Inferring Hydrograph Components from Rainfall and Streamflow Records Using a Kriging Method-Based Linear Cascade Reservoir Model1

Cheng, Shin-jen, 2010. Inferring Hydrograph Components From Rainfall and Streamflow Records Using a Kriging Method-Based Linear Cascade Reservoir Model. Journal of the American Water Resources Association (JAWRA) 46(6):1171–1191. DOI: 10.1111/j.1752-1688.2010.00484.x Abstract: This study investigates the characteristics of hydrograph components in a Taiwan watershed to determine their shapes based on observations. Hydrographs were modeled by a conceptual model of three linear cascade reservoirs. Mean rainfall was calculated using the block Kriging method. The optimal parameters for 42 events from 1966-2008 were calibrated using an optimal algorithm. Rationality of generated runoffs was well compared with a trusty model. Model efficacy was verified using seven averaged parameters with 25 other events. Hydrograph components were characterized based on 42 calibration results. The following conclusions were obtained: (1) except for multipeak storms, a correlation between base time of the surface runoff and soil antecedent moisture is a decreasing power relationship; (2) a correlation between time lag of the surface flow and soil antecedent moisture for single-peak storms is an increasing power relationship; (3) for single-peak events, times to peak of hydrograph components are an increasing power correlation corresponding to the peak time of rainfall; (4) the peak flows of hydrograph components are linearly proportional to that of total runoff, and the peak ratio for the surface runoff to total runoff is approximately 78 and 13% for subsurface runoff to total runoff; and (5) the relationships of total discharges have direct ratios between hydrograph components and observations of total runoffs, and a surface runoff is 60 and 32% for a subsurface runoff.     

CALIBRATION OF SNYDER COEFFICIENTS FOR PENNSYLVANIA1

ABSTRACT Unit hydrograph theory is one of the most widely used techniques to predict surface runoff. The present study is concerned with the Snyder unit hydrograph and the calibration of the Snyder coefficients for Pennsylvania. Twenty-seven study basins were selected, located randomly across the state. With the rainfall and runoff recorded for several events for each basin (more than 500 events were analyzed) unit hydrographs were calculated and the Snyder coefficients determined. A map of the coefficients was drawn to illustrate the variability in the coefficients and two equations using multiple regression theory were developed. The unexplained variability of the coefficients suggests that upper and lower bounds on the peak flow might be placed on storm hydrographs developed for ungaged watersheds.     

Sensitivity of SCS Models to Curve Number Variation1

ABSTRACT: The Soil Conservation Service (SCS) models, including the TR-20 computer program and the simplified methods in TR-55, are widely used in hydrologic design. The runoff curve number (CN), which is an important input parameter to SCS models, is defined in terms of land use tretments, hydrologic, condition, antecedent soil moisture, and soil type. The objective of this study was to evaluate the sensitivity of the SCS models to errors in CN estimates. The results show that the effects of CN variation decrease as the design rainfall depth increases, such as for the larger storm events. The value and use of the sensitivity curves are demonstrated using a comparison of Landsat and conventionally derived curve numbers for three watersheds in Pennsylvania.     

HYDROLOGIC PARAMETERIZATION OF WATERSHEDS FOR RUNOFF PREDICTION USING SWAT1

ABSTRACT: The use of continuous time, distributed parameter hydrologic models like SWAT (Soil and Water Assessment Tool) has opened several opportunities to improve watershed modeling accuracy. However, it has also placed a heavy burden on users with respect to the amount of work involved in parameterizing the watershed in general and in adequately representing the spatial variability of the watershed in particular. Recent developments in Geographical Information Systems (GIS) have alleviated some of the difficulties associated with managing spatial data. However, the user must still choose among various parameterization approaches that are available within the model. This paper describes the important parameterization issues involved when modeling watershed hydrology for runoff prediction using SWAT with emphasis on how to improve model performance without resorting to tedious and arbitrary parameter by parameter calibration. Synthetic and actual watersheds in Indiana and Mississippi were used to illustrate the sensitivity of runoff prediction to spatial variability, watershed decomposition, and spatial and temporal adjustment of curve numbers and return flow contribution. SWAT was also used to predict stream runoff from actual watersheds in Indiana that have extensive subsurface drainage. The results of this study provide useful information for improving SWAT performance in terms of stream runoff prediction in a manner that is particularly useful for modeling ungaged watersheds wherein observed data for calibration is not available.     

RELIABILITY OF THE DESIGN STORM CONCEPT IN EVALUATING RUNOFF PEAK FLOW1

A comparative study was undertaken to evaluate peak runoff flow rates using (1) a continuous series of actual rainfall events and (2) design storms. The ILLUDAS computer model was used to simulate runoff over a catchment within the city of Montreal, Canada. A ten-year period, five-minute increment rainfall data base was used to derive peak flow frequency curves. Two types of design storms were analyzed: one derived from intensity duration frequency curves (Chicago type), the other from averaging actual rainfall patterns (Huff type). Antecedent soil moisture conditions were considered in the analyses. It was found that the probability distribution of runoff peak flow was sensitive to the choice of design storm pattern and to the antecedent soil moisture condition. A symmetrical, Chicago-type design storm with antecedent dry soil moisture produced a flow frequency curve similar to the one obtained from a series of historical rainfall events.     

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.     

DEVELOPMENT AND EVALUATION OF A DIMENSIONLESS UNIT HYDROGRAPH1

ABSTRACT: A generalized unit hydrograph method is developed and evaluated for ungaged watersheds. A key component in this method is the value of a dimensionless storage coefficient. Procedures to estimate this coefficient are given using calibrated values from 142 rainfall-runoff events gaged in watershed located mainly in the Eastern US. Only limited success was obtained in predicting this storage coefficient. Thirty-seven, independent rainfall-runoff events were used to test the proposed technique. The generalized unit hydrograph predicted the observed runoff hydrographs fairly well with considerable improvement in accuracy over the SCS dimensionless unit hydrograph. Approximately one-half of test storms had percent errors in predicted peak flow rates that were less than 34 percent compared to percent error of 88 percent with the SCS method.     

THE EFFECT OF DATA INDEPENDENCE IN MODEL CALIBRATION AND MODEL TESTING1

ABSTRACT: With the increased use of models in hydrologic design, there is an immediate need for a comprehensive comparison of hydrologic models, especially those intended for use at ungaged locations (i.e., where measured data are either not available or inadequate for model calibration). But some past comparisons of hydrologic models have used the same data base for both calibration and testing of the different models or implied that the results of model calibration are indicative of the accuracy at ungaged locations. This practice was examined using both the regression equation approach to peak discharge estimation and a unit hydrograph model that was intended for use in urban areas. The results suggested that the lack of data independence in the calibration and testing of regression equations may lead to both biased results and misleading statements about prediction accuracy. Additionally, although split-sample testing is recognized as desirable, the split-samples should be selected using a systematic-random sampling scheme, rather than random sampling, because random sampling with small samples may lead to a testing sample that is not representative of the population. A systematic-random sampling technique should lead to more valid conclusions about model reliability. For models like a unit hydrograph model, which are more complex and for which calibration is a more involved process, data independence is not as critical because the data fitting error variation is not as dominant as the error variation due to the calibration process and the inability of the model structure to conform with data variability.     

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.     

Investigation of the Curve Number Method For Surface Runoff Estimation In Tropical Regions

This study tests the applicability of the curve number (CN) method within the Soil and Water Assessment Tool (SWAT) to estimate surface runoff at the watershed scale in tropical regions. To do this, surface runoff simulated using the CN method was compared with observed runoff in numerous rainfall‐runoff events in three small tropical watersheds located in the Upper Blue Nile basin, Ethiopia. The CN method generally performed well in simulating surface runoff in the studied watersheds (Nash‐Sutcliff efficiency [NSE] > 0.7; percent bias [PBIAS] < 32%). Moreover, there was no difference in the performance of the CN method in simulating surface runoff under low and high antecedent rainfall (PBIAS for both antecedent conditions: ~30%; modified NSE: ~0.4). It was also found that the method accurately estimated surface runoff at high rainfall intensity (e.g., PBIAS < 15%); however, at low rainfall intensity, the CN method repeatedly underestimated surface runoff (e.g., PBIAS > 60%). This was possibly due to low infiltrability and valley bottom saturated areas typical of many tropical soils, indicating that there is scope for further improvements in the parameterization/representation of tropical soils in the CN method for runoff estimation, to capture low rainfall‐intensity events. In this study the retention parameter was linked to the soil moisture content, which seems to be an appropriate approach to account for antecedent wetness conditions in the tropics.     

Runoff Curve Numbers at the Agricultural Field‐Scale and Implications for Continuous Simulation Modeling

This study used monitoring in the waterways of agricultural fields to understand the use of the runoff curve number (CN) in continuous simulation models. The CN has a long history as a design tool for estimating runoff volumes for large, single storms on small watersheds, but its use in continuous simulation models to describe runoff from smaller storms and relatively small areas is more recent and controversial. We examined 788 nonwinter rainfall events on four agricultural fields over five years (2004‐2008) during which runoff was generated in 87 events. The largest 20 runoff events on each field generated approximately 90% of the total runoff volume. The runoff event CNs showed an inverse correlation with storm depth that could not consistently be explained by previous precipitation. We review how small areas of higher runoff generation within larger areas will systematically increase the apparent CN of the larger area as the storm size decreases. If this variation is not incorporated into a model explicitly, continuous simulation modelers must understand that when source areas are aggregated or when runoff generation is spatially variable, the overall CN is not unique when smaller storms are included in the calibration set.     

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.     

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.     

Curve Number Derivation for Watersheds Draining Two Headwater Streams in Lower Coastal Plain South Carolina,USA

The objective of this study was to assess curve number (CN) values derived for two forested headwater catchments in the Lower Coastal Plain (LCP) of South Carolina using a three‐year period of storm event rainfall and runoff data in comparison with results obtained from CN method calculations. Derived CNs from rainfall/runoff pairs ranged from 46 to 90 for the Upper Debidue Creek (UDC) watershed and from 42 to 89 for the Watershed 80 (WS80). However, runoff generation from storm events was strongly related to water table elevation, where seasonally variable evapotranspirative wet and dry moisture conditions persist. Seasonal water table fluctuation is independent of, but can be compounded by, wet conditions that occur as a result of prior storm events, further complicating flow prediction. Runoff predictions for LCP first‐order watersheds do not compare closely to measured flow under the average moisture condition normally associated with the CN method. In this study, however, results show improvement in flow predictions using CNs adjusted for antecedent runoff conditions and based on water table position. These results indicate that adaptations of CN model parameters are required for reliable flow predictions for these LCP catchments with shallow water tables. Low gradient topography and shallow water table characteristics of LCP watersheds allow for unique hydrologic conditions that must be assessed and managed differently than higher gradient watersheds.     

NORMALIZED UNIT HYDROGRAPH AGGREGATION1

ABSTRACT: The unit hydrograph is a common tool in hydraulic design. Used correctly, it allows a design engineer to estimate a runoff hydrograph from a drainage basin given a rainfall event. The typical method for estimating a unit hydrograph for a gaged watershed is by deconvolution. However, distinct storms produce different unit hydrographs for a single watershed. Consequently, a design engineer usually develops a composite, or average, unit hydrograph based on several recorded storm events. Common methods for estimating this composite unit hydrograph include curve fitting, simple aggregation, and multistorm optimization techniques. This paper introduces a new method to perform aggregation of unit hydrographs. The method is an extension to the simple averaging technique, in which prior to averaging, the individual unit hydrograph time ordinates are normalized with respect to the average time to peak. The normalization method is compared to a simple averaging technique and two multistorm aggregation techniques at six rural watersheds in Alabama. The results indicate that on average the normalization method predicts runoff nearly as accurately as the multistorm techniques, and displays improvement for 60 percent of the storms tested when compared with the simple averaging technique.     

Hydrology of small field plots used to study phosphorus runoff under simulated rainfall

Use of small plots and rainfall simulators to extrapolate trends in runoff water quality requires careful consideration of hydrologic process represented under such conditions. A modified version of the National Phosphorus Runoff Project (NPRP) protocol was used to assess the hydrology of paired 1 x 2 m plots established on two soils with contrasting hydrologic properties (somewhat poorly drained vs. well drained). Rain simulations (60 mm h(-1)) were conducted to generate 30 min of runoff. For the somewhat poorly drained soil, simulations were conducted in October and May to contrast dry conditions typically targeted by NPRP protocols with wet conditions generally associated with natural runoff. For the well-drained soil, only dry conditions (October) were evaluated. Under dry antecedent moisture conditions, an average of 64 mm of rainfall was applied to the somewhat poorly drained soil to generate 30 min of runoff, as opposed to 96 mm to the well-drained soil. At an extreme, differences in rainfall were equivalent to a 50-yr rainfall-return period. An absence of detectable spatial trends in surface soil moisture suggests uniformity of runoff processes within the plots. No differences in applied rainfall were evident between wet and dry antecedent conditions for the somewhat poorly drained soil. However, significant differences in runoff generation processes were observed in dissolved P concentrations between wet and dry conditions. As natural runoff from the somewhat poorly drained soil is largely under wet antecedent conditions, this study highlights the need for care in interpreting findings from generalized protocols that favor infiltration-excess runoff mechanisms.     

Modeling Nutrient Export From Coastal California Watersheds

Nitrate and phosphate export coefficient models were developed for coastal watersheds along the Santa Barbara Channel in central California. One approach was based on measurements of nutrient fluxes in streams from specific land use classes and included a watershed response function that scaled export up or down depending on antecedent moisture conditions. The second approach for nutrient export coefficient modeling used anthropogenic nutrient loading for land use classes and atmospheric nutrient deposition to model export. In an application of the first approach to one watershed, the nitrate and phosphate models were within 20% of measured values for most storms. When applied to another year, both nitrate and phosphate models generally performed adequately with annual, storm‐flow, and base‐flow values within 20% of measured nutrient loadings. Less satisfactory results were found when applied to neighboring watersheds with difference percentages of land use and hydrologic conditions. Application of the second approach was less successful than the first approach.     

WATER LOSS EQUATIONS AND COEFFICIENTS TO ESTIMATE RUNOFF FROM RAINFALL1

Infiltration models are based on physical characteristics of the soil and initial soil moisture. For a given soil it is based on the initial soil moisture distribution. A computer simulation model for flood runoff systems (FH-Model) was used to analyze 39 sets of rainfall-runoff data on four small watersheds ranging in size from 17 to 342 square kilometers located in the Yamaska River basin in Quebec. From these analyses, parameters and coefficients have been determined for a water loss (infiltration) equation. A method for determining the loss parameters, using a nonlinear least square curve fitting technique, is presented. Expressions were made to relate the loss parameters to antecedent precipitation. The equations were tested on 11 storm rainfall and runoff events on a watershed located in the same region and close agreements were found.     

Pesticide transport pathways from a sloped Litchi orchard to an adjacent tropical stream as identified by hydrograph separation

This study was performed to identify the transport pathways of pesticides from a sloped litchi ( Sonn.) orchard to a nearby stream based on a three-component hydrograph separation (baseflow, interflow, surface runoff). Dissolved silica and electrical conductivity were chosen as representative tracers. During the study period (30 d), 0.4 and 0.01% of the applied mass of atrazine and chlorpyrifos, respectively, were detected in the stream after 151 mm of rainfall. Baseflow (80-96%) was the dominant hydrological flow component, followed by interflow (3-18%) and surface runoff (1-7%). Despite its small contribution to total discharge, surface runoff was the dominant atrazine transport pathway during the first days after application because pesticide concentrations in the surface runoff flow component declined quickly within several days. Preferential transport with interflow became the dominant pathway of atrazine. Because chlorpyrifos was detected in the stream water only twice, it was not included in the hydrograph separation. A feature of the surface runoff pathway was the coincidence of pesticide and discharge peaks. In contrast, peak concentrations of pesticides transported by interflow occurred during the hydrograph recession phases. Stormflow generation and pesticide transport depended on antecedent rainfall. The combination of high-resolution pesticide concentration measurements with a three-component hydrograph separation has been shown to be a suitable method to identify pesticide transport pathways under tropical conditions.     

DETERMINING SIGNIFICANCE AND PRECISION OF ESTIMATED PARAMETERS FOR RUNOFF FROM SEMIARID WATERSHEDS1

ABSTRACT Significant parameters for predicting thunderstorm runoff from small semiarid watersheds are determined using data from the Walnut Gulch watershed in southern Arizona. Based on these data, thunderstorm rainfall is dominant over watershed parameters for predicting runoff from multiple linear regression equations. In some cases antecedent moisture added significantly to the models. A technique is developed for estimating precision of predicted values from multiple linear regression equations. The technique involves matrix methods in estimating the variance of mean predicted values from a regression equation. The estimated variance of the mean predicted value is then used to estimate the variance of an individual predicted value. A computer program is developed to implement these matrix methods and to form confidence limits on predicted values based on both a normality assumption and the Chebyshev inequality.