GENETIC PROGRAMMING: A NEW PARADIGM IN RAINFALL RUNOFF MODELING1

ABSTRACT: Genetic Programming (GP) is a domain‐independent evolutionary programming technique that evolves computer programs to solve, or approximately solve, problems. To verify GP's capability, a simple example with known relation in the area of symbolic regression, is considered first. GP is then utilized as a flow forecasting tool. A catchment in Singapore with a drainage area of about 6 km² is considered in this study. Six storms of different intensities and durations are used to train GP and then verify the trained GP. Analysis of the GP induced rainfall and runoff relationship shows that the cause and effect relationship between rainfall and runoff is consistent with the hydrologic process. The result shows that the runoff prediction accuracy of symbolic regression based models, measured in terms of root mean square error and correlation coefficient, is reasonably high. Thus, GP induced rainfall runoff relationships can be a viable alternative to traditional rainfall runoff models.     

APPLICATION OF GREY MODEL TOWARD RUNOFF FORECASTING1

ABSTRACT: A reliable forecasting model is essential in real‐time flood forecasting for reducing natural damage. Efforts to develop a real‐time forecasting model over the past two decades have been numerous. This work applies the Grey model to forecast rainfall and runoff owing to the model's relative ability to predict the future using a small amount of historical data. Such a model significantly differs from the stochastic and deterministic models developed previously. Ten historical storm events from two catchment areas in northern Taiwan are selected to calibrate and verify the model. Results in this study demonstrate that the proposed models can reasonably forecast runoff one to four hours ahead, if the Grey error prediction method is further used to update the output of the model.     

SHORT-TERM FORECASTING OF SNOWMELT RUNOFF USING ARMAX MODELS1

ABSTRACT: Time series models of the ARMAX class were investigated for use in forecasting daily riverflow resulting from combined snowmelt/rainfall. The Snowmelt Runoff Model (Martinec-Rango Model) is shown to have a form similar to the ARMAX model. The advantage of the ARMAX approach is that analytical model identification and parameter estimation techniques are available. In addition, previous forecast errors can be included to improve forecasts and confidence limits can be estimated for the forecasts. Diagnostic checks are available to determine if the model is performing properly. Finally, Kalman filtering can be used to allow the model parameters to vary continuously to reflect changing basin runoff conditions. The above advantages result in improved flow forecasts with fewer model parameters.     

ANN OUTPUT UPDATING OF LUMPED CONCEPTUAL RAINFALL/RUNOFF FORECASTING MODELS1

ABSTRACT: Artificial neural networks (ANNs) are tested for the output updating of one‐day‐ahead and three‐day‐ahead streamflow forecasts derived from three lumped conceptual rainfall/runoff (R‐R) models: the GR4J, the IHAC, and the TOPMO. ANN output updating proved superior to a parameter updating scheme and to the ‘simple’ output updating scheme, which always replicates the last observed forecast error. In fact, ANN output updating was able to compensate for large differences in the initial performance of the three tested lumped conceptual R‐R models, which the other tested updating approaches were not able to achieve. This is done mainly by incorporating input vectors usually exploited for ANN R‐R modeling such as previous rainfall and streamflow observations, in addition to the previous observed error. For one‐day‐ahead forecasts, the performance of all three lumped conceptual R‐R models, used in conjunction with ANN output updating, was equivalent to that of the ANN R‐R model. For three‐day‐ahead forecasts, the performance of the ANN‐output‐updated conceptual models was even superior to that of the ANN R‐R model, revealing that the conceptual models are probably performing some tasks that the ANN R‐R model cannot map. However, further testing is needed to substantiate the last statement.     

MONTHLY RUNOFF PREDICTIONS BASED ON RAINFALL FORECASTS IN A SMALL OKLAHOMA WATERSHED1

ABSTRACT: Conditions under which monthly rainfall forecasts translate into monthly runoff predictions that could support water resources planning and management activities were investigated on a small watershed in central Oklahoma. Runoff response to rainfall forecasts was simulated using the hydrologic model SWAT. Eighteen scenarios were examined that represented combinations of wet, average, and dry antecedent rainfall conditions, with wet, normal, and dry forecasted rainfall. Results suggest that for the climatic and physiographic conditions under consideration, rainfall forecasts could offer potential application opportunities in surface water resources but only under certain conditions. Pronounced wet and dry antecedent rainfall conditions were shown to have greater impact on runoff than forecasts, particularly in the first month of a forecast period. Large forecast impacts on runoff occurred under wet antecedent conditions, when the fraction of forecasted rainfall contributing to runoff was greatest. Under dry antecedent conditions, most of the forecasted rainfall was absorbed in the soil profile, with little immediate runoff response. Persistent three‐month forecasts produced stronger impacts on runoff than one‐month forecasts due to cumulative effects in the hydrologic system. Runoff response to antecedent conditions and forecasts suggest a highly asymmetric utility function for rainfall forecasts, with greatest decision‐support potential for persistent wet forecasts under wet antecedent conditions when the forecast signal is least dampened by soil‐storage effects. Under average and dry antecedent conditions, rainfall forecasts showed little potential value for practical applications in surface water resources assessments.     

PROBLEMS IN FORECASTING WATER REQUIREMENTS1

ABSTRACT. Methodological problems associated with forecasting water requirements by use of regression analysis are examined. Problems occurring when long-range forecasts are based on linear and nonlinear extrapolation of time series models include possible changes in socioeconomic conditions, water allocation system structure, and limits to growth. Problems arising in forecasting based on multiple regression models are likely to involve serially dependent errors, multicollinear explanatory variables, and difficulties inherent to the presence of explanatory variables that must themselves be predicted.     

RUNOFF AND SEDIMENT YIELD UNDER GRAZING IN FOOTHILLS FESCUE GRASSLANDS OF ALBERTA1

ABSTRACT: Grazing can have a profound impact on infiltration and thus runoff and erosion. The objectives of this study were to quantify the effects of select grazing systems on rainfall and snowmelt induced runoff and sediment yield from sloped areas of the foothills fescue grasslands of Alberta, Canada. The effects of two grazing intensities (heavy and very heavy) for two durations (short duration and continuous throughout the growing season) were compared to an ungrazed control between June 1988 and April 1991. Runoff was measured using 1-rn² runoff frames and collection bucket systems. Sediment yields were then determined on samples from the collected runoff. Snowmelt was the dominant source of runoff. Snowmelt runoff was higher from the heavily grazed areas than from the very heavily grazed areas, due to the higher standing vegetation which accumulated snow in the former areas. Sediment yields as a result of snowmelt were generally low in all areas. Only a few summer storms caused runoff. Runoff volumes and sediment yields from summer rainstorms were low, due to low rainfall and to generally dry antecedent soil moisture conditions. The greatest risk of summer runoff, and thus sediment yield, appears to occur in August.     

MULTIFRACTAL SCALING OF DAILY RUNOFF TIME SERIES IN AGRICULTURAL WATERSHEDS1

Abstract: Multifractal scaling behavior of long-term records of daily runoff time series in 32 subwatersheds covering a wide range of sizes was examined. These subwatersheds were associated with four agricultural watersheds with different climates and topography. The empirical moment scaling curves obtained using the trace moment method showed that the runoff time series exhibited a multifractal behavior, which was valid over a time scale range from one day to about three years. The multi-fractal scaling of the runoff time series was well described by the Universal Multifractal Model. The spectral analysis (β < 1) and the order of fractional integration (H ⋍; 0) indicated that the runoff time series were conservative. The multifractal parameters, α (multifractal index) and C₁ (co-dimension), were reasonably close to each other for subwatersheds within each of the watersheds and were generally similar among the four watersheds. The α values of the four watersheds were 1.10 ± 0.13, 1.61 ± 0.06,1.61 ± 0.24, and 1.63 ± 0.19. The C₁ values of four watersheds were 0.19 ± 0.01, 0.17 ± 0.01, 0.17 ± 0.04, and 0.11 ± 0.02. The multifractal analyses provided useful insight into the runoff time series, especially the occurrence and distribution of extreme events.     

RESPONSE OF GREEN‐AMPT MEIN‐LARSEN SIMULATED RUNOFF VOLUMES TO TEMPORALLY AGGREGATED PRECIPITATION1

ABSTRACT: Data collection frequency in automated systems is user determined and can range from seconds to hours or days. Currently, there is no standard or recommended frequency interval for collecting precipitation data from automated systems for input to event‐based models such as Green‐Ampt Mein‐Larsen (GAML). Data from 47 storm events at seven locations were used to simulate the response of GAML excess rainfall to temporally aggregated precipitation data. No difference in model efficiency was recognized when comparing one‐minute interval data (R²= 1.00) to five‐minute data (R²= 1.00). Very little model efficiency was lost at a 10‐minute (R²= 0.96) interval. After 10‐minutes, decline in efficiency became more rapid with R²= 0.16 at one hour. The combined effect of time interval with respect to drainage area, hydraulic conductivity, maximum 30‐minute intensity, and total precipitation also revealed similar results.     

BASIN SCALE WATER MANAGEMENT AND FORECASTING USING ARTIFICIAL NEURAL NETWORKS1

ABSTRACT: Water scarcity in the Sevier River Basin in south‐central Utah has led water managers to seek advanced techniques for identifying optimal forecasting and management measures. To more efficiently use the limited quantity of water in the basin, better methods for control and forecasting are imperative. Basin scale management requires advanced forecasts of the availability of water. Information about long term water availability is important for decision making in terms of how much land to plant and what crops to grow; advanced daily predictions of streamflows and hydraulic characteristics of irrigation canals are of importance for managing water delivery and reservoir releases; and hourly forecasts of flows in tributary streams to account for diurnal fluctuations are vital to more precisely meet the day‐to‐day expectations of downstream farmers. A priori streamflow information and exogenous climate data have been used to predict future streamflows and required reservoir releases at different timescales. Data on snow water equivalent, sea surface temperatures, temperature, total solar radiation, and precipitation are fused by applying artificial neural networks to enhance long term and real time basin scale water management information. This approach has not previously been used in water resources management at the basin‐scale and could be valuable to water users in semi‐arid areas to more efficiently utilize and manage scarce water resources.     

APPLICATION OF LINEAR SYSTEM'S THEORY AND LINEAR PROGRAMMING TO GROUND WATER MANAGEMENT IN KANSAS1

ABSTRACT: A ground water management model based on the linear systems theory and the use of linear programming is formulated and solved. The model maximizes the total amount of pound water that can be pumped from the system subject to the physical capability of the system and institutional constraints. The results are compared With analytical and numerical solutions. Then, this model is applied to the Pawnee Valley area of south-central Kansas. The results of this application support the previous studies about the future ground water resources of the Valley. These results provide a guide for the ground water resources management of the area over the next ten years.     

SPATIAL VARIABILITY IN WATER‐BALANCE MODEL PERFORMANCE IN THE CONTERMINOUS UNITED STATES1

ABSTRACT: A monthly water‐balance (WB) model was tested in 44 river basins from diverse physiographic and climatic regions across the conterminous United States (U.S.). The WB model includes the concepts of climatic water supply and climatic water demand, seasonality in climatic water supply and demand, and soil‐moisture storage. Exhaustive search techniques were employed to determine the optimal set of precipitation and temperature stations, and the optimal set of WB model parameters to use for each basin. It was found that the WB model worked best for basins with: (1) a mean elevation less than 450 meters or greater than 2000 meters, and/or (2) monthly runoff that is greater than 5 millimeters (mm) more than 80 percent of the time. In a separate analysis, a multiple linear regression (MLR) was computed using the adjusted R‐square values obtained by comparing measured and estimated monthly runoff of the original 44 river basins as the dependent variable, and combinations of various independent variables [streamflow gauge latitude, longitude, and elevation; basin area, the long‐term mean and standard deviation of annual precipitation; temperature and runoff; and low‐flow statistics (i.e., the percentage of months with monthly runoff that is less than 5 mm)]. Results from the MLR study showed that the reliability of a WB model for application in a specific region can be estimated from mean basin elevation and the percentage of months with gauged runoff less than 5 mm. The MLR equations were subsequently used to estimate adjusted R‐square values for 1,646 gauging stations across the conterminous U.S. Results of this study indicate that WB models can be used reliably to estimate monthly runoff in the eastern U.S., mountainous areas of the western U.S., and the Pacific Northwest. Applications of monthly WB models in the central U.S. can lead to uncertain estimates of runoff.     

REAL CODED GENETIC ALGORITHM OPTIMIZATION OF LONG TERM RESERVOIR OPERATION1

ABSTRACT: An optimization and simulation model holds promise as an efficient and robust method for long term reservoir operation, an increasingly important facet of managing water resources. Recently, genetic algorithms have been demonstrated to be highly effective optimization methods. According to previous studies, a real coded genetic algorithm (RGA) has many advantages over a binary coded genetic algorithm. Accordingly, this work applies an RGA to obtain the 10‐day (the traditional period of reservoir operation in Taiwan) operating rule curves for the proposed reservoir system. The RGA is combined with an effective and flexible scheme for coding the reservoir rule curves and applied to an important reservoir in Taiwan, considering a water reservoir development scenario to the year 2021. Each rule curve is evaluated using a complex simulation model to determine a performance index for a given flow series. The process of generating and evaluating decision parameters is repeated until no further improvement in performance is obtained. Many experiments were performed to determine the suitable RGA components, including macro evolutionary (ME) selection and blend‐α crossover. Macro evolution (ME) can be applied to prevent the premature problem of the conventional selection scheme of genetic algorithm. The purpose of adjusting a of a crossover scheme is to determine the exploratory or exploitative degree of various subpopulations. The appropriate rule curve searched by an RGA can minimize the water deficit and maintain the high water level of the reservoir. The results also show that the most promising RGA for this problem consists of these revised operators significantly improves the performance of a system. It is also very efficient for optimizing other highly nonlinear systems.     

Ensemble Streamflow Forecast: A GLUE‐Based Neural Network Approach1

Abstract: While training a Neural Network to model a rainfall‐runoff process, generally two aspects are considered: its capability to be able to describe the complex nature of the processes being modeled and the ability to generalize so that novel samples could be mapped correctly. The general conclusion is that, the smallest size network capable of representing the sample distribution is the best choice, as far as generalization is concerned. Oftentimes input variables are selected a priori in what is called an explanatory data analysis stage and are not part of the actual network training and testing procedures. When they are, the final model will have only a “fixed” type of inputs, lag‐space, and/or network structure. If one of these constituents was to change, one would obtain another equally “optimal” Neural Network. Following Beven and others' generalized likelihood uncertainty estimate approach, a methodology is introduced here that accounts for uncertainties in network structures, types of inputs, and their lag‐space relationships by looking at a population of Neural Networks rather than target in getting a single “optimal” network. It is shown that there is a wide array of networks that provide “similar” results, as seen by a likelihood measure, for different types of inputs, lag‐space, and network size combinations. These equally optimal networks expose the range of uncertainty in streamflow predictions and their expected value results in a better performance than any of the single network predictions.     

NUTRIENT AND β17‐ESTRADIOL LOSS IN RUNOFF WATER FROM POULTRY LITTERS1

ABSTRACT: A main water quality concern is accelerated eutrophication of fresh waters from nonpoint source pollution, particularly nutrient transport in surface runoff from agricultural areas and confined animal feeding operations. This study examined nutrient and β₁₇‐estradiol concentrations in runoff from small plots where six poultry litters were applied at a rate of about 67 kg/ha of total phosphorus (TP). The six poultry litter treatments included pelleted compost, pelleted litter, raw litter, alum (treated) litter, pelleted alum litter, and normal litter (no alum). Four replicates of the six poultry litter treatments and a control (plots without poultry litter application) were used in this study. Rainfall simulations at intensity of 50 mm/hr were conducted immediately following poultry litter application to the plots and again 30 days later. Composite runoff samples were analyzed for soluble reactive phosphorus (SRP), ammonia (NH₄), nitrate (NO₃), TP, total nitrogen (TN) and β₁₇‐estradiol concentrations. In general, poultry litter applications increased nutrient and β₁₇‐estradiol concentrations in runoff water. Ammonia and P concentrations in runoff water from the first simulation were correlated to application rates of water extractable NH₄ (R²= 0.70) and P (R²= 0.68) in the manure. Results suggest that alum applications to poultry litter in houses in between flocks is an effective best management practice for reducing phosphorus (P) and β₁₇‐estradiol concentrations in runoff and that pelleted poultry litters may increase the potential for P and β₁₇‐estradiol loss in runoff water. Inferences regarding pelleted poultry litters should be viewed cautiously, because the environmental consequence of pelleting poultry litters needs additional investigation.     

TEMPORAL RESPONSES OF SURFACE‐WATER AND GROUND‐WATER TO PRECIPITATION IN ILLINOIS1

ABSTRACT: Illinois data from 168 months (1986–1999) were investigated to determine the responses of surface‐water and ground‐water resources to precipitation. Such responses were generally within the month of occurrence or one to two months later, with recovery being reached another one to three months into the future, depending on season of the year. Although the drought of 1988 immediately impacted surface‐water and ground‐water resources, the time of recovery was substantially longer compared to those of individual dry months, generally continuing for several months. The extremely wet summer of 1993 resulted in elevated responses in water resources almost immediately, but in this instance continued through the following fall and winter, into the spring of 1994.     

A REVISED VERSION OF PnET‐II TO SIMULATE THE HYDROLOGIC CYCLE IN SOUTHEASTERN FORESTED AREAS1

ABSTRACT: The PnET‐II model uses hydroclimatic data on maximum and minimum temperatures, precipitation, and solar radiation, together with vegetation and soil parameters, to produce estimates of net primary productivity, evapotranspiration (ET), and runoff on a monthly time step for forested areas. In this study, the PnET‐II model was employed to simulate the hydrologic cycle for 17 Southeastern eight‐digit hydrologic unit code (HUC) watersheds dominated by evergreen or deciduous tree species. Based on these control experiments, model biases were quantified and tentative revision schemes were introduced. Revisions included: (1) replacing the original single soil layer with three soil layers in the water balance routine; (2) introducing calibrating factors to rectify the phenomenon of overestimation of ET in spring and early summer months; (3) parameterizing proper values of growing degree days for trees located in different climate zones; and (4) adjusting the parameter of fast‐flow (overland flow) fraction based on antecedent moisture condition and precipitation intensity. The revised PnET‐II model, called PnET‐II3SL in this work, substantially improved runoff simulations for the 17 selected experimental sites, and therefore may offer a more powerful tool to address issues in water resources management.     

Dynamic Modeling of Ground‐Water Quality Using Bayesian Techniques1

Abstract: Water industry experts have been arguing that the traditional techniques are not an accurate means of measuring water contamination. This is mainly because these techniques emphasize neither the stochastic nature of the water contamination process nor the precision and the accuracy of the tested methods used by environmental laboratories. In this work, we describe the development and application of prototype Dynamic Bayesian Networks (DBNs) that model ground‐water quality to determine the impact of chemical contaminants on ground‐water quality in the Salalah area, which is allocated to the south of Oman. We also present a new technique for data pre‐processing because it is needed for the treatment of ground‐water datasets that are used as the data source to learn the probabilities for dynamic decision models. Among more than 20 wells in area, only four wells were selected to be analyzed and the results show that we achieved an acceptable level of efficiency.     

THE LEGAL‐INSTITUTIONAL ANALYSIS MODEL AND WATER POLICYMAKING IN A BI‐NATIONAL SETTING1

ABSTRACT: This paper reports the use of a water negotiation model, the Legal‐Institutional Analysis Model (LIAM), in the bi‐national setting of the U.S. and Mexico in the Paso del Norte region. The following study discusses the results of developing baseline data where interstate, international, and cultural factors, as well as a long history of conflict, impact on negotiations and the extent to which the LIAM is a valuable tool for analyzing behavior among institutional actors in such a setting. The findings suggest that most water policy actors in the region prefer brokered solutions as defined within the LIAM framework.