GIS‐Based Spatial Precipitation Estimation: A Comparison of Geostatistical Approaches1

Abstract: As one of the primary inputs that drive watershed dynamics, the estimation of spatial variability of precipitation has been shown to be crucial for accurate distributed hydrologic modeling. In this study, a Geographic Information System program, which incorporates Nearest Neighborhood (NN), Inverse Distance Weighted (IDW), Simple Kriging (SK), Ordinary Kriging (OK), Simple Kriging with Local Means (SKlm), and Kriging with External Drift (KED), was developed to facilitate automatic spatial precipitation estimation. Elevation and spatial coordinate information were used as auxiliary variables in SKlm and KED methods. The above spatial interpolation methods were applied in the Luohe watershed with an area of 5,239 km², which is located downstream of the Yellow River basin, for estimating 10 years’ (1991‐2000) daily spatial precipitation using 41 rain gauges. The results obtained in this study show that the spatial precipitation maps estimated by different interpolation methods have similar areal mean precipitation depth, but significantly different values of maximum precipitation, minimum precipitation, and coefficient of variation. The accuracy of the spatial precipitation estimated by different interpolation methods was evaluated using a correlation coefficient, Nash‐Sutcliffe efficiency, and relative mean absolute error. Compared with NN and IDW methods that are widely used in distributed hydrologic modeling systems, the geostatistical methods incorporated in this GIS program can provide more accurate spatial precipitation estimation. Overall, the SKlm_EL_X and KED_EL_X, which incorporate both elevation and spatial coordinate as auxiliary into SKlm and KED, respectively, obtained higher correlation coefficient and Nash‐Sutcliffe efficiency, and lower relative mean absolute error than other methods tested. The GIS program developed in this study can serve as an effective and efficient tool to implement advanced geostatistics methods that incorporate auxiliary information to improve spatial precipitation estimation for hydrologic models.     

PARTITIONING SMALL SCALE SPATIAL VARIABILITY OF RUNOFF AND EROSION ON SAGEBRUSH RANGELAND1

ABSTRACT: Most hydrologic models require input parameters which represent the variability found across an entire landscape. The estimation of such parameters is very difficult, particularly on rangeland. Improved model parameter estimation procedures are needed which incorporate the small-scale and temporal variability found on rangeland. This study investigates the use of a surface soil classification scheme to partition the spatial variability in hydrologic and interrill erosion processes in a sagebrush plant community. Four distinct microsites were found to exist within the sagebrush coppice-dune dune-interspace complex. The microsites explained the majority of variation in hydrologic and interrill erosion response found on the site and were discernable based on readily available soil and vegetation information. The variability within each microsite was quite low and was not well correlated with soil and vegetation properties. The surface soil classification scheme defined in this study can be quite useful for defining sampling procedures, for understanding hydrologic and erosion processes, and for parameterizing hydrologic models for use on sagebrush range-land.     

PARAMETER ESTIMATION IN HYDROLOGY: THE STATE OF THE ART1

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

KALMAN FILTER ESTIMATION AND PREDICTION OF DAILY STREAM FLOWS: II. APPLICATION TO THE POTOMAC RIVER1

Results are reported from an application of the state space formulation and the Kalman filter to real-time forecasting of daily river flows. It is shown that the application of filtering techniques improves the overall forecasting performance of the model. As is true for most hydrologic systems, the model is not completely known. Therefore, the procedures pertaining to on-line parameter and noise statistics estimation, as presented in the first paper, are implemented. The example in this paper shows that these techniques also perform satisfactorily when applied to a real-world situation.     

Integrating Modeling and Field Experiments to Evaluate Impacts of Vegetative Practices on Ponderosa Pine Watersheds1

Abstract: Determining watershed response to vegetation treatment has been the subject of numerous hydrologic studies over the years. However, generalizing the information obtained from traditional paired‐watershed studies to other watersheds in a region is problematic because of the empirical nature of such studies and the context dependence of hydrologic responses. This paper addresses the issue of generalizing hydrologic information through integration of process‐based modeling and field observations from small‐scale watershed experiments. To this end, the results from application of a process‐based model were compared with the results from small‐scale watershed experiments in ponderosa pine forests of Arizona. The model simulated treatment impacts reasonably well when compared to the traditional paired‐watershed approach. However, the model tended to overestimate water yields during periods of low flow, and there was a significant difference between the two approaches in the estimation of treatment impacts during the first four years following treatment. The results indicate that the lumped‐parameter modeling approach used here may be limited in its ability to detect small changes, and tends to overestimate changes that occur immediately following treatment. It is concluded that watershed experiments can be highly informative due to their direct examination of cause‐effect relationships, while process‐based models are useful for their processing power and focus on functional relationships. The integrated use of both watershed experiments and process‐based models provides a way to generalize hydrologic information, illuminate the processes behind landscape treatment effects, and to generate and test hypotheses.     

COMPARING METHODS OF HYDROLOGIC REGIONALIZATION1

ABSTRACT: Data splitting is used to compare methods of determining “homogeneous” hydrologic regions. The methods compared use cluster analysis based on similarity of hydrologic characteristics or similarity of characteristics of a stream's drainage basin. Data for 221 stations in Arizona are used to show that the methods, which are a modification of DeCoursey's scheme for defining regions, improve the fit of estimation data to the model, but that is is necessary to have an independent measure of predictive accuracy, such as that provided by data splitting, to demonstrate improved predictive accuracy. The methods used the complete linkage algorithm for cluster analysis and computed weighted average estimates of hydrologic characteristics at ungaged sites.     

PARAMETER ESTIMATION OF THE NONLINEAR MUSKINGUM MODEL USING HARMONY SEARCH1

ABSTRACT: A newly developed heuristic algorithm, Harmony Search, is applied to the parameter estimation problem of the nonlinear Muskingum model. Harmony Search found better values of parameters in the nonlinear Muskingum model than five other methods including another heuristic method, genetic algorithm, in terms of SSQ (the sum of the square of the deviations between the observed and routed outflows), SAD (the sum of the absolute value of the deviations between the observed and routed outflows), DPO (deviations of peak of routed and actual flows), and DPOT (deviations of peak time of routed and actual outflow). Harmony Search also has the advantage that it does not require the process of assuming the initial values of design parameters. The sensitivity analysis of Harmony Memory Considering Rate showed that relatively large values of Harmony Memory Considering Rate makes the Harmony Search converge to a better solution.     

THE FLEXIBLE TOLERANCE METHOD FOR ESTIMATING HYDROLOGIC PARAMETERS IN THE ROOT ZONE1

In this study, a constrained minimization method, the flexible tolerance method, was used to solve the optimization problems for determining hydrologic parameters in the root zone: water uptake rate, spatial root distribution, infiltration rate, and evaporation. Synthetic soil moisture data were first generated using the Richards' equation and its associated initial and boundary conditions, and these data were then used for the inverse analyses. The results of inverse simulation indicate the following. If the soil moisture data contain no noise, the rate of estimated water uptake and spatial root distribution parameters are equal to the true values without using constraints. If there is noise in the observed data, constraints must be used to improve the quality of the estimate results. In the estimation of rainfall infiltration and surface evaporation, interpolation methods should be used to reduce the number of unknowns. A fewer number of variables can improve the quality of inversely estimated parameters. Simultaneous estimation of spatial root distribution and water uptake rate or estimation of evaporation and water uptake rate is possible. The method was used to estimate the water uptake rate, spatial root distribution, infiltration rate, and evaporation using long‐term soil moisture data collected from Nebraska's Sand Hills.     

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.     

Reducing Streamflow Forecast Uncertainty: Application and Qualitative Assessment of the Upper Klamath River Basin,Oregon1

Abstract: The accuracy of streamflow forecasts depends on the uncertainty associated with future weather and the accuracy of the hydrologic model that is used to produce the forecasts. We present a method for streamflow forecasting where hydrologic model parameters are selected based on the climate state. Parameter sets for a hydrologic model are conditioned on an atmospheric pressure index defined using mean November through February (NDJF) 700‐hectoPascal geopotential heights over northwestern North America [Pressure Index from Geopotential heights (PIG)]. The hydrologic model is applied in the Sprague River basin (SRB), a snowmelt‐dominated basin located in the Upper Klamath basin in Oregon. In the SRB, the majority of streamflow occurs during March through May (MAM). Water years (WYs) 1980‐2004 were divided into three groups based on their respective PIG values (high, medium, and low PIG). Low (high) PIG years tend to have higher (lower) than average MAM streamflow. Four parameter sets were calibrated for the SRB, each using a different set of WYs. The initial set used WYs 1995‐2004 and the remaining three used WYs defined as high‐, medium‐, and low‐PIG years. Two sets of March, April, and May streamflow volume forecasts were made using Ensemble Streamflow Prediction (ESP). The first set of ESP simulations used the initial parameter set. Because the PIG is defined using NDJF pressure heights, forecasts starting in March can be made using the PIG parameter set that corresponds with the year being forecasted. The second set of ESP simulations used the parameter set associated with the given PIG year. Comparison of the ESP sets indicates that more accuracy and less variability in volume forecasts may be possible when the ESP is conditioned using the PIG. This is especially true during the high‐PIG years (low‐flow years).     

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.     

KALMAN FILTER ESTIMATION AND PREDICTION OF DAILY STREAM FLOWS: I. REVIEW,ALGORITHM, AND SIMULATION EXPERIMENTS1

An important class of models, frequently used in hydrology for the forecasting of hydrologic variables one or more time periods ahead, or for the generation of synthetic data sequences, is the class of autoregressive(AR) models. As the AR models belong to the family of linear stochastic difference equations, they have both a deterministic and a stochastic component. The stochastic component is often assumed to have a Gaussian distribution. It is well known that hydrologic observations (e.g., stream flows) are heavily affected by noise. To account explicitly for the observation noise, the linear stochastic difference equation is expressed in state variable form and an observation model is introduced. The discrete Kalman filter algorithm can then be used to obtain estimates of the state variable vector. Typically, in hydrologic systems, model parameters, system noise statistics and measurement noise statistics are unknown, and have to be estimated. In this study an adaptive algorithm is discussed which estimates these quantities simultaneously with the state variables. The performance of the algorithm is evaluated by using simulated data.     

Hydrologic Modeling Uncertainty Resulting From Land Cover Misclassification1

Abstract: A stochastic, spatially explicit method for assessing the impact of land cover classification error on distributed hydrologic modeling is presented. One‐hundred land cover realizations were created by systematically altering the North American Landscape Characterization land cover data according to the dataset’s misclassification matrix. The matrix indicates the probability of errors of omission in land cover classes and is used to assess the uncertainty in hydrologic runoff simulation resulting from parameter estimation based on land cover. These land cover realizations were used in the GIS‐based Automated Geospatial Watershed Assessment tool in conjunction with topography and soils data to generate input to the physically‐based Kinematic Runoff and Erosion model. Uncertainties in modeled runoff volumes resulting from these land cover realizations were evaluated in the Upper San Pedro River basin for 40 watersheds ranging in size from 10 to 100 km² under two rainfall events of differing magnitudes and intensities. Simulation results show that model sensitivity to classification error varies directly with respect to watershed scale, inversely to rainfall magnitude and are mitigated or magnified by landscape variability depending on landscape composition.     

SIMULTANEOUS EQUATION SYSTEMS: A CONSISTENT ESTIMATOR FOR UNKNOWN PARAMETERS IN CONFINED AQUIFERS1

ABSTRACT: This paper presents criteria for establishing the identification status of the inverse problem for confined aquifer flow. Three linear estimation methods (ordinary least squares, two-stage least squares, and three-stage least squares) and one nonlinear method (maximum likelihood) are used to estimate the matrices of parameters embedded in the partial differential equation characterizing confined flow. Computational experience indicates several advantages of maximum likelihood over the linear methods.     

AN APPLICATION OF COMPUTER GRAPHICS TO ANALYSIS OF EXTREMES1

ABSTRACT: A convenient method for the statistical analysis of hydrologic extremes is to use probability papers to fit selected theoretical distributions to extremal observations. Three commonly accepted statistical distributions of extreme hydrologic events are: the double exponential distribution, the bounded exponential distribution, and the Log Pearson Type III distribution. In most cases, probability papers are distribution specific. But, for the Log Pearson Type III distribution, the probability paper is characterized by a population-specific parameter, namely, the coefficient of skewness. It is not practicable to procure probability papers for all possible values of this parameter. Therefore, a computer program is developed to generate population-specific probability papers and to perform statistical analysis of the data using computer graphics. Probability papers covering return periods up to 1000 years or more are generated for the three distributions mentioned above. Using a plot routine, available extremal observations are plotted on selected probability papers and a linear regression analysis is used to fit a straight line to the data. Predictions of hydrologic extremes for higher recurrence intervals can be made by extrapolating the fitted straight lines.     

A RAPID METHOD OF ESTIMATING MEAN AREAL RAINFALL1

ABSTRACT. A special case of generalized trend surface analysis is examined. This includes a linear surface. It is shown that for most hydrologic problems this case determines mean areal rainfall sufficiently accurately. Based on this conclusion, equations for rapid computation of mean areal rainfall are derived for this linear case. Results of the linear case are compared with other traditional methods of estimating mean areal rainfall.     

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.     

PREDICTIVE MODELS FOR GREAT LAKES HYDROLOGY1

ABSTRACT: The individual hydrologic components are assumed to be normally distributed for each month and linear regression equations are estimated for predicting the value of the individual monthly hydrologic components. It is shown that some of the hydrologic components for downwind (in this case downstream) lakes are dependent upon hydrologic events for the upwind lakes. This is particularly so for precipitation in the downwind lake basins which appears to be dependent upon evaporation values for upwind lakes.     

REGIONALIZATION AND PREDICTION OF FLOODS IN THE FRASER RIVER CATCHMENT,B.C.1

Probability distributions that model the return periods of flood characteristics derived from partial duration series are proposed and tested in the Fraser River catchment of British Columbia. Theoretical distributions describing the magnitude, duration, frequency and timing of floods are found to provide a goof fit to the observed data. The five estimated parameters summarizing the flood characteristics of each basin are entered into a discriminant analysis procedure to establish flood regions. Three regions were identified, each displaying flood behavior closely related to the physical conditions of the catchment. Within each region, regression equations are obtained between parameter values and basin climatic and physiographic variables. These equations provide a satisfactory prediction of flood parameters and this allows the estimation of a comprehensive set of flood characteristics for areas with sparse hydrologic information.