APPLICATION OF GREY MODEL AND ARTIFICIAL NEURAL NETWORKS TO FLOOD FORECASTING1

The main focus of this study was to compare the Grey model and several artificial neural network (ANN) models for real time flood forecasting, including a comparison of the models for various lead times (ranging from one to six hours). For hydrological applications, the Grey model has the advantage that it can easily be used in forecasting without assuming that forecast storm events exhibit the same stochastic characteristics as the storm events themselves. The major advantage of an ANN in rainfall‐runoff modeling is that there is no requirement for any prior assumptions regarding the processes involved. The Grey model and three ANN models were applied to a 2,509 km² watershed in the Republic of Korea to compare the results for real time flood forecasting with from one to six hours of lead time. The fifth‐order Grey model and the ANN models with the optimal network architectures, represented by ANN1004 (34 input nodes, 21 hidden nodes, and 1 output node), ANN1010 (40 input nodes, 25 hidden nodes, and 1 output node), and ANN1004T (14 input nodes, 21 hidden nodes, and 1 output node), were adopted to evaluate the effects of time lags and differences between area mean and point rainfall. The Grey model and the ANN models, which provided reliable forecasts with one to six hours of lead time, were calibrated and their datasets validated. The results showed that the Grey model and the ANN1010 model achieved the highest level of performance in forecasting runoff for one to six lead hours. The ANN model architectures (ANN1004 and ANN1010) that used point rainfall data performed better than the model that used mean rainfall data (ANN1004T) in the real time forecasting. The selected models thus appear to be a useful tool for flood forecasting in Korea.     

GENETIC PROGRAMMING AND ITS APPLICATION IN REAL‐TIME RUNOFF FORECASTING1

ABSTRACT: Genetic programming (GP), a relatively new evolutionary technique, is demonstrated in this study to evolve codes for the solution of problems. First, a simple example in the area of symbolic regression is considered. GP is then applied to real‐time runoff forecasting for the Orgeval catchment in France. In this study, GP functions as an error updating scheme to complement a rainfall‐runoff model, MIKE11/NAM. Hourly runoff forecasts of different updating intervals are performed for forecast horizons of up to nine hours. The results show that the proposed updating scheme is able to predict the runoff quite accurately for all updating intervals considered and particularly for updating intervals not exceeding the time of concentration of the catchment. The results are also compared with those of an earlier study, by the World Meteorological Organization, in which autoregression and Kalman filter were used as the updating methods. Comparisons show that GP is a better updating tool for real‐time flow forecasting. Another important finding from this study is that nondimensionalizing the variables enhances the symbolic regression process significantly.     

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.     

THE IMPORTANCE OF ACCURATE CURVE NUMBERS IN THE ESTIMATION OF STORM RUNOFF1

ABSTRACT: Storm runoff as calculated by the runoff curve number method is shown to be of varying sensitivity to both input rainfall and curve number. Using an assumed input error of 10%, a runoff error chart is given. Up to about 9 inches of rainfall, runoff is more sensitive to curve number than to rainfall. The importance of accurate curve number selection in this range is stressed.     

A QUASI-LINEAR SPATIALLY DISTRIBUTED CELL MODEL FOR THE SURFACE RUNOFF SYSTEM1

ABSTRACT: The paper presents a spatially distributed model consisting of cells that are interconnected in a pattern similar to the major drainage network of the watershed. Each cell receives as input the rainfall excess for the area represented by the cell as well as inflows from cells located upstream. Outflow from the cell is derived by routing the total input through the cell assuming it to be a linear reservoir during the storm. The time constant of the cells is however allowed to vary from storm to storm so that the model may be described as a quasi-linear model. The model was tested with rainfall excess and direct surface runoff data available for a medium size watershed with satisfactory results. The time constant was found to be related to the rainfall excess of the storms studied, its value decreasing with the increase in the total rainfall excess.     

AN APPLICATION RUNOFF MODEL STRATEGY FOR UNGAGED WATERSHEDS1

ABSTRACT: Mathematical models for predicting watershed surface flow responses are available, most of which are elaborate nonlinear numerical surface and channel flow models linked with infiltration models. Such models may be used to make predictions for ungaged areas, assuming an acceptable fitting of the model to the topography and roughness of the real system. For some application purposes, these models are impractical because of their complexity and expensive computer solutions. A procedure is developed that uses a complex model of an ungaged area to derive a simpler parametric nonlinear system model for repetitious simulation with input sequences. The predicted flow outputs are obtained with the simpler model at significant savings of money and time. The procedures for constructing a complex kinematic model of a 40 acre (161,880 m²) reference watershed and deriving the simpler system model are outlined. The results of predictions from both models are compared with a selected set of measured events, all having essentially the same initial conditions. Peak discharges ranged from 3 to 118 ft³/sec (0.085 to 3.34 m³/sec), which includes the largest event of record. The inherent limitations of lumped systems models are demonstrated, including the bias caused by their inability to model infiltration losses after rainfall ceases. Computer costs and times for the models were compared. The derived simple model has a cost advantage when repeated use of a model is required. Such an applications hydrologic model has an engineering tradeoff of reduced accuracy, and lumping bias, but is more economical for certain design purposes.     

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.     

EFFECTS OF STORM PATTERNS ON RUNOFF HYDROGRAPHS1

ABSTRACT: As an alternative to the conventional single-peak design storms commonly used in hydrologic practice, a large number of Southeastern Pennsylvania storm events were selected from hourly U.S. National Oceanographic and Atmospheric Administration (NOAA) records, and their temporal distributions were analyzed. From these recorded events, design storms of a typical distribution were developed for storm durations between 6 and 18 hours. All of these generated design storms have two or more peaks. The conventional single peak as well as the “typical” multi-peak storms were then applied to a simulated watershed. It was found that the multi-peak storms consistently produced more dispersed hydrographs with lower runoff peaks than the conventional single peak storms.     

APPLICATION OF DIFFUSIVE TANK MODEL IN DRAINAGE ANALYSIS OF PADDY FIELDS1

ABSTRACT: A diffusive tank model has been successfully applied to the simulation of runoff from paddy fields in Japan because it can well describe the features of local water flows. The main goal of the study is to evaluate the performance of the diffusive tank model with the calibrated parameters obtained in Jyau‐Shi to simulate discharge from paddy fields in two experimental catchments located in the areas of Shing‐Ying and Ta‐Liao, Southwestern Taiwan. The simulations were verified by comparing the model results with observed runoff data from the two experimental catchments. The model predicted the discharge from the paddy fields well. This indicates that the model with the calibrated parameters may be used in other paddy fields in Taiwan.     

A PARAMETRIC MODEL CALIBRATED WITH A PHYSICALLY BASED MODEL FOR RUNOFF PREDICTION FROM UNGAGED STREAMS1

ABSTRACT: Recent developments in the numerical solution of the governing partial differential equations for overland and channel flow should make possible physically based models which predict runoff from ungaged streams. However, these models, which represent the watershed by sets of intersecting planes, are complex and require much computer time. Parametric models exist that have the advantage of being relatively simple, and once calibrated are inexpensive to use and require limited data input. In this study, a procedure was developed for calibrating a parametric model against a physically based model, utilizing base areas of one acre and one square mile, with the expectation that base areas can be combined to model real watersheds. Simulation experiments with the physically based model showed that, for the one-acre base area, the dominant parameter (cell storage ratio, K) related to the slope and friction of the planes, whereas for one square-mile areas, the dominant parameters (K plus a lag factor, L) relate to channel properties. These parameters decreased exponentially as rainfall intensity increased.     

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.     

APPLICATION OF THE SNOWMELT RUNOFF MODEL USING MULTIPLE-PARAMETER LANDSCAPE ZONES ON THE TOWANDA CREEK BASIN,PENNSYLVANIA1

ABSTRACT: The Snowmelt Runoff Model (SRM) is designed to compute daily stream discharge using satellite snow cover data for a basin divided into elevation zones. For the Towanda Creek basin, a Pennsylvania watershed with relatively little relief, analysis of snow cover images revealed that both elevation and land use affected snow accumulation and melt on the landscape. The distribution of slope and aspect on the watershed was also considered; however, these landscape features were not well correlated with the available snow cover data. SRM streamflow predictions for 1990, 1993 and 1994 snowmelt seasons for the Towanda Creek basin using a combination of elevation and land use zones yielded more precise streamflow estimates than the use of standard elevation zones alone. The use of multiple-parameter zones worked best in non-rain-on-snow conditions such as in 1990 and 1994 seasons where melt was primarily driven by differences in solar radiation. For seasons with major rain-on-snow events such as 1993, only modest improvements were shown since melt was dominated by rainfall energy inputs, condensation and sensible heat convection. Availability of GIS coverages containing satellite snow cover data and other landscape attributes should permit similar reformulation of multiple-parameter watershed zones and improved SRM streamflow predictions on other basins.     

VERIFICATION AND APPLICATION OF REGIONAL EQUATIONS FOR THE STORAGE FUNCTION RUNOFF MODEL1

The storage function model is a nonlinear rainfall-runoff model that has been developed for and applied to flood runoff analysis in Japan. This paper extends the model applicability by developing practical equations for estimating model parameters which are appropriate on a regional basis, i.e., so-called regional equations. Previously, the parameters were computed from historical data for a specific basin or from relationships that do not account for land use and topography. To develop the regionalized equations, model parameters were identified for 91 flood events from 22 watersheds in Japan by applying a mathematical optimization technique. Results from 39 of these events were statistically compared and regional relationships were determined as a function of land use, basin area and rainfall intensity. The utility of the estimated equations were tested by computing runoff hydrographs for lumped basins. The estimated parameters were also applied in a distributed watershed model formulation. Both applications showed acceptable results that validate the use of the regionalized relationships.     

QUALITY OF RUNOFF FROM PLOTS WITH SIMULATED GRAZING1

ABSTRACT: Grazed pastures represent a potential source of non‐point pollution. In comparison to other nonpoint sources (e.g., row‐cropped lands), relatively little information exists regarding possible magnitudes of nutrient losses from grazed pasture, how those losses are affected by management variables, and how the losses can be minimized. The objective of this study was to measure concentrations of nitrogen (N), phosphorus (P), and solids in runoff from fescue plots and relate those measurements to simulated forage management strategy. The study was conducted at the University of Kentucky Maine Chance Agricultural Experiment Station north of Lexington. Plots (2.4 m wide by 6.1 m long) were constructed and established in Kentucky 31 fescue (Festuca arundinacea Schreb.) to represent pasture. The experimental treatments applied to the plots varied in terms of forage height and material applied (none, manure, or manure and urine). Runoff was sampled for six simulated rainfall events applied over the summer of 1997 and analyzed for nitrate N (NO₃‐N), ammonia N (NH3‐N), total Kjeldahl N (TKN), ortho‐P (PO₄‐P), total P (TP), and total suspended solids (TSS). All runoff constituents exhibited dependence on the date of simulated rainfall with generally higher concentrations measured when simulated rainfall followed relatively dry periods. The effects of forage height and manure addition were mixed. Highest runoff N concentrations were associated with the greatest forage heights, whereas highest P concentrations occurred for the least forage heights. Manure/urine addition increased runoff P concentrations relative to controls (no manure/urine) for both the greatest and least forage heights, but runoff N concentrations were increased only for the greatest forage heights. These findings indicate that runoff of N and P is at least as sensitive to amount and proximity of preceding rainfall and suggest that managing forage to stimulate growth and plant uptake can reduce runoff of N.     

FORECASTING URBAN WATER USE: THE IWR-MAIN MODEL1

ABSTRACT: In the current forecasting practice, future water requirements of a growing urban area are often represented as the product of the number of people to be served by the water system and an assumed quantity of gross per capita water use. This paper describes a forecasting approach that differs from the per capita method in two important aspects. First, it disaggregates urban water use into a large number of categories, each consisting of a relatively homogeneous group of water users. Second, it links water use in each category to factors that determine both the need for water as well as the intensity of water use. This approach is incorporated into a computerized forecasting system referred to as IWR-MAIN. The advantages of the IWR.MAIN model over the traditional per capita method are illustrated in a case study of Anaheim, California.     

APPLICATION OF SCS INFILTRATION MODEL1

ABSTRACT: The SCS infiltration model was applied to the Ralston Creek watershed in eastern Iowa. The criteria to determine the various model parameters were revised to obtain a better agreement between the observed and computed total runoffs. A procedure to calibrate the infiltration model is presented. The infiltration model was used in conjunction with an overland flow model to develop flood hydrographs. The results indicate that SCS infiltration model adequately describe the distribution of losses.     

CONTRIBUTIONS OF RAINFALL TO CONSTITUENT LOADS IN STORM RUNOFF FROM URBAN CATCHMENTS1

ABSTRACT: Rainfall is a significant source of some constituents, particularly nitrogen species, in storm runoff from urban catchments. Median contributions of rainfall to storm runoff loads of 12 constituents from 31 urban catchments, representing eight geographic locations within the United States, ranged from 2 percent for suspended solids to 74 percent for total nitrite plus nitrate nitrogen. The median contribution of total nitrogen in rainfall to runoff loads was 41 percent. Median contributions of total-recoverable lead in rainfall to runoff loads varied by as much as an order of magnitude between catchments in the same geographic location. This indicates that average estimates of rainfall contributions to constituent loading in storm runoff may not be suitable in studies requiring accurate constituent mass-balance computations.     

AN EVALUATION OF FLOOD FREQUENCY ESTIMATES BASED ON RAINFALL/RUNOFF MODELING1

ABSTRACT: An evaluation of flood frequency estimates simulated from a rainfall/runoff model is based on (1) computation of the equivalent years of record for regional estimating equations based on 50 small stream sites in Oklahoma and (2) computation of the bias for synthetic flood estimates as compared to observed estimates at 97 small stream sites with at least 20 years of record in eight eastern states. Because of the high intercorrelation of synthetic flood estimates between watersheds, little or no regional (spatial) information may be added to the network as a result of the modeling activity. The equivalent years of record for the regional estimating equations based totally on synthetic flood discharges is shown to be considerably less than the length of rainfall record used to simulate the runoff. Furthermore, the flood estimates from the rainfall/runoff model consistently underestimate the flood discharges based on observed record, particularly for the larger floods. Depending on the way bias is computed, the synthetic estimate of the 100-year flood discharge varies from 11 to 29 percent less than the value based on observed record. In addition, the correlation between observed and synthetic flood frequency estimates at the same site is also investigated. The degree of correlation between these estimates appears to vary with recurrence interval. Unless the correlation between these two estimates is known, it is not possible to compute a weighted estimate with minimum variance.     

THE VALUE OF STREAMFLOW FORECASTING IN RESERVOIR OPERATION1

ABSTRACT: The value of streamflow forecasts in reservoir operation depends on a number of factors and may vary considerably. Assessment of forecast benefits is presented here for three specific systems. Statistical streamflow models of increasing forecasting ability are coupled with a recently developed stochastic control method in extensive simulation experiments. The performance of the system is statisticafly evaluated with regard to energy generation and flood and drought prevention. The results indicate that forecast benefits are system specific and may range from quite substantial to fairly minimal.