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

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

THE APPLICATION OF HYDROLOGIC MODELS TO SMALL WATERSHEDS HAVING MILD TOPOGRAPHY1

ABSTRACT: The application of hydrologic models to small watersheds of mild topography is not well documented. This study evaluates the applicability of hydrologic models described by Huggins and the Soil Conservation Service to small watersheds by comparing the simulated and actual hydrograph for both gaged and ungaged situations. The annual maximum rainfall events plus storms exceeding 2.5 inches from 25 years of rainfall and runoff data for two small watersheds were selected for the model evaluations. These storms had a variety of patterns and occurred on many different watershed conditions. Simulated and actual hydrographs were compared using a parameter which contained volume, peak, and shape factors. One-half of the selected storms were used to calibrate the models. For both models, there were no significant differences between the simulated and actual runoff volumes and peak runoff rates. Parameters obtained during the calibration process and relationships developed to estimate antecedent moisture and to modify tabulated runoff curve numbers were used to simulate the runoff hydrograph from the remaining storms. These remaining storms or test storms were simulated only once in order to imitate an ungaged situation. In general, both the Huggins and SCS model performed similarly on the test storms, but the level of model performance was lower than that for the calibration storms. For both models, the two-day antecedent rainfall was more important than the five-day in determining antecedent moisture and modifying tabulated curve numbers. The time of concentration which resulted in good hydrograph simulations was about three times larger than that estimated using published empirical relationships.     

ESTIMATING REFERENCE EVAPORATION IN THE CENTRAL VALLEY OF CALIFORNIA USING THE LINACRE MODEL1

ABSTRACT: The Linacre (1988) model for calculating evaporation from open water or well-watered surfaces only requires inputs of air temperature, latitude and elevation, and windspeed if it is available. The model was developed using data collected at a large number of sites in different climatic regions of the world, while independent tests of the model have shown it to be suitable for estimating evaporation in a variety of locations. This study was intended to contribute to the broad goal of evaluating temperature-based evaporation models for use in California by testing the Linacre model in the agriculturally intensive Central Valley. Observed monthly mean reference evaporation (E_o) and meteorological data for periods ranging up to 72 months were obtained from 25 California Irrigation and Management Information System (CIMIS) stations distributed throughout the Central Valley. Uncalibrated and calibrated Linacre models were used to estimate monthly mean reference evaporation, and the performance of each model was evaluated using indices that quantified the random and systematic errors and overall model performance. The accuracy of the radiation and ventilation components of the model were evaluated separately. The uncalibrated model was found to systematically overestimate E_o with most of the model error being attributed to the ventilation component. Calibration of the radiation and ventilation components removed most of the systematic model errors, and the root mean square error for monthly mean E_o was 0.676 mm day^?1 (16.8 percent of the mean observed value). (KEY TERMS: reference evaporation; Linacre model; irrigation scheduling.)     

STEP WISE,MULTIPLE OBJECTIVE CALIBRATION OF A HYDROLOGIC MODEL FOR A SNOWMELT DOMINATED BASIN1

ABSTRACT: The ability to apply a hydrologic model to large numbers of basins for forecasting purposes requires a quick and effective calibration strategy. This paper presents a step wise, multiple objective, automated procedure for hydrologic model calibration. This procedure includes the sequential calibration of a model's simulation of solar radiation (SR), potential evapotranspiration (PET), water balance, and daily runoff. The procedure uses the Shuffled Complex Evolution global search algorithm to calibrate the U.S. Geological Survey's Precipitation Runoff Modeling System in the Yampa River basin of Colorado. This process assures that intermediate states of the model (SR and PET on a monthly mean basis), as well as the water balance and components of the daily hydrograph are simulated consistently with measured values.     

APPLICATION OF THE RHESSys MODEL TO A CALIFORNIA SEMIARID SHRUBLAND WATERSHED1

ABSTRACT: Distributed hydrologic models which link seasonal streamflow and soil moisture patterns with spatial patterns of vegetation are important tools for understanding the sensitivity of Mediterranean type ecosystems to future climate and land use change. RHESSys (Regional Hydro‐Ecologic Simulation System) is a coupled spatially distributed hydroecological model that is designed to be able to represent these feedbacks between hydrologic and vegetation carbon and nutrient cycling processes. However, RHESSys has not previously been applied to semiarid shrubland watersheds. In this study, the hydrologic submodel of RHESSys is evaluated by comparing model predictions of monthly and annual streamflow to stream gage data and by comparing RHESSys behavior to that of another hydrologic model of similar complexity, MIKESHE, for a 34 km² watershed near Santa Barbara, California. In model intercomparison, the differences in predictions of temporal patterns in streamflow, sensitivity of model predictions to calibration parameters and landscape representation, and differences in model estimates of soil moisture patterns are explored. Results from this study show that both models adequately predict seasonal patterns of streamflow response relative to observed data, but differ significantly in terms of estimates of soil moisture patterns and sensitivity of those patterns to the scale of landscape tessellation used to derive spatially distributed elements. This sensitivity has implications for implementing RHESSys as a tool to investigate interactions between hydrology and ecosystem processes.     

BASSETT CREEK WATERSHED MODEL1

ABSTRACT: A synthetic hydrograph method was utilized in the development of a watershed model for a small urbanizing watershed. The model was applied to the watershed and the largest flood of record was accurately reproduced. Because the model would be utilized for design of flood control plans with complete urbanization, the method was also applied to an urbanized watershed and reproduced a measured event with good results. The method does not require extensive hydrologic data for its implementation, can be applied to watersheds in various stages of urbanization, and permits consideration of natural or potential floodwater storage.     

EFFICIENCY OF HYDROLOGIC DATA COLLECTION SYSTEMS ROLE OF TYPE I AND II ERRORS1

ABSTRACT The efficiency of hydrologic data collection systems is relevant to solution of environmental problems, scientific understanding of hydrologic processes, model-building and management of water resources. Because these goals may be overlapping and non-commensurate, design of data networks is not simple. Identified are four elements of error or risk in such networks: (a) choice of variables and mathematical model for the same process, (b) accuracy of model parameter estimates, (c) acceptance of wrong hypothesis or rejection of correct hypothesis and (d) economic losses associated with error. Of these four, the classical hypothesis testing problem is specifically evaluated in terms of costs of type I and II errors for simple and composite hypotheses; mathematical models for these economic analyses also include costs of sample data and costs of waiting while new data is obtained. An illustrative computational example focuses on the hypothesis that natural recharge might be augmented by a system of pumping wells along an ephemeral channel. The relationship of the hypothesis testing problem to Bayesian decision theory is discussed; it is felt that the latter theory offers a more comprehensive framework for design and use of hydrologic data networks.     

A COMPUTERIZED DATA BASE FOR FLOOD PREDICTION MODELING1

ABSTRACT: A computerized geographic information system (GIS) was created in support of data requirements by a hydrologic model designed to predict the runoff hydrograph from ungaged basins. Some geomorphologic characteristics (i.e., channel lengths) were manually measured from topographic maps, while other parameters such as drainage area and number of channels of a specified order, land use, and soil type were digitized and manipulated through use of the GIS. The model required the generation of an integrated Soil Conservation Service (SCS) curve number for the entire basin. To this end, soil associations and land use (generated from analysis of Landsat satellite data) were merged in the GIS to acquire a map representing SCS runoff curve numbers. The volume of runoff obtained from the Watershed Hydrology Simulation (WAHS) Model using this map was compared to the volume computed by hydrograph separation and found to be accurate within 19 percent error. To quantify the effect of changing land use on basin hydrology, the GIS was used to vary percentages from the drainage area from forest to bare soil. By changing the basin runoff curve numbers, significant changes in peak discharge were noted; however, the time to peak discharge remained essentially independent of change in area of land use. The GIS capability eliminated many of the more traditional manual phases of data input arid manipulation, thereby allowing researchers to concentrate on the development and calibration of the model and the interpretation of presumably more accurate results.     

UNIT HYDROGRAPHS DERWED FROM THE NASH MODEL1

ABSTRACT: Unit hydrograph ordinates are often estimated by deconvoluting excess rainfall pulses and corresponding direct runoff. The resulting ordinates are given at discrete times spaced evenly at intervals equal to the duration of the rainfall pulse. If the new duration is not a multiple of the parent duration, hydrograph interpolation is required. Linear interpolation, piece-wise nonlinear interpolation and graphical smoothing have been used. These interpolation schemes are expedient but they lack theoretical basis and can lead to undesirable results. Interpolation can be avoided if the instantaneous unit hydrograph (IUH) for the watershed is known. Here two issues connected with the classic Nash IUH are examined: (1) how should the Nash parameters be estimated? and (2) under what conditions is the resulting hydrograph able to reasonably represent watershed response? In the first case, nonlinear constrained optimization provides better estimates of the IUH parameters than does the method of moments. In the second case, the Nash IUH gives good results on watersheds with mild shape unit hydrographs, but performs poorly on watersheds having sharply peaked unit hydrographs. Overall, in comparison to empirical interpolation alternatives, the Nash IUH offers a theoretically sound and practical approach to estimate unit hydrographs for a wide variety of watersheds.     

MACROSCALE HYDROLOGIC MODELING FOR REGIONAL CLIMATE ASSESSMENT STUDIES IN THE SOUTHEASTERN UMTED STATES1

ABSTRACT: A macroscale hydrologic model is developed for regional climate assessment studies under way in the southeastern United States. The hydrologic modeling strategy is developed to optimize spatial representation of basin characteristics while maximizing computational efficiency. The model employs the “grouped response unit” methodology, which follows the natural drainage pattern of the area. First order streams are delineated and their surface characteristics are tested so that areas with statistically similar characteristics can be combined into larger computational zones for modeling purposes. Hydrologic response units (HRU) are identified within the modeling units and a simple three‐layer water balance model, Soil and Water Assessment Tool (SWAT), is executed for each HRU. The runoff values are then convoluted using a triangular unit hydrograph and routed by Muskingum‐Cunge method. The methodology is shown to produce accurate results relative to other studies, when compared to observations. The model is used to evaluate the potential error in hydrologic assessments when using GCM predictions as climatic input in a rainfall‐runoff dominated environment. In such areas, the results from this study, although limited in temporal and spatial scope, appear to imply that use of GCM climate predictions in short term quantitative analyses studies in rainfall‐runoff dominated environments should proceed with caution.     

A CRITICAL APPROACH TO THE CALIBRATION OF A WATERSHED MODEL1

ABSTRACT: A complex watershed-scale water quality simulation model, the Hydrological Simulation Program-FORTRAN (HSPF) model, was calibrated for a 16 km² catchment. The simulation step size was 0.33 hours with predicted and recorded hydrologic flows compared on an annual and monthly basis during a total calibration period of four years. Unguided numerical optimization when applied alone did not yield a model parameter set with acceptable predictive capability; instead, it was necessary to apply a critical process that included sensitivity analysis, numerical optimization, and testing of derived model parameter sets to evaluate their performance for periods other than those for which they were determined. Using this critical calibration process, the model was proven to have significant predictive capability. Numerical optimization is an aid for model calibration, but it must not be used blindly.     

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.     

APPLICATION OF AN INTEGRATED BASIN-SCALE HYDROLOGIC MODEL TO SIMULATE SURFACE-WATER AND GROUND-WATER INTERACTIONS1

ABSTRACT: Hydrologic models have become an indispensable tool for studying processes and water management in watersheds. A physically-based, distributed-parameter model, Basin-Scale Hydro-logic Model (BSIIM), has been developed to simulate the hydrologic response of large drainage basins. The model formulation is based on equations describing water movement both on the surface and in the subsurface. The model incorporates detailed information on climate, digital elevation, and soil moisture budget, as well as surface-water and ground-water systems. This model has been applied to the Big Darby Creek Watershed, Ohio in a 28-year simulation of rainfall-runoff processes. Unknown coefficients for controlling runoff, storativity, hydraulic conductivity, and streambed permeability are determined by a trial-and-error calibration. The performance of model calibration and predictive capability of the model was evaluated based on the correlation between simulated and observed daily stream discharges. Discrepancies between observed and simulated results exist because of limited precipitation data and simplifying assumptions related to soil, land use, and geology.     

History and Development of the NRCS Lag Time Equation1

Abstract: Many of the hydrologic methods that are used in engineering practice today resulted from the Spring Flood of 1936, which blanketed the Northeastern portion of the United States. Because of the flood damage that was caused by this rainfall‐snowmelt event, many federal agencies including the U.S. Army Corp of Engineers and the Soil Conservation Service (SCS) implemented the hydrologic theories that were available in the literature at this time and developed hydrologic procedures for design flow estimation. Sherman had recently published his unit hydrograph theory in 1932, and later in 1938 Snyder, who had been charged by the Water Resource Council to develop a synthetic unit hydrograph, published his famous paper. The SCS unit hydrograph theory was developed by Victor Mockus in the late 1950s. Most if not all of the theories at that time reported the rainfall‐runoff process for floods as a surface phenomenon, and as such those theories all required some type of a timing parameter to estimate watershed response time. This article documents the development of the SCS lag equation.     

CALIBRATION OF STORM LOADS IN THE SOUTH PRONG WATERSHED,FLORIDA, USING BASINS/HSPF1

ABSTRACT: The South Prong watershed is a major tributary system of the Sebastian River and adjacent Indian River Lagoon. Continued urbanization of the Sebastian River drainage basin and other watersheds of the Indian River Lagoon is expected to increase runoff and nonpoint source pollutant loads. The St. Johns River Water Management District developed watershed simulation models to estimate potential impacts on the ecological systems of receiving waters and to assist planners in devising strategies to prevent further degradation of water resources. In the South Prong system, a storm water sampling program was carried out to calibrate the water quality components of the watershed model for total suspended solids (TSS), total phosphorous (TP), and total nitrogen (TN). During the period of May to November 1999, water quality and flow data were collected at three locations within the watershed. Two of the sampling stations were located at the downstream end of major watercourses. The third station was located at the watershed outlet. Five storm events were sampled and measured at each station. Sampling was conducted at appropriate intervals to represent the rising limb, peak, and recession limb of each storm event. The simulations were handled by HSPF (Hydrologic Simulation Program‐Fortran). Results include calibration of the hydrology and calibration of the individual storm loads. The hydrologic calibration was continuous over the period 1994 through 1999. Simulated storm runoff, storm loads, and event mean concentrations were compared with their corresponding observed values. The hydrologic calibration showed good results. The outcome of the individual storm calibrations was mixed. Overall, however, the simulated storm loads agreed reasonably well with measured loads for a majority of the storms.     

SENSITIVITY CONSIDERATIONS WHEN MODELING HYDROLOGIC PROCESSES WITH DIGITAL ELEVATION MODEL1

ABSTRACT: The purpose of this paper is to investigate the sensitivity of a hydrologic models to the type of DEM used. This was done while modeling basin water quality with 1:24,000 and 1:250,000 U.S. Geological Survey DEMs as input to model hydro‐logical processes. The manner in which the model results were sensitive to the choice of raster cell size (scale) is investigated in this study. The Broadhead watershed, located in New Jersey, USA, was chosen as a study area. Curve numbers were estimated by a trial and error to match simulated and observed total discharge. Monthly runoff for the watershed was used in the calibration process. Higher runoff volumes were simulated by the model when the 1:24,000 DEM were used as input data, probably due to the finer resolution which simulated increased average slope and hence higher estimated runoff from the watershed. As the simulated slope of the watershed is flatten with the 1:250,000 DEM, the response of stream flow was delayed and simulated less runoff volume.     

PREDICTING TEMPORAL AND SPATIAL FLOOD DYNAMICS USING A PRECALIBRATED MODEL1

ABSTRACT: A large storm in December 1990 allowed the evaluation of flood predictions from a hydrologic model (TOPMODEL) that had been previously calibrated on the West Fork of Walker Branch Watershed, a gauged 37.5 ha catchment near Oak Ridge, Tennessee. The model predicts both hydrograph dynamics and the spatial distribution of overland flow using an index based on topography. Maximum extent of overland flow during the storm was determined from patterns of leaf litter removal from valley bottoms. Both the flood hydrograph and the extent of overland flow were accurately predicted using model parameters obtained from a three-month period of normal flow conditions during 1983.     

AN ANALOG COMPUTER DEMONSTRATION OF DOUBLE-PEAKED INSTANTANEOUS UNIT HYDROGRAPHS1

The properties of an instantaneous unit hydrograph model consisting of two cascades of linear reservoirs in parallel were explored with the aid of an analog computer. By proper choice of the model parameters it is possible to produce two-peaked instantaneous unit hydrographs. The relative magnitudes and locations of the two peaks can be varied by changing the values of the parameters. An example of the use of the analog computer to select the parameters of the model giving the best fit to an observed runoff hydrograph is also included. The analog computer used in the study was the ASTRAC II developed at the University of Arizona.     

GENERATING DESIGN HYDROGRAPHS BY DEM ASSISTED GEOMORPHIC RUNOFF SIMULATION: A CASE STUDY1

ABSTRACT: The geomorphic instantaneous unit hydrograph (GIUH) may be one of the most successful methodologies for predicting flow characteristics in ungauged watersheds. However, one difficulty in applying the GIUH model is determination of travel time, and the other difficulty is the large amount of geomorphologic information required in the study watershed. Recently, using the kinematic-wave theory Lee and Yen (1997) have analytically determined the travel times for overland and channel flows in watersheds. The limitation of using an empirical velocity equation to estimate the runoff travel time for a specified watershed is then relaxed. To simplify the time-consuming work involved in geomorphic parameter measurement on topographic maps, the GIUH model is linked with geographic information systems to obtain geomorphic parameters from digital elevation models. In this paper, a case study performed for peak flow analysis in an ungauged watershed is presented. The geomorphic characteristics of the study watershed were analyzed using a digital elevation model and were used to construct the runoff simulation model. The design storm was then applied to the geomorphic runoff simulation model to obtain the design hydrograph. The analytical procedures proposed in this study can provide a convenient way for hydrologists to estimate hydrograph characteristics based on limited hydrologic information.     

WATER QUALITY MODEL CALIBRATION: A COMPARISON OF INPUT AND OUTPUT ERROR CRITERIA1

ABSTRACT: A common framework for the analysis of water resources systems is the input-parameter-output representation. The system, described by its parameters, is driven by inputs and responds with outputs. To calibrate (estimate the parameters) models of these systems requires data on both inputs and outputs, both of which are subject to random errors. When one is uncertain as to whether the predominant source of error is associated with inputs or outputs, uncertainty also exists as to the correct specification of a calibration criterion. This paper develops and analyzes two alternative least squares criteria for calibrating a numerical water quality model. The first criterion assumes that errors are associated with inputs while the second assumes output errors. Statistical properties of the resulting estimators are examined under conditions of pure input or output error and mixed error conditions from a theoretical perspective and then using simulated results from a series of Monte Carlo experiments.