Dual Objective Control of Nutrient Loading into a Lake1

ABSTRACT: The control of nutrient loading into a water body is approached from a multiobjective viewpoint. The example of phosphorus (P) loading into Lake Balaton, Hungary, is used as a case study. The element P is chosen because it appears to be the limiting factor of eutrophication in the lake considered, as in many other lakes. About one-half of P loading originates from nonpoint sources; furthermore, the mechanism is poorly known and only few observation data are available. The objective of eutrophication control is to minimize P loading, while the objective of watershed management is to maximize agricultural revenue. These two objectives often appear to be in conflict. A discrete set of alternative control methods is defined, consisting in controlling a mix of the following elements: point sources, runoff, fertilizer type and application, cropping management, erosion, and sedimentation. The system dynamics is provided by a previously developed stochastic model, whose output is an empirical prohability density function (pdf) of P-loading reflecting the control policy. A compromise solution of “satisfactum” can then be chosen as a mix of the best ranked policies.     

A MULTI-BASIN PLANNING STRATEGY1

ABSTRACT. The purpose of this paper is to present and discuss a procedure for finding an optimal staging plan for implementing a multi-basin water resource system-a system that must meet, with tolerable shortages, pre-specified but highly variable demands for water that increase over time-a system such as the proposed Texas Water System. The paper stresses that, in the past, planners have paid little attention to quantifying explicitly the impact that uncertainty has on the decision process, and in that context, presents a means for explicitly evaluating the impact that uncertainty has on finding and evaluating the performance of the optimal and several alternate staging plans. The procedure presented evaluates the impact that uncertainty, in both the hydrologic and the economic variables, has on the decisions that need to be made. The decisions requiring resolution are (1) which of an over-specified set of facilities should be constructed, (2) how large each of the facilities should be at various points in time, and (3) how should the system be operated so as to minimize the capital plus operational costs over the planning period.     

THE UNIT HYDROGRAPH: A SATISFACTORY MODEL OF WATERSHED RESPONSE?1

ABSTRACT: Some 96 flood events larger than the mean annual flood from 16 watersheds in the Commonwealth of Pennsylvania were used to derive unit hydrographs by the least-squares method. Analyses of the unit hydrographs were conducted to ascertain their response to watershed parameters, climatic and storm variables and locations within different hydrologic regions. Significant differences both within and among watersheds led to the formulation and testing of hypotheses stating that differences among watersheds are caused by physiographic differences while differences within watersheds result from climatic and storm differences. The analysis showed, that while many watersheds parameters strongly influence the shape of the unit hydrograph, only the storm variables duration and volume of precipitation excess produce significant differences. Seasonal differences were apparent but not proven statistically significant.     

ON THE MISMATCH BETWEEN DATA AND MODELS OF HYDROLOGIC AND WATER RESOURCE SYSTEMS1

ABSTRACT: Many difficulties exist in the matching of models with data. This paper identifies elements of this problem and discusses considerations involved in model evaluation. The well known multivariate linear regression model is used to illustrate the distinctions between accuracy and precision and between estimation and prediction (because the model is commonly misused.) No amount of additional data will improve the accuracy of a poor model. A high R², while indicative of a good matching between the observed data and model estimates, is a poor criterion for judging adequacy of the model to make good predictions of future events. Model evaluation also includes the problem of introducing secondary data and proxy variables into a model. Secondary data frequently enter, for example, the mass, energy and water budget equations because of difficulties in measuring the primary variables. Proxy variables arise because of a desire to collapse a vector of incomparable values, say, of water quality into a single number. Review of the above issues indicates that model evaluation is a multi-criterion problem, often imbedded in a larger framework where models are intended to meet multiple objectives. The mismatch of models and data has increasing legal and social consequences.     

ONE APPROACH TO IRRIGATION MODELING UNDER RISK1

Recent progress in operations research has refined stochastic programming with recourse sufficiently to significantly increase its potential for use in water resource planning. To demonstrate its strengths and weaknesses this paper considers an irrigation planning problem and illustrates how more and more refined variants of this problem are successively cast into stochastic programming with recourse forms. The result is an outline of the state of the art with method limitations and demands on model formulation clearly indicated.     

GENERATION OF HOURLY RAINFALL1

ABSTRACT: A rainfall model was developed to divide daily rainfall into storms and distribute storm depths over storm duration for input into the Stanford Watershed Model.     

STOCHASTIC FLOW DURATION CURVES FOR EVALUATION OF FLOW REGIMES IN RIVERS1

ABSTRACT: A stochastic estimation of low flow in the upper reaches of streams is needed for the planning, development, and management of water resources and/or water use systems. In this paper, the definition and development procedure for the stochastic flow duration curve is presented and applied to five catchments located in eastern Japan and to two catchments in western Thailand. The probability distribution of N‐year daily discharge data is extracted at various percentages of time for which specified discharges are equaled or exceeded in a water year. Such a distribution is usually represented with a straight line on log‐normal probability paper. However, some of the probability plots for the annual minimum daily discharge are best represented with a straight line on Weibull probability paper. The effectiveness of the stochastic flow duration curve defined for the evaluation of flow regime is illustrated through its application. The ten year probability for the discharge exceeded 97 percent of the time may be recognized as an index of low flow. The recession shape of the lower part of the flow duration curve is dependent on the strength of low flow persistence.     

UNCERTAINTY BASED OPERATION OF LARGE SCALE RESERVOIR SYSTEMS: DEZ AND KAROON EXPERIENCE1

ABSTRACT: Reservoir operation involves a complex set of human decisions depending upon hydrologic conditions in the supply network including watersheds, lakes, transfer tunnels, and rivers. Water releases from reservoirs are adjusted in an attempt to provide a balanced response to different demands. When a system involves more than one reservoir, computational burdens have been a major obstacle in incorporating uncertainties and variations in supply and demand. A new generation of stochastic dynamic programming was developed in the 1980s and 1990s to incorporate the forecast and demand uncertainties. The Bayesian Stochastic Dynamic Programming (BSDP) model and its extension, Demand Driven Stochastic Dynamic Programming (DDSP) model, are among those models. Recently, a Fuzzy Stochastic Dynamic Programming model (FSDP) also was developed for a single reservoir to model the errors associated with discretizing the variables using fuzzy set theory. In this study the DDSP and the FSDP models were extended and simplified for a complex system of Dez and Karoon reservoirs in the southwestern part of Iran. The simplified models are called Condensed Demand Driven Stochastic Programming (CDDSP) and Condensed Fuzzy Stochastic Dynamic Programming (CFSDP). The optimal operating policies developed by the CDDSP and the CFSDP models were simulated in a classical model and a fuzzy simulation model, respectively. The case study was used to demonstrate the advantages of implementing the proposed algorithm, and the results show the significant value of the proposed fuzzy based algorithm.     

AN ECONOMIC ANALYSIS OF ALTERNATIVE WATER USE STRATEGIES AT CATCHMENT LEVEL TAKING INTO ACCOUNT AN INSTREAM FLOW REQUIREMENT1

ABSTRACT: A mathematical model of agricultural water use and a hydrological and economic simulation model were linked to quantify the economic and hydrological impact of deficit irrigation, increased water application efficiency, and farm storage dams when maintaining an IFR (instream flow requirement) under stochastic water supply conditions. The main finding was that a water conservation policy aimed at reducing the amount of water withdrawn from the river could bring more pressure to bear on stream flow. Water can only be saved if consumptive use is reduced. Increased water application efficiency is detrimental to other users as a result of reduced return flow. The economic cost of maintaining a specific IFR increases with the use of all three strategies as the probability of maintaining the IFR increases. Because of the control that can be exercised over the supply of water, a farm storage dam is the best strategy for minimizing the costs for irrigators. The interaction between water legislation, water policy administration, technology, hydrology, and human value systems necessitates an integrated approach to facilitate water management at catchment level and to formulate policies that will be in the interest of society.     

RESERVOIR RELEASES TO USES WITH DIFFERENT RELIABILITY REQUIREMENTS1

ABSTRACT: Releases from a reservoir may be allocated to a number of uses, each of which may require a given volume of water at a different reliability. The paper provides a method that can be used to estimate the volume of water associated with a given reliability for each use of water when the proportion of releases allocated to each use is known. These results can be used to evaluate the meeting of specified objectives under a published release policy derived by stationary stochastic dynamic programming. The results can also be used to solve water allocation problems when the probability distribution of available water is known (or can be estimated) and water has multiple uses, each of which has different volume and reliability requirements.