Introduction

MHWs have substantial impacts on global biological and socio-ecological systems1,2,3,4,5. Extensive research has been conducted to characterize the timing, intensity, duration, and drivers of surface MHWs6,7,8,9. Marine organisms use two major pathways to cope with extremely warm ocean temperatures— poleward migration10 and vertical migration to deeper ocean layers11 which could be equally important, particularly in regions like the continental shelves of North America12. Vertical migration requires movement in depth that is three to four orders of magnitude smaller than horizontal migration. Notably, across all oceans, among regions with the highest category of marine biodiversity warm-edge exposure, only 6% occurs at the surface, while this number rapidly increases at depths ≥ 100 m, with up to 22% at depths of 1000 m13.

Research on the vertical distribution and variation of MHWs is still limited and typically focuses on individual locations or events14,15,16,17,18. For example, Argo float- and ship-based conductivity‒temperature‒depth data from the Northeast Pacific Ocean indicate that SMHWs may persist two years longer than surface MHWs19. A prominent example is the famous “Blob”, which occurred during 2013‒2015 (ref. 20). Global-scale reanalysis data indicates an even stronger intensification of MHWs at depths of 50–200 m compared to the surface over the past three decades13, emphasizing the need to better understand and characterize SMHWs and their future evolution.

Surface MHW and SMHW events can occur simultaneously21, defined as compound MHW events. In situ temperature measurements on the southeastern Australian continental shelf show that MHW events can extend from the surface to the depths of the water column, even reaching the seabed when upper ocean stratification is weak from 1992-2016 (ref. 18). Similar compound MHW events have been recorded on the North American continental shelf based on reanalysis data17, posing an amplified threat to subaquatic algae and benthic coral reefs and partially limiting the ability of marine organisms to migrate to deeper regions to escape extremely high surface temperatures. However, little is known about how these compound MHW events respond to a warming climate, particularly when considering biological adaptability.

SMHWs over the continental shelves are the focus here as they compose regions of high biodiversity, also defined as large marine ecosystem (LME) regions22. Ocean dynamics in these regions depend on small-scale regional bathymetry and processes, which are not captured by standard 100 km-resolution ocean models used in coupled climate simulations. As low-resolution ocean datasets are not eddy-resolving, high-resolution datasets are preferred when available23. For instance, a study of MHWs at depths ≤ 400 m on North America’s continental shelves using a high-resolution ocean reanalysis at ~8 km (ref. 17) found that SMHWs could be more severe than surface MHWs in terms of duration and intensity.

In the future, under a warming climate, ocean temperatures at depths of 0-2000 m are predicted to increase across most regions of the world24. Previous studies of MHWs, primarily focusing on the sea surface, have indicated that MHWs will become more intense and occur more frequently in the future7,25,26,27. However, there is limited information on how the statistics and vertical structure of SMHWs, as well as compound surface and subsurface MHWs, will respond to a warming climate. Here, using a mesoscale-eddy-resolving ( ~10 km), ultra-high-resolution Earth System Model (CESM-HR), along with future thresholds established in our previous study to partially account for marine biological adaptation28, we examine the characteristics of SMHWs historically and project their future changes under a warming climate. First, we perform a comprehensive comparison between CESM-HR and low-resolution models to demonstrate CESM-HR’s superior ability to accurately reproduce SMHWs. Next, we investigate future changes in SMHWs, revealing a widespread increase in both intensity and occurrence days across global oceans, extending into deeper waters. Finally, we analyze compound MHWs, showing that even with the application of future thresholds to remove the effect of the mean warming, a warming climate leads to more frequent simultaneous occurrences of MHWs at both surface and subsurface levels.

Results

Observed and simulated SMHWs in the historical period

Global Ocean Physics Reanalysis (GLORYS, see “Methods”) data suggests that between 1993 and 2020, the frequency of MHWs from the surface to 1000 meters between 70°N and 70°S decreased with ocean depth (Fig. 1a), e.g., from 1.8 events per year at 50 m to 1.4 events per year at 1000 m. In contrast, the mean duration of SWMWs increased with depth (Supplementary Fig. 1a). This phenomenon is primarily due to the reduced variability in sea temperature with increasing depth (Supplementary Fig. 2). Vertically, the mean intensity of SMHWs increased from the surface, peaking at 1.6 °C at 100 m before decreasing with depth (Supplementary Fig. 3a,d). Spatially, higher intensities were observed in western boundary current (WBC) regions. In the eastern equatorial Pacific, which is influenced by the El Niño–Southern Oscillation (ENSO) (ref. 29,30), SMHWs are more persistent and intense at 50 m and 100 m compared to other global regions (Supplementary Figs. 1a and 3a), aligning with surface data8,31 due to stronger temperature anomalies induced by vertical movement of the thermocline. However, in deeper waters, SMHW intensity and duration are reduced due to the shallower mixed layer depths.

Fig. 1: Observed and simulated frequencies of marine heatwaves (MHWs) during the historical period.
figure 1

a‒c Contemporary (1993–2020) annual surface and subsurface MHW frequencies at five different depths based on (a) GLORYS, (b) CESM‒HR, and (c) CESM‒LR data. White grid squares in deeper layers represent areas with no available corresponding sea temperature data. d Latitudinal plots representing the mean magnitudes of annual SMHW frequency in 1° bins latitude for GLORYS (black), CESM‒HR (red), and CESM‒LR (blue) data. Results show that CESM-HR provides an improved simulation of MHWs compared to CESM-LR.

Full size image

Both the spatial distribution and zonal mean (Fig. 1; Supplementary Figs. 1 and 3) clearly demonstrate that at all depths, the high-resolution CESM‒HR simulation is more similar to GLORYS than the low-resolution CESM‒LR simulation or models in the Coupled Model Intercomparison Project Phase 6 (CMIP6) (Supplementary Fig. 4). For instance, the mean bias in SMHW frequency across all depths ranged from 28% to 45% in CESM‒LR, which is reduced to 6%‒24% in CESM‒HR. In terms of SMHW intensity, CESM‒LR shows considerable underestimation in WBC regions due to the strong modulation of eddies on SMHW intensity, whereas CESM‒HR simulated values closely matching GLORYS, with bias reductions of up to 83% (Supplementary Fig. 3). Similar results were found for surface MHW simulations (Supplementary Fig. 3). These findings for SMHWs are consistent with a previous study28, which compared surface MHW between CESM‒HR, CESM‒LR, and two ocean satellite products with a spatial resolution of 0.25°. The study showed that while CESM‒HR intensities were more similar to satellite data than those from CESM‒LR, the high-resolution model still overestimated MHW intensity compared to the satellite data. This discrepancy led to the hypothesis that low-resolution (0.25°) satellites may not capture the full strength of MHW intensity in eddy-rich areas, highlighting the need for analysis based on high-resolution datasets. The CESM‒LR results are consistent with other low-resolution climate models from the CMIP6 archive (Supplementary Fig. 4).

Focusing further on coastal LME regions, which house higher biomass compared to other areas at equivalent depths13, we classified these regions into six groups, following Fig. 2 (ref. 28). We found that CESM‒HR (red) more closely aligns with the frequency, duration, and mean intensity of SMHWs derived from GLORYS (black) than CESM‒LR (blue; Supplementary Fig. 5). The substantial improvement in simulating SMHWs using CESM‒HR in these LME regions, as well as globally, is primarily attributed to the better representation of vertical heat transport by eddies, thereby reducing the reliance on eddy parameterization choices32,33. Furthermore, CESM‒HR can more accurately resolve complex topography and better simulate mixed-layer depth34. These improvements increase confidence when analyzing future climate impacts on SMHWs.

Fig. 2: Map of oceanic regions and large marine ecosystems (LMEs).
figure 2

his map provides a comprehensive visual representation of various oceanic regions and LMEs across the globe, focusing specifically on the areas between 70 degrees north and 70 degrees south latitude. Oceanic regions are represented with distinct hatching patterns, and the Atlantic Ocean, Pacific Ocean, and Indian Ocean are represented by backslashes (\\), horizontal dashes (---), and vertical lines (|), respectively. LMEs are shaded in different colors corresponding to different continents, with the number representing the index of different LME regions.

Full size image

Changes in SMHWs under a warming climate based on the mean warming-inclusive threshold

The entire ocean is projected to become warmer by the end of this century under various shared socioeconomic pathway (SSP) scenarios35. However, a detailed examination of how subsurface temperature anomalies respond to climate change is necessary to understand changes in SMHWs. To evaluate these changes, it is first necessary to choose a threshold for defining MHWs (refs. 26,28). Most previous studies on surface MHWs used a reference based on a fixed baseline from a historical period to examine future MHWs, known as the “mean warming-inclusive threshold”7,25,26,36. However, it is also informative to shift the reference temperature for the future to isolate the effects of temperature variability and other higher-order temperature statistics on MHWs, the so-called “future threshold”37. The future threshold is particularly relevant when considering the adaptation of marine ecosystems to new climatic conditions. Following our previous study28, we use both the mean warming-inclusive and future thresholds to define SMHWs, effectively differentiating between the effects of long-term warming trends and higher-order temperature statistics on SMHWs. Given that CESM‒HR demonstrates substantial improvements in simulating SMHWs compared with CESM‒LR and other low-resolution CMIP6 models, the analysis below primarily relies on CESM‒HR unless otherwise stated.

In the historical period, the mean MHW intensity between 70°N and 70°S gradually increases with depth, reaching a peak at around 100 m, before declining sharply (Figs. 3a, Supplementary Fig. 6). However, by the end of the 21st century (2071‒2100), under the high-emission representative concentration pathway (RCP) 8.5 scenario and using the mean warming-inclusive threshold, the highest MHW intensity is projected to shift from a depth of 100 m to the surface (Supplementary Fig. 6) due to faster warming at the ocean surface38. Annual MHW days, which are more relevant for marine organisms (e.g., coral and kelp) than mean or maximum sea surface temperature (SST) (ref. 3), are generally projected to increase throughout the water column. The increase in annual MHW days is expected to be larger in the upper ocean compared to deeper levels, with a global average increase of 288.5 days at the surface versus 206.0 days at 1000 m depth (orange lines in Supplementary Figs. 6a, c).

Fig. 3: Meridional‒depth profiles of zonal-mean historical values and projected changes in subsurface marine heatwaves (SMHWs).
figure 3

Historical values and projected changes in mean intensity (a, b, c) and annual days (d, e, f) of MHWs over the historical period (a, d), future changes based on the mean warming-inclusive threshold (b, e) and future threshold (c,f) from CESM-HR in the upper 1000 m of the Pacific, Atlantic, and Indian oceans. The solid horizontal lines in the panels divide the latitudinal ranges into tropical (black) and western boundary current and frontal regions (green). The dashed gray line represents a depth of 100 meters. Results show a general increase based on the future threshold for both the annual MHW days and mean MHW intensity.

Full size image

Focusing on the three major ocean basins (the Pacific, Atlantic, and Indian Oceans; Fig. 2), the mean intensity and annual MHW days are projected to increase substantially at depths from 0 to 1000 m (Fig. 3). Consistent with the overall warming trend of the oceans38,39, the projected increase is larger in the Northern Hemisphere compared to the Southern Hemisphere, and is more pronounced in the upper ocean layers compared to deeper levels. Future changes in MHWs vary distinctly across the three ocean basins. The Atlantic Ocean shows the most widespread areas of high MHW intensity throughout the water column. For example, it exhibits a more pronounced increase in mean MHW intensity at depths of 500‒1000 m compared to the Pacific and Indian Oceans at similar depths (Fig. 3b). This pattern is consistent with the largest mean warming at depths below 700 m, which occurs in the North Atlantic Deep Water24. This is particularly evident between 40°N and 55°N in the North Atlantic (green line in Fig. 3b), a region with high species richness and a large number of species at the warm edge of their distribution exposed to MHWs. In contrast to the deeper ocean, the projected intensity increases near the surface (0‒250 m) is weaker in the northern part of the North Atlantic (e.g., around 60°N) compared to the same latitude in the Pacific. This pattern is likely due to weakened northward heat transport in the North Atlantic, resulting from a slowdown of the Atlantic Meridional Overturning Circulation (AMOC)40,41,42.

Next, we analyze the future changes in the vertical structure of MHWs, keeping in mind that this structure is latitude-dependent and controlled by ocean circulation13. The following description focuses on tropical regions, with a later focus on WBC and Southern Ocean fronts (demarcated by the solid lines in Fig. 3). In the tropics, historical SMHWs are largely disconnected from surface MHWs, and this pattern is expected to continue in the future. Specifically, future changes over this region in the mean intensity and annual days of MHWs at about 100 m depth, approximately close to the multi-year mean depth of the mixed layer in this region, exhibit only small increase magnitudes, accompanied by higher magnitude increases in both the surface and deeper layers (Fig. 3b, e). As a result, changes in both the intensity and annual MHW days in the equatorial region display a quadruple structure, characterized by a strong-weak-strong-weak pattern, with two high-value peaks occurring at the ocean’s surface and at 100 m depth. An exception is the Atlantic, where the annual MHW days form a tri-pole structure. In many equatorial areas, a permanent SMHW state is projected (Fig. 3e), which poses a potential threat to species living near their high-temperature tolerance43.

In the WBC and frontal regions, historical MHWs typically extend below the thermocline (Supplementary Fig. 3), consistent with a previous study using reanalysis data showing high synchronous MHWs between upper and lower ocean layers (ref. 13). Compared to other regions, the projected changes in annual MHW days in the WBC and frontal areas are less pronounced (Fig. 3e). This is because MHWs in these regions are primarily driven by temperature variability rather than mean temperature anomalies44. When the mean warming inclusive threshold is used, the changes in MHWs are dominated by warming trends, diminishing the role of temperature variability in driving those changes. Nonetheless, the WBC and frontal regions experience more intense MHW events in both the historical and future periods compared to other regions at similar depths, with these events extending as deep as 1000 m (Fig. 3a, b). Notably, there is a projected northward and downward propagation of MHWs across the Southern Hemisphere under a warming climate (Fig. 3b), which is linked to the strengthening of the Southern Hemisphere westerlies45, enhancing northward and downward ocean heat transport.

Future changes in MHWs based on the future threshold

In contrast to the previous discussion, using the future threshold, which excludes the influence of background warming on future MHWs, results in much smaller increases in both the annual MHW days and the mean intensity at depths spanning 0‒1000 m (Fig. 3c, f). For instance, MHW annual days and mean intensity are projected to increase by only 1.4 days and 0.13 °C, respectively, by the end of the century compared to the historical period for the layer closest to the surface (50 m), averaged across the three major ocean basins.

In tropical regions, future changes in MHW annual days and mean intensity show a distinct discontinuity above and below the 100 m depth mark across all three ocean basins (Fig. 3c, f), aligning with projections based on the mean warming-inclusive threshold. Subsurface MHW days in tropical regions exhibit exceptionally high values compared to other regions.

WBC and frontal regions exhibit a meridional dipole in temperature from surface to deeper layers (Fig. 3f), with an intensity increase on the poleward side and a decrease on the equatorial side. This pattern is less pronounced near the East Australian Current, where the response is weaker (around 40°S). The simulated dipole pattern can be attributed to future changes in detrended sea temperature variance (Supplementary Fig. 7), driven by shifts in the frontal position in WBC regions46. The largest intensity increases with depth occur in the Atlantic, where warm-edge species and biodiversity in areas13 poleward of 40°N face an increasing threat due to a poleward shift in MHW intensity.

We also conduct an analysis for the 2030-2059 period, when global warming is expected to reach the 2 °C target set by the Paris Agreement. Based on the nearly linear temperature increase shown in a previous study47, this transient climate scenario provides robust projections of subsurface MHWs. The projected changes in mean intensity and annual MHW days are slightly weaker than those projected for the end of the century under both thresholds (Supplementary Fig. 8).

Future changes in MHWs in LME regions

Large marine ecosystem regions are rich in biodiversity and account for 95% of the global fish catch, despite covering only 22% of the total ocean area22. Given the importance of marine biology and the abundance of fish in LMEs, as well as the potential for oceanic organisms to adapt to climate change to some extent48, we focus on results from the future threshold, assuming that ocean organisms will be able to fully adapt to a slow increase in temperature28,37 in these regions.

Most LME regions are projected to face intensified threats resulting from more abundant and more intense MHWs, even when using the future threshold (Fig. 4). Notably, 83% of LMEs have at least one subsurface layer projected to experience intensity comparable to or stronger than at the surface, and 43% of LMEs show a similar change in the number of MHW days. The largest intensity increases are not expected to occur at the surface; instead, they are projected at depths of approximately 50‒100 m in LMEs such as the northwest Atlantic Ocean, including the Newfoundland–Labrador Shelf (ID 9) and Hudson Bay (ID 63; Fig. 4a). In these regions, the phylogenetic species variability of deep-ocean communities is highly sensitive to temperature changes and vulnerable to environmental perturbations48. In particular, Hudson Bay near the Arctic exhibits the highest projected intensity increase (1.4 °C) at a depth of 50 m across all LMEs. This intensity change is even greater than that based on the mean warming-inclusive threshold, which is attributed to a much larger increase in temperature variability in the region. This finding suggests that, even under the optimistic assumption that marine organisms can fully adapt to average warming, the future threat posed by MHWs to subsurface-dwelling organisms may be significantly higher than that for surface-dwelling species. While the rate of adaptation may vary across regions and species43,49, even this “most optimistic” scenario may not be achievable due to the rate at which sea temperatures are changing relative to what ecosystems have historically experienced. It is important to note that we focus on regions between 70°N and 70°S to minimize the effects of sea ice melting on future MHW projections. The stronger increases in MHW intensity in certain high-latitude LMEs, such as Hudson Bay (ID 63 in Fig. 2), may be partly due to greater temperature variability driven by ice melt.

Fig. 4: Projected changes in marine heatwave (MHW) mean intensity and annual days in large marine ecosystem (LME) regions.
figure 4

Future changes (2071‒2100 minus 1993‒2020) in (a) mean MHW annual days and (b) mean MHW intensity among LMEs are defined on the basis of the future threshold under the RCP 8.5, with the number at the top of the x-axis representing the LME region index. The gray text indicates that the future changes in MHWs in this LME are not significant (p ≥ 0.05). Results show an enhanced MHW intensity and annual days over most of the LMEs in the future even with MHWs defined using a future threshold that removes the effect of mean warming.

Full size image

Compound surface‒subsurface MHWs

Global warming alters temperature boundaries and affects the horizontal extent of MHWs. Previous studies have primarily focused on the spatial distribution in the upper ocean, neglecting the simultaneous vertical changes throughout the water column50. Here, we introduce a method to define simultaneous MHW events that extend from the surface to deeper ocean levels as “compound MHWs” (see “Methods”). These events are spatiotemporally continuous, and we emphasize investigating the vertical extent of compound events under a changing climate. The depth of a compound event is defined as the deepest point of a vertically continuous MHW occurrence, based on CESM‒HR results for both historical and future periods, using both the mean warming-inclusive and future thresholds.

During the historical period, compound MHW events had a global mean depth of 140.5 m (Fig. 5a). WBC and frontal regions experience more severe MHW impacts in the deeper ocean compared to other regions, with compound MHW depths reaching up to 1000 m. In these regions, MHW conditions occur simultaneously across the entire water column, from the surface to 1000 m. In 28% of LME regions, a depth of 1000 m is enough to reach the seafloor. In contrast, compound MHW depths are shallower in equatorial and some midlatitude regions, such as the North Pacific, where the mixed layer depth is shallow. Since the mixed layer is typically less than 500 m deep in most parts of the world (ref. 34), a compound event extending to significant depths is likely influenced by physical processes beyond the mixed layer. Some SMHW events can occur without noticeable surface signals, potentially due to the subduction of sea surface temperature anomalies and adiabatic processes. The delay in the vertical movement of these surface anomalies can cause subsurface heat content to remain unusually high even after surface conditions have normalized.

Fig. 5: Vertical distribution of surface‒subsurface compound marine heatwaves (MHWs) and proportion of single-layer MHW events involved in compound events.
figure 5

Spatial distributions of the vertical extended depth of surface‒subsurface compound MHWs (a) in the historical period and the future change (2071‒2100 minus 1993‒2020) based on (c) the future threshold. Note that the color-bar range is different in each plot. The box-and-whisker panels (b, d) depict the proportion of SMHWs that are compound MHW events at different depths for (b) the historical period and the future change using (d) the future threshold, with the minimum and maximum (line endpoints), 25th and 75th percentiles (boxes), medians (horizontal lines), and averages (gray triangles) marked. The gray dots on right-hand side of panels (b, d) represent the proportion of SMHWs in each layer that does not occur synchronously with surface MHWs.

Full size image

Even when mean warming is excluded by applying the future threshold, over two-thirds of the oceans still show an increase in the depth of compound MHW events, with a mean relative increase of 17% (Fig. 5c). In the vicinity of WBCs, there is also a poleward shift of these subsurface events. The results based on the future threshold highlight the contribution of higher-order ocean temperature statistics, such as variance, to the increased occurrence of future surface‒subsurface compound MHWs. They also show that marine species in most oceans are expected to experience increased exposure to surface MHWs, even if they adapt to a slow increase in mean temperature.

We further examine the proportion of SMHW compound events as a function of depth (boxplots in Fig. 5b, d). Historically, this proportion decreases with depth, ranging from 75% at 50 m to 5% at 1000 m. The pattern of concurrent surface and subsurface MHWs holds true even when the future threshold is applied, and the likelihood of compound events in subsurface ocean layers is projected to increase (Fig. 5d), meaning that even when mean warming is excluded, subsurface ocean warming tends to be more connected (dots in Fig. 5b, d) to surface.

To analyze compound MHWs (Table 1), the MHW change rate is defined as the ratio of the change in the number of MHW days (future minus historical period) to the number of MHW days in the historical period. MHW days during compound and non-compound MHW events are composited separately, and these composites are used to calculate the change rates for both compound and non-compound MHWs. The ratio of the compound to non-compound MHW change rate represents the compound MHW amplification effect, which shows that the increase in compound MHWs under climate warming exceeds that of non-compound MHWs by an order of magnitude. This compound MHW amplification effect generally becomes larger with increasing depth, whether or not mean warming is considered. For instance, at a depth of 50 meters, the amplification effect of compound MHWs is close to 10, but it rises rapidly to 40 as the depth increases.

Table 1 Future changes in compound marine heatwave (MHW) amplification effect
Full size table

Discussion

Using an eddy-resolving high-resolution Earth system model (CESM‒HR), we have demonstrated improved accuracy in simulating the mean intensity, duration, and frequency of SMHWs in the 50‒1000 m depth range compared to low-resolution models. By employing a future threshold to define MHWs—one that removes the effect of long-term warming—we gain insights into the threat posed to marine organisms that may adapt to gradual temperature increases. We find that, due to changes in sea temperature variability, MHW intensity is projected to increase more rapidly at subsurface levels than at the sea surface. This research highlights the growing impact of climate change on MHWs and underscores the need for proactive measures to mitigate their potential consequences.

Compound MHWs, defined as simultaneous MHW events that extend from the surface to deeper ocean levels, are projected to increase in depth across more than two-thirds of the ocean under a warming climate, even when using a threshold that removes mean warming. On average, the increase in compound MHW days is ten times greater than that of individual surface or subsurface MHW events. These results reveal that subsurface ocean warming is likely to become more connected to surface warming due to increased temperature variability, promoting the occurrence of compound MHW events. This suggests a decline in the occurrence of independent SMHWs, indicating a shift toward compound MHWs that encompass the entire water column—from the sea surface to the seabed in some coastal locations. With subsurface waters becoming more acidic51,52 and less oxygenated53 under climate warming, the increase in SMHWs poses a compounding threat to deep-sea biodiversity.

Methods

Model configurations

A 250-year simulation using a high-resolution Earth system model was conducted covering the period from 1850 to 210034,54. The model was driven by the Coupled Model Intercomparison Project Phase 5 (CMIP5) historical forcings until 2005 and continued with the RCP 8.5 (high-emission) scenario thereafter. The simulation employed the high-resolution configuration of CESM1.3, with atmospheric and land components operating at a nominal horizontal resolution of 0.25°, and ocean and sea-ice components at a nominal horizontal resolution of 0.1°. This high-resolution configuration, known as CESM‒HR, allows for better representation of mesoscale eddies and their interactions with large-scale circulations, contributing to a marked improvement in reproducing observed surface MHWs28. For comparison, a counterpart low-resolution CESM (CESM‒LR) was run at a spatial resolution of 1° for both the atmosphere and the ocean. The historical period was set as 1993‒2020 to match with the reanalysis data outlined below, while the future period was set as 2071‒2100, All simulations were interpolated to a resolution of 1° for analysis.

Identifying MHW events

MHW events were identified following the method outlined in a previous study (ref. 55), which defines MHWs as discrete and prolonged episodes of anomalously warm water. Specifically, for each grid cell at a given depth, a daily threshold was determined based on the 90th percentile of daily sea potential temperature in an 11-day moving window centered on each day, over a long-term segment (e.g., 30 years), to ensure a sufficient sample size. A varying daily threshold was used to identify MHW events throughout the year. An MHW event was defined as a period of five or more consecutive days with sea temperatures above the threshold. If two events were separated by only one or two days, they were considered part of the same event. The duration (days), frequency (number of events per year), and mean intensity (sea temperature deviation from the threshold) were calculated for each event. This study primarily focused on regions between 70°N and 70°S to minimize the influence of sea ice on the MHW threshold. The term “MHW” is used to represent events occurring at any depth, while “SMHW” refers to MHWs occurring only in subsurface regions.

For the future period (2071‒2100), two thresholds were used: (1) the mean warming-inclusive threshold, based on the 90th percentile of historical data from 1993‒2020, and (2) the future threshold, based on the 90th percentile of data from 2071‒2100.

Information on global ocean temperature reanalysis data

To evaluate how well the model reproduces observed MHWs, we used the Global Ocean Physics Reanalysis (GLORYS) 12V1 (ref. 56) product, which covers the period 1993‒2020. This global, eddy-resolving (1/12° horizontal resolution, 50 vertical levels) reanalysis was generated by the Copernicus Marine Environmental Monitoring Service (CMEMS). The GLORYS reanalysis is based on the Nucleus for European Modeling of the Ocean (NEMO) platform, with atmospheric forcing from European Center for Medium-Range Weather Forecasts reanalysis data. The GLORYS product has been validated against in-situ observations, showing excellent performance in reproducing ocean temperature and mixed-layer depth variability, particularly in the northeast U.S. Shelf and California Current System23,57,58. For comparison with the model simulations, the GLORYS product was interpolated to a 1° resolution.

Information on model evaluation

Due to data availability (e.g., daily ocean temperature at various depths), only one CMIP6 model (FGOAL‒F3‒H) was used for comparison with CESM results. MHWs in GLORYS were calculated using the same method as for the model simulations, and the results were compared in terms of spatial distribution and zonal mean. Zonal means of MHW parameters were calculated at each 1° latitude interval by averaging values along longitudes from 0° to 360°.

Definition of compound MHW events

To characterize the vertical structure of MHWs, an event was defined as a compound surface‒subsurface MHW if MHWs occurred simultaneously and continuously from the surface to deeper layers. The maximum depth reached by such an event was defined as the depth of the compound MHW event. Examples of how compound events are identified and their depths are illustrated in Fig. 6.

Fig. 6: Illustration of surface‒subsurface compound marine heatwaves (MHWs) and their extension depths.
figure 6

A compound surface‒subsurface MHW refers to a MHW that occurs simultaneously and continuously from the surface to deeper layers. For instance, examples 1 and 2 qualify as compound MHWs, with depths of 50 m and 100 m, respectively. In examples 3 and 4, there is a break in continuity; taking only the portion before the break, example 3 is a compound MHW with a depth of 50 m, while example 4 occurs only at the surface and cannot be classified as a compound MHW. In example 5, no MHW occurs at the surface, so it also cannot be classified as a compound MHW.

Full size image