Review of "Transporting CRM Variance in a Multiscale Modelling Framework" by Walter Hannah and Kyle Pressel, egusphere-2022-397

Fredrik Jansson

General comments

The article considers the E3SM-MMF climate model, where every grid column of the global model (GCM) is coupled to a local cloud-resolving model (CRM), in order to resolve cloud and convection processes. These processes are important for the evolution of the model state but too small to be resolved directly on the GCM grid. This method of coupling coupling atmospheric models is known as a Multiscale Modelling Framework (MMF) or superparameterization (SP) .

The article points out an important issue with MMF/SP in general, namely that only the CRM mean state is communicated back to the GCM and then to the neighboring CRMs. For this reason, structures like clouds and convection may get stuck in a particular CRM, instead of being advected to the neighbor CRM. In the E3SM-MMF considered here, this shows up as a persistent checkerboard pattern of convection. The authors then suggest a remedy in the form of transporting not just the CRM mean state through the global model, but also the variance of CRM quantities as new passive scalars in the global model. They have implemented this scheme in E3SM-MMF and shown that the checkerboard problem is reduced. The article is well written and both the issue in MMF models as well as the remedy proposed are important. I recommend the article is accepted once the following remarks have been addressed.

Specific comments

In this article, https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021MS002892 , we have addressed a similar issue in superparameterized climate models, specifically for the transport of cumulus clouds in a high-resolution regionally super-parameterized model. We see the same issue of small-scale structures, in particular clouds, getting stuck in the CRMs where they are formed. We proposed a somewhat different solution to the one presented here, namely adjusting the total humidity variance (keeping the mean constant), in order to match the GCM liquid water content. Please consider referring to this article. I believe the similarities and differences in approach are interesting. 

In our SP model with humidity variance adjustment, we saw that clouds and variability added through the coupling mechanism doesn't always persist in the CRM but can dissipate rapidly, if the receiving CRM is in a different state for example lacking the convection to support the clouds. It would be interesting to see if or how much this happens in the E3SM-MMF.

Section 3.2 E3SM-MMF Description:

Please mention whether the CRM uses the same vertical grid as the global model or something different.

3.4 Satellite Observation Data

When re-gridding 1x1 degree satellite data to ne30pg2 of comparable grid size, isn't there a risk that the re-gridding operation may affect the presence of checker-board features? Regridding the much finer IMERG data to ne30pg seems safer.

Technical corrections

Line 9: The first sentence is hard to parse because one can read it as "... cannot otherwise resolve convective scale circulations by coupling ..."

Eq. (2) B_g should be B_G, or is not defined

line 65: <q_C^n>^n  one n too much

Eq. (4) Left-hand term has a q without index, should be q_G?

Eq. (11) What is F?

line 93: "Since the CRM columns do have any specific location within the parent GCM column,"

do -> do not

Line 180: Unclear "gains performance by limiting radiation to operate of even subsets of the CRM domain"

Figure 4. Is the data averaged in time before or after checkerboard detection? 

Figure 9. Axis labels would be helpful, and a mention in the caption of what wave numbers are considered (e.g. which direction).

Line 132: "However, experiments with this approach exhibited some odd behavior that we could not fully explain" and Line 140: "with some subtle, but unique, changes to certain climatological features." I'd recommend either saying more or less about these. Now I wonder what exactly happened in these two cases, while also suspecting that it may not be particularly relevant.

Review of “Transporting CRM variance in a Multiscale Modeling Framework” by Hannah and Pressel, submitted to GMD.

This manuscript reports development of a technique that helps removal of what the authors refer to the “checkboard pattern”. Overall, I find the paper suitable for GMD. I have two general comments and several specific points that should lead to an improved presentation. The paper can be published after some revisions and clarifications in response to my general and specific comments below. I do not need to see the revised manuscript.

My first general comment concerns the stand-alone aspect of the submission. The presentation follows already published manuscripts concerning E3SM-MMF and reports developments motivated by those publications, up to the point of repeating some of the figures. I feel the authors assume that readers are familiar with the past work, and thus they use terms and concepts that are unclear unless you are familiar with those past manuscripts. Since I was not familiar, I had to go back to those previous manuscripts. I feel this needs to change to make the paper more stand-alone. I have serval specific questions and suggestions below that should improve that aspect of the manuscript.

My second comment concerns conservative properties of the model with variance transport. The original GCM-CRM coupling conserves energy (in its simplified representation) and water substance by design. Is that true for the system with variance transport? I think it is by design as well, but perhaps worth commenting on it and maybe even illustrating by some additional analysis.

Specific comments:

1. Title: I suggest replacing “CRM” with “cloud-scale” or “convective-scale” to avoid the acronym that might be unclear to some readers.

2. A general comment on the introduction: I do not think the key problem with MMF is the presence of the spectral gap between scales resolved by GCM and those in CRM. The key is that CRM domain is periodic and the cloud-scale signal cannot propagate from one GCM box (i.e., one CRM) to the CRM in the next GCM box. In other words, small-scale perturbations are trapped in a GCM. This is why transporting variance helps, correct? One way to stress that in the discussion would be to emphasize that CRMs feature periodic lateral boundaries. For instance, adding cyclic or periodic in line 11 would help. Periodicity is important from the energy conservation point of view. Making CRMs open brings essential problems with keeping track of what comes in and comes out. The sentence in line 24, “Another consequence…” is simply incorrect. Lack of advection has little to do with the scale gap; it comes from periodicity of CRM domains. Another comment is that it would help if the checkboard pattern is already documented in the introduction to set the readers on the right pass. This is only mentioned now (line 19-23), but adding a figure from a previous paper would help. And, again, I do not agree that the key is the scale gap, the lack of large-scale advection is the culprit.

3. Section 2.2. I think it would help if the technique is illustrated by a figure. If I understand the approach, you simply “scale up” the variance in each CRM based on GCM advection from the neighboring columns, correct? The key is that alpha is advected by the GCM, correct? If the CRM field (at a given height?) is q, you make it alpha q, correct? Can this be shown in a figure? Also, alpha is height-dependent, correct? It would help to state this clearly.

4. What is F in (11)?

5. Section 3.1. I feel a figure describing the detection would help. This is not clear unless one goes back to Hannah et al (2022). A figure or two from that paper would help.

6. Section 4.1. Several statements in this section are hardly evident in the figures. Line 234: perhaps a hint of a double ITCZ? L. 235: I do not see the checkboard pattern. My suggestion is to improve the figure, maybe with a small insert, so the features mentioned are better documented. I think Fig 2 does show that pattern, correct?

7. Section 4.2. How is “fractional occurrence” defined? It is unclear to me what Fig. 3 shows. How the “extremum in the local neighborhood” is defined (in IMERG and in the model results)? Figure 4 shows clear differences, but if I do not know what the fractional occurrence is how can I gauge the significance of those differences? Fig. 5 provides a clear impact of the improvement and good comparison with observations. I do not understand what Fig. 6 shows, please explain.

8. Please clearly define what each panel of Fig. 7 is showing. Also, do the numbers shown have some relevance to the real world? For instance, the maximum temperature variance (temperature or potential temperature?) is around 0.6 K**2. Does this mean that the CRM variance is less than 1 K? How this compares to either observations or cloud-scale simulations of tropical convection? Can you explain why GCM and CRM transport panels seem to have the same pattern but the opposite sign? What is the reason for that? Some physical interpretation would be good. This is briefly discussed, but I would like to see more physical interpretation. Similar comments apply to Fig. 8 (please define all panels in the figure caption).