| 17 Aug 2026
Maximum updraft velocity beyond CAPE: the role of boundary layer dynamics and pressure perturbations
Abstract. Deep convective updraft velocities play a key role in the Earth's climate system, influencing precipitation extremes, lightning, and the planetary energy budget. While Convective Available Potential Energy (CAPE) is widely used to explain maximum updraft velocity (wmax), CAPE is an imperfect predictor as updrafts are also influenced by entrainment, boundary layer dynamics, pressure perturbations, and condensate loading. However, the relative importance of these processes and how they interact to set wmax in individual clouds remains unclear. Here, we use equation learning to identify compact, physically interpretable relationships linking environmental and in-cloud conditions to wmax in individual tracked clouds across idealized radiative–convective equilibrium regimes spanning a range of sea surface temperatures and radiative cooling rates. For pre-storm prediction, CAPE and local mean boundary layer vertical velocity (wbl) together explain nearly half the variance in wmax across regimes (R2=0.47). While CAPE captures regime-mean differences, it has little predictive value within a single simulation. wbl is essential for capturing cloud-to-cloud variability, including the suppression of wmax even at high CAPE values. At the time of peak intensity, a simple approximate Bernoulli-like invariant combining maximum pressure perturbation and maximum cloud condensate explains 89 % of the variance (R2=0.89). The tight link between wmax and pressure perturbation supports the sticky thermals hypothesis and highlights the importance of dynamic pressure effects, often neglected in updraft theories. These results highlight wbl as an important regulator of convective intensity alongside CAPE, and demonstrate that dynamic pressure plays an important role within individual updrafts.
The authors use machine learning techniques to understand the factors controlling convective updraft velocities in deep convective clouds. They consider both environmental predictors and covariates within the cloud. Using neural-network and equation-learning techniques, they come up with a range of physically plausible connections between cloud and environment variables and maximum updraft velocity within simulated clouds.
The paper is overall well written, although some aspects of the methodology could be explained in more detail (see below). I recommend the manuscript is published subject to the comments below.
1) I appreciate that the authors have chosen simplicity and analysed RCE rather than a more complex scenario. The limitations of this are well covered in the conclusions section (although one thing not mentioned is that the mean precipitation rate does not vary as much across the RCE simulations as similar-sized regions in the tropics), but it would be useful to have some more motivation for why RCE is chosen in the introduction. At present it is just stated that RCE is used - but why is RCE a useful place to start? Are there some simplicities in this framework that are more likely to lead to interpretable results? Are there specific questions that the authors are seeking to answer that lend themselves to RCE?
2) The 1 km grid spacing is rather coarse, and is more convection permitting than resolving. Given the point is to study extreme updrafts, I think it is necessary to do some analysis on how resolution might affect the picture. Even a single simulation at half the grid spacing would help understand whether similar kinds of variables turn up as important as the resolution is changed, and this would not be particularly expensive.
3) The authors describe results for CAPE, but actually they are using the buoyancy of an entraining plume (which is approximately CAPE when epsilon = 0). This should be made a bit clearer, and it should be introduced earlier in the manuscript. It should also be explained what relative humidity is used for the calculation (mean over the 10x10 boxes, or over the environment or something else) and some details on the calculation should be presented. Is it the usual moist static energy approximation, or do you take into account the heat capacity, virtual, and fallout effects (as in the original Singh & O'Gorman, 2013). It is only briefly mentioned that the validation scores are similar for both non-entraining and entraining CAPE. This is a bit surprising - previous work has shown that the environmental profiles in RCE tend to follow an entraining plume, and as one increases the entrainment rate, the CAPE should increase less rapidly with warming (e.g., Singh & O'Gorman, 2015). Can the authors explain this result? Do different levels of entrainment do differently well in getting the mean w_max across the simulations?
4) The authors talk about the non-linear interaction between w_bl and CAPE, and state that w_bl does not simply act as an initial kinetic energy on top of which one can add the CAPE. But this might be consistent with a model in which the CAPE is calculated using a plume that is initialised with some temperature or moisture anomaly, such that it is already buoyant at the cloud base (and therefore has non-zero w_bl). This may non-linearly increase the CAPE, as it may change the level at which the parcel/plume becomes neutrally buoyant (which would be consistent with the results for z_max). It would be interesting to see whether including such a "CAPE with boundary layer perturbation" as the relevant CAPE measure could reproduce the machine learned results. However, I am happy if the authors simply bring up this possibility in the manuscript.
Minor comments:
- 2.3: Cloud tracking - The methodology here needs a few more details. I don't really understand what was done here. There is a tracking algorithm based on cloud water, and a bunch of minimum criteria on volume, duration, height, lifetime, and starting height (which need to be specified). Using these alone wouldn't you get a set of tracked clouds? So what was left for the manual labelling and machine learning algorithm? Maybe I am missing something.
- Table A1/A2: Need more information about some of the features. Do you mass weight the variables in the BL from surface to 1 km? Does an overbear mean domain average, or average over the 10 km subdomain? Is the environment the entire 10 km x 10 km, or only outside the cloud mask?
- Section 2.6: What (or who) is Adam? Same with Pareto fronts. I'm sure these are very basic in the machine learning literature, but it wouldn't hurt to give a one sentence explanation of what they are and how one uses them to choose the optimal number of features.
- 3.1.1: Until now I assumed CAPE was an adiabatic parcel, but now I find out it is the buoyancy of an entraining plume.
- 3.1.2: Does using both z_max and w_bl improve the validation scores substantially? Or is using either one enough.
- page 15, second last paragraph: I think this becomes clear later, but the larger cloud condensate and latent heating could be a result of stronger w_max rather than a cause. Thus the better prediction from qc compared to buoyancy might be because stronger updrafts produce more condensation, and it happens to fast for the condensate to turn into rain, so the cloud condensate is very large.
- 3.2.2: In the discussion of slippery versus sticky thermals, my understanding was that the original Sherwood paper was talking primarily about entrainment diluting the momentum of updrafts. They argued that certain vortex structures could avoid this momentum dilution even when the mixing was large. This is different to whether or not there is large form drag from pressure gradients. This would be useful to clarify in this discussion, as I don't think this is well appreciated.
- Fig. 9: I don't understand how panel b is calculated. How is the linear fit done? Is it the Eulerian change at the level of w_max that is estimated?