مقایسه‌ نکویی شاخص‌های آماری مختلف برای ارزیابی مدل‌های نفوذ آب به خاک

نوع مقاله : مقالات پژوهشی

نویسندگان

1 دانشگاه شهرکرد

2 دانشگاه ارومیه

چکیده

قابلیت مدل‌ها در شبیه سازی فرایندهای خاک عموماً با مقایسه مقادیر اندازه گیری و برآورد شده سنجیده می‌شود. انتخاب و استفاده از شاخص-های آماری مناسب و تفسیر نتایج برای ارزیابی مدل های نفوذ آب به خاک، چالشی اساسی است، زیرا هر کدام از شاخص ها بر نوع خاصی از خطاها تاکید دارد. هدف از این پژوهش، مقایسه نکویی شاخص های آماری مختلف برای ارزیابی مدل های نفوذ آب به خاک است. بدین منظور، مجموعه داده ای دربرگیرنده 145 نقطه-داده اندازه‌گیری شده از نفوذ آب به خاک‌های مختلف ایران با روش استوانه های مضاعف استفاده شد. پارامترهای مدل ها به روش بهینه سازی حداقل مربعات خطا با استفاده از نرم افزار MatLab 7.7.0 (R2008b) تعیین شد. سپس، قابلیت مدل های نفوذ آب به خاک با شاخص های ضریب تبیین (R2)، ریشه میانگین مربعات خطا (RMSE) و شاخص کارآیی (NSEI) و فرم‌های اصلاح شده آن (از جمله NSEjI، NSESQRTI، NSElnI و NSEiI) تعیین و نکویی این شاخص‌ها در انتخاب مدل برتر مقایسه شد. نتایج نشان داد که میانگین شاخص RMSE همیشه نمی‌تواند شاخص مناسبی برای ارزیابی مدل‌های نفوذ آب به خاک باشد. شاخص NSEI، NSEjI، NSESQRTI و NSElnI نیز به دلیل حساس بودن به مقادیر بزرگ داده ها نتوانستند تمایز بین مدل ها را در برآورد نفوذ تجمعی آشکار کنند. شاخص NSEiI با وزن دهی بیش‌تر به داده های نفوذ در زمان های کوتاه تر، به عنوان شاخص آماری مناسب برای مقایسه قابلیت مدل ها نفوذ انتخاب شد. به طورکلی، نتایج این پژوهش نشان داد که قابلیت شاخص‌های آماری مختلف برای ارزیابی مدل ها بستگی به میزان تاثیر آن ها از مقادیر داده های نفوذ در سری های متفاوت زمانی است.

کلیدواژه‌ها


عنوان مقاله [English]

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

نویسندگان [English]

  • S. Mirzaee 1
  • S. Ghorbani Dashtaki 1
  • H. Khodaverdiloo 2
1 Shahrekord University
2 Urmia University
چکیده [English]

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

کلیدواژه‌ها [English]

  • Error
  • Statistical criteria
  • Infiltration water into soil
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