Comparison of calculation methods of fractal dimension on agricultural soil surface roughness

Abstract

[Objectives]How the fractal theory as an efficient tool to describe rough and irregular geometrical feature in nonlinear system and nature is applied into agricultural soil research is hot issue at present. [Methods]The roughness data of agricultural soil surface after sowed(perpendicular to the sowed direction), sowed surface(along with the sowed direction), ploughed surface(perpendicular to the ploughed direction), and rolled surface(along with the rolled direction)were obtained by laser roughness measuring instrument. The fractal dimensions, non-scale space and correlation coefficient were computed respectively by three methods, i.e.variate-difference method, the structure function method, and the mean square root method. [Results]The undulation of surface after ploughed was large, but with small fractal dimension and less fine structure, and low complex degree as a consequence;the undulation of surface in perpendicular direction after sowed was also large, but with low complicated degree, while the undulation in parallel direction was conversely small with high complicated degree;the undulation of surface in rolled direction after rolled was larger than that was sowed, but with low complicated degree. [Conclusions]The fractal dimension calculated by using the mean square root method was the most accurate, which had good correlation of linear regression and small variation of non-scale range.