Improving the representation of shallow cumulus convection with the Simplified Higher-Order Closure Mass-Flux (SHOC+MF v1.0) approach

By Maria J. Chinita, Mikael Witte, Marcin J. Kurowski, Joao Teixeira, Kay Suselj, Georgios Matheou, and Peter Bogenschutz

The goal of this paper is to test whether the addition of a mass flux scheme, which represent non-local transport by updrafts, to the turbulence scheme called SHOC improves the representation of shallow cumulus convection by the SCREAM climate model.

For this purpose, the authors use a single-column model with the SCREAM model physics, and with or without the multiplume mass flux scheme developed by Suselj et. al (2013, 2019a,b). By simulating two cloudy boundary layers and comparing them with large-eddy simulations, they show that the addition of this mass flux parameterization improves the representation and evolution of cloud features and turbulent transport.

Knowing that uncertainties in the representation of low clouds by climate models remaing important, it is still very valuable to continue working on improving these clouds. The paper presents interesting results, a relevant methodology, and is well written. Therefore, the article is very suitable for publication. I’m nevertheless concerned about the pontential implementation of the SHOC+MF in the parent 3D climate model for several reasons: the adjustement of tunable parameters, the relevance of the EDMF scheme in a model that aims to simulate at high resolution (scale awareness), and the coupling with other parameterization such as radiation, and microphysics. These points are not addressed in this study. More information about would be very valuable for the community.

Major comments:

- I know that it could be complicated, but I really find it problematic that the authors avoid the question of tuning when testing their new parameterization. Here there are several parameters that need to be ajusted when combining SHOC and MF schemes, e.g. number of plumes N, epsilon_0, ‘a’ for the entrainment length scale, … The authors justify the tuning parameters’ values by the original studies that set them. However, this study highlights a coupling between parameterizations that might suggest that these values may be outdated. Without asking the authors to test all tunable parameters, I would like to know if (1) values they use remain physically consistent in their new SHOC-MF framework, and (2) if their conclusions remain similar when some important tunable paremeters are modified. I guess that the second point is feasible given the simple SCM framework the authors use.

- The authors show improvements when implementing the MF scheme in SHOC. However, the heat and moisture transports remain biased low (Fig 8-9). Could the authors describe improvements to reduce this bias? Would it be possible to reduce it by a better tuning strategy or switching on radiation scheme?

Minor comments:

- I understand that removing some parameterization schemes is useful to highlight the novelty of SHOC+MF. Yet I’m surprised that the authors removed the radiation schemes. I would assume that some large-scale cooling and drying forcing are imposed in large-eddy simulations. Removing these schemes would also compromise the ability of the model development to be used in the parent global climate model.

- Figures 1+5: I'm confused with the notation. You have two simulations SHOC (A), and SHOC+MF (B). Therefore, you plot results from A and B experiments, but also the relative contribution of SHOC and MF in turbulent fluxes (we can call it B[SHOC] and B[MF]). MF in Figure 1 seems to be B[MF], but this is confusing because MF could also be understood as the difference B-A in Figure 1. I guess that non-linear interactions could make these contributions different (i.e. B-A != B[MF]). Could you clarify this a little bit (differences between experiments vs the MF contribution that is saved from SHOC+MF) ?

- Line: 311: Could you use a single time notation, either “hour XX” or “+YYh” relative to the start of the simulation (as done in Fig 4).

- Figure 8: I don’t think the dashed and the dotted-dashed lines are described.

This manuscript describes the implementation of a stochastic, multi-plume Eddy Diffusivity Mass Flux (EDMF) boundary layer parameterization in the SCREAM GCM, using the Simplified Higher Order Closure (SHOC) to calculate eddy diffusivity and cloud properties. Single column model experiments are used to evaluate the scheme against large eddy simulations for marine shallow cumulus and continental convection cases.  Improvements are shown relative to experiments using SHOC alone.  

The topic is certainly of scientific interest, as boundary layer clouds remain one of the largest sources of uncertainty in future climate projections, and boundary layer parameterization is a topic of active research.  The paper is well written and logically organized.  However, a few details are missing that are needed for readers to interpret and reproduce results, as noted in comments below.  I believe these can be addressed with minor revisions.

Minor Comments:

1) There are some discrepancies in cloud top height in the continental convection case between this study, Bogenschutz and Krueger (2013) describing SHOC, and Brown et. al. (2002) documenting the continental case.  The two previous papers show LES cloud top heights around 2800 m, while in Fig. 7 here the deepest cloud tops are close to 2400 m. I am wondering if there are differences in case specification that might explain the LES difference, or if it may be due to the use of different LES codes and grid spacings?  This has implications for the conclusion that SHOC-MF matches the LES, while SHOC by itself produces too-deep clouds.  The original SHOC (Bogenschutz and Krueger, 2013) appeared to match LES in this case fairly well, so the different behavior here warrants some discussion.

2) Additional details are needed regarding the SHOC length scale and how it has been changed since Bogenschutz and Krueger (2013).  The length scale formulation can have a major impact on PBL behavior, and should be described in the paper.

3) It is not entirely clear how convective clouds are treated in this study.  Is there any special treatment of cumulus cloud detrained from the mass flux?  Or do the updrafts impact clouds only indirectly, through the mean state?  This could be noted in Section 2.

4) The experiments here used N=40 updrafts, while previous papers (e.g., Suselj et al 2013) have typically used a smaller number (N=10).  Was N=40 chosen to reduce the effects of stochasticity, and do the results show any sensitivity to the value of N?

5) Are the simple updraft microphysics mentioned on lines 61-64 included in this implementation?  If so, do they have a non-negligible impact?  This is relevant to the comparison with LES, for which precipitation was disabled.

6) On Line 247, which constant in SHOC was increased to reduce the mixing length, and by how much? 

L113: Typo: Eqn 1 is missing a “partial” symbol.

Please see the attached PDF for my complete review.