Access this dataset on Dryad

Summary

This dataset contains the processed numerical data and MATLAB plotting scripts used to reproduce Figures 1–4 and Supplementary Figures S1–S4 for the study “Submesoscale Feedback Suppresses Marine Heatwaves.” The files include:

• marine heatwave (MHW) event statistics derived from the LLC4320 simulation and NOAA OISST v2.1;
• phase-averaged upper-ocean MHW heat-budget terms from LLC4320;
• statistics for four MHW driver types;
• submesoscale heat-flux, activity, and mixed-layer-depth diagnostics; and
• GLORYS12V1-based parameterized submesoscale vertical heat-flux diagnostics.

The repository contains processed data used for the figures, not the full raw LLC4320, OISST, or GLORYS12V1 source datasets. Links to those source datasets are provided below.

There are paired files for each reproduced figure: FigN.mat contains the processed data and FigN.m is the MATLAB script that reads that file and creates the corresponding figure. Files beginning with FigS correspond to Supplementary Figures. Figure 5 is a conceptual schematic and therefore has no numerical data file in this repository.

Terminology and common conventions

• MHW: marine heatwave.
• LLC4320: the nominal 1/48° global MITgcm simulation used for the high-resolution analysis.
• OISST: NOAA Optimum Interpolation Sea Surface Temperature v2.1, 0.25° daily SST.
• GLORYS12V1: Copernicus Marine global ocean reanalysis at 1/12° horizontal resolution.
• Onset / grow phase: the period from MHW onset to the time of maximum spatially integrated temperature anomaly.
• Decay phase: the period from that maximum to the end of the MHW.
• T_Tendency: tendency of the horizontally integrated upper-50-m temperature anomaly.
• T_Qnet: contribution from anomalous net surface heat flux.
• T_BF: heat-budget contribution associated with the background current field.
• T_SF: heat-budget contribution associated with submesoscale currents.
• T_SVF: vertical heat-flux contribution driven by submesoscale perturbations.
• T_MSVF: mean/background submesoscale vertical heat flux, obtained from the 60-day moving-average fields.
• BF&BF: T_BF is the dominant driver during both onset and decay.
• BF&Qnet: T_BF dominates onset and T_Qnet dominates decay.
• Qnet&BF: T_Qnet dominates onset and T_BF dominates decay.
• Qnet&Qnet: T_Qnet is the dominant driver during both onset and decay.
• Qnet-dominated MHWs: the Qnet&BF and Qnet&Qnet types combined.

Unless otherwise stated, longitude is in degrees east on a 0–360° grid and latitude is in degrees north (negative values indicate the Southern Hemisphere).

Sign convention in the saved heat-budget arrays

Some .mat files retain the internal sign convention used during the budget calculation. The supplied plotting scripts apply the sign changes used in the published figures. In particular:

• Fig2.m plots -Qnet_*_grid, -mean_*_grid, and -sub_*_grid, while dTdt_*_grid is plotted without a sign change.
• Fig3.m similarly plots -Qnet_*, -mean_*, and -sub_* from the structures in Fig3.mat.
• Fig4.m plots -sub_tot, -sub_vert, and -sub_vert_mean.
• FigS4.m plots the variables in FigS4.mat without this additional sign reversal.

Users wishing to reproduce the published panels should therefore use the paired .m scripts rather than applying an independent sign convention.

File naming and file structure

The repository contains the following research files:

• Fig1.m, Fig1.mat — data and plotting code for main Figure 1.
• Fig2.m, Fig2.mat — data and plotting code for main Figure 2.
• Fig3.m, Fig3.mat — data and plotting code for main Figure 3.
• Fig4.m, Fig4.mat — data and plotting code for main Figure 4.
• FigS1.m, FigS1.mat — data and plotting code for Supplementary Figure S1.
• FigS2.m, FigS2.mat — data and plotting code for Supplementary Figure S2.
• FigS3.m, FigS3.mat — data and plotting code for Supplementary Figure S3.
• FigS4.m, FigS4.mat — data and plotting code for Supplementary Figure S4.

FigS1.mat is stored in MATLAB v7.3/HDF5 format. The other .mat files use the standard MATLAB MAT-file format.

No special numeric missing-value code such as -9999 is used. Where present, NaN denotes a missing/unavailable grid value. In padded event-by-time arrays in Fig1.mat, only the first dur_time(i) columns for event i should be interpreted as valid event days.

Main Figure 1 — Fig1.mat and Fig1.m

Purpose

Figure 1 compares wintertime MHW counts and space-time integrated MHW intensity from LLC4320 and OISST, both globally and in selected subregions.

The regional abbreviations are:

• glb: global ocean;
• cnp: Central North Pacific (CNP);
• gulf: Gulf Stream (GS);
• iso: Indian Ocean sector of the Southern Ocean (ISO);
• pso: Pacific Ocean sector of the Southern Ocean (PSO);
• bcs: Brazil Current System (BCS).

Top-level variables in Fig1.mat

• xx0 (18 × 36): longitude coordinates for the 10° × 10° plotting grid, degrees east.
• yy0 (18 × 36): latitude coordinates for the 10° × 10° plotting grid, degrees north.
• mhw_llc: structure containing LLC4320 event-level and gridded MHW information.
• mhw_oisst: structure containing the corresponding OISST information.
• glb, cnp, gulf, iso, pso, bcs: regional summary structures.

Fields in mhw_llc and mhw_oisst

The two structures use the same field names.

• x (720 × 1440): longitude-column index matrix for the underlying 0.25° grid; integer index, no physical unit.
• y (720 × 1440): latitude-row index matrix for the underlying 0.25° grid; integer index, no physical unit.
• mhw_event1 (event × time cell array): for each event day, an N × 2 list of [row_index, column_index] grid cells belonging to that spatial MHW event. Cells after the event duration are padding/unused.
• temp_area_event1 (event × time): daily SST anomaly integrated over the event area, °C km².
• temp_mean_event1 (event × time): daily spatial-mean SST anomaly over the event area, °C.
• area_event1 (event × time): daily MHW area, km².
• dur_time (event): event duration, days.
• temp_area_mean (event): sum of temp_area_event1 over the valid event days; this is the space-time integrated event intensity, °C km² days.
• temp_mean_mean (event): sum of temp_mean_event1 over the valid event days, °C days.
• area_mean (event): sum of area_event1 over the valid event days, km² days.
• loc_event (event × 2): representative event location [longitude, latitude], defined from the event geometry and used for spatial binning; degrees east and degrees north.
• dur_grid (18 × 36): gridded accumulated event-duration diagnostic, days.
• num_grid (18 × 36): number of spatial MHW events assigned to each 10° × 10° grid box, count.
• intense_grid (18 × 36): gridded accumulated time-integrated spatial-mean MHW intensity, °C days.
• area_grid (18 × 36): gridded accumulated area-time diagnostic, km² days.
• intense_area_grid (18 × 36): gridded cumulative space-time integrated SST anomaly used for the MHW-intensity maps, °C km² days.

Fields in the regional summary structures

Each of glb, cnp, gulf, iso, pso, and bcs contains:

• num_mhw_llc: number of LLC4320 spatial MHW events in that region, count.
• intense_mhw_llc: total LLC4320 space-time integrated MHW intensity in that region, °C km² days.
• num_mhw_oisst: number of OISST spatial MHW events in that region, count.
• intense_mhw_oisst: total OISST space-time integrated MHW intensity in that region, °C km² days.

Fig1.m reads these variables and exports Fig1.pdf.

Main Figure 2 — Fig2.mat and Fig2.m

Purpose

Figure 2 shows the global spatial distributions of the phase-averaged upper-50-m MHW heat-budget terms during the onset and decay phases.

Variables in Fig2.mat

All heat-budget arrays are 36 × 18 and are stored as longitude × latitude. Their physical unit before the plotting factor of 1e3 is °C km² s⁻¹.

• xx0 (36): longitude centers of the 10° × 10° grid, degrees east.
• yy0 (18): latitude centers of the 10° × 10° grid, degrees north.
• dTdt_grow_grid: phase-averaged T_Tendency during MHW onset, °C km² s⁻¹.
• dTdt_decay_grid: phase-averaged T_Tendency during MHW decay, °C km² s⁻¹.
• Qnet_grow_grid: saved net-surface-heat-flux budget term during onset, °C km² s⁻¹; Fig2.m multiplies this field by -1 for the plotted T_Qnet convention.
• Qnet_decay_grid: corresponding decay-phase field; same units and sign treatment.
• mean_grow_grid: saved background-current budget term during onset, °C km² s⁻¹; plotted as T_BF after multiplication by -1.
• mean_decay_grid: corresponding decay-phase field; same units and sign treatment.
• sub_grow_grid: saved submesoscale-current budget term during onset, °C km² s⁻¹; plotted as T_SF after multiplication by -1.
• sub_decay_grid: corresponding decay-phase field; same units and sign treatment.

grow in the variable name means the onset/intensification phase. decay means the decay phase.

Fig2.m transposes the 36 × 18 data arrays for map plotting and exports Fig2.pdf.

Main Figure 3 — Fig3.mat and Fig3.m

Purpose

Figure 3 compares the globally averaged MHW heat-budget terms for four objectively classified MHW types and for the onset and decay phases. Error bars are 95% confidence intervals estimated from event-based samples using 5000 bootstrap resamples.

Top-level structures and MHW-type mapping

• mhw_mean_mean → BF&BF.
• mhw_mean_Qnet → BF&Qnet.
• mhw_Qnet_mean → Qnet&BF.
• mhw_Qnet_Qnet → Qnet&Qnet.

The word mean in these structure names refers to the background-flow/BF branch used in the original analysis naming; it should not be interpreted as a generic arithmetic mean.

Fields in each structure

All central estimates have units of °C km² s⁻¹. Each field ending in _ci is a two-element vector [lower, upper] giving the bootstrap 95% confidence interval in the same units and in the same saved sign convention as its corresponding estimate.

• dTdt_grow, dTdt_grow_ci: onset-phase T_Tendency and 95% CI.
• dTdt_decay, dTdt_decay_ci: decay-phase T_Tendency and 95% CI.
• Qnet_grow, Qnet_grow_ci: saved onset-phase surface-heat-flux term. Fig3.m multiplies it by -1 to obtain the plotted T_Qnet.
• Qnet_decay, Qnet_decay_ci: decay-phase equivalent.
• mean_grow, mean_grow_ci: saved onset-phase background-current term. Fig3.m multiplies it by -1 to obtain the plotted T_BF.
• mean_decay, mean_decay_ci: decay-phase equivalent.
• sub_grow, sub_grow_ci: saved onset-phase submesoscale term. Fig3.m multiplies it by -1 to obtain the plotted T_SF.
• sub_decay, sub_decay_ci: decay-phase equivalent.
• wt_grow, wt_grow_ci: auxiliary onset-phase submesoscale vertical heat-flux diagnostic associated with the vertical w'T' contribution (T_SVF); this field is retained in the data file but is not used directly by Fig3.m.
• wt_decay, wt_decay_ci: corresponding decay-phase vertical heat-flux diagnostic; also not used directly by Fig3.m.

The residual shown in Figure 3 is not stored as a separate variable. It is calculated in Fig3.m from T_Tendency minus the sum of the displayed T_Qnet, T_BF, and T_SF terms.

Fig3.m exports Fig3.pdf.

Main Figure 4 — Fig4.mat and Fig4.m

Purpose

Figure 4 shows the spatial distributions of submesoscale heat-flux terms during Qnet-dominated MHWs.

Variables in Fig4.mat

The 36 × 18 fields are stored as longitude × latitude. Units are °C km² s⁻¹ before the plotting factor of 1e3.

• xx0 (36): longitude centers of the 10° × 10° grid, degrees east.
• yy0 (18): latitude centers of the 10° × 10° grid, degrees north.
• sub_tot (36 × 18): total submesoscale heat-budget contribution corresponding to T_SF, °C km² s⁻¹.
• sub_vert (36 × 18): submesoscale vertical heat-flux contribution corresponding to T_SVF, °C km² s⁻¹.
• sub_vert_mean (36 × 18): mean/background submesoscale vertical heat flux corresponding to T_MSVF, °C km² s⁻¹.

Fig4.m multiplies all three heat-flux arrays by -1 before plotting and exports Fig4.pdf.

Supplementary Figure S1 — FigS1.mat and FigS1.m

Purpose

Figure S1 compares MHWs detected in OISST and LLC4320 at the example location 175.875°W, 31.375°N over 15 October 2011–15 October 2012.

FigS1.mat is a MATLAB v7.3/HDF5 file.

Variables in FigS1.mat

• time (367): daily time coordinate stored as MATLAB serial date numbers; spans 2011-10-15 through 2012-10-15.
• temp_oisst (367): daily OISST SST at the example grid point, °C.
• temp_llc (367): daily LLC4320 SST at the example grid point, °C.
• mclim_oisst (366): day-of-year climatological SST used for OISST MHW detection, °C.
• mclim_llc (366): day-of-year climatological SST used for LLC4320 MHW detection, °C. In this file the observational climatology is used as the reference for the model detection.
• m90_oisst (366): day-of-year 90th-percentile SST threshold, °C.
• m90_llc (366): day-of-year 90th-percentile SST threshold used for LLC4320, °C.
• MHW_oisst (9 events × 9 columns): OISST MHW event table.
• MHW_llc (8 events × 9 columns): LLC4320 MHW event table.

Column definitions for MHW_oisst and MHW_llc

1. start date, integer YYYYMMDD;
2. end date, integer YYYYMMDD;
3. duration, days;
4. maximum MHW intensity relative to the climatology, °C;
5. mean MHW intensity relative to the climatology, °C;
6. within-event intensity variability (standard deviation), °C;
7. cumulative MHW intensity, °C days;
8. longitude-grid index for the selected location, integer index;
9. latitude-grid index for the selected location, integer index.

FigS1.m uses these data to shade detected MHW periods and exports FigS1.pdf.

Supplementary Figure S2 — FigS2.mat and FigS2.m

Purpose

Figure S2 compares grid-point MHW statistics between LLC4320 and OISST, including event counts, duration, mean intensity, and cumulative intensity. These are grid-point MHW statistics and therefore the event counts are not the same quantity as the spatially connected event counts in Figure 1.

Coordinates

• lon (1440): longitude of the 0.25° grid, degrees east.
• lat (720): latitude of the 0.25° grid, degrees north.

Spatial structures

llc_spatial and oisst_spatial each contain 1440 × 720 longitude × latitude arrays:

• num: number of detected grid-point MHW events, count.
• dur: average MHW duration at the grid point, days.
• int_max: average maximum MHW intensity, °C.
• int_mean: average mean MHW intensity, °C.
• int_var: average MHW intensity variability, °C.
• int_cum: average cumulative MHW intensity, °C days.

NaN values in these spatial metrics indicate locations without an available metric (for example, where no qualifying MHW statistic is present).

Regional summary structures

The file contains paired summary structures for LLC4320 and OISST:

• glb_llc, glb_oisst — global;
• cnp_llc, cnp_oisst — Central North Pacific;
• gulf_llc, gulf_oisst — Gulf Stream;
• iso_llc, iso_oisst — Indian Ocean sector of the Southern Ocean;
• pso_llc, pso_oisst — Pacific Ocean sector of the Southern Ocean;
• bcs_llc, bcs_oisst — Brazil Current System.

Each regional structure contains:

• num: total grid-point MHW count in the region, count.
• dur: regional mean MHW duration, days.
• dur_std: standard deviation associated with duration, days.
• int_mean: regional mean MHW mean intensity, °C.
• int_mean_std: standard deviation associated with mean intensity, °C.
• int_cum: regional mean cumulative MHW intensity, °C days.
• int_cum_std: standard deviation associated with cumulative intensity, °C days.

FigS2.m exports FigS2.pdf.

Supplementary Figure S3 — FigS3.mat and FigS3.m

Purpose

Figure S3 shows integrated submesoscale activity and mixed-layer-depth (MLD) diagnostics during Qnet-dominated MHWs.

Submesoscale activity is characterized in the analysis by the standard deviation of normalized vertical relative vorticity (ζ/f) within a 0.25° × 0.25° neighborhood. The anomaly fields are obtained relative to the corresponding 60-day moving-average background before integration over the MHW area.

Variables in FigS3.mat

• lon4 (36): longitude centers of the 10° × 10° composite grid, degrees east.
• lat4 (18): latitude centers of the 10° × 10° composite grid, degrees north.
• ro_an (18 × 36, latitude × longitude): integrated submesoscale-activity anomaly during MHWs, km². The plotted figure divides this value by 1e3 and labels the scale as ×10³ km².
• rom (18 × 36): integrated mean/background submesoscale activity, km². The plotted figure divides by 1e3.
• mld_an (18 × 36): integrated mixed-layer-depth anomaly during MHWs, m km². The plotted figure multiplies by 1e-5 and labels the scale as ×10⁵ m km².
• mldm (18 × 36): integrated mean/background mixed-layer depth, m km². The plotted figure multiplies by 1e-5.

The mixed-layer depth is defined as the depth at which the density differs by 0.03 kg m⁻³ from the value at 10 m depth.

FigS3.m exports FigS3.pdf.

Supplementary Figure S4 — FigS4.mat and FigS4.m

Purpose

Figure S4 contains the GLORYS12V1-based estimate of submesoscale-induced vertical heat flux during MHWs using the Fox-Kemper et al. mixed-layer eddy parameterization, including sensitivity calculations that isolate the influence of mixed-layer depth and horizontal buoyancy/temperature gradients.

Variables in FigS4.mat

The 36 × 18 fields are stored as longitude × latitude. Units are °C km² s⁻¹ before the plotting factor of 1e3.

• xx0 (36): longitude centers of the 10° × 10° grid, degrees east.
• yy0 (18): latitude centers of the 10° × 10° grid, degrees north.
• subflx (36 × 18): MHW-related submesoscale vertical heat-flux anomaly, T_SVF, after removal of the mean/background flux, °C km² s⁻¹.
• subflx_mean (36 × 18): mean/background submesoscale vertical heat flux, T_MSVF, °C km² s⁻¹.
• subflx_mld (36 × 18): vertical heat-flux change associated with MLD variability while horizontal buoyancy and temperature gradients are replaced by their 60-day moving averages, °C km² s⁻¹.
• subflx_bgrd (36 × 18): vertical heat-flux change associated with buoyancy- and temperature-gradient variability while MLD is replaced by its 60-day moving average, °C km² s⁻¹.

A small number of cells contain NaN; these should be treated as missing/unavailable values. FigS4.m exports FigS4.pdf.

Sharing/Access information

Raw/source datasets from which the processed files were derived

• LLC4320 / ECCO simulation output: https://data.nas.nasa.gov/ecco/data.php
  The data can also be accessed using the xmitgcm package: https://xmitgcm.readthedocs.io/en/latest/index.html
• NOAA OISST v2.1: https://www.ncei.noaa.gov/data/sea-surface-temperature-optimum-interpolation/v2.1/access/avhrr/
• GLORYS12V1 / Copernicus Marine Service: https://doi.org/10.48670/moi-00021

The present Dryad deposit contains only the processed values needed for the figure-level analyses and does not redistribute the complete source datasets listed above.

Code/Software

All plotting scripts are written in MATLAB. The exact MATLAB release used to create the archived files is not encoded in the submitted files. The scripts use exportgraphics, so a MATLAB release supporting that function is needed for unchanged execution.

Required or referenced MATLAB functionality

• Standard MATLAB plotting and MAT-file functions.
• M_Map mapping toolbox for functions such as m_proj, m_contourf, m_pcolor, m_plot, m_coast, m_grid, and m_text.
• cptcmap for GMT-style color maps.
• cmocean for the matter color map used in Fig1.m.
• FigS1.m also uses internal.stats.parseArgs and internal.stats.getParamVal in its plotting setup; these are MATLAB internal Statistics functions in installations where they are available.

Important note for FigS1.m

FigS1.m calls a local helper function named datemon to generate date tick positions. That helper is not included in the supplied archive. It affects only x-axis tick placement and does not alter the underlying numerical data or MHW identification. To execute FigS1.m unchanged, users should either provide the original datemon.m helper on the MATLAB path or replace that call with an equivalent standard MATLAB date/datetime tick vector spanning October 2011 to October 2012.

Basic workflow

1. Place each .m file and its paired .mat file in the same working directory.
2. Add the required third-party plotting packages to the MATLAB path.
3. Run the corresponding script, e.g. Fig2.m for Figure 2.
4. Each script exports a PDF figure with the corresponding name.

The .mat files can also be read independently in MATLAB. FigS1.mat is HDF5-based (MATLAB v7.3) and can additionally be inspected with HDF5-compatible software; the remaining MAT files can be read by software that supports standard MATLAB MAT-file formats.