Multi-site post-processing of numerical forecasts using a polynomial network substitution for the general differential equation based on operational calculus

Abstract

Precise daily forecasts of local wind speed are necessary for planning of the changeable wind power production. 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. Based on a 2-stage approach of the Perfect Prog method, used routinely in meteorology, the article proposes an enhanced forecast correction procedure with initial estimations of the optimal numbers of training days whose latest data observations are used to elicit daily prediction models. Determination of this main training parameter allows for improvements in the middle-term numerical forecasts of wind speed in the majority of prediction days. Subsequently in the 2nd stage the correction model post-processes numerical forecasts of the training input variables to calculate 24-hour prediction series of the target wind speed at the corresponding time. Differential polynomial network is used to develop the test and post-processing models, which represent the current spatial data relations between the relevant meteorological inputs->output quantities. This innovative machine learning method defines and substitutes for the general linear partial differential equation being able to describe the local atmospheric dynamics which is too complex and uncertain to be represented by standard soft-computing techniques. The complete derivative formula is decomposed into specific sub-solutions of node unknown sum functions in the multi-layer polynomial network structure using Operational Calculus to model the searched separable output function.