Automated procedures are developed to change scales so that long tails in frequency distributions of morphometric variables are avoided. They minimize the skewness of slope gradient frequency distributions, and modify the kurtosis of profile and plan curvature distributions towards that of the Gaussian (normal) model. Box-Cox (for slope) and arctangent (for curvature) transformations are tested on nine digital elevation models (DEMs) of varying origin and resolution, and different landscapes, and shown to be effective. Our results show considerable improvements over those for previously recommended slope transformations (sine, square root of sine, and logarithm of tangent). By avoiding long tails and outliers, they permit parametric statistics such as correlation, regression and principal component analysis to be applied, with greater confidence that requirements for linearity, additivity and even scatter of residuals (constancy of error variance) are likely to be met. It is suggested that such transformations should be routinely applied in all parametric analyses of long-tailed variables. Our Box-Cox and curvature automated transformations are based on a Python script, implemented as an easy-to-use script tool in ArcGIS.
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