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

• Published in: Annales geophysicae (1988) Vol. 24; no. 10; pp. 2451 - 2460
• Main Authors: GALANIS, G, LOUKA, P, KATSAFADOS, P, PYTHAROULIS, I, KALLOS, G
• Format: Journal Article
• Language: English
• Published: Katlenburg-Lindau European Geophysical Society 20.10.2006; European Geosciences Union; Copernicus Publications
• Subjects: Earth Sciences; Earth, ocean, space; Exact sciences and technology; External geophysics; Ocean, Atmosphere; Physics of the high neutral atmosphere; Physics of the ionosphere; Physics of the magnetosphere; Sciences of the Universe; algorithms; Weather forecast; sensitivity analysis; Bias; Regional scope; Non linear filter; Non linear function; Wind velocity; Nonlinear problems; Atmospheric dynamics; Mesoscale; Atmospheric temperature; Linear filter; Meteorology and atmospheric dynamics Mesoscale meterology; instability; Mapping manifolds; Numerical forecast; Kalman filters; Instruments and techniques
• ISSN: 0992-7689; 1432-0576; 1432-0576
• DOI: 10.5194/angeo-24-2451-2006

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.