Comparing the Goodness of Different Statistical Criteria for Evaluating the Soil Water Infiltration Models

Introduction: The infiltration process is one of the most important components of the hydrologic cycle. Quantifying the infiltration water into soil is of great importance in watershed management. Prediction of flooding, erosion and pollutant transport all depends on the rate of runoff which is directly affected by the rate of infiltration. Quantification of infiltration water into soil is also necessary to determine the availability of water for crop growth and to estimate the amount of additional water needed for irrigation. Thus, an accurate model is required to estimate infiltration of water into soil. The ability of physical and empirical models in simulation of soil processes is commonly measured through comparisons of simulated and observed values. For these reasons, a large variety of indices have been proposed and used over the years in comparison of infiltration water into soil models. Among the proposed indices, some are absolute criteria such as the widely used root mean square error (RMSE), while others are relative criteria (i.e. normalized) such as the Nash and Sutcliffe (1970) efficiency criterion (NSE). Selecting and using appropriate statistical criteria to evaluate and interpretation of the results for infiltration water into soil models is essential because each of the used criteria focus on specific types of errors. Also, descriptions of various goodness of fit indices or indicators including their advantages and shortcomings, and rigorous discussions on the suitability of each index are very important. The objective of this study is to compare the goodness of different statistical criteria to evaluate infiltration of water into soil models. Comparison techniques were considered to define the best models: coefficient of determination (R2), root mean square error (RMSE), efficiency criteria (NSEI) and modified forms (such as NSEjI, NSESQRTI, NSElnI and NSEiI). Comparatively little work has been carried out on the meaning and interpretation of efficiency criteria (NSEI) and its modified forms used to evaluate the models. Materials and Methods: The collection data of 145 point-data of measured infiltration of water into soil were used. The infiltration data were obtained by the Double Rings method in different soils of Iran having a wide range of soil characteristics. The study areas were located in Zanjan, Fars, Ardebil, Bushehr and Isfahan provinces. The soils of these regions are classified as Mollisols, Aridisols, Inceptisols and Entisols soil taxonomy orders. The land use of the study area consisted of wheat, barley, pasture and fallow land.The parameters of the models (i.e. Philip (18), Green and Ampt (3), SCS (23), Kostiakov (6), Horton (5), and Kostiakov and Lewis (11) models) were determined, using the least square optimization method. All models were fitted to experimental infiltration data using an iterative nonlinear regression procedure, which finds the values of the fitting parameters that give the best fit between the model and the data. The fitting process was performed using the MatLab 7.7.0 (R2008b) Software Package. Then, the ability of infiltration of water into soil models with the mean of coefficient of determination (R2), root mean square error (RMSE), efficiency criteria(NSEI) and modified forms (such as NSEjI, NSESQRTI,NSElnI and NSEiI) were determined and goodness of criteria was compared for the selection of the best model. Results and Discussion: The results showed the mean of RMSE for all soils cannot always be a suitable index for the evaluation of infiltration of water into soil models. A more valid comparison withNSEI, NSEjI, NSESQRTI, NSElnI indices indicated that these indices also cannot apparently distinguish among the infiltration models for the estimation of cumulative infiltration. These indices are sensitive to the large amount of data. The NSEiI index with giving more weight to infiltration data in shorter times was selected as the most appropriate index for comparing models. According to the NSEiI index, Kostiakov and Lewis, Kostiakov, SCS, Philip, Horton, and Green and Ampt models were the best models in approximately 72.42, 44.83, 26.9, 53.11, 11.73 and 1.0 percent of soils, respectively. Conclusion: The results of this study indicated that the ability of modified forms of NSE indices in evaluation of infiltration of water into soil models depend on the influence of models from infiltration data values in different time series. This encourages us to be cautious on the application and interpretation of statistical criteria when evaluating the models. Keywords: Error, Statistical criteria, Infiltration water into soil