The thermal gap constraint: why satellite degree heating weeks fail where reefs need them most

Abstract

Degree heating weeks (DHW), the global standard for coral bleaching prediction, shows large regional variation in skill. Whether this reflects data quality or an architectural limitation is unresolved. Using Japan’s Monitoring Site 1000 (26 sites, 5 years) and the Global Coral Bleaching Database (7,286 records, 51 countries), I identify a thermal gap constraint: as climatological SST rises above ~28.5°C, anomaly accumulation compresses, preventing DHW from reaching alert thresholds. Metric architecture dominated prediction skill over SST product choice (Δ AUC = 0.24 vs 0.02). DHW’s AUC declined from 0.705 to 0.568 globally. An absolute-temperature metric bypassed the constraint (AUC = 0.884 vs 0.624). With a reef mask applied, 63% of global reef area falls within the constraint zone (29% across all warm-ocean pixels). A two-tier prediction approach is warranted.

Introduction

Degree Heating Weeks (DHW) is the operational standard for satellite-based coral bleaching prediction. Defined as the cumulative positive sea surface temperature (SST) anomaly above a local Maximum Monthly Mean (MMM) climatology, DHW translates thermal stress into a single index with fixed alert thresholds: DHW ≥ 4° C-weeks signals significant bleaching likely, and DHW ≥ 8 signals mass bleaching and mortality likely (Liu et al., 2014). This architecture has been deployed globally by NOAA Coral Reef Watch since the early 2000s (Heron et al., 2016), underpinning early warning systems, management interventions, and retrospective attribution of bleaching events including the recently declared fourth global mass bleaching event (Spady et al., 2026; Skirving et al., 2019).

The accuracy of DHW-based prediction matters increasingly as bleaching events accelerate in frequency and geographic scope. The fourth global mass bleaching event, declared in 2024, affected reef systems across all major ocean basins and underscored the need for reliable early warning (Spady et al., 2026). Yet DHW’s predictive performance is far from uniform across regions (Hughes et al., 2018). Whitaker and DeCarlo (2024) showed that regionally optimizing DHW parameters substantially improves prediction skill, implying that no single parameterization works universally. Lachs et al. (2021) demonstrated that adjusting the HotSpot threshold filter and accumulation window affects accuracy, and Lachs et al. (2023) simulated how progressive rises in MMM erode DHW signal strength over decadal timescales. Compilations of global bleaching observations (Donner et al., 2017; van Woesik and Kratochwill, 2022) have enabled broad-scale analyses of bleaching drivers (Sully et al., 2019; Donovan et al., 2021; Sully and van Woesik, 2020), yet these studies take the DHW metric as given and focus on environmental covariates of bleaching rather than on the structural properties of the prediction metric itself. Whether DHW’s regional performance variation reflects a correctable data quality issue or an inherent architectural limitation remains unresolved.

Two competing hypotheses could explain this regional variation. The first is that SST product choice drives performance differences: Lachs et al. (2025) reported that CoralTemp (the 5 km daily SST product of NOAA Coral Reef Watch) outperformed MUR (Multi-scale Ultra-high Resolution SST, 1 km) for DHW-based bleaching prediction at Palau, suggesting that spatial resolution or product-specific bias could be the limiting factor. If so, the solution lies in selecting or improving the input SST data. The second hypothesis is that DHW’s anomaly-based design contains a structural constraint that limits performance regardless of input data quality, in which case the solution requires redesigning the metric itself. Distinguishing between these hypotheses has significant operational consequences: improving SST products requires substantial investment in satellite infrastructure, whereas redesigning the metric is a computational exercise that can be implemented on existing data streams.

This study tests the competing hypotheses using two independent datasets at contrasting scales, following a two-stage logic: mechanism identification in a controlled system followed by generality testing across diverse populations. This approach is complementary to Lachs et al. (2023), who demonstrated temporal erosion of DHW signal strength over decadal timescales through simulation; the present study identifies the spatial, contemporaneous constraint that operates across a latitudinal gradient at any given time point. First, Japan’s Monitoring Site 1000 program (26 sites, 24–35° N, 5 years, standardized quantitative protocol) serves as the controlled system. This latitudinal gradient creates a natural experiment in which MMM varies from ~27° C at marginal temperate sites to ~30° C at subtropical reef sites, allowing derivation of identical thermal stress metrics from two independent SST products with a fivefold difference in spatial resolution. Second, the Global Coral Bleaching Database (GCBD; van Woesik and Kratochwill, 2022) provides 7,286 observations across 51 countries spanning four decades to test whether the constraint identified in Japanese waters operates globally. The GCBD has been used to analyze bleaching drivers including thermal tolerance (Sully et al., 2019), local environmental conditions (Donovan et al., 2021), and turbidity (Sully and van Woesik, 2020), but the structural properties of the DHW metric used in those analyses have not themselves been examined.

A prior analysis of the Monitoring Site 1000 dataset established that bleaching prevalence follows a bimodal distribution and that an absolute-temperature metric outperformed DHW, but the causal mechanism—why DHW values near zero coexisted with severe bleaching—remained unidentified (Fukui, 2026). The present study makes three contributions: (1) identification of the thermal gap constraint as the structural mechanism underlying DHW’s regional failure, (2) global validation of this constraint using the largest available bleaching database, and (3) proof-of-concept demonstration that absolute-temperature metric architectures bypass the constraint entirely.

Method

Monitoring site 1000 bleaching data

Bleaching data were obtained from Japan’s Monitoring Site 1000 coral reef survey program (Ministry of the Environment, Japan; permit Kansei-Tahatsu No. 2602271). The program employs standardized belt transect surveys at 585 points across 26 sites, covering 24.26-34.98° N. Bleaching prevalence (ratio of bleached to total colony area) was recorded annually in autumn (September-November). Point-level data were aggregated to site-level medians for each site x fiscal year combination (n = 113 site-years). A balanced panel of 21 sites with all five years of data (n = 105) was used for inferential analyses. Sites were classified into three latitudinal bands: low (≤ 26° N; 9 sites), mid (26–30° N; 6 sites), and high (> 30° N; 6 sites).

Satellite SST products

Daily SST was obtained from two products for all 585 survey points over 2019-2024: (1) Multi-scale Ultra-high Resolution SST (MUR v4.1; 0.01°, ~1 km; Chin et al., 2017), and (2) NOAA CoralTemp v3.1 (0.05°, ~5 km). Values were extracted from the nearest grid cell to each point. Within-site daily SST was averaged across points to produce site-level time series.

Thermal stress metrics

From each SST product independently, the following metrics were computed: (1) DHW following Lachs et al. (2021): MMM = maximum of monthly mean SSTs (2019-2024); HotSpot = max(SST - MMM, 0); DHW = sum of HotSpots over a trailing 56-day window/7, yielding ° C-weeks. (2) days30: count of days with SST ≥ 30° C during the 90 days preceding each site’s survey date. The 30° C threshold was selected after testing a range of candidate thresholds for predictive sensitivity (Supplementary Figure 2), 30° C yielding the best discrimination in Japanese waters. This yielded four predictor variables from the two SST products (MUR; CoralTemp, abbreviated CT): DHW_MUR, DHW_CT, days30_MUR, and days30_CT.

Predictive performance

Discriminatory performance was assessed using the area under the receiver operating characteristic curve (AUC; the ROC curve plots true-positive against false-positive rate across classification thresholds, and AUC summarizes overall discrimination, 0.5 = chance, 1.0 = perfect), derived from generalized estimating equations (GEE; binomial family, logit link, exchangeable correlation, site clusters; Liang and Zeger, 1986). GEE-predicted probabilities were used to construct ROC curves; for single-predictor models, this yields AUC values equivalent to those from standard nonparametric estimates while accounting for within-site correlation in the confidence intervals. Pairwise AUC differences were tested via cluster bootstrap (1,000 site-level resamples; 95% CI by percentile method). Four comparisons were pre-specified: days30_MUR vs DHW_MUR, days30_CT vs DHW_CT, DHW_CT vs DHW_MUR, and days30_CT vs days30_MUR. No correction for multiple comparisons was applied as all four comparisons were pre-specified; the smallest p-value (p < 0.001) would remain significant under Bonferroni correction. The primary outcome was ≥ 50% bleaching prevalence. To characterize the structure of the bleaching response, non-zero bleaching prevalence values (n = 65) were modeled as a beta mixture: prevalence (bounded on [0,1]) was fitted with a mixture of one to three beta components, estimated by the expectation-maximization (EM) algorithm, with the number of components selected by the Bayesian Information Criterion (BIC). This tests whether the bleaching response is unimodal or partitions into distinct low- and high-prevalence modes.

Robustness analyses

To address the statistical concerns inherent in a five-year, 26-site dataset, I conducted a suite of pre-specified robustness analyses on the balanced panel (n = 105).

Effective sample size and clustering structure

Although the balanced panel comprises 105 site-year observations, the effective degrees of freedom are reduced by within-site temporal correlation. I quantified this using intraclass correlation coefficients (ICCs) from a two-level binomial mixed model (site and year as crossed random effects) on the ≥ 50% bleaching outcome. The design effect (1 + (m_bar - 1) * ICC, where m_bar is the average cluster size) was used to convert the nominal sample size to an effective sample size (n_eff), and a between-site agreement coefficient (phi) was computed to summarize inter-site coherence in bleaching incidence.

Extended skill metrics

Beyond AUC, three additional metrics were computed to characterize different aspects of predictive performance: (1) Brier score, the mean squared difference between predicted probability and outcome, capturing both calibration and discrimination; (2) Youden’s J statistic (sensitivity + specificity - 1) at the optimal threshold, summarizing classification skill at the operating point; and (3) the Hosmer-Lemeshow goodness-of-fit test (10 deciles of predicted probability), evaluating calibration. Predicted probabilities were derived from the same GEE models used for AUC estimation.

Leave-one-year-out cross-validation

To assess sensitivity to extreme bleaching years, particularly the severe events of 2023 and 2024, I refit each metric’s GEE model with one year omitted and computed AUC on the held-out year. The range of out-of-sample AUC values across the five iterations quantifies temporal robustness; metrics with narrow ranges are insensitive to which year dominates the training data. A supplementary two-year-out analysis (omitting 2023 and 2024 jointly) tested performance under the most adverse training scenario.

Baseline sensitivity for DHW

To address whether short-baseline MMM estimation could inflate apparent DHW failure relative to the NOAA CRW operational implementation, I computed DHW under two baseline definitions: (1) the Lachs et al. (2021) implementation used in primary analyses (2019–2024 baseline, MMM HotSpot threshold, 8-week accumulation), and (2) the NOAA CRW operational implementation (1985–2012 baseline, MMM + 1° C threshold, 12-week accumulation), using CoralTemp daily SST extracted at the same 26 sites. AUC was computed at the ≥ 50% bleaching outcome for each variant, both pooled and stratified by latitudinal band, to test whether longer climatological baselines materially alter DHW skill in warm-water sites where the thermal gap constraint operates.

Global coral bleaching database

To test whether the thermal gap constraint generalizes beyond Japanese waters, I used the Global Coral Bleaching Database (GCBD; van Woesik and Kratochwill, 2022), accessed from figshare as a SQLite database. The GCBD contains 34,878 records from 90 countries spanning 1980-2020, compiled from seven data sources with associated environmental covariates from the Coral Reef Temperature Anomaly Database (CoRTAD v6; Saha et al., 2018). Key variables include ClimSST (climatological SST, analogous to MMM), TSA_DHW (thermal stress anomaly degree heating weeks, 12-week accumulation), and Bleaching_Percent.

Of the 34,878 records, 18,565 originate from Reef Check surveys. Preliminary analysis showed that Reef Check’s semi-quantitative bleaching severity categories (Bleaching_Level 1 = no bleaching, 2 = bleaching observed; binary classification) produced AUC values indistinguishable from chance across all environmental variables—both anomaly-based (TSA_DHW AUC = 0.498) and absolute (Temperature_Maximum AUC = 0.502)—indicating that the non-discriminatory performance reflects data quality limitations rather than metric-specific bias (Supplementary Table 2; Virgen-Urcelay and Donner, 2023). All subsequent GCBD analyses therefore used the non-Reef Check subset. Of the 34,878 total records, 18,565 are Reef Check surveys (excluded as above), leaving 16,313 non-Reef Check records; of these, records lacking a valid TSA_DHW value or bleaching status were removed by the quality filter, yielding the analysis set of n = 7,286 records from 51 countries (comprising AGRRA, Donner, FRRP, and McClanahan sources; Supplementary Figure 3).

Records were stratified by ClimSST into four bands (< 27, 27-28, 28-29, ≥ 29° C). Within each band, AUC was computed for TSA_DHW predicting any bleaching (Bleaching_Percent > 0%). A supplementary analysis using a ≥ 50% threshold tested whether the constraint differentially affects detection of moderate versus severe bleaching. To assess dose-response, records were divided into thermal gap quartiles (ClimSST subtracted from a regional maximum temperature reference) and AUC computed within each quartile.

As a sensitivity analysis to verify that the declining-trend pattern is not an artifact of the Reef Check exclusion, I additionally computed band-stratified AUC on the full GCBD (incl_RC) and compared it with the non-Reef Check subset (excl_RC). The quality filter retained records with non-missing TSA_DHW and bleaching status, yielding incl_RC = 25,851 records (Reef Check = 18,565; non-Reef Check = 7,286) and excl_RC = 7,286 (Reef Check entries removed). Bootstrap 95% CIs (1,000 resamples) were derived for the ≥ 29° C band to test whether AUC differs from the chance level (0.50).

Calibrated absolute thermal stress

To test whether absolute-temperature metrics can structurally bypass the thermal gap constraint, I developed a proof-of-concept Calibrated Absolute Thermal Stress (CATS) metric. CATS is defined as the cumulative exceedance above a bleaching-onset temperature threshold: CATS = sum of max(SST_daily - T_bleach, 0)/7, in ° C-weeks, accumulated over the 90 days preceding each survey. For the site-specific variant (CATS_site), T_bleach was estimated for each site by ROC optimization using all available years (12 of 21 sites had sufficient bleaching variability). A fixed-threshold variant (CATS_30) used T_bleach = 30° C for all sites, providing a direct comparison with days30 in a DHW-like accumulation framework.

Global thermal gap assessment

The NOAA CRW v3.1 MMM climatology (1985–2012 baseline; 0.05° global grid) was used to quantify the extent of reef area subject to the thermal gap constraint. Two nested spatial definitions were applied. First, warm-ocean pixels were defined as grid cells within ± 35° latitude with MMM ≥ 24° C (n = 6,344,142 pixels), providing a broad upper bound on potential reef habitat. Second, to restrict the estimate to areas where coral reefs are actually present, these pixels were intersected with the UNEP-WCMC Global Distribution of Coral Reefs polygon layer (WCMC008 v4.1; UNEP-WCMC et al., 2021): each reef polygon was rasterized to the 0.05° grid, and a pixel was retained as a reef cell if any reef polygon intersected it (52,358 reef cells; total reef area 899,466 km2). The proportion with MMM ≥ 29° C was computed under both definitions as the primary indicator of thermal gap vulnerability. The warm-ocean definition includes open-ocean and deep-water pixels with no reef and therefore underestimates the reef-specific constraint; the reef-masked estimate is the more appropriate measure of the proportion of global reef area within the constraint zone.

Results

Metric design dominates SST product choice (monitoring site 1000)

At the primary outcome (≥ 50% bleaching prevalence), switching SST products changed DHW’s AUC by only 0.017 (MUR: 0.671; CoralTemp: 0.688; bootstrap 95% CI [-0.025, 0.062], p = 0.170). For days30, the inter-product difference was similarly small (MUR: 0.912; CoralTemp: 0.894; Δ = -0.018). In contrast, replacing DHW with days30 within the same SST product produced large AUC gains: Δ = 0.242 for MUR (95% CI [0.136, 0.333], p < 0.001) (Supplementary Figure 6) and Δ = 0.206 for CoralTemp (95% CI [0.121, 0.283], p < 0.001). The inter-product difference (0.02) was thus an order of magnitude smaller than the inter-metric difference (0.24), demonstrating that the choice of metric architecture, not SST product, is the dominant determinant of bleaching prediction skill (Supplementary Table 4, Figure 1). The latitudinal decomposition reveals that the metric-design advantage is concentrated in the low-latitude band (Δ = 0.274, p < 0.001), precisely where the thermal gap constraint operates, while at high-latitude sites where DHW already performs well (AUC = 0.964), days30 offers no improvement (Supplementary Table 4).

Figure 1

Inter-product differences were real but small (AUC Δ approximately 0.02) and inconsistent in direction, consistent with high MMM concordance between products (mean difference = +0.068 ° C; Supplementary Figure 1). Lachs et al. (2025) reported that CoralTemp outperformed MUR at Palau; the present results confirm such differences exist but are an order of magnitude smaller than the metric-design effect. Using the NOAA CRW operational DHW (v3.1; 12-week window, MMM + 1° C threshold, 1985–2012 climatology) raised AUC to 0.753 (from the 2019-2024-baseline CoralTemp value of 0.688) but still fell substantially short of days30 (0.912; Supplementary Table 1), confirming that longer baselines partially widen the thermal gap but cannot resolve the structural limitation as warming continues.

The metric-design advantage is robust to a battery of sensitivity checks (Methods, § Robustness analyses). Effective sample size analysis confirmed that the 105 site-year balanced panel, after accounting for within-site temporal correlation (ICC_site = 0.30, ICC_year = 0.18, design effect = 2.20), corresponds to n_eff = 47.8 — sufficient to detect the observed AUC differences of 0.24 with high confidence. Mean pairwise between-site agreement on the ≥ 50% bleaching outcome was phi = 0.48 (78 site pairs, 82.1% with phi > 0), indicating moderate inter-site synchrony in bleaching incidence consistent with shared regional thermal forcing.

Across three additional skill metrics, days30 outperformed DHW on every measure (Table 1): Brier score (days30_MUR = 0.095 vs DHW_MUR = 0.179; lower is better), Youden’s J statistic at the optimal threshold (0.721 vs 0.351), and Hosmer-Lemeshow goodness-of-fit (days30_MUR p = 0.782, indicating good calibration; DHW_CT p = 0.034, indicating significant misfit; DHW_MUR p = 0.071, borderline).

Leave-one-year-out cross-validation revealed striking temporal robustness: days30_MUR’s out-of-sample AUC ranged only from 0.917 to 0.932 (range = 0.015) across the five iterations, whereas DHW_MUR ranged from 0.577 to 0.723 (range = 0.146), with the lowest value occurring when the severe 2024 bleaching year was excluded from training. Even when both 2023 and 2024 — the two most extreme bleaching years on record — were jointly omitted, days30 retained AUC = 0.907 versus DHW = 0.597, a 0.310 advantage that persists under the most adverse training scenario.

Baseline sensitivity analysis revealed that the NOAA CRW operational implementation (1985–2012 baseline, MMM + 1° C threshold, 12-week accumulation) materially improves DHW skill in the constraint zone: AUC rose from 0.562 (Lachs et al., 2021 implementation) to 0.792 in the low-latitude band, with a smaller pooled gain (0.671 to 0.753; Supplementary Table 1). This improvement is real, not an artifact, and indicates that part of the apparent DHW failure under a contemporary baseline reflects baseline drift — the elevation of recent MMM by ongoing warming, which compresses computed anomalies. Even within the present 5-year observation window, however, the CRW baseline narrows but does not close the gap to days30: in the low-latitude band, days30 (AUC = 0.833) still outperforms CRW DHW (0.792), and pooled across all sites the gap is wider still (0.912 vs 0.753; Supplementary Table 1). Moreover, this is precisely the mechanism that erodes DHW signal strength over time: Lachs et al. (2023) demonstrated that progressive MMM rise progressively weakens DHW in simulation; the present results show the same effect manifesting spatially across latitudes within a single decade. The CRW baseline’s advantage is therefore temporary, and will erode as warming continues to inflate the climatological reference. By contrast, days30 retained AUC = 0.833 in the low-latitude band and AUC = 0.912 pooled (Supplementary Table 4), because absolute-temperature metrics are anchored to physical bleaching thresholds rather than statistical baselines that drift with the climate.

The thermal gap mechanism (monitoring site 1000)

Beta mixture modeling of non-zero bleaching prevalence (n = 65 site-years) identified a bimodal distribution (2-component BIC = -31.9 vs 1-component = -20.7): a low-prevalence mode (weight = 0.36, mean = 2.8%) and a high-prevalence mode (weight = 0.64, mean = 59.4%). The critical finding is that high-prevalence events are concentrated at near-zero DHW values (median DHW = 0.26° C-weeks), well below any operational alert threshold, whereas days30 cleanly separates the two modes (high-prevalence median = 15.75 days vs low-prevalence median = 0 days; Figure 1).

This failure traces to a thermal gap constraint. MMM increases with decreasing latitude (r = -0.915), and the thermal gap (summer maximum SST minus MMM) compresses as MMM rises (Figure 2a). At sites with MMM > 29° C, thermal gap is typically < 1.0° C, capping the maximum daily HotSpot and preventing DHW from reaching alert thresholds even during severe bleaching. The median number of days with SST > MMM at these sites during the peak summer window was only 16 (IQR: 11-36), producing intermittent, low-magnitude HotSpot pulses that accumulated to a median DHW of just 0.17° C-weeks. This compression is structural rather than statistical. With site-level MMM reaching 29.9° C in the present dataset and observed summer maxima of 31.0-31.1° C, the available margin for anomaly accumulation is approximately 1.2° C even at peak; sustained accumulation over the 56-day DHW window therefore cannot generate values approaching the operational alert threshold of 4° C-weeks under realistic forcing. The constraint follows directly from the arithmetic of any anomaly-based metric anchored to MMM: as MMM rises toward the absolute physical ceiling that tropical SST cannot exceed, the upper-tail margin available for anomaly accumulation shrinks deterministically. This is not a calibration problem — no threshold adjustment can rescue discrimination when the metric’s dynamic range is mathematically compressed below the alert level.

Figure 2

Global validation with GCBD

The thermal gap constraint identified in Japanese waters is not a regional anomaly. Analysis of 7,286 non-Reef Check records from the GCBD across 51 countries revealed a systematic decline in DHW predictive performance with increasing climatological SST (Figure 3). Fine-grained analysis (0.5° C bins; Supplementary Figure 7) showed that the bin-to-bin AUC profile is non-monotonic, reflecting variation in data source composition across ClimSST bands (Supplementary Figure 8; correlation between AGRRA source proportion and AUC, r = -0.78, p = 0.005). Therefore, I used four broad bands, which average over this source heterogeneity and provide stable estimates of the overall trend. For the detection of any bleaching (> 0%), TSA_DHW AUC declined monotonically across ClimSST bands: 0.705 (< 27° C), 0.665 (27–28° C), 0.670 (28–29° C), and 0.568 (≥ 29° C), a drop of 0.137 from coolest to warmest band (Supplementary Table 5). At finer resolution, the decline accelerates above 29° C and reaches AUC = 0.513 above 30° C (n = 275, 95% CI [0.47, 0.56]), where even the dominant data source (AGRRA) alone shows AUC = 0.459. Across the non-Reef Check subset, 83.3% of observations recorded bleaching; within the ≥ 29° C band, 74.6% of observations recorded bleaching. The declining trend with ClimSST is not contingent on Reef Check exclusion: when Reef Check records were included (incl_RC; n = 25,851), TSA_DHW AUC declined from 0.565 (< 27° C) to 0.502 (≥ 29° C), with the ≥ 29° C band CI of [0.495, 0.510] enclosing the chance level of 0.50. Both subsets — with and without Reef Check — yield the same qualitative pattern of monotonic decline; what differs is only the absolute AUC level, lowered uniformly across all bands by Reef Check’s data quality limitations (Supplementary Table 2). Reef Check exclusion therefore amplifies the apparent skill of TSA_DHW in cooler bands but does not create the declining trend, which is reproduced within every quality-filtered subset examined.

Figure 3

This pattern is not specific to the TSA_DHW formulation. SSTA-based DHW showed the same declining trend (0.724 to 0.601), confirming that the constraint operates at the level of the anomaly-based architecture. By contrast, Temperature_Maximum showed no systematic decline across bands (0.421 to 0.440; Figure 3), though its overall discriminatory power was low due to its single-timepoint nature. The critical comparison is the direction of the trend across ClimSST bands: anomaly-based metrics decline, absolute metrics do not (Supplementary Figure 5).

The dose-response relationship between thermal gap magnitude and DHW performance further supports the mechanistic interpretation. Records in the smallest thermal gap quartile (Q1; mean ClimSST = 29.0° C) had AUC = 0.583, substantially lower than Q2-Q4 (AUC approximately 0.69; Figure 3). The constraint binds most tightly where the gap is smallest. The transition is progressive rather than abrupt: degradation begins around 28.5° C, accelerates through 29° C, and becomes nearly complete above 30° C.

The operational consequence of the thermal gap constraint is starkly illustrated by DHW alert threshold sensitivity. In the ≥ 29° C band, the DHW ≥ 4° C-weeks alert threshold achieved a sensitivity (true positive rate) of only 0.055 — a false negative rate of 94.5% (Supplementary Figure 4). In practical terms, for every 20 bleaching events in warm reef regions, the standard DHW alert would miss 19 of them. This is not a matter of threshold calibration; it reflects the structural inability of anomaly-based metrics to generate values above the alert threshold when the thermal gap is compressed.

An important nuance emerges from the severity-stratified analysis. At the ≥ 50% bleaching threshold, AUC in the ≥ 29° C band was 0.718 — substantially higher than for any-bleaching detection (0.568; Supplementary Table 5). DHW retains moderate capacity to detect severe mass bleaching events even where the thermal gap is compressed, because the rare extreme heatwaves that push SST well above MMM can still generate DHW exceedance. However, for routine bleaching detection — the early warning function that DHW is operationally designed for — the metric is effectively non-functional in the warmest reef regions.

CATS: an absolute-threshold alternative

The Calibrated Absolute Thermal Stress (CATS) metric demonstrates that the thermal gap constraint is a property of the anomaly-based architecture, not an inherent limitation of cumulative thermal stress metrics. The CATS comparison is computed on the subset of site-years for which a calibrated bleaching threshold could be estimated and uses uncorrected ROC AUC (rather than the GEE-adjusted values of the main analysis); the DHW and days30 values reported here therefore differ slightly from those in the primary analysis (Supplementary Table 4) but preserve the same ranking. At the primary outcome (≥ 50% bleaching), CATS_30 (T_bleach = 30° C) achieved AUC = 0.884, comparable to days30 (0.906) and far exceeding DHW (0.624; Figure 4). This near-equivalence of CATS_30 and days30 provides theoretical justification for the simpler days30 metric: both measure cumulative absolute thermal exposure, differing only in whether exceedance is summed (CATS) or counted (days30).

Figure 4

The site-specific variant (CATS_site) was particularly informative in the low-latitude band, where the thermal gap constraint binds most tightly. At low-latitude sites, CATS_site achieved AUC = 0.877, compared to DHW = 0.531 — a Δ of 0.346 (Figure 4). The estimated T_bleach values were on average 0.42° C below MMM, indicating that bleaching onset occurs at temperatures lower than the climatological maximum, consistent with the notion that absolute thermal thresholds, not anomaly exceedance, govern bleaching initiation.

CATS is presented as a proof of concept, not a finished operational metric. Cross-validated AUC for CATS_site was 0.471, indicating that site-specific calibration from five years of data is unstable. The important conclusion is architectural: metrics grounded in absolute temperature, whether simple (days30) or cumulative (CATS_30), consistently outperform anomaly-based metrics where MMM is high. Critically, CATS_30 requires no site-specific calibration yet achieves AUC = 0.884, demonstrating that the absolute-threshold design principle is operationally viable without the local tuning that limits CATS_site. The optimal absolute threshold will necessarily vary regionally — just as days30 would become uninformative in the Persian Gulf (Coles and Riegl, 2013) where SST routinely exceeds 30° C — but the design principle of referencing absolute temperature rather than anomaly is robust.

Discussion

The mechanism: arithmetic compression and its empirical signature

The thermal gap constraint is, at its core, an arithmetic property of the DHW definition. DHW accumulates daily HotSpot values (max(SST - MMM, 0)) over a trailing window; the upper bound on this accumulation is fixed by the gap between MMM and the absolute physical ceiling that tropical SST cannot exceed. Across the present dataset, site-level MMM reached 29.9° C while observed summer maxima rarely exceeded 31.1° C, leaving a peak-day margin of approximately 1.2° C and a typical daily HotSpot well below this. Sustained accumulation over the 56-day window therefore cannot, even in principle, generate values approaching the operational alert threshold of 4° C-weeks. This compression is deterministic and metric-architectural: it follows from the definition of DHW combined with the physical bound on tropical SST and would persist regardless of how the metric were calibrated, validated, or applied.

Whether interannual SST variance might also compress in warm regions — beyond the arithmetic compression of the mean gap — is a separate empirical question. The thermodynamic regulation hypothesis (Ramanathan and Collins, 1991), in which evaporative cooling and convective heat loss damp tropical SST excursions near the upper bound, predicts exactly such variance compression: a tightening of interannual variability around an already-elevated mean. Quantification of this effect in the present dataset, however, was inconclusive: across 21 sites spanning MMM 27.1-29.9° C, the correlation between MMM and interannual SD of summer maximum SST was weakly positive and non-significant (Spearman rho = 0.31, p = 0.17; rank correlation reported, as the small sample (n = 21) and bounded range favor a nonparametric measure), and the band-stratified comparison was uninterpretable because only one site had MMM < 28° C, leaving the cool-band reference effectively empty. The Japanese latitudinal gradient is too narrow to test the variance hypothesis with statistical power. Importantly, this null result does not weaken the structural argument: the arithmetic compression of the mean gap is sufficient on its own to explain DHW’s failure and operates regardless of whether variance also compresses. Variance compression, where it exists globally (Ramanathan and Collins, 1991), would deepen the constraint but is not necessary to produce it.

This spatial pattern — DHW skill declining as MMM rises within a single decade of observation — is the cross-sectional analogue of the temporal erosion that Lachs et al. (2023) demonstrated through simulation: as global warming progressively raises MMM, anomaly-based metrics progressively lose signal strength. The two views are facets of the same phenomenon. Lachs et al. observed it in time, projecting forward from contemporary baselines; the present study observes it in space, across a contemporary latitudinal gradient. Both converge on the conclusion that any prediction architecture anchored to a moving climatological reference will, sooner or later, lose its operational utility in the warmest reef regions. The structural fix is not a recalibration but a reformulation: anchoring thermal stress to absolute biological thresholds rather than to climatological anomalies.

Regional calibration of absolute thresholds

The absolute-threshold design principle is universal; the threshold value itself is not. The 30° C cutoff used in days30 is calibrated to the thermal regime of Japanese reefs, where MMM ranges from 27.1 to 29.9° C and bleaching onset occurs at temperatures within this band. Applying the same value to a fundamentally different thermal regime — for instance, the Persian Gulf, where SST routinely exceeds 30° C and resident corals tolerate temperatures unparalleled elsewhere (Coles and Riegl, 2013) — would be uninformative; the metric would saturate and lose discriminatory power, just as DHW does at the other end of the spectrum. The point of the present analysis is not to propose 30° C as a global threshold, but to demonstrate that thermal stress metrics anchored to absolute temperature, rather than to a climatological anomaly, retain discriminatory power in regimes where DHW does not. The threshold value itself must be calibrated to local biology.

Regional calibration is straightforward in principle: in any reef system with sufficient bleaching observations and matched daily SST, ROC optimization identifies the absolute-temperature value at which sensitivity and specificity are jointly maximized. CATS_site demonstrates this approach: T_bleach values estimated independently for each site of the Monitoring Site 1000 panel averaged 0.42° C below MMM, consistent with the proposition that bleaching onset is anchored to absolute temperatures rather than to anomalies above climatology. The absolute level at which bleaching is initiated may shift over time with acclimatization to consecutive heatwaves (DeCarlo et al., 2019), but the architectural distinction between absolute-temperature and anomaly-based metrics is preserved regardless of such shifts. The instability of CATS_site under cross-validation reflects the limited training data (five years per site) rather than a flaw in the design principle: CATS_30, which substitutes a fixed regional threshold for site-specific tuning, achieved AUC = 0.884 without any local calibration. This suggests a hierarchy of calibration: a regional threshold suffices for most operational purposes, with site-specific tuning becoming necessary only where biological heterogeneity is large and training data sufficient.

The two-tier framework that emerges is operationally tractable. In reef regions with MMM below approximately 28.5° C, DHW continues to function as designed, and the considerable infrastructure built around it — alert systems, management protocols, retrospective attribution — remains valid. In reef regions with MMM at or above this threshold, an absolute-temperature criterion calibrated to local thermal biology should supplement or replace DHW for bleaching prediction. Both metrics can be computed from existing satellite SST products on identical operational timescales; the architectural change requires no new observational infrastructure. Adoption is therefore primarily a matter of methodological consensus rather than technical capacity. As warming continues to elevate MMM globally — and the constraint zone expands — the operational case for absolute-temperature criteria will only strengthen, not because the metric is novel, but because the alternative is becoming progressively unfit for its early-warning purpose in the regions where early warning matters most.

Implications and limitations

Analysis of the NOAA CRW global MMM climatology (1985–2012 baseline) revealed a marked contrast between the two spatial definitions (Figure 2b). Across all warm-ocean pixels (MMM ≥ 24° C, ± 35° latitude), 29.2% (1,854,517 of 6,344,142) have MMM ≥ 29° C. When the estimate is restricted to pixels containing coral reef using the UNEP-WCMC reef mask, however, this proportion rises to 63.4% (33,182 of 52,358 reef cells), with a further 27.2% in the 28–29° C band — placing more than 90% of global reef area at MMM ≥ 28° C. The warm-ocean figure is diluted by open-ocean and deep-water pixels that contain no reef; the reef-masked value of 63.4% is therefore the operationally relevant measure, indicating that nearly two-thirds of global reef area already lies within the thermal gap constraint zone. Both estimates are conservative with respect to the operational baseline: the 1985–2012 reference is the standard NOAA operational basis for current DHW alerts, and a more recent baseline (e.g., 2019-2024) would push more pixels above the 29° C threshold because contemporary MMM values are already elevated by ongoing warming. The highest-MMM regions — the Coral Triangle, western Pacific warm pool, and parts of the Caribbean — are precisely the areas where coral reef biodiversity and ecosystem service values are greatest. Under continued warming, MMM values will rise globally (Donner et al., 2005), expanding the constraint zone and mirroring the temporal erosion described by Lachs et al. (2023). The constraint is structurally analogous to the ceiling effect in clinical measurement, where an instrument loses sensitivity as scores approach the upper bound of its range and can no longer discriminate further change (Terwee et al., 2007). Recognizing degree heating weeks as an anomaly-referenced instrument subject to the same attenuation — a perspective imported from diagnostic test theory rather than reef ecology — reframes its regional failure not as miscalibration but as a structural property of the metric’s architecture.

Several limitations warrant consideration. The Monitoring Site 1000 panel is small in nominal size (26 sites, 5 years; 105 site-years in the balanced subset), and the within-site temporal correlation reduces the effective sample size to n_eff = 47.8 — a constraint that the cluster-bootstrap and leave-one-year-out analyses presented above were specifically designed to address, and that the GCBD validation across 7,286 records and 51 countries further mitigates. The GCBD itself contains data only through 2020, missing the severe 2022 and 2024 bleaching events; the corresponding signal in Japanese waters during those years (Results, § Robustness) is internally consistent with the constraint identified globally.

The non-Reef Check GCBD subset is regionally heterogeneous: AUC estimates in the warmest ClimSST band are dominated by Caribbean records (AGRRA, 83%) while cooler bands draw heavily from the Great Barrier Reef (FRRP). The declining-trend pattern persists within the AGRRA subset alone (AUC: 0.613, 0.533, 0.535, 0.488 across the four bands; Supplementary Table 3) and within the FRRP subset where bands are populated, ruling out a source-composition artifact, and the same trend is reproduced when Reef Check records are included rather than excluded (Results, § Global validation with GCBD). Donner records contain exclusively bleaching-positive observations and therefore inflate the overall bleaching rate (83.3%) without contributing to AUC estimation. Convergent evidence from the western Pacific (Monitoring Site 1000), the Caribbean (AGRRA), and the Coral Sea (FRRP) supports global generality across three major ocean basins.

Coral species composition varies across the Japanese latitudinal gradient and may co-vary with bleaching susceptibility; within-site temporal contrast — the same species assemblages exhibiting both high and low bleaching across years, tracking days30 variation rather than species turnover — provides partial mitigation. More fundamentally, even if biological adaptation contributes to reduced DHW sensitivity in warm regions, the operational conclusion is unchanged: a metric that cannot discriminate bleached from unbleached states fails its early-warning function regardless of the underlying cause. Acclimatization to consecutive heatwaves (DeCarlo et al., 2019) further modifies bleaching susceptibility in ways that neither DHW nor days30 currently capture; incorporating thermal history into absolute-threshold metrics is a logical next step. The 30° C threshold in days30 is calibrated to Japanese waters and would require regional re-calibration for other thermal regimes, as discussed above (§ Regional calibration of absolute thresholds). The global reef-area estimate intersects the NOAA CRW grid with the UNEP-WCMC reef polygon layer (WCMC008 v4.1) at 0.05° resolution; fine-scale reef features below the 5 km grid may be incompletely captured, but this does not affect the order-of-magnitude conclusion that the majority of reef area lies within the constraint zone.

Finally, the GCBD provides only summary statistics (Temperature_Maximum, TSA_DHW), not daily SST time series, so cumulative absolute-temperature metrics (e.g., days30, CATS) cannot be computed from it. The low AUC of Temperature_Maximum (approximately 0.43) in the GCBD therefore reflects the inherent weakness of a single-timepoint metric, not a failure of the absolute-temperature concept; the superiority of cumulative absolute metrics is demonstrated only in the Monitoring Site 1000 dataset, where daily SST is available. Extending this test to global scale would require linking GCBD records to gridded daily SST archives, an undertaking beyond the scope of the present study but a natural extension.

Conclusions

The predictive failure of satellite-derived Degree Heating Weeks for coral bleaching is not a data quality issue but a structural constraint inherent in the anomaly-based metric architecture. Where the Maximum Monthly Mean climatology approaches bleaching-relevant absolute temperatures, the thermal gap compresses below the margin required for DHW to generate operationally meaningful values. This constraint, first identified in Japan’s Monitoring Site 1000 network (26 sites, 5 years), is reproduced in the Global Coral Bleaching Database across 7,286 observations from 51 countries: DHW’s AUC declines from 0.705 in cooler reef regions to 0.568 where MMM exceeds 29° C. Absolute-temperature metrics bypass the constraint entirely, achieving substantially higher discriminatory performance (AUC = 0.91 vs 0.67 in the Monitoring Site 1000 dataset, AUC = 0.88 vs 0.62 for CATS vs DHW). With 63% of global reef area already within the constraint zone (reef-masked; 29% across all warm-ocean pixels) and this fraction expanding under continued warming, a two-tier approach—retaining DHW for cooler reef regions where it performs well while incorporating absolute-temperature criteria for regions with MMM above approximately 28.5° C—offers a pragmatic path toward improved early warning that can be implemented on existing satellite data streams.

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