agriculture. Therefore,the-goal is to install drainage systems that will be most beneficial to the agricultural economy as a whole. Planning for agricultural drainage has been decomposed in this thesis as a three level process. The first level is the project evaluation and scheduling phase, the second level is the planning of the collector drain network, and the third level is the design of field level lateral drains. This thesis focuses on the second and third levels of drainage planning and the interactions between these levels. Level three drainage design is based upon the physics of groundwater flow. This thesis uses the steady state Hooghoudt equation for drain design currently employed in many areas of the world to determine the depth and spacing of subsurface lateral drains. This thesis analyzes the uncertainty in the parameters of the Hooghoudt equation. A detailed analysis of soil permeability shows that uncertainty and spatial variability are important issues in drain design and should be incorporated into the design process. First order-second moment analysis is a methodology that provides a measure of uncertainty in a system output (mean and variance) given uncertainty in system inputs. A first order second moment analysis is performed on the Hooghoudt equation than relates uncertainty in drain performance to parameter uncertainty and system design. Two models are developed to optimally design lateral drains given uncertainty in drain performance: Chance Constraint and Stochastic Programming. The thesis shows that the Chance Constraint approach is not valid when the system response function is not monotonically non-decreasing. In drainage design the system response function is many times not monotonically non-decreasing, however, the stochastic programming approach is valid for all types of response functions. A multicrop spatially distributed loss stochastic programming model for uniform lateral design over a collector area that accounts for uncertainty and spatial variability of soil permeability by Kriging, an optimal data interpolation technique that accounts for spatial structure, as well as accounting for economic response of multiple cropping of agricultural land. A simulation model for level two collector drain network planning is developed. This model provides the designer with a tool for drain sizing and cost estimation of complex network alignments allowing many alternatives to be evaluated and the least cost alternative system to be selected. An analysis is performed that-show that as a result of spatial variability the efficiency of the lateral field drain system. Present drainage planning is a sequential process that does not evaluate the impact of level two design upon level three. This thesis presents a dynamic multi-level planning process that incorporates feedback between level two and level three planning. A synthesis of the collector network simulation model and the multi-crop spatially distributed loss stochastic programming model with Kriged input for the lateral drainage system is performed to provide a methodology for dynamic multi-level planning. A case study of this proposed methodology on a drainage region in the Nile Delta in Egypt is carried out. The case study shows that this methodology can provide more efficient drainage systems while providing the most economical design. Scanning notes: Disclaimer inserted for illegible graphs and text.; The authors would like to thank the MIT Technology Adaptation Program for their support of this research through a grant from Agency for International Development of the U.S. Department of State. 1982-07-01T00:00:00Z https://hdl.handle.net/1721.1/143033 Irrigated Agricultural Expansion Planning in Developing Countries: Performance vs. Resilience vs. Reliability Allam, Mohamed Nasr; Marks, David H. Agricultural expansion planning in developing countries where there is extensive government involvement in the planning process can be defined in a two level hierarchy. At the first level, strategic planning on the agricultural sector level is to be performed. At this level, the feasibility of the agricultural expansion as well as the other investments is to be examined and the role of each investment in achieving the strategic goals of the sector is to be determined. At the second level, analysis to the planning issues of agricultural expansion investment is to be provided. The analysis should be developed in such a way that the strategic decisions from the first level can be implemented. This report focuses only on the second planning level. Three issues are addressed. First, is the investment scheduling in such a way that the growing agricultural demands can be satisfied and the budget and resource constraints are not violated. The second issue is the income redistribution. The third issue is the uncertainty and its effect on the performance of agricultural expansion investment. A mathematical optimization model is built to aid in analyzing the scheduling problems of land development, crop selection, drainage water reuse, and capacity expansion of the irrigation and drainage networks. A minimum cost criterion is used, where costs of land development, farming, irrigation and drainage infrastructures, maintenance and operation, and pump stations are considered. The model is presented with a nonlinear objective function accounting for economies of scale and linear and nonlinear constraint sets. A fixed charge approximation is used for the non-convex cost functions and a mixed integer programming algorithm along with an enumeration procedure is used for solving the model. The solution procedure guarantees global optimality for the approximated problem. A hypothetical expansion on the order of 70,000 acres based on data from the Nile Delta in Egypt is used as a case study. The expansion extends over five areas of different sizes and soil types, and has only one source of fresh water for irrigation. The model is used for developing three alternate planning schemes for the case study. The first alternative is based on using fresh water for irrigation. The second alternative is based on using only saline water (drainage water of the existing cultivated areas) in irrigation. In the third alternative, the possibility of recycling the drainage water of the new land in irrigation after being mixed with fresh water is considered. The role of agricultural expansion investment in improving the income redistribution conditions in a society is investigated. The approach of distributing the new land to a poorer sector (landless farmers) is selected. A mathematical optimization model is built to determine the distribution of the land and a pricing policy established for the new areas in such a way that: 1) a specified income increase to the farmers can be achieved; 2) a predetermined level of recovery of the expansion cost can be insured; 3) high agricultural efficiency in the new lands can be maintained; and 4) redistribution benefits can be maximized. In a case study application of the model, no conflict is found between the economic efficiency and income redistribution criteria. For a specified cost recovery condition, it is found that the least cost planning alternatives give the opportunity to the largest number of landless farmers to own the new land and get a specified income increase from the agricultural revenues. But a conflict between the government return from the investment and income redistribution objectives is found. This conflict is addressed and the trade-off between the two objectives is illustrated. A multi-criteria optimization model is built to determine performance as well as operating rules of the agricultural systems under future uncertainties inherent in the planning parameters. Performance of agricultural systems is measured in terms of the economic efficiency and income redistribution criteria. The operating decisions are determined in such a way that the reduction in performance due to unpleasant surprises in the planning parameters can be minimized. The multi-criteria model is used in deriving the relationship between the performance of the case study under the different planning schemes and the unpleasant changes in the planning parameters. A resiliency index in terms of gradients of these functional relationships is provided. It is developed in deterministic as well as probabilistic framework. Based on this resiliency index, a definition of resilient system design is reached. A conflict between the resiliency and the cost of agricultural system designs is found. It is found that the overbuilt designs (the most costly designs) are the most resilient ones. The trade-off between the cost and the resiliency of the case study is derived and investigated. This study was sponsored by the M.I.T. Technology Adaptation Program which is funded through a grant from the Agency for International Development, United States Department of State. 1983-06-01T00:00:00Z https://hdl.handle.net/1721.1/143032 A Derived Flood Frequency Distribution Based on the Geomorphoclimatic IUH and the Density Function of Rainfall Excess Diaz-Granados, Mario A.; Valdes, Juan B.; Bras, Rafael L. The geomorphoclimatic theory is used, along with the joint probability density function of storm duration and storm intensity and the representation of the infiltration process, to derive the flood frequency distribution for a given catchment. The infiltration process is represented by two different approaches: a simple time averaged potential infiltration rate and a more realistic model based on Philip's infiltration equation. The resulting flood frequency distributions are in analytical form, containing only few climatologic and physiographic parameters of the catchment. These frequency distributions are tested against historic records from arid and wet climates with very satisfactory results. They will be very valuable in the design of flood control systems since they provide a theoretical basis for estimating flood frequencies in the absence of streamflow records. Scanning notes: Disclaimer inserted for illegible graphs and text. Missing pages 105-106.; This study was sponsored by the MIT Technology Adaptation Program, which is funded through a grant from the Agency for International Development, United States Department of State. 1983-07-01T00:00:00Z https://hdl.handle.net/1721.1/143031 Incorporation of Channel Losses in the Geomorphologic IUH Diaz-Granados, Mario A.; Bras, Rafael L.; Valdes, Juan B. The infiltration losses along the streams of a basin are included into the Instantaneous Unit Hydrograph (IUH). The IUH is derived as a function of the basin geomorphologic and physiographic characteristics, and the response of the individual channels to upstream and lateral inflows. This response is obtained by solving the linearized continuity and momentum equations, including infiltration losses terms, for the boundary conditions established by the definition of a linear system response to an instantaneous unit input. A methodology is proposed for the estimation of the parameters involved in the channel response. Based on this result, a procedure is suggested to include infiltration losses in the common linear reservoir representation of channel segments. Comparisons indicate that this approximation is adequate Scanning notes: Disclaimer inserted for illegible graphs and text.; This study was sponsored by the MIT Technology Adaptation Program, which is funded through a grant from the Agency for International Development, United States Department of State. 1983-07-01T00:00:00Z https://hdl.handle.net/1721.1/143030 Extensions and Applications of a Second-order Landsurface Parameterization Andreou, Stefanos A.; Eagleson, Peter S. Scanning notes: Contains text that runs off edge of pages. Disclaimer scanned.; Prepared under the support of the National Aeronautics and Space Administration Grant NAG 5-134 1983-07-01T00:00:00Z https://hdl.handle.net/1721.1/143029 Hydrothermal-biological Coupling of Lake Eutrophication Models Wang, Ming-Pin; Harleman, Donald R. F. A deterministic model capable of simulating lake response to changes in hydrologic conditions or nutrient input has been developed. This model may provide a convenient means of evaluating management strategies and identifying weak points in our current knowledge. The emphasis of this model development is to minimize the number of calibrated parameters. A summary of the state-of-the-art of hydrothermal modeling in a phosphorus limited condition is presented in this work. It is demonstrated that a mixed layer hydrothermal model, which calculates the daily vertical temperature profile and thickness of the upper fully mixed layer based on the meteorological and hydrological information, is capable of simulating the transport and diffusive process in a stratified lake with a minimum number of calibrated parameters. Since our ability to mathematically represent complex aquatic biological processes is less well developed than our corresponding ability in the geophysical area, field data plays an important role in defining the final biological model structure. Phytoplankton modeling of L227 is used as a case study to illustrate the methodology for arriving at a biological model whose complexity is consistent with the available data. A procedure is indicated for extracting biological rate constants from primary productivity measurement. The extent to which the linked hydrothermal-biological model simulates the phytoplankton dynamics of the following summer is discussed. Finally, the importance of capturing the short term dynamics of the fully mixed layer in the modeling of phytoplankton variation is illustrated by simulation runs. The simulation runs compare phytoplankton predictions of three lake phytoplankton models with different specifications of the daily fully mixed layer depths. Both a surface nutrient input case and an intermediate depth nutrient input case are considered. Prepared under the support of the National Science Foundation Water Resources and Environmental Engineering Program. CEE-7906125. 1982-04-01T00:00:00Z https://hdl.handle.net/1721.1/143028 Coupled Flux of Heat and Moisture Across a Snowcovered Landsurface with Vegetation Gordon, Matthew J.; Eagleson, Peter S. A theoretical study of snow accumulation and ablation in vegetated areas is presented. A one-dimensional energy and mass balance model of winter (non-transpiring) vegetation is coupled to an existing one-dimensional energy and mass balance model of the surface snowcover. A sensitivity analysis of the simulated energy fluxes is conducted with respect to canopy density, interception characteristics, and atmospheric temperature. Results indicate that the presence of vegetation can alter the heat and mass exchange between the snowcovered area and the atmosphere by at least three different processes. At lower canopy densities, the increased surface area available can increase the magnitude of the energy and mass fluxes. At higher canopy densities, the increased attenuation of ventilating wind tends to limit increases in turbulent transfer. At high canopy densities, the total shielding by the canopy of shortwave radiation and sensible and latent heat transfer to the surface from the atmosphere tends to cool the surface in warm or moderately cold weather. This causes an increase in temperature gradient and sensible heat flux from the canopy to the ventilating air. The persistence of snow on the canopy has a dramatic effect on the energy balance of the area. A snow-less canopy can become very warm and transmit more heat than a snowcovered canopy. Part of the research discussed herein was sponsored by the National Science Foundation under Grant, "A Dynamic Landsurface Boundary Condition for Climate Models" ATM-8114723 1982-04-01T00:00:00Z https://hdl.handle.net/1721.1/143027 Constrained Stochastic Climate Simulation Curtis, David Carleton; Eagleson, Peter S. A stochastic, multivariate, hydrometeorological data generation algorithm is presented. Hourly values of precipitation, cloud cover, shortwave radiation, longwave radiation, temperature, dewpoint, wind speed, and wind direction are jointly generated for the two-meter level. The procedure is designed to provide coherent sets of input data for models of various land surface processes. The model's flexibility and economy allow the study of land surface responses to different atmospheric forcings. Generated data plots, model output statistics, and generated mean diurnal curves are compared to observations for the months of January and July at two sites, Boston, Massachusetts and Dodge City, Kansas. Data representing three "climates", normal, wet, and temperature-biased were generated and applied to a detailed model of the land surface. The resulting energy fluxes across the land-atmosphere interface are reviewed and the differences are noted. Prepared with the Support of the National Oceanic and Atmospheric Administration, the National Weather Service, and the National Science Foundation. 1982-05-01T00:00:00Z https://hdl.handle.net/1721.1/143026 Optimal Irrigation Control Using Stochastic Cluster Point Processes for Rainfall Modelling and Forecasting Rodriguez, Jorge Alberto Ramirez; Bras, Rafael L. Optimal irrigation control is performed. The control accounts for the intraseasonal variation of the crop water requirements and for tie dynamics of soil moisture depletion process. The clustering dependence structure of rainfall occurrences is explicitly accounted for. Stochastic rainfall inputs to the soil-plant system are characterized by storm intensities, storm durations, interarrival times, and number of storms in a given period of time. Precipitation occurrences are modelled as a Neyman-Scott cluster process; and using Palm-Khinchin theory conditional distributions of the time to the next rainfall events are derived. These distributions are conditional on part of the immediate history of storm arrivals. The derived distributions are seen to possess characteristics desired for short term forecasting of rainfall occurrences. Particularly, they exhibit the ability to detect short term trends in precipitation occurrences. The probabilistic description of precipitation is coupled with a probabilistic description of cumulative infiltration from storms and a Markov chain approach to the dynamics of soil moisture throughout the growing season. Conditional probabilities of soil moisture are derived and used within a Stochastic Dynamic Programming algorithm to obtain irrigation decisions. The control is obtained in the form of decision functions which yield the optimal irrigation depth as a function of soil moisture content at the root zone, volume of irrigation water available, and number of days since the last rainfall occurrence. Case study results confirm the existence of a clustering dependence structure in rainfall occurrences as well as the goodness of the Neyman- Scott process in its modelling. However, there appears to be no significant difference in expected maximum net benefits when comparing results obtained with the control model under the homogeneous Poisson assumption and under the conditional Neyman-Scott model. Furthermore, slightly lower expected benefits are obtained with the conditional Neyman- Scott model than with the non-homogeneous Poisson model. This report is based upon work supported by the National Science Foundation under NSF Grant No. 78-20245 ENG 1982-05-01T00:00:00Z https://hdl.handle.net/1721.1/143025 Agricultural Expansion Planning: Incorporating Water Reuse Allam, Mohamed Nasr; Marks, David Hunter A mathematical model has been built to guide decisions required for agricultural expansion planning. Of particular interest is the case when some, or all, of the irrigation sources available have saline water. These decisions generally are quantities and locations of all resource inputs, mixing ratio between different waters, if mixing is possible, irrigation network design, required enlargement in the existing irrigation system, and crop pattern distribution in the new lands. These decisions are based on the maximum net benefit criterion and are carried out in a mathematical optimization framework. A comprehensive study of the use of this model in a large scale planning problem has been done. This case is based upon the proposed agricultural expansion in the-Nile Delta and the Sinai in Egypt. The available irrigation sources 'in-these regions are fresh and saline waters from the River Nile, and from the drains of the existing cultivated lands, respectively. Different alternative schemes for irrigating the new lands have been obtained. An economic approach for enabling the decision makers to analyze the different alternatives has been presented. In addition, the equity concerns in scheduling and cost allocation have been discussed. Prepared under the support of the Technology Adaptation Program. 1982-03-01T00:00:00Z https://hdl.handle.net/1721.1/143024 Value of Categorical and Probabilistic Temperature Forecasts for Scheduling of Power Generation Alexandridis, Mark G.; Krzysztofowicz, Roman Bayesian decision models are formulated for the use and evaluation of categorical and probabilistic forecasts of continuous variables. The models are applied to the problem of short-term scheduling of power generation in an electric system on the basis of a single-period temperature forecast. Likelihood functions are constructed using results of experiments conducted at the National Weather Service. The probabilistic forecasting scheme is of the type wherein the forecaster quantifies his degree of uncertainty in terms of variable-width, fixed-probability credible intervals. Each forecasting scheme, categorical and probabilistic, is evaluated in a coupling with two decision procedures: (1) an optimal (Bayesian) procedure which accounts for forecast uncertainty, and (2) a more conventional, non-optimal, procedure which disregards forecast uncertainty, but which would be optimal if the forecasts were perfect. Numerical examples are presented to illustrate the economic values of both types of forecasts, gains from probabilistic forecasts, and expected opportunity losses to be incurred by decision makers who ignore forecast uncertainty. Key words; Bayesian decision theory, value of information, meteorologic forecasts, probabilistic forecasts, electric power generation, power load forecasting. Prepared under the support of The National Science Foundation Grant No. CEE-8107204 1982-05-01T00:00:00Z https://hdl.handle.net/1721.1/143023 Identification and Estimation of a Monthly Multivariate Stochastic Streamflow Model for the Nile River Basin Diaz-Granados, Mario A.; Bras, Rafael L. This report is one of a series of publications which describe various studies undertaken under the sponsorship of the Technology Adaptation Program at the Massachusetts Institute of Technology. The United States Department of State, through the Agency for International Development, awarded the Massachusetts Institute of Technology a contract to provide support at M.I.T. for the development, in conjunction with institutions in selected developing countries, of capabilities useful in the adaptation of technologies and problem-solving techniques to the needs-of those countries. This particular study describes research conducted in conjunction with Cairo University, Cairo, Egypt. In the process of making this TAP supported study some insight has been gained into how appropriate technologies can be identified and adapted to the needs of developing countries per se, and it is expected that the recommendations developed will serve as a guide to other developing countries for the solution of similar problems which may be encountered there. Scanning notes: Best image quality available. Disclaimer scanned.; This work was sponsored by the M.I.T. Technology Adaptation Program which is funded through a grant from the Agency for International Development, United States Department of State. 1982-07-01T00:00:00Z https://hdl.handle.net/1721.1/143022 Interaction of the Saturated and Unsaturated Soil Moisture Zones. 1. Analytical Solution of the Linearized Richards Equation. 2. The Role of Climate in Shaping the Phreatic Surface Miller, Scott Allan; Eagleson, Peter S. In Part I, dimensionless analytical expressions are derived describing the hydrologic processes and the moisture distribution of a high water table unsaturated soil column, by linearizing Richards' equation. The finite Fourier transform method is used to solve for the moisture content, which is the basis for the solutions for the depth-averaged moisture content, ponding time, boundary fluxes and their integral quantities. The effects of transpiration are included through three models of soil-water extraction by plants. Simplified, physically-based expressions for infiltration rate-and ponding time which include water table effects, are proposed in the appendix. Examples of the solutions are presented and several cases are compared with a numerical finite-element model of the non-linear problem. Fitted parameter estimates are compared with analytical expressions from the literature. Comparisons are for average moisture content, ponding time and cumulative infiltration. Good to excellent agreement is found for all cases. The exfiltration solutions, with and without vegetation, are untested. In Part II, the dynamic relation between soil-moisture, water table depth, and accretion to groundwater is studied. Derived relations between the moisture content, water table depth, and net accretion are compared over a range of climate and soil types. These are used in a one dimensional non-linear finite-difference model for the water table shape and the longer run influence of climate upon it. The boundaries are constant potentials. The water table is shown to have an influence for depths from less than one meter to over one hundred meters, with the greater influence for clay soils and larger potential evaporation rates. Climate-induced water table depressions and swamplands are shown to be dependent upon the unsaturated zone water balance and upon the hydraulic conductivity of the soil. Case studies for the water table-water balance model use data from the El-Gizera and Bahr-el-Ghazal regions of Sudan. In both parts of this work, dimensionless parameters are developed to describe when the water table influences the water balance of unsaturated soil and when the climate influences the water table shape. Scanning notes: Disclaimer inserted for quality (too many pencil marks to erase).; Prepared under the support of the M.I.T. Technology Adaptation Program, which is funded through a grant from the Agency for International Development, United States Department of State. 1982-08-01T00:00:00Z https://hdl.handle.net/1721.1/143021 Solar Pond Feasibility Study for Egypt: Preliminary Report Salhotra, Atul; Adams, E. Eric; Harleman, Donald R. F. The report presents a preliminary feasibility study for salt gradient solar ponds in Egypt. Chapter 1 gives a brief review of the technical and economic aspects of solar ponds. Chapter 2 includes a discussion of the ongoing analytical and experimental research at the Ralph M. Parsons Laboratory. Chapter 3 investigates the potential and technical feasibility of construction and operation of large scale solar ponds in the Qattara Depression. Performance of the proposed solar ponds has been simulated using the Solar Pond Model developed at M.I.T. Chapter 4 gives details of the construction, operation and performance of small demonstration solar ponds at Lake Qarun or Lake Maruit. Scanning notes: Disclaimer inserted for illegible graphs and text.; This work was sponsored by the M.I.T. Technology Adaptation Program which is funded through a grant from the Agency for International Development, United States Department of State. 1983-01-01T00:00:00Z https://hdl.handle.net/1721.1/143020 A Comparison of Linear and Nonlinear Random Field Estimators Angulo, Carlos Enrique Puente; Bras, Rafael L. The estimation of random fields from limited samples is an important issue in most fields of geophysics, such as Hydrology and Meteorology. Work by Matheron and others at the Paris School of Mines has popularized Kriging techniques to estimate random fields at specified locations or to get areal averages. This work presents the theoretical and practical aspects of both Linear and Nonlinear (Disjunctive) Kriging estimators, and provides a comparison of their performance in estimating point and areal values of generated fields. The experiments performed were designed to closely resemble actual and practical situations. The results show that small sample based inconsistencies lead to a Disjunctive Kriging solution which does not give more accurate estimates than the theoretically less precise Linear Kriging estimator. The results also suggest the use of a multi-realization approach when using these techniques in network design problems. Scanning notes: Disclaimer inserted for illegible graphs and text.; Prepared with support of National Science Foundation and Office of Surface Mining through Grants CME-7919836 G5105071 1982-11-01T00:00:00Z https://hdl.handle.net/1721.1/143019 A Second-order Budyko-type Parameterization of Landsurface Hydrology Andreou, Stefanos A.; Eagleson, Peter S. This work develops a simple, second-order parameterization of the water fluxes at a landsurface for use as the appropriate boundary condition in general circulation models of the global atmosphere. The derived parameterization incorporates the high non-linearities in the relationship between the near-surface soil moisture and the evaporation, runoff and percolation fluxes. Based on the one-dimensional statistical-dynamic derivation of the annual water balance developed by Eagleson (1978), it makes the transition to short term prediction of the moisture fluxes, through a Taylor expansion around the average annual soil moisture. A comparison of the suggested parameterization is made with other existing techniques and available measurements. A thermodynamic coupling is applied in order to obtain estimations of the surface ground temperature. Prepared under the Support of The National Aeronautics and Space Administration Grant NAG 5-134 1982-06-01T00:00:00Z https://hdl.handle.net/1721.1/143018 A Precipitation Model and Its Use in Real-time River Flow Forecasting Georgakakos, Konstantine P.; Bras, Rafael L. A one-dimensional, physically based, station precipitation model is proposed and tested. The model state variable is the liquid water equivalent mass in a unit area cloud column. Model inputs are the air temperature, dew-point temperature, and pressure at the ground surface. The precipitation rate at the ground surface is the model output. Simplified cloud microphysics give expressions for the moisture input and output rates in and from the unit area column. Parameterization of the model physical quantities: updraft velocity, cloud top pressure, and average layer cloud-particle diameter is proposed, so that parameters, will remain reasonably constant for different storms. Conceptual soil and channel routing models were used together with the proposed precipitation model in formulating a general Rainfall-Runoff model. Hourly data from eleven storms of different types and from two different locations in the US, served as the data-base for the station precipitation model tests. Performance in predicting the hourly precipitation rate was good, particularly when a sequential state estimator was used with the model. The general Rainfall-Runoff model formulated, complemented by a sequential state estimator, was used with six-hourly hydrological data from the Bird Creek basin, Oklahoma, and with six-hourly meteorological data from the somewhat distant Tulsa, Oklahoma, site. Forecasts of both the mean areal precipitation rate and the basin outflow discharge were obtained. Performance indicated the value of the precipitation model in the real-time river flow forecasting. U.S. Dept. of Commerce, National Weather Service, Contract no. NA79SAC00650 1982-07-01T00:00:00Z https://hdl.handle.net/1721.1/143017 The Linear Channel and Its Effect on the Geomorphologic IUH Kirshen, Diana M; Bras, Rafael L. The Instantaneous Unit Hydrograph (IUH) is derived as a function of the basin's geomorphological and physiographic characteristics. Inherent in the basin IUH is the response of the individual channels composing the basin. The response of the individual channels is derived by solving the continuity and momentum equations for the boundary conditions defined by the IUH. Both the effects of upstream and lateral inflow to the channels is taken into account in the derivation of the basin's IUH. The time to peak and peak response are used as a basis for comparison between the results produced by this model and those produced by a model where the channel's response is assumed to be an exponential distribution. The comparisons indicate that if the approach taken in this paper is indeed accurate, for example, the assumptions used do not invalidate the model, then the type of channel response used for the basin's IUH is significant, and future efforts must be directed towards parameter estimation. Prepared with the Support of The Agency for International Development, The United States Department of State. 1982-06-01T00:00:00Z https://hdl.handle.net/1721.1/143016 Infiltration and Evaporation at Inhomogeneous Land Surfaces Milly, P. Christopher D.; Eagleson, Peter S. The local response of the land surface to atmospheric forcing is determined by the surface parameters, the surface state, and the forcing. Because these factors are highly variable at length scales smaller than those of many hydrologic analyses, and because they enter nonlinearly into the hydrologic response functions, the calculation of areal average response in terms of real physical parameters is non-trivial. Treating an inhomogeneous soil surface as a battery of independent, parallel soil columns, we calculate the areal average infiltration that results from a spatially variable storm event. The spatial variability of soil and storm properties turns out to be critical in shaping the infiltration function for an inhomogeneous basin. A particular feature of the average response is that increased spatial variability of soil type or of storm depth almost invariably leads to decreased infiltration and increased surface runoff. The calculation of the areal average evapotranspiration rate is complicated by atmospheric advection, which provides a feedback mechanism whereby the downstream evaporation is influenced by the upstream. The upstream influence may persist over a fetch of hundreds of kilometers. A conceptual model of the atmospheric boundary layer is developed and applied to the analysis of evapotranspiration from a surface whose supply of water and energy may be characterized by spatially variable canopy resistances and available energies (net radiation minus heat flux into the ground). The surface roughness is also considered to be variable in space. An explicit dependence of areal average evapotranspiration upon the patch size -- the characteristic length of the variability -- is derived. The effect of local advection is shown to be most significant when there is a great variation of the canopy resistance between patches. Otherwise, the individual patches behave in a relatively independent manner. This points to the importance of spatial variability of the water supply in the analysis of areal average evapotranspiration. This material is based upon work supported by the National Science Foundation Under Grant Numbers ATM-7812327 ATM-8114723 1982-06-01T00:00:00Z https://hdl.handle.net/1721.1/143015 Linked Hydrodynamic and Biogeochemical Models of Water Quality in Shallow Lakes Shanahan, Peter; Harleman, Donald R. F. Approaches to lake water quality modeling are critically examined with particular attention to the formulation of water quality transport as the link between hydrodynamics and biogeochemical reaction. A linked water quality model for shallow lakes includes three major components: a biogeochemical reaction component, a lake hydrodynamics component and a water quality transport component. State-of-the-art modeling approaches for each component are reviewed, and a synopsis of phosphorus dynamics in shallow lakes is given. For the water quality transport component, review of the literature shows two significantly different approaches to water transport: a lumped component approach based upon multiple fully-mixed boxes, and a continuum approach employing the finite difference method to approximate the continuous governing equations. The multiple-box model is shown in an analysis of the kindred fully-mixed tanks-in-series conceptual reactor model to create an excessive implicit dispersion due to its formulation. This leads to a model in which the model mass transport is not closely related to the properties of the physical system. being modeled. Rather, dispersive transport in the model is shown to depend heavily upon the model formulation -- the model transport parameters thus cannot be specified from hydrodynamic data but must be found by calibration. In direct contrast, the finite difference model maintains a far closer approximation to the physical system and permits direct specification of water quality transport from the actual lake hydrodynamics. To support these arguments, a computer program incorporating both a multiple-box model and an alternative one-dimensional finite difference model is developed and applied to Lake Balaton in Hungary. The biogeochemical component of both models is a four component phosphorus-phytoplankton interaction model originally proposed by van Straten (1980). Hydrodynamic information is supplied to the one-dimensional finite difference model by linkage to a transient two-dimensional single-layer model of wind-driven circulation. A one-dimensional dispersion coefficient is computed from the two-dimensional velocity field using a method based upon that of Fischer (1966, 1969) and Holley, Harleman and Fischer (1970), but proceeding from the assumption that advection rather than turbulent diffusion dominates lateral mixing. The finite difference model developed for Lake Balaton consists of forty grids and is used to simulate a representative period from early spring to late summer. The results are contrasted with those produced by a four-box model of the lake using long-term average advection and calibrated dispersive exchange flows. The finite difference model is found to lead to a predicted behavior more similar to that observed in field data collected from Lake Balaton. Experimentation with the models is conducted to examine the behavior of the lake and the dominant factors leading to that behavior. Scanning notes: Disclaimer inserted for illegible graphs and text.; Prepared under the support of the National Science Foundation Water Resources and Environmental Engineering Program. 1982-03-01T00:00:00Z https://hdl.handle.net/1721.1/143014 Parameterization of Moisture and Heat Fluxes Across the Land Surface for Use in Atmospheric General Circulation Models Milly, P. Christopher D.; Eagleson, Peter S. The response of a bare soil surface to atmospheric forcing -- rain, wind, sunshine, etc. -- may be expressed in terms of the resultant evaporation rate and sensible and radiant heat losses. Examining the earth-atmosphere interface in an idealized one-dimensional framework, we evaluate a hierarchy of mathematical models in terms of their ability to predict this land surface response. The evaluation is based on simulation, using typical climatologic and soil parameters. The reference model, against which the other models are tested, is based on a numerical solution of a very detailed description of heat and moisture movement in porous media. The alternative models are, to a greater or less extent, simpler both conceptually and computationally than the reference model. They include the following: 1. A family of models obtained by introducing various sinplifying assumptions in the reference model. These corcern the roles of water vapor, of soil moisture retention hysteresis, and of a few other minor effects. 2. A set of models constructed by linking the forcerestore method of soil temperature prediction to each of three soil moisture parameterizations -- a two-node finite element model, a conceptualization used by climate modelers, and a nonlinear diffusion model. Using the nominal soil and climatologic parameters, we determine the critical physical mechanisms affecting the surface fluxes of water and heat. We find that an isothermal moisture equation, with the hydraulic conductivity augmented by a vapor conductivity, and accounting for hysteresis, is sufficient. The nonlinear diffusion parameterization, which includes these effects, is extended to account for redistribution. In conjunction with the force-restore method, it successfully predicts evaporation under various climatic and soil conditions. This material is based upon work supported by the National Science Foundation Under Grant Numbers ATM-7812327 ATM-8114723 1982-06-01T00:00:00Z https://hdl.handle.net/1721.1/143013 Calibration and Verification of the Cooling Lake Model for North Anna Power Station: During the Period July 1978 - September 1981 Wells, Scott A.; Adams, E. Eric; Harleman, Donald R. F. The North Anna Power Station (3 proposed nuclear units with a total capacity of 2820MWe) is located in the State of Virginia about 41 miles northwest of Richmond. The plant condenser heat dissipation system consists of a complex geometric arrangement including a Waste Heat Treatment Facility (WHTF), consisting of a series of separate ponds with attached dead-end side arms, and Lake Anna which is a deep reservoir created by impounding the North Anna River. A segmented mathematical model was used to simulate thermal structure within the Lake Anna system. Initial model development, calibration based on pre-operational data (1977-1976), and predictions under station operation for the historical period 1957-1966 are documented in Jirka et al (1977). Since Unit 1 came on line in the Summer of 1978 and Unit 2 in Fall of 1980, an extensive data collection effort was undertaken to calibrate the model to operational data. Continuous measurements were made of meteorological variables, plant load, water temperature at various points in the system and current speeds in one of the WHTF side-arms. Supplemental data, with greater spatial resolution, were collected at weekly or monthly intervals. Calibration of the model included examination of assumptions inherent in the model development and refinement of model coefficients. Major areas of investigation included surface heat transfer processes (short wave solar radiation, long-wave atmospheric radiation and evaporation), dilution and entrance mixing, dead end side arm flow dynamics, vertical diffusion of heat below the well-mixed upper layer in the main lake, and linkage of the WHTF calculations with those of the main lake. Comparison against a three year period of operational data (1978-1981) showed that the model predictions were very accurate. An error analysis detailed explicitly the model's strengths and weaknesses, with mean surface errors (prediction-data) ranging from + 0.9 �F to-0.4 �F at four diagnostic control points and standard error ranging from 2.8 �F to 1.8 �F. Excellent agreement was also found in the vertical temperature profiles in the main lake. After verification, the model was used in a predictive mode to simulate temperatures for 1, 2 and 3 nuclear units under a range of meteorological conditions. Synthetic meteorological data had previously been prepared for the ten year period, 1957-1966, by means of a regionalization procedure. Temperature predictions for this ten year period could then be used to characterize both average and extreme conditions. During extremely warm periods (e.g., the Summer of 1959), the temperature of water released from Lake Anna to the N. Anna River downstream would have exceeded the present temperature standard of 89.6 �F (32 �C). A one-dimensional river temperature model was developed to predict downstream temperatures. Furthermore, several possibilities for reducing downstream temperatures were examined including: (i) dilution reduction in the WHTF, (ii) rerouting of the flow through the WHTF sidearms, (iii) reduction in condenser flow rate, (iv) bubble aerators in the main lake, and (v) a siphon to mix hypolimnetic cool water with warm surface water for discharge into the N. Anna River. For the siphon, which appears to be the most efficient option, simulations were performed to identify the maximum flow rate and the total volume of hypolimnetic water withdrawn, in order to comply with downstream temperature standards in each of the ten years simulated. Prepared under the support of Virginia Electric and Power Company, Richmond, Virginia. 1982-03-01T00:00:00Z https://hdl.handle.net/1721.1/143012 Automatic Parameter Estimation of a Large Conceptual Rainfall-runoff Model: A Maximum Likelihood Approach Restrepo Posada, Pedro J.; Bras, Rafael L. A stochastic parameter estimation procedure to be applied to large conceptual rainfall-runoff models is proposed. The procedure is based on a maximum likelihood approach, which is enhanced to allow for the use of prior information about some of the parameters. A stochastic model of base flow is proposed, and an algorithm for automatic identification of the time interval of base flow activity is developed. This algorithm, which permits the estimation of prior values for the base flow discharge coefficients, is successfully applied to two basins in the United States. The application of the maximum likelihood estimation procedure to large conceptual rainfall-runoff models is divided into two stages. In the first stage the procedure is applied to a simplified version of the National Weather Service River Forecasting System model, the parameters of which are estimated by using synthetically generated data. This stage produces valuable information about the performance of stochastic parameter estimation procedures in large conceptual rainfall-runoff models. In the second stage the maximum likelihood procedure is applied to estimating the parameters of the National Weather Service River Forecasting System model for the Bird Creek and for the Cohocton River basins, respectively. In the first case a severe structural error arising from a deficient formulation of the channel causes some of the parameters to converge to unrealistic values. In the second case the stochastic model performs in a mathematically correct but hydrologically unappealing fashion. The reasons for this problems are attributed to the non-identifiability of the threshold parameter of the upper zone tension water element and to interaction between several of the percolation function parameters. Hydrologic Research Laboratory of the National Weather Service, U.S. Dept. of Commerce NA 80AA-H-00044 1982-03-01T00:00:00Z https://hdl.handle.net/1721.1/143011 Conservation in Long-term Conjunctive Use: Irrigation Demands Using Disaggregate Choice Models Marks, David H.; Wilson, John L. Section 1:This report presents the hierarchy of sub-problems involved in modelling the demand for conjunctive use. An historical description of the development of conjunctive user irrigation and a review of current policy initiatives of local water management institutions support the contention that the prime determinants of the demand for new conjunctive use systems for irrigation are their profitability and local water policies. The possible future implementation of comprehensive water management policies needs to be explored by 1) examining the institutional objectives of local water management agencies, and 2) developing a predictive model of the acceptance of conjunctive use policies by irrigators. The research needs identified in this section are further developed in Section II (Institutional Objectives in Conjunctive Management of Surface and Groundwater) and Section III (Predicting the Acceptance of Water Conservation Policies by High Plains Irrigators: An Application of Probabilistic Choice Modelling). Section 2: Local irrigation agencies are not centralized institutions with complete power over all surface and groundwater decisions in their basins. Instead, the three major types of irrigation agencies: public irrigation districts, mutual water companies and commercial water companies have different and relatively limited powers. Most importantly, with certain exceptions, they cannot directly control excessive groundwater withdrawals and have to resort to indirect methods to achieve this goal. The study of the decision-making process of two important types of local irrigation agencies, public irrigation districts and mutual companies can be simplified by hypothesizing that these agencies have similar objectives. However, single objective models should be discarded because they fail to predict actual decisions. Instead, multi-objective models should be used: aggregate profit maximization, local control, conflict resolution, equity and internal motives play an important role in shaping the choice between different policies. An accurate analysis of the nature and objective of irrigation agencies paves the way for the construction of detailed conceptual models of the decision-making process of these institutions. These models can either predict or describe the behavior of a particular agency and can be incorporated into a general framework suitable for the analysis of most issues relating to the conjunctive management of surface and groundwater. Section 3: This study addresses the groundwater depletion problem in the Ogallala aquifer beneath the High Plains and examines the suitability of probabilistic choice models for predicting the acceptability of alternative water conservation policies to the irrigators. The nature of the policy acceptance problem is discussed and the social, institutional, and legal environments present on the High Plains are described. An overview of choice models and behavioral factors of individual information processing is presented. Use of the Elimination by Aspects (EBA) model and the Luce choice model is explored in the context of predicitng the degree of acceptance of alternative water conservation policies by irrigators. The existing and proposed policies of the groundwater management districts on the High Plains are reviewed and their characterization in terms of aspects is proposed. These alternatives are then used in an experimental application of the EBA and Luce choice models. Two laboratory experiments are conducted to examine the performance of these models in the context of predicting water conservation policy acceptance. The experiments confirm the validity of the regularity and moderate stochastic transitivity assumptions (EBA model) and the multiplicative inequality (both models) but do not confirm the validity of the similarity hypothesis (EBA model), or the constant ratio rule and strong stochastic transitivity (Luce's model). In the experiments, the EBA model was a more accurate predictor of the choice probabilities than Luce's model. Furthermore, use of the EBA model appears to be most appropriate for problems characterized by many feasible alternatives which can be described by many concrete aspects which are easily recognized by the decision makers. Recommendations are made concerning field applications of the EBA model and future research needs of predictive choice modelling. Grant no. 14-34-001-9430. 1981-03-01T00:00:00Z https://hdl.handle.net/1721.1/143010 Simulation of Random Fields with the Turning Bands Method Mantoglou, Aristotelis; Wilson, John L. This report presents and extends the Turning Bands Method (TBM) for the synthetic simulation of random fields. Originally introduced by G. Matheron (1973) of the Ecole des Mines de Paris, the TBM can be applied to stationary or non-stationary fields. For two and three dimensional stationary isotropic fields the general TBM equations are derived with particular emphasis on the two dimensional case. In a new approach the unidimensional line process is generated by a simple spectral method, a technique which can be generally applied for any two dimensional covariance function and is easily extended to anisotropic processes. In a second approach the line process is generated as a moving average process for which corresponding one dimensional equivalents are derived for special two dimensional covariance functions. The convergence properties of the TBM with the number of lines is described mathematically and by example, and guidelines are presented for the selection of model parameters. The TBM is compared to other methods in terms of cost and accuracy, demonstrating that the TBM is as accurate and far less expensive than any other existing technique. Using the unidimensional spectral method the TBM is extended to the direct generation of stationary anisotropic processes. Examples of this generation are given with a comparison between theoretical and sample statistics. Equations are derived giving the covariance function and the spectral density function for the process of areal averages of stationary processes. It is observed that reduced covariance between areas can damp out quickly, relative to the size of the areas, suggesting the possibility of approximating areal average covariance by point covariance in some instances. The areal average process is, in general, anisotropic. Thus the anisotropic TBM is applied for direct generation of the areal average process. The comparison of the theoretical and sample statistics is excellent. The Turning bands method for the simulation of nonstationary random fields (IRF) is presented, using a Wiener-Levy process for line generation as suggested by Matheron (1973). Examples are given for IRF's of zero, first and second order. Prepared with the partial support of the Office of Surface Mining, Department of Interior through M.I.T.'s Mining and Mineral Resources Research Institute, and the Agency for International Development, Department of State, through M.I.T.'s Technology Adaptation Program. 1981-07-01T00:00:00Z https://hdl.handle.net/1721.1/143009 Study of a Real-time Adaptive Closed-loop Control Algorithm for Reservoir Operation Buchanan, Ross B.; Bras, Rafael L. Recent studies on the optimal control of the High Aswan Dam in Egypt have illustrated the usefulness of steady-state stochastic dynamic programming techniques for deriving optimal release policies. This work likewise uses stochastic dynamic programming for the determination of optimal High Dam releases, but a new adaptive reservoir control scheme capable of handling a nonstationary system is investigated. Using results of the stationary control problem as boundary conditions, a finite horizon optimization problem is solved in order to incorporate the multi-lead forecasts of reservoir inflows and any other nonstationarities into the solution procedure. A comparison is made of a heuristic operating policy for the High Aswan Dam with that resulting from a steady-state stochastic dynamic programming solution and that from the suggested real-time adaptive control formulation. The objective is to minimize losses due to irrigation deficits, power production deficits and damages due to flooding. It can be concluded that performance is better with the steady-state solution, and it is best using the adaptive formulation. Particularly, the use of forecasts and the adaptive formulation significantly reduces flood damages. Prepared with the support of the Agency for International Development, the United States Department of State. 1981-07-01T00:00:00Z https://hdl.handle.net/1721.1/143008 The Practice of Kriging Kafritsas, John; Bras, Rafael L. The theory of intrinsic random functions of order k (IRF-K) and its use in optimal linear interpolation is presented using a simple deterministic formulation. Also outlined are the procedures for identification of generalized covariances corresponding to an IRF-K. Included is documentation, example and listing of a general purpose computer package for point and block kriging using IRF-K theory. The accessibility of such a tool should be welcomed by mining engineers, hydrologists and other geophysicists. Prepared with the support of the National Science Foundation grant no. CME-7919836 1981-01-01T00:00:00Z https://hdl.handle.net/1721.1/143007 Mathematical Predictive Models for Cooling Ponds and Lakes Octavio, Kathleen Hurley; Watanabe, Masataka; Adams, E. Eric; Jirka, Gerhard H.; Helfrich, Karl R.; Harleman, Donald R. F.; Part C: Adams, E. Eric; Koussis, Antonis D. Part B. User's manual and applications of MITEMP / Kathleen Hurley Octavio, Masataka Watanabe, E. Eric Adams, Gerhard H. Jirka, Karl R. Helfrich [and] Donald R.F. Harleman -- Part C. A transient analytical model for shallow cooling ponds / E. Eric Adams, Antonis D. Koussis. Prepared Under the Support of Commonwealth Edison Company Chicago, Illinois; NUS Corporation Rockville, Maryland; Environmental Control Technology Division U.S. Department of Energy, Washington, D.C.; and Electric Power Research Institute Palo Alto, California 1980-04-01T00:00:00Z https://hdl.handle.net/1721.1/143006 Water Balance Studies of the Bahr El Ghazal Swamp Chan, Siu-On; Eagleson, Peter S. Future increases in Egyptian and Sudanese water resources may come from reduction of the large water losses of the Upper White Nile's swampy regions, particularly from the Bahr el Ghazal swamp. In this work, new methods of water balance estimation which incorporate the dynamic interaction of climate, soil and vegetation are applied to the Bahr el Ghazal basin in order to study its contribution to the flow of the White Nile, and to estimate the potential water recovery through drainage of this swamp. Prepared under the Support of. The Agency for International Development The United States Department of State and the Technology Adaptation Program. 1980-12-01T00:00:00Z https://hdl.handle.net/1721.1/143005 Water Balance Estimates of the Machar Marshes El-Hemry, Ismail Ibrahim; Eagleson, Peter S. Further increases of the River Nile discharge may come from reducing the water losses in the upstream swampy areas in the Nile basin. The Machar region is one of the main losers of water in this basin. In this work, the general water balance of the Machar region is studied using new models which incorporate the dynamic interaction of climate, soil and vegetation. Also, the random variability of the different hydrologic components are investigated. Probabilistic estimates of annual water yield of the Machar catchments are presented. These estimates show the amount of water that may be saved and they provide a guide to the Egyptian and Sudanese water resource planners in their design of a channelization system in the region. Prepared under the support of The Agency for International Development The United States Department of State. 1980-08-01T00:00:00Z https://hdl.handle.net/1721.1/143004 Empirical Temperature Forecasting: Extensions of the Model Output Statistics Method Langseth, David E.; Bras, Rafael L. Deterministic models of complex natural phenomena such as streamflow or weather events are usually either unknown or unwieldy and thus are often augmented or replaced by stochastic or empirical models. For example, the National Weather Service (NWS) uses a combination of deterministic and empirical models to predict several weather parameters. An approximate deterministic model of the atmosphere provides predictions of some meteorological parameters at the grid points used in the numerical solution of the model. Some of these deterministic predictions, along with recent measured data, are then used as input variables to an empirical prediction equation. The National Weather Service uses a stepwise least-squares regression algorithm to develop the empirical equations. The prediction of maximum surface air temperature is investigated in this work. The NWS currently uses 10 variable linear models to predict maximum temperatures. The 10 variable restriction is based on research and the linear restriction is based primarily on the prohibitive amount of time and effort required to develop non linear models. The potential model improvements from relaxing these two restrictions are examined in this work. Data from Huntsville, Alabama, supplied by the NWS, is used. Non linear models are created by applying a non linear model identification algorithm called the Group Method of Data Handling to the data. Two linear model identification algorithms are also used. The usefulness of the removal of harmonic components and the identification of principal components were investigated along with each of the model identification algorithms. It is shown that, for the site investigated, the linear restriction does not hurt model quality and that while 10 is a reasonable number of variables, models with fewer variables can also perform well. Also, modeling the mean trends separately from the more transient effects improves model quality. Prepared with the support of the U.S. Dept. of Energy under Contract no. EX-76-A-01-2295 1980-06-01T00:00:00Z https://hdl.handle.net/1721.1/143003 A Statistical Linearization Approach to Real Time Nonlinear Flood Routing Georgakakos, Konstantine P.; Bras, Rafael L. Sponsored by the Hydrologic Research Laboratory, National Weather Service, U.S. Dept. of Commerce under Contract no. NA79SAC00650 1980-06-01T00:00:00Z https://hdl.handle.net/1721.1/143002 Effect of Wind-mixing on the Thermocline Formation in Lakes and Reservoirs Bloss, Siegfried; Harleman, Donald R. F. Prepared with the support of the Ford Professorship at MIT and the German Research Society. 1979-11-01T00:00:00Z https://hdl.handle.net/1721.1/143001 Description of and User's Manual for a Finite Element Aquifer Flow Model AQUIFEM-1 Townley, Lloyd R.; Wilson, John L. A detailed user's and programmer's manual for "AQUIFEM-1," a versatile two-dimensional finite element model for groundwater flow, is presented. The model is based on the hydraulic equations of essentially horizontal flow, but can also be used for the analysis of vertical cross-sectional flow. AQUIFEM-1 employs the Galerkin finite element technique, with linear interpolation functions and triangular elements. Leakage from an adjacent aquifer, pumping and recharge wells, flowing wells, lateral inflows and outflows, induced infiltration, rising water conditions, evapotranspiration and numerous other boundary conditions and sources/sinks are accounted for. Both steady state and transient solutions for confined, phreatic or mixed (changing status) aquifers can be computed. The report provides a review of the mathematical formulation of the model and a detailed description of its capacilities. Techniques are described for the simulation of springs, agricultural drainage, geologic faults, excavation dewatering, and other features of interest to the modeler. Numerous examples are given for horizontal flow models; there are also illustrations of vertical cross-sectional models. AQUIFEM-1 is based on any consistent set of units. It utilizes dynamic storage allocation. All input data are automatically checked for completeness and consistency, and appropriate messages generated. The code can be run in either time-sharing or batch modes. Output, which can be printed, print-plotted, or saved on file, includes a mimic of -the input and, at each time step, heads, drawdowns, flow rates, boundary fluxes, aquifer status, etc. The finite element matrix equations are solved in-core using a direct "skyline" equation solving algorithm based on Crout's method. All matrices are stored in vector form. Non-linear problems are handled with fixed-point iteration using one of several options that can be used to reduce computational costs. An example problem is used to illustrate model features and typical AQUIFEM-1 input and output. There is a detailed list of variables and description of input data requirements. The programmer's guide provides information on the structure of the program, to make it easier to implement modifications. A program listing is included. This report should be used in conjunction with Wilson, Townley and Sa da Costa [1979], which describes the mathematical development of AQUIFEM-1 and provides numerous illustrations of its application. Prepared with the support of the Agency for International Development, U.S. Dept. of State. 1980-02-01T00:00:00Z https://hdl.handle.net/1721.1/143000 Geochemistry of Municipal Waste in Coastal Waters Morel, Francois M. M.; Schiff, Sherry L. Introduction: As we mine primary ores at an increasing rate, as we synthesize more exotic compounds in greater quantities, as we produce expanding heaps of waste, as we reroute rivers through our faucets, we are becoming an important and sometimes a dominant agent of the global geochemical cycle. Disposal of municipal wastes is a key process in this anthropic part of the elemental fluxes, for a municipal sewage system is a giant funnel which brings in one place at each instant the end products of much of the dispersed consumptive activities of a whole community. In addition to its net contribution to the flux of natural elements and to the exotic nature of some of its constituents, it is this increasingly prevalent concentration process that gives human waste its unique position in the elemental economy of the planet. Lest we should be too conceited, even in our ability to pollute, the laws of nature must have their way. Ultimately all elements in the sea must be controlled by the biogeochemical processes that govern their oceanic cycles. The question posed by the practice of municipal waste disposal into the ocean is then principally one of rates: are natural biogeochemical processes in the oceans fast enough to "assimilate" human waste? Are the dispersive and degradative mechanisms suitably rapid to maintain the concentration of all potential toxicants at acceptably low concentrations? Are the ecological processes sufficiently dynamic to buffer the impact of concentrated elemental loads, to adapt to the presence of new chemical constituents? These questions can be asked on various geographical scales, from local to global, and on various time scales from hours to centuries. On the whole we are still quite ignorant of the functioning of oceanic systems; we do not comprehend sufficiently many of the processes that govern the fate of waste constituents; we cannot answer some of our basic questions. Yet, we are in the process of learning a great deal. This chapter is an attempt at organizing some of the key known facts on the biogeochemistry of waste in coastal waters, at developing a conceptual framework for research and decision making. There are on the order of ten thousand chemical constituents in wastewaters, only about a hundred of which we know anything about. It appears that our sole hope is to develop general principles to provide, in the long run, some of the necessary answers. Municipal wastewaters are a varied lot. Although domestic sewage has a fairly uniform composition throughout the country, the industrial wastes that are often added to it do not. Metal finishing plants contribute high concentrations of some metallic compounds; chemical manufacturing processes release highly specific sets of organic constituents. In cities with combined sewers, urban storm water runoff, with its own characteristic composition, is included in the municipal sewer system. Also varied are the levels of treatment and the methods of disposal. A few cities still dispose of their raw sewage while others have added tertiary treatment to their systems. Efficient outfalls with diffusers are used in some places to carry the effluents far offshore and dilute it effectively; in many others, wastewaters are released close to shore with inefficient mixing. Barge dumping of sludge is prevalent in many areas. Just as diverse are the hydrodynamic and hydrological characteristics of the receiving waters: confined bays, harbors and estuaries in some places, open coastline in others; rapidly increasing water depth offshore on one coast, extended continental margins on the other. Current and tidal regimes which vary with time and location result in widely different waste dilution and transport processes. All this variability in effluent composition, in initial mixing, and in short and long term transport processes affects to a large degree the fate of the waste constituents. At this point, it would be a hopeless task to attempt to cover all combinations of these, to consider the problem of disposal of all types of municipal wastes in all types of receiving waters. By a fortune of sorts, one is quite limited by the available information. We have made no attempt in this chapter to be exhaustive; rather we have concentrated on these systems for which extensive data were available. In this way it is hoped that a self coherent picture will be obtained from which one may draw information to be applied to other situations. However, major caveats are clearly in order: i) the available information concerns almost exclusively the major urban centers; in some instances it may be of little relevance to small or medium size communities; ii) the Southern California Bight--which is by no means typical--has been the locus of the most intensive and extensive research efforts on the geochemistry of waste. As such it provided the data for much of this chapter. (For convenient reference on names and locations, a map of the major Southern California outfalls is provided in Fig. 0-1). One should keep in mind these demographic and geographical biases. Prepared with the support of Marine Ecosystems Analysis Program of the National Oceanic and Atmospheric Administration. 1980-07-01T00:00:00Z https://hdl.handle.net/1721.1/142999 The Coupled Transport of Water and Heat in a Vertical Soil Column Under Atmospheric Excitation Milly, P. Christopher D.; Eagleson, Peter S. The purpose of this work is to develop a detailed, physically-based model of the response of the land surface to atmospheric forcing. The coupled, nonlinear partial differential equations governing mass and heat transport in the soil are derived. The theory of Philip and de Vries is re-cast in terms of the soil water matric potential, accounting for soil inhomogeneities and hysteresis of the moisture retention process. An existing model of hysteresis is modified to incorporate the effect of temperature and to facilitate numerical analysis. The Galerkin finite element method is applied in the development of a numerical algorithm for the solution of the governing equations. The numerical procedure is coded in FORTRAN for computer solution and several examples are run in order to test the method. The various modes of mass and heat transport are simulated accurately. A proposed procedure for the evaluation of non-linear storage coefficients in the numerical scheme yields excellent mass and energy balances. NSF Grant no. ATM-7812327 1980-07-01T00:00:00Z https://hdl.handle.net/1721.1/142998 Estimation of Stationary and Non-stationary Random Fields: Kriging in the Analysis of Orographic Precipitation Chua, Siong Huat; Bras, Rafael L. The theory of kriging, an optimal linear estimation technique for spatial stochastic processes, is presented and applied to the estimation of mean areal precipitation under stationary and non-stationary mean assumptions. In the stationary mean cases, the alternate use of semivariograms and covariances was investigated in conjunction with the adoption of a single realization versus a multirealization approach to defining the ensemble of events. Results favor the multirealization approach. The issue of the choice of covariogram model and optimization procedure appears questionable for the stationary mean case since traditional subjective areal averaging methods do as well as kriging. For non-stationary mean cases, assumed for storms in regions under orographic influence, kriging results with generalized covariances, identified under the necessary assumptions for intrinsic random functions of order k, were compared with a "detrending" procedure postulating a deterministic drift linearly related to ground elevation. The latter procedure gave more accurate kriging estimates but did not perform as well in representing the kriging estimation error variance. Generally, results point to the feasibility and attractiveness of kriging methods for MAP estimation, especially for non-stationary mean storms. The present work shows the need for further investigation in covariogram model inference and the effect of model errors on kriging results, particularly on the kriging estimation error variance. Prepared under support of the Dept. of Energy through M.I.T. Energy Laboratory and the Office of Surface Mining, Dept. of the Interior, through M.I.T.'s Mining and Mineral Resources Research Institute, Grant no. G5195022 1980-04-01T00:00:00Z https://hdl.handle.net/1721.1/142997 Multivariate Seasonal Time Series Forecast with Application to Adaptive Control Curry, Kevin D.; Bras, Rafael L. A general multivariate model for seasonal riverflow is proposed. The formulation relates discharge at a particular station to current discharge at other stations as well as previous discharges at any station. Additionally, the formulation allows for moving average terms and accounts for seasonality in the mean and variance. An identification strategy is suggested and two general parameter estimation algorithms are discussed. A technique to obtain multi-lead forecasts from an identified model and the use of these to obtain approximate conditional Markovian transition matrices is given. The identification, estimation and validation of univariate and multivariate models is demonstrated using historical monthly discharges of the Nile basin. A new adaptive reservoir control algorithm which uses the approximate conditional Markovian transition matrices is also derived. It uses a dynamic programming formulation of the value iteration type with previous inflow and present storage as states. The number of stages over which the algorithm must be solved at each decision, and thus the computational burden, is dramatically reduced by using a tabulated boundary value function derived from the stationary control problem. The control algorithm is not evaluated in this work. Prepared under support of the Agency for International Development, U.S. Dept. of State and the M.I.T. Technology Adaptation Program 1980-03-01T00:00:00Z https://hdl.handle.net/1721.1/142996 The Effects of Annual Storage and Random Potential Evapotranspiration on the One-dimensional Annual Water Balance Metzger, Bernhard H.; Eagleson, Peter S. An analysis is presented leading to the incorporation of storage terms into an existing first-order dynamic water balance. Annual change in storage in the unsaturated zone of an idealized soil column is included through the addition of one characteristic vegetal parameter, the estimated depth of the root zone. This defines the storage volume in the unsaturated zone. Annual change in storage in the saturated zone of the soil column is accounted for by assuming the dynamic linkage between percolation to the groundwater table and discharge from the groundwater reservoir to behave as a linear reservoir. The storage coefficient of this reservoir must be determined from streamflow data. The effect on the frequency of annual basin yield of annual change in storage is tested for two contrasting climates. In both test cases, the model is found to reduce the unexplained variance of the basic model without storage mechanisms. A simplified analysis is conducted to determine the effect on the frequency of the annual basin yield of a randomly varying rate of annual average potential evaporation. A modified Penman equation is used to derive an approximate relationship for the annual average rate of potential evaporation. A cdf is derived for the annual basin yield from a Gamma distribution for annual point precipitation and a double exponential distribution for the annual average rate of potential evaporation. A linearized version of the water balance model indicates for two contrasting climates that a random rate of potential evaporation has little effect on the variance of the annual basin yield. This is interpreted as a justification for considering the rate of potential evaporation to be constant when modeling the water balance on a seasonal basis. Prepared under the support of the Agency for International Development, U.S. Dept. of State. 1980-02-01T00:00:00Z https://hdl.handle.net/1721.1/142995 Estimation of Effective Hydrologic Properties of Soils from Observations of Vegetation Density Tellers, Tobin E.; Eagleson, Peter S. An existing one-dimensional model of the annual water balance is reviewed. Slight improvements are made in the method of calculating the bare soil component of evaporation, and in the way surface retention is handled. A natural selection hypothesis, which specifies the equilibrium vegetation density for a given, water-limited, climate-soil system, is verified through comparisons with observed data and is employed in the annual water balance of watersheds in Clinton, Ma., and Santa Paula, Ca., to estimate effective areal average soil properties. Comparison of CDF's of annual basin yield derived using these soil properties with observed CDF's provides excellent verification of the soil-selection procedure. This method of parameterization of the land surface should be useful with present global circulation models, enabling them to account for both the non-linearity in the relationship between soil moisture flux and soil moisture concentration, and the variability of soil properties from place to place over the earth's surface. Prepared with the support of the National Aeronautics and Space Administration Grant NSG 5306 1980-03-01T00:00:00Z https://hdl.handle.net/1721.1/142994 Time Series Analysis of Cyclostat Data for the Determination of Cell Division Patterns in Phytoplankton Grown on Light/Dark Cycles Slocum, Warren M. A method of data analysis employing digital filtering technique is described which has been used to smooth time series of cell density data from cyclostat experiments (Chisholm and Costello, 1980) and to estimate cell division rates. This report serves as technical reference material for Chisholm and Costello (1980). Sponsored by NSF OCE77-08999. 1980-01-01T00:00:00Z https://hdl.handle.net/1721.1/142993 A Stochastic Dynamic Programming Model for the Operation of the High Aswan Dam Alarcon, Luis F.; Marks, David H. With the construction of the High Aswan Dam in Egypt, reliable irrigation throughout the whole year and the use of water for the generation of a high percentage of the electricity needs of the country are possible. Moreover, as a result of the construction of the High Aswan Dam, some important changes in the hydraulic regime of the river occurred; in particular, due to the absence of suspended material downstream of Aswan, increasing concern exists about the prevention of bank erosion of the river channel. This report presents a stochastic dynamic programming model to obtain guidelines for the operation of the dam, taking into consideration the conflicting nature of the purposes for which the dam is to be operated. For the solution of the model, a successive approximations method is used in which advantage is taken of some special characteristics of the functions involved in the model in order to provide a computationally efficient algorithm. Some examples, for several combinations of parameters of the system, are presented and the policies obtained tested using a simulation model. These results are compared with the ones obtained when a more heuristic approach to the operation problem is used. Prepared under the support of the Agency for International Development [of] the United States Department of State 1979-11-01T00:00:00Z https://hdl.handle.net/1721.1/142992 Stochastic Modeling of Groundwater Systems Gelhar, Lynn W.; Ko, Peter Y.; Kwai, Herman H.; Wilson, John L. This research developed important new results on the use of spectral analysis techniques to evaluate groundwater resources. The linear theory of aquifer spectral response in the frequency domain is developed, including effects of aquifer slope, vertical flow, variable transmissivity and other features. Numerical simulations of the nonlinear effects in the spectral domain are developed and show that the nonlinear effects are typically quite small, thus making the simple linear theory applicable for most field situations. Some additional features which are explored are the effects of spatial variability of hydraulic conductivity and the influence of transient flow in the partially saturated zone above the water table. Through spectral analysis in the wave number domain, an error criterion is established for a simple observation network which is used to measure groundwater flow. The effects of storage in the partially saturated zone on the frequency spectrum of groundwater fluctuations are estimated and found to be negligible in most cases. The theoretical results are applied to evaluate, through spectral analysis, time series of groundwater levels, precipitation and stream stage for a site in Kansas. From these data, using a procedure based on the linear spectral theory, estimates of aquifer transmissivity and storativity are developed. The procedure yields parameter estimates which are in agreement with those obtained from pumping tests. The results of the study should be applicable under specified conditions to the estimation of aquifer parameters from natural fluctuations of groundwater level. The work upon which this publication is based was supported in part by funds provided by the United States Department of the Interior as authorized under the Water Resources Research Act of 1964 as amended. 1974-09-01T00:00:00Z https://hdl.handle.net/1721.1/142991 Salinity Effects on Velocity Distributions in an Idealized Estuary Harleman, D. R. F.; Hoopes, J. A.; McDougall, D.; Goulis, D. A. An experimental and analytical investigation of the two-dimensional (i.e. longitudinal and vertical) convective-diffusion processes in an idealized laboratory estuary. The estuary is idealized to obtain steady-state salinity and velocity distributions. The mixing effect of tidal motion is produced by homogeneous turbulence generated by vertically oscillating screens. A fresh water inflow at one end and the introduction of saline water near the other end produces an estuarine salinity intrusion condition. The cyclic convection motion of the tide is not reproduced. The investigation was conducted in three phases which are outlined below. (1) The need for an accurate determination of the salt concentration distribution led to the development of a highly sensitive conductivity probe suitable for measurement in situ. (2) In order to predict the vertical diffusion coefficient from a knowledge of the turbulence intensity, a vertical column was built, and the diffusion coefficient was determined from measurements of the one-dimensional, time dependent, non-convective diffusion process. The horizontal diffusion coefficient is known from previous studies. (3) The horizontal and vertical distribution of salinity was measured in a long, horizontal flume. With an assumption as to the distribution of vertical velocity component, the longitudinal velocity profile was determined. The local value of the bottom velocity was found to correlate with the local, densimetric Frounde Number. The discussion of the experimental investigation concludes with some speculations on the engineering applications of the results. Prepared under Research Grant , Public Health Service, National Institute of Health, Department of Health, Education and Welfare, no. 4815 1962-01-01T00:00:00Z https://hdl.handle.net/1721.1/142990 The Effects of Trailing Edge Geometry and Chord Length on the Early Wake of Stationary Flat Plates Eagleson, P. S.; Daily, J. W.; Grace, R. A. This report presents the results of an investigation of the average and fluctuating two-dimensional structure of the early wake of fixed, flat plates at zero mean angle of attack as a function of trailing edge configuration and chord length. The experimental program provides for the measurement of the distribution of local mean velocity, static pressure, longitudinal velocity fluctuation and the spectral distribution of the kinetic energy of this turbulence component. The investigation was carried out in the 7-1/2" x 9" test section of an open-circuit water tunnel in the MIT Hydrodynamics Laboratory. An average free stream velocity of approximately 9.5 feet per second and plates of 1/h-inch thickness were used. All measurements were made between 1.50 and 9.75 plate thicknesses downstream of the trailing edge of the test plates, and between 0 and 2.80 plate thicknesses from the longitudinal plate centerline. Plate chord lengths used were 2" and 7". A primary aim of this study is the explanation of the vibrational behavior of the same test plates as found in a previous investigation. An attempt is made, wherever possible, to draw together the related facets of both studies. Information from both investigations is combined to infer certain characteristics of the vortex street and these characteristics are compared with those found by other investigators for bodies of various shapes. The primary conclusions to be drawn from the experiments on these particular plates are: 1. Downstream increase of wake width, for a plate of given trailing edge, is suppressed to a distance dependent upon the boundary layer thickness at the trailing edge. 2. At a plate thickness Reynolds number, It = 1.8 x 10h, transition between the inertial and viscous zones of wake development takes place at approximately x/t = 3.25. 3. With distance in the downstream direction there is an increase in the transverse spacing, h, of the discrete vortices in the wake. 4. The plate thickness Strouhal number varies with trailing edge configuration at a given Reynolds number. 5. The mean drag coefficient decreases as the trailing edge becomes more tapered. 6. The strength of the discrete vortices at a given station in the early wake becomes greater as the trailing edge becomes more tapered. 7. For a plate of given thickness and trailing edge geometry an increase in chord length reduces the frequency of vortex shedding. 8. The proportion of the total wake vorticity which is concentrated in discrete vortices increases with increasing chord length Reynolds number. 9. An increase in chord length decreases the intensity of turbulence, increases the mean velocity defect and decreases the pressure recovery at a given station in the early wake. 10. For constant chord length, the amplitude of plate vibration when pivoted at the leading edge increases with increasing vortex strength and with decreasing mean drag coefficient (both quantities determined with stationary plate). 11. Barring self-excitation of the plate motion, the frequency of plate vibration is precisely that at which discrete vorticity is shed into the wake from the stationary plate. Prepared under Bureau of Ships Fundamental Hydromechanics Research Program, Project S-R009 01 01 Contract no. NONR-1841 (21) 1962-04-01T00:00:00Z https://hdl.handle.net/1721.1/142989 Enclosed Rotating Disks with Superposed Throughflow: A Survey of Basic Effects Daily, James W.; Arndt, Roger E. A. A qualitative study was made of the flow field induced by an enclosed rotating disk with a radially outward throughflow superposed using air as the test fluid. The purpose of this survey is a determination of the range of variables at which important phenomena occur so that a quantitative study of surface resistance, pressure and velocity distribution and other observed phenomena such as unsteadiness, boundary layer separation and stall may be made. Disks of 18-1/8 inches diameter enclosed in a housing in which axial spacing could be varied from 1/8 inch to 2-1/8 inches were used in this study. Througflow was admitted in the axial direction at the front and rear of the disk housing in such a way as to make the flow on both sides of the disk as symmetrical as possible. Flow visualization was made possible using smoke injected at various points. Stroboscopic photography aided the visual observations of the flow field. Transition to turbulence was observed to be a function of the local Reynolds number ... and the axial spacing. It was observed that the torque was increased by throughflow over the corresponding value without throughflow. A systematic change in the pressure field was observed with increasing amounts of throughflow. Of particular interest is the observation under certain conditions of large periodic fluctuations, the frequency of which is related to the rotational speed, and the amount of throughflow. Scanning notes: p.B-5 is an oversized foldout scanned via the Bookeye.; Prepared under Army Research Office (Durham) grant nos. DA-ORD-31-124-61-G5 DA-ORD-31-124-G131 DA Proj. No. 59901004 AROD Proj. 2500-E 1962-06-01T00:00:00Z https://hdl.handle.net/1721.1/142988 Control Structures in Stratified Flows Harleman, D. R. F.; Goda, Y. During the past decade the Tennessee Valley Authority has designed and built several structures for the purpose of withdrawing cold bottom water from thermally stratified reservoirs. The cold water is used to supply condenser water for steam-generated power plants. During the summer months the primary flows in the Tennessee River system are controlled by releases from upstream storage dams through low level turbine intakes. The cold water, discharged by the turbines, forms a density underflow in the downstream river and reservoirs which may be from 10 to 150F colder than the overlying surface water (Ref. 1, 2, 3). The intake structures in the form of submerged sluice gates are known as "skimmer walls". The water in the condenser water channel downstream of the gate is homogeneous and has a specific gravity equal to the lower, colder water in the intake channel upstream of the gate. The colder water is caused to flow through a vertical opening at the bottom of the gate by virtue of a head differential across the wall. The problem is to determine the maximum discharge of the colder water through the gate without inducing a steady state withdrawal from the warmer layer upstream of the gate. A basic experimental and analytical investigation of this problem was conducted in the Hydrodynamics Laboratory of the Department of Civil Engineering at the request of TVA in the spring and summer of 1954 (Ref. 4) as part of a continuing program of research in stratified flow (Ref. 5, 6). The flow configuration is shown schematically in Figure 1. While the information obtained from this study has proved to be a valid basis for design of skimmer walls of the type shown in Figure 1, questions have been raised in regard to the relative efficiency of other possible geometrical configurations. The proposed Bull Run steam power plant of the TVA is to be located at mile 48 on the Clinch River in the backwater of the Melton Hill Dam (under construction). After completion of Melton Hill, the normal depth of water in the Clinch River at this point will be approximately 20 feet. The Bull Run condenser water intake will be approximately 32 miles downstream from Norris Dam which is the source of cold water during the summer period of thermal stratification in Melton Hill reservoir. In the absence of the Bull Run plant the normal "plunge point" for the cold water in the reservoir would probably be in the vicinity of the Bull Run site. It is estimated that condenser water requirements will cause diversion of most of the river flow for sizeable periods of time. The heated water is to be returned to the river approximately one mile below the intake structure. This addition of heat will result in a reinforcement of the reservoir stratification and will probably move the cold water "plunge point" upstream. Due to the topography, the maximum length of an intake structure is approximately 400 feet. In the horizontal intake skimmer wall the lip of the skimmer wall is essentially at the elevation of the river bed. This configuration requires the excavation of a bottom step of height (b) in order for the fluid to pass through the horizontal opening (a) and flow under the gate into the condenser water channel. In order to have an accurate comparison for the two skimmer wall configurations, the experiments on the two types of walls were conducted using the same quantitative basis for the determination of the discharge at incipient drawdown. The drawdown discharge criterion for the 1954 tests was essentially a visual one, hence.,the tests on the type I structure were repeated. In addition, it was desired to obtain quantitative information on the magnitude of the energy loss across the skimmer wall. The experiments were conducted in the M. I. T. Hydrodynamics Laboratory using salt water and fresh water to simulate the prototype density differences due to thermal effects. For laboratory purposes and reproducibility of results a sharp interface between the two layers is obtained. It is recognized that in the field such a sharp interface is not possible; however, equivalent interfacial heights may be determined by using the depth at which the vertical density gradient is a maximum. Prepared for Engineering Laboratory Division of Water Control Planning Tennessee Valley Authority Norris, Tennessee. 1962-05-01T00:00:00Z https://hdl.handle.net/1721.1/142987 Secondary Motion and Turbulence in Circular Couette Flow Gelhar, L. W.; Schriek, W.; Benham, F. A. The flow in an annular space between two separately rotating cylinders of finite length is investigated. It is found that when the outer cylinder rotates faster than, and in the same direction as, the inner cylinder, the fluid moves largely in solid body rotation with the outer cylinder. In order to understand the dynamics of this type of flow, a laminar theory is formulated. The equations of motion are linearized by developing the solution as a perturbation of the state of solid body rotation. The theory predicts tangential velocities which are independent of the axial co-ordinate in the interior region. It also predicts the streamline pattern of the secondary motion in that region. The observed tangential velocities at mid-height in the annular space, using water and air, are in good agreement with the predicted velocities from the theory. Hot wire anemometers are used for the measurement of turbulence intensities in air. In light of these measurements the agreement with the theory is somewhat surprising, since the flow is observed to be turbulent in all the experiments. The turbulence intensities near the inner cylinder wall are found to be of the same order of magnitude as those found near the wall in pipe flow. Prepared under research grant, Engineering division National Science Foundation no. GK-110 1966-07-01T00:00:00Z https://hdl.handle.net/1721.1/142986 Wave Reflection and Transmission in Open Channel Transitions Bourodimos, E. L.; Ippen, A. T. The topics of this report are a theoretical development and an experimental investigation of the transformation of water-wave characteristics in the reflection and transmission processes through channel transitions of varying geometry, connecting two prismatic channels of constant cross section. The theoretical developments are based on small amplitude linearized wave theory in an inviscid, homogeneous and incompressible fluid. Two theoretical aspects have been treated: 1. The wave amplitude variation in a channel of constant width for a bottom of arbitrary configuration was obtained for the various characteristics of the oncoming waves. The basis of this development is the energy transmission undiminished by reflection or friction. The general expression of the integral type was solved for two limiting cases: for shallow water waves resulting in Green's law and for the range from deep water to intermediate depth water waves resulting in an exponential formula. 2. Reflection and transmission coefficients were derived for shallow water waves for gradual channel transitions, specifically for four cases: A - for linearly varying depth and constant width B - for linearly varying depth and width C - for linearly varying width and constant depth D - for parabolic variation of depth and constant width A numerical evaluation of the theoretical expressions for reflection and transmission coefficients shows essentially fair agreement with the experimental findings for shallow water waves. The experimental part of the report is concerned with the determinations of reflection and transmission coefficients and of the energy relations including dissipation for the above cases A, B, and C. The experimental range of wave conditions extended from deep water to shallow water waves. The results are compared to previous investigations and to the conventional classical theories, as the theoretical derivations above are restricted to shallow water waves. Relations were also found with regard to wave steepness, a factor which cannot be theoretically dealt with so far in channel transitions. Reflection and transmission coefficients show considerable dependence on wave steepness, the decrease being most pronounced for the former. Reflection coefficients are generally higher than those predicted by Lamb's theory for abrupt transitions. Transmission coefficients therefore are exhibiting the opposite trend. Prepared under contract with the Fluid Dynamics Branch, Office of Naval Research no. Nonr-1841(59) 1966-08-01T00:00:00Z https://hdl.handle.net/1721.1/142985 Turbulent Pipe Flow with Rough and Porous Walls Munoz Goma, R. J.; Gelhar, L. W. The characteristics of turbulence in shear flow near rough and porous walls are investigated theoretically and experimentally. Flows of this nature are present, for instance, in the case of a erodible particulate stream-bed. The fluctuating flow generated in the porous wall by the external turbulent flow is analyzed using a macroscopic, linearized equation of motion, with the boundary condition at the surface defined by a pressure distribution of the same form as that observed at smooth walls. Two different specifications for the wall pressure are applied, one as- a random function of space and time and the other as a sinusoidal wave. The intensity of the longitudinal velocity fluctuations at the wall surface, normalized with respect to shear velocity, is shown to approach an asymptotic value of 0.38 as the permeability increases, whereas the fraction of the total energy dissipation that occurs within the porous medium has a maximum for a characteristic dimensionless combination of permeability, viscosity and external velocity. The Reynolds stress is identically zero throughout the porous medium. Experiments were conducted in two pipes, 10" in diameter, one with 1/8" spherical roughness elements and the other with a 1.20" thick porous lining, 5 5 for Reynolds numbers between 10 and 5 x 105. The rough pipe behavior with respect to friction factor and mean velocity distribution is in good agreement with classical experiments for sand roughness. The porous pipe has very high friction factors, between 0.06 and 0.08, which increase with Reynolds number. Both friction factor and the displacement of mean velocity profile with respect to the smooth law indicate an equivalent relative roughness of the order of 0.10. A value of 0.40 for Karman constant K is consistent with the observations, but deviations from the logarithmic velocity law occur at a distance from the wall less than 10% of the radius. Both the eddy viscosity and the velocity defect distributions show systematic variations in the core region depending on the nature of the wall. Measurements of turbulence intensity in the longitudinal and radial directions made with hot wire anemometers show a universal distribution, in velocity. However, the intensities relative to the local velocity increase with the effective roughness of the wall. The ratio between the radial and longitudinal intensities agrees with the smooth wall distribution throughout most of the pipe, except very close to the wall where it remains at a constant level of 0.6 for the rough and porous cases. Energy spectra for both components of turbulence indicate a definite change with distance to the wall. In normalized form, the spectral measurements for both rough and porous walls are in substantial agreement with previous smooth wall measurements. Prepared under National Science Foundation, Engineering Division, Grant no. GK-114.1 1968-04-01T00:00:00Z https://hdl.handle.net/1721.1/142984 Wave Induced Oscillations in Harbors: The Solution for a Rectangular Harbor Connected to the Open-sea Ippen, A. T.; Goda, Y. The determination of an amplification factor for a given harbor and a given wave period is an important problem concerning long period oscillations in harbors. The present study presents a means of computing the response of a rectangular harbor to the excitation by incident waves. With the aid of a digital computer, the complete response curve can be computed for any rectangular harbor. The results of experiments on model harbors have confirmed the validity of the computation. Experimental response curves, however, do not show the marked increase of the amplification factor at resonance with a narrowing of the harbor entrance, because of energy dissipation in a model harbor. The analysis of the response factor for waves with a continuous power spectrum also suggests that a narrowing of the entrance will lead to a reduction in the amplitude of long period oscillations in actual harbors, because of increasing sharpness of the response curves and the presence of energy dissipation mechanisms in harbors. Hence, the problem of the harbor paradox presented by Miles and Munk does not exist in actual harbors. In addition to the above resonant characteristics, a study was conducted on the minimum effectiveness of wave absorbers and filters to simulate the open-sea conditions in a wave basin of finite dimensions. A reflection coefficient less than 0.2 is recommended for wave absorbers and filters. The importance of the basin size is also discussed. Prepared under Office of Naval Research, U.S. Department of the Navy, contract no. Nonr-1841(69) NR-062-228 1963-07-01T00:00:00Z https://hdl.handle.net/1721.1/142983 Enclosed Rotating Disks with Superposed Throughflow: Mean Steady and Periodic Unsteady Characteristics of Induced Flow Daily, J. W.; Ernst, W. D.; Asbedian, V. V. This is a report of a study of enclosed rotating disks with radial outward throughflow superposed on the fluid motion induced by the disk. The report presents information on the flow mechanics in the axial clearance space between the disk and stationary endwall including mean steady velocity distributions and unsteady periodicities. Also included are data on the interactions between fluid and boundaries as evidenced by torque transmission (disk friction) and by radial pressure gradients. A theoretical analysis is presented to predict the steady state values of torque and pressure distribution and is compared with experimental results. Quantitative measurements of unsteadiness and periodicities which result under some conditions are analyzed and compared with previous smoke visualization data. Prepared under grant nos. DA-ORD-31-124-61-G5 DA-ORD-31-124-G131 Da Proj. No. 59901004 AROD Proj. 2500-E, Army Research Office. (Durham) 1964-04-01T00:00:00Z https://hdl.handle.net/1721.1/142982 Modelling of Unidirectional Thermal Diffusers in Shallow Water Lee, Joseph H.; Jirka, Gerhard H.; Harleman, Donald R. F. This study is an experimental and theoretical investigation of the temperature field and velocity field induced by a unidirectional thermal diffuser in shallow water. A multiport thermal diffuser is essentially a pipe laid along the bottom of the water body and discharging heated water in the form of turbulent jets through a series of ports spaced along the pipe. A unidirectional diffuser inputs large momentum in one direction; it can achieve rapid mixing within relatively small areas, and has the advantage of directing the thermal effluent away from the shoreline. The theory considers a unidirectional diffuser discharging into shallow water of constant depth in the presence of a coflowing ambient current. A fully mixed condition is hypothesized downstream of the diffuser. A two dimensional potential flow model is formulated and solved in the near field, where flow is governed by a dominant balance of pressure and inertia. A control volume analysis gives the total induced flow, which is used as an integral boundary condition in the potential flow solution. The shape of the slip streamline is solved using Kirchoff's method; the velocity and pressure field are then computed by a finite difference method. The correct boundary conditions along the diffuser are deduced. Knowledge of the flow field defines the extent of the near field mixing zone. The near field solution is coupled into an intermediate field theory. In this region turbulent lateral entrainment, inertia and bottom friction are the governing mechanisms of the flow, and the mixed flow behaves like a two dimensional friction jet. An integral model is formulated and solved numerically. The model predictions of induced temperature rises, velocities, plume widths enable comparisons of the overall effectiveness of different heat dissipation schemes. A model for calculating the near field dilution and plume trajectory of a unidirectional diffuser discharging into a perpendicular crossflow is formulated and solved. The phenomenon of heat recirculation from the far field is ascertained in the laboratory and a semi-empirical theory is developed to evaluate the potential temperature buildup due to far field recirculation. A comprehensive set of laboratory experiments have been carried out for a wide range of diffuser and ambient design conditions. The model is validated against the experimental results of this study as well as those of hydraulic scale model studies by other investigators. The analytical and experimental insights gained in this study will aid future numerical modelling efforts and in better design of physical scale models. The principal results are applied to establish general design guidelines for diffusers operating in coastal regions. The ecological implications of the model predictions are discussed. Scanning notes: Disclaimer inserted for illegible graphs and text.; Prepared under the support of the New England Electric System, Westboro, Mass. and Northeast Utilities Service Company, Hartford, Conn. under the Electric Power Program of the M.I.T. Energy Laboratory. 1977-07-01T00:00:00Z https://hdl.handle.net/1721.1/142981 Ocean Thermal Energy Conversion Plants: Experimental and Analytical Study of Mixing and Recirculation Jirka, Gerhard H.; Johnson, R. Peter; Fry, David J.; Harleman, Donald R. F. Ocean thermal energy conversion (OTEC) is a method of generating power using the vertical temperature gradient of the tropical ocean as an energy source. Experimental and analytical studies have been carried out to determine the characteristics of the temperature and velocity fields induced in the surrounding ocean by the operation of an OTEC plant. The condition of recirculation, i.e. the re-entering of mixed discharge water back into the plant intake, was of particular interest because of its adverse effect on plant efficiency. The studies were directed at the mixed discharge concept, in which the evaporator and condenser water flows are exhausted jointly at the approximate level of the ambient ocean thermocline. The OTEC plant was of the symmetric spar-buoy type with radial or separate discharge configurations. A distinctly stratified ocean with uniform, ambient current velocity was assumed. The following conclusions are obtained: The recirculation potential of an OTEC plant in a stagnant ocean is determined by the interaction of the jet discharge zone and a double sink return flow (one sink being the evaporator intake, the other the jet entrainment). This process occurs in the near-field of an OTEC plant up to a distance of about three times the ocean mixed layer depth. The stratified internal flow beyond this zone has little effect on recirculation, as have small ocean current velocities (up to 0.10 m/s prototype). Conditions which are conducive to recirculation are characterized by high discharge velocities and large plant flow rates. A design formula is proposed which determines whether recirculation would occur or not as a function of plant design and ocean conditions. On the basis of these results, it can be concluded that a 100 MW OTEC plant with the mixed discharge mode can operate at a typical candidate ocean site without incurring any discharge recirculation. Prepared under the support of Division of Solar Energy, U.S. Energy Research and Development Administration, Contract no. EY-76-S-02-2909.M001 1977-09-01T00:00:00Z https://hdl.handle.net/1721.1/142980 MINEQL: A Computer Program for the Calculation of Chemical Equilibrium Composition of Aqueous Systems Westall, John C.; Zachary, Joseph L.; Morel, Francois M. M. Introduction: This report describes the computer program for the computation of chemical equilibria in aqueous systems, MINEQL. The purpose of the report is to present the program in sufficient detail that the reader not only can use the program exactly as it is written, but also can modify it to suit whatever his particular needs may be. The evolution of the program, examples of its use, and general approach to the chemical equilibrium problem are described in Part I of the report. Part II presents a "MINEQL-1 User's Manual". A detailed mathematical description of the solution to the chemical equilibrium problem used in MINEQL appears in Appendix 1. It was felt that the solution could best be presented by an abstract description of the mathematical problem (without any reference to its chemical analog), followed by a very simple example of a chemical problem (which is given in Appendix 2). This avoids the intermingling of chemical and mathematical concepts which is sometimes confusing. Appendix 3 gives a description of the program itself. The three appendices are related in that they present the same concepts - the actual theory and its application in MINEQL - from three different viewpoints: mathematical, chemical, and computational. They should be read in conjunction with one another. First the concepts involved in the basic chemical equilibrium problem, (i.e., where there are no solid phases present) should be mastered, and then the extension to the consideration of solid phases, which is somewhat more complicated, should be undertaken. This report contains a complete description of all of the concepts employed in the program MINEQL. However, a working knowledge of the program is obtainable without attention to all of the details. It is hoped that this roadmap through MINEQL will enable the reader to maximize his use of the program without becoming bogged down in the details of the report. Sponsored by EPA Grant no. R-803738 1976-01-01T00:00:00Z https://hdl.handle.net/1721.1/142979 Staged Diffusers in Shallow Water Almquist, Charles W.; Stolzenbach, Keith D. The discharge of waste heat from electric power plants into natural water bodies has the potential for adversely affecting the aquatic ecology of the receiving water. Because each discharge site has its own physical and biological characteristics, design and siting of such discharges to insure that potential impacts are within acceptable levels requires both the flexibility to tailor the discharge design to the site and the ability to predict the induced temperature rise over a broad range of spatial and temporal scales. In this study, the class of semi-infinite, shallow receiving water bodies (which includes large lakes and eastern coastal regions of the U.S.) is identified as being an important subset of potential sites for waste heat disposal. On the basis of previous investigations of heated discharges, one particular discharge design, the "staged" diffuser, is shown to be particularly suited to many water bodies of this class. The analysis of the near field temperature rise induced by the staged diffuser for quiescent conditions in a semi-infinite, shallow receiving water body is defined as the objective of the study. A theory describing performance of the staged diffuser under the defined conditions is developed by schematizing the diffuser as a continuous line source of momentum. The analysis proceeds from a set of integrated continuity and momentum equations, similar to those used in free turbulent jet analysis, but with the addition of a region with a continuous input of momentum. The theory requires the specification of similarity functions for lateral velocity and temperature profiles, and the values of the entrainment coefficients. The theory yields plume average and centerline dilutions, and isotherm areas for areas less than the order of the square of the diffuser length. A particular result of the theory is the prediction of a region over the diffuser in which centerline velocities and temperatures remain approximately constant. The centerline temperature rise in this region, which is the region of minimum dilution, can be given approximately by ... is the average centerline temperature in this region, [Delta]To is the discharge temperature rise, c is a coefficient, s is the port spacing, H is the water depth and ao the discharge area of an individual discharge port. An experimental study and an analysis of existing data verifies the predictions of the theory. It is found that an elliptical similarity profile and classical free turbulent jet entrainment coefficients adequately describe observed results. Predictions of dilutions, plume areas, and rate of lateral spreading compare well with observed values, and in particular the centerline temperature rise coefficient in the above equation is found to be c ' 0.4. Limits on the validity of the parameters derived in the theoretical analysis are identified. Application of the theory to the field and to physical model studies are demonstrated. Of particular interest with respect to physical model studies is the development of a relationship describing the effect of temperature probe spacing on the ability to resolve the true value of the maximum temperature rise. It is shown that consistent identification of 90% of the actual maximum temperature rise requires a probe spacing on the order of 1/10 to 1/5 of the diffuser length. Examples from previous physical model studies demonstrate how inadequate probe spacing can lead to inconclusive results with respect to the dependence of the maximum temperature rise on the diffuser design. Prepared with the support of United Engineers and Constructors, Inc., Boston, Mass. and New York State Electric and Gas Corporation, Binghamton, N.Y. 1976-06-01T00:00:00Z https://hdl.handle.net/1721.1/142978 Prediction of Unsteady Salinity Intrusion in Estuaries: Mathematical Model and User's Manual Thatcher, M. Llewellyn; Harleman, Donald R. F. Foreword: This report is intended as a documentation of the computer program and as a user's manual for the implementation of the mathematical model for the prediction of unsteady salinity intrusion in estuaries. The details of the model development and verification are contained in the following report: "A Mathematical Model for the Prediction of Unsteady Salinity Intrusion in Estuaries" by M. Llewellyn Thatcher and Donald R. F. Harleman, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Technical Report No. 144, February 1972 also published by M.I.T. Sea Grant Project Office as Report No. MITSG 72-7 (index No. 72-307-Ccb)]. The unsteady salinity intrusion model is one-dimensional, although varying degrees of stratification are accounted for in the assumed longitudinal dispersion relationship. This model is a component in two additional studies, one of which is concerned with the two-dimensional aspects of salinity intrusion (i.e. vertical salinity and velocity distributions in estuaries): "Mathematical Simulation of Tidal Time-Averages of Salinity and Velocity Profiles in Estuaries" by John S. Fisher, John D. Ditmars and Arthur T. Ippen, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Technical Report No. 151, July 1972 [also published by M.I.T. Sea Grant Project Office as Report No. MITSG 72-11 (index No. 72-311-Ccb)] The second study is concerned with the development of a model for predicting the transient longitudinal distribution of water quality parameters in estuaries: "Numerical Model for the Prediction of Transient Water Quality in Estuary Networks" by James E. Dailey and Donald R. F. Harleman, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Technical Report No. 158, October 1972 [also published by M.I.T. Sea Grant Project Office as Report No. MITSG 72-15 (index No. 72-315-Ccb)] This user's manual therefore assists in the implementation of the analytical and numerical models listed above. Scanning notes: Disclaimer inserted for illegible graphs and text.; Prepared under the support of the Office of Sea Grant National Oceanic and Atmospheric Administration U. S. Department of Commerce through Coherent Area Project Grant GH-88 2-35150 1972-11-01T00:00:00Z https://hdl.handle.net/1721.1/142977 The Design of Rainfall Networks in Time and Space Rodriguez-Iturbe, Ignacio; Mejia, Jose M. A methodology for the design of precipitation networks is formulated. The network problem is discussed in its general conception and then focus is made in networks to provide background information for the design of more specific gaging systems. The rainfall process is described in terms of its correlation structure in time and space. A general framework is developed to estimate the variance of the sample long-term mean areal precipitation and mean areal rainfall of a storm event. The variance is expressed as a function of correlation in time, correlation in space, length of operation of the network and geometry of the gaging array. The trade of time-vs-space is quantitatively developed and realistic examples are worked out showing the influence of the network design scheme in the variance of the estimated values. Prepared under the support of U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service with the cooperation of the Instituto Venezolano de Investigaciones Cientificas, Caracas, Venezuela Contract No. 2-36235 1973-11-01T00:00:00Z https://hdl.handle.net/1721.1/142976 Sediment Transport in the Coastal Environment Madsen, Ole Secher; Grant, William D. The subject of sediment transport in the coastal zone is investigated and the answers to some of the basic questions of sediment transport in unsteady, oscillatory flow are presented. By adopting Jonsson's (1966) results for the bottom shear stress associated with a simple wave motion, it is shown that Shield's criterion for the initiation of sediment movement on a flat bed holds in unsteady as well as steady flow. A simplified analysis as well as experimental data show the side effects associated with the experimental procedure in which a tray containing sediment is oscillated in still water is generally insignificant and is, therefore, a valid procedure for studying certain aspects of wave sediment interaction. Also, Shields Parameter is identified as the physically important parameter quantifying the fluid sediment interaction. An empirical relationship between a non-dimensional average sediment transport rate and Shields Parameter is found by reanalyzing the experimental data on the rate of sediment transport in oscillatory flow obtained by Einstein and co-workers at Berkeley. This relationship is similar to the Einstein-Brown sediment transport relationship in unidirectional, steady flow. By generalizing Jonsson's expression for the bottom shear stress associated with a sinusoidal wave motion, it is shown that the empirical sediment transport relationship may be derived from a quasi steady application of the Einstein-Brown sediment transport relationship. Also, it is demonstrated that the empirical relationship obtained using a friction factor based on grain roughness is capable of predicting sediment transport rates observed in experiments where bed forms were present. The general application of the derived sediment transport relationship for predicting net rates of sediment transport in the presence of second order effects such as bottom slope, wave asymmetry, mass transport currents and coastal currents is discussed. This discussion serves also to identify needed areas for future research. It is concluded that only the case of a small amplitude wave and a steady current seems to be understood to the extent that it is reasonable to evaluate the resulting sediment transport with any degree of confidence. Fortunately, this is a rather important situation in most offshore regions. A general numerical model is developed for the sediment transport and topographical changes resulting from spatially varying wave and current conditions. A simple numerical example of the evaluation of the topographical changes in the vicinity of the tip of a long straight breakwater is presented for periodic waves normally incident on the breakwater and a current parallel to the breakwater. This numerical example is chosen to resemble rather severe conditions for the Atlantic Generating Station (AGS) site with a maximum orbital wave velocity of 3.2 ft/sec (1 m/sec) and a current velocity 0.5 ft/sec (.15 m/sec). The results are.presented in a topographical relief map showing areas of scour and accretion of the order 0.78 inches/day (2 cm/day) at a maximum. Although the results of the example are somewhat more qualitative than-quantitative, it is felt that they provide a representative picture of the expected bottom changes in the vicinity of the AGS. Prepared under the support of Dames and Moore, Consultants in the Environmental and Applied Earth Sciences, Cranford, New Jersey, through funds provided by New Jersey Public Service Electric and Gas Company, Newark, New Jersey. 1976-01-01T00:00:00Z https://hdl.handle.net/1721.1/142975 Theoretical and Experimental Investigation of Emergency Heat Releases from Floating Nuclear Power Plants Jirka, Gerhard H.; Wood, Duncan W.; Harleman, Donald R. F. A combined analytical and experimental study is made of the hydrodynamic and heat transport aspects of transient heat releases during emergency cooling operations at floating nuclear power plants located in protective enclosures. The study has two major objectives, namely (i) the development of a mathematical prediction model for the distribution within the protective enclosure of the released heat and (ii) the specific application of the predictive model to the Atlantic Generating Station (AGS) proposed by the Public Service Electric and Gas Company of New Jersey. The development of the analytical model proceeded concurrently with the construction and use of an undistorted scale model of the AGS basin. The physical model could not be used to directly predict actual conditions at the AGS due to scaling and operating limitations, but the data gathered were used to aid in understanding the complex mixing and transport phenomena and thus assist in the development of the analytical model. The analytical model schematized the temperature field within the basin as a two-layered stratified system with a uniform layer depth and temperature rise. The heated upper layer was used as the control volume and all fluxes of heat and mass in or out of the control volume were accounted for at each time step. The four physical processes responsible for the fluxes are: 1) Jet entrainment at the interface due to the near-surface jet discharges, 2) Stratified counterflow through the openings in the breakwater, 3) Selective withdrawal at the submerged intakes into the cooling system, and 4) Surface heat dissipation to the atmosphere. The model was used to predict conditions at the AGS for a variety of emergency cooling situations. Sensitivity studies on the design parameters of the AGS and the modeling parameters included in the model were conducted. The analytical model is verified by comparison with experimental results and presented as a legitimate predictive tool for simulating this complex phenomena. The report contains a complete listing of the analytical model and appropriate user instructions. Scanning notes: Disclaimer inserted for illegible graphs and text.; Prepared under the support of Offshore Power Systems, Jacksonville, Florida. 1975-11-01T00:00:00Z https://hdl.handle.net/1721.1/142974 Groundwater Pollution: Technology, Economics and Management Wilson, J. L.; Lenton, R. L.; Porras, J. A review of the technical, economic and management aspects of groundwater pollution is presented. The groundwater pollution problem is described and several of its important characteristics are pointed out. A description of the physical, chemical and biological aspects of groundwater pollution is given. The technology of groundwater pollution detection and observation is reviewed, including elements in the design and operation of a groundwater quality monitoring system. The concept of pollution is related to the economic concept of externalities, and the interrelationships of technology, institutions and economics in groundwater pollution management are presented. Technical, institutional, legal and economic measures to induce pollution control in groundwater systems are reviewed. The financial aspects, and the costs and benefits of groundwater pollution control are discussed. The causes, types and extent of groundwater pollution are described. These include agricultural, industrial, domestic and urban, radiological, and natural or induced sources of pollution. Methods of control for each are given. Methods of analysis as applied to groundwater pollution management are described within the context of total resource management and long range planning. Criteria for choosing among alternative plans, systems analysis, and optimization and simulation techniques are discussed. A case study of integrated groundwater-surface water management with specific groundwater quality considerations is described and discussed. Prepared with the support of the United Nations Food and Agricultural Organization (acting as executing agency for the United Nations Development Program) 1976-01-01T00:00:00Z https://hdl.handle.net/1721.1/142973 An Analytical and Experimental Study of Transient Cooling Pond Behavior Ryan, Patrick J.; Harleman, Donald R. F. Cooling ponds offer many advantages as a means of closed cycle heat dissipation. These are simplicity, low maintenance.and power requirements, aesthetic and possible recreational values, and high thermal inertia. A cooling pond is also subject to minimal environmental problems, since fogging tends to be localized, blowdown water can be stored for long periods, and make-up water requirements are intermittent and often lower than for other closed systems. In s~pite of the above advantages it is presently estimated that less than one third of the closed cycle power stations. built in the next 30 years, will utilize cooling ponds. One reason for this is lack of land, but another reason is the lack of confidence in the ability of existing models to predict cooling pond performance under transient heat loads and meteorological conditions. The use of simple steady state models and various commonly used assumptions as to surface heat loss and circulation patterns can lead to differences of at least 100% in the predicted required land area. Physical models have severe limitations, and this uncertainty in design often results in the rejection of the cooling pond alternative, which may be a mistake from economic, aesthetic and environmental considerations. An analytical and experimental investigation of cooling ponds is conducted. The guiding principle of this investigation is that a cooling pond can be designed on a rational basis only if the desired pond behavior is first clearly defined and the important mechanisms of heat transfer both within the pond itself, and at the water surface, are isolated and quantified. An efficient pond has been defined in terms of maximum surface heat transfer and maximum response time; this leads to the requirement that a pond be capable of sustaining a vertical temperature stratification, that entrance mixing be a minimum, and that a skimmer wall intake be used. The various components of heat transfer at a water surface are discussed, and existing empirical formulae are reviewed. Existing formulae for predicting evaporative flux from an artificially heated water surface are found to be unsatisfactory. Field data indicates that commonly used formulae may predict evaporative losses that are too low by as much as 50% for a heavily loaded water surface. A new formulae is proposed which explicitly accounts for mass transfer due to free convection. This can be very significant at low wind speeds. The proposed formula for evaporative flux performs well both in the laboratory and the field. The effect of entrance mixing and density currents on both the steady state and transient behavior of a cooling pond is examined in the laboratory,,and where possible laboratory results are supported by field observations. It is concluded that the reduction of entrance mixing is a very significant factor in improving the pond performance. In a stratified pond density currents can be of paramount importance in distributing the heat to backwater areas, thus making the pond performance essentially independent of shape. Steady state analytical models and a numerical transient model for the prediction of cooling pond performance are developed. The steady state models demonstrate the effect of entrance mixing and different circulation patterns. The major components of the transient model are a relatively thin surface region with horizontal temperature gradients overlying a deeper subsurface region with vertical temperature gradients. The entrance mixing is determined using the Stolzenbach- Harleman surface jet model, and the M.I.T. reservoir model is used to simulate the subsurface behavior. Output is given in terms of transient surface temperature distribution (area under isotherms), transient vertical temperature distribution, and transient intake temperatures. The transient model has been tested in the laboratory, and against five years of field data on two ponds with completely different characteristics, with very satisfactory results. The input data required by the transient model are that which are available before the pond is built, i.e. the model is predictive. The transient mathematical model is relatively simple and inexpensive, with an execution time of less than 1 minute per simulated year on an IBM 370/155. Thus the model can be used as a design tool, or as a component of a management model which compares different heat disposal alternatives. Design considerations, such as design of outlet and intake, the use of internal diking, and the use of physical models are briefly discussed, and a design approach is recommended. Supported by The Hydrologic Engineering Center, Corps of Engineers, U.S. Army Contract No. DACW05-71-0113. Supported by National Science Foundation, Engineering Energetics Program Grant No. GK-32472. Supported by Duke Power Company, Charlotte, North Carolina. 1973-01-01T00:00:00Z https://hdl.handle.net/1721.1/142972 Evaluation of Techniques for Numerical Calculation of Storm Surges Pagenkopf, James R.; Pearce, Bryan R. Two numerical models are employed to describe the water motion in a coastal region associated with the passage of a hurricane or severe storm. The first is two-dimensional, employs the vertically integrated or "tidal" equations of motion and utilizes a finite-difference scheme. The second is also two-dimensional, also employs the vertically integrated conservation of mass and momentum equations and utilizes a finite element solution scheme. Model results are compared and evaluated through various parametric studies such as computer time and accuracy. Boundary condition sensitivity is investigated. In application, storm surge heights are computed for various hurricane systems at the Atlantic Generating Station site using both models. Results are also compared to bathystrophic calculations. It is concluded that under certain instances of storm size and speed the bathystrophic approach may be non-conservative due to the ignoring of inertial terms and two-dimensional effects. The resulting storm surge calculations indicate no significant advantage in using the finite element method over the finite difference method or vice versa, although the same may not be true for other hydrodynamic applications. Other results include maximum surge heights as a function of forward velocity and angle of incidence, as well as historical verification studies for the hurricane of September 14, 1974. Prepared with the Support of Dames and Moore, Inc. Cranford, New Jersey, and Sea Grant Office National Oceanic and Atmospheric Administration Department of Commerce Washington, D.C. 1975-02-01T00:00:00Z https://hdl.handle.net/1721.1/142971 Simulation of the Continuous Snowmelt Process Laramie, Richard L.; Schaake, Jr., John C. The efficient design of many water management projects requires the ability to predict the time distribution of runoff from a melting snowfield. A continuous model of the snow accumation and melting processes is presented for this purpose. The empirical and theoretical equations that have been used to represent these processes are integrated into a model developed to have a wide range of applicability owing to its flexible data requirements. The snowmelt model is tested using various combinations of recorded data thought likely to be available in practical design problems. A comparison of the generated values of certain important snowpack variables with those actually observed shows good agreement. Application of the model to an experimental catchment is made to estimate streamflows resulting from the computed snowmelt. Although the results were favorable, suggestions are made as to how they may be improved. The work upon which this publication is based was supported by the Subsecretar�a de Recursos H�dricos, Ministerio de Obras y Servicios P�blicos, Argentina. 1972-01-01T00:00:00Z https://hdl.handle.net/1721.1/142970 The Methodology of Bayesian Inference and Decision Making Applied to Extreme Hydrologic Events Wood, Eric F.; Rodriguez-Iturbe, Ignacio; Schaake, Jr., John C. This study presents the methodology of Bayesian inference and decision making applied to extreme hydrologic events. Inference procedures must consider both the natural or 'modelled' uncertainty of the hydrologic process and the statistical uncertainty due to a lack of information. Two types of statistical uncertainty were considered in this study. The first type is the uncertainty in modelling the hydrologic process, and the second type is the uncertainty in the values of the model parameters. The uncertainty is reduced by considering prior sources of information (regional regression, theoretical flood frequency analysis or subjective assessment) and historical flood data. A 'Bayesian distribution' of flood discharges is developed that fully accounts for parameter uncertainty. In an analogous manner, model uncertainty is analyzed, which leads to a 'composite Bayesian distribution'. The uncertainty in flood frequency curves from rainfall-runoff models is also analyzed, due to the uncertainty in the parameters of the models. The Bayesian inference model is then applied to a Bayesian decision model, where the decision rule is the maximization of expected net monetary benefits. A case study of determining the optimal size of local flood protection for Woonsocket, Rhode Island, was considered, using realistic flood damage and cost functions. The results indicate that Bayesian inference procedures can be used to fully account for statistical uncertainty and that Bayesian decision procedures provide a rational approach for making decisions under uncertainty. Scanning notes: Disclaimer inserted for illegible graphs and text.; Project supported by Office of Water Resources Research grant no. 14-31-0001-9021 1974-01-01T00:00:00Z https://hdl.handle.net/1721.1/142969 Porous Boundary Effects in Turbulent Shear Flow Ruff, J. F.; Gelhar, L. W. A technique of measuring seepage velocities is developed in order to investigate the velocity distribution in a porous boundary exposed to a turbulent shear flow. Measurements are performed in a 1.2 in. thick polyurethane foam lining of 12 in. inside diameter pipe using hot wire anemometer and a helium tracer technique involving the determination of the travel time of the peak concentration. In the shear zone, seepage velocities are determined directly from shielded hot wire anemometer data. In the pressure gradient flow zone, the helium tracer technique is used to measure the seepage velocities. Results of the velocity measurements indicate that the shear effect penetrates a relatively small distance into the porous boundary (approximately 0.25 to 0.30 in.). Measurements of the permeability and longitudinal dispersion coefficient are also made. Three analytical models based upon the eddy viscosity concept are developed in an effort to gain some insight into 'the mechanism relating the turbulent shear flow and the porous boundary flow through the velocity distribution in the boundary. The models are extended to relate the core and boundary flow regions and an attempt is made to predict the friction factor for the pipe. The models provide a reasonable agreement with the observed velocity profile but indicate a decreasing friction factor with increasing Reynolds number whereas the observed friction factor increases. Development of the helium tracer technique for velocity measurements requires additional information concerning the concentration distribution of a tracer in a shear flow. Perturbation methods are used to develop analytical solutions of the convective dispersion equation with an instantaneous point source in a shear flow for both constant and variable dispersion coefficients and the limitations of the solutions are defined. The analysis indicated shear effects caused no distortion on the longitudinal axis and the distortion due to dispersion was insignificant for the dimensions used in the experiments. Prepared Under National Science Foundation Engineering Division Grant No. GK-4180 1970-07-01T00:00:00Z https://hdl.handle.net/1721.1/142968 Wave Reflection and Transmission at Permeable Breakwaters Sollitt, Charles K.; Cross, III, Ralph H. Rubble mound breakwaters are designed to protect exposed marine areas from excessive wave activity. Observations of breakwaters interacting with surface waves in laboratory models and in full scale field applications demonstrate that significant wave energy is transmitted through the interstices of structures commonly regarded as being impervious. The objective of this investigation is the development of a theoretical analysis to account for this phenomenon. The results are intended for use by coastal engineers to compare the effectiveness of alternative breakwater configurations, independent of repetitive experimental programs. Three breakwater configurations are considered: 1) crib style breakwaters with vertical walls and homogeneous fill, 2) conventional trapezoidal shape breakwaters with layered fill, and 3) pile array breakwaters composed of vertical piles placed in symmetric patterns. The two dimensional problem is studied. Waves are assumed to arrive at normal incidence. The theoretical development begins with the unsteady equations of motion for flow in the voids of an arbitrary porous structure. The equations are linearized using a technique which approximates the known turbulent damping condition inside the structure. This yields a potential flow problem satisfied by an eigen series solution. Linear wave theory is assumed to apply outside the structure and the excitation is provided by a monochromatic incident wave. The reflected, transmitted and internal wave amplitudes are determined by matching the general solutions at the sea-breakwater interfaces and requiring continuity of pressure and horizontal mass flux. Inclusion of sloping face structures necessitates an estimation of the breaking losses incurred on the windward slope. A semi-empirical method, adapted from Miche's work, is used to approximate the effect of wave breaking. An experimental program is conducted to verify the analytical models. Theory and experiment yield the following general conclusions: 1) the transmission coefficient decreases with decreasing wave length, breakwater porosity and permeability, and increasing wave height and breakwater width; 2) the reflection coefficient decreases with increasing wave length, breakwater porosity and permeability, and decreasing breakwater width. Application of the theory is limited to wave heights which exceed the medium grain diameter. Experimental results correlate better with the theoretical transmission coefficient than with the reflection coefficient. This seems to be due to the sensitivity of the reflection coefficient to surface effects. The theory provides useful design estimates for all three breakwater configurations and a full range of wave lengths. The proposed wave breaking calculation gives favorable results for the sloping face structure tested in this study. However, further comparison is needed to establish the general validity of the breaking wave analysis. 1972-03-01T00:00:00Z https://hdl.handle.net/1721.1/142967 A Distributed Linear Representation of Surface Runoff Maddaus, William O.; Eagleson, Peter S. A distributed quasi-linear model of direct catchment runoff is developed consisting of cascades of linear reservoirs connected by linear channels. By fitting to the kinematic wave, the model parameters are expressed in terms of the physical characteristics of the catchment and the impulse response function is constrained to be input-dependent. Separate models of overland flow and stream flow are developed facilitating consideration of spatially variable inputs. Investigation into the sensitivity of the catchment to distributed inputs illustrates the failure of the kinematic wave method to provide realistic hydrograph dispersion when applied to the flood-routing problem. Supported financially by the Office of Water Resources Research, U.S. Department of the Interior under Grant No. 14-01-0001-1576 1969-06-01T00:00:00Z https://hdl.handle.net/1721.1/142966 Mass Transport in Water Waves; Theory and Experiments Mei, Chiang Chung; Liu, Philip L-F.; Carter, Trevor G. When a fluid is in periodic wave motion, a fluid particle is carried by a velocity field varying from place to place. At different instants the location of the particle differs and so does the velocity field in its immediate neighborhood. As a result the time-averaged velocity of a particle may be different from the local velocity field. In particular, a fluid particle may have a net mean drift even if the local velocity field has zero mean; this is indeed the case in irrotational gravity waves. In a viscous fluid, the wave-induced Reynolds stress imparts a steady momentum to the fluid; a steady shear is set up to balance it and hence a further mean velocity field results. The sum of these two steady currents provides the total drift by which a fluid particle migrates, and is termed the mass transport velocity. It is of importance to the study of sediment motion in coastal waters. The present report describes a coordinated inquiry into both theoretical and experimental aspects of mass transport by waves. In accordance with the division of effort, it is separated into two parts. However, nearly all ideas expressed and actions taken in both parts have been influenced by extensive mutual discussions. Part I (Theory) begins with a review of the basic assumptions underlying existing theories. General formulas of mass transport velocity components throughout the Stokes boundary layer near a solid body are then derived; details of two examples are calculated. The three-dimensional mass transport distribution throughout the cross section of a wave tank is worked out for progressive waves of very small amplitudes. The effects of finite width is studied with the assumption that vorticity is diffused by molecular viscosity throughout the entire cross section. For a wave obliquely incident and reflected from a vertical sea wall, the structure in the second boundary layer between the Stokes layer and the inviscid core is investigated. This is appropriate for amplitudes much greater than the Stokes layer thickness. Part II (Experiments), were intended in part to check and to evaluate the theoretical deductions in Part I. In particular, extensive measurements were made for the longitudinal mass transport velocity in a progressive wave in a long tank with a smooth bottom. For standing waves and partially standing waves, possible features of erosion and deposition were observed by spreading (1) a small amount of sand on a smooth bottom and (2) a thick layer of sand on the bottom. The relevance of mass transport very near the bottom to the bed load transport is discussed in the light of the real beach environment. Final report on research work done under Contract DACW 72-68-C-0012 with the Coastal Engineering Center, U.S. Army Corps of Engineers, Washington, D.C. Prepared under the support of the Coastal Engineering Research Center U.S. Army Corps of Engineers Contract No. DACW 72-68-C-0012 1972-04-01T00:00:00Z