Review of “The Hydro-ABC model (Vn 2.0): a simplified convective-scale model with moist dynamics” by Zhu and Bannister

This manuscript extends the existing dry ABC model to include mixing ratios of water vapor and cloud water, termed the “hydro-ABC model”. This manuscript introduces and evaluates the extended equations for the “hydro-ABC model”. The success of simulation for a realistic-looking anvil cloud offers the possibility of exploring convective-scale DA strategies within a low-cost model. Investigations of error statistics are also conducted. Generally, this manuscript is a complete work and provides a cheaper approach to studying convective-scale DA. My overall recommendation is for acceptance pending minor revisions.

1. Line 7: “-” is missing after “Hydro”.
2. Line 101: Check the equation. The first “=” sign seems to be “+”?
3. Fig. 5: I am confused about the vertical correlations of w with q and qc at 80 and onward. Both correlations show strong positive values in the low levels. Intuitively, the increased qc means the reduced q. Why do we see positive correlations for both of them?
4. The proposed “hydro-ABC model” does not include the precipitation processes. However, the precipitation can lead to the development of cold pools, which facilitate the maintenance of convections. Will the authors have plans to include the processes related to cold pools in the proposed model?
5. Figure 6: It is unclear how the authors define the three zones in this figure. Because Figure 7 suggests that the authors attempt to find indicators for determining the three zones.
6. Figure 7: I suggest using qc, w, or their variants, and they may be good potential choices for the indicators as well.

Publisher’s note: a supplement was added to this comment on 17 May 2023.

The manuscript of Zhu and Bannister presents a novel, moist-dynamics version of the ABC-model, the new model is called Hydro-ABC, with the aim to perform future DA simulations for testing (new) DA schemes. The Hydro-ABC is a reduced model (no y-derivatives) relative to NWP models and it supports vortical dynamics, gravity and acoustic waves, as well as simplified moist dynamics. The moist dynamics included concerns the dynamics of water vapour and condensate fields and the model is constructed in such a way that the total energy including the moist component is conserved. The authors present preliminary (ensemble) simulations including correlations between various fields of interest. These developments for DA simulations are very interesting and such a reduced moist dynamics approach deserves due attention. So this is excellent news.

Yet the work described to date in the manuscript has some shortcomings. The manuscript requires therefore seemingly some modifications, with the following suggestions for improvement:

1. The formulation of the moist dynamics (in section 2.3) is rather implicit and unclear, and immediately leads to a parameterisation that seems to hinge on the discrete time-step splitting between dry and moist dynamics. The dynamics should be described first on a continuum level before mixing it up with the time-step splitting.
2. Whether the description is implicit or not, e.g. for S_b’, in the end, a closed-form formulation should be reached/available, otherwise a numerical implementation would not be achieved or possible. (1) What is required is a complete, final closed-form description of the entire continuum dynamics, presumably including implicit relations to be solved. Presently, section 2.3 is rather unclear and it is difficult if not impossible to figure out what the final formulation is. E.g., the implied relation for S_b’ seems to become 0/0 when b’=0, which presumably can be fixed via some l’Hopital rule being invoked implicitly?
   
   (2) In addition, it would be useful to have a (pseudo)code available of the moist-dynamics algorithm, which would presumably involve the split time-stepping.
3. I cannot follow the second option in (6) at all.
4. The time-stepping scheme used and the time-splitting should be defined and as such explained better.
5. (1) There is an accumulation of minor issues, including a few sentences and statements which are nearly or completely incomprehensible. An anonymised, annotated manuscript is made available to assess and address these. (2) Also note the various queries and remarks therein on resolution and timestep issues.
6. Please consider better explaining figure 6 in the text; please tie statements in the text with a clear pointing out in how the reader can discern the statement from an identifed observational feature in the figure. At the moment it is difficult to link text to features in the figure.
7. CIN does not seem to reveal very much in contrast to what is stated.
8. In Appendix A, CAPE and CIN for hydro-ABC are defined, after noting that there is no T and T_environmental available in the model; yet in eqn (12) a temperature is defined, used earlier in q_s, which could serve as such? Why is the approach followed to define CAPE and CIN valid and how does this link to an approach using the T of eqn (12) and its T_environmental analog. Why is the algorithm to define “environmental variable” valid; can one prove that (numerically); how does it depend on the chosen averaging?

While the goals and approaches followed in the presented research are great, and the simulations promising, the above queries seem to warrant some revisions to address the above queries.

Kind regards.