Impact of Spatial Aliasing on Sea-ice Thickness Measurements

Abstract:

A frequency distribution of snow and sea ice is generated by counting and then binning the number of thicknesses into contiguous intervals (typically in 10 cm bins). Because sea ice is only meters thick but spans thousands of kilometers, these distributions serve as a "Rosetta Stone" to communicate proportions of thickness across scales - especially for characterizing deformation processes. Because the frequency distribution is such an important communication tool, we explore the impact of spatial aliasing on non-Gaussian distributions of snow and sea ice thickness. Using a heuristic model and >1000 in situ measurements, we show how different instrument footprint sizes and shapes can cluster thickness distributions into artificial modes, thereby distorting frequency distributions and making it difficult to compare and communicate information across spatial scales. This problem has not been dealt with systematically for sea ice until now, largely because it appears to incur no significant change in integrated thickness, which often serves as a volume proxy. The problem is of second order at any one scale but becomes a first order problem for non-Gaussian distributions when data are collected at different scales. We quantify the impact of spatial aliasing by computing resolution error (Er) over a range of horizontal scales (x) from 5 to 500 m. Results are summarized through a power law (Er=bx^m) with distinct exponents (m) from 0.3 to 0.5 using example mathematical functions including Gaussian, inverse linear, and running mean filters. The most important finding is that a running mean filter introduces a great deal of aliasing and should be avoided whenever possible. A simple and effective substitute for the running mean is an inverse linear filter which is commonly used in numerical model data interpolation. In this study, inverse linear filters were as effective as a Gaussian filter in terms of minimizing aliasing. There is much to be gained at the community level by eliminating running-mean filters especially during underway data reduction field experiments. Removing this one filter alone will significantly decrease a number of aliasing problems that currently make it very difficult to compare and combine different in situ and airborne measurements.