Exploring hydrological similarity during soil moisture recession periods using time dependent variograms

Abstract. This study proposes a new method for identifying temporally stable spatial patterns in soil moisture. Soil moisture patterns during rainfall-driven wetting conditions and during radiation-driven drying essentially reflect different processes with specific underlying controls. Consequently we expect that these patterns exhibit different covariance structures, and their spatial analysis should be separated accordingly. More specifically we hypothesize that: (H1): An ensemble of distributed soil moisture observations will converge to a rank-stable configuration during long-term drying periods and re-organize to stable ranks after disturbances; (H2): Variograms of these soil moisture ranks converge towards a stable configuration during drying periods, reflecting the covariance of the underlying time-invariant controls. These hypotheses were tested using soil moisture measurements which were recorded within the CAOS research unit in Luxembourg. We found evidence of stable rank configurations for time spans of several weeks. During rainfall events, these stable ranks were disturbed but later reorganized into the same pre-event configuration. Coupling time-shifting variograms with a density-based clustering algorithm enabled us to identify a convergence towards stable spatial variogram configurations. Moreover, the spatial organization of soil moisture showed preferred states with distinct patterns, depending on their respective drivers. This corroborates that the proposed method can be used to disentangle spatial structure originating from rainfall patterns from those controlled by the internal terrestrial system properties. Furthermore, we conclude that during stable states variogram aggregates originating from the density-based clustering could in principle be used for interpolation purposes, as they represent a temporally stable covariance. In contrast, an interpolation can be problematic while covariance is not stable in time. While the method has been developed and tested based on spatially distributed soil moisture data, it is also suitable for analyzing other state variables.