ارزيابي ساختار خطا در برخي مدل هاي توزيع اندازه ذرات خاك

Characterizing the Error Structure of Selected Soil Particle Size Distribution Models

توزيع اندازه ذرات (PSD) خاك يكي از اساسي ترين مشخصه هاي فيزيكي خاك است كه به طور گسترده در برآورد بسياري از ويژگي هاي كليدي خاك كاربرد دارد. بنابراين توصيف صحيح و پيوسته منحني PSD خاك ها با استفاده از توابع رياضي ضروري است. هدف از اين مطالعه بررسي ساختار خطاي تعدادي از مدل هاي برتر PSD در 24 نمونه خاك با كلاس هاي بافتي لوم شني تا رس سيلتي از اراضي حاشيه غربي درياچه اروميه با سطوح مختلف شوري (از 0.8-85.4 دسي زيمنس بر متر) متاثر از شوري و سديم بود. براي اين منظور 6 مدل برتر PSD شامل لوجستيك (MLG)، فردلاند چهار و سه پارامتري (Fred-4p و Fred-3p)، اندرسون (AD)، (ONL) Offset-Nonrenormalized Lognormal و ويبول (Wei) انتخاب شده و جنبه هاي گوناگون كارآيي آن ها ارزيابي شد. نتايج نشان داد كه بر اساس ضرايب كارآيي شامل R2 (ضريب تبيين)، RMSE (ريشه ميانگين مربعات خطا) و Er (خطاي نسبي) همه مدل هاي مورد بررسي داراي كارآيي بالايي بوده و كمترين مقدار ميانگين R2 در مدل ها برابر با 0.992 و بيشترين مقدار RMSE و Er نيز به ترتيب برابر با 0.028 و 0.045 بود. با اين حال، بين كارآيي مدل ها با درصد شن نمونه ها ارتباط معني داري از نوع چندجمله اي درجه دو مشاهده شد كه بر اساس آن مدل هاي مورد بررسي در خاك هاي حاوي 30 تا 45 درصد شن كمترين كارآيي را داشتند. ساختار خطاي نقطه به نقطه مدل ها بيانگركاهش خطاي سيستماتيك در برآورد ذرات درشت خاك توسط مدل ها بود در حالي كه اغلب مدل ها فراواني ذرات ريز خاك را (كوچكتر از 100 ميكرومتر) بيشتر از واقعيت برآورد كردند.افزون بر اين، مقدار خطاي نسبي نيز براي ذرات درشت خاك كم تر بود به گونه اي كه مدل ويبول (براي نمونه) براي ذرات با قطر 100 تا 500 ميكرومتر حداقل درصد خطاي نسبي را داشت. همبستگي نسبتا بالا بين پارامتر هاي مدل Fred- 3 p، MLG و ONL بيانگرامكان كاهش تعداد پارامترهاي اين مدل ها است. باتوجه به نتايج بدست آمده، علي رغم كارآيي عمومي بالاي مدل هاي مورد بررسي در برآورد كل منحني PSD، كارآيي هر مدل وابسته به اندازه ذرات بود. بنابراين، يك مدل ممكن است براي برآوردكل PSD خاك دقت كافي داشته باشد ولي براي برآورد گستره اي خاص از PSD خاك مناسب نباشد. استفاده از چنين مدلي مي تواند خطايي چشمگير در برآورد گستره اندازه اي موردنظر ايجاد كند.

Introduction: Particle size distribution (PSD) is one of the most fundamental features of soil physics that is widely used as the most common input to predict several key soil attributes. The mathematically representing the PSD provides several benefits to soil mechanics, physics, and hydrodynamics as well as helps to convert PSD data of various particle size classification systems to the desired one. Consequently, the correct and consistent descriptions of soil PSD using mathematical functions is necessary. The PSD models have often been evaluated in terms of their general performances to predict the entire PSD curve. Although given model may be feasible and globally perform well to generate the whole PSD curve, locally may fail to predict some specific points on the curve. To our knowledge, as well as, PSD models have not been widely tested for salt-affected soils with different levels of salinity and sodicity. The aim of this study was to determine the error structure of several more accurate PSD models in selected soil samples with different levels of salinity and sodicity. Materials and Methods: 24 locations neighboring the western edge of threatened hypersaline Lake Urmia were sampled in this study. The locations were selected based on the available soil maps and soils with wide range of salinity/sodicity were sampled. Selected physical and chemical properties of the soil samples were determined by standard methods. The performance of six PSD models including Modified Logistic Growth (MLG), Fredlund type models with three (Fred-4p) and four (Fred-3p) parameters, Anderson (AD), ONL, and Weibull (Wei), which have been reported as the most accurate PSD models by previous studies, was evaluated using different efficiency criteria that offer various performances depending on the range of particle sizes. An iterative nonlinear optimization procedure was used to fit the observed cumulative PSD data of the soils to the PSD models. Since every statistical criterion evaluates a part and some (and not all) aspects of the correspondence between measured and predicted values, we suggest that an effective assessment of model performance should include a suitable combination of criteria. Furthermore, dependency of the models performance was examined to the range of soil particle sizes. Results and Discussion: The soils differed widely in their EC (range = 85dS/m and CV = 159%), ESP (range = 67 % and CV = 71 %), and PSD (CV of clay and silt particles, 48 and 55 %, respectively). Soil textural class of the soils was differed widely from sandy loam to clay. All the soils were calcareous and alkaline. The results showed that according to the efficiency criteria, including R2 (coefficient of determination), RMSE (Root Mean Square Error) and Er (Relative Error), all of the models have high efficiency, so that, the lowest average value of R2 in models was 0.992 and the maximum value of RMSE and Er was 0.028 and 0.045, respectively. Prediction error of the models was dependent on the diameter for which we predict the cumulative fraction and decreases with increasing of the soil particles diameter. The performance of the models showed a significant quadratic polynomial relationship with sand content of the samples, so that, the studied models had the lowest performance in soils containing 30 to 45 percent sand. The point-to-point error structure of the model represents a decrease in systematic error in estimating coarse soil particles, while the models over-estimated the relative frequency of the fine soil particles. In addition, the values of relative error were also lower for coarse particles of the soil, so that, the Wei model (for example) had the lowest Er value for 100 to 500 μm diameter soil particles. The relatively high correlations between parameters of Fred-3p, MLG and ONL models show insights to reduce the number of their parameters. Furthermore, parameters a and c of MLG model, parameters μ and α of ONL model and parameter α and m of Fred-3p model had a statistically significant correlations. The relatively high correlations between parameters of the PSD models show insights to reduce the number of their parameters which increases their applicability. Conclusion: The studied models generally performed well to predict the whole PSD curve, but their performances were particle size dependent. This implies that, one should consider the range of sizes of soil particles for different models. A model might be accurate enough to predict some ranges of particle diameter or the whole PSD, but not for particular range of particle sizes. Using such models might lead to large errors in predicting the specific PSD range of interest.