Statistical aspects of sea-ice ridge distributions

Abstract

A theoretical distribution function for pressure-ridge, sail heights and keel depths is derived from fundamental assumptions about the randomness of the ridges. It is shown that the distribution function for ridge spacings (distance between ridges) can also be predicted from the assumption of spatially random occurrence. The suggested distribution functions are, in form, negative exponentials of the ridge height (or depth) squared and the ridge spacing, respectively. Extremely good fits were achieved to extensive data collected from sonar profiles of the lower surface of the pack ice and to laser profiles, as well as visual roughness data from the upper ice surface. Using these models, it is possible to completely characterize the ridging, in a one-dimensional sense, by two parameters: 〈N〉, the mean number of ridges per unit length, and 〈h〉, the mean ridge height (or depth). In addition, there is a linear correlation between 〈N〉 and 〈h〉. This suggests that maps showing the distribution of 〈N〉 or 〈h〉 over an ocean covered with pack ice can be used to statistically characterize both the spacing and the height distribution of the ridges.