The paper addresses how the cloud droplet concentration (N) affects the liquid water path (LWP) in terms of a factor m = d ln (LWP)/d ln (N). The paper contains some interesting ideas, and could be a nice addition to existing MLM studies. However, a central question is whether the MLM framework, and in particular the set up of the experiments in terms of construction of the buoyancy flux from the fluxes of energy and water (do they give a steady-state?), and the boundary conditions (constant surface fluxes?) justifies a generalization of the results. The results may depend strongly on the assumptions made in the model, like a zero entrainment response to simultaneous changes in N and the liquid water path (see the sentence "The conclusions drawn in this study are built upon the assumption that an increase in entrainment rate (w_e) due to an increase in N is exactly offset by a commensurate decrease in LWP, resulting in the same w_e irrespective of N".) I recommend to pay more attention to the validity of this assumption, in particular for some extreme values of N and LWP used in the study. Another concern is that the model framework builds on existing mixed layer model studies, but for the reader not familiar with this modeling technique it may be difficult to follow. 

Main:

The conclusions of this study are  "... built upon the assumption that an increase in entrainment rate (w_e) due to an increase in N is exactly offset by a commensurate decrease in L, resulting in the same we irrespective of N".

The setup is somewhat unclear, and there may be inconsistencies, though I may be mistaken. For example, the surface fluxes are treated as constant, which seems to contradict the systematic changes in LWP. Since the boundary layer height is kept constant, the changes in LWP must stem from changes in humidity or temperature within the boundary layer, or both. I suspect that the thermodynamic profiles in the boundary layer are altered, as inferred from the dependence of the buoyancy jump (Delta b, line 183) on the settings. However, if the thermodynamic profiles in the boundary layer are modified, this would lead to changes in surface fluxes (see Bretherton and Wyant, 1997). Notably, most MLM studies cited in this paper (e.g., Wood 2007, Dal Gesso, Jones et al.) use surface boundary conditions dependent on wind speed and the difference between surface conditions and the air just above it. 

A particularly confusing sentence appears on line 232: "The decrease in Delta b is due to the stronger latent heat release at higher L, which decreases the temperature difference relative to the warmer free troposphere, as indicated by (11), enabling stronger entrainment." Here the factor Delta b (the vertical static energy jump across the inversion) depends on the inversion jumps of temperature and humidity, yet the sentence suggests that the boundary layer is warming (i.e., "decreasing the temperature difference", as stated). If this is the case, shouldn’t the surface fluxes also change?

In Section 2.3.2 it is unclear whether an equilibrium state is assumed? In any case the boundary layer depth h_t is assumed to be constant, and this leads to Eq 35, w_e(N,LWP)=w_e(N+dN,L+dL), with w_e being the entrainment velocity. The question arises whether Eq. 35 holds for large deviations dN and dL? It is not explicitly stated whether the key assumption of a zero entrainment response to changes in N to minimum and maximum values applied in the study have  been tested with the LES, for example for some extreme values of N, say 10 and 1000 cm-3, and for L = 10 or 1000 g/m2? Perhaps the reader could be directed to relevant sections in the accompanying paper. The assumption of constant entrainment is special, as other perturbations, such as changes in surface temperature or free tropospheric conditions, would likely lead to a nonlinear entrainment response. For instance, De Roode et al. (2014) examined the entrainment response to changes in large-scale conditions and found that the entrainment response significantly altered the feedback strength.  Additionally, numerous studies using LES models show that changing cloud droplet concentration has a strong impact on entrainment and I am not sure whether those results are in line with the assumption of w_e(N,LWP)=w_e(N+dN,L+dL). The implications of the latter condition warrant a more critical discussion. 

It is difficult to read for non-experts. It could help to start with stating upfront that you will apply a summation of the individual fluxes. An explanation of the MLM,  its setup and some of its results in a figure would be helpful, for example like Fig. 11 from the MLM paper by Nicholls (1984) or Figure  4 by Bretherton and Wyant (1997). As a reason, I am not able to derive whether the total fluxes of the conserved variables are linear in height? Actually, one would expect them to be  constant with height, as this implies a steady state. 

"Under well-mixed conditions, contributions to the buoyancy flux that originate from the surface or the top of the boundary layer can be assumed to increase or decrease linearly within the boundary layer". Note that linear flux profiles are only valid for moist conserved thermodynamic variables. This is now stated only implicitly. If the fluxes of conserved variables are linear with height this means that the shape of the vertical profile of the mean state is constant in time. Well-mixedness is not a necessary constraint here: d/dz d/dt X_mean = d/dt d/dz X_mean =  - d/dz d/dz w'X' = 0 for a linear flux profiles (the term in the middle indicates the shape of the vertical profile is constant in time).   

 

The discussion on optically thin clouds is interesting. I would like to mention the works of Stephens (1978) or Slingo et al. (1982) who showed the relation between the LWP and the downwards emissivity being discussed in the study. It would also be nice to mention that this regime is commonly present, which would strengthen the discussion, for example Leahy et al. (On the nature and extent of optically thin marine low clouds, JGR, 2012). 

One additional issue to consider is that thin clouds may appear broken, in which case the assumptions of the MLM may break down. This possibility should be discussed further.

Deardorff's entrainment relation (7) parameterization. Note that Van Zanten et al. (1999) write about Deardorff's (1976) constant: "The value of Add1 is not constant (we found an order of magnitude variation) with respect to all types of convective boundary layers, so the closure is rejected.". Perhaps the equation that introduced the factor k*  can be omitted as it is not applied directly in the study, but instead the other entrainment efficiency factor A, which is not constant (Eq. 25). 

A weak point of the study is that solar radiation is not taken into account. Solar radiation  constitutes a key radiative forcing. The absorption of solar radiation strongly impacts cloud dynamics, as it reduces the effect of longwave radiative cooling. I can imagine that it may have an impact on  the results. 

Fig. 3c analyzes the influence of free tropospheric humidity on the feedback factor m by halving or doubling the value of the humidity jump across the inversion. Line 375 summarizes the findings:  "Further, we showed that increasing free-tropospheric humidity strengthens negative cloud-water adjustments, in contrast to modeling by Glassmeier et al. (2021), but in agreement with Chun et al. (2023) and our companion paper (Chen et al., 2024a)." Dussen et al. (2015) also found that the inversion humidity jump strongly affects the (equilibrium) LWP and inversion height. With respect to the latter I have difficulties to understand how the experiment in the study was set-up. Is it just a matter of changing the humidity jump Dqt in the entrainment parameterization while keeping the rest the same? 

De Roode, S. R., Siebesma, A. P., Dal Gesso, S., Jonker, H. J., Schalkwijk, J., & Sival, J. (2014). A mixed‐layer model study of the stratocumulus response to changes in large‐scale conditions. Journal of Advances in Modeling Earth Systems, 6(4), 1256-1270.

Van der Dussen, J. J., S. R. De Roode, S. Dal Gesso, and A. P. Siebesma. "An LES model study of the influence of the free tropospheric thermodynamic conditions on the stratocumulus response to a climate perturbation." Journal of Advances in Modeling Earth Systems 7, no. 2 (2015): 670-691

Leahy, L. V., R. Wood, R. J. Charlson, C. A. Hostetler, R. R. Rogers, M. A. Vaughan, and D. M. Winker. "On the nature and extent of optically thin marine low clouds." Journal of Geophysical Research: Atmospheres 117, no. D22 (2012).

Vanzanten, M. C., Duynkerke, P. G., & Cuijpers, J. W. (1999). Entrainment parameterization in convective boundary layers. Journal of the atmospheric sciences, 56(6), 813-828.

Summary:

In this paper, the author’s examine the relationship between liquid water path (L) and cloud droplet number concentration (N) in the DYCOMS-II nocturnal stratocumulus case using an entrainment parameterization from Deardorff (1976), a partitioning of the buoyancy flux profile into contributions from surface fluxes, entrainment fluxes, long-wave radiation, and precipitation, and a slope parameter (m = dlog(L)/dlog(N)). The mixed-layer model assumes well-mixed boundary layers; therefore, the analysis is restricted to non-precipitating or weakly precipitating profiles. The mixed-layer analysis finds that at low N, the major driver of negative L adjustments is precipitation (virga). At high N, decreased sedimentation velocities increase droplet residence times near cloud top and result in greater entrainment and negative L. At low L (less than 30 g/m²), an increase in droplet size can cause negative L through more efficient long-wave cooling (which enhances entrainment). Overall, L adjustments tend to be strongly negative for N = 10-100 cm^-3 and tail off to smaller values at very high N (1000 cm^-3), which differs from the steady-state m in Glassmeier et al. (2021).

Main comments:

The writing is thorough and technical, but at times hard to digest. I would suggest a title change, as one of the main results of the paper pertains to the effects of precipitating condensate on the mixed-layer state. I find reduced-order approaches such as the MLM outlined in this paper to be attractive and helpful in teasing out causality, but I question just how many “real” environments the results may apply to. If I am not mistaken, all of the L-N phase space is explored from a single research flight with fixed surface fluxes, moisture/energy jumps, and boundary layer depth. Some of these imposed environments may be very unlikely to occur in nature. It would be beneficial to the reader to see some connection between the DYCOMS-II case (perhaps even a few LES cases probing the L-N phase space) and MLM results. For example, how do entrainment rates in the MLM compare to the field campaign (or buoyancy flux profiles from the LES)? It would be nice to see some exercise to constrain the behavior of the MLM and describe differences between the idealized and observed profiles. 

It is stated within the conclusions that “This study was built upon the assumption that an increase in entrainment rate we due to an increase in N is exactly offset by a commensurate decrease in L, resulting in the same we irrespective of N.”

This statement is at odds with Figure 1a, with the entrainment rate contours sloping with changing N. Additionally, it is not clear from Chen et al. (2024a) that this assumption is justified. In Chen et al. (2024a), the L-N phase space (L ranges from 65-95 g/m²; N ranges from 100-600 cm^-3) is much smaller than the phase space examined in this paper. Given how critical this assumption remains to the results of the paper, justification for this simplification needs to be provided within the manuscript. It’s also unclear why this assumption is necessary. In Section 2.3.2, the timescale of 18 hours to reach an equilibrium entrainment rate is mentioned, but this would require a longer time period than a single night to equilibrate. Please explain why entrainment cannot vary as a function of N. In addition to the entrainment assumption, it seems odd to fix the boundary layer depth in the MLM. Is there a reason the moisture and energy equations are decoupled from the mass budget?  

Minor comments:

 1. Line 6: “At higher N, the cessation”… here and on line 370, I would recommend not using “cessation”, as sedimentation continues to exist, it is just smaller. 

2. Line 23: It may be useful to mention the diurnal cycle of LWP (Wood et al., 2002). Recent LES of polluted environments have shown larger diurnal variability of LWP (at nearly constant N). It’s important to consider how the diurnal cycle of entrainment rate/buoyancy flux may influence the interpretation of m. Additionally, it may be worth noting that the free troposphere can act as a source of N, complicating a clean relationship between the entrainment rate and the liquid water response (Chun et al., 2023).   

3. Line 55: The boundary-layer depth mass budget can also depend on horizontal advection of ht (Caldwell et al., 2005). 

4. Line 217: This may need to be quantified. What value of negative cloud-base buoyancy flux was used to determine decoupling? 

5. Line 226: Why is a cloud-base precipitation rate necessary to omit cases if we only care about decoupling? If a precipitating case remains fairly well-mixed (no significant negative cloud-base buoyancy flux) there is no need to get rid of that profile. 

6. Line 232: A decrease in the buoyancy jump does not necessarily guarantee an increase in entrainment rate. Stronger buoyancy jumps can be created by more effective long-wave cooling (McMichael et al., 2019). Also, low cloud fraction environments may have diffuse inversion layers but reduced entrainment in the absence of radiatively- and evaporatively-driven turbulence.

7. Line 270: Negative buoyancy near cloud base may not guarantee a decrease in entrainment, but may aid in decoupling. Turbulence production near cloud-top is the more critical quantity. 

8. Lines 336-341: This paragraph makes it seem like the diurnal cycle was taken into consideration. I would recommend emphasizing the diurnal uncertainties that still exist in m. 

References:

Wood, R., C. S. Bretherton, and D. L. Hartmann, Diurnal cycle of liquid water path over the subtropical and tropical oceans, Geophys. Res. Lett., 29(23), 2092, doi:10.1029/2002GL015371, 2002.

McMichael LA, Mechem DB, Wang S, Wang Q, Kogan L, Teixeira J. Assessing the mechanisms governing the daytime evolution of marine stratocumulus using large-eddy simulation. Q J R Meteorol Soc. 2019; 145: 845–866. https://doi.org/10.1002/qj.3469