Statistical description of seedbed cloddiness by structuring objects using digital elevation models

The set of detected objects enables to derive the statistical distributions characterizing the ellipse variables (orientation angle, major and minor axis lengths) and the half-cosine amplitude. Because of interdependence of lengths of major and minor axes, we introduce the horizontal compression factor which measures the ellipse flattening. We show plausible independence of the major axis length with the horizontal compression factor and we find that the major axis length minus its minimum is well fitted by the Gamma distribution and the normalized horizontal compression factor by the Beta distribution. We propose to infer the value of the minor axis length from the values of the two preceding variables knowing their statistical occurrences. Same reasoning is handled for inference of the half-cosine amplitude from the major axis length and the normalized vertical compression factor, which is also well fitted by the Beta distribution.