Vario functions of higher order  definition and application to characterization of snow surface roughness
Vario functions are lag-dependent experimental functions introduced to characterize spatial properties of surfaces and profiles in a general algebraic sense and their derivatives. Vario functions of higher order are defined recursively. Under certain mathematical conditions, first-order vario functions coincide with experimental variograms. Vario functions of higher order provide a useful extension of the geostatistical classification method, in particular in the cases of poor signal-to-resolution ratio and in the cases of complex morphogenesis. Several theoretical questions concerning vario functions are investigated: feature detection and quantitative analysis in a situation of poor signal-to-resolution ratio, the divergence criterion for determination of the usable distance range of the second-order vario function, characterization of superimposed features (of the geo-variable) by secondary minima and convexity or concavity of the (second-order) vario function, effects of increasing resolution in vario-function calculation for the study of small-scale features, and the question of homogeneity of a data set. Higher-order vario functions prove essential in the characterization of snow surface roughness, demonstrated for microtopographic data from Niwot Ridge, Colorado Front Range. Application of the geostatistical classification approach to vario functions of higher order leads to conclusions on snow surface morphogenesis and its dependence on environmental and geographical conditions that are not obtainable otherwise.
variogram geostatistical classification higher-order vario function res function resvar function microtopography snow hydrology