Main

Owing to the tightly coupled dependence of corals on temperature, coral reefs have been among the first ecosystems to manifest dramatic change under a warming climate, suffering intense periods of near-total loss of symbiotic algae (bleaching)1. Reefs have seen four global bleaching events (1998, 2010, 2014–2017 and 2023–2024)2, and the estimated return time of severe bleaching is now just 6 years (ref. 3). Heat stress projections are increasingly being operationalized for the management of coral reefs4,5,6,7.

Now-casts of heat stress are performed on satellite-measured sea-surface temperature (SST) using Degree Heating Weeks (DHW), the number of weeks of anomalous temperature in the past quarter, expressed in units of °C weeks (ref. 8). DHW now-casts are applied globally to allow reef managers to understand, communicate and monitor the magnitude and distribution of impacts. Moreover, analyses of reef futures under climate change rely heavily on projections of SST output from atmosphere–ocean general circulation models9. Frequently, data from such climate models are used to calculate Degree Heating Months (DHM)—the cumulative anomaly of sea temperature over a 3–4-month window—which can then be standardized to a weekly basis (that is, converted to units of °C weeks) using a multiplier of approximately 4 (ref. 10) (Fig. 1, Extended Data Table 1 and Extended Data Fig. 1). Analysis at a monthly resolution is also used in historical SST studies11 and in seasonal outlook forecasting12. As there is the potential for confusion, DHM in this study always refers to DHM standardized to a weekly basis (that is, multiplied by ~4), and DHW always refers to the DHW algorithm, not to weekly standardized DHM.

Fig. 1: Values of DHM with a 3-month accumulation window versus DHW at the Great Barrier Reef over the 2001–2020 period.
figure 1

Heat stress calculated using DHM typically exceeds that calculated using DHW for observational and climate model data. a–g, Outer plots show cumulative frequency of heat stress (°C weeks) from DHM with a 3-month window versus DHW calculated from observed SST data (a) and hindcast SST data (six CMIP5 climate models: GISS-E2-R (b), GFDL-ESM2M (c), CESM1-WACCM (d), CCSM4 (e), HadGEM2-ES (f) and MIROC5 (g)), for 2,014 reefs of Australia’s Great Barrier Reef over 2001–2020. The widely used predictive criteria for substantial bleaching (≥4 °C weeks but <8 °C weeks) and for severe bleaching with substantial mortality (≥8 °C weeks) are shown by the shaded areas. Cumulative frequencies are normalized to 1. Insets: scatter plots depicting every value of DHM plotted against the corresponding value of DHW, both expressed as °C weeks. DHM was standardized to a weekly basis through multiplication by 4.

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Conventional thresholds for substantial coral bleaching and severe coral bleaching with substantial mortality are 4 °C weeks and 8 °C weeks, respectively13. These thresholds are currently applied in the operational use of the DHW algorithm and in the research use of both DHW and DHM. Of key relevance here is the practice of using DHM with bleaching thresholds that have been calculated through the correspondence of observed DHW values to bleaching observations13 (Extended Data Table 1). Our analysis, using two different threshold schemes calculated in this manner, suggests that a departure between the predictions of DHM and DHW is generalized and not dependent on the specific thresholds used.

The DHM algorithm has been used in several key studies of reef futures that have been influential in the policy domain1,14,15,16,17 and in studies of the functional responses of corals under climate change18,19. For the majority of studies, no credible alternative to DHM existed, as, until recent iterations of the Coupled-Model Intercomparison Program (CMIP), information technology limitations restricted the provision of some climate model outputs to monthly timesteps20. Other than brief comparisons when DHM was first proposed10,21, an examination of the interchangeability of DHM and DHW and the equivalency of the bleaching thresholds for both indices has not been performed.

In our first analysis, we conduct a detailed comparison of DHM against DHW at each of 2,014 individual reefs of Australia’s Great Barrier Reef. For each index, we first determined, at each reef, the number of years in the 2001–2020 period that the reef had experienced heat stress (using the conventional thresholds), and then summed this number of heat stress ‘incidents’ across all 2,014 reefs (thus, n = 40,280). We calculated DHM, with a 3-month accumulation window, and DHW from the observational SST record for the past two decades encompassing 4 years with severe thermal anomalies that triggered mass bleaching (2002, 2016, 2017 and 2020). We performed an equivalent analysis within each 2001–2020 SST hindcast of six recent (CMIP5) climate models, calculating heat stress in °C weeks using both the conventional DHM approach with monthly data, as well as from daily model data using DHW—an identical approach to operationalized DHW warning systems that use satellite-observed SST. For each climate model, both output types stemmed from the same underlying ensemble of runs.

In the observational record and under four of six climate models, DHM substantially overestimated heat stress compared with DHW over 2001–2020. In the observational record, DHM predicted 414% more incidents of substantial bleaching (≥4 but <8 °C weeks, ‘bleaching’) and 418% more incidents of severe bleaching with substantial mortality (≥8 °C weeks, ‘severe bleaching’) than DHW (Fig. 1a). DHM predicted from 277% to 1,584% more bleaching incidents than DHW under the GISS-E2-R, GFDL-ESM2M, CESM1-WACCM and CCSM4 climate models (Fig. 1b–e). In the severe bleaching range, DHM predicted 191–1,564% more incidents than DHW among these models. A bias towards greater prediction of bleaching and severe bleaching under DHM, compared with DHW, was statistically supported by a generalized linear mixed model analysis (Extended Data Table 2 and Supplementary Information).

In a further two climate models, DHM demonstrated overestimation or spurious patterns in the bleaching range and under- or overestimation in the severe bleaching range, compared with DHW. Under HadGEM2-ES, DHM predicted 33% more bleaching incidents than DHW but 43% fewer severe bleaching incidents than DHW (Fig. 1f). Under MIROC5, bulk DHM and DHW predictions were closer but DHW predictions displayed a long tail compared with DHM and the modes of the component of each distribution above 5 °C weeks were not concordant (Extended Data Fig. 2). Under MIROC5, DHM predicted 5% fewer bleaching events and 19% more severe bleaching events than DHW (Fig. 1g). Our climate models varied widely in their degree of pessimism of heat stress predictions (Fig. 1b–g), but for all models DHM overestimated either bleaching or severe bleaching or both, compared with DHW.

The discrepancy between heat stress predicted by the standard method for observational data, DHW, versus the usual method for climate models, DHM, has practical consequences for the projection of coral reef trajectories. In our second analysis, we used DHM from monthly outputs and DHW from daily outputs of six climate models to apply heat stress in separate ensembles of runs of the ReefMod-GBR ecosystem model22 simulating the Great Barrier Reef between 2022 and 2099. ReefMod-GBR incorporates many drivers of coral demographic change, including background mortality rates, warming, cyclones, pest species, coral larval self-recruitment and connectivity, but currently not genetic adaptation. Multi-model ensemble predictions of coral cover on the Great Barrier Reef were noticeably more pessimistic when DHM, as opposed to DHW, was applied to generate heat stress (Fig. 2). The projected date at which coral cover falls to critically low levels (below 5%) is delayed by 15–20 years in Representative Concentration Pathways (RCPs) 4.5 and 6.0, and by 10 years in RCP 8.5. Coral cover trajectories nevertheless decline to zero under DHM for RCP 4.5 and under both DHM and DHW for RCP 6.0 and 8.5, but stabilize at 3–5% under DHW for RCP 4.5. Under RCP 2.6, coral cover reaches a low of 5% under DHM versus 12% under DHW, recovering to 8–12% (DHM) versus 18–24% (DHW) by the end of the century. With the increasing popularity of ecosystem modelling incorporating ensembles of climate models, our earlier results imply that the direction and magnitude of differences in ecosystem projections under DHM versus DHW may strongly depend on the choice of climate models included in the ensemble, underscoring the implications of the divergent outputs of these two algorithms.

Fig. 2: Coral cover projections over the twenty-first century performed in ReefMod-GBR using DHM versus DHW.
figure 2

Projections of mean coral cover over the Great Barrier Reef are more pessimistic when DHM with a 3-month window, as opposed to DHW, is used to calculate heat stress from climate model outputs. The multi-model ensemble used consisted of CCSM4, HadGEM2-ES, MIROC5, GFDL-ESM2M, CESM1-WACCM and GISS-E2-R. For RCP 2.6, GISS-E2-R atmosphere–ocean general circulation model output was not available and for RCP 6.0, CESM1-WACCM and GISS-E2-R outputs were not available.

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The interpretation of coral reef projections based on DHM in older studies is complicated by the comparatively coarse resolution of climate model outputs typically used. The damping of local SST extremes caused by coarse spatial resolution may somewhat counteract DHM’s tendency to overpredict bleaching10,21,23. However, some studies applied statistical or dynamic downscaling to climate outputs before the calculation of heat stress10,16,24, which possibly alleviated this effect. A large part of the divergence between the two algorithms may be due to the use of a 1 °C threshold above the maximum monthly mean (MMM) for SST anomaly accumulation in DHW but not DHM, although the application of an equivalent threshold to DHM is not effective10,21.

The use of DHM, as opposed to DHW, substantively shifts ecosystem projections for coral reefs over the next three decades, a critical period for reef interventions25. Under RCP 4.5 and RCP 6.0, the two most likely pathways for greenhouse gas concentrations over coming decades, coral cover under DHW was typically double that of DHM during 2030–2050. Planning intervention strategies to support reefs under climate change is a complex but uncertain task, and accurate coral reef projections are important for the portfolio selection, multi-criteria decision-making and risk management involved in the planning process26,27,28,29. The magnitude of divergence of coral cover between DHM versus DHW in our multi-model ensemble suggests that ecosystem projections relying on DHM are currently not suitable for reef management decision-making. While there is legitimate criticism that DHW is too conservative30,31, extensive work has recently been done to fine-tune DHW on the basis of observational datasets32,33,34, including the DHW thresholds used in our second analysis22. The credibility of DHM for coral reef projections will be contingent on the characterization of DHM-specific bleaching thresholds using observational data and the assessment of skill under these thresholds. Until then, the daily SST temporal resolution delivered by most current-generation climate models should be utilized to facilitate heat stress estimates using DHW in coral reef modelling efforts.

Methods

Projected SSTs (variable code ‘tos’) were obtained for six CMIP5 climate models (HadGEM2-ES, GFDL-ESM2M, MIROC5, GISS-E2-R, CESM1-WACCM and CCSM4) from the World Climate Research Program (https://esgf-node.llnl.gov/search/cmip5/) or from the University Corporation for Atmospheric Research (https://www.cesm.ucar.edu/models). The rationale for the selection of the CMIP5 climate models used (in brief, their skill at simulation of El Niño conditions) is provided in ref. 35. Historical simulations for the 1985–2005 period were concatenated with RCP 8.5 simulations for the 2006–2020 period to form one continuous timeseries for each climate model. SST values within each month of the timeseries were adjusted by subtracting the difference between the observational record (CoralTemp v 3.1)8 and the climate model for the 1985–2000 mean SST of the respective month. The MMM was determined as the monthly mean of the hottest month averaged over the 1985–2000 observational record1,36,37.

DHM values were calculated for the 2001–2020 period by summing anomalies of the mean monthly SST above the MMM, over a rolling 3-month period38 and, in a separate analysis, over a rolling 4-month period36. DHW values were calculated by summing daily SST anomalies above the MMM, if those anomalies exceeded the MMM + 1 °C, for a rolling 84-day window, and then dividing by 7, as currently implemented operationally by Coral Reef Watch, the global coral bleaching information service run by the National Oceanic and Atmospheric Administration (NOAA)39. For consistency with DHM, we used the 1985–2000 climatology for DHW, even though the 1985–2012 period, detrended back to April 1988, is used in the operational DHW product8. DHM values were standardized to a weekly basis, through multiplication by 4, for comparison with DHW. Values of both 4 and 4.35 are used in the literature (Extended Data Table 1), but as these result in only an 8–9% difference in the converted value, we simply chose the more conservative conversion factor (4). The bleaching thresholds we used included the 4 °C week (substantial bleaching) and 8 °C week (severe bleaching with substantial mortality) thresholds used operationally by NOAA Coral Reef Watch since the early 2000s, but exclude three additional thresholds (12, 16 and 20 °C weeks) added by NOAA Coral Reef Watch in late 2023 to specify grades of mortality. The original two thresholds have been widely used in research (Extended Data Table 1).

The maximum annual DHM and DHW values were extracted at the centroid of each of 2,014 reefs on the Great Barrier Reef for each year in the 2001–2020 period (reef centroids courtesy of the Great Barrier Reef Marine Park Authority). Graphical comparisons of DHM and DHW were made using cumulative frequency histograms (outer plots in Fig. 1 and Extended Data Fig. 1) and scatter plots (inset plots in Fig. 1 and Extended Data Fig. 1). Cumulative frequency histograms displayed the cumulative proportion of samples (y axis), out of our sample size of 40,280, that had a particular heat stress value (x axis); for instance, the cumulative frequency at 3 °C weeks is the sum of the raw frequencies at 1, 2 and 3 °C weeks. The scatter plots indicate the heat stress value resulting from DHM (y axis) and DHW value (x axis) at each reef in each year. DHM with a 4-month accumulation window produced very similar patterns (Extended Data Fig. 1) to DHM with a 3-month accumulation window (Fig. 1); therefore, we chose only one (the 3-month window) for the analysis in the main text.

Simulations of coral reef cover over 2022–2099 under DHM- or DHW-derived heat stress were performed over 3,806 reefs of the Great Barrier Reef using the ReefMod-GBR individual-based model22. For each RCP, simulations were performed for up to six CMIP5 models, with the ecosystem model outputs then averaged to form one multi-model ensemble. Climate models, data sources and heat stress calculation methods are as described above. As opposed to our 2001–2020 analysis, we used a 1985–2012 period for DHW climatology and 1985–2000 period for DHM climatology, as demonstrating the operational outcomes was a priority in these simulations. In this analysis, coral mortality was modelled as a continuous, nonlinear function of heat stress values >3 °C weeks, calibrated on survey data31,40.

We analysed differences in heat stress from DHM and DHW indices among six climate models and the observational data, using a Poisson generalized linear mixed-effects model. The maximum annual DHM and DHW values were extracted at the centroid of each of 2,020 reefs on the Great Barrier Reef for each year in the 2001–2020 period (reef centroids courtesy of the Great Barrier Reef Marine Park Authority). These data formed the response variable of the generalized linear mixed-effects model, with heat stress algorithm (DHM or DHW) and SST data source (observational record, CCSM4, HadGEM2-ES, GFDL-ESM2M, GISS-E2-R, CESM1-WACCM or MIROC5) as fixed effects, and year as a random effect

$${v}_{{{i}}} \sim {\rm{Pois}}({\delta }_{{{i}}})$$
$${\mathrm{ln}}({\delta }_{{i}})={\mathbf{\upomega}} {{{W}}}_{i}+{\mathbf{\upgamma}} {{{Y}}}_{{i}},$$

where vi is the heat stress values (in °C weeks); ω is the vector of fixed-effects parameters; γ is the vector of random effects parameters; W is the matrix containing the overall intercept and effects of heat stress algorithm and SST data source and their interaction on the heat stress value; and Y is the matrix containing the random intercepts associated with year. For this model, the dataset was further reduced by removing duplicate reefs that fell in the same pixel of the climatological data layer used in MMM calculation, resulting in a final sample size of 1,176 reefs.