The effective sample size quantifies the amount of independent information contained in a dataset, accounting for redundancy due to correlation between observations. While widely used in geostatistics for scalar data, its extension to functional spatial data has remained largely unexplored. In this work, we introduce a novel definition of the effective sample size for functional geostatistical data, employing the trace-covariogram as a measure of correlation, and show that it retains the intuitive properties of the classical scalar ESS. We illustrate the behavior of this measure using a functional autoregressive process, demonstrating how serial dependence and the allocation of variability across eigen-directions influence the resulting functional ESS. Finally, the approach is applied to a real meteorological dataset of geometric vertical velocities over a portion of the Earth, showing how the method can quantify redundancy and determine the effective number of independent curves in functional spatial datasets.

翻译：有效样本量用于量化数据集中所含独立信息的数量，同时考虑观测值间相关性导致的冗余。虽然该方法在地统计学标量数据分析中已被广泛应用，但其向函数型空间数据的扩展仍基本处于空白。本文针对函数型地统计数据提出了一种新的有效样本量定义，采用迹协变差图作为相关性度量，并证明该定义保持了经典标量ESS的直观性质。我们通过函数型自回归过程阐释了该度量的行为特征，展示了序列依赖性及变异在特征方向上的分配如何影响所得的函数型ESS。最后，该方法被应用于地球部分区域几何垂直速度的真实气象数据集，说明了本方法如何量化冗余度并确定函数型空间数据集中独立曲线的有效数量。