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

Abstract

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 σL2. 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 σ2L 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 σL2 is proportional to L−1+2δ. 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 σL 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.