The return periods calculated here are based
on transient warming estimates under the Rep-
resentative Concentration Pathway 8.5 (RCP8.5)
high-emissions scenario. We obtain similar re-
sults when using the RCP2.6 scenario (fig. S10).
However, we caution that the return periods for
individual MHWs under stabilized 1.5° or 2°C
warming levels might be different from those
under transient warming levels because the
climate system is closer to equilibrium and the
oceanhashadmoretimetotakeupheatand
redistribute it within the ocean ( 36 ).
Both the FAR values and the estimated re-
turn periods are sensitive to several factors, in-
cluding the framing of the attribution question,
model evaluation and preselection, statistical
uncertainties, uncertainties in the preindustrial
SST reconstructions, and choice of the present-
day time period ( 18 , 37 , 38 ). To increase robust-
ness of our assessments, we performed several
sensitivity tests to quantify these uncertainties.
First, we explicitly evaluate how well climate
models reproduce the observed distributions
of heatwave duration and intensity. We re-
strict our analysis to models that simulate
statistically indistinguishable distributions of
heatwave duration, intensity, and cumulative
intensity when compared with observations.
We also avoid bias adjustment to match the
SST variance of the models with the variance
of the satellite data ( 6 , 24 ), as it is unclear
whether this ensures a more realistic simula-
tion of heatwave distribution. Notably, adjust-
ing the variance does not necessarily improve
the temporal and spatial variability in the sim-
ulated temperature data above a high percentile.
However, even with our rigorous model eval-
uation and selection, the attribution statement
depends inherently on the quality of the under-
lying model simulations.
Second, many studies do not quantify the
goodness of the fit when estimating the oc-
currence probability of heatwaves. Particularly
for rare, extreme events, which have very low
occurrence probabilities, even small deviations
in occurrence probability might strongly affect
the FAR value. We address this issue by cal-
culating 95% confidence intervals of the occur-
rence probability (materials and methods) to
achieve more-robust attribution statements.
Third, regional disagreements between dif-
ferent pre–satellite era SST reconstructions
might result in different MHW characteristics,
which potentially might affect the FAR value.
We therefore repeated our analysis using two
additional SST reconstructions (tables S3 to
S5) to show that, for the analyzed MHWs, the
uncertainty introduced by the SST reconstruc-
tion is small for most heatwaves. The only ex-
ceptions are the duration of the NW Atlantic
2012 MHW, for which warming estimates be-
tween 0° and 0.74°C result in FAR values be-
tween 0.77 and 0.96, and the intensity of the
Western Australian 2011 MHW, for which the
FAR varies between 0.47 and 0.73 under warm-
ing estimates between 0.51° and 0.77°C.
Finally, previous studies have defined dif-
ferent time periods as the present day, some-
times using data that reach up to 25 years into
the future ( 22 ) when oceans are projected to
be substantially warmer, thereby overestimat-
ing today's anthropogenic influence on heat-
wave occurrence risk. Here, we use the 1981 to
2017 period as the present day, which results
in a conservative estimate of the present frac-
tion of attributable risk.
Our study highlights the strong human in-
fluence on the occurrence probabilities of all
recent large and severe MHWs, and it illus-
trates the substantially reduced return periods
these extreme heat events will have under fur-
ther global warming. Recent MHWs have had
severe impacts on marine ecosystems, and
these systems have required a long time to re-
cover in the aftermath—if they have recovered
at all ( 30 , 31 ). Early warning systems such as
seasonal to annual forecast systems of SST
mayhelptoreducetheriskofMHWsforeco-
systems and human systems by enabling pre-
ventive measures, such as reducing fishing
pressure ( 39 ). However, strongly reduced re-
turn periods of large MHWs will likely push
marine organisms and ecosystems beyond
their thermal limits and stress tolerance ( 3 ),
potentially causing irreversible changes. Some
ofthemostvaluableandpreciousmarineeco-
systems, such as warm-water coral reefs, will
likely be irretrievably lost. To maintain the ex-
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from reaching a continuous, severe heat-
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ACKNOWLEDGMENTS
We thank the World Climate Research Programme's Working
Group on Coupled Modelling, which is responsible for the fifth
phase of the Coupled Model Intercomparison Project (CMIP5), and
the climate modeling groups for producing and making available
their model output. COBE SST2, NOAA ERSST V5, and HadISST
V1.1 data were provided by the NOAA/OAR/ESRL PSD, Boulder,
Colorado, USA, from their website at http://www.esrl.noaa.gov/psd/.
We also thank M. Schulte and P. Naveau for their very helpful
advice on the theory of probabilities and general statistics and
T. Stocker for feedback on the manuscript.Funding:C.L., T.L.F.,
and J.Z. acknowledge support from the Swiss National Science
Foundation under grants 174124 (to C.L.), 170687 (to T.L.F.), and
179876 (to J.Z.). T.L.F. also received funding from the European
Union’s Horizon 2020 research and innovation program under
grant agreement no. 820989 (project COMFORT, Our common
future ocean in the Earth system–quantifying coupled cycles of
carbon, oxygen, and nutrients for determining and achieving
safe operating spaces with respect to tipping points) and
computing resources from the CSCS Swiss National Supercomputing
Center.Author contributions:C.L. and T.L.F. designed the study.
All authors developed the statistical methods and analyzed the
results. Calculations were made by C.L. The manuscript was written
by C.L. with extensive input from T.L.F. and J.Z.Competing
interests:The authors declare that they have no competing interests.
Data and materials availability:The CMIP5 model data, SST
satellite observations, and SST reconstructions are available online
(see materials and methods for details). All other data are available
in the main text or the supplementary materials. The code used
to calculate the FAR values and the return periods can be found
on OSF ( 40 ).SUPPLEMENTARY MATERIALS
science.sciencemag.org/content/369/6511/1621/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S11
Tables S1 to S8
References ( 41 – 51 )
4 November 2019; accepted 4 August 2020
10.1126/science.aba0690SCIENCEsciencemag.org 25 SEPTEMBER 2020•VOL 369 ISSUE 6511 1625
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