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

Marine heatwaves can have disastrous impacts on ecosystems and marine industries. Given their potential consequences, it is important to understand how broad-scale climate variability influences the probability of localised extreme events. Here, we employ an advanced data-mining methodology, archetype analysis, to identify large scale patterns and teleconnections that lead to marine extremes in certain regions. This methodology is applied to the Australasian region, where it identifies instances of anomalous sea-surface temperatures, frequently associated with marine heatwaves, as well as the broadscale oceanic and atmospheric conditions associated with those extreme events. Additionally, we use archetype analysis to assess the ability of a low-resolution climate model to accurately represent the teleconnection patterns associated with extreme climate variability, and discuss the implications for the predictability of these impactful events.

Zooming out to investigate the teleconnection patterns, shown in Supplemen-51 tary Fig. 2. We note that, in contrast to the marine heatwave case-study pre-52 sented in the main text, there is no strong SST signature in the tropical Pacific. The relationship between Marine Coldspells and Archetypes #5 and #6 in the southeast Indian ocean : a Seasurface temperature (SST) anomaly composite average of all marine coldspells at a representative location (at 30 • S,112.5 • E, shown as a grey dot) in the southeast Indian Ocean; b,d snapshot of SST anomalies for the peak for the peak day of the strong marine coldspell event on the 23rd of June, 2017, and the moderate event on the 6th of June 2018; c,e the SST anomalies for best matching archetypal pattern (archetype #5 archetype #6); f time-series of SST anomalies (black) and the reconstruction from archetype 3 (orange) at the representative location shown in panels a-c ; e time-series of archetype affiliation probability for archetype 3. Colored bands in panels d,e indicate marine coldspell occurrences, coded by the severity category described in Hobday et al. 2018 [3]. 3 In contrast, the spatial structure of the best matching archetype (Sup- EAC, and atmospheric effects [5]. In this case, the spatial structure of SSTs for anomalies for all eight archetypal patterns computed over the Australasian region (indicated by the black box), ranked from most likely to least likely to occur, and (right) associated affiliation time-series (black solid line) and the C-matrix weights applied to each time snapshot to form the archetypes (orange bars). The AA is conducted in the domain in the left-hand column. Archetypes  #1 (panels a,b), #2 (panels c,d), #3 (panels e,f ) and #4 (panels a,b) are used in the regional case studies in the main text (locations indicted in the text) while archetype #8 (panels i,j) is shown to illustrate classical El Niño type variability. Archetypes #5 (panels i,j), #6 (panels k,l), and #4 (panels g,h) are used in regional case studies in the supplementary material.
Supplementary Figure 7: Temporal Occurrence of Archetype Patterns: a Coloured blocks indicate period where a particular archetype was dominant for at least 20 days. The y-axis indicates the year, while the x-axis indicates the calendar days. Blanked periods show days where no qualifying event was found; the total number of archetype event days for each archetype that occur b for each year; and c for each 5-day period over the annual cycle. Maps to the right show spatial patterns of sea-surface temperature (SST) anomaly for each archetype.
associated with El-Niño or La-Niña like modes).

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To better assess the temporal evolution of the extreme climate modes de-  194 In order to evaluate the statistical significance of archetypal spatial patterns 195 and the composite fields, we employ a brute-force Monte-Carlo approach. First,

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we generate synthetic stochastic matrix, designed to replicate the features of 197 the C or S matrices. The elements of these matrices is drawn from a uniform 198 distribution between 0 and 1. The rows or columns of these synthetic stochastic 199 matrices are them normalised appropriately to ensure that the constraints. For 200 example, in the case of a synthetic C-matrix, the normalisation is applied to 201 rows to ensure that the constraint T t c t,j = 1 is satisfied. In the case of a 202 synthetic S-matrix, the normalisation is performed column-wise, to satisfy the 203 constraint P j s t,j = 1. We then form composite fields on these synthetic ma-204 trices. The procedure is repeated 1000 times and the 5th and 95th percentiles 205 computed (shown in Supplementary Fig. 13). A pixel is declared 'significant' if 206 it is less than the 5th percentile, or greater than the 95th percentile.  In Supplementary Fig. 15, we show the statistical significance of the geopo-