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A spatio-temporal model for Red Sea surface temperature anomalies


This paper details the approach of team Lancaster to the 2019 EVA data challenge, dealing with spatio-temporal modelling of Red Sea surface temperature anomalies. We model the marginal distributions and dependence features separately; for the former, we use a combination of Gaussian and generalised Pareto distributions, while the dependence is captured using a localised Gaussian process approach. We also propose a space-time moving estimate of the cumulative distribution function that takes into account spatial variation and temporal trend in the anomalies, to be used in those regions with limited available data. The team’s predictions are compared to results obtained via an empirical benchmark. Our approach performs well in terms of the threshold-weighted continuous ranked probability score criterion, chosen by the challenge organiser.


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We would like to thank the referees and Associate Editor for their helpful comments. Christian Rohrbeck is beneficiary of an AXA Research Fund postdoctoral grant. Emma Simpson’s work is supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-CRG2017-3434. Ross Towe is supported by Engineering and Physical Sciences Research Council (Grant Number: EP/P002285/1) ‘The Role of Digital Technology in Understanding, Mitigating and Adapting to Environmental Change’.

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Correspondence to Christian Rohrbeck.

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Empirical analysis of the spatial and extremal spatial dependence

We produce variograms and F-madograms for the four sub-regions in Fig. 4. The left column in Fig. 5 shows that spatial dependence varies across sub-regions. Furthermore, there appears to be a temporal variation in the spatial dependence for two of the sub-regions. The right column of Fig. 4 indicates that the extremal spatial dependence exhibits less spatial variation than the overall spatial dependence. Furthermore, the plots demonstrate slight changes in the extremal spatial dependence, but not as strong as for the overall spatial dependence.

Fig. 4
figure 4

Subregions used to explore spatial and extremal dependence

Fig. 5
figure 5

Variograms (left) and F-Madograms (right) for the four subregions in Fig. 4. The black curve corresponds to the time horizon t = 1, … , 5000, and the grey curve corresponds to the period t = 5001, … , 11315. The dashed lines are the central 80% confidence intervals

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Rohrbeck, C., Simpson, E.S. & Towe, R.P. A spatio-temporal model for Red Sea surface temperature anomalies. Extremes 24, 129–144 (2021).

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  • Extreme value analysis
  • Gaussian processes
  • Red Sea
  • Spatio-temporal dependence

AMS 2000 Subject Classifications

  • 62H11
  • 62P12
  • 62M30