农业土壤表面不平度分形维数计算方法的对比与分析

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

[目的]分形理论作为描述自然界和非线性系统中不光滑和不规则几何形体的有效工具,如何运用到农业土壤表面的研究中,是目前研究的热点问题。[方法]采用非接触式激光不平度测量仪测量了播种后地表(垂直于播种方向)、播种后地表(平行于播种方向)、犁地后地表(垂直于犁地方向)和整地后地表(平行于整地方向)4种农业地表的不平度,分别采用变差法、结构函数法和轮廓均方根法分析了4种农业地表不平度的分形维数、无标度区间及相关系数。[结果]犁地后地表起伏大,但分维小,细微结构少,复杂程度小;播种后地表(垂直于播种方向)起伏大,但复杂程度小,播种后地表(平行于播种方向)起伏小,但复杂程度高;同在平行于耕作方向,整地后地表的起伏大于播种后地表的起伏,但其复杂程度低于后者。[结论]均方根法计算农业土壤表面不平度的分形维数更精确,线性回归的相关性更好,无标度区间变化很小。

[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.