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The term now cast in hydro meteorology reflects the need for timely and accurate predictions of risky environmental situations, which are related to the development of severe meteorological events at short time scales. The objective of this paper is to apply a fully neural-network approach to the rainfall field now casting from infrared (IR) and microwave (MW) passive-sensor imagery aboard, respectively, geostationary Earth orbit (GEO) and low Earth orbit (LEO) satellites. The multisatellite space-time prediction procedure, which is named Neural Combined Algorithm for Storm Tracking (NeuCAST), consists of two consecutive steps. First, the IR radiance field measured from a geostationary satellite radiometer (e.g., Meteosat) is projected ahead in time (e.g., 30 min); second, the projected radiance field is used in estimating the rainfall field by means of an MW-IR combined rain retrieval algorithm exploiting GEO-LEO observations. The NeuCAST methodology is extensively illustrated and discussed in this paper. Its accuracy is quantified by means of quantitative error indexes, which are evaluated on selected case studies of rainfall events in Southern Europe in 2003 and 2005.