Soil moisture: variable in space but redundant in time

Abstract

Abstract. 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?). We 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.

The role and value of distributed precipitation data in hydrological models

“…Even the gridded spatial resolution of 100 m proposed in the comment by Wood et al (2011) for hyper-resolution models seems from a purely physical perspective on hydrological processes questionable given the importance of hillslopes as key building blocks in a hydrological landscape (Fan et al, 2019). This is underpinned by the fact that hillslopes in the upper part of the Colpach are barely longer than 100 m, but different segments of these hillslopes can vary substantially in their wetness and connections to the river (e.g., Martínez-Carreras et al, 2016). Hydrological physically based modeling with top-down or bottom-up models without a delineation of the underlying system in smaller sub-units is hence up-to-date constrained to rather short length scales, at least if applications do not compromise the underlying physics.…”

Preferential Pathways for Fluid and Solutes in Heterogeneous Groundwater Systems: Self-Organization, Entropy, Work

“…While the second law of thermodynamic refers to physical entropy (introduced by Clausius (1857), section 3.1), information entropy (introduced by Shannon (1948)) is closely related and well suited for diagnosing spatial organization (section 3.3). The concepts of information and Shannon entropy haven been used widely to characterize irreversible mixing and reaction processes and their predictability (Chiogna and Rolle, 2017), the emergence of order in distributed time series (Malicke et al, 2020), information in multiscale permeability data (Dell`Oca et al, 2020) and the role of spatial variability of rainfall and topography in distributed hydrological modelling (Loritz et al, 2018(Loritz et al, , 2021. Woodbury and Ulrych (1993) and Kitanidis (1994) used the Shannon entropy to describe the spatial-time development and dilution of tracer plumes in groundwater systems.…”

Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics

“…S. Thiesen et al: HER: an information-theoretic alternative for geostatistics 2016; Thiesen et al, 2019;Mälicke et al, 2020), quantifying uncertainty and evaluating model performance (Chapman, 1986;Liu et al, 2016;Thiesen et al, 2019), estimating information flow (Weijs, 2011;Darscheid, 2017), and measuring similarity, quantity, and quality of information in hydrological models (Nearing and Gupta, 2017;Loritz et al, 2018Loritz et al, , 2019. In the spatial context, information-theoretic measures were used to obtain longitudinal profiles of rivers (Leopold and Langbein, 1962), to solve problems of spatial aggregation and quantify information gain, loss, and redundancy (Batty, 1974;Singh, 2013), to analyze spatiotemporal variability (Mishra et al, 2009;Brunsell, 2010), to address risk of landslides (Roodposhti et al, 2016), and to assess spatial dissimilarity (Naimi, 2015), complexity (Pham, 2010), uncertainty (Wellmann, 2013), and heterogeneity (Bianchi and Pedretti, 2018).…”