Outgassing of carbon dioxide (CO\(_2\)) from river surface waters, estimated using partial pressure of dissolved CO\(_2\), has recently been considered an important component of the global carbon budget. However, little is still known about the high-frequency dynamics of CO\(_2\) emissions in small-order rivers and streams. To analyse such highly dynamic systems, we propose a time-varying functional principal components analysis (FPCA) for non-stationary functional time series (FTS). This time-varying FPCA is performed in the frequency domain to investigate how the variability and auto-covariance structures in a FTS change over time. This methodology, and the associated proposed inference, enables investigation of the changes over time in the variability structure of the diurnal profiles of the partial pressure of CO\(_2\) and identification of the drivers of those changes. By means of a simulation study, the performance of the time-varying dynamic FPCs is investigated under different scenarios of complete and incomplete FTS. Although the time-varying dynamic FPCA has been applied here to study the daily processes of consuming and producing CO\(_2\) in a small catchment of the river Dee in Scotland, this methodology can be applied more generally to any dynamic time series.Supplementary materials accompanying this paper appear online.

使用溶解的 CO \(_2\)的分压估算的河流地表水中二氧化碳 (CO \(_2\) ) 的释气最近被认为是全球碳预算的重要组成部分。然而，关于 CO \(_2\)的高频动力学仍然知之甚少。小河流和溪流的排放。为了分析这种高度动态的系统，我们提出了一种用于非平稳函数时间序列（FTS）的时变函数主成分分析（FPCA）。这种时变 FPCA 在频域中执行，以研究 FTS 中的可变性和自协方差结构如何随时间变化。这种方法和相关的建议推论能够研究 CO \(_2\)分压的昼夜分布的可变性结构随时间的变化。并确定这些变化的驱动因素。通过仿真研究，研究了时变动态 FPC 在完全和不完全 FTS 的不同场景下的性能。虽然时变动态 FPCA 已被应用于研究苏格兰迪河小流域消耗和产生 CO \(_2\)的日常过程，但这种方法可以更普遍地应用于任何动态时间序列。本文随附的补充材料出现在网上。