Over the past two decades, considerable research has been carried out in hydrology for developing stochastic models for short- and long-term forecasting of river flows.
The form of these models generally follows the ARMA, ARMAX, and transfer function type of models (Box and Jenkins, 1976), with the last two proving to be more reliable for multiple forecasting periods (Burns and McBean, 1985; Awwad and Valdes, 1992). After defining the mathematical model, usually in a state-space form, the Kalman filter is widely used as a powerful tool for obtaining optimal hydrologic forecasts and updates of the states (e.g., Chiu, 1978; O'Connell, 1980; Wood and O'Connell, 1985).
Implementation of real-time stochastic models in large-scale hydrologic systems has been thoroughly discussed by Wood (1985) and Awwad and Valdes (1992). Furthermore, adaptive filters have also been used in combination with conceptual hydrologic models for streamflow forecasting since the late 1970s. Bras and collaborators at MIT, developed techniques to represent the National Weather Service River Forecasting System (NWSRFS) land component in a state-space form. Some of the research results are discussed in the next section. Alternative techniques such as stepwise regression and transfer function models have also been used. Later in this chapter the application of ANN in streamflow forecasting will be presented. In addition, probabilistic, interval, forecasts using the standard conceptual rainfallrunoff models for short-term forecasting has been developed. The most widely used is the ESP (extended streamflow prediction, now called ensemble streamflow prediction), which is described later in this chapter.
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