Information content and complexity of simulated soil water fluxes

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 in a 1-m deep loamy Eutric Regosol in Bekkevoort, Belgium. We used the (a) 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. The two models had the similar accuracy of water flux simulations. Precipitation input data demonstrated a moderate complexity and relatively high information content. 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 was perceived to be conceptually more complex than the WMBUS model. An increase in the complexity of water flux time series occurred in parallel with the decrease in the information content. Using both complexity and information content measures allowed us to discriminate between the soil water models that gave the same accuracy of soil water flux estimates.