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.

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

1. Section 2.1 proceeds from Sect. 2.1.2 directly to Sect. 2.1.4.
2. Consistent name for the multi-satellite product throughout the manuscript. Both “multi-sat” and “all-sat” are currently used.
3. “the parameter set yielding relatively smallest errors” is grammatically and methodologically unclear. Please specify the exact optimization criterion.
4. Equations 5-7: please define explicitly which dataset is represented by x and which by y.
5. Please describe the temporal collocation between the 20-minute NDBC buoy observations and the gridded data.
6. A compact table summarizing the final datasets, including temporal coverage, spatial resolution, temporal resolution, variables and approximate data volume is needed.
7. The number of observations used in each validation experiment should be reported.
8. The improvement of approximately 0.005 m is very small. Please state whether this difference is statistically significant.
9. Lack of jointly calibration -> Lack of joint calibration
10. It provide hourly data many wave parameters -> It provides hourly data for many wave parameters
11. grided -> gridded, meterological -> meteorological, Ribl & Young -> Ribal and Young
12. 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"
13.  The Code and Data Availability section should distinguish clearly between input datasets and the final fused products.
14.  Figure 4 caption – which time period?
15.  Why Figure 7 demonstrates results for 2020?