Abstract
Abstract The occurrence of rainfall in the semiarid regions is notoriously unreliable and characterized by great spatial variability over a large spectrum of timescales. Based on analytical considerations, an integrated approach is presented here in order to describe the spatial structure of rain fields for timescales used in climatological studies, that is from the daily to the seasonal scales and beyond to the interannual scale. At the scale of the rain event, two factors determine the spatial structure of rain fields. One is the spatial variability of the conditional rainfall H* (H > 0), represented by its variogram γ*e. The other is the intermittency, its spatial structure being described by the indicator variogram γ1. It is shown that the spatial structure of rain fields for time steps larger than the event may be analytically derived from γ*e and γ1, taking into account the anisotropy and nonstationarity that may affect either of these two functions, which are thus two timescale invariants of the ra...
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