Post-processing of Wind-Speed Forecasts Using the Extended Perfect Prog Method with Polynomial Neural Networks to Elicit PDE Models

Abstract

Anomalies in local weather cause inaccuracies in daily predictions using meso-scale numerical models. Statistical methods using historical data can adapt the forecasts to specific local conditions. Differential polynomial network is a recent machine learning technique used to develop post-processing models. It decomposes and substitutes for the general linear Partial Differential Equation being able to describe the local atmospheric dynamics which is too complex to be modelled by standard soft-computing. The complete derivative formula is decomposed, using a multi-layer polynomial network structure, into specific sub-PDE solutions of the unknown node sum functions. The sum PDE models, using a polynomial PDE substitution based on Operational Calculus, represent spatial data relations between the relevant meteorological inputs->output quantities. The proposed forecasts post-processing is based on the 2-stage approach of the Perfect Prog method used routinely in meteorology. The original procedure is extended with initial estimations of the optimal numbers of training days whose latest data observations are used to elicit daily prediction models in the 1^st stage. Determination of the optimal models initialization time allows for improvements in the middle-term numerical forecasts of wind speed in prevailing more or less settled weather. In the 2^nd stage the correction model is applied to forecasts of the training input variables to calculate 24-h prediction series of the target wind speed at the corresponding time.