Data Driven Regional Weather Forecasting: Example using the Shallow Water Equations

Abstract

Using data alone, without knowledge of underlying physical models, nonlinear discrete time regional forecasting dynamical rules are constructed employing well tested methods from applied mathematics and nonlinear dynamics. Observations of environmental variables such as wind velocity, temperature, pressure, etc allow the development of forecasting rules that predict the future of these variables only. A regional set of observations with appropriate sensors allows one to forgo standard considerations of spatial resolution and uncertainties in the properties of detailed physical models. Present global or regional models require specification of details of physical processes globally or regionally, and the ensuing, often heavy, computational requirements provide information of the time variation of many quantities not of interest locally. In this paper we formulate the construction of data driven forecasting (DDF) models of geophysical processes and demonstrate how this works within the familiar example of a 'global' model of shallow water flow on a mid-latitude beta plane. A sub-region, where observations are made, of the global flow is selected. A discrete time dynamical forecasting system is constructed from these observations. DDF forecasting accurately predicts the future of observed variables.