A global gridded dataset of significant wave height via fusion of multi-mission altimetry and numerical hindcast

Jiang, Haoyu; Su, Hao

doi:10.5194/essd-2025-694

Preprints

https://doi.org/10.5194/essd-2025-694

Preprints

03 Dec 2025

| 03 Dec 2025

Status: this preprint is currently under review for the journal ESSD.

A global gridded dataset of significant wave height via fusion of multi-mission altimetry and numerical hindcast

Haoyu Jiang and Hao Su

Abstract. Satellite altimeters provide long-term, high-accuracy observations of significant wave height (SWH) over the global ocean. However, their sparse spatial and temporal sampling introduces undersampling errors in wave climate analyses. Direct gridding of multi-mission altimeter data through spatiotemporal interpolation still results in low-accuracy global SWH fields due to this limitation. To overcome this challenge, we use SWH outputs from a WAVEWATCH III hindcast as a background field and apply an offline post-fusion with along-track, jointly calibrated altimeter observations from the Climate Change Initiative Sea State dataset. Unlike data assimilation within numerical wave models, this offline fusion approach allows retrospective correction of past model outputs using future observations. Validation against buoy measurements and independent satellite data demonstrates that the fused gridded product achieves high accuracy. To address different application needs, we provide two versions of the fused dataset: 1) A "two-sat" version that incorporates data from only two satellites at any given time, designed for wave climate studies. This configuration ensures temporal consistency by maintaining a stable data volume over the entire time span. 2) A "multi-sat" version that integrates data from as many altimeter missions as possible, intended to support applications such as the training of artificial intelligence-based wave models, where higher spatial and temporal accuracy is prioritized. The dataset is freely available at https://doi.org/10.57760/sciencedb.29314 (Su and Jiang, 2025).

Received: 17 Nov 2025 – Discussion started: 03 Dec 2025

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Haoyu Jiang and Hao Su

Status: final response (author comments only)

RC1:
'Comment on essd-2025-694', Anonymous Referee #1, 29 Jun 2026

Review of "A global gridded dataset of significant wave height via fusion of multi-mission altimetry and numerical hindcast"
a paper by Jiang and Su

Synopsis
The authors evaluate the "data fusion" method for blending SWH fields from wave model(s) and altimetry. The method and dataset (or a subset of the dataset, at least) has been previously published. I interpret the methods as a kind of enhanced optimal interpolation. The authors find high accuracy with their product. They offer two forms of their product. One prioritizes temporal stability, which is useful for climate studies. The other prioritizes general accuracy (lower RMSE). The authors encourage others to download and use their dataset.

Recommendation: I think this should be published, after some modest revision.

General remark

What is the original reference for the data fusion method? I'm not familiar with the history of the method, but lines 430-432 indicate that there was a previous publication, Wang and Jiang 2024, in which a subset of this same data-fusion dataset was used. I would expect this to come up in Section 2.2, but I didn't find it there.

Comments

Line 14: is there a distinction between "fusion" and "post-fusion"?

Line 86-92: It is not clear from this text if all three limitations are addressed.

101: I'm not familiar with the CCI dataset. What is "1-Hz" here? Does this refer to one cycle per day? Is this a normal definition for "Hz"? (usually 1/sec?)

101 again: I guess this is a daily product on a fixed, regular, lat-lon grid?

183: Has the "parameter set" been introduced?

191-210: This block of text deserves a heading of some kind.

Fig. 2 caption: to assist readers who are skimming, add 3-4 more words to the caption to explain what CMEMS is.

350: for clarity, "data fusion" ==> "data fusion is applied to both datasets"

448: This section "Data description and availability" looks weird to me. There are two sections about data availability. Is it a normal practice for this journal to have a very small section prior to the Summary, about data availability? Why not put this content in the section after the Summary, "Code and data availability"?

468-473: The basis for these findings should be given.

The summary section is not too long, but is a jumble. Here's my attempted categorization of the content:
458-460 : background
460-462 : methods
462-463 : findings
463-467 : methods
468-473 : findings
474 : method
475-479 : background
479-484 : discussion
485-490 : future work
This structure means that the reader has to sort it out. If a reader just wants a bald statement of the outcome of the research, it should be easier to find.
I don't want to micromanage this, but I suggest to at least have a section or sub-section with a clear list of findings. Here, "finding" = something that is a direct outcome of the analysis and experiments described in the paper. It does not include conclusions that could have been made without the work in the paper.

Minor comments:

Fig. 2 and 3 and possibly other figures. The statistics are given to too many decimal places

Typos: Line 67, Line 68

Citation: https://doi.org/10.5194/essd-2025-694-RC1
- AC1: 'Reply on RC1', Haoyu Jiang, 09 Jul 2026
  
  Thank you for your careful review and constructive comments. We have addressed all comments in the attached point-by-point response PDF and revised the manuscript accordingly.
  
  Citation: https://doi.org/10.5194/essd-2025-694-AC1
RC2:
'Comment on essd-2025-694', Anonymous Referee #2, 18 Jul 2026

Owing to lack of data used as a benchmark in global wave modeling authors of the current paper look at the proper approach of correction satellite altimetry products and their conclusion is quite clear. Their research focuses on the important question of how to create trustful dataset of significant wave height (Hs) by fusing multi-mission satellite altimeter observations with numerical wave models and understand its effects on precision. From technical point of view the proposed fusion method employs a space-time optimal interpolation that incorporates spatial, temporal, and Hs differences, as well as a correlation-based threshold, to optimally blend model and observational data. Furthermore, the size of the period taken into consideration is relatively small (2010-2016) to draw a reliable conclusion. The standard operational baseline period designated by the World Meteorological Organization (WMO) is 1991–2020. Besides this fact modeled wave climate is not fully Hs climate (due to wave systems partition method, e.g PTM), however multi-mission satellite wave climate is purely Hs climate (nrt, inter-calibrated, calibrated by buoys), as aptly pointed out by the authors in the main body of the text when they describe discrepancies in observations. It is not entirely clear whether we are improving the model or the observations.
I have carefully read the paper and I believe that it is an interesting study worth publishing after minor revision.

Minor comments

Lines 43-45: "...satellite based wave sensors and wave model of SAR or scatterometer..." sentencem probably need to be rephrased. Current understanding in this particular sentence is that "wave model" can be defined in multiple meaning, e.g. Generattion/type/empirical method to retrieve. Can authors write more precisely what did they mean using term of wave model sensor.

Lines 64-65 "...higher accuracy of satellite altimeter observations." Another question for auhtors: what is the measurement error according to the type and the manner by which the data is collected or stored?

Lines 67:70: Besides the fact that ERA5 wave model assimilation of along track data with optimum interpoaltion method (of 5 satellite missions out of 10 that are in operational use nowdays) there is WAVERYS (MERCATOR) https://data.marine.copernicus.eu/product/GLOBAL_MULTIYEAR_WAV_001_032/description

that also assimilates satellite altimetry products (such as family of missions named after Sentinel and SAR). Do you agree with the statetment that for the purpose of validation numerical models versus observations: already assimilated satellite measurements could not be used for postrpocessing output as it consists of data fusion (model+observations)?

Fig 4, 6 should be rearanged and colormaps should be enhanced especially to repeat the same colormap for RMSE, CC. Bias on Figs. 4-7 is not meaningful, better enhance the limits.

Citation: https://doi.org/10.5194/essd-2025-694-RC2
- AC2: 'Reply on RC2', Haoyu Jiang, 19 Jul 2026
  
  Thank you for the comments. Please refer to the attached PDF for details.
  
  Citation: https://doi.org/10.5194/essd-2025-694-AC2
RC3:
'Comment on essd-2025-694', Anonymous Referee #3, 20 Jul 2026
Review of the manuscript "A global gridded dataset of significant wave height via fusion of multi-mission altimetry and numerical hindcast " by Haoyu Jiang and Hao Su, submitted to the Earth System Science Data.
The manuscript presents a new global gridded SWH dataset produces by retrospective “fusion” of the WAVEWATCH III hindcast with satellite altimetry data. There a two version of the dataset – WW III fused with two altimeters (for consistency in time on the decadal scales) and WW III fused with multiple altimeters for higher precision at a given time and space.
The dataset aims to reproduce better accuracy for extremes in wave statistics and to be a more reliable source of wave data for climate studies.
The topic is an important and valuable for climate studies, however the manuscript characterized by missing of essential methodological and quantitative assessments of the dataset. I suggest that the manuscript can be published in the ESSD after the Major revision. I provide the list of my Major and Minor comments below.
MAJOR COMMENTS
Major comment 1
Authors declare that the method of fusion is an optimal interpolation, although the scheme is rather closer to a spatio-temporal interpolation model than to classical optimal interpolation.
The methodology lacks important statistics, including background and observation-error covariances, the error correlation function and the variance of observational errors. An extensive analysis of uncertainties should be provided. I also suggest naming the method in a more neutral way, e.g. “weighted time-space fusion for SWH”.
Major comment 2
I suggest to provide more technical details for the look-up table that was used for the correction of both WW III hindcast and altimeter data. How was the look-up table built, e.g., was it built globally or regionally, and what time period was used? The Jason-2 independent data for comparison excluded from the lookup table?
From lines 166–175 it is not clear how the look-up table is related to the exclusion of observations according to the specified thresholds. Is the observation filtering performed using the look-up table, or is it a separate processing stage? This procedure should be described more clearly and illustrated with a plot or a schematic diagram.
Major comment 3
The statement that Jason-2 observations were withheld from the 2020 CCI Sea State dataset appears inconsistent with the mission selection reported elsewhere in the manuscript: Table 1 indicates that Jason-3, rather than Jason-2, was used during this period. In addition, the text below Eqs. (5)–(7) refers to a fused dataset “without Jason-1” validated against Jason-1, which is inconsistent with the preceding description and appears to be another mission-name error. These inconsistencies should be carefully checked and corrected.
The tuning needs a quantitative description, including tested ranges and increments, whether parameters were varied individually or jointly, and the objective criterion used to combine bias, RMSE, and CC. The statement that all parameters were varied from −50% to +100% cannot be interpreted literally for the CC threshold of 0.7, since a 100% increase would produce 1.4, outside the range of a correlation coefficient.
Major comment 4
The independence of the Jason-2 data for validation is questionable, as the CCI Sea State data are intercalibrated across missions. While the leave-one-out validation is a common and appropriate approach, Jason-2 is not fully statistically independent. This needs to be explicitly clarified.
Also, was Jason-2 excluded from all processing stages? Look-up table correction, parameter tuning?
Major comment 5
The justification for the two-satellite version of the dataset is the temporal homogeneity of the data for climate studies, which I fully support. However, the constant number of altimeters does not guarantee the homogeneity of the time series. It should be demonstrated that the replacements of TOPEX/Poseidon/Jason and ERS/Envisat/CryoSat do not introduce artificial trends or inconsistencies in the fused dataset. A dedicated analysis of possible discontinuities at satellite mission transitions is still required. A simple analysis may be added in a separate figure:
- the time series of global and regional mean SWH and differences A−M
- trends in the two-satellite dataset
-a global map of SWH trends.
The analysis should be provided both globally and regionally, with a focus on the polar regions.
Although the authors state that the initial CCI Sea State v4 data have undergone extensive inter-mission calibration for consistency, this does not directly imply the temporal homogeneity of the resulting two-satellite fused product. I would suggest providing basic time series and global and regional plots for the two-satellite dataset for the whole period, 1992–2020, in order to identify possible discontinuities at satellite mission transitions.
Major comment 6
I don’t quite get why all comparisons are performed for a single year, 2011? Authors state that 2011 was chosen to reduce the volume of the data processing. At the same time, producing the dataset for 1992 – 2020 period already took the data processing time and effort. Therefore, the argument of reducing the data-processing volume is not convincing enough to justify validation based on only one year.
The authors make conclusions about the accuracy, performance, and advantages of the resulting dataset, while almost all scatter plots, maps, and statistical comparisons are presented only for 2011. It is not clear whether this particular year is representative of the complete period. The wave climate may vary significantly between different years. For a dataset covering almost three decades and intended for climate applications, validation based on a single year seems insufficient.
Major comment 7
The manuscript does not provide a single table with the main characteristics of the dataset. The following information should be clearly presented:
- the exact period of each product version;
- the spatial resolution;
- the temporal step;
- the rules used for filling missing values;
- the version of WW3-ST6 used;
- the total dataset volume;
- the available variables.
The manuscript states at the same time that the product keeps the original NWM resolution of 0.25° and that its native resolution is 0.5°. The CCI Sea State v4 dataset is described as starting in August 1991, while the two-sat product in the table starts in October 1992. The terms “multi-sat” and “all-sat” are also used in different sections. These inconsistencies should be corrected.
Major comment 8
A more detailed description of the observation filtering near sea ice is required. These are exactly the regions where the largest errors remain in Figure 4.
Minor comments
Section 2.1 proceeds from Sect. 2.1.2 directly to Sect. 2.1.4.

Consistent name for the multi-satellite product throughout the manuscript. Both “multi-sat” and “all-sat” are currently used.

“the parameter set yielding relatively smallest errors” is grammatically and methodologically unclear. Please specify the exact optimization criterion.

Equations 5-7: please define explicitly which dataset is represented by x and which by y.

Please describe the temporal collocation between the 20-minute NDBC buoy observations and the gridded data.

A compact table summarizing the final datasets, including temporal coverage, spatial resolution, temporal resolution, variables and approximate data volume is needed.

The number of observations used in each validation experiment should be reported.

The improvement of approximately 0.005 m is very small. Please state whether this difference is statistically significant.

Lack of jointly calibration -> Lack of joint calibration

It provide hourly data many wave parameters -> It provides hourly data for many wave parameters

grided -> gridded, meterological -> meteorological, Ribl & Young -> Ribal and Young

The statement that the bias is “statistically negligible at the climate scale” should be supported quantitatively or rephrased as “small relative to the mean SWH"

The Code and Data Availability section should distinguish clearly between input datasets and the final fused products.

Figure 4 caption – which time period?

Why Figure 7 demonstrates results for 2020?
Citation: https://doi.org/10.5194/essd-2025-694-RC3
- AC4: 'Reply on RC3', Haoyu Jiang, 27 Jul 2026
  
  Thank you for the helpful comments. Please find our detailed response in the attached PDF.
  
  Citation: https://doi.org/10.5194/essd-2025-694-AC4
EC1:
'Comment on essd-2025-694', Davide Bonaldo, 24 Jul 2026

Dear authors, I report below some comments from an anonymous colleague who declined to serve as a reviewer but nonetheless provided some useful elements for discussion.
Best wishes
Davide Bonaldo

While the authors present a high-resolution gridded product, the scientific justification is weak. By bypassing spectral information, the product lacks the physical consistency. Furthermore, given that established reanalyses (ERA5) already assimilate this data at the spectral level, and existing climate-standard products (ESA CCI, Ribal/Young) already address temporal consistency, this manuscript offers a redundant statistical patch rather than a significant scientific advancement. The risk of promoting circularity by using this product to train future AI models outweighs the convenience of having a pre-fused grid.

1. Lack novelty (ERA5 redundancy)

The primary scientific justification for a new data product is that it fills a gap or offers a significant improvement over existing, established datasets.

->ERA5 (and the upcoming ERA6) already assimilates satellite altimetry (using 4D-Var or similar frameworks) to produce a globally gridded SWH product.

->If the authors' "fusion" is simply a statistical post-processing of a hindcast, it is effectively a Reanalysis-lite. The manuscript must demonstrate that their product significantly outperforms ERA5-Wave in a way that isn't just fitting the observations closer (which is trivial with ML). If the improvement is marginal, the community is better served by the physically consistent ERA5 than by a fragmented, offline statistical product.

2. Physical inconsistency

The authors explicitly state that their method bypasses the need for wave spectral information. To expert users, this might be a major issue.

->SWH is an integrated parameter of the 2D wave spectrum

->By correcting only the SWH using a black box statistical method, the authors create a physical mismatch between SWH and all other spectral parameters (Mean Period, Peak Direction, etc.). A dataset where the SWH is "corrected" but the underlying spectrum remains tied to the original erroneous hindcast could be dangerous… users might perform secondary analyses (like wave power or stress calculations) that are physically impossible. There is not much discussion about this or analysis to show that they thought it through.

3. Circularity

One of the stated goals is to provide a multi-sat version for training future AI wave models.

->ML should be trained on the best possible representation of reality (observations) or high-fidelity physics

->If we use an AI-corrected product to train other AI models, we are creating an endless loop. We risk training future models on the artifacts and biases of the authors' specific statistical correction rather than on true ocean physics. This data incest can lead to overconfident models that fail when faced with non-linear extreme events that were not in the training fusion logic (they are smoothed out or highly distorted).

4. Time-space issues

The authors mention that their offline approach allows retrospective correction of past model outputs using future observations.

->While mathematically sound for gap-filling, this is physically problematic for wave climate analysis.

->Waves propagate… using future satellite passes to correct a past state in a non-causal way can smear out the temporal evolution of swell events. For wave climate trends (their two-sat version), this smoothing might hide the very variability or subtleties the researchers are looking for…

5. Climate trend justification

The authors claim their "two-sat" version is for climate studies to ensure temporal consistency.

->The ESA CCI Sea State dataset already exists for this exact purpose, using a very rigorous, inter-calibrated multi-mission approach.

->The manuscript should address: Why is this better than the ESA CCI product? If the answer is just "it's on a grid," that is a processing step, not a significant contribution… Gridding can be done by anyone with a basic interpolation script; it doesn't necessitate a new global dataset publication.

6. More broadly...

->Scientific progress comes from fixing the source terms (Sin, Sds) in models like WAVEWATCH3.
->This work treats the model as a "black box" that is "wrong" and needs a statistical patch. In a data journal, the goal should be to provide data that reveals new truths. If the corrected data simply masks model bias without explaining it, it serves as a band-aid that discourages researchers from doing the hard work of improving model physics.

Citation: https://doi.org/10.5194/essd-2025-694-EC1
- AC3: 'Reply on EC1', Haoyu Jiang, 25 Jul 2026
  
  Dear Dr. Davide Bonaldo,
  Thank you for forwarding these comments. Although they were posted after Reviewer 3’s comments, we have chosen to address them first because they raise fundamental concerns regarding the motivation, methodology, novelty, and suitability of the dataset, and several of these concerns appear to arise from misunderstandings of the scope and implementation of our study. We believe that clarifying these issues promptly will be helpful for the subsequent discussion.
  We will respond separately to the remaining reviewer comments as soon as possible and will ensure that all comments are fully addressed before completing the final response phase.
  Please find our detailed response in the attached PDF.
  Best regards,
  
  Haoyu
  
  Citation: https://doi.org/10.5194/essd-2025-694-AC3

Haoyu Jiang and Hao Su

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Significant wave height fusing multi-mission altimetry and WW3 hindcast Hao Su and Haoyu Jiang https://doi.org/10.57760/sciencedb.29314

Haoyu Jiang and Hao Su

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Short summary

We created a global, high-accuracy wave height dataset by combining sparse but precise satellite data with computer simulations to fill gaps and reduce errors, especially for extreme waves. It's freely available in two versions: one for climate trend analysis and another for training AI wave models, providing a valuable tool for ocean research and forecasting.


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