Improved Forecasts of Global Extreme Marine Heatwaves Through a Physics-guided Data-driven Approach

Fanghua Xu; Hao Wu; Ruijian Gou; Ruiqi Shu; Xiaomeng Huang; Yuan Gao

REVIEW 5 major objections 6 minor 13 references

Improved Forecasts of Global Extreme Marine Heatwaves Through a Physics-guided Data-driven Approach

T0 review · 5 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A physics-guided neural network sharply improves 10-day extreme marine heatwave forecasts.

desk verdict A useful deterministic MHW forecasting framework, but the probabilistic augmentation's 15% extreme-event gain rests on oracle selection and needs major rework before the headline claim is credible. read the letter →

arxiv 2412.15532 v1 pith:ZXLJMAET submitted 2024-12-20 physics.ao-ph cs.AI

Ruiqi Shu , Hao Wu , Yuan Gao , Fanghua Xu , Ruijian Gou , Xiaomeng Huang This is my paper · ORCID

classification physics.ao-phcs.AI

keywords marineheatwavesseasurfacetemperatureanomalydeeplearningforecastensembleVQVAEdataaugmentationexplainableAIwindforcing

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that a purely data-driven forecast system can predict global marine heatwaves 10 days ahead more accurately than existing machine-learning models and competitively with a leading numerical ocean forecast, while computing a global forecast in about 0.2 seconds. The system is built around two physically motivated modules: a 'coupler' that feeds atmospheric forcing into the ocean forecast, and a probabilistic data-augmentation module that uses a vector-quantized variational autoencoder (VQVAE) to generate pseudo-ensembles of extreme SSTA fields. Retraining the deterministic model on these pseudo-ensembles lifts the critical success index for the most extreme events (99th percentile) by about 15%. An explainability analysis concludes that surface wind forcing is the dominant short-term driver of MHW intensity changes, acting mainly through latent heat flux.

What carries the argument

The central object is the probabilistic data-augmentation loop built on a vector-quantized variational autoencoder (VQVAE). The VQVAE is trained with a reconstruction (MSE) loss claimed to let it learn the conditional distribution $p(\overline{T}_t' \mid \overline{T}_0', A_{0:t})$ of mixed-layer SSTA anomalies; sampling proceeds by taking the $k{=}10$ nearest latent codes in Euclidean distance to the deterministic forecast's code, decoding them into pseudo-ensemble SSTA fields, selecting the $m$ fields closest to the ground truth, and retraining the deterministic forecaster on the augmented dataset. A second named component is the 'coupler' $\phi^{(1)}_\theta$, which mimics the atmosphere-to-ocean flux driving in the governing heat budget so that the forecast model receives heat-flux anomalies rather than raw atmospheric fields.

What would settle it

A controlled experiment that retrains the deterministic model on pseudo-ensembles chosen uniformly at random from the decoder instead of by ground-truth proximity, and then checks whether the ~15% CSI gain survives, would directly test whether the gain comes from the learned distribution or from the oracle-like selection step.

Watch

Extended reading notes

Core claim

The paper's central claim is that representing SSTA evolution as a composition of two learned maps—a coupler that converts atmospheric variables and initial SSTA into surface heat flux anomalies, and a second network that maps those fluxes plus initial SSTA into future SSTA—yields a 10-day global MHW forecast that beats prior data-driven models by 30-40% in RMSE and matches or exceeds the GOFS 3.1 numerical forecast at a tiny fraction of the cost. The probabilistic module learns the conditional distribution of future SSTA with a VQVAE and draws pseudo-ensemble members by perturbing latent codes and decoding; selecting the members closest to the observed target and retraining on them materially improves detection of extreme MHWs, including small-scale mesoscale structures in a 1/12-degree regional test. The authors further state that explainable-AI contribution maps identify wind speed as the primary driver of subseasonal MHW variability, via latent heat flux, and that the framework can partly reproduce subsurface mixed-layer effects from surface inputs.

Load-bearing premise

The load-bearing premise is that the VQVAE, trained only to reconstruct SSTA fields, actually learns the conditional distribution of future SSTA, and that decoding the nearest latent neighbors produces physically valid extreme-event samples; if that sampling assumption fails, the ~15% gain in extreme-event skill is not explained.

Editorial extensions

If this is right

Global 10-day MHW forecasts become substantially more accurate than prior data-driven baselines, with 30-40% lower RMSE and higher CSI/SEDI.
Extreme-event prediction improves materially: the probabilistic module raises the CSI for 99th-percentile MHW events by about 15%.
The framework is competitive with the numerical GOFS 3.1 forecast (20-30% lower RMSE at a 6-day lead when initialized from GOFS analysis) while taking about 0.2 seconds per global forecast on one A100 GPU.
In a 1/12-degree North Pacific test, the probabilistic module restores small-scale mesoscale MHW structures that the deterministic model smooths out.
XAI attribution indicates surface wind forcing, through latent heat flux, is the key control on short-term MHW evolution, suggesting that better atmospheric forecasts would directly improve MHW predictions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: Because the pseudo-ensembles in Eq. (11) are selected by closeness to the observed target, part of the ~15% CSI gain may reflect oracle-style label information leaking into the augmented training set; a fair test would compare against randomly selected pseudo-ensembles.
Editorial inference: The same VQVAE augmentation recipe could be transplanted to other deterministic AI forecasters (land heatwaves, extreme precipitation, drought) as a generic extreme-event booster, provided a suitable conditional latent space can be learned.
Editorial inference: The XAI result that wind dominates predictability implies that coupling this ocean model to a stronger subseasonal atmospheric model—not just retraining the ocean network—is the highest-leverage next step for longer-lead MHW forecasts.
Editorial inference: The claim that subsurface entrainment is parameterized from surface data could be checked directly by comparing forecast errors in regions with Argo-observed mixed-layer depth anomalies, rather than inferring it from the CNP-MHW case.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

I'll cut to the chase. The deterministic half of this paper is worth reading: the coupler that separates heat-flux forcing from advection/mixing is a sensible way to inject physics into an SST anomaly forecast, the global 10-day results beat the cited data-driven baselines, and the 1/12-degree North Pacific test is a nice stress case. The XAI attribution pointing to wind speed via latent heat flux is plausible and consistent with the heat budget. Credit also for posting source code.

The soft spot is the probabilistic augmentation. Equation (11) selects pseudo-ensemble members by their L2 distance to the true future field over MHW points. That is oracle selection: the augmented training targets are chosen using the labels the model is supposed to predict. So the roughly 15% CSI gain in Section 3.2 does not demonstrate skill from a learned conditional distribution; it likely reflects fitting to selected targets that already resemble ground truth. In operation you don't have the truth to pick from. The derivation of Eq. (8) is also nonstandard—the KL term in a discrete VQVAE doesn't simply vanish, and the equivalence to MSE is asserted rather than shown. These two issues together mean the headline claim about extreme-event improvement is not supportable as written.

Minor but real: the baseline comparisons (Giamalaki et al., W. Sun et al.) don't give enough protocol detail to ensure same training data and same MHW masks, and there are no uncertainty estimates on the score differences. That matters for a claim of 20-50% CSI improvements over a numerical system. The reference list covers the relevant recent work, so the novelty claim is reasonably positioned.

My overall read: the deterministic framework and the regional experiment are solid and citable on their own. The probabilistic module is a good idea but needs a redesign that avoids truth-based filtering—for example, sampling from the learned latent prior and validating on held-out extremes—plus a proper derivation of the training objective. The paper deserves a serious referee, but it needs major revision before the headline claim is trustworthy. I'd send it to review with a clear request to fix the augmentation protocol.

Referee Report

5 major / 6 minor

Summary. The manuscript proposes a two-module deep learning framework for global and regional 10-day marine heatwave (MHW) forecasting. The deterministic module decomposes the SSTA evolution operator into a 'coupler' that ingests atmospheric forcing and a second network that predicts future SSTA; the probabilistic module uses a VQVAE to learn conditional distributions and generate pseudo-ensemble targets for data augmentation. The authors report improved RMSE, CSI, and SEDI relative to existing data-driven models and competitiveness with GOFS 3.1, and use occlusion-based explainability to attribute MHW evolution to surface wind forcing. The central claim is that the probabilistic augmentation yields approximately 15% CSI improvement for the most extreme (99th percentile) MHWs.

Significance. If the claims are substantiated, the framework is of practical value: a computationally efficient global 10-day extreme MHW forecast system with a physically motivated architecture, a source-code release, and an explainability analysis linking wind forcing to latent heat flux. The deterministic coupler decomposition is a reasonable inductive bias. However, the probabilistic augmentation core has methodological flaws that undermine the headline extreme-event improvement, and the evaluation protocol for baselines and metrics needs substantial clarification.

major comments (5)

[Section 2.3, Eq. (11)] The selection of augmented samples uses ground truth T_true^i as the selection criterion (L2 distance to truth over MHW grid points). The augmented training set D_aug then contains training targets that were chosen with future information. Because the model is retrained on these targets (Eq. 13), the reported CSI improvement in Section 3.2 (approximately 15% at the 99th percentile) does not establish that the learned conditional distribution p(T'_t | T'_0, A_{0:t}) adds forecast skill; it may be a fit to oracle-selected labels. An operational forecast cannot use this selection. Please remove the oracle dependence (e.g., select pseudo-members based on diversity or physics constraints without reference to the target) or provide a strictly time-split evaluation where selection is performed only on the training period and test metrics are reported for the un-augmented versus augmented models.
[Section 2.3, Eqs. (6)-(8)] The claim that the VQVAE loss reduces to MSE because 'the K-L divergence term vanishes' for discrete z is not correct as stated. For a discrete latent distribution with finite codebook, the KL divergence between q_phi(z|X) and p(z|X) does not generally vanish, and the standard VQVAE training objective includes a codebook loss and a commitment loss with straight-through gradient estimation. The derivation also does not define p(z|X) or justify the identification of log p_theta with MSE. This is not merely a presentation issue: it is the theoretical basis for claiming that the VQVAE learns the conditional distribution p(T'_t | T'_0, A_{0:t}). Please state the actual loss function used (with exact terms) and cite the relevant VQVAE formulation, or correct the mathematical derivation.
[Section 2.3, Eq. (9)] The nearest-neighbor latent selection is written as min_{z in Z} ||z - q_phi(T'_t)||, where T'_t appears to be the target future field. If T'_t is the ground truth, then the latent perturbations themselves are conditioned on the target, further reinforcing the oracle dependence described above. If T'_t is instead meant to be the deterministic forecast output phi_theta(X_i), the notation must be corrected and the text clarified. As written, both Step 3 and Step 4 use target information in the construction of pseudo-ensembles.
[Section 2.4, Eq. (16)] The false alarm rate is defined as F = FP/(FP+TP), which is the false discovery rate, not the false alarm rate required by the SEDI formula. In the standard SEDI definition, F = FP/(FP+TN). As written, the computed SEDI scores do not correspond to the stated formula, and the reported SEDI improvements in Section 3.2 may not measure what is claimed. Please correct the definition and rerun the evaluation, or clarify if a different convention was used in the code.
[Section 3.1 and Figure 2] The comparisons with 'existing data-driven models' (Giamalaki et al., 2022; W. Sun et al., 2023) and with GOFS 3.1 lack essential protocol details. Please specify whether the baseline models were run by the authors or results were taken from the original papers, what input variables and resolutions were used, and whether the same test period and MHW detection thresholds were applied. In particular, the statement that 'we use GOFS's analysis field as the input initial condition of the model' needs clarification: was the frozen model trained on GLORYS reanalysis then applied to GOFS analysis initial conditions, and is that a deliberate domain shift? Without these details and uncertainty estimates (e.g., bootstrap confidence intervals over test years), the reported 20-50% coastal CSI improvements are difficult to verify.

minor comments (6)

[Throughout] The term 'argumentation' is used where 'augmentation' is meant (e.g., in the abstract and the Section 2.3 heading), and there are scattered typos ('evalute', 'T able', 'ECWMF', 'similiar'). Please correct these throughout.
[Section 2.4, Eq. (16) and surrounding text] The text after Eq. (15) says 'FP, FN, and TN (True Positive)', but 'True Positive' is the definition of TP, not TN; TN should be 'True Negative'. Please fix this definitional inconsistency.
[Section 2.1] The notation with overbars (e.g., T'_t) is introduced but not fully defined: 'the brackets denote the average over the mixed layer' is mentioned, but the precise vertical integration and how the bar relates to the SSTA fields used in the data description should be specified.
[Section 2.4, Eqs. (17)-(18)] The masking procedure for the contribution maps is described as replacing 'the jth element' with zero, but the input variables are full spatial fields; please clarify whether the entire channel is zeroed and how the per-grid-point contribution is aggregated.
[Figure 2 caption and text] Several panels are referenced in the text but not clearly described in the caption (e.g., the dashed and solid blue lines in Figure 2a, and the shading in Figure 2e-f). A fully self-contained caption would help the reader.
[Open Research] The ERA5 link provided points to pressure-level data, which does not match the surface variables used in the study; please provide the correct dataset link.

Circularity Check

2 steps flagged · score 6.0 of 10

Probabilistic augmentation selects pseudo-targets by oracle distance to the ground-truth future field (Eq. 11), so the reported extreme-MHW CSI gain is partly a fit to truth-selected labels rather than independent forecast skill.

fitted input called prediction [Section 2.3, Step 4, Eqs. (11)-(13)]
"Specifically, from the forecast ensembles T i 1 , T i 2 , . . . ,T i k generated in Step 3 for each input Xi, we select a subset of m high-quality samples ˆT i 1 , ˆT i 2 , . . . ,ˆT i m based on their proximity to the ground truth T true i . The selection criterion is defined using the L2 norm between the generated samples and the ground truth: ˆT i j = arg min T i j ∈{T i 1 ,...,T i k } ||T i j − Ttrue i || 2 2 , j = 1, . . . , m."

The augmented training targets are selected by minimizing L2 distance to the future true field T_true, i.e., the very quantity the model is supposed to predict. These truth-selected samples are then inserted into the augmented set (Eq. 12) and the deterministic model is retrained against them (Eq. 13). Consequently, the reported improvement in extreme-MHW CSI (Sec. 3.2, ~15% at the 99th percentile) is not a clean demonstration of learned conditional forecast skill: the training labels have been cherry-picked using oracle knowledge of the future. In an operational forecast, no such future truth is available to perform the selection, so a substantial part of the claimed gain reduces by construction to fitting targets that are close to the verification field.
self definitional [Section 2.3, Step 3, Eq. (9)-(10)]
"Then, we perturb these latent representations by finding the top-k closest for each input sample (in this study, we choose k = 10): z(1) i , z(2) i , ..., z(k) i = minz∈Z ||z − qϕ(Tt')||. Those latent vectors is then fed into the decoder pθ to generate the forecast ensembles ... {T i 1 , T i 2 , . . . ,T i k } = pθ(z(1) i , z(2) i , ..., z(k) i ) = ψ(ϕθ(Xi), z) ∼ p(Tt'|T0', A0:t)."

Step 3 claims to sample from the conditional forecast distribution p(T_t' | T_0', A_{0:t}), but the ensemble members are constructed by taking latent codes nearest to q_phi(T_t'), the VQVAE encoder's representation of the target future field. The generated 'forecast ensembles' are therefore defined in terms of the future truth itself, not drawn independently from the learned conditional distribution. Eq. (10) then relabels these target-conditioned reconstructions as samples from p(T_t' | T_0', A_{0:t}), making the probabilistic sampling step self-referential: the pseudo-ensembles are selected using the very field they are claimed to predict.

full rationale

The deterministic coupler framework and the comparisons against GOFS 3.1 are self-contained benchmark results and are not circular. The circularity is concentrated in the probabilistic data-augmentation module, which carries the paper's central claim that extreme-MHW forecasts are substantially improved. Two target-conditioned steps break the independence of the derivation. First, Eq. (9) forms pseudo-ensembles by nearest-neighbor matching to the latent encoding of the true future SSTA field q_phi(T_t'), so the supposedly sampled conditional distribution is not independent of the verification target. Second, and more decisively, Eq. (11) selects the pseudo-training targets by L2 proximity to the ground-truth field over MHW grid points; these oracle-selected targets are then used in Eq. (12)-(13) to retrain the deterministic model. The 15% CSI gain reported in Sec. 3.2 is therefore a reduction by construction: the augmented training labels are fitted to the future truth, so evaluating on future truth measures fit to truth-selected pseudo-targets rather than generalizable ensemble forecast skill. The derivation of the VQVAE loss in Eqs. (7)-(8) is also nonstandard (the KL term does not simply vanish), but that is a methodological correctness concern rather than a circularity. After removing the oracle selection in Eq. (11) and the target-aware latent selection in Eq. (9), the claimed extreme-event improvement would need to be re-established; the deterministic results retain independent value. Overall circularity is partial rather than total: score 6.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a physics-inspired architectural split, a surface-data sufficiency assumption, and an unproven VQVAE sampling scheme; no new physical entities are introduced. The main free choices are the latent neighborhood size, the number of selected pseudo-ensembles, the input variable set, and the 10-day forecast horizon.

free parameters (5)

Latent neighborhood size k = 10
Eq (9) fixes k = 10 nearest latent codes per sample; no sensitivity analysis is shown, and the number of ensemble members directly affects the augmented dataset and skill scores.
Number of selected augmented samples per input, m = not specified
Eqs (11)-(13) use an unspecified m; the size of the augmentation set and its weighting in the loss are not stated, so the reported gains cannot be reproduced from the text.
VQVAE codebook size / latent dimension = not reported
Controls the granularity of the learned conditional distribution and is needed to reproduce the augmentation; not stated in the text.
Input variable set = U10, V10, T2m, Qlat, Qsens, QSW, QLW, SSTA
The authors chose 8 surface variables 'to ensure that our model is operational and lightweight' (Section 4), excluding horizontal velocity and subsurface state; the central claim depends on this choice.
Forecast lead time T = 10 days
The framework predicts a fixed 10-day window (T=10 in Section 2.2); skill at shorter lead times is reported, but the model is trained specifically for this horizon.

assumptions (7)

ad hoc to paper The SSTA evolution operator can be decomposed into a coupler for atmospheric heat fluxes and a second network for advection/mixing, both approximated by neural networks (Eq. 5).
This is the core physics-guided architectural assumption; it assumes the split in Eq. (5) is identifiable from surface data alone.
domain assumption Surface-only inputs suffice to parameterize advection, mixing, and subsurface entrainment in phi(2).
Used to explain CNP-MHW forecast skill (Section 3.1) and stated as a limitation in Section 4; if false, subsurface-driven MHWs cannot be forecast.
ad hoc to paper The VQVAE reconstruction loss equals the ELBO because the KL divergence vanishes for discrete latent distributions (Eq. 8).
This is asserted in Section 2.3 but is not a standard property of VQVAEs; the paper does not include codebook or commitment losses.
ad hoc to paper Top-k nearest neighbor latent perturbations produce forecast ensembles distributed as p(T'_t | T'_0, A_{0:t}) (Eqs. 9-10).
No proof or empirical validation that this sampling scheme matches the conditional distribution; the selection in Eq. (11) uses ground truth.
domain assumption ERA5 and GLORYS reanalysis fields are accurate enough to serve as ground truth and initial conditions.
Standard observational assumption; the paper does not quantify reanalysis errors.
domain assumption Hobday et al. (2016) MHW category definitions are appropriate for evaluating extreme events.
Categorical thresholds (90th, 92.5th, 95th percentiles) come from prior literature; the evaluation metrics depend on them.
domain assumption Training on 1993-2017 generalizes to the 2018-2021 test period.
Standard supervised learning assumption; no distribution-shift analysis beyond Figure 3c.

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Cite this review

Pith. "Pith review of Improved Forecasts of Global Extreme Marine Heatwaves Through a Physics-guided Data-driven Approach." pith.science (2026). https://pith.science/paper/ZXLJMAET

@misc{pith2026241215532,
  author       = {Pith},
  title        = {Pith review of: Improved Forecasts of Global Extreme Marine Heatwaves Through a Physics-guided Data-driven Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZXLJMAET}},
  note         = {Machine review of arXiv:2412.15532}
}

read the original abstract

The unusually warm sea surface temperature events known as marine heatwaves (MHWs) have a profound impact on marine ecosystems. Accurate prediction of extreme MHWs has significant scientific and financial worth. However, existing methods still have certain limitations, especially in the most extreme MHWs. In this study, to address these issues, based on the physical nature of MHWs, we created a novel deep learning neural network that is capable of accurate 10-day MHW forecasting. Our framework significantly improves the forecast ability of extreme MHWs through two specially designed modules inspired by numerical models: a coupler and a probabilistic data argumentation. The coupler simulates the driving effect of atmosphere on MHWs while the probabilistic data argumentation approaches significantly boost the forecast ability of extreme MHWs based on the idea of ensemble forecast. Compared with traditional numerical prediction, our framework has significantly higher accuracy and requires fewer computational resources. What's more, explainable AI methods show that wind forcing is the primary driver of MHW evolution and reveal its relation with air-sea heat exchange. Overall, our model provides a framework for understanding MHWs' driving processes and operational forecasts in the future.

Figures

Figures reproduced from arXiv: 2412.15532 by the authors.

**Figure 1.** The overall framework of our global MHWs forecast framework. a) The deterministic forecast. b) The probabilistic part designed to improve extreme MHWs’ prediction. –16– [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗

**Figure 2.** The overall performance of our global MHWs forecast model. a)-c) The RMSE, CSI, SEDI of our framework comparing to existing subseasonal MHWs forecast at a 10-day lead. d) The CSI score around global coastal regions. e) The 10-day roll-out forecast of our framework initialized on 2021-08-22. f) The forecast result (SSTA) of our framework initialized on 2021-10- 03. It is important to highlight that we deduct 90th per… view at source ↗

**Figure 3.** A comparison of our deterministic and probabilistic forecasts. a)-b) The RMSE and CSI of our deterministic and probabilistic forecasts. c) The probability density function (PDF) of our deterministic and probabilistic forecast results. d)-e) A 10-day forecast of 2020 CNP-MHW initialized on 2020-08-14 [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The performance of our model in the high-resolution regional forecast (North Pacific). a) The 10-day forecast result of MHWs on 2020-07-17. The purple to orange parts of the image represent MHW events and the shade of color represents its intensity. b)-c) A comparison…

**Figure 5.** Figure 5: The explainability of our model. a) The contribution map of each input variables on the SSTA during intensifying/decaying phase of MHWs. From top to the bottom: unsigned map during intensifying phase and decaying phase, signed map during intensifying and decaying phase…

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Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

A., Smith, G

Benthuysen, J. A., Smith, G. A., Spillman, C. M., & Steinberg, C. R. (2021). Sub- seasonal prediction of the 2020 great barrier reef and coral sea marine heat- wave. Environmental Research Letters, 16 (12), 124050. Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., & Tian, Q. (2022). Pangu-weather: A 3d high-resolution model for fast and accurate global weathe...

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a)-c) The RMSE, CSI, SEDI of our framework comparing to existing subseasonal MHWs forecast at a 10-day lead

The overall performance of our global MHWs forecast model. a)-c) The RMSE, CSI, SEDI of our framework comparing to existing subseasonal MHWs forecast at a 10-day lead. d) The CSI score around global coastal regions. e) The 10-day roll-out forecast of our framework initialized on 2021-08-22. f )The forecast result (SSTA) of our framework initialized on 2021-10-

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a)-b) The RMSE and CSI of our deterministic and probabilistic forecasts

A comparison of our deterministic and probabilistic forecasts. a)-b) The RMSE and CSI of our deterministic and probabilistic forecasts. c) The probability density function (PDF) of our deterministic and probabilistic forecast results. d)-e) A 10-day forecast of 2020 CNP-MHW initialized on 2020-08-14. Figure

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a) The 10-day forecast result of MHWs on 2020-07-17

The performance of our model in the high-resolution regional forecast (North Pa- cific). a) The 10-day forecast result of MHWs on 2020-07-17. The purple to orange parts of the image represent MHW events and the shade of color represents its intensity. b)-c) A comparison of our deterministic and probabilistic forecasts, similiar to Figure 3a-b. d) The powe...

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