STOCHASTIC ANALYSIS OF TIME-AGGREGATED HYDROLOGIC DATA1

Stochastic models fitted to hydrologic data of different time scales are interrelated because the higher time scale data (aggregated data) are derived from those of lower time scale. Relationships between the statistical properties and parameters of models of aggregated data and of original data are examined in this paper. It is also shown that the aggregated data can be more accurately predicted by using a valid model of the original data than by using a valid model of the aggregated data. This property is particularly important in forecasting annual values because only a few annual values are usually available and the resulting forecasts are relatively inaccurate if models based only on annual data are used. The relationships and forecasting equations are developed for general aggregation time and can be used for hourly and daily, daily and monthly or monthly and yearly data. The method is illustrated by using monthly and yearly streamflow data. The results indicate that various statistical characteristics and parameters of the model of annual data can be accurately estimated by using the monthly data and forecasts of annual data by using monthly models have smaller one step ahead mean square error than those obtained by using annual data models.     

Utility of Gridded Rainfall for IHACRES Daily River Flow Predictions in Southern California Watersheds1

Abstract: Studies to regionalize conceptual hydrologic models generally require rainfall and river flow data from multiple watersheds. Besides the considerable time (cost) to assemble and process rainfall data for many watersheds, investigators often need to choose from a number of candidate gauges, subjectively weighing the relative importance of proximity and elevation to select a representative rainfall dataset. The Unified Raingauge Dataset (URD) is a gridded daily rainfall dataset that covers the conterminous United States at 0.25 × 0.25 degrees spatial resolution and is available from 1948 to present. The objective of this study was to determine whether uncertainty in daily river flow predictions using the conceptual hydrologic model IHACRES in small to moderate size watersheds (50‐400 km²) in southern California would increase if URD gridded rainfall data were used in place of single rain gauge data to calibrate the model. Rain gauge data were obtained from the gauge nearest the watershed centroid and the gauge closest in elevation to the watershed mean elevation. Results from 20 randomly selected watersheds indicated that IHACRES calibration performance was similar using rainfall data from the URD grids and rain gauge data. There was some evidence of greater uncertainties associated with the URD calibrations in areas where topography may affect rainfall amounts. In contrast to the URD data, monthly gridded data produced by the Parameter‐Elevation Regressions on Independent Slopes Model (PRISM) includes adjustments for elevation and produces gridded values at a finer spatial resolution (4 km²). A limited test on two watersheds demonstrated that scaling the URD daily rainfall estimates to match the PRISM monthly values may improve rainfall estimates and model simulation performance.     

GENERALIZED WATERSHED LOADING FUNCTIONS FOR STREAM FLOW NUTRIENTS1

ABSTRACT: Loading functions are proposed as a general model for estimating monthly nitrogen and phosphorus fluxes in stream flow. The functions have a simple mathematical structure, describe a wide range of rural and urban nonpoint sources, and couple surface runoff and ground water discharge. Rural runoff loads are computed from daily runoff and erosion and monthly sediment yield calculations. Urban runoff loads are based on daily nutrient accumulation rates and exponential wash off functions. Ground water discharge is determined by lumped parameter unsaturated and saturated zone soil moisture balances. Default values for model chemical parameters were estimated from literature values. Validation studies over a three-year period for an 850 km² watershed showed that the loading functions explained at least 90 percent of the observed monthly variation in dissolved and total nitrogen and phosphorus fluxes in stream flow. Errors in model predictions of mean monthly fluxes were: dissolved phosphorus - 4 percent; total phosphorus - 2 percent; dissolved nitrogen - 18 percent; and total nitrogen - 28 percent. These results were obtained without model calibration.     

COMPARISON OF TWO AUTOREGRESSIVE MODELS FOR MONTHLY STREAM FLOW GENERATION1

ABSTRACT: Two autoregressive models for monthly stream flow generation are compared based on the reproduction of the historical record in terms of several important statistics such as the mean, standard deviation, skewness coefficient, correlation coefficient, and the reservoir storage components. In the comparison, both theoretical considerations and practical applications are employed to evaluate the performance of each model.     

SEQUENTIAL GENERATION OF STREAMFLOW1

ABSTRACT: An auto-regressive model has been developed for hydrologic data simulation. The model is computationally easier, parsimonious in number of model parameters and more stable in statistical characteristics than the existing auto-regressive model. The proposed model was used for synthesizing 10 sequences, each of 100 year length, of monthly flows for the river Beas. The statistical parameters were calculated using 49-year historical record for the river. The data was also synthesized using existing auot-regressive model. The synthesized sequences have been compared. The results indicate that the proposed model is as good as the existing auto-regressive model in preserving the mean and standard deviation of historical record. It is further shown that the proposed model requires less parameters than the auto-regressive model for simulation of long-term dependence.     

AN EVALUATION OF WEEKLY AND MONTHLY TIME SERIES FORECASTS OF MUNICIPAL WATER USE1

ABSTRACT: A cascade model for forecasting municipal water use one week or one month ahead, conditioned on rainfall estimates, is presented and evaluated. The model comprises four components: long term trend, seasonal cycle, autocorrelation and correlation with rainfall. The increased forecast accuracy obtained by the addition of each component is evaluated. The City of Deerfield Beach, Florida, is used as the application example with the calibration period from 1976–1980 and the forecast period the drought year of 1981. Forecast accuracy is measured by the average absolute relative error (AARE, the average absolute value of the difference between actual and forecasted use, divided by the actual use). A benchmark forecast is calculated by assuming that water use for a given week or month in 1981 is the same as the average for the corresponding period from 1976 to 1980. This method produces an AARE of 14.6 percent for one step ahead forecasts of monthly data and 15.8 percent for weekly data. A cascade model using trend, seasonality and autocorrelation produces forecasts with AARE of about 12 percent for both monthly and weekly data while adding a linear relationship of water use and rainfall reduces the AARE to 8 percent in both cases if it is assumed that rainfall is known during the forecast period. Simple rainfall predictions do not increase the forecast accuracy for water use so the major utility of relating water use and rainfall lies in forecasting various possible water use sequences conditioned on sequences of historical rainfall data.     

APPLICATION OF THE HEC-4 MONTHLY STREAM FLOW SIMULATION MODEL1

ABSTRACT: The HEC-4 monthly stream flow simulation model, developed by the Hydrologic Engineering Center, Davis, California, is used to extend the available historical stream flow records in the Central Ohio area. The principal objective of this paper is to examine the effectiveness of the HEC-4 model in generating synthetic monthly flows. Important statistical parameters are evaluated in order to relate the statistical properties of the historical and generated flows. In doing so, it is observed that the mean, standard deviation, and skewness of the generated flows are consistently larger than the corresponding estimates based on historical flows. However, results show that these statistics, as well as the lag-1 serial correlation, are generally well maintained by the generated sequences. The degree to which any statistical dissimilarities would be critical, from an engineering design point of view, is demonstrated by utilizing their low flow characteristics. Estimates of reservoir safe-yields, based on a nonsequential mass-curve analysis of the historical and generated low flows, indicate a nominal difference in this particular study.     

A COMPARISON OF STREAMFLOW GENERATION MODELS FOR RESERVOIR CAPACITY-YIELD ANALYSIS1

ABSTRACT: An analysis of four streamflow generation schemes for the use in the estimation of the required conservation storage for a single reservoir is presented. The comparison of the generating schemes should aid in the selection of an appropriate model type for the reservoir sizing problem. The streamflow generation models are compared using two criteria. The first comparison is between the statistics of the generated streamflow sequences and the corresponding statistics from the historical record. The second evaluation compares the median reservoir size determined by each model with the required storage based on the historical flow sequence. The results of a comparative analysis for monthly streamflow data for the Rzav River in Yugoslavia are presented and discussed. The results indicate that both evaluation criteria are required to discriminate between the various options.     

GENERATING STREAMFLOW SEQUENCES WITH TREND AND CYCLICAL MOVEMENTS1

ABSTRACT: A first-order autoregressive model had been modified with the trend and cyclical movements to generate the streamflow sequences. Three main portions were involved in this modified model, i.e., six-year cycle with trend changing; six-year cycle without trend changing; and both annual and six-year cycles with trend changing. The synthetic sequences of monthly streamflow sequences were compared with the historical records obtained from the Kissimmee River basin by using the Chi-Square test for goodness-of-fit. The results indicated that the newly proposed model has a better solution than the original model because the trend and cyclical movements involved in generating sequences are much closer to the historical records.     

Managing the impact of climate change on the hydrology of the Gallocanta Basin,NE-Spain

The Gallocanta Basin represents an environment highly sensitive to climate change. Over the past 60 years, the Laguna de Gallocanta, an ephemeral lake situated in the closed Gallocanta basin, experienced a sequence of wet and dry phases. The lake and its surrounding wetlands are one of only a few bird sanctuaries left in NE-Spain for grey cranes on their annual migration from Scandinavia to northern Africa. Understanding the impact of climate change on basin hydrology is therefore of utmost importance for the appropriate management of the bird sanctuary. Changes in lake level are only weakly linked to annual rainfall, with reaction times between hours and months after rainfall. Both the total amount of rainfall over the reaction period, as well as individual extreme events, affect lake level. In this study the characteristics and frequencies of daily, event, monthly and bi-monthly rainfall over the past 60 years were analysed. The results revealed a clear link between increased frequencies of high magnitude rainfall and phases of water filling in the Laguna de Gallocanta. In the middle of the 20th century, the absolute amount of rainfall appears to have been more important for lake level, while more recently the frequency of high magnitude rainfall has emerged as the dominant variable.     

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.     

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.     

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.     

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.     

EFFECT OF RAINFALL EXCESS CALCULATIONS ON MODELED HYDROGRAPH ACCURACY AND UNIT-HYDROGRAPH PARAMETERS1

ABSTRACT: Two methods of computing rainfall excess in the U.S. Army Corps of Engineers’flood hydrograph package (HEC-1), the Initial and Uniform method and the Exponential method, are compared to evaluate the effects on modeled hydrograph accuracy. Two computed unit-hydrograph parameters, time of concentration and storage coefficient, were also compared. Rainfall and runoff data from 209 storms in 32 gaged basins in Illinois were used to calibrate the HEC-1 model. Three hydrograph characteristics - sum of incremental flows, peak discharge, and time of peak discharge - were used to evaluate modeled hydrograph accuracy. Mean percent error for each basin and hydrograph characteristic was computed. An evaluation of the mean errors indicates that, although some bias in modeled hydrograph accuracy is evident, rainfall excess computed using either method results in a computed hydrograph accuracy that is within generally accepted limits. Application of a linear-regression model shows no significant differences in computed values of unit-hydrograph parameters.     

TEMPORAL AND SPATIAL CHARACTERIZATION OF RAINFALL OVER CENTRAL AND SOUTH FLORIDA1

requency evaluation and spatial characterization of rainfall in Central and South Florida are presented. Point frequency analysis performed at all available sites has shown that the 2‐parameter Gamma probability density function is the best model for monthly rainfall frequency over Central and South Florida. The model's parameters estimated at 145 stations were used to provide monthly rainfall estimates for 10‐ and 100‐year dry and wet return periods. Experimental and theoretical variograms computed for these estimates, as well as the Kriging estimation variance maps, show that the existing rain gage network is less capable of resolving monthly rainfall variation in the wet season than the dry season. May is the dry‐to‐wet transition month, while October is the wet‐to‐dry transition month with average rainfall of 4.5 inches. Monthly average rainfall is above 7 inches during the wet season and below 3 inches during the dry season. Two‐thirds of the annual rainfall is accumulated in the wet season. Annual average rainfall is maximum (above 60 inches) in many areas along the east coast, and is minimum (below 45 inches) in many areas over Lake Okee‐chobee and Central Florida. Rainfall maps show a changing pattern between the wet and the dry seasons. Frontal rainfall occurs in the dry season, while convective rainfall, tropical depression, and hurricanes occur in the wet season. Average rainfall is higher along the east coast area in the dry season and it is higher along the west coast area in the wet season.     

EFFECTS OF SIMULATED CLOUD SEEDING ON STREAMFLOW OF SELECTED WATERSHEDS IN PENNSYLVANIA1

A mathematical model was developed to simulate the hydrologic behavior of five small watersheds in central Pennsylvania. Continuous hydrographs for the 6-month period, April to September 1964, were simulated. Synthesized rainfall cycles consisting of increasing rainfall by 10, 20, and 30 percent to simulate the effects of cloud seeding were processed through the watershed model to determine the effects on low flow augmentation. Other rainfall cycles used consisted of increasing every third storm by 30 percent and of developing a rainfall cycle by processing daily radiosonde data through a mathematical cumulus cloud model to obtain a prediction of rainfall following seeding. A comparison of actual and predicted hydrographs indicated that simulated cloud seeding resulted in significant monthly and seasonal water yields. In general, the results of the study appear to indicate that on a theoretical basis cloud seeding would be a feasible method of augmenting low stream-flow during the summer months on watersheds in the northern Appalachian region.     

A COMPARATIVE STUDY OF A SWEDISH AND A CHINESE HYDROLOGICAL MODEL1

ABSTRACT: There are a large number of conceptual hydrological models available today. It is not easy to immediately identify the similarities and differences between the different models. The Swedish HBV model and the Chinese Xinanjiang model are two examples of conceptual, semi-distributed, rainfall-runoff models. The Xinanjiang model was designed for use in humid and semi-humid regions, with no routine for the snowmelt runoff, whereas the snow routine is an important part of the HBV model in many applications. The model structures of the two models may be described in four routines, compared in this paper. The integral structures of them are similar, but there are some differences, especially in the runoff production routine. The physical significance and physical definitions of some model parameters were analyzed. Both models were tested in two basins. Both models gave similar results, and both models performed well in the application. The similarity of the results obtained by different model structures leads to the following two conclusions. First, more effort should probably be spent on the improvement of input data quality and coverage than on the development of more detailed model structures only. Second, inference about basin behavior and characteristics from the values of calibrated model parameters must be made with great caution.     

SEASONAL ARIMA INFLOW MODELS FOR RESERVOIR SIZING1

ABSTRACT: The reliable sizing of reservoirs is a very important task of hydraulic engineering. Although many reservoirs throughout the world have been designed using Rippl's mass curves with historical inflow volumes at the dam site, this technique is now considered outdated. In this paper, synthetic series of monthly inflows are used as an alternative to historical inflow records. These synthetic series are generated from stochastic SARIMA (Seasonal Autoregressive Integrated Moving Average) models. The analyzed data refer to the planned Almopeos Reservoir on the Almopeos River in Northern Greece with 19‐year monthly inflow series. The analysis of this study demonstrates the ability of SARIMA models, in conjunction with the adequate transformation, to forecast monthly inflows of one or more months ahead and generate synthetic series of monthly inflows that preserve the key statistics of the historical monthly inflows and their persistence Hurst coefficient K. The forecasted monthly inflows would be of help in evaluating the optimal real time reservoir operation policies and the generated synthetic series of monthly inflows can be used to provide a probabilistic framework for reservoir design and to cope with the situation where the design horizon of interest exceeds the length of the historical inflow record.