ABSTRACT When a marine study area is large, the environmental variables often present spatially stratified non-homogeneity, violating the spatial second-order stationary assumption. The stratified non-homogeneous surface can be divided into several stationary strata with different means or variances, but still with close relationships between neighboring strata. To give the best linear-unbiased estimator for those environmental variables, an interpolated version of the mean of the surface with stratified non-homogeneity (MSN) method called point mean of the surface with stratified non-homogeneity (P-MSN) was derived. P-MSN distinguishes the spatial mean and variogram in different strata and borrows information from neighboring strata to improve the interpolation precision near the strata boundary. This paper also introduces the implementation of this method, and its performance is demonstrated in two case studies, one using ocean color remote sensing data, and the other using marine environment monitoring data. The predictions of P-MSN were compared with ordinary kriging, stratified kriging, kriging with an external drift, and empirical Bayesian kriging, the most frequently used methods that can handle some extent of spatial non-homogeneity. The results illustrated that for spatially stratified non-homogeneous environmental variables, P-MSN outperforms other methods by simultaneously improving interpolation precision and avoiding artificially abrupt changes along the strata boundaries.

中文翻译：

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使用 P-MSN 对海洋环境数据进行空间插值

摘要 当海洋研究区域较大时，环境变量往往呈现空间分层的非均匀性，违反空间二阶平稳假设。分层的非均质表面可分为若干个具有不同均值或方差的静止地层，但相邻地层之间仍具有密切的联系。为了给出这些环境变量的最佳线性无偏估计量，推导出了具有分层非均匀性 (MSN) 方法的表面均值的内插版本，称为具有分层非均匀性的表面点均值 (P-MSN)。P-MSN 区分不同地层的空间均值和变异函数，并借用相邻地层的信息来提高地层边界附近的插值精度。本文还介绍了该方法的实现，并通过两个案例研究展示了其性能，一个使用海洋颜色遥感数据，另一个使用海洋环境监测数据。将 P-MSN 的预测与普通克里金法、分层克里金法、具有外部漂移的克里金法和经验贝叶斯克里金法进行了比较，这是最常用的方法，可以处理一定程度的空间非均匀性。结果表明，对于空间分层的非均匀环境变量，P-MSN 通过同时提高插值精度和避免沿地层边界人为地突然变化而优于其他方法。另一种是利用海洋环境监测数据。将 P-MSN 的预测与普通克里金法、分层克里金法、具有外部漂移的克里金法和经验贝叶斯克里金法进行了比较，这是最常用的方法，可以处理一定程度的空间非均匀性。结果表明，对于空间分层的非均匀环境变量，P-MSN 通过同时提高插值精度和避免沿地层边界人为地突然变化而优于其他方法。另一种是利用海洋环境监测数据。将 P-MSN 的预测与普通克里金法、分层克里金法、具有外部漂移的克里金法和经验贝叶斯克里金法进行了比较，这是最常用的方法，可以处理一定程度的空间非均匀性。结果表明，对于空间分层的非均匀环境变量，P-MSN 通过同时提高插值精度和避免沿地层边界人为地突然变化而优于其他方法。