Soil moisture: variable in space but redundant in time

Soil moisture at the catchment scale exhibits a huge spatial variability. This suggests that even a large amount of observation points would not be able to capture soil moisture variability.

We present a measure to capture the spatial dissimilarity and its change over time. Statistical dispersion among observation points is related to their distance to describe spatial patterns. We analyzed the temporal evolution and emergence of these patterns and used the mean shift clustering algorithm to identify and analyze clusters. We found that soil moisture observations from the 19.4 km2 Colpach catchment in Luxembourg cluster in two fundamentally different states. On the one hand, we found rainfall-driven data clusters, usually characterized by strong relationships between dispersion and distance. Their spatial extent roughly matches the average hillslope length in the study area of about 500 m. On the other hand, we found clusters covering the vegetation period. In drying and then dry soil conditions there is no particular spatial dependence in soil moisture patterns, and the values are highly similar beyond hillslope scale.

By combining uncertainty propagation with information theory, we were able to calculate the information content of spatial similarity with respect to measurement uncertainty (when are patterns different outside of uncertainty margins?). ... mehrWe were able to prove that the spatial information contained in soil moisture observations is highly redundant (differences in spatial patterns over time are within the error margins). Thus, they can be compressed (all cluster members can be substituted by one representative member) to only a fragment of the original data volume without significant information loss.

Our most interesting finding is that even a few soil moisture time series bear a considerable amount of information about dynamic changes in soil moisture. We argue that distributed soil moisture sampling reflects an organized catchment state, where soil moisture variability is not random. Thus, only a small amount of observation points is necessary to capture soil moisture dynamics.