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Ann. Geophys., 24, 2451-2460, 2006
www.ann-geophys.net/24/2451/2006/
© European Geosciences Union 2006
Applications of Kalman filters based on non-linear functions to numerical weather predictions
G. Galanis1,2, P. Louka1,3, P. Katsafados1, I. Pytharoulis1,4, and G. Kallos1
1University of Athens, School of Physics, Division of Applied Physics, Atmospheric Modelling and Weather Forecasting Group, University Campus, Bldg. PHYS-V, 15784 Athens, Greece
2Naval Academy of Greece, Section of Mathematics, Xatzikyriakion, Piraeus 185 39, Greece
3Hellenic National Meteorological Service, El. Venizelou 14, Hellinikon 167 77, Athens, Greece
4Section of Meteorology and Climatology, Department of Geology, Aristotle University of Thessaloniki, University Campus, 54124 Thessaloniki, Greece.
Abstract. This paper investigates the use of non-linear functions in classical Kalman filter
algorithms on the improvement of regional weather forecasts. The main aim is
the implementation of non linear polynomial mappings in a usual linear
Kalman filter in order to simulate better non linear problems in numerical
weather prediction. In addition, the optimal order of the polynomials
applied for such a filter is identified. This work is based on observations
and corresponding numerical weather predictions of two meteorological
parameters characterized by essential differences in their evolution in
time, namely, air temperature and wind speed. It is shown that in both
cases, a polynomial of low order is adequate for eliminating any systematic
error, while higher order functions lead to instabilities in the filtered
results having, at the same time, trivial contribution to the sensitivity of
the filter. It is further demonstrated that the filter is independent of the
time period and the geographic location of application.
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