The variance of mean sea‐ice thickness: Effect of long‐range dependence
The variance of mean sea‐ice thickness: Effect of long‐range dependence
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平均海冰厚度的方差：长程依赖性的影响
DOI：
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发表时间：
2008
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通讯作者：
T. Gneiting
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作者：
D. Percival;D. Rothrock;A. Thorndike;T. Gneiting
[1] 测量的海冰吃水在各个尺度上都有变化。我们将长达数百公里的吃水剖面视为是从平稳随机过程中绘制的。我们重点关注过程平均吃水的估计。该基本统计量通常根据长度为 L 的轮廓段计算得出，并具有一定的不确定性或采样误差，可通过其方差 σL2 进行量化。通过使用更多数据（即增加 L）可以如何有效地降低方差？数据的三个属性表明需要非标准统计模型： 的方差 σ2L 比 L−1 下降得更慢；自相关序列不会快速降至零；并且光谱不会随着波数的减少而变平。这些表明冰吃水作为一种基本几何特性，表现出“长程依赖性”。这种依赖性的一个很好的模型是分数差分过程，其方差 σL2 与 L−1+2δ 成正比。根据北冰洋海底冰吃水数据，我们发现 δ = 0.27。根据 50 公里样本估算的平均吃水，样本标准偏差为 0.29 m； 200 km 为 0.21 m。表格值提供了直线和玫瑰花或辐条图案中样本的各种 L 值的样本标准差 σL，从而可以有效设计观测程序以测量吃水达到所需的精度。
[1] 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.