Variography of rainfall accumulation in presence of advection

Abstract

Summary This study provides a coherent theoretical framework between the field structures of rainfall accumulations over different durations. Following a classical geostatistical approach, we assume the existence of an elemental space–time stationary rainfall process and we consider rainfall accumulation as a regularization of this elemental process over time supports of various sizes. The corresponding space–time elemental variogram is used to derive the spatial and temporal variograms of accumulated values. In addition to an elemental variance, the framework incorporates both the anisotropy between time and space variability (Taylor velocity) and a constant advection of the rain fields. The proposed formulation verifies empirical observations made in past variographic studies like an increasing spatial range and a decreasing sill with increasing accumulation times. It provides new insights about the respective influence of accumulation and advection on the variogram shape and, as a side product, about Eulerian and Lagrangian properties of rainfall variability. From a set of experimental variograms calculated for different accumulation durations, we use the proposed formulation through a simple optimization algorithm to infer a four-parameter model characterizing the elemental rainfall process and the advection. A network of 21 daily rain gauges over the Loire Basin, France, gives an application illustration. We use a set of experimental space and time variograms corresponding to accumulation durations of 1–4 days. The identified parameters provide a fairly good fit of the experimental variogram set and their orders of magnitude look meteorologically sound. The main limitations and further developments of the method are discussed.