MODELING RAINFALL-RUNOFF PROCESS INCLUDING LOSSES1

ABSTRACT: Existing discrete, linear rainfall-runoff models generally require the effective rainfall of a given storm as the input for computing the runoff hydrograph. This paper proposes a method for estimating, simultaneously, the optimal values of model parameters and the rainfall losses frem the measured rainfall hyetograph and the runoff hydrograph. The method involves an ARMA model for the rainfall-runoff process and a nonlinear iterative technique. The number of model parameters to be estimated for the ARMA model is much less than the unit hydrograph model. Applications of the model to three different watersheds show that the computed runoff hydrographs agree well with the measurements.     

PLANNING METHODOLOGY FOR ANALYSIS AND MANAGEMENT ON LAKE EUTROPHICATION1

ABSTRACT: The effects of changing nutrient inputs through land use management, waste water treatment, or effluent diversion are not clear, and managers are discovering that decisions which were effective in reversing eutrophication for one lake are often unsuccessful when applied to another. Simple empirical relationships are often used to predict the impact of management decisions. Errors in estimation could result in either substantial costs for overdesign or failure to meet desired eutrophication levels. This paper presents and illustrates a methodology to evaluate the impact of land use and water resource management decisions on lake eutrophication. The problems of worth of additional information, and uncertainty of estimates were handled within a cost-effectiveness framework. The probability of exceeding a critical level of eutrophication was considered as a measure of effectiveness. The cost criterion is the expected value of opportunity costs, costs of analysis and costs of additional information. Uncertainty analysis techniques were used to estimate the effectiveness of various management alternatives. Bayesian methods can be utilized to determine the worth of additional information. The methodology was applied to Beseck Lake, Connecticut, and the cost and effectiveness measures estimated for a number of land management alternatives. Worth of additional information was not determined in this initial effort in uncertainty analysis for lake eutrophication management.     

THE USE OF A SIMPLE MODEL AND UNCERTAINTY ANALYSIS IN LAKE MANAGEMENT1

ABSTRACT: A simple, black-box lake model was developed for phosphorus, using nonlinear regression analysis on a data base of north temperate lakes. The uncertainty associated with the model was then combined with the parameter uncertainty and the independent variable uncertainty to provide an estimate of the confidence limits associated with a predicted value. The prediction uncertainty is often neglected, yet it is an important measure of the usefulness of a model. Prediction uncertainty reflects the modeler's confidence in the model, and it should be used by a decision maker as a weight indicating the value of the model prediction. A procedure is outlined that combined lake modeling and uncertainty analysis for use in lake quality assessment and lake management. An example is provided illustrating the use of this procedure in nutrient budget sampling design, data analysis, and the evaluation of lake management strategies for a 208 program in New Hampshire.     

PARAMETER UNCERTAINTY IN RAINFALL-RUNOFF MODELING FOR POLDER SYSTEM DESIGN1

ABSTRACT: An approach is developed for incorporating the uncertainty of parameters for estimating runoff in the design of polder systems in ungaged watersheds. Monte Carlo Simulation is used to derive a set of realizations of streamflow hydrographs for a given design rainstorm using the U. S. Soil Conservation Service (SCS) unit hydrograph model. The inverse of the SCS curve number, which is a function of the antecedent runoff condition in the SCS model, is the random input in the Monte Carlo Simulation. Monte Carlo realizations of streamfiow hydrographs are used to simulate the performance of a polder flood protection system. From this simulation the probability of occurrence of flood levels for a particular hydraulic design may be used to evaluate its effectiveness. This approach is demonstrated for the Pluit Polder flood protection system for the City of Jakarta, Indonesia. While the results of the application indicate that uncertainty in the antecedent runoff condition is important, the effects of uncertainty in rainfall data, in additional runoff parameters, such as time to peak, in the hydraulic design, and in the rainfall-runoff model selected should also be considered. Although, the SCS model is limited to agricultural conditions, the approach presented herein may be applied to other flood control systems if appropriate storm runoff models are selected.     

PARAMETER ESTIMATION IN HYDROLOGY: THE STATE OF THE ART1

ABSTRACT A detailed review of current methods and criteria used in parameter estimation in hydrology is presented. The effect of errors in the data set and the effect of interactions between methods of analysis, criteria, data set errors, and modeling assumptions are reviewed and discussed briefly. It is concluded that study of techniques, criteria, data set errors and particularly interactions between these, is essential to further progress in hydrologic modeling.     

METHODOLOGIES FOR CALIBRATION AND PREDICTIVE ANALYSIS OF A WATERSHED MODEL1

ABSTRACT: The use of a fitted parameter watershed model to address water quantity and quality management issues requires that it be calibrated under a wide range of hydrologic conditions. However, rarely does model calibration result in a unique parameter set. Parameter nonuniqueness can lead to predictive nonuniqueness. The extent of model predictive uncertainty should be investigated if management decisions are to be based on model projections. Using models built for four neighboring watersheds in the Neuse River Basin of North Carolina, the application of the automated parameter optimization software PEST in conjunction with the Hydrologic Simulation Program Fortran (HSPF) is demonstrated. Parameter nonuniqueness is illustrated, and a method is presented for calculating many different sets of parameters, all of which acceptably calibrate a watershed model. A regularization methodology is discussed in which models for similar watersheds can be calibrated simultaneously. Using this method, parameter differences between watershed models can be minimized while maintaining fit between model outputs and field observations. In recognition of the fact that parameter nonuniqueness and predictive uncertainty are inherent to the modeling process, PEST's nonlinear predictive analysis functionality is then used to explore the extent of model predictive uncertainty.     

PERIODIC AUTOREGRESSIVE-MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES1

Results involving correlation properties and parameter estimation for autoregressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.     

A FRAMEWORK FOR PHOSPHORUS TRANSPORT MODELING IN THE LAKE OKEECHOBEE WATERSHED1

ABSTRACT: A modeling framework was developed to determine phosphorus loadings to Lake Okeechobee from watersheds located north of the lake. This framework consists of the land-based model CREAMS-WT, the in-stream transport model QUAL2E, and an interface procedure to format the land-based model output for use by the in-stream model. QUAL2E hydraulics and water quality routines were modified to account for flow routing and phosphorus retention in both wetlands and stream channels. Phosphorus loadings obtained from previous applications of CREAMS-WT were used by QUAL2E, and calibration and verification showed that QUAL2E accurately simulated seasonal and annual phosphorus loadings from a watershed. Sensitivity and uncertainty analyses indicated that the accuracy of monthly loadings can be improved by using better estimates of in-stream phosphorus decay rates, ground water phosphorus concentrations, and runoff phosphorus concentrations as input to QUAL2E.     

ASSESSMENT OF NUTRIENT EFFECTS AND NUTRIENT LIMITATION IN LAKE OKEECHOBEE1

ABSTRACT: Lake Okeechobee, the third largest lake in the United States, is a shallow, mixing basin with annual total phosphorus concentrations ranging from 50–100 μg P/L. Data, mainly from unpublished agency reports, are analyzed to determine if nutrients limit phytoplankton, to describe spatial and temporal variability in trophic state parameters, and to evaluate conclusions obtained from empirical trophic state models. Algal bioassay experiments that have been used to assess nutrient limitation have produced equivocal results. However, seasonal minima in orthophosphorus and inorganic nitrogen indicate that both nutrients may be limiting seasonally. Strong, but reverse north-south gradients and large seasonal changes in phosphorus and nitrogen concentrations, show that empirical models based on annual phosphorus loadings or concentrations are not adequate to predict chlorophyll concentrations or other trophic state variables. Spatially-segmented, multi-class phytoplankton-nutrient models of seasonal phytoplankton responses that are coupled with hydrodynamic models may provide predictability in assessing effects of changing nutrient loads on phytoplankton composition and standing crop. Successful modeling efforts of responses to nutrients also must deal with resuspended and benthic algae, periphyton, and emergent and submergent aquatic plants that must play important trophic roles in some of the lake basin.     

APPLICATION OF PARAMETER OPTIMIZATION METHOD FOR CALIBRATING TANK MODEL1

ABSTRACT: Many automatic calibration processes have been proposed to efficiently calibrate the 16 parameters involved in the four‐layered tank model. The Multistart Powell and Stuffed Complex Evolution (SCE) methods are considered the best two procedures. Two rainfall events were designed to compare the performance and efficiency of these two methods. The first rainfall event is short term and the second designed for long term rainfall data collection. Both rainfall events include a lengthy no‐rainfall period. Two sets of upper and lower values for the search range were selected for the numerical tests. The results show that the Multistart Powell and SCE methods are able to obtain the true values for the 16 parameters with a sufficiently long no‐rainfall period after a rainfall event. In addition, by using two selected objective functions, one based on root mean square error and one based on root mean square relative error criteria, it is found that the no‐rainfall period lengths necessary to obtain the converged true values for the 16 parameters are roughly the same. The SCE method provides a more efficient search based on an appropriate preliminary search range. The Multistart Powell method, on the other hand, leads to more accurate search results when there is no suitable search range selected based on the parameter calibration experience.     

WATERSHED AND LAKE WATER QUALITY ASSESSMENT: AN INTEGRATED MODELING APPROACH1

Watershed planning groups and action agencies seek to understand how lake water quality responds to changes in watershed management. This study developed and demonstrated the applicability of an integrated modeling approach for providing this information. An integrated model linking watershed conditions to water-quality of the receiving lake incorporated the following components: (1) an event-based AGNPS model to estimate watershed pollutant losses; (2) annualization of AGNPS results to produce annual lake pollutant loadings; (3) a base flow separation package, SAM, to estimate base flow; (4) estimates of nutrients in base flow and point sources; and (5) linkage of watershed loadings directly to EUTROMOD lake water quality algorithms. Results are presented for Melvern Lake, a 28-km² multipurpose reservoir with a 900-km² agricultural watershed in east central Kansas. Reasonable estimates of current lake quality were attained using an average phosphorus availability factor of 31 percent to calibrate model results to measured in-lake phosphorus. Comparison of a range of possible scenarios, including all cropland changed to no-till (best case) and all CRP and good-condition grasslands changed to cropland (worst case), indicated only a (4 percent change for in-lake phosphorus and a (2 percent change for chlorophyll a. These results indicated that this watershed is not sensitive to projected changes in land use and management.     

INPUT/OUTPUT MODELS AS DECISION AIDS FOR LAKE RESTORATION1

ABSTRACT: Over the past several years, input/output models have been used increasingly as decisionmaking aids in the design of lake restoration activities because they provide an approximation of the link between nutrient influx and lake trophic status. To evaluate the applicability of these models as design tools, a study was conducted in which “before” and “after” data were obtained for 25 lakes which experienced reductions in nutrient inflow, and comparisons were made of observed and predicted changes in lake conditions. Three input/output models were used as predictive tools to describe lake response: those reported by Dillon and Rigler (1974) and by Vollenweider (1975, 1976). Based on described trophic states of oligotrophic, mesotrophic, and eutrophic, it was found that all three models yielded accurate predictions for at least 70 percent of the study lakes. The model of Vollenweider (1976) performed slightly better than the other two (80 percent correct) on the data set studied.     

INTEGRATION OF WATER QUALITY MODELING,REMOTE SENSING,AND GIS1

ABSTRACT: Water quality modeling has been developed for more than three quarters of a century, but is limited to the study of trends instead of making accurate short-term forecasts. A major barrier to water quality forecasting is the lack of an efficient system for water quality monitoring. Traditional water quality sampling is time-consuming, expensive, and can only be taken for small sizes. Remote sensing provides a new technique to monitor water quality repetitively for a large area. The objective of this research is to use remotely sensed data in a water quality model - QUAL2E - in a case study of the Te-Chi Reservoir in Taiwan. The water quality variables developed from the simulations are displayed in map form. The developed forecasting system is designed to predict water quality variables using remote sensing data as an input to initialize and update water quality conditions.     

ACCURACY AND RELIABILITY OF NUMERICAL RIVER MODELS1

ABSTRACT: Over the last 20 years, our possibilities to model river flows numerically have increased enormously. In this paper, the question is addressed whether a more sophisticated model is always better than a simpler one. Increased detail, both in finer resolution and in physical processes taken into account, has its price in more computer time, higher data need, and perhaps more unknown coefficients to be calibrated. Moreover, uncertainty in actual physical conditions (e.g., bottom roughness), inflow and parameters remains, which may dominate the uncertainty of the results. Also, the questions asked by a decision maker may not always be very precise. For a schematic but relevant example, we show that a better model does not necessarily give more reliable results because some of the basic uncertainties remain. It is concluded that we should use the simplest model that will answer the question as to the accuracy needed, taking into account uncertainties in the data     

NONLINEAR MODELING AND PREDICTION OF A RIVER FLOW SYSTEM1

ABSTRACT: Model estimation and prediction of a river flow system are investigated using nonlinear system identification techniques. We demonstrate how the dynamics of the system, rainfall, and river flow can be modeled using NARMAX (Nonlinear Autoregressive Moving Average with eXogenuous input) models. The parameters of the model are estimated using an orthogonal least squares algorithm with intelligent structure detection. The identification of the nonlinear model is described to represent the relationship between local rainfall and river flow at Enoree station (inputs) and river flow at Whitmire (output) for a river flow system in South Carolina.     

APPLICATION OF COMPUTER INTENSIVE STATISTICS TO PARAMETER UNCERTAINTY IN STREAMFLOW SYNTHESIS1

ABSTRACT: This paper introduces the application of Computer Intensive Statistics (CIS) to the evaluation of parameter uncertainty with specific reference to the parameters in the ARMA models used in the synthesis of streamflows. The CIS provides an empirically derived joint distribution for all parameters. Random values from this distribution can be drawn for application in the model for the generation of a specific synthetic sample. The CIS originally proposed by Efron and discussed herein is of general applicability in the evaluation of uncertainty in any statistic derived from a set of data. Some comments and limitations of the CIS are discussed in the concluding remarks.     

LAKE RESTORATION BY SEDIMENT REMOVAL1

ABSTRACT: Fresh water lake sediment removal is usually undertaken to deepen a lake and increase its volume to enhance fish production, to remove nutrient rich sediment, to remove toxic or hazardous material, or to reduce the abundance of rooted aquatic plants. Review of more than 60 projects and five case histories reveals that the first three objectives are usually met through sediment removal. Dredging to control aquatic plants has not been well documented. Disadvantages of dredging include cost, temporary phosphorus release from sediment, increased phytoplankton productivity, noise, lake drawdown, temporary reduction in benthic fish food organisms, the potential for toxic material release to the overlying water and potential for environmental degradation at the dredged material disposal site. The technique is recommended for deepening and for long range reduction of phosphorus release from sediment. Sediment removal to control toxic materials is possible with minimal environmental impact when proper equipment is used, but it may more than double the cost. Lack of definitive information about rooted plant regrowth rates in dredged areas prohibits explicit recommendations on sediment removal to control plant growth.     

A STATISTICAL MODEL FOR SMALL LAKE WATER QUALITY MANAGEMENT1

ABSTRACT: Phosphorus loading tolerances of small lakes are analyzed by means of a statistical model of lake eutrophication based upon the work of Vollenweider and Dillon. Using a sample of 195 midwestern and eastern U. S. lakes, it was found that Vollenweider and Dillon's method of predicting the trophic status of relatively deep, slow-flushing lakes can be applied to shallower lakes with much shorter retention times. The statistical model used to replicate the results of Vollenweider and Dillon is stated in detail, for convenience of application to small lake water quality management problems. The model extends the Vollenweider and Dillon results by associating each alternative phosphorous loading with a probability that a given lake can achieve or maintain noneutrophis status. It is applicable to lakes for which only minimal data are available. The major policy conclusion is that the highly variable tolerance for phosphorus loading must be considered in legislating efficient effluent limitations. The paper concludes with a comparison to a recent contribution employing a similar approach.     

CHANGE IN LAKE TROPHIC STATE AND INTERNAL PHOSPHORUS RELEASE AFTER ALUMINUM SULFATE APPLICATION1

ABSTRACT: Recovery of eutrophic lakes after nutrient diversion may be delayed if the lake experiences significant internal phosphorus (p) loading to the water column. A maximum dose of aluminum sulfate, defined herein, was applied to the anaerobic sediments of the hypolimnia of two dimictic Ohio lakes following septic tank diversion, with the objective of attaining long term control of the release of phosphorus to the water column from these sediments. The results were compared to a similar, downstream, untreated lake. Total phosphorus concentration declined sharply after treatment and has remained so through 1980 for both lakes, a period of 5 and 6 years of control, respectively. Internal P loading from anaerobic, hypolimnetic sediments was partially controlled by the treatment but there are other important sources, perhaps in the littoral zone, in these lakes. Algal biomass is Smaller and water transparency has increased. Both lakes became mesotrophic after treatment, as described by the Carlson (1977) trophic state index, and remain in that improved condition to date. No deleterious side effects were observed, although one lake experienced a significant decrease in diversity of planktonic microcrustacea and a lakeward extension of the macrophyte community. This method appears to be an effective and lasting means of accelerating the recovery of a eutrophic lake following nutrient diversion.     

LAKE QUALITY DISCRIMINANT ANALYSIS1

ABSTRACT: Despite the fact that lake phosphorus loading criteria have proven to be valuable tools in lake management, they are generally subjective in nature or incomplete in form. In order to address these shortcomings, the oxic-anoxic transition point was selected as an objective quality criterion and discriminant analysis was used to construct a lake classification function. This function is dependent upon lake phosphorus loading, mean depth, and overflow rate. The value of the function may be expressed as a probability of classification (as either oxic or anoxic). When used in prediction, inclusion of the input error permits the estimation of the change in classification probability as input uncertainty is reduced. Further, the form of the discriminant function suggests that the annual volumetric loading is a more informative term for the expression of phosphorus loading than is the annual areal loading.