用于重建由深潜海洋哺乳动物部分采样的温度和盐度剖面的条件多元功能主成分分析
Conditional multivariate functional PCA for the reconstruction of temperature and salinity profiles partially sampled by deep-diving marine mammals
AI总结：
该研究提出条件多元功能PCA方法，结合地理协变量，利用南象海豹部分采样的不完整温盐剖面数据，实现南大洋印度 sector 大范围温盐剖面的高精度重建。
AI中文摘要：
我们提出一种统计方法，用于重建南大洋印度 sector 的垂直温盐条件，该区域的温度和盐度剖面由雌性南象海豹部分采样。生物记录器收集的数据集提供了前所未有的海洋状况时空覆盖范围，但记录的最大深度随动物行为变化，仅能提供垂直环境的部分视图。使用多元功能主成分分析（PCA），从一组完整的双变量剖面中对协方差结构和均值函数进行参数估计，可构建特征函数基。通过考虑测量误差方差，可将部分采样的温度和盐度剖面投影到完整剖面的特征空间中，具体方法是对其功能主坐标进行条件估计，然后在定义的域上进行重建。对于在最大深度z_max=250米处截断的模拟片段剖面，并在Z=[20,500]米的域上进行重建，当纳入地理协变量时，温度的重建精度提高了30%，盐度的重建精度提高了33%。随后，我们利用达到500米的约10,000个剖面的多元功能PCA，重建了约90,000个不完整剖面，覆盖了法国亚南极群岛周围约300万平方公里的区域。
英文摘要：
We present a statistical method to reconstruct the vertical thermohaline conditions in the Indian Sector of the Southern Ocean, where temperature and salinity profiles are partially sampled by female southern elephant seals. Datasets collected by biologgers provide unprecedented spatial and temporal coverage of ocean conditions. However, the maximum recorded depth varies with the animals' behaviour, offering only a partial view of the vertical environment. Using multivariate functional Principal Component Analysis (PCA), a parametric estimation of the covariance structure and mean function from a set of complete bivariate profiles allows the construction of an eigenfunction basis. By accounting for measurement error variance, partially sampled temperature and salinity profiles can be projected into the eigenspace of the complete profiles through conditional estimation of their functional principal coordinates and then reconstructed over the defined domain. For simulated snippet profiles truncated at depth $z_{\max} = 250$ m and reconstructed over $\mathcal{Z} = [20,500]$ m, reconstruction accuracy increases by 30 % for temperature and 33 % for salinity when incorporating geographical covariates. We then reconstruct ~90,000 incomplete profiles from the multivariate functional PCA of ~10,000 profiles reaching 500 m, covering approximately 3 million km$^2$ around the French subantarctic islands.
