ارزیابی ساختار خطا دربرخی مدل‌های توزیع اندازه ذرات خاک

نوع مقاله : مقالات پژوهشی

نویسندگان

دانشگاه ارومیه

چکیده

توزیع اندازه ذرات (PSD) خاک یکی از اساسی‌ترین مشخصه‌های فیزیکی خاک است که به طور گسترده‌ در برآورد بسیاری از ویژگی‌های کلیدی خاک کاربرد دارد. بنابراین توصیف صحیح و پیوسته منحنی PSD خاک‌ها با استفاده از توابع ریاضی ضروری است. هدف از این مطالعه بررسی ساختار خطای تعدادی از مدل‌های برتر PSD در 24 نمونه خاک با کلاس های بافتی لوم شنی تا رس سیلتی از اراضی حاشیه غربی دریاچه ارومیه با سطوح مختلف شوری (از 4/85-8/0 دسی‌زیمنس بر متر) متاثر از شوری و سدیم بود. برای این منظور 6 مدل برتر PSD شامل لوجستیک (MLG)، فردلاند چهار و سه پارامتری (Fred-4p و Fred-3p)، اندرسون (AD)، (ONL) Offset-Nonrenormalized Lognormal و ویبول (Wei) انتخاب شده و جنبه‌های گوناگون کارآیی آن‌ها ارزیابی شد. نتایج نشان داد که براساس ضرایب کارآیی شامل) R2ضریب تبیین)، RMSE (ریشه میانگین مربعات خطا) و Er (خطای نسبی) همه‌ی مدل‌های مورد بررسی دارای کارآیی بالایی بوده و کمترین مقدار میانگین R2 در مدل‌ها برابر با 992/0 و بیشترین مقدار RMSE و Er نیز به ترتیب برابر با 028/0 و 045/0 بود. با این حال، بین کارآیی مدل‌ها با درصد شن نمونه‌ها ارتباط معنی‌داری از نوع چندجمله‌ای درجه دو مشاهده شد که براساس آن مدل‌های مورد بررسی در خاک‌های حاوی 30 تا 45 درصد شن کمترین کارآیی را داشتند. ساختار خطای نقطه به نقطه مدل‌ها بیانگرکاهش خطای سیستماتیک در برآورد ذرات درشت خاک توسط مدل‌ها بود در حالی که اغلب مدل‌ها فراوانی ذرات ریز خاک را (کوچکتر از 100 میکرومتر) بیشتر از واقعیت ‌برآورد کردند. افزون بر این، مقدار خطای نسبی نیز برای ذرات درشت خاک کم‌تر بود به گونه‌ای که مدل ویبول (برای نمونه) برای ذرات با قطر 100 تا 500 میکرومتر حداقل درصد خطای نسبی را داشت. همبستگی نسبتا بالا بین پارامتر‌های مدل Fred-3p،MLG و ONL بیانگرامکان کاهش تعداد پارامترهای این مدل‌ها است. باتوجه به نتایج بدست آمده، علی‌رغم کارآیی عمومی بالای مدل‌های مورد بررسی در برآورد کل منحنی PSD، کارآیی هر مدل وابسته به اندازه ذرات بود. بنابراین، یک مدل ممکن است برای برآوردکل PSD خاک دقت کافی داشته باشد ولی برای برآورد گستره‌ای خاص از PSD خاک مناسب نباشد. استفاده از چنین مدلی می‌تواند خطایی چشمگیر در برآورد گستره اندازه‌ای موردنظر ایجاد کند.

کلیدواژه‌ها


عنوان مقاله [English]

Characterizing the Error Structure of Selected Soil Particle Size Distribution Models

نویسندگان [English]

  • F. Afrasiabi
  • H. Khodaverdiloo
  • F. Asadzadeh
Department of Soil Science, Urmia University, Urmia, Iran.
چکیده [English]

Introduction Particle size distribution (PSD) is one of the most fundamental features of soil physics that is widely used as the most common input for predicting 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 by using mathematical functions is necessary.
The PSD models have often been evaluated in terms of their general performance for predicting the entire PSD curve. However, a given model may be feasible and globally perform well to generate the whole PSD curve but 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/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 Twenty four locations neighboring the western edge of threatened hypersaline Lake Urmia were sampled in this study. The locations were selected considering the available soil maps so that 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 by 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, dependence of the models performance to the range of soil particle sizes was examined.

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 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 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 performance was particle size dependent. This implies that, one should consider the range of sizes of soil particles for which the model are used. A model might be accurate enough for predicting 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.

کلیدواژه‌ها [English]

  • Lake Urmia
  • Particle Size Distribution models
  • Prediction error
  • Saline-sodic soil
1- Afrasiabi F. 2015. Relationship between quantitativeparameters of particle size distribution of salt-affected soils around Lake Urmia with selected soil quality indices. MSc Thesis, Urmia University, Urmia, Iran. (in Persian with English abstract)
2- Andersson S. 1990. “Markfysikaliska unders¨okningar I odlad jord, XXVI. Om mineraljordens och mullens rumsutfyllande egenskaper,” in En Teoretisk Studie, Swedish University of Agricultural Sciences, Uppsala, Sweden, (Swedish).
3- Assouline S., Tessier D. and Bruand, A. 1998. A conceptual model of the soil water retention curve. Water Resources Research, 34: 223–231.
4- Boadu F. 2000. Hydraulic conductivity of soils from grain-size distribution: new models. Journal of Geotechnical and Geoenvironmental Engineering, 126:739–746
5- Botula Y.D., Cornelis W.M., Baert G., Mafuka, P. and Van Ranst E. 2013. Particle size distribution models for soils of the humid tropics. Journal of Soils and Sediments, 13: 686– 698.
6- Broersma K. and Lavkulich L. 1980. Organic matter distribution with particle- size in surface horizons of some sombric soils in Vancouver Island. Canadian Journal of Soil Science, 60: 583- 586.
7- Buchan G.D., Grewal K.S. and Robson A.B. 1993. Improved models of particle- size distribution: An illustration of model comparison techniques. Soil Science Society of America Journal, 57: 901– 908.
8- Flemming B.W. 2007. The influence of grain-size analysis methods and sediment mixing on curve shapes and textural parameters: implications for sediment trend analysis. Sediment Geology, 202:425–435
9- Fredlund M.D., Fredlund D.G. and Wilson G.W. 2000. An equation to represent grain-size distribution. Canadian Geotechnical Journal, 37: 817– 827
10- Gee G.W. and Or D. 2002. Particle-size analysis. p. 255–293. In J.H. Dane and G.C. Topp (ed.) Methods of Soil Analysis. Part 4. Soil Science Society of America Book Series No. 5. Soil Science Society of America, Madison, WI.
11- Ghorbani Dashtaki S., Homaee M. and Khodaverdiloo H. 2010. Derivation and validation of pedotransfer functions for estimating soil water retention curve using a variety of soil data. Soil Use and Management, 26: 68-74.
12- Handreck KA. 1983. Particle-size and the physical-properties of growing media for containers. Communications in Soil Science and Plant Analysis, 14:209–222.
13- Haverkamp R. and Parlange J.Y. 1986. Predicting the water retention curve from a particle size distribution: 1. Sandy soils without organic matter. Soil Science, 142: 325– 339.
14- HwangS.I., Lee K.P., Lee D.S. and Powers S.E. 2002. Models for estimating soil particle-size distributions. Soil Science Society of America Journal, 66: 1143–1150.
15- Hwang S.I. 2004. Effect of texture on the performance of soil particle size distribution models.Geoderma, 123: 363– 371.
16- Khodaverdiloo H. and Samadi A. 2011. Batch equilibrium study on sorption, desorption, and immobilization of cadmium in some semiarid-zone soils as affected by soil properties. Soil Research, 49(5): 444-454.
17- Khodaverdiloo H., Homaee M., van Genuchten M. Th. and Ghorbani Dashtaki Sh. 2011. Deriving and Validating Pedotransfer Functions for some Calcareous Soils. Journal of Hydrology, 399: 93-99.
18- Khodaverdiloo H. and Hosseini Arablu N. 2014. Derivation, Validation and Comparison of Class and Continuous Pedotransfer Functions for Predicting Soil Cation Exchange Capacity in Several Textural Classes. Journal of Water and Soil Science, 18: 311-320. (in Persian with English abstract).
19- Lal R. 2004. Soil carbon sequestration impacts on global climate change and food security. Science, 304: 1623- 1626.
20- Lassabate`re L., Angulo-Jaramillo R., SoriaUgalde J. M., Cuenca R., Braud I. and Haverkamp R. 2006. Beerkan estimation of soil transfer parameters through infiltration experiments – BEST. Soil Science Society of America Journal,70: 521–532.
21- Lavkulich L.M. 1981. Methods Manual, Pedology Laboratory. Department of Soil Science, University of British Columbia, Vancouver, British Columbia, Canada.
22- Liu J., Xu S. and Liu H. 2003. Investigation of different models to describe soil particle- size distribution data, Advances in Water Science, 14: 588– 592.
23- Liu J., Xu S., Liu H. and Guo F. 2004. Application of parametric models to description of particle-size distribution in loamy soils. Acta Pedologica Sinica, 41: 375–379.
24- McLean E.O. 1982. Soil pH and lime requirement. P. 199- 224. In A.L. Page et al. (ed.) Methods of Soil Analysis. Part 2. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI.
25- Minasny B. and Hartemink A.E. 2011. Predicting soil properties in the tropics. Earth ScienceReview, 106:52–62.
26- Minasny B. and McBratney A.B. 2007. Estimating the water retention shape parameter from sand and clay content. Soil Science Society of America Journal, 71 (4): 1105– 1110.
27- Nabizadeh, E. and BeigiHarchegani H. 2011. Performance of Eight Mathematical Models in Describing Particle Size Distribution of Some Soils from Charmahal-va-Bakhtiari Province. Water and Soil Science, 15: 63-75. (in Persian with English abstract).
28- Nemes A. and Rawls W.J. 2004. Soil texture and particle-size distribution as input to estimate soil hydraulic properties. p. 36-50. In Y.A. Pachepsky and W. J. Rawls (eds.) Development of Pedotransfer Functions in Soil Hydrology, Developments in Soil Science, 30. Elsevier, Amsterdam.
29- Nemes A., Schaap M.G. and Wösten J.H.M. 2003. Functional Evaluation of Pedotransfer Functions Derived from Different Scales of Data Collection. Soil Science Society of America Journal, 67: 1093-1102.
30- Puckett W.E., Dane J.H. and Hajek B.F. 1985. Physical and mineralogical data to determine soil hydraulic-properties. Soil Science Society of America Journal, 49:831–836.
31- Rastgo M., Bayat H., Rastgo A. and Ebrahimi E. 2014. The Effect of Textural Groups on the Fitting Capability of Soil Particle Size Distribution Curve Models. Water and Soil, 28: 111-126. (in Persian with English abstract).
32- Shangguan W., Yongjiu D., Gutierrez C.G. and Yuan H. 2014. Particle- Size Distribution Models for the conversion of Chinese data to FAO/ USDA system. The Scientific World Journal, 1- 11.
33- Sparks D.L., Page A.L., Helmke P.A., Leoppert R.H., Soltanpour P.N., Tabatabai M.A.,Johnston G.T. and Sumner M.E. 1986. Methods of soil Analysis.Soil Science Society of America. Madison, Wisconsin, USA.
34- Su Y.Z., Zhao H.L., Zhao W.Z. and Zhang T.H. 2004. Fractal features of soil particle size distribution and the implication for indicating desertification. Geoderma, 122: 43– 49.
35- Wang D., Fu B.J., Zhao W.W., Hu H.F. and Wang Y.F. 2008. Multifractal characteristics of soil particle size distribution under different land- use types on the Loess Plateau, China. Catena, 72: 29– 36.
36- Xu G., Li Z. and Li P. 2013. Fractal features of soil particle-size distribution and total soil nitrogen distribution in a typical watershed in the source area of the middle Dan River, China. Catena, 101: 17–23.
37- Zhang Z., Yang X., Drury C., Reynolds W. and Zhao L. 2010. Mineralization of active soil organic carbon in particle size fractions of a Brookstonclay soil under no- tillage and mouldboard plough tillage. CanadianJournal of Soil Science, 90: 551-557.
38- Zhao P., Shao M. and Horton R. 2011. Performance of soil particle-size distribution models for describing deposited soils adjacent to constructed dams in the China loess plateau. Acta Geophysica, 59: 124-138.