Post-processing of Numerical Forecasts Using Polynomial Networks with the Operational Calculus PDE Substitution

Abstract

Large-scale weather forecast models are based on the numerical integration of systems of differential equation which can describe atmospheric processes in light of physical patterns. Meso-scale weather forecast systems need to define the initial and lateral boundary conditions which can be supplied by global numerical models. Their overall solutions, using a large number of data variables in several atmospheric layers, represent the weather dynamics on the earth scale. Post-processing methods using local measurements were developed in order to adapt numerical weather prediction model outputs for local conditions with surface details. The proposed forecasts correction procedure is based on the 2-stage approach of the Perfect Prog method using data observations to derive a model which is applied to the forecasts of input variables to predict 24-h series of the target output. The post-processing model formation requires an additional initial estimation of the optimal number of training days in consideration of the latest test data. Differential polynomial network is a recent machine learning technique using a polynomial PDE substitution of Operational calculus to form the test and prediction models. It decomposes the general PDE into the 2^nd order sub-PDEs in its nodes, being able to describe the local weather dynamics in the surface level. The PDE sum models represent the current local data relations in a sort of settled weather which allow improvements in local forecasts corrected with NWP utilities in the majority of days.