A UTILITARIAN APPROACH TO MODELING NON-GAUSSIAN CHARACTERISTICS OF A TOPOGRAPHIC FIELD

This paper develops a general framework for the analysis of the moment s greater than 2 of a topographic field. This framework uses ''iterate d'' expectation to reduce a statistical moment function to component p arts involving the vertical (disjoint) moment of the same order, lower moments, and two-point conditional expectations. In this way it is po ssible to isolate the unique informational contribution of each moment . Use of this framework necessitates a ''bootstrap'' or perturbation m ethod, where lower moments are modeled first and then are used ag cons traints in the modeling of higher moments. Functional modeling of any moment is thus reducible to characterization of the disjoint moment (e .g., skewness, kurtosis) and the two-point conditional expectation. In this paper, I demonstrate how it is possible to ''design'' a statisti cal model most sensitive to specific non-Gaussian topographic characte ristics by solving for the two-point conditional expectation under an invertable mapping between Gaussian and non-Gaussian fields of interes t. Mappings of this son are useful both for the fact that they can be intuitive descriptions of non-Gaussian characteristics and for their u tility in generating non-Gaussian synthetic topography. The primary in tent of this methodology is to forge a link between physical topograph ic characteristics, the information we want to know, and statistical m oments, our tool for quantitatively measuring topographic fields. In a ddition, mapping models can be used to calculate the skewness and kurt osis (or higher moments) of topographic slopes directly. The applicabi lity of these methods is demonstrated for mapping models which create vertical and lateral asymmetry and peakiness in a topographic field.