| 24 Jul 2026
A global assessment of warm-phase convective invigoration from aerosol-cloud interactions. Part 1: Theory
Abstract. The theory of warm-phase convective invigoration from aerosol-cloud interactions posits that polluted cloud updrafts consume supersaturation more readily, causing them to release latent heat sooner and attain larger buoyancies and updraft speeds. An analytical model is developed to predict how much this mechanism changes cloud-updraft speeds when the cloud-droplet number concentration increases but the meteorological environment is fixed. For any perturbation in cloud-droplet number concentration, the model predicts an optimal updraft speed for warm-phase invigoration. Updrafts that are much slower than the optimal value experience invigoration that is directly proportional to the non-polluted updraft speed. In contrast, updrafts that are much faster than the optimal value experience a powerful feedback mechanism that resists invigoration due to changes in the drag force. For typical atmospheric conditions, shallow convective updrafts are generally closer to the optimal updraft speed than deep convective updrafts, making shallow convective clouds more susceptible to warm-phase invigoration. These predictions constrain the conditions under which substantial warm-phase invigoration can be expected to occur in nature.
I find this to be an interesting and valuable study that develops a theoretical framework for understanding warm-phase convective invigoration due to aerosol–cloud interactions. Given the complexity of the problem and the substantial remaining knowledge gaps in our understanding of cloud dynamics, entrainment, and the coupling between cloud microphysics and dynamics, an analytical treatment of this kind necessarily requires simplifying assumptions. I therefore do not regard the use of such assumptions as a weakness in itself. However, some of the assumptions required to make the problem analytically tractable also enter directly into the mechanisms controlling the predicted magnitude of invigoration. I am therefore concerned that the consequences of some of these assumptions are not yet sufficiently quantified. In particular, the assumptions concerning entrainment and the representation of thermal drag appear potentially important for the main conclusions. I think the manuscript would be considerably strengthened if the authors clarified their physical basis and quantified the sensitivity of the results to relaxing them.
1-Â The assumption that clean and polluted thermals have identical fractional entrainment rates is an imposed closure and is important because it leads directly to equal MSE at a given height and hence Eq. (1). Established entrainment theory allows fractional entrainment to depend on cloud radius, updraft velocity, and exchange across the cloud boundary; organized entrainment can also depend on (1/w)\partial w/\partial z. Thus, although an increase in w does not necessarily imply a particular change in \epsilon, the aerosol-induced changes in buoyancy, velocity, and acceleration could themselves modify entrainment.
This is potentially important because dynamically induced entrainment provides a negative feedback on updraft acceleration, i.e. increased buoyancy and acceleration may enhance environmental inflow and dilution, thereby opposing the increase in w. Prescribing \hat{\epsilon}=\epsilon removes this possible feedback from the theory. I therefore suggest that the authors not only justify this assumption, but propagate uncertainty in \hat{\epsilon}/\epsilon through the derivation to the final predicted \Delta w. This would establish whether the main invigoration results remain robust when the entrainment response is allowed to differ between clean and polluted thermals.
2- The treatment of drag also requires further justification. The manuscript varies prescribed values of c_d, but assumes the same c_d for clean and polluted thermals despite predicting \hat w\neq w. Romps and Öktem (2015) show that the wave-drag component of the effective drag coefficient depends on the Froude number F=w/(Nr), and therefore on w, r, and stratification. They also show regimes in which wave-drag magnitude decreases with increasing w, whereas constant c_d produces drag proportional to w^2.
Since the negative drag feedback at large w is central to the conclusions, could the authors justify treating c_d as invariant or test the sensitivity using a velocity-dependent c_d(F)? In addition, the time-dependent momentum equation does not appear to include the added-mass effect considered by Romps and Öktem (2015), i.e. it is missing the effective-inertia factor of 3/2 for a spherical thermal. This term does not affect the terminal steady-state solution, but it would modify the transient adjustment timescale and therefore the adjustment length used to justify the steady-state approximation. Could the authors clarify the omission of this term?