This manuscript explores the optimal strategy for initializing coupled climate prediction systems by comparing between strongly and weekly coupled data assimilation. Through a series of experiments, the authors have reach to the two conclusions described in the last section. While the conclusion is reasonable to me, I am not fully convinced of the significance of the manuscript. The conclusions presented in Chapter 5 were largely consistent with previous studies. This also indicates that the findings obtained in this study are quite limited. Consequently, I cannot be very positive to the paper because this study seems to be a simple extension of previous studies. I have some suggestions for improving the manuscript, as described below.

(1) Usage of more complex model(s): One of the main discussions in coupled data assimilation is how to differentiate real and erroneous error covariance. Therefore, exploring a better localization strategy is essential for coupled data assimilations. However, the present manuscript uses a very simple top model, which is unsuitable for investigations on localization. It is also important to investigate optimal observation frequency (=data assimilation) of the fast and slow-mode models for the coupled data assimilation.

(2) To investigate various coupled data assimilation strategies: Kurosawa et al. (2023; NPG) investigated various options of coupled data assimilation, as indicated in Figure 2. I would suggest investigating such options together with the sensitivity investigations on observation frequency, ensemble size and localization.

General comment:

The authors tried to clarify when the strongly coupled data assimilation (SCDA) is preferrable to weakly coupled data assimilation (WCDA) by a two-components coupled Lorenz-63 system (one component representing the atmosphere, fast component; the other one representing the ocean, slow component), with changing the parameters of observation networks (FULL, ATM, OCN), spatial scales (S, 0.05 - 2.0), and temporal scales (\tau, 0.075 – 1.0). The data assimilation implemented in this study is EnKF with perturbed observations and adaptive inflation. In WCDA, the assimilation is applied to the individual components separately by using the observations available for that component. In SCDA, the observations from one component impact the other components directly during the assimilation.

The manuscript described the stability analysis of the coupled Lorenz-63 model, which is a simpler version of Tondeur et al. (2020). The results were discussed with respect to the observation networks: (1) in a well-observed system, SCDA degrades the system’s performance slightly compared to WCDA; (2) SCDA improves over WCDA when only one component is observed. Similar conclusions have been reported by previous studies. I think the interpretation from the instability analysis on why the SCDA shows different responses from WCDA would be interesting to the readers, whereas the results and conclusions of the paper are not consistent. My concerns are listed as followings.

Major comments:

1. Lines 5 – 7. (a) In full observations, “SCDA and WCDA yield similar performances”. Does this mean that the spatial scale (S) and temporal scale (\tau) have very few influences on the coupled data assimilation? (b) If the SCDA performs marginally worse than WCDA could be explained by the approximation in the EnKF – linear analysis update and sampling error, I will encourage the authors to explicitly describe how the linear analysis update and sampling error in the SCDA differs from those in the WCDA.

2. Lines 7 – 8. When observations are only in one of the components, “SCDA systematically outperforms WCDA” is contradictory with the discussions in Chapter 4.3 and Figure 12 (a), where the dotted area means SCDA degrades over WCDA (Figure 10).

3. Lines 8 – 10. “The spatio-temporal scale separation determines SCDA’s performance in this scenario, and the largest improvements are found when the observed component has a smaller spatial scale.” (a) The first part of this sentence says that the spatio (S) -temporal (\tau) scale affects the SCDA’s performance, whereas the second part says that only the spatial scale (S) affects the performance, which is not consistent. (b) In Figure 12, when only the ocean was observed, the large improvements were found when the spatial scale is larger, which is contradictory with the sentence in the abstract.

4. Lines 10. “This suggests that SCDA of fast atmospheric observations can potentially improve the large-slow ocean component.” This sentence is contradictory with the discussion in the Chapter 4.2, Lines 326 – 327: “This result can be explained as the atmosphere → ocean error propagation is smaller (Fig. 8); thus, the atmospheric data has no impact over the ocean.”

References:

Tondeur, M., Carrassi, A., Vannitsem, S., and Bocquet, M.: On Temporal Scale Separation in Coupled Data Assimilation with the Ensemble Kalman Filter, Journal of Statistical Physics, 179, 1161–1185, https://doi.org/10.1007/s10955-020-02525-z, 2020.