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The accuracy-based performance measures may not suffice to discriminate among soil water flow models. The objective of this work was to attempt using information theory measures to discriminate between different models for the same site. The Richards equation-based model HYDRUS-1D and a water budget-type model MWBUS were used to simulate one-year long observations of soil water contents and infiltration fluxes at various depths along the trench in a 1-meter deep loamy Eutric Regosol in Bekkevoort, Belgium. We used the (a) the metric entropy and (b) the mean information gain as information content measures, and (c) the effective measure complexity and (d) the fluctuation complexity as complexity measures. To compute the information content and complexity measures, time series of fluxes were encoded with the binary alphabet; fluxes greater (less) than the median value were encoded with one (zero). Fifty Monte Carlo simulation runs were performed with both models using hydraulic properties measured along a trench for soil profile consisting of five layers differing in their hydraulic properties.

The two models had the similar accuracy of water flux simulations. Precipitation time series demonstrated a low complexity and a relatively high information content. Both models simulated behavior of soil as an information filter with respect to water fluxes. Simulated soil water flux time series had smaller information content as compared with precipitation time series. The complexity of simulated water flux time series was higher than the complexity of precipitation time series, so that the water flux time series appeared to be more structured as compared with precipitation time series.

Model outputs showed distinct differences in their relationships between complexity and information content. Overall, more complex simulated soil flux time series were obtained with the HYDRUS-1D model that used a continuum mechanics representation of soil water flow and was perceived to be conceptually more complex than the WMBUS model. The MWBUS model generated flux time series that had the range of complexity measure values much narrower than the HYDRUS -1D model. An increase in the complexity of water flux time series occurred in parallel with the decrease in the information content.

An increase in complexity of the conceptual soil water flow models is often being associated with considering a layered flow domain instead of a single homogeneous layer. For one, this definitely causes an increase in the number of parameters, as each layer has its own set of soil hydraulic properties. We ran fifty Monte Carlo simulations of soil water fluxes for the single soil homogeneous layer. The information content and complexity of simulated soil water fluxes appeared to be affected by the type of water flow transport mechanism descriptions rather than by the variation of parameters within the flow domain.

The good model discrimination was achieved when both information content and complexity measures were used to characterize the simulated time series. Using the effective measure complexity in combination with the mean information gain was the most efficient way to discriminate models in this work.

Keywords: soil water flow simulations, information, complexity, water flux, model comparison

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