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Published by the American Geophysical Union as part of the Water Science and Application Series, Volume 6. During the past four decades, computer-based mathematical models of watershed hydrology have been widely used for a variety of applications including hydrologic forecasting, hydrologic design, and water resources management. These models are based on general mathematical descriptions of the watershed processes that transform natural forcing (e.g., rainfall over the landscape) into response (e.g., runoff in the rivers). The user of a watershed hydrology model must specify the model parameters before the model is able to properly simulate the watershed behavior.
This thesis provides a critique and evaluation of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology, and provides an appraisal of sensitivity analysis methods for watershed models with calibrated parameters. The first part of this thesis explores the strengths and weaknesses of the GLUE methodology with commonly adopted subjective likelihood measures using a simple linear watershed model. Recent research documents that the widely accepted GLUE procedure for describing forecasting precision and the impact of parameter uncertainty in rainfall-runoff watershed models fails to achieve the intended purpose when used with an informal likelihood measure (Christensen, 2004; Montanari, 2005; Mantovan and Todini, 2006; Stedinger et al., 2008). In particular, GLUE generally fails to produce intervals that capture the precision of estimated parameters, and the distribution of differences between predictions and future observations. This thesis illustrates these problems with GLUE using a simple linear rainfall-runoff model so that model calibration is a linear regression problem for which exact expressions for prediction precision and parameter uncertainty are well known and understood. The results show that the choice of a likelihood function is critical. A likelihood function needs to provide a reasonable distribution for the model errors for the statistical inference and resulting uncertainty and prediction intervals to be valid. The second part of this thesis discusses simple uncertainty and sensitivity analysis for watershed models when parameter estimates result form a joint calibration to observed data. Traditional measures of sensitivity in watershed modeling are based upon a framework wherein parameters are specified externally to a model, so one can independently investigate the impact of uncertainty in each parameter on model output. However, when parameter estimates result from a joint calibration to observed data, the resulting parameter estimators are interdependent and different sensitivity analysis procedures should be employed. For example, over some range, evaporation rates may be adjusted to correct for changes in a runoff coefficient, and vice versa. As a result, descriptions of the precision of such parameters may be very large individually, even though their joint response is well defined by the calibration data. These issues are illustrated with the simple abc watershed model. When fitting the abc watershed model to data, in some cases our analysis explicitly accounts for rainfall measurement errors so as to adequately represent the likelihood function for the data given the major source of errors causing lack of fit. The calibration results show that the daily precipitation from one gauge employed provides an imperfect description of basin precipitation, and precipitation errors results in correlation among flow errors and degraded the goodness of fit.
Methods and guidelines for developing and using mathematical models Turn to Effective Groundwater Model Calibration for a set of methods and guidelines that can help produce more accurate and transparent mathematical models. The models can represent groundwater flow and transport and other natural and engineered systems. Use this book and its extensive exercises to learn methods to fully exploit the data on hand, maximize the model's potential, and troubleshoot any problems that arise. Use the methods to perform: Sensitivity analysis to evaluate the information content of data Data assessment to identify (a) existing measurements that dominate model development and predictions and (b) potential measurements likely to improve the reliability of predictions Calibration to develop models that are consistent with the data in an optimal manner Uncertainty evaluation to quantify and communicate errors in simulated results that are often used to make important societal decisions Most of the methods are based on linear and nonlinear regression theory. Fourteen guidelines show the reader how to use the methods advantageously in practical situations. Exercises focus on a groundwater flow system and management problem, enabling readers to apply all the methods presented in the text. The exercises can be completed using the material provided in the book, or as hands-on computer exercises using instructions and files available on the text's accompanying Web site. Throughout the book, the authors stress the need for valid statistical concepts and easily understood presentation methods required to achieve well-tested, transparent models. Most of the examples and all of the exercises focus on simulating groundwater systems; other examples come from surface-water hydrology and geophysics. The methods and guidelines in the text are broadly applicable and can be used by students, researchers, and engineers to simulate many kinds systems.
Watershed modeling is at the heart of modern hydrology, supplying rich information that is vital to addressing resource planning, environmental, and social problems. Even in light of this important role, many books relegate the subject to a single chapter while books devoted to modeling focus only on a specific area of application. Recognizing the
Abstract : Climate change and anthropogenic activities create uncertainty with respect to future hydrological conditions, and thus pose challenges in predicting streamflow, particularly the magnitude of extreme events. Several studies have focused on understanding future flood risk under climate and land use/land cover (LULC) changes using hydrological models. In addition to biases from climate data, biases from hydrological models, especially on peak flow simulations were reported to be large (usually underestimations). This could limit the dependability of flood risk projections and their applicability for future decision making. This research study investigates techniques and approaches for improved simulation of streamflows with focus on peak flows using the Soil and Water Assessment Tool (SWAT) for three case study watersheds. In particular, evaluations include choice of criteria for sensitivity analysis and parameter identification, choice of objective function for calibration, and impact assessment when calibrated models are applied for periods with alternate climate and physical characteristics. For ease of calibration, sensitivity analysis is crucial to identify relevant parameters; however, it can provide different parameter sets based upon the implemented sensitivity criteria. Herein, four sensitivity criteria, namely the Nash-Sutcliffe Efficiency (NSE), coefficient of determination (R2), modified R2 (bR2), and percent bias (PBIAS) were compared in watersheds of contrasting climate, hydrology, and land cover. For rainfall-runoff dominated agricultural watersheds, NSE, bR2, and R2 produced relatively similar parameter sets, and thus these criteria can be used individually or together for the purposes of sensitivity analysis, especially if peak flows are the target. For a snowmelt dominated forested watershed, R2 was found to be the best sensitivity criterion to identify parameters affecting peak flows. Moreover, for this watershed, sensitivity analysis and light calibration of snowmelt related parameters separately followed by calibration of the hydrological parameters resulted in improved flow simulations compared to the default approach where all parameters were analyzed together. The ability of models calibrated to a given set of climate and LULC data to simulate flood risk under altered conditions was assessed in each watershed by applying parameters calibrated for 2002-2005 to 1970-1999. Simulated annual maximum daily flows for the latter period were used to estimate the instantaneous annual maximum flow (AMF) series, and the impact of altered parameter values on the resulting flood distribution was assessed via a one-at-a-time sensitivity analysis. As anticipated, AMFs in the agricultural rainfall-runoff dominated watersheds were sensitive to changes in runoff related parameters, whereas AMFs in the forested snowmelt and dominated watershed were sensitive to changes in snowmelt related parameters. Alteration of the bank storage recession constant was found to significantly affect AMFs in all three watersheds. It was observed that simulation of the flood risk distribution under altered climate can be improved by modifying snow related parameters based upon the observed change in temperature from the calibration period. In flood risk studies with projected urbanization and expansion of agricultural areas, the curve number parameter should be adjusted by the proportion of change relative to the baseline (or calibration) period.
This book comprehensively accounts the advances in data-based approaches for hydrologic modeling and forecasting. Eight major and most popular approaches are selected, with a chapter for each — stochastic methods, parameter estimation techniques, scaling and fractal methods, remote sensing, artificial neural networks, evolutionary computing, wavelets, and nonlinear dynamics and chaos methods. These approaches are chosen to address a wide range of hydrologic system characteristics, processes, and the associated problems. Each of these eight approaches includes a comprehensive review of the fundamental concepts, their applications in hydrology, and a discussion on potential future directions.