Application of Fractal Theory to Quantify Structure from Some Soil Orders

Document Type : Research Article

Authors

• alidad karami
• R. Zara
• vahid alah jahandideh mahjan abadi

Azad University, Marvdashat Branch

https://doi.org/10.22067/jsw.v31i4.57888

Abstract

Introduction: Fractal geometry concepts have been widely applied as a useful tool to describe complex natural phenomena, in particular,for a better understanding of soil physical systems. However, limited information is available on the fractal characteristics of soil properties or soil aggregation. A soil aggregate is made of closely packed sand, silt, clayand organic particles building upsoil structure. Soil aggregation is a soil quality index integrating the chemical, physical, andbiological processes involved in the genesis of soil structure. Soil structure and its stability are important issuesfor many agronomic and environmental processes. Thus, quantitative description of soil structure is very important. Soil forming factors in different soils (various orders) and forms affect the soil structureformation. Characterizing aggregate size distribution for different soil orders using fractal theory is necessary for evaluating the impact of soil forming factors on soil structure and quantifying the relationship between fractal dimension and other important soil properties. Therefore, the aims of this research were quantifying the structure of different soil orders using fractal geometry, mean weight diameter of aggregates (MWD)and geometric mean diameter of aggregates (GMD). In addition, MWD and GMD indices and fractal parameters of soil aggregate size distribution were compared toevaluate soil structure and determinethe relationship between fractal parameters with MWD, GMDand other soil properties.
Materials and Methods: Fractal models which simulate soil structure are also used to better understand soil behaviors. Aggregate size distribution is determined by sieving a fixed amount of soil mass under mechanical stress and is commonly synthesized by the MWD, GMDand fractal dimensions such as the fragmentation fractal dimensions. Therefore, aggregate size distribution and its stability variation were evaluated using some fractal models and MWD and GMD (empirically indices).In the current study, the original data were obtained from analysis of diagnostic horizons of seven important soil orderslocated in Fars Province in the Southern Iran. Soil samples were collected from diagnostic horizons of seven soil orders includingEntisols, Vertisols, Aridisols, Mollisols, Alfisols, Histosols and Inceptisols. The measured physico-chemical properties of soil were aggregate size distribution, soil particle size percentage (sand, silt, and clay), saturation percentage (SP), organic carbon (OC), pH, calcium carbonate equivalent (TNV), gypsum content, soil electrical conductivity (EC) and soil bulk density (BD). The MWD and GMD indices, the fractal dimensions and fractal parameters of aggregates were then calculated. Relationships between soil properties with MWD, GMD and the fractal dimension were also determined.
Results and Discussion: The results showed that there was a significant correlation between fractal dimension of Riue and Sposito and Taylor and Wheatcraft models and soil aggregate stability indices (MWD and GMD indices of aggregates) with the other soil characteristics. This correlation between fractal parameters with organic matter, bulk density, clay and sand percentage was stronger than other soil properties. There was a significant and negative correlation (p< 0.01) between fractal dimension of Riue and Sposito and Taylor and Wheatcraft models with mean weight diameter of aggregates and geometric mean diameter of aggregates. Inverse correlation between fractal dimension and aggregate stability indices illustrateed thatlower fractal dimensionswere calculated for the soils with more stable aggregates which have the highest mean weight diameter of aggregates and geometric mean diameter of aggregates. Subsequently, the fractal dimension of aggregates could reflect the aggregate stability factors. The values of coefficient of determination (R2) and mean error (ME), root mean square error (RMSE), residual some of squares (RSS), mean square of non-fitted (Sr2) and Akaike) AIC (statistical criteria indicated that Taylor and Wheatcraft model had the better performance. Although largerfractal dimensions were estimated by Riue and Sposito modelwhich can be explained by the great model sensitivity, this model overall performed well.
Conclusion: The results indicated that fractal theory can be used to characterize soil structure at different soil orders and fractal dimensions of soil aggregate seems to be more effective in this regard, except forHistosols. Fractal dimension can be estimated using some easily available soil properties. Fractal theory can be applied to characterize and quantify soil structure in different soil orders of Fars Province.

Keywords

• Aggregates size distribution
• Aggregates stabilit
• Fractal models
• Soil orders
• Soil structure

20.1001.1.20084757.1396.31.4.6.9

References

1. Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control AC, 19: 716-723.

2. Ataei A., Gorgi, M. and Parvizi, Y. 2014. Evaluation of the suitability of fractal dimension of soil aggregates in assessing different soil management practices. Iranian Journal of Soil Research, 28: 701-712. (in Persian with English abstract).

3. Bayat H., Neyshabouri M.R., Mohammadi K. and Narimanzadeh, N. 2011. Estimating water retention with pedotransfer functions using multi-objective group method of data handling and ANNs. Pedosphere, 21: 107–114.

4. Beare M.H., Hendrix P.F. and Coleman D.C. 1994. Water- stable aggregates and organic matter fractions in conventional and no-tillage soils. Soil Science Societyof American Journal, 58: 777-786.

5. Belaid H. and Habaieb H. 2015. Soil aggregate stability in a Tunisian semi-arid environment with reference to fractal analysis. Journal of Soil Science Environment Management, 6(2): 16-23.

6. Boix-FayosC., Calvo-Cases A. and Imeson A.C. 2001. Influence of soil properties on the aggregation of some Mediterranean soils and the use of aggregate size and stability as land degradation indicators. Journal of Catena, 44: 47– 67.

7. Bronik C.J. and Lal R. 2005. Soil structure and management: a review. Geoderma, 124: 3-22.

8. Cambardella C.A. 2006. Aggregation and organic matter. P52-55, In: Lal R. (Ed.), Encyclopedia of Soil Science. Taylor and Francis, Boca Raton, FL.

9. Caruso T., Barto E.K., Siddiky M.R.K., Smigelski J. and Rillig M.C. 2011. Are power laws that estimate fractal dimension a good descriptor of soil structure and its link to soil biological properties. Soil Biology and Biochemestry, 43: 359-366.

10. Chepil W.S. 1950. Methods of estimating apparent density of discrete soil grains. Soil Science, 70: 351-362.

11. Dahiya I.S., Richter J. and Malik R.S. 1984. Soil spatial variability: A review. International Tropical Agriculture, 77: 1-102.

12. Diaz-Zorita M., Perfect E., Grove J.H. 2002. Descriptive methods for assessing soil structure. Soil and Tillage Research, 64: 3-22.

13. Ding Q. and Ding W. 2007. Comparing stress wavelets with fragment fractals for soil structure quantification. Soil and Tillage Research, 93: 316–323.

14. Duhour A., Costa C., Momoa F., Falco L. and Malacalza L. 2009. Response of earthworm communities to soil disturbance: Fractal dimension of soil and species’ rank-abundance curves. Applied Soil Ecology, 43: 83–88.

15. Eghball B., Mielke L.N., Calvo G.A. and Wilhelm W.W. 1993. Fractal description of soil fragmentation for various tillage methods and crop sequences. Soil Science Society American Journal, 57: 1337-1341.

16. Filgueira R.R., Fournier L.L., Sarli G.O., Aagon A. and Rawals, W.J. 1999. Sensitivity of fractal parameters of soil aggregates to different management practices in a Phaeozem in central Argentina. Soil and Tillage Research, 52: 217-222.

17. Gardner W.R. 1956. Representation of soil aggregate-size distribution by a logarithmic-normal distribution. Soil Science American Proceeding, 20: 151-153.

18. Gee G.W. and Bauder J.W. 1986. Particle size analysis. P383-411, In: Klute, A. (Ed.), Methods of Soil Analysis, Part I, 2d Madison, WI. American Society Agronomy.

19. Grossman R.B. and Reinsch T.G. 2002. Bulk density and linear extensibility. P201-228, In: Warren, A.D. (ed.). Methods of Soil Analysis. Part 4. Physical Methods. Soil Science SocietyAmerican Inc.

20. Gulser C. 2006. Effect of forage cropping treatments on soil structure relationships with fractal dimensions. Geoderma. 131: 33–44.

21. Huang G. and Zhang R. 2005. Evaluation of soil water retention curve with the pore-solid fractal model. Geoderma. 127: 52-61.

22. Karami A., Homaeea M., Afzalinia S., Ruhipour H. and Basirat S. 2012. Organic resource management: Impacts on soil aggregate stability and other soil physico-chemical properties. Agricutural Ecosystem and Environment, 148: 22–28.

23. Kutlu T., Ersahin S. and Yetgin B. 2008. Relations between solid fractal dimension and some physical properties of soils formed over alluvial and colluvial deposits. Journal of Food Agricultural Environment, 6: 45-449.

24. Larney F.J. 2008. Dry-aggregate size distribution. P821-83, In: Carter M.R., Gregorich E.G. (Eds.), Soil Sampling and Methods of Analysis. Canadian Society of Soil Science, CRC Press, Boca Raton, FL.

25. Mazurak A.P. 1950. Effect of gaseous phase on water-stable synthetic aggregates. Soil Science, 69: 135–148.

26. McLean E.O. 1988. Soil pH and lime requirement. PP199-224, In: Page A. L. (Ed.), Methods of Soil Analysis. Part, American Society of Agronomy, Soil Science Society America, Madison, Wis.

27. Millan H., Gonzalez-Posada M., Aguilar M., Dominguez J. and Cespedes L. 2003. On the fractal scaling of soil data. Particle-size distributions. Geoderma, 117: 117-128.

28. Nadler A., Perfect E. and Kay B.D. 1996. Effect of polyacrylamide application on the stability of dry and wet aggregate. American Journal of Soil Science Society, 60: 555-561.

29. Olawale O.J., Abu S.T. and Dorcas, O.O. 2016. Evaluation of soil aggregate stability under long term land management system. International Journal of Plant and Soil Science, 9(2): 1-7.

30. Page A.L., MillerR.H, and Keeney, D.R. 1982. Methods of soil analysis, Part II, Physical properties, ASA, Soil Science Society of America, Madison, WI.

31. Parent L.E., Parent S.E., KättererT. and Egozcue J.J. 2011. Fractal and compositional analysis of soil aggregation. Proceedings of the 4th International Workshop on Compositional Data Analysis. P9-13.

32. Perfect E. and Blevnis R.L. 1997. Fractal characterization of soil aggregation and fragmentation as influenced by tillage treatment. Soil Science Society American Journal, 61: 896-900.

33. Perfect E. and Kay B.D. 1991. Fractal theory applied to soil aggregation. Soil Science SocietyAmerican Journal, 55: 1552-1558.

34. Perfect E., Kay B.D. and Rasiah V. 1993. Multifractal model for soil aggregate fragmentation. Soil Science SocietyAmerican Journal, 57: 896-900.

35. Perfect E., Kenst A.B., Diaz-Zorita M. and Grove J.H. 2004. Fractal analysis of soil water desorption data collected on disturbed samples with water activity meters.Soil Science Society American Journal, 68:1177–1184.

36. Perfect E., Pachepsky Y. and Martin M.A. 2009. Fractal and multiracial models applied to porous media. Vadose Zone Journal, 7: 174–176.

37. Perfect E., Rasiah V. and Kay B.D. 1992. Fractal dimension of soil aggregate- size distribution calculated by number and mass. Soil Science Society American Journal, 56: 1407-1409.

38. Pirmoradian N., Sepaskhah A.R. and Hajabbasi M.A. 2005. Application of fractal theory to quantify soil aggregate stability as influenced by tillage treatments. Biosystem Engineering, 90: 227-234.

39. Puri A.M. and Puri B.R. 1939. Physical characteristics of soil. ΙΙ. Expressing mechanical analysis and state of aggregation of soil values. Soil Science, 33: 141-163.

40. Rasiah V., Kay B.D. and Perfect E. 1992. Evaluation of selected factors influencing aggregate fragmentation using fractal theory. Canadian Journal of Soil Science, 72: 97-106.

41. Rasiah V., Kay B.D. and Perfect E. 1993. New mass – based model for estimating fractal dimension of soil aggregates. Soil Science Society American Journal, 57: 891-895.

42. Rieu M. and Sposito G. 1991. Fractal fragmentation, soil porosity, and soil water properties: Π. Applications. Soil Science Society American Journal, 55:1239-1244.

43. Soil Survey Division Staff. 2010. Soil Survey Manual United States Department of Agriculture, Washington. P97-123.

44. Sparks D.L., Page A.L., Helmke P.A., Leoppert R.H., Soltanpour P.N., Tabatabai M.A., Johnston G.T. and summer M.E. 1996. Methods of soil analysis. Madison. Soil Science Society of America.

45. 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.

46. Tyler S.W. and Wheatcraft S.W. 1992. Fractal scaling of soil particle-size distributions: analysis and limitations. Soil Science Society American Journal, 56: 362-369.

47. vanBavel C.H.M. 1949. Mean weight-diameter of soil aggregation as a statistical index of aggregation. Soil Science Society American Journal, 14: 20–23.

48. Walczak R.T., MorenoF., Sławinski C., Fernandez E. and Arru J.L. 2006. Modeling of soil water retention curve using soil solid phase parameters. Journal of Hydrology, 329: 527–533.

49. Wang D., Fu B., Zhao W., Hu H., and Wang Y. 2008. Multifractal characteristics of soil particle size distribution under different land-use types on the Loess Plateau, China. Catena, 72: 29–36.

50. Zicheng Z., Shuqin H. and Tingxuan L. 2011. Fractal dimensions of soil structure and soil anti-erodibility under different land use patterns. African Journal of Agricultural Research, 6: 5496-5504.