Comparing model-generated and real bedform patterns by measuring the distance between state-space plots

A. B. Murray, R. Moeckel, and B. T. Werner

Characterizing bedform patterns using spectral analysis and simple statistics such as the average wavelength provides a valuable first step in comparing real and model-generated bedforms. Here we present a method for further comparison that assesses the degree of similarity in downstream sequences of geometrical variables such as wavelengths. Such sequences implicitly contain information about the influence one bedform has on the next bedform(s), via the flow and sediment transport, in a fully developed train of bedforms. We begin by plotting, for example, the wavelength of each bedform versus that of the previous bedform(s). Then we treat this state-space plot as a probability distribution, and adapt a theoretical probability-distribution metric to measure the distances in state space between the distributions representing real and model patterns. We have constructed state-space plots of real subaqueous current ripples and aeolian ripples. As an example of using these plots to evaluate models, we compare the wind ripple patterns with those generated by a cellular wind-ripple model.