Annual stream flow simulation by ARMA processes and prediction by Kalman filter
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ORIGINAL PAPER
Annual stream flow simulation by ARMA processes and prediction by Kalman filter Khadidja Boukharouba
Received: 27 October 2011 / Accepted: 24 January 2012 / Published online: 10 February 2012 # Saudi Society for Geosciences 2012
Abstract Algeria is a semi-arid country where water resources are not sufficient to cope with the important socio-economic development demands. Any sustainable development strategy is basically dependent on a rigorous management of water resources potential, which presents a true challenge to be tackled for such countries. Classic mathematical models based on time invariability and ignorance of the stochastic and non-linear nature of hydrological variables are not sufficient for simulation and prediction studies. The present study subscribes to the stochastic hydrological processes modeling and prediction in case of time-varying linear systems through adaptive Kalman filter (KF) methodology. It focuses upon stream flows as a water resources component, which is directly related to the socioeconomic development meanwhile it opts for Kalman filter as principal tool of work. The main objective is the application of (KF) technique to model and predict annual streamflow volumes in Northern Algeria and the obtained results are satisfactory. Keywords Kalman filter . ARMA . Prediction . Stream flow . Béni-Badel . Algeria
Introduction Hydrologic variables occur in nature as a result of interconnected physical elements, among which unknown K. Boukharouba (*) Laboratoire de Recherche des Sciences de l’Eau-LRS-EAU, Ecole Nationale Polytechnique (E.N.P), 10 Av. Hacène-badi, BP182, El-Harrach, Algiers 16200, Algeria e-mail: [email protected] URL: http//www.enp.edu.dz
climatic and physiographic factors play a dominant role. Hence, hydrologic variables such as rainfall are products of complex time-varying phenomena which can be measured by a finite number of observations. These observations indicate that hydrologic variables are stochastic in nature (Yevjevich 1972) and that they are non-linear (Amorcho and Orlob 1961), as a result of (1) time-variable geologic processes of erosion, deposition, weathering, etc., (2) climatic changes, (3) state uncertainty in time, and (4) energy transfer of the hydrologic cycle, which is non-linear in its character. A detailed study of hydrologic phenomena requires mathematical models that should take into account time variability. Hence, the planner might want either to simulate the underlying generating mechanism of the phenomenon concerned or to make future predictions. Jazwinski (1969) wrote a book which presents a united treatment of linear and non-linear filtering theory for engineers, with sufficient importance on applications to make possible the reader to use the theory. Non-linear filtering results are derived first, and these are then specialized to linear systems. The treatment of linear filtering includes filter stability and model error sensitivity. The performance of these non-linear filters is critically analyzed. On the other hand, Gelb
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