Applications of Kalman filters based on non-linear functions to numerical weather predictions

摘要

This paper investigates the use of non-linear functions in classical Kalman filteralgorithms on the improvement of regional weather forecasts. The main aim isthe implementation of non linear polynomial mappings in a usual linearKalman filter in order to simulate better non linear problems in numericalweather prediction. In addition, the optimal order of the polynomialsapplied for such a filter is identified. This work is based on observationsand corresponding numerical weather predictions of two meteorologicalparameters characterized by essential differences in their evolution intime, namely, air temperature and wind speed. It is shown that in bothcases, a polynomial of low order is adequate for eliminating any systematicerror, while higher order functions lead to instabilities in the filteredresults having, at the same time, trivial contribution to the sensitivity ofthe filter. It is further demonstrated that the filter is independent of thetime period and the geographic location of application.