Submitted to: Hydrological Sciences Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 4/14/2011
Publication Date: 9/9/2011
Citation: Pan, F., Pachepsky, Y.A., Guber, A.K., Hill, R. 2011. Information and Complexity Measures Applied to Observed and Simulated Soil Moisture Time Series. Hydrological Sciences Journal. 56:1027-1039. Interpretive Summary: Modeling of soil moisture dynamics is used as an important tool in many engineering and regulatory decisions. Pathways of water in soils are very complex. This complexity is easy to perceive, but is difficult to represent in mathematical terms without making broad simplifying assumptions. Different sets of assumptions have been proposed and many different models of soil water flow have been developed as a result. The critical question, then, is to decide which model is better. The usual approach to model evaluation is to use the differences between simulated and measured water contents to evaluate model accuracy. This approach, however, often does not discriminate between models; therfore, other methods to select models are needed. We attempted to use information theory methods of pattern analysis, akin to methods of bioinformatics to analyze the simulated and measured soil water content time series. The model was then evaluated in terms of its ability to reproduce patterns in time series along with the model point accuracy. Using one-year-monitoring data from the OPE3 USDA-ARS site, we found that pattern discrimination methods worked well in characterization of soil water model output. We observed, that soil functions as an information filter; as the depth increases, soil moisture patterns gain more and more structure and order as compared to the random patterns of rainfall. Results of this work are important for micrometeorologists, hydrologists, agronomists, and environmental engineers in that they suggest a method that can help to improve the reliability of soil moisture forecasts and soil moisture availability evaluations.
Technical Abstract: Time series of soil moisture-related parameters provides important insights in functioning of soil water systems. Analysis of patterns within these time series has been used in several studies. The objective of this work was to compare patterns in observed and simulated soil moisture contents to understand whether modeling leads to a substantial loss of information or complexity. The time series was observed at four plots in sandy soils within the USDA-ARS OPE3 experimental watershed for a year, precipitation and evapotranspiration were measured and estimated, respectively, thereby, and soil water flow was simulated with the HYDRUS-1D software. Information content measures were the metric entropy and the mean information gain, and complexity measures were the fluctuation complexity and the effective measure complexity. These measures were computed based on the binary encoding of soil moisture time series, and used probabilities of patterns, i.e. probabilities of joint or sequential appearance of symbol sequences. The information content of daily soil moisture content time series was much smaller than the one of rainfall data, and had the higher complexity, indicating soil worked essentially as the information filter. The information content and complexity decreased and increased with the depth respectively, demonstrating the increase in the information filtering action of soil. The information measures of simulated soil moisture content were close to the ones of the measurements, indicating the successful simulation of patterns in data. The spatial variability of the information measures for simulated soil moisture content at all depths was less pronounced than the one of measured time series. Compared with precipitation and estimated ET, soil moisture time series had more structure and less randomness in this work. The information measures can provide useful complementary knowledge about model performance and patterns in observation and modeling results.