Prediction of atmospheric temperature fields using the extended Kalman filter

Abstract

A combined method for forecasting temperature fields of the atmosphere, based on statistical data from the reanalysis of atmospheric parameters, is proposed. The first component of the method is to obtain least squares estimates of the parameters of the Crank-Nicolson finite difference scheme. However, these estimates turn out to be biased due to the presence of errors in the regressors. In order to reduce the specified bias, the extended Kalman filter is used as the second component of the method. Using the found parameter estimates, substituted into the Crank-Nicholson finite-difference scheme, the temperature values at the internal nodes were predicted from the test part of the sample. A full-scale computational experiment is presented, confirming the effectiveness of the proposed method, based on the data of time series of atmospheric temperatures obtained from the NCEP/DOE AMIP II Reanalysis system. The conducted studies have shown that the quality of model parameter estimates in the form of parabolic differential equations is significantly affected by the choice of the type of difference approximation; the quality of the estimates improves when stable finite difference schemes are used and their order is increased. The combination of LSM and the extended Kalman filter with an evolution model based on the Crank-Nicolson finite-difference scheme developed as a result of research provides an increase in the accuracy of forecasting changes in atmospheric temperature fields by an average of 38%. The obtained mathematical models of temperature fields of the atmosphere can be used in the study of the meteorological situation, which determines the safety of aviation flights.