22The mean squared error (MSE) and the related normalization, the Nash-Sutcliffe efficiency (NSE

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Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state-parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously;(2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model.

An artificial neural network (ANN) is a flexible mathematical structure which is capable of identifying complex nonlinear relationships between input and output data sets. ANN models have been found useful and efficient, particularly in problems for which the characteristics of the processes are difficult to describe using physical equations. This study presents a new procedure (entitled linear least squares simplex, or LLSSIM) for identifying the structure and parameters of three-layer feed forward ANN models and demonstrates the potential of such models for simulating the nonlinear hydrologic behavior of watersheds. The nonlinear ANN model approach is shown to provide a better representation of the rainfall-runoff relationship of the medium-size Leaf River basin near Collins, Mississippi, than the linear ARMAX (autoregressive moving average with exogenous inputs) time series approach or the conceptual SAC-SMA (Sacramento soil moisture accounting) model. Because the ANN approach presented here does not provide models that have physically realistic components and parameters, it is by no means a substitute for conceptual watershed modeling. However, the ANN approach does provide a viable and effective alternative to the ARMAX time series approach for developing input-output simulation and forecasting models in situations that do not require modeling of the internal structure of the watershed. IntroductionThe rainfall-runoff (R-R) process is believed to be highly nonlinear, time-varying, spatially distributed, and not easily described by simple models [Singh, 1964; Kulandais•amy and Subramanian, 1967;Chiu and Huang, 1970; Pilgrim, 1976]. Two major approaches for modeling the R-R process have been explored in the literature: "conceptual" (physical) modeling and "system theoretic" modeling (sometimes referred to as "black box") [Amorocho and Hart, 1964;Sorooshian, 1983; Guoeta, 1984;Singh, 1988;Duan, 1991; O'Connell and Clarke, 1981; Young and Wallis, 1985]. Conceptual rainfall-runoff (CRR) models are designed to approximate within their structures (in some physically realistic manner) the general internal subprocesses and physical mechanisms which govern the hydrologic cycle. CRR models usually incorporate simplified forms of physical laws and are generally nonlinear, time-invariant, and deterministic, with parameters that are representative of watershed characteristics. Until recently, for practical reasons (data availability, calibration problems, etc.) most conceptual watershed models assumed lumped representations of the parameters. Among the more widely used and reported lumped parameter watershed models are the Sacramento soil moisture accounting (SAC-SMA) model of the U.S. National Weather Service [Burnash et al., 1973; Brazil and Hudlow, 1980], HEC-1 [U.S. Army Corps of Engineers, 1990], and the Stanford watershed model (SWM) [Crawford and Linsley, 1966]. While such models ignore the spatially distributed, time-varying, and stochastic properties of the R-R process, they attempt to incorporate realistic rep...

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