Review for “ Towards Strongly-coupled Ensemble Data Assimilation with Additional Improvements from Machine Learning” by Kalnay et al.

This manuscript reviews the coupled data assimilation and strongly coupled data assimilation research conducted by Dr. Kalnay’s group.  The manuscript is well-written, with appropriate literature references.  The content is very beneficial for the data assimilation community as well as the general readers who are interested in coupled data assimilation. I think it is well fit for NPG.  In terms of the manuscript, I only have a few minor comments.

1 I can understand the abbr. SC and WC represent strongly-coupled and weakly-coupled, respectively. Please define them in the manuscript.

   The same comment also applies to abbr. “NMC”  

Ln 11-12 the simple coupled Lorenz model —> a simple coupled Lorenz model

2 Ln 19   I am confused about the “full-rank” EnKF

3 Ln 24 55 upper oceans —> upper ocean

4 Ln 125-126, The smallest RMSE shows at an assimilation interval of 8 time-steps that is your smallest assimilation interval. I think it is worth pointing out here.

5 Fig. 2  From my understanding, ECCO only updates the boundary forcing and parameters, not ocean state variables.  From the figure, the initial conditions of model states are updated by DA. Please clarify it.  

6.  Comparisons of 3/4D-Var and EnKF in a coupled QG Model

      There are UC_clim, UC_3days and UC_1day.  it is worth providing details on their adjustment. Which is equivalent to the regular UC applying in the atmosphere and ocean?   

      The improved ocean does not enhance the RMSE in the atmosphere throng dynamic coupling, which needs some discussion.

     Ln 225-226 Fig. 4(a-b) only demonstrates two CDAs (WC, SC), not three methods, From fig. 4b, I can not conclude SC is better than WC. 

7 Ln 255  “lower than SC 3D-Var” should be “higher than SC 3D-Var”

8 Ln 257 “For 4D-Var, applying more outer loops and longer assimilation window lengths further reduces the analysis error”. The state mentioned here has no support. 

9 “accuracies smaller than SC 3D-Var” should be “higher than”

10 Fig.6 shows that the different RMSE between SC and WC has not reached to equivalent, especially the surface T/S, which needs to point out.  

11 Ln 340 it is confusing for the statement “due to the missing vertical localization not used in the Ocean-LETKF.” Please rephrase. 

12  LN 356  “states are assimilated by the SC EnKF”. The mean of SC EnKF here indicates the cross-model update, which is different from the other places indicating the whole DA algorithm.