This is well-written and a good presentation of a new model for downwelling long wave.  As a reader I kept looking for but did not find the motivation for developing the model.  I suggest it would improve the paper to explain the motivation.  What is the need for a new model?  Why not use satellite based long wave radiation at the surface (As Pinker et al describe - this seems to be more accurate than the model you developed.)?  Why not use surface radiation from ERA5 reanalysis or from ECMWF model - you import cloud information from ERA5, so why not just take surface radiation from that model?  Years ago, absent satellite or model based surface radiation, folks needed a model such as your to estimate surface long wave to force, for example, an ocean model.  But now people use model or satellite fields.  So will anybody utilize your new model?  What was the purpose in developing it?

Review of “Development and Comparison of Empirical Models for All-sky Downward Longwave Radiation Estimation at the Ocean Surface Using Long-Term Observations” by Peng et al

Recommendation:  Major Revision

This study uses data from 65 moored buoys, supplemented with satellite and reanalysis data to evaluate eight existing models for downward longwave radiation Rl, as well as a new model developed here called “modnew”. The hourly and daily-averaged Rl estimated from modnew model have overall relatively low errors – very good news as these observations are not widely available.

I applaud the authors for gathering so many historic LWR buoy measurements!  What a job and what a resource. My major concern though is with the universal application of the Pascal & Josey 2000 (PJ2000) longwave radiation (LWR) correction applied to all 65 buoy timeseries.

 The PJ2000 LWR Correction = (a + lambda)Rsolar + b(Rsolar)^2  ,    

with a=0.00434, lambda = 0.011, b= 1.72^10^(-6).   This is a large correction if Rsolar ~ 1000 W/m2!  

The polynomial terms involving a & b (a*Rsolar + b*Rsolar^2) are a correction for the differential heating of the dome and casing. The last sentence in PJ2000 is “We suggest that such a correction should be made in future analyses if the component temperatures are not logged in order to improve the accuracy of the measured longwave flux”. I have emphasized the “if” part here because most if not all of the OceanSITES (including all from NOAA/PMEL, e.g., GTMBA, KEO, Papa, ARC ) LWR sensors are the 3 output Eppley sensors that measure case and dome temperature and correct for this effect. This correction has been done by the data provider and should not be done by the user. Essentially the authors here have double corrected these data.

The lambda term, on the otherhand, is intended to correct for solar radiation leakage caused by pinholes or degradation of the dielectric coating on the sensor dome. It is not a universal problem and PJ2000 found that the lambda ranged from 0.007 to 0.024. The 0.011 lambda value is thus a middle of the road case. In some cases, the authors will be adding an error, while in other cases, they will be partially fixing it. Perhaps if the authors keep this correction, it might be also treated as an uncertainty estimate.

Alternatively, its more work, but one indication that solar radiation leakage is an issue is if there is a noontime peak in LWR during clearsky days. Perhaps this correction should be applied only in those cases?

The bottom line is that I think the authors should go back and check which sensors are 3-output LWR and then redo the analysis without the a & b terms in the correction for those sites. The authors may also want to review their use of the lambda term correction.

Most of my other comments are to help clarify text, figures, and tables.

With the analysis redone with corrections only applied to the subset of observations that do not already have the correction for heating & solar radiation leakage, and with the manuscript revised for clarity, I expect this will eventually make for a well-cited paper.

Comments to improve clarity:

1. Table 1 Caption: Add statement that Variables are defined in Table 2.
2. Table 1. Consider expanding this to also include Modnew model. I think this would help the reader find the equation and see its structure in relation to the other models.
3. Table 2 show all variables used in this study, including Rl, Rg, DSRtoa, CBH etc.
4. Table 3. In the text, it would be nice if you said where or who these 8 OceanSITES stations are. If 4 of these OceanSITES stations are from TAO (this needs to be clarified), then you only need to describe 4 stations, or even fewer groups as some of these stations (e.g. KEO and Papa) are from one group (NOAA Ocean Climate Stations). These smaller groups making these long OceanSITES time series would benefit from being named in this analysis.
5. Figure 2 caption. What is being represented by the color bar in the left column? What are its units? In the right column, what are the error levels in the “box plots”?
6. Figure 3 caption. What is being represented by the color bar in a and b? What are the units?
7. Figure 4 caption. Same as #6 comment. Also, what is the daytime vs. nighttime criteria?
8. Figure 7 caption. Same as #6 comment.
9. Figure 11. Could you make the y-axis labeling more concise so that it is legible? Also please define what the different levels are in the box plots.
10. Throughout the text, the observations are described as “screen-level”. What does this mean? I’ve never heard of this.
11. Line 41, “Although the ocean-surface Rl is routinely measured at most buoy sites…”. Unfortunately, this hasn’t been true. Of the 55 TAO sites, only 4 have routinely measured longwave radiation. This is being changed in response to the Tropical Pacific Observing System (TPOS) 2020 project (Kessler et al. 2021), but historically and currently, this statement is only true for OceanSITES bulk flux buoy stations.
12. Line 52. “complicacy” is the wrong word I think. Perhaps “complexity” ?
13. Line 81 “mid-high”  -->  “mid-to-high” ?
14. Line 312 “At last” -->  “In total” ?
15. Line 324 “On the contrary”  -->  “On the otherhand” ? or “In contrast”
16. Line 331. For regions where winds are weak, afternoon near surface stratification can cause the skin temperature to be quite a bit warmer than the bulk SST. This is mainly an issue in the tropics, but can also matter in the summer elsewhere. See Cronin et al. (2024) or Clayson and Bogdanoff (2013)
17. Line 369, this should reference Table 2, not Table 1.
18. Line 403. What is CBH ? Perhaps this needs to be included in Table 2.
19. Section 4.2.1 Clear sky, is very short. Section 4.2 is Model comparison results, but this 4.2.1 has no results/analysis. How do we interpret these results? Or will that be discussed later? Please let the reader know.
20. Line 519. “On the contrary” --> “In contrast”
21. Paragraph 2 of the Conclusion. Could you use some more words to describe the physical dependencies of the model? This paragraph relies too heavily upon variable names which may be unfamiliar to some readers.
22. Paragraph 2 of the Conclusion. Please also clarify how satellite data must be used to run the Modnew