Conceptual Basis of Seasonal Streamflow Time Series Models

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Abstract
Conceptual models of watershed processes and stochastic models of precipitation and streamflow processes are often needed in the planning and management of hydraulic systems. A number of such models have been proposed in the literature, and many of them are actually used in current practice. This paper focuses on identification of stochastic models for representing storage and streamflow processes of a natural watershed subject to a stochastic precipitation input. More specifically, a natural watershed is considered in which all inputs, state variables, outputs, and parameters vary with the season. Assuming that the precipitation input is uncorrelated with periodic mean and periodic variance, that the ground-water storage is the only significant storage in the watershed, and under further linear reservoir assumptions, it has been shown that the seasonal ground-water storage is represented by a periodic autoregressive moving average process of order (1,0), i.e., a PARMA(1,0) process, and the seasonal streamflow is a PARMA(1,1) process. If surface storage is considered, in addition to ground-water storage, then for the same periodic uncorrelated precipitation input, the seasonal ground water becomes a PARMA(2,0) process, and the model of seasonal streamflow becomes a PARMA(2,1) process. Furthermore, extensions have been made considering the general case of PARMA(p,q) precipitation inputs.