Based on a series of coupled GCM experiments in this study, the authors investigated how changes in the air-sea coupling frequency will affect the model performance in simulating the Madden-Julian Oscillation (MJO). As the MJO remains poorly simulated in our present-day climate models, results presented in this paper is useful and can provide important guidance for improved MJO modeling and also understanding of key processes underlying the air-sea coupling involved with the MJO variability. In general, I found this paper very interesting and clearly written, although there is still room for further improvement, both scientifically and technically, before it can be accepted for publication. The following lists some of my major and minor comments and suggestions.

General major/minor comments:

I felt that the length of the paper can be reduced to make it more concise. Discussions in many places are redundant, and not necessary. For example, descriptions of the SST influences on the MJO in the lines of 249-256 can be integrated with the introduction part, not necessarily to mention this again in section 3.1; also Lines 490-492 on the leading EOF modes. Similarly for many other places as also further mentioned below.

I also had a general question on the determination of MJO phases based on the WH04 approach for different model simulations. Since the combined EOF for OLR, u850, u200 is conducted separately for different model experiments, how to make sure all the leading combined EOF modes from the experiments are same with the observations. Otherwise, this will lead to phase differences among model simulations and observations.

One of the main findings from this study is that “The increasing feedback periodicity of SST in low-frequency experiments leads to the accumulation of short-wave and long-wave radiations and surface heat fluxes from the atmosphere, resulting in an increase in the upper oceanic temperature and its variances (Lines 813-816)”. Although this seems supported by the results in this study, I do not completely understand why this is the case. My understanding is that for an intraseasonal time scale, such as 30 days corresponding to the coupling time-scale in the C-30days experiment, the variations in radiation or heat fluxes can be in positive and negative phases, so they can be cancelled out if averaged over 30 days - not necessary always accumulating large positive or negative values.

Several figures look very busy, such as Figs. 12, 14, could be further improved to make them more readable.

Other comments:

Line 9: what is “TKE”?

Line 27: what is “lower results”? You meant weaker amplitude?

Line 90: what is “dynamic range”?

Line 99: “weakness”?

Line 100: “Understanding the manifestation of heat fluxes in …”. I don’t quite follow this sentence.

Line 119: Jiang (2017), Gonzalez and Jiang (2017) are very relevant to the discussions here on the relationship between the mean MSE/moisture pattern and MJO propagation.

Jiang, X., 2017: Key processes for the eastward propagation of the Madden-Julian Oscillation based on multimodel simulations. Journal of Geophysical Research: Atmospheres, 10.1002/2016JD025955.

Gonzalez, A. O. and X. Jiang, 2017: Winter Mean Lower-Tropospheric Moisture over the Maritime Continent as a Climate Model Diagnostic Metric for the Propagation of the Madden-Julian Oscillation. Geophys. Res. Lett., 10.1002/2016GL072430.

 Line 119-121: Moisture convergence in the MBL is mainly through vertical moisture advection; meanwhile, recent MJO moisture mode theory also emphasizes that the horizontal moisture advection in the lower-troposphere plays a crucial role for moisture preconditioning to the east.

Line 122-123: On the first order, the PBL convergence ahead of the MJO convection is due to Kelvin-wave dynamics, rather than SST induced.

Line 127: what is the “positive trend” being discussed here? This sentence needs to be improved.

Line 188: is there a gradual transition belt between the coupled and uncoupled zones?

Lines 204-205: is there a reason for the different nudging time-scale for different depth in the ocean?

Line 249: “interseasonal” needs to be fixed here, as well as in several other places in the paper

Line 251: “the behavior of the MJO behavior”….

Lines 256-257: How the “Cooler than average SST to the east of MJO convection is associated with the passage of the MJO”?

Lines 286-287: “the atmospheric heat/cooling”?

Line 322-324: I did not follow this sentence - suggest to modify it.

Fig. 3: Labels for x- and y-axes are missing

Line 366: suggest change “MJO” to “intraseasonal”, since the MJO band is within wavenumber 1-5.

Line 367-368: this sentence needs to be connected with the following sentences.

Line 383: suggest change “became” to “becomes”

Lines 403-405: in ERA5, why the warm T near surface is located to the west of MJO, seems not consistent with the SST.

Lines 423-425: Does this sentence mean the land convection over the MC is critical for MJO eastward propagation over the MC region? But in the reality, when MJO propagates over MC, the active MJO convection is largely over the oceanic region, while the convection over the land is suppressed. If you want to emphasize this point, may need to provide more evidence. Similar statements were also discussed in the conclusion part.

Fig. 6d The grey color for the thick contours needs to be corrected for consistency.

Lines 451-463: discussions in this part are largely reductant with previous discussions, particularly in the introduction part, so can be significantly reduced to be concise.

Line 465: is vertical or horizontal gradient discussed here?

Line 475: “a cooling effect in the upper ocean” mentioned here is not obvious to me

Line 477: this sentence can be improved – “…characterized by stronger intraseasonal MJO variability” is for C-CTL or C-3days?  

Lines 488-500: discussions here can also be more concise since these have been discussed earlier.

Lines 556-559: Just curious that the phase delay of 30-m T relative to surface T seems not seen in Fig. 7. Any thoughts on this?

Lines 632-637: This part again can be more concise since these have been previously mentioned. In general, I felt that the Section 4.4 is a bit lengthy, can be more concise and make important points more clearly delivered.

Fig. 13b,c: why not combine these two panels together as in the upper panel?

Line 778: suggest change “ERA5” to “observations” since this also involves GPCP and SST data.

Lines 773-786: In this part, when mentioning the related figures, may just provide the figure number, for example, just use “(Fig. 1)” instead of “(as shown in Fig. 1)” in Line 778, and similarly for many others.

Line 790: suggest change “oceanic heat fluxes” to “surface heat fluxes”

Lines 802-805: “… it becomes evident that the high frequency (low-frequency) SST experiments tended to underestimate (overestimate) the MJO simulation “. Just wonder if this statement can be model-dependent?

This manuscript describes a series of climate-model experiments aimed at understanding the feedback of the upper-ocean on the Madden Julian Oscillation (MJO). It has long been known that ocean-atmosphere coupling is important to the MJO because the characteristic timescales of heat storage in the upper ocean are in the intraseasonal range (Watterson 2002, Sobel and Gildor 2003, Maloney and Sobel 2004, Sobel et al. 2010). This manuscript could contribute to a deeper understanding of the ocean-atmosphere feedbacks beyond this first-order effect. In its current version, the manuscript shows many analyses which describe the non-linear sensitivity of the model to the time step of the update of the sea-surface temperature (SST) seen by the atmospheric model, with a maximum of variability for a time step of 18 days. I think the experimental configuration raises questions that should be addressed and the manuscript could be more concise.

My main comment is about the experimental setup. The "frequency" that is varied here is the frequency of the update of the SST seen by the atmospheric model. While the SST is held fixed, the ocean-model SST evolves in time in response to the surface heat fluxes and vertical mixing. When the SST is updated for the atmospheric model, it increases or decreases abruptly. The less frequent the update, the larger the potential jump in SST. This is probably why, as the frequency is decreased  down to 1/(30 days), there is a lot of unorganized variability rather than a simulation that becomes similar to the atmosphere-only simulation, as one could have expected if this experimental setup actually filtered the subseasonal variability of SST (I expect the atmosphere-only experiment to use the classical configuration with smoothly varying SST). The SST jumps seen by the atmosphere raise a number of questions.  Potentially, they could themselves, occasionally, trigger the development of an intraseasonal convective disturbance, in which case they become a forcing instead of expressing a feedback. Otherwise, they happen at fixed dates and one can wonder how they can be properly phased with an intraseasonal disturbance. The case with a SST-updating timestep of 18 days is probably optimum because it corresponds to half the period of the MJO: locally, a warm SST jump ushers the development phase of the MJO which extracts energy from the surface, and the downward SST jump starts its decline. But does the ocean feed back on the atmosphere in this case, as we expect for the MJO, or does the atmosphere feed back on the SST jumps ? The fact that the signal is so strong is suspicious: considering because there is also a sampling problem associated with this experimental setup: with an SST-update timestep of 18 days and the simulation duration of 30 years, the SST update happens less than twice at the same date, and there are rarely more than 4 MJO events per year. To get a very clear signal, we need most of the SST updates to occur within a couple of days of the maximum or minimum convective activity. This seems unlikely to me considering the small numbers of update days at a given date and the expected number of spontaneously-generated MJO events. The probability that the SST jumps time the MJO events is non-negligible, which probably means that the SST plays some role in forcing these events, instead of providing a feedback to these events. For this reason, there is a need to better understand the impact of the experimental setup. This could be done by looking at singular MJO events rather than composites and/or conducting additional experiments with different configurations (updating the SST seen by the atmospheric model with smoothed tendencies using the tendency history, maybe).

My second comment is on the length of the manuscript. I feel that some figures and analyses aim to show modest sensitivities and don't explain their physical cause. I think the manuscript would benefit from being more concise and to the point.

References:

Maloney, E., and A. H. Sobel, 2004: Surface fluxes and ocean coupling in the tropical intraseasonal oscillation. J. Climate, 17, 4368–4386.

Sobel, A. H., and H. Gildor, 2003: A simple time-dependent model of SST hot spots. J. Climate, 16, 3978–3992.