Local improvements in numerical forecasts of relative humidity using polynomial solutions of general differential equations

Abstract

Large‐scale forecast models are based on the numerical integration of differential equation systems, which can describe atmospheric processes in light of global meteorological observations. Mesoscale forecast systems need to define the initial and lateral boundary conditions, which may be carried out with robust global numerical models. Their overall solutions are able to describe the dynamic weather system on the Earth scale using a large number of complete globe 3D matrix variables in several atmospheric layers. Post‐processing methods using local measurements were developed in order to clarify surface weather details and adapt numerical weather prediction model outputs for local conditions. Differential polynomial network is a new type of neural network that can model local weather using spatial data observations to process forecasts of the input variables and revise the target 24 h prognosis. It defines and solves general partial differential equations, being able to describe unknown dynamic systems. The proposed forecast correction method uses a differential network to estimate the optimal numbers of training days and form derivative prediction models. It can improve final numerical forecasts, processed with additional data analysis and statistical techniques, in the majority of cases. The two‐stage procedure presented is analogous to the perfect‐prognosis method using real observations to derive a model, which is applied to the forecasts of the predictors to calculate output predictions.