INFORMATION CONTENT AND COMPLEXITY OF SIMULATED SOIL WATER FLUXES

Authors: Pachepsky, Yakov; GUBER, ANDREY - U. OF CA, RIVERSIDE, CA; JACQUES, D - SCK-CEN, BELGIUM; SIMUNEK, J - U. OF CA, RIVERSIDE, CA; Van Genuchten, Martinus; NICHOLSON, T - USNRC, ONRR, WASH,DC; CADY, R - USNRC, ONRR, WASH,DC

Submitted to: Geoderma
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/1/2006
Publication Date: 4/19/2006
Citation: Pachepsky, Y.A., Guber, A.K., Jacques, D., Simunek, J., Van Genuchten, M.T., Nicholson, T.J., Cady, R.E. 2006. Information content and complexity of simulated soil water fluxes. Geoderma. (134):253-266.

Interpretive Summary: Examples of similar accuracy of strikingly different hydrologic models appear more and more often in literature. It becomes imperative to find a quantitative criterion to assess the performance of models and discriminate models without referring to their accuracy. The objective of this work was to attempt using information theory parameters to discriminate between simulated time series of soil water fluxes obtained from different models for the same site. The Richards equation-based model HYDRUS1D 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-meter deep loamy Eutric Regosol in Bekkevoort, Belgium. We used the metric entropy as the information content measure, and the effective the fluctuation complexity as the complexity measure. The two models gave the same accuracy of water flux simulations but had distinct differences in their relationships between complexity and information content. Overall, the HYDRUS-1D model generated flux time series that were more complex and had less information in them as compared with the WMBUS model. Using both complexity and information content parameters allowed us to discriminate between the soil water models that gave the same accuracy of soil water flux estimates.

Technical Abstract: The accuracy-based performance measures may not suffice to discriminate among soil water flow models. Comparing complexity of the model structures does not lead to quantifiable results. The objective of this work was to attempt using information theory parameters to discriminate between simulated time series of soil water fluxes obtained from different models for the same site. The Richards equation-based model HYDRUS1D 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-meter deep loamy Eutric Regosol in Bekkevoort, Belgium. We used the metric entropy and the mean information gain as information content measures, and the effective complexity measure and 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 parameters allowed us to discriminate between the soil water models that gave the same accuracy of soil water flux estimates.