The variance of mean sea‐ice thickness: Effect of long‐range dependence

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 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 σ L 2 . How efficiently can the variance of 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 σ 2 L of 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 wave number. 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 σ L 2 is proportional to L −1+2 δ . From submarine ice draft data in the Arctic Ocean, we find δ = 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 σ 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 observational programs to measure draft to a desired accuracy.