| 17 Jul 2025
Entrainment and the tropical tropospheric thermal structure in global climate models
Abstract. The observed relationship between stability and humidity in the tropical troposphere has been argued to be strongly influenced by moist convective entrainment (Palmer and Singh, 2024). In this study, we investigate this relationship in fourteen models from phase 6 of the Coupled Model Intercomparison Project with the aim of evaluating their representation of such entrainment processes.
We define a diagnostic of convective entrainment using the climatological slope of the relationship between measures of lower-tropospheric stability and humidity in precipitating regions of the tropics. While some models reproduce the sign of this slope as estimated from reanalyses, others produce weak or opposing relationships between stability and humidity, implying unphysical entrainment rates. We relate these contrasting behaviours to aspects of the models’ convection schemes; models that employ plume-based cloud models and traditional “CAPE” closures, where convection is assumed to remove cloud buoyancy over a specified timescale, tend to better reproduce reanalyses.
We also explore the use of the stability-humidity relationship to constrain projections of extremes in convective available potential energy (CAPE) and boundary-layer moist static energy (MSE). These quantities have been argued to be influenced by convective entrainment and are relevant to intense thunderstorms and humid heatwaves, respectively. We find that models that quantitatively reproduce the stability-humidity relationship in reanalyses tend to produce higher increases in CAPE and boundary-layer MSE under warming. However, due to observational uncertainties and model scatter, no strong emergent constraint is found.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Weather and Climate Dynamics.
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This is a great paper which builds upon theoretical and observational insights in a prior piece (Palmer and Singh, 2024) to develop a process-oriented diagnostic (POD) for convective entrainment in climate models. Reading the paper, I was very impressed that the POD was able to (at least somewhat) differentiate between models' differing representations of convection (e.g., their cloud model/trigger).
I have a few minor comments related to the details of the methodology, and presentation, but want to reiterate that this is a very impressive piece of work.
On Equation (2):
I may be missing something, but I don't really follow how you get Equation (2). If I was to integrate Eq. (1) between two pressure levels, I would have:
dh*/dz = -ε L (q*-q)
∫ (dh*/dz) dz= -ε L ∫ (q*-q) dz = -ε L ∫ (q*-q) ( (-Ra T )/ (p g ) ) dp
where the second equality comes from hydrostatic balance & the ideal gas law. I'm not entirely sure how you get from this to the right hand side of Eq. (2). A few more steps would be appreciated.
Assorted clarifications/comments
Are you using daily data for CMIP6? Could the diurnal cycle be playing a role?
L110, when introducing the axis ratio, it would be helpful to state that a 'stronger relationship'='larger axis ratio'
For the scatter plots, please remove the lines behind the markers in the legend key, and make the markers bigger (it's difficult to read them at the moment). For the zero-entrainment lines in the scatter plots, please use "zorder=-10" to put that line behind the scatter points. Also, could you please put the Pearson correlation coefficient/p-value in all scatter plots?
It would be more intuitive to flip the axes in Figures 6 and 7.
Is there a way to measure the uncertainty in your POD of convective entrainment? For example, the CCCma has negative εd but I imagine this is not statistically different from zero (eyeballing the pdf in Fig 3)? I have a similar skepticism of MPI-ESM-LR's/MIROC6's εd values. Could you bootstrap the slope estimates and give some measure of the uncertainty that way?