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

In this paper the selected approach to analyze seedbed roughness is to study soil surface structural elements, such as aggregates and clods lying on the soil substrate. Recently their identification has been made possible on millimetric resolution digital elevation models (DEMs) by new developed segmentation algorithms relying on contour-based procedure. Here we consider two DEMs of 30 cm and 40 cm by 90 cm recorded on a freshly tilled seedbed of moderate roughness and build up a dataset of several hundreds of clods and large aggregates (sizes greater than 7 mm). We show that these irregular shaped objects can be represented by simple approached forms: an ellipse for the base and a half-cosine function for the height. Values of areal (and volume) overlap rates indicate that half of clods bases are matched with very good rates greater than 0.74 up to 0.89 (respectively 0.70 up to 0.87). t 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.