Archetypal Analysis of Geophysical Data Illustrated by Sea Surface Temperature

Abstract

The ability to find and recognize patterns in high-dimensional geophysical data is fundamental to climate science and critical for meaningful interpretation of weather and climate processes. Archetypal analysis (AA) is one technique that has recently gained traction in the geophysical science community for its ability to find patterns based on extreme conditions. While traditional empirical orthogonal function (EOF) analysis can reveal patterns based on data covariance, AA seeks patterns from the points located at the edges of the data distribution. The utility of any objective pattern method depends on the properties of the data to which it is applied and the choices made in implementing the method. Given the relative novelty of the application of AA in geophysics it is important to develop experience in applying the method. We provide an assessment of the method, implementation, sensitivity, and interpretation of AA with respect to geophysical data. As an example for demonstration, we apply AA to a 39-year sea surface temperature (SST) reanalysis data set. We show that the decisions made to implement AA can significantly affect the interpretation of results, but also, in the case of SST, that the analysis is exceptionally robust under both spatial and temporal coarse-graining.

A large-scale view of marine heatwaves revealed by archetype analysis

“…We note that native implementation of the AA algorithm as described by Eq. ( 6) is incapable of directly extracting temporal patterns, such as serial correlation or persistence, from data 25 . For example, a re-ordering of the time index of the data matrix, represented by the operation X 0 = RX will result in reordered but otherwise identical affiliation and mixture weight matrices, given by S 0 = SR T and C 0 = RC.…”

“…For example, a re-ordering of the time index of the data matrix, represented by the operation X 0 = RX will result in reordered but otherwise identical affiliation and mixture weight matrices, given by S 0 = SR T and C 0 = RC. Although options for including temporal patterns directly into the AA procedure have been discussed 25 , at present, it is only possible to extract through interrogation of the resultant affiliation time-series from the S matrix.…”

“…In this study, we present an 'outside-in' methodology that directly identifies large-scale patterns associated with extreme seasurface temperatures by employing a powerful data-mining methodology-Archetype Analysis (herein AA). AA seeks to represent a high-dimensional spatiotemporal dataset as a mixture of a smaller number of 'archetypal' spatial patterns along with a probabilistic timeseries [22][23][24][25] . The archetypal patterns are themselves constructed as a weighted average of a small number of snapshots of the original dataset, x, that correspond to 'extreme' states 22,24,25 .…”

“…AA seeks to represent a high-dimensional spatiotemporal dataset as a mixture of a smaller number of 'archetypal' spatial patterns along with a probabilistic timeseries [22][23][24][25] . The archetypal patterns are themselves constructed as a weighted average of a small number of snapshots of the original dataset, x, that correspond to 'extreme' states 22,24,25 . An approximation of the original dataset, x, is given by: xðspace, timeÞ ≈ xðspace, timeÞ = X P i s i ðtimeÞ z i ðspaceÞ ð1Þ…”

Archetypal Analysis++: Rethinking the Initialization Strategy

“…Archetypal analysis has been applied, e.g., for global gene expression (Thøgersen et al, 2013), bioinformatics (Hart et al, 2015), apparel design (Vinué et al, 2015), chemical spaces of small organic molecules (Keller et al, 2021), geophysical data (Black et al, 2022), large-scale climate drivers (Hannachi and Trenda lov, 2017;Chapman et al, 2022), and population genetics (Gimbernat-Mayol et al, 2022).…”