D. B. Percival, D. A. Rothrock, A. S. Thorndike and T. Gneiting (2008), `The Variance of Mean Sea-Ice Thickness: Effect of Long-Range Dependence,' Journal of Geophysical Research - Oceans, 113, C01004, doi:10.1029/2007JC004391.
Measured sea-ice draft exhibits variations on all scales. We regard draft profiles up to several hundred kilometers in length as being drawn from a stationary stochastic process. We focus on the estimation of the mean draft H of the process. This elementary statistic is typically computed from a profile segment of length L and has some uncertainty, or sampling error, that is quantified by its variance sigma^2_L. How efficiently can the variance of H be reduced by the use of more data, that is, by increasing L? Three properties of the data indicate the need for a non-standard statistical model: the variance sigma^2_L of H falls off more slowly than L^{-1}; the autocorrelation sequence does not fall rapidly to zero; and the spectrum does not flatten off with decreasing wavenumber. These indicate that ice draft exhibits, as a fundamental geometric property, `long-range dependence.' One good model for this dependence is a fractionally differenced process, whose variance sigma^2_L is proportional to L^{-1+2delta}. From submarine ice draft data in the Arctic Ocean, we find delta = 0.27. Mean draft estimated from a 50-km sample has a sample standard deviation of 0.29 m; for 200 km, it is 0.21 m. Tabulated values provide the sample standard deviation sigma_L for various values of L for samples both in a straight line and in a rosette or spoke pattern, allowing for the efficient design of observation programs to measure draft to a desired accuracy.
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