Please see attached PDF for comments.

This study aims to provide observational constraints on the seasonality of the H2 soil sink, the most uncertain term in the H2 budget. 

First, the authors use a box model constrained by HFC-152a observations to optimize the seasonality of OH. 

Then this optimized OH field and H2 observations are used to optimize the different parts of the H2 budget (H2 emissions, H2 chemical production, H2 soil sink). 

The approach is interesting, and the manuscript is well-suited for publication in ACP once the following comments are addressed. 

Main comments

1.  The box model used in this study includes only 3 boxes, with the Northernmost box spanning the 20-90N range. 

     The magnitude but also the seasonality of H2 exhibits significant meridional variations in this region (e.g., Tardito Chaudhri (2025), Paulot (2024)).

     This suggests that the choice of the box boundary may have a significant impact on the optimization.  The authors allude to it in line 275 but more discussion and analysis are needed. 

     For instance, the authors could use the H2 concentration simulated by a global model with H2 deposition (see Sand (2023), Brown (2025) but any sensible pattern would work) to demonstrate that the 3-box model framework 

     can recover the deposition velocity used in the aformentioned model if given the simulated H2 concentration at MHD

2. Line 260-265 What is the implied seasonality of the deposition velocity of H2? How does it compare with the (few) observations in the NH and to global models (e.g., Brown (2025), Paulot (2024), …)? =

                          Does the retrieval provide information on the interannual variability of vd(H2)? 

    

3. The title should be revised to more clearly convey the focus of the manuscript on the “seasonal amplitude” of the H2 sink (rather than its magnitude)

4. Fig. 4. shows that the amplitude of the optimized seasonal cycle of the land sink is not significantly different from the prior (no seasonality). 

    It’s not clear whether this is because the information content provided by the measurements is insufficient in these regions or because the seasonality is weak. 

    In other words, how much lower is the posterior uncertainty relative to the prior?

5. Line 257.  “It is important to emphasize that the prior soil sink is constant over the course of a year, so that the seasonal information that is retrieved is not constrained to the choice of prior”

    Do you mean that your choice of prior has little to no impact on your solution? The authors should discuss this in more details. How would a different soil sink apriori and soil sink apriori uncertainty impact the results?

    Additional justification for the 35% error in soil first order loss (see TC3) would also be helpful given the large observed seasonal variation of vd(H2) (see HFR data from Meredith et al. for instance)

Technical comments

1. Line 101: It’s not clear why a 20% increase is applied to SMO.

2. Line 113. What is the interannual variability in HFC-152a emissions

3. Line 150. Can you be more explicit? If I understand well, you assume a first order loss proportional to the land area. However, in Table 1, it is stated that the 35% error is applied to the absolute magnitude of the soil sink. Do you mean H2 lifetime wrt soil sink?

4. Fig. S1. should include the range of H2 observations across NOAA observations. The spread should be discussed when assessing the choice of the MHD station to represent the 20-90N band.

   Please include a map of the locations of the NOAA and AGAGE sites

5. Fig. S3. I believe a “+” is missing between jch2o and kch2o

6. Line 172. “retrieved with cross-correlation between OH established in the prior covariance to ensure correct chemical production seasonality”

    I am not sure to understand what you mean here. Please rephrase.

  

7. Line 190: what is the impact of using a longer temporal correlation for non-biomass burning emissions?

8. Line 190: what is the assumption for the soil sink temporal correlation? If it’s neglected, wouldn’t this lead the optimization to favor adjusting the soil sink to capture the seasonal variability?