Fractal approach in characterization of spatial pattern of soil properties

Abstract

The objective of the study was to characterize spatial pattern of soil properties (CaCO3, soil organic carbon, P2O5, K2O, and clay content) using fractal concept. Total of 141 top-soil samples (0-30 cm) were collected on 1850 ha in karst polje (Petrovo polje, Croatia) and analyzed for listed soil properties. The semi-variogram method was used to estimate fractal dimension (D) value which was performed from both of isotropic and anisotropic perspective. The D value of soil properties ranged between 1.76 to 1.97, showing a domination of the short-range variations. The SOC and K2O fractal D values 1.79 and 1.76 respectively, exhibited a spatial continuity at the entire analysed range of the scale. The D value for P2O5 (1.97) showed a nearly total absence of the spatial structure at all scales. The CaCO3 and clay content indicated a multifractal behavior mainly attributed to effects of alluviation, differences in geology and its spatial changes and transitions. The results of anisotropic analysis of soil properties pattern have showed strong relations with directions and partial self-similarity over limited ranges of scales defined by scale-break. Finally, our results showed that fractal analysis can be used as a appropriate tool for the characterization of spatial pattern irregularities of soil properties and detection of soil forming factors that cause it. 

Keywords

• Fractal dimension,scale independency,self-similarity,semi-variogram

References

1. Armstrong, A.C., 1986. On the fractal dimensions of some transient soil properties. European Journal of Soil Science 37(4): 641-652.
2. Anderson, A.N., McBratney, A.B., Crawford, J.W., 1998. Applications of fractals to soil studies. In: Sparks, D.L. (Ed.). Advances in Agronomy. Vol. 63. Academic Press, New York, pp.1–76.
3. Bartoli F., Burtin G., Royer J.J., Gury M., Gomendy, V., Philippy, R., Leviandier, Th., Gafrej, R., 1995. Spatial variability of topsoil characteristic within one silty soil type. Effect of clay migration. Geoderma 68(4): 279-300.
4. Beckett, P.H.T., Webster. R., 1971. Soil variability: A review. Soils and Fertilizers 34: 1-15
5. Burgess, T.M., Webster, R., 1980. Optimal interpolation and isarithmic mapping of soil properties. I. Semivariogram and punctual kriging. II. Block kriging. European Journal of Soil Science 31(2): 315-342.
6. Burrough, P.A., 1981. Fractal dimensions of landscapes and other environmental data. Nature 294: 240-242.
7. Burrough, P.A., 1983a. Multiscale sources of spatial variation in soil. I. The application of fractal concepts to nested levels of soil variation. European Journal of Soil Science 34(3): 577-597.
8. Burrough, P. A., 1983b. Multiscale sources of spatial variation in soil. II. A non- brownian fractal model and its application in soil survey. European Journal of Soil Science 34(3): 599–620.

9. Burrough, P.A., 1984. The application of fractal ideas to geophysical phenomena. Bulletin of the Institute of Mathematics and its Application 20: 36-42
10. Culling, W.E.H., 1986. Highly erratic spatial variability of soil-pH on Iping Common, West Sussex. Catena 13(1–2): 81-98.
11. Culling, W.E.H. and Datko M.,1987. The fractal geometry of the soil-covered landscape. Earth Surface Processes and Landforms 12 (4): 369-385.
12. IUSS Working Group WRB, 2014. World reference base for soil resources 2014. World Soil Resources Reports No. 106, FAO, Rome, Italy.
13. Ivanović, A., Sikirica, V., Marković, S.. Sakač, K., 1972. Bacic geological map of SFRJ, Drniš K 33-9, M=1:100 000. Institute for geological investigations, Beograd [in Croatian].
14. JDPZa, 1966. Chemical methods for soil analysis, Beograd [in Croatian].
15. JDPZb, 1966. Physical methods for soil analysis, Beograd [in Croatian].
16. Klinkenberg, B., 1992, Fractals and morphometric measures: Is there a relationship? Geomorphology 5(1-2): 5-20.
17. Klinkenberg, B., Goodchild, M.F., 1992. The fractal properties of topography: a comparison of methods. Earth Surface Processes and Landforms 17 (3): 217–234.
18. Mandelbrot, B., B., 1967. How long is the coast of britain? Statistical self-similarity and fractional dimension. Science 156: 636–638.
19. Mandelbrot, B., B., 1977. Fractals: Form, Chance and Dimension. Freeman, London
20. Mark, D.M., Aronson, P.B., 1984. Scale-dependent fractal dimensions of topographic surfaces: an empirical investigation, with applications in geomorphology and computer mapping. Journal of the International Association for Mathematical Geology 16 (7): 671–683.
21. McBratney, A.B., Webster, R., 1981. Spatial dependence and classification of the soil along a transect in North-east Scotland. Geoderma 26(1-2), 63-82.
22. Miloš, B., 1987. Numerical classification of hydromorphic soils, PhD thesis, Faculty of Forestry University of Sarajevo, Sarajevo, Bosnia and Herzegovina [in Croatian].
23. Miloš, B., 2000. Geostatistical soil data analysis. I. Measuring spatial variability of soil properties with semivariograms. Agriculturae Conspectus Scientificus 65(4): 219-228.
24. Peitgen H.O., Saupe D., 1988. The science of fractal images. Springer-Verlag, New York, USA.
25. Webster, R., Butler, B., 1976. Soil classification and survey studies at Ginninderra. Australian Journal of Soil Research 14(1): 1-24.