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15 October 2013 [Publications]
Precipitation, friction and wind in JAS

The key physical parameters governing frictional dissipation in a precipitating atmosphere. Journal of the Atmospheric Sciences, 70, 2916-2929. [на англ. яз.] Abstract. PDF (0.8 Mb).

Complex condensation-induced dynamics

For those of our readers who are far from the problems of atmospheric dynamics, we explain below how this paper contributes to the biotic regulation concept. The humanitarian aspect of our scientific activity comprises our hope for our quantitative results to help persuade the humanity that natural ecosystems constitute an indispensable pre-requisite for the existence of our civilization. Biotic pump of atmospheric moisture, which supplies forest-covered continents with moisture, is among the most conspicuous and important examples of biotic regulation.

Condensation-induced atmospheric dynamics is the physical basis of the biotic pump: where condensation occurs the air pressure drops which brings about winds bringing moisture to the condensation area. In our previous work on this topic "Where do winds come from?" we showed that the theoretical estimate of the global circulation power obtained for condensation-driven winds is in excellent agreement with observations. Thus, condensation-induced dynamics is the only theoretical concept currently in existence which gives a quantitative answer to the following question: why is the wind power on Earth about 1% of the power of solar radiation? Lorenz considered this question to be one of the key problems for the theory of atmospheric circulation.

However, besides a pressure fall, condensation of atmospheric water vapor is accompanied by precipitation of liquid and solid particles--droplets, snowflakes, hailstones-- that appear during condensation. In principle, this process could significantly reduce the power of condensation-driven winds. For the physical basis of the biotic pump to remain quantitatively sound, it is necessary to investigate how precipitation impacts atmospheric circulation.

Let us use some pictures to explain how precipitation could interfere with air circulation. Air circulation which includes an area of ascent can be compared to a working escalator. In Fig. A the air circulates without condensation. Cumulative masses of the ascending and descending air volumes are equal -- as are equal masses of the ascending and descending parts of an empty (people-free) escalator. The power of the gravity force that impedes the circulation in the ascending branch (it pulls the rising air down) is equal in magnitude to the opposite power of the gravity force in the descending branch. Here gravity facilitates air motion: it pulls the sinking air down. Thus the motor which drives the escalator (air) does not have to work against gravity. It only must compensate the friction losses that are highest at the Earth's surface.

Air circulation as an escalator
Air circulation without condensation (A) and with condensation (B). Gray squares are the air volumes, which in case (B) contain water vapor shown by small blue squares inside gray ones. White squares indicate those air volumes that have lost their water vapor owing to condensation. Blue arrows at the Earth's surface represent evaporation that replenishes the store of water vapor in the circulating air.

On Fig. B we can see a circulation accompanied by water vapor condensation (water vapor is shown by blue squares). At a certain height water vapor condenses leaving the gaseous phase, while the remaining air continues to circulate deprived of water vapor (this depletion is shown by empty white squares): it first rises and then descends. As one can see, in such a circulation total mass of the rising air would be larger than total mass of the descending air (cf. an escalator transporting people up). The motor driving such a circulation would not only have to compensate the friction losses, but also have to work against gravity that is acting on the ascending air.

One can see from Fig. B that the difference between the cumulative masses of the ascending and descending air parcels grows with increasing height where condensation occurs. This difference also grows with increasing amount of water vapor in the air (i.e. with increasing size of the blue squares). The dynamic power of condensation, on the other hand, is also proportional to the amount of water vapor, but it is practically independent of condensation height. Condensation height (a proxy for precipitation pathlength) grows with increasing temperature of the Earth's surface. It is shown in the paper that power losses associated with precipitation of condensate particles become equal to the total dynamic power of condensation at surface temperatures around 50 degrees Celsius. Since the observed power of condensation-driven winds is equal to the total dynamic power of condensation (the "motor") minus the power spent on compensating precipitation, at such temperatures the observed circulation power becomes zero and the circulation must stop. For commonly observed values of surface temperature these losses do no exceed 40% of condensation power and cannot arrest the condensation-induced circulation. Over 60% of condensation power is spent on friction at the Earth's surface.

As shown in the paper, previous theoretical evaluation of power losses associated with precipitation published in 2000 in the meteorological literature overestimated these losses by approximately two times because of an incorrect estimate of condensation height. To the best of our knowledge, the first estimate of the global power of precipitation was published in Gorshkov, Dol'nik (1980), see Table 1, p. 444.

For interested readers we note that the illustrated analogy between air circulation (motion of a compressible fluid) and escalators (solid bodies) naturally has some important limitations. In particular, in a real circulation the circulation's motor -- condensation -- works to re-distribute of air masses in the circulation area. In the result, in the descending branch of the circulation the surface air pressure (proportional to total mass of air in the column) becomes higher than surface pressure in the ascending branch.
Moreover, in the stationary case the large-scale air flow of the main circulation dissipates into smaller-scale turbulent eddies. Turbulent air flows work to distribute the water vapor that evaporates from the Earth's surface over the entire atmospheric column. Thus, while being a product of dissipation, these turbulent flows also perform some "useful" work by raising a certain amount of water vapor. According to our estimates (see Makarieva, Gorshkov 2007, p. 1023) approximately one half of the ascending water vapor flux owes itself to turbulent diffusion (the second half is raised by the main circulation as in Fig. B). Consequently, for common temperatures the decrease in the circulation power due to precipitation constitutes only 20% of the total dynamic power of condensation (the "motor").
Finally, the estimated decrease in the circulation power compared to the dynamic power of condensation would take place even if the droplets annihilated immediately upon their origin or fell down without interacting with the air. Frictional dissipation of precipitation per se, i.e. the formation of tiny eddies around droplets, makes a contribution to turbulent viscosity, which determines stationary wind velocities for a given circulation power.

Complex condensation-induced dynamics