A Modified Kalman Filter Based on Radial Basis Function Neural Networks for the Improvement of Numerical Weather Prediction Models

Abstract

This study introduces a novel enhancement to the Kalman filter algorithm by integrating it with Radial Basis Function neural networks to improve numerical weather prediction models. Traditional Kalman filters frequently underperform when used by dynamical systems due to their reliance on fixed covariance matrices, resulting in inaccuracies and forecast uncertainty. The proposed modified Kalman filter utilizes Radial Basis Function neural networks to estimate covariance matrices adaptively during the filtering process. This self-adaptive computational system enables the simultaneous targeting of the systematic and the remaining non-systematic parts of the forecast error, producing an innovative and efficient post-process strategy. The suggested methodology is evaluated on predictions of 10-meter wind speed and 2-meter air temperature obtained from the Weather Research and Forecasting model for observation stations in northern Greece. The derived results demonstrate a significant reduction in systematic error, as the bias decreased by up to 88% for 10-meter wind speed and 58% for 2-meter air temperature. Additionally, the forecast variability was successfully mitigated, with the RMSE reduced by 39% and 40%, respectively. Compared to the traditional Kalman filter, which exhibited increased RMSE in several cases and failed to control forecast uncertainty, the proposed approach consistently outperformed by providing stable and reliable predictions across all examined scenarios. These improvements validate the robustness of the method in comparison to conventional techniques, highlighting its potential to produce reliable and stable predictions for environmental applications.