DIRECT 1.0: A diffusion-based generative model for dense sea surface temperature reconstructions from sparse satellite observations

Rovšček, Grega; Ličer, Matjaž; Barth, Alexander; Kristan, Matej

doi:10.5194/egusphere-2026-1339

Preprints

https://doi.org/10.5194/egusphere-2026-1339

Preprints

03 Jun 2026

| 03 Jun 2026

DIRECT 1.0: A diffusion-based generative model for dense sea surface temperature reconstructions from sparse satellite observations

Grega Rovšček, Matjaž Ličer, Alexander Barth, and Matej Kristan

Abstract. Satellite sea surface temperature (SST) observations are frequently obscured by cloud cover, creating large gaps that must be reconstructed for many oceanographic and climate applications. Because multiple high-resolution SST fields may be consistent with the same sparse observations, this reconstruction problem is inherently ambiguous. Nevertheless, most existing approaches remain deterministic, producing a single estimate that is often overly smooth, may contain unrealistic artifacts, and provides limited or unreliable uncertainty estimates. To address these limitations, we introduce DIRECT, a conditional generative framework for dense SST reconstruction that models the full distribution of plausible solutions rather than a single deterministic estimate. DIRECT is based on a rectified flow-matching formulation, conditioned on temporal context and day-of-year seasonality, and presents an observation-guided rectification that anchors the generative trajectory to measured pixels at every integration step. By sampling multiple reconstructions, DIRECT produces an ensemble of physically plausible SST fields, enabling both an accurate mean reconstruction and spatially resolved uncertainty estimates that are calibrated using a lightweight post-hoc variance correction. Experiments on three Level-3 SST datasets (Mediterranean, Adriatic, and Atlantic) show that DIRECT sets a new state-of-the-art, reducing Root Mean Square Error (RMSE, in °C) by 6–14 % compared with the strongest published method, while better preserving mesoscale structure. Further analysis of spatial scale correlations indicates that DIRECT maintains physically consistent textures even when reconstructing large, completely unobserved regions. Performance improvements remain robust across a wide range of cloud-coverage conditions, enabling reliable SST reconstruction from sparse satellite observations over much of the global ocean.

Received: 11 Mar 2026 – Discussion started: 03 Jun 2026

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Grega Rovšček, Matjaž Ličer, Alexander Barth, and Matej Kristan

Status: final response (author comments only)

CC1:
'Comment on egusphere-2026-1339', Scott Martin, 02 Jul 2026
General Comments:
This study presents a novel conditional flow-matching method for SST gap-filling. The authors provide a clear exposition of the method, extensive evaluations, ablation studies for various design choices, and the comparison against prior state-of-the-art ML approaches suggests this method has strong potential for operational applications. This study is of high quality and novelty and the extensive evaluations and ablations make this a particularly strong contribution. With some minor revisions (see below) it is suitable for publication in GMD.
Congratulations on a great paper and I look forward to seeing it published in GMD.
Best wishes,
Scott A. Martin

Specific Comments:
The proposed method re-injects the raw observations back in pixels where they are available. While this ensures small error against available observations it is not necessarily desirable. Observations contain sensor noise and errors themselves, which under this approach will propagate into the reconstructed SST fields. Secondly, this approach will induce strong artifacts in each ensemble member reconstruction at the border between observed and unobserved regions, complicating downstream scientific analysis and interpretation. I think this limitation is just inherent to the approach chosen in this study, so I'm not suggesting the authors modify the method, but the manuscript would benefit from a discussion of this limitation and the motivation for this design choice somewhere in the text.

The SST reconstruction methods benchmarked against here (as in the CRITER paper) are all experimental ML methods. While this helps to establish DIRECT as state of the art among ML approaches, the reader is left unclear on whether any of these methods outperform non-ML approaches like objective analysis used in real operational L4 products. The manuscript would be significantly strengthened by including one or more of the operational L4 products (e.g. from CMEMS or PO.DAAC) in the evaluation to the extent possible.

DIRECT leverages only the sparse, high-resolution L3 SST observations but microwave sensors provide additional observations that penetrate clouds but with coarser spatial resolution. It would be interesting to consider how the DIRECT approach could be modified in future to incorporate these valuable mesoscale-resolving constraints beneath clouds. Not suggesting the authors modify the method for this study, but it would be an interesting future research direction and could be discussed in the Discussion section.

Figs 10 & 11 present isotropic PSD of SST. My understanding is these were computed by taking 2D spectrum of total SST field and then azimuthally averaging? There appears to be a large-scale anisotropic SST background in the ROI which will distort the inferred isotropic PSD. I think this may be part of why all the curves lie so closely on top of each other at all but the highest wavenumbers. A more appropriate metric would be to compute these spectra on the SST anomaly from a coarse background (e.g. linear plane fit to the ROI?).

Figs 12 & 13: the pixel scales are hard to interpret physically. Either replace with km or add an additional approximate km reference scale to help orient the reader.

The CRPS values in Table 3 are not particularly informative without any form of reference to compare against. I'm not familiar with CRITER, but you present estimated uncertainty from that method so why can't we also get a CRPS for it? I'd honestly suggest just removing CRPS from the paper if there is nothing to benchmark against, another option would be to include MAE of the deterministic methods as reference values in the table since CRPS reduces to MAE for single member predictions?

Multi-panel figures like Fig 6 throughout the paper would benefit from clearer sub-panel labels (e.g. panel a, b, etc.) and panel 6 is particularly hard to follow at first glance.

Line ~109: typo "networ".

The fact the method can be trained exclusively on sparse real observations is to my mind a major strength compared to existing literature and could be better emphasized with a prominent mention somewhere in the abstract.
Citation: https://doi.org/10.5194/egusphere-2026-1339-CC1
- RC2:
  'Reply on CC1', Scott Martin, 02 Jul 2026
  
  I got my EGU accounts mixed up and submitted reviewer comment as "community comment". You can disregard this one and respond to the RC which is identical.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1339-RC2
  - AC3: 'Reply on RC2', Grega Rovšček, 28 Aug 2026
    
    Thank you for the clarification. Our response to the identical referee comment is available at https://doi.org/10.5194/egusphere-2026-1339-AC1.
    
    Citation: https://doi.org/10.5194/egusphere-2026-1339-AC3
RC1:
'Comment on egusphere-2026-1339', Scott Martin, 02 Jul 2026
General Comments:
This study presents a novel conditional flow-matching method for SST gap-filling. The authors provide a clear exposition of the method, extensive evaluations, ablation studies for various design choices, and the comparison against prior state-of-the-art ML approaches suggests this method has strong potential for operational applications. This study is of high quality and novelty and the extensive evaluations and ablations make this a particularly strong contribution. With some minor revisions (see below) it is suitable for publication in GMD.
Congratulations on a great paper and I look forward to seeing it published in GMD.
Best wishes,
Scott A. Martin

Specific Comments:
The proposed method re-injects the raw observations back in pixels where they are available. While this ensures small error against available observations it is not necessarily desirable. Observations contain sensor noise and errors themselves, which under this approach will propagate into the reconstructed SST fields. Secondly, this approach will induce strong artifacts in each ensemble member reconstruction at the border between observed and unobserved regions, complicating downstream scientific analysis and interpretation. I think this limitation is just inherent to the approach chosen in this study, so I'm not suggesting the authors modify the method, but the manuscript would benefit from a discussion of this limitation and the motivation for this design choice somewhere in the text.

The SST reconstruction methods benchmarked against here (as in the CRITER paper) are all experimental ML methods. While this helps to establish DIRECT as state of the art among ML approaches, the reader is left unclear on whether any of these methods outperform non-ML approaches like objective analysis used in real operational L4 products. The manuscript would be significantly strengthened by including one or more of the operational L4 products (e.g. from CMEMS or PO.DAAC) in the evaluation to the extent possible.

DIRECT leverages only the sparse, high-resolution L3 SST observations but microwave sensors provide additional observations that penetrate clouds but with coarser spatial resolution. It would be interesting to consider how the DIRECT approach could be modified in future to incorporate these valuable mesoscale-resolving constraints beneath clouds. Not suggesting the authors modify the method for this study, but it would be an interesting future research direction and could be discussed in the Discussion section.

Figs 10 & 11 present isotropic PSD of SST. My understanding is these were computed by taking 2D spectrum of total SST field and then azimuthally averaging? There appears to be a large-scale anisotropic SST background in the ROI which will distort the inferred isotropic PSD. I think this may be part of why all the curves lie so closely on top of each other at all but the highest wavenumbers. A more appropriate metric would be to compute these spectra on the SST anomaly from a coarse background (e.g. linear plane fit to the ROI?).

Figs 12 & 13: the pixel scales are hard to interpret physically. Either replace with km or add an additional approximate km reference scale to help orient the reader.

The CRPS values in Table 3 are not particularly informative without any form of reference to compare against. I'm not familiar with CRITER, but you present estimated uncertainty from that method so why can't we also get a CRPS for it? I'd honestly suggest just removing CRPS from the paper if there is nothing to benchmark against, another option would be to include MAE of the deterministic methods as reference values in the table since CRPS reduces to MAE for single member predictions?

Multi-panel figures like Fig 6 throughout the paper would benefit from clearer sub-panel labels (e.g. panel a, b, etc.) and panel 6 is particularly hard to follow at first glance.

Line ~109: typo "networ".

The fact the method can be trained exclusively on sparse real observations is to my mind a major strength compared to existing literature and could be better emphasized with a prominent mention somewhere in the abstract.
Citation: https://doi.org/10.5194/egusphere-2026-1339-RC1
- AC1: 'Reply on RC1', Grega Rovšček, 28 Aug 2026
  
  Thank you for the constructive comments. Please find our responses in the attached PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1339-AC1
RC3:
'Comment on egusphere-2026-1339', Anonymous Referee #2, 16 Aug 2026

This manuscript addresses an important problem and proposes a reliable method for reconstructing SST fields with uncertainty estimates. The experiments are extensive and generally convincing. I recommend a minor revision, with the following comments.
1. The Introduction should include recent work on spatiotemporal diffusion models for climate and SST reconstruction, for example, Qian et al. (2026, arXiv:2602.16515) and Li et al. (2026, arXiv:2603.16272). A brief comparison would help clarify DIRECT's contribution relative to these studies.
2. Figure 2 and the corresponding description in Section 2 are somewhat confusing and difficult to follow. In particular, (x{t-1}) and (x{t+1}) are pixelwise composites from several dates, while (M_{t-1}), (M_t), and (M_{t+1}) have different meanings. A clearer schematic, example, or brief pseudocode would be helpful. The fixed three-day search range and nearest-valid-observation rule are also rather empirical, so their motivation and possible limitations should be discussed more explicitly.
3. Cloud masks from other dates are used to construct training samples. This is practical, but cloud occurrence may be coupled with atmospheric conditions and SST variability. Therefore, the missingness mechanism is not necessarily independent of the target SST field. The authors should discuss this assumption and clarify that the evaluation is based on synthetically withheld observed pixels rather than direct validation beneath real clouds.
4. The variance correction provides a lightweight global calibration, but it does not necessarily demonstrate good pixelwise or conditional calibration. I suggest reporting the empirical coverage of nominal, for example, 50%, 80%, 90%, and 95% prediction intervals on the test set. Coverage before and after the correction would be particularly informative.
5. The satellite SST product is treated as ground truth, although it has its own retrieval uncertainty. I understand that explicitly incorporating observation errors would require substantial methodological changes, but this issue should at least be discussed because the reported residuals may include both reconstruction and observation errors.
I strongly recommend adding a short Discussion section covering the empirical temporal-context construction, the use of transferred cloud masks, the global nature of the variance correction, and the neglect of observation uncertainty.

Citation: https://doi.org/10.5194/egusphere-2026-1339-RC3
- AC2: 'Reply on RC3', Grega Rovšček, 28 Aug 2026
  
  Thank you for the constructive comments. Please find our responses in the attached PDF.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1339-AC2

Grega Rovšček, Matjaž Ličer, Alexander Barth, and Matej Kristan

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Short summary

Satellite measurements of sea surface temperature are often blocked by clouds, leaving large gaps in the data used to study the ocean and climate. We developed a new computer model that fills in these missing areas while also estimating how uncertain the reconstruction is. Tests on several ocean regions show more accurate results and more realistic patterns, helping scientists better analyze and model ocean conditions.


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