Convergence, Shrinking and Implosion
Divergence, Expansion and Explosion
during Condensation

A. M. Makarieva, V. G. Gorshkov, 15 October 2013.

Some confusion apparently continues to surround the question of whether condensation lowers local pressure (and hence leads to convergence towards the condensation area) or whether it leads to a rise in local pressure and hence divergence of air from the condensation area. Three quotes below from colleagues whose diverse attitudes towards condensation-induced dynamics span the entire spectrum of possible attitudes, provide an illustration.

Why am I growing?
Why am I growing?

"Cloud formation looks like an explosion and not like an implosion. So the expansion due to the temperature rise is clearly stronger than the pressure drop due to condensation."

"If condensation drives winds by a decreasing the number density of water vapor in the air, then as clouds form they should shrink in size due to the negative pressure. OTOH, if the release of the heat of condensation is the primary driver, they should expand. Guess what?"

"Yesterday I was gazing upon a deep blue sky when a puffy white cloud came into view. It was small, but I could notice its slow growth at the diffuse edges, which I could see due to the stark contrast to the blue background. I kept watching for a time, as it grew and grew, remembering one of the classic explanations from the conventional meteorology, that is, clouds grow as a response to "latent heat" release and ensuing expansion."

Let us try to clarify this issue.

First of all, anyone accepting that condensation occurs in the ascending air must accept -- to respect the mass conservation law -- that the air comes to the area of ascent in the lower part of the atmospheric column and leaves the area of ascent somewhere higher in the atmosphere. Independent of what drives convection and cloud formation, these processes are accompanied by both convergence and divergence.

The wide-spread view is that latent heat release drives the divergence aloft: the warm air expands and leaves the atmospheric column where the ascent occurs. This lowers hydrostatic pressure at the surface and causes convergence below the cloud. In contrast, according to condensation-induced dynamics, condensation lowers pressure at the surface as the water vapor leaves the gaseous phase. This causes convergence in the lower part of the atmosphere, of which the divergence aloft is an indispensable consequence. It is caused dynamically and would take place irrespective of whether latent heat remains within the column (if the ascent is adiabatic) or not (if it is diabatic).

While the first view is indeed wide-spread, it can be better characterized as a kind of vox populi rather than a professional consensus. Indeed, in the meteorological literature it is debated. The following questions are considered: (A) Is the potential energy associated with latent heat release sufficient to drive the circulation leading to deep convection or, alternatively, (B) Is convection driven dynamically by surface pressure gradients that are associated with surface temperature gradients (see, e.g., Back and Bretherton (2009) for a discussion). Condensation-driven dynamics partially supports view B and quantifies these surface pressure gradients -- although showing that they are not related to surface temperature and can exist on a horizontally isothermal surface as well.

Thus, when we are looking at a growing puffy cloud we should keep at least two things in mind. First, when the cloud grows in the horizontal dimension it means that its convergence zone expands -- i.e. the low pressure zone at the surface grows, allowing for a more extensive convergence. In other words, when the cloud becomes thicker while growing, it is not because the cloudy air continuously expands -- it is the condensation area, i.e the area of convergence ("shrinking", "implosion"), that is growing. This is illustrated very well in the following animated picture taken from the University of Albany web site.

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Stages of deep convection.

As we can see, early in its life the cloud expands in all directions, meanwhile the air continues to converge towards the (growing) condensation area. This process is at the core of condensation-induced dynamics: as condensation occurs and local pressure drops, this initiates convergence and ascent. They, in their turn, feedback positively on condensation intensity, such that the air pressure lowers further, convergence becomes more extensive and so on -- as long as there is enough water vapor around to feed the process.

Another point to consider -- and this holds true for quasi-stationary clouds as well -- is that condensation intensity declines with height following the decrease in the partial pressure of atmospheric water vapor (see, for example, Fig. 2 here and Fig. 4f here). Therefore, according to condensation-induced dynamics, the intensity of convergence ("shrinking", "implosion") should be maximal immediately below the cloud base and then decline with growing height. This agrees well with observations.

On the other hand, the conventional latent-heat-based line of thought presumes that if the air ascends moist adiabatically it becomes warmer than the surroundings only above the level of free convection (LFC). Thus, despite latent heat is being released most rapidly near the cloud base (where condensation intensity is at its maximum), this does not immediately make the ascending air warmer than its surroundings and does not help the air expand (diverge, explode) until it reaches the LFC. So even the conventional wisdom prohibits such an expansion.

Furthermore, as one can see in the animation, even above the LFC convergence dominates in most part of the atmospheric column despite, as indicated by the isotherms, the cloudy air is apparently warmer than the surroundings. This shows that the low pressure caused by condensation spreads upwards up to a few kilometers in the atmosphere, see Makarieva et al. (2013), Fig. 1c. This prevents the rising air from divergence, which is therefore confined to the upper atmospheric layers where condensation is minimal. As soon as condensation discontinues during the later stages of cloud development, the divergence aloft markedly intensifies eventhough the air is no longer warmer than the surroundings. All these processes are consistent with the dominating dynamical role of condensation-induced pressure drop over latent heat release. (Note also that the air flow can transport condensate particles well outside the area where condensation actually occurs.)

Convective clouds
Cloud formation in June approx. 70oN. Left photo: local time 21:53, a second high cloud starts to develop to the left of the one already formed. Right photo: the same system 45 minutes later. One can see an outflow formed by the second cloud.

We conclude that without a somewhat deeper quantitative understanding of the dynamic processes accompanying condensation it is not possible to meaningfully interpret even the very common every-day observations like those of cloud formation.

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