NWP Model Revisions Using Polynomial Similarity Solutions of the General Partial Differential Equation

Abstract

Global weather models solve systems of differential equations to forecast large-scale weather patterns, which do not perfectly represent atmospheric processes near the ground. Statistical corrections were developed to adapt numerical weather prognoses for specific local conditions. These techniques combine complex long-term forecasts, based on the physics of the atmosphere, with surface observations using regression in post-processing to clarify surface weather details. Differential polynomial neural network is a new neural network type, which generates series of relative derivative terms to substitute for the general linear partial differential equation, being able to describe the local weather dynamics. The general derivative formula is expanded by means of the network backward structure into a convergent sum combination of selected composite polynomial fraction terms. Their equality derivative changes can model actual relations of local weather data, which are too complex to be represented by standard computing techniques. The derivative models can process numerical forecasts of the trained data variables to refine the target 24-h prognosis of relative humidity or temperature and improve the statistical corrections. Overnight weather changes break the similarity of trained and forecast patterns so that the models are improper and fail in actual revisions but these intermittent days only follow a sort of settled longer periods.