Stochastic Models with Periodic-Correlation of Seasonal River Runoff Variations

Abstract

Development of stochastic models for seasonally varying processes is one of the problems insufficiently studied in hydrology. The complexity of this problem arises in the nonstationary character of these processes (or, to be more specific, their periodic correlation), the lack of adequate mathematical tools, the necessity for consideration of a large number of parameters, and the computational instability of the methods used. Specialists in this field suggest different approaches varying in complexity for modelling hydrological processes involving seasonal variations. The method of fragments and the method of sequential determination of linear autoregression, suggested by G.G.Svanidze [14]; the method of canonical expansions, suggested by Busalaev and Davletgaliev [3]; the method of normalisation, modified by Reznikovsky and others [10], are some examples of these methods. A large number of approaches for solving this problem are touched upon in [3,13,16]. Priestley [6] and Tong [16] recommend complex non-linear models. The above methods reproduce with different certainty the properties of the observed series but have a common limitation. When studying the seasonal runoff variations, the performance in terms of two-dimensional and multi-dimensional distributions by the empirical data is not evaluated, and the properties of the stochastic models, as well as their optimal complexity are usually not discussed.