Kalman Filter Empirical Fitting on Monthly Rainfall-Runoff Responses

The majority of the methods for fitting rainfall-runoff Kalman filters use the statistical characteristics of the input (rainfall) and the output (runoff) series according to the systems analysis and control theory methodology. The problem arising with these techniques is essentially related with their inabilityto describe variations of the basin runoff response when the relevant information concerning the causes of such variations is not contained into the input to the filter. The presented empirical method of fitting solves this problem by taking into account additional input information and improving the knowledge about the hydrological system, but without changing the simple two-variable structure of the filter. This information consists of the percentage of snowfall into the monthly basin rainfall, the magnitude of basin rainfall at month t in comparison to the rainfall at month t-1 (increasing, constant, or decreasing) and the amount of basin rainfall associated with basin's moisture and runoff characteristics. The Kalman filter empirically fitted on monthly rainfall-runoff responses of the Aliakmon and Acheloos river basins in Greece is shown to be more accurate and adequate than the automatically fitted filter by using conventional statistical methods. The filter has been used in hydroelectric energy studies of the area, where accurate runoff estimation from rainfall was necessary.