Trabajo de los rusos.pdf

Atmos. Chem. Phys., 13, 10391056, 2013www.atmos-chem-phys.net/13/1039/2013/doi:10.5194/acp-13-1039-2013 Author(s) 2013. CC Attribution 3.0 License.

AtmosphericChemistry

and Physics

Where do winds come from? A new theory on how water vaporcondensation influences atmospheric pressure and dynamicsA. M. Makarieva1,2, V. G. Gorshkov1,2, D. Sheil3,4,5, A. D. Nobre6,7, and B.-L. Li21Theoretical Physics Division, Petersburg Nuclear Physics Institute, 188300, Gatchina, St. Petersburg, Russia2XIEG-UCR International Center for Arid Land Ecology, University of California, Riverside, CA 92521, USA3School of Environment, Science and Engineering, Southern Cross University, P.O. Box 157, Lismore, NSW 2480, Australia4Institute of Tropical Forest Conservation, Mbarara University of Science and Technology, Kabale, Uganda5Center for International Forestry Research, P.O. Box 0113 BOCBD, Bogor 16000, Indonesia6Centro de Ciencia do Sistema Terrestre INPE, Sao Jose dos Campos SP 12227-010, Brazil7Instituto Nacional de Pesquisas da Amazonia, Manaus AM 69060-001, Brazil

Correspondence to: A. M. Makarieva ([email protected]) and D. Sheil ([email protected])

Received: 5 August 2010 Published in Atmos. Chem. Phys. Discuss.: 15 October 2010Revised: 29 April 2011 Accepted: 3 December 2012 Published: 25 January 2013

Abstract. Phase transitions of atmospheric water play aubiquitous role in the Earths climate system, but their directimpact on atmospheric dynamics has escaped wide attention.Here we examine and advance a theory as to how conden-sation influences atmospheric pressure through the mass re-moval of water from the gas phase with a simultaneous ac-count of the latent heat release. Building from fundamentalphysical principles we show that condensation is associatedwith a decline in air pressure in the lower atmosphere. Thisdecline occurs up to a certain height, which ranges from 3to 4 km for surface temperatures from 10 to 30 C. We thenestimate the horizontal pressure differences associated withwater vapor condensation and find that these are comparablein magnitude with the pressure differences driving observedcirculation patterns. The water vapor delivered to the atmo-sphere via evaporation represents a store of potential energyavailable to accelerate air and thus drive winds. Our estimatessuggest that the global mean power at which this potentialenergy is released by condensation is around one per cent ofthe global solar power this is similar to the known station-ary dissipative power of general atmospheric circulation. Weconclude that condensation and evaporation merit attentionas major, if previously overlooked, factors in driving atmo-spheric dynamics.

1 Introduction

Phase transitions of water are among the major physical pro-cesses that shape the Earths climate. But such processeshave not been well characterized. This shortfall is recognizedboth as a challenge and a prospect for advancing our un-derstanding of atmospheric circulation (e.g., Lorenz, 1983;Schneider, 2006). In A History of Prevailing Ideas about theGeneral Circulation of the Atmosphere Lorenz (1983) wrote:

We may therefore pause and ask ourselveswhether this step will be completed in the man-ner of the last three. Will the next decade see newobservational data that will disprove our presentideas? It would be difficult to show that this can-not happen.Our current knowledge of the role of the variousphases of water in the atmosphere is somewhat in-complete: eventually it must encompass both ther-modynamic and radiational effects. We do not fullyunderstand the interconnections between the trop-ics, which contain the bulk of water, and the re-maining latitudes . . . Perhaps near the end of the20th century we shall suddenly discover that weare beginning the fifth step.

Deluc (1812, p. 176) mentioned that conversion of watervapor to rain creates a kind of airfree space that may cause

Published by Copernicus Publications on behalf of the European Geosciences Union.

1040 A. M. Makarieva et al.: Condensation-induced atmospheric dynamics

wind gusts. Lorenz (1967, Eq. 86), as well as several otherauthors after him (Trenberth et al., 1987; Trenberth, 1991;Gu and Qian, 1991; Ooyama, 2001; Schubert et al., 2001;Wacker and Herbert, 2003; Wacker et al., 2006), recognizedthat local pressure is reduced by precipitation and increasedby evaporation. Qiu et al. (1993) noted that the mass de-pletion due to precipitation tends to reduce surface pressure,which may in turn enhance the low-level moisture conver-gence and give a positive feedback to precipitation. Van denDool and Saha (1993) labeled the effect as a physically dis-tinct water vapor forcing. Lackmann and Yablonsky (2004)investigated the precipitation mass sink for the case of Hur-ricane Lili (2002) and made an important observation thatthe amount of atmospheric mass removed via precipitationexceeded that needed to explain the model sea level pressuredecrease.

Although the pressure changes associated with evapora-tion and condensation have received some attention, the in-vestigations have been limited: the effects remain poorlycharacterized in both theory and observations. Previous in-vestigations focused on temporal pressure changes not spa-tial gradients. Even some very basic relationships remainsubject to confusion. For example, there is doubt as towhether condensation leads to reduced or to increased atmo-spheric pressure (Poschl, 2009, p. S12436). Opining that thestatus of the issue in the meteorological literature is unclear,Haynes (2009) suggested that to justify the claim of pres-sure reduction one would need to show that the standardapproaches (e.g., set out in textbooks such as Thermody-namics of Atmospheres and Oceans by Curry and Webster,1999) imply a drop in pressure associated with condensa-tion.

Here we aim to clarify and describe, building from basicand established physical principles, the pressure changes as-sociated with condensation. We will argue that atmosphericwater vapor represents a store of potential energy that be-comes available to accelerate air as the vapor condenses.Evaporation, driven by the sun, continuously replenishes thestore of this energy in the atmosphere.

The paper is structured as follows. In Sect. 2 we analyzethe process of adiabatic condensation to show that it is al-ways accompanied by a local decrease of air pressure. InSect. 3 we evaluate the effects of water mass removal andlapse rate change upon condensation in a vertical air col-umn in approximate hydrostatic equilibrium. In Sect. 4 weestimate the horizontal pressure gradients induced by watervapor condensation to show that these are sufficient enoughto drive the major circulation patterns on Earth (Sect. 4.1).We examine why the key relationships have remained un-known until recently (Sects. 4.2 and 4.3). We evaluate themean global power available from condensation to drive thegeneral atmospheric circulation (Sect. 4.4). Finally, we dis-cuss the interplay between evaporation and condensation andthe essentially different implications of their physics for at-mospheric dynamics (Sect. 4.5). In the concluding section

we discuss the importance of condensation as compared todifferential heating as the major driver of atmospheric cir-culation. Our theoretical investigations strongly suggest thatthe phase transitions of water vapor play a far greater role indriving atmospheric dynamics than is currently recognized.

2 Condensation in a local air volume

2.1 Adiabatic condensation

We will first show that adiabatic condensation is always ac-companied by a decrease of air pressure in the local volumewhere it occurs. The first law of thermodynamics for moistair saturated with water vapor reads (e.g., Gill, 1982)dQ= cVdT +pdV +Ld, (1)

pvp 1, d

= dpv

pv dp

p. (2)

Here pv is partial pressure of saturated water vapor, p isair pressure, T is absolute temperature, Q (J mol1) is mo-lar heat, V (m3 mol1) is molar volume, L 45 kJ mol1is the molar heat of vaporization, cV = 52R is molar heatcapacity of air at constant volume (J mol1 K1), R =8.3 J mol1 K1 is the universal gas constant. The smallvalue of < 0.1 under terrestrial conditions allows us to ne-glect the influence made by the heat capacity of liquid waterin Eq. (1).

The partial pressure of saturated water vapor obeys theClausius-Clapeyron equation:

dpvpv

= dTT, L

RT, (3)

pv(T )= pv0 exp(0 ), (4)where pv0 and 0 correspond to some reference tempera-ture T0. Below we use T0 = 303 K and pv0 = 42 hPa (Bolton,1980) and neglect the dependence of L on temperature.

We will also use the ideal gas law as the equation of statefor atmospheric air:

pV = RT, (5)

dpp+ dV

V= dT

T. (6)

Using Eq. (6) the first two terms in Eq. (1) can be writtenin the following form

cVdT +pdV = RT

(dTTdp

p

),

(7) R

cp= 2

7= 0.29, cp = cV+R.

Atmos. Chem. Phys., 13, 10391056, 2013 www.atmos-chem-phys.net/13/1039/2013/

A. M. Makarieva et al.: Condensation-induced atmospheric dynamics 1041

Writing d in Eq. (1) with use of Eqs. (2) and (3) asd= dT

T dp

p(8)

and using the definition of (Eq. 3) we arrive at the followingform for the first law of thermodynamics (Eq. 1):

dQ= RT

{dTT(1+ 2)dp

p(1+ )

}. (9)

In adiabatic processes dQ= 0, and the expression inbraces in Eq. (9) turns to zero, which implies:dTT= dp

p(,), (,) 1+

1+ 2 . (10)

Note that , and are all dimensionless; and are vari-ables and is a constant, (0,0)= . This is a general de-pendence of temperature on pressure in an adiabatic atmo-spheric process that involves phase transitions of water vapor(evaporation or condensation), i.e. change of . At the sametime itself is a function of temperature as determined byEq. (8):d= dT

T dp

p= dT

T

1

= ( 1)dpp. (11)

One can see from Eqs. (10) and (11) that the adiabatic phasetransitions of water vapor are fully described by the relativechange of either pressure dp/p or temperature dT/T . For thetemperature range relevant for Earth we have L/RT18so that

1 4.3. (12)Noting that , , are all positive, from Eqs. (10), (11)

and (12) we obtain

1= 1+ 1+ 2 1=

11+ 2 > 0. (13)

Condensation of water vapor corresponds to a decrease of , d < 0. It follows unambiguously from Eqs. (11) and (13)that if d is negative, then dp and dT are negative too. Thisproves that water vapor condensation in any adiabatic pro-cess is necessarily accompanied by reduced air pressure.

2.2 Adiabatic condensation cannot occur at constantvolume

Our previous result refutes the proposition that adiabatic con-densation can lead to a pressure rise due to the release oflatent heat (Poschl, 2009, p. S12436). Next, we show thatwhile such a pressure rise was implied by calculations as-suming adiabatic condensation at constant volume, in factsuch a process is prohibited by the laws of thermodynamicsand thus cannot occur.

Using Eqs. (6), (10) and (8) we can express the relativechange of molar volume dV/V in terms of d / :dVV= 1

1d. (14)

Putting dV = 0 in Eq. (14) we obtain(1)d( 1) = 0. (15)The denominator in Eq. (15) is greater than zero, seeEqs. (12) and (13). In the numerator we note from the def-inition of (Eq. 10) that 1= 27+2 2

[5

2 +(1)]. The

expression in square brackets lacks real roots:

52

+ 2 = 0, = 12

(1 i

10

), 1. (16)

In consequence, Eq. (15) has a single solution d=0. Thisproves that condensation cannot occur adiabatically at con-stant volume.

2.3 Non-adiabatic condensation

To conclude this section, we show that for any process whereentropy increases, dS=dQ/T>0, water vapor condensation(d


will now explore the consequences of condensation for thevertical air column.

Most circulation patterns on Earth are much wider thanthey are high, with the ratio height/length being in the orderof 102 for hurricanes and down to 103 and below in largerregional circulations. As a consequence of mass balance, ver-tical velocity is smaller than horizontal velocities by a similarratio. Accordingly, the local pressure imbalances and result-ing atmospheric accelerations are much smaller in the verti-cal orientation than in the horizontal plane, the result beingan atmosphere in approximate hydrostatic equilibrium (Gill,1982). Air pressure then conforms to the equation

dpdz= g, p(0) ps = g

0

(z)dz. (19)

Applying the ideal gas equation of state (Eq. 5) we have fromEq. (19)dpdz=p

h, h RT

Mg. (20)

This solves as

p(z)= ps exp

z0

dz

h(z)

. (21)Here M is air molar mass (kg mol1), which, as well as tem-perature T (z), in the general case also depends on z.

The value of ps (Eq. 19), air pressure at the surface, ap-pears as the constant of integration after Eq. (19) is integratedover z. It is equal to the weight of air molecules in the at-mospheric column. It is important to bear in mind that psdoes not depend on temperature, but only on the amount ofgas molecules in the column. It follows from this observa-tion that any reduction of gas content in the column reducessurface pressure.

Latent heat released when water condenses means thatmore energy has to be removed from a given volume of satu-rated air for a similar decline in temperature when comparedto dry air. This is why the moist adiabatic lapse rate is smallerthan the dry adiabatic lapse rate. Accordingly, given one andthe same surface temperature Ts in a column with rising air,the temperature at some distance above the surface will beon average higher in a column of moist saturated air than ina dry one.

However, this does not mean that at a given height air pres-sure in the warmer column is greater than air pressure in thecolder column (cf. Meesters et al., 2009; Makarieva and Gor-shkov, 2009c), because air pressure p(z) (Eq. 21) dependson two parameters, temperature T (z) and surface air pres-sure (i.e., the total amount of air in the column). If the totalamount of air in the warmer column is smaller than in thecolder column, air pressure in the surface layer will be lowerin the warmer column despite its higher temperature.

In the following we estimate the cumulative effect of gascontent and lapse rate changes upon condensation.

3.2 Moist adiabatic temperature profile

Relative water vapor content (Eq. 2) and temperature T de-pend on height z. From Eqs. (10), (11) and (20) we have

dTdz 0 = T

h, 1+

1+ 2 , (22)

1

ddz= 1

h 1

1+ 21h. (23)

Equation (22) represents the well-known formula for a moistadiabatic gradient as given in Glickman (2000) for small < 0.1. At = 0 we have (,)= and 0d =Mdg/cp =9.8 K km1, which is the dry adiabatic lapse rate that is in-dependent of height z, Md = 29 g mol1. For moist saturatedair the change of temperature T and relative partial pressure of water vapor with height is determined by the system ofdifferential equations (Eqs. 22, 23).

Differentiating both parts of the Clapeyron-Clausius equa-tion (Eq. 3) over z we have, see Eq. (22):

dpvdz

=pvhv

, hv RT2

L0= T

0= h

,

(24)pv(z)= pvs exp

z

0

dz

hv

, pvs pv(0).The value of hv represents a fundamental scale height for thevertical distribution of saturated water vapor. At Ts = 300 Kthis height hv is approximately 4.5 km.

Differentiating both parts of Eq. (2) over z with use ofEqs. (20) and (24) and noticing that hv=h/() we have

1

ddz

= 1pv

dpvdz

1p

dpdz= 1

hv 1h 1

h,

h hvhhhv . (25)

This equation is equivalent to Eq. (23) when Eqs. (22)and (24) are taken into account. Height h represents thevertical scale of the condensation process. Height scales hv(Eq. 24) and h (Eq. 25) depend on (,) (Eq. 22) and,consequently, on . At Ts = 300 K height h 9 km, inclose proximity to the water vapor scale height described byMapes (2001).

3.3 Pressure profiles in moist versus dry air columns

We start by considering two static vertically isothermal at-mospheric columns of unit area, A and B, with temperatureT (z)= Ts independent of height. Column A contains moistair with water vapor saturated at the surface, column B con-tains dry air only. Surface temperatures and surface pressures



, km , K , km

hnHzL d psHTsL pAHzL - pBHzL , hPa, hPa, kmhHzL , kmhvHzL, km Ts 303 K

Ts 293 KTs 283 K

0 2 4 6 8 10 12 14z

0

2

4

6

8

10

12

14HaL

260 270 280 290 300 310Ts

0

10

20

30

40 HbL

0 2 4 6 8z

-40

-30

-20

-10

0

10

20

30

40 HcL

Fig. 1. (a) Scale height of saturated water vapor hv(z) (Eq. 24), hydrostatic scale height of water vapor hn(z) (Eq. 26), and scale height ofmoist air h(z) (Eq. 20) in the column with moist adiabatic lapse rate (Eq. 22) for three values of surface temperature Ts; (b) condensation-induced drop of air pressure at the surface (Eq. 27) as dependent on surface temperature Ts; (c) pressure difference versus altitude z betweenatmospheric columns A and B with moist and dry adiabatic lapse rates, Eqs. (30) and (31), respectively, for three values of surface temperatureTs. Height zc at which pA(zc)pB(zc)=0 is 2.9, 3.4 and 4.1 km for 283, 293 and 303 K, respectively. Due to condensation, at altitudes belowzc the air pressure is lower in column A despite it being warmer than column B.

in the two columns are equal. In static air Eq. (19) is exactand applies to each component of the gas mixture as wellas to the mixture as a whole. At equal surface pressures, thetotal air mass and air weight are therefore the same in bothcolumns. Water vapor in column A is saturated at the surface(i.e., at z= 0) but non-saturated above it (at z > 0). The sat-urated partial pressure of water vapor at the surface pv(Ts)(Eq. 4) is determined by surface temperature and, as it is inhydrostatic equilibrium, equals the weight of water vapor inthe static column.

We now introduce a non-zero lapse rate to both columns:the moist adiabatic 0 (Eq. 22) to column A and the dry adia-batic 0d in column B. (Now the columns cannot be static: theadiabatic lapse rates are maintained by the adiabatically as-cending air.) Due to the decrease of temperature with height,some water vapor in column A undergoes condensation. Wa-ter vapor becomes saturated everywhere in the column (i.e.,at z0), with pressure pv(z) following Eq. (24) and densityv=pvMv/(RT )pv/(ghn) following

v(z)= v(Ts) hnshn(z)

exp

z

0

dz

hv(z)

,(26)

v(Ts) pv(Ts)ghn(Ts)

, hn RT (z)Mvg

, T (z)= Ts0z.

Here hn(z) is the scale height of the hydrostatic distributionof water vapor in the isothermal atmosphere with T (z)=Ts.

The change in pressure ps in column A due to water va-por condensation is equal to the difference between the initialweight of water vapor pv(Ts) and the weight of saturated wa-ter vapor:

ps = pv(Ts) g

0

v(z)dz pv(Ts) v(Ts)ghv(Ts)

= pv(Ts)(

1 hvshns

)= pv(Ts)

(1 MvgTs

L0s

). (27)

The inequality in Eq. (27) represents a conservative estimateof ps due to the approximation hv(z)=hv(Ts) made whileintegrating v(z) (26). As far as hv(z) declines with heightmore rapidly than hn(z), Fig. 1a, the exact magnitude ofthis integral is smaller, while the value of ps is larger. Thephysical meaning of estimate (Eq. 27) consists in the factthat the drop of temperature with height compresses the wa-ter vapor distribution hns/hvs-fold compared to the hydro-static distribution (Makarieva and Gorshkov, 2007, 2009a;Gorshkov et al., 2012).

The value of ps (Eq. 27) was calculated as the differ-ence between the weight per unit surface area of vapor inthe isothermal hydrostatic column and the weight of watervapor that condensed when a moist adiabatic lapse rate wasapplied. This derivation can also be understood in terms ofthe variable conventionally called the adiabatic liquid watercontent (e.g., Curry and Webster, 1999, Eq. 6.41). We canrepresent the total mixing ratio of moisture (by mass) as qt qv+ql = (v+l)/, where v is the mass of vapor and l isthe mass of liquid water per unit air volume; qt1. The totaladiabatic liquid water content in the column equals the inte-gral of ql over z at constant qt, ql = qtqv = qtv.The value of ps (Eq. 27) is equal to this integral (mass perunit area) multiplied by the gravitational acceleration (givingweight per unit area):

www.atmos-chem-phys.net/13/1039/2013/ Atmos. Chem. Phys., 13, 10391056, 2013


ps = g

0

qldz= g

0

qtdz

0

vdz

. (28)The first integral in braces gives the mass of vapor in theconsidered atmospheric column if water vapor were a non-condensable gas, qv=qt=const. This term is analagous to thefirst term, pv(Ts), in the right-hand side of Eq. (27), wherea static isothermal column was considered. The second termis identical to the second term, g

0 vdz, in Eq. (27).

Using the definition of hv(Ts) (Eq. 24), hn(Ts) (Eq. 26)and recalling that Mv/Md=0.62 and pv(Ts)=sps, seeEq. (4), we obtain the following expression for the ps es-timate (Eq. 27), Fig. 1b:ps

ps s

(1 0.62 1+ s

2s

s+ s2s

). (29)

Note that ps/ps is proportional to s and increases exponen-tially with the rise of temperature.

After an approximate hydrostatic equilibrium is estab-lished, the vertical pressure profiles for columns A and Bbecome, cf. Eq. (21):

pA(z)=ps(

1psps

)exp

z

0

dz

hA(z)

, hA RTMg ; (30)pB(z)= ps exp

z

0

dz

hB(z)

, hB RTdMdg . (31)Here M(z)=Md(1 )+Mv ; pv(z)/pA(z) and T (z)obey Eqs. (22) and (23), Td(z)Ts0dz.

In Fig. 1c the difference pA(z)pB(z) is plotted for threesurface temperatures, Ts=10 C, 20 C and 30 C. In all threecases condensation has resulted in a lower air pressure in col-umn A compared to column B everywhere below zc2.9, 3.4and 4.1 km, respectively. It is only above that height that thedifference in lapse rates makes pressure in the moist columnhigher than in the dry column.

3.4 Comparing forces due to condensation andbuoyancy

Fig. 1c describes the relative contributions of latent heat re-lease and the condensation vapor sink to the horizontal pres-sure differences. This result can also be illustrated by com-paring the vertical forces associated with phase transitions ofwater vapor.

The buoyant force acting per unit moist air volume can bewritten as

fB = pg(

p 1

)=

pg

(T (z)

Td(z)

11 (Mv/Md) (z) 1

).

Here p is the density of the air moist air parcel that ascendsin the environment with density . (When fB is taken per unitmass by dividing by density p and integrated over z, oneobtains the convective available potential energy (CAPE)(Glickman, 2000), which represents work performed by thebuoyant force on the rising air parcel. As work of the buoy-ant force on the air parcel that is descending dry adiabaticallyis usually negative, total energy available for a buoyancy-induced circulation can be close to zero even at large positiveCAPE (Gorshkov et al., 2012).)

Figure 2a shows the buoyant force acting on an air vol-ume from column A that rises moist adiabatically in thedry adiabatic environment of column B: p = pB(z)M/RT , = pB(z)Md/RTd. Here pB is given by Eq. (31), Td fol-lows the dry adiabatic profile Td(z)= Ts0dz, where 0d =9.8 K km1, while temperature T (z) and molar mass M(z)=Md[1 (Mv/Md) (z)] of the rising air satisfy Eqs. (22)(23). The positive value of the buoyant force at the surfaceis due to the lower molar density of the moist versus dry air.

The same figure shows the condensation pressure gradi-ent force that acts in the column where moist saturated airascends adiabatically:

fC = pvp

p

z pv

z=p

z.

Here p and conform to Eqs. (22)(23).As Fig. 2a shows, the two forces have different spatial lo-

calization. The condensation force has a maximum in thelower atmosphere where the amount of vapor is maximized.The buoyant force grows with height following the accumu-lating difference between the moist adiabatic and dry adia-batic temperatures. At Ts = 300 km at z= 8 km the differ-ence theoretically amounts to over 50 K.

The buoyant force estimated in Fig. 2 represents a the-oretical upper limit that assumes no heat transfer betweenthe ascending air and its environment. Maximum tempera-ture differences observed in the horizontal direction in realweather systems are typically much smaller than 50 K atany height. Indeed, even in the warm-core tropical storms i.e., in intense precipitation events the horizontal temper-ature difference between the core and the external environ-ment rarely exceeds a few degrees Kelvin (e.g., Knaff et al.,2000). In Fig. 2b the same forces are plotted, but for thebuoyant force estimated for an environment having a meantropospheric lapse rate of 6.5 K km1 (rather than the dryadiabatic lapse rate 9.8 K km1). As Fig. 2b shows, themagnitude of the buoyant force drops rapidly with dimin-ishing differences in temperature. Convective available po-tential energy associated with the buoyant force shown inFig. 2a is

8km0 (fB/p)dz= 8.5 103 J kg1. This figure is

several times higher than the typical values calculated fromthe lapse rate soundings of the atmospheric column below12 km height in the most intense convection events likethunderstorms and tornadoes (e.g., Thompson et al., 2003;Kis and Straka, 2010). Furthermore, in a recent comparison



0 1 2 3 4 5 6 7 8z , km

0

1

2

3

4

5

6

7

8

9

10

mba

rkmHaL

0 1 2 3 4 5 6 7 8z , km

0

1

2

3

4

5

6

7

8

9

10

mba

rkm

HbLTs 303 KTs 293 KTs 283 K

Fig. 2. Condensation force fC (solid curves) and buoyant force fB (dashed) acting at height z on a moist air volume ascending in anenvironment with dry adiabatic lapse rate 9.8 K km1 (a) and mean tropospheric lapse rate 6.5 K km1 (b) for different values of surfacetemperature Ts.

of nocturnal and diurnal tornadoes (Kis and Straka, 2010) itwas found that significant tornadoes can form at both largeand very small CAPE values, pointing to the importance ofdifferent mechanisms for the generation of intense circula-tion systems.

The key message from Fig. 2 is that the condensationforce remains comparable in magnitude to the buoyant forceeven when the latter is allowed (for the sake of argument) totake unrealistically high values. Furthermore the condensa-tion force dominates in the lower atmosphere with the buoy-ant force more pronounced only in the upper atmosphere.We note that both the buoyant and condensation forces arevertically directed. But we emphasise that their action in theatmosphere is manifested in the formation of horizontal pres-sure gradients. This follows from the independent stipulationthat the atmosphere is vertically in approximate hydrostaticequilibrium. In Sect. 4 we derive the horizontal pressure gra-dients associated with the condensation force.

4 Relevance of the condensation-induced pressurechanges for atmospheric processes

4.1 Horizontal pressure gradients associated with vaporcondensation

We have shown that condensation of water vapor producesa drop of air pressure in the lower atmosphere up to an al-titude of a few kilometers, Fig. 1c, in a moist saturated hy-drostatically adjusted column. In the dynamic atmosphericcontext the vapor condenses and latent heat is released dur-ing the ascent of moist air. The vertical displacement of airis inevitably accompanied by its horizontal displacement.This translates much of the condensation-induced pressure

difference to a horizontal pressure gradient. Indeed, as theupwelling air loses its water vapor, the surface pressure di-minishes via hydrostatic adjustment producing a surface gra-dient of total air pressure between the areas of ascent anddescent. The resulting horizontal pressure gradient is propor-tional to the the ratio of vertical to horizontal velocity w/u(Makarieva and Gorshkov, 2009b).

We will illustrate this point regarding the magnitude of theresulting atmospheric pressure gradient for the case of a sta-tionary flow where the air moves horizontally along the x-axis and vertically along the z-axis; there is no dependenceof the flow on the y coordinate. The stationary continuityequation for the mixture of condensable (vapor) and non-condensable (dry air) gases can be written as(Ndu)

x+ (Ndw)

z= 0; (32)

(Nvu)

x+ (Nvw)

z= S; (33)

S w(Nv

z Nv

N

N

z

)= wN

z, N =Nv+Nd. (34)

Here Nd and Nv are molar densities of dry air and satu-rated water vapor, respectively; Nv/N , see Eq. (2), S(Eq. 34) is the sink term describing the non-conservation ofthe condensable component (water vapor). Saturated pres-sure of water vapor depends on temperature alone. Assum-ing that vapor is saturated at the isothermal surface we haveNv/x=0, so Nv only depends on z. (This condition ne-cessitates either that there is an influx of water vapor viaevaporation from the surface (if the circulation pattern is



immobile), or that the pressure field moves as vapor is lo-cally depleted. The second case occurs in compact circula-tion patterns like hurricanes and tornadoes (Makarieva andGorshkov, 2011; Makarieva et al., 2011).) As the air ascendswith vertical velocity w, vapor molar density decreases dueto condensation and due to the expansion of the gas alongthe vertical gradient of decreasing pressure. The latter ef-fect equally influences all gases, both condensable and non-condensable. Therefore, the volume-specific rate S(x,z) atwhich vapor molecules are locally removed from the gaseousphase is equal to w[Nv/z(Nv/N)N/z], see Eqs. (1)and (2). The second term describes the expansion of vapor ata constant mixing ratio which would have occurred if vaporwere non-condensable as the other gases. (If vapor did notcondense, its density would decrease with height as a con-stant proportion of the total molar density of moist air aswith any other atmospheric gas.) Further clarification of themeaning of (Eq. 34) is provided in Sect. 4.2 below, and inAppendix A which offers additional interpretation, see also(Gorshkov et al., 2012).

The mass of dry air is conserved, Eq. (32). Using this fact,Eq. (34) and Nv/x=0 in Eq. (33) one can see that

N

(u

x+ w

z

)+wN

z= 0. (35)

Now expressing N/x=Nd/x+Nv/x from Eqs. (32)and (33) with use of Eq. (35) we obtainN

x= w

u

(Nv

z Nv

N

N

z

). (36)

Using the equation of state for moist air p=NRT and watervapor pv=NvRT we obtain from Eqs. (36) and (25):p

x=(pv

z pv

p

p

z

)w

u=p

h

w

u. (37)

Here velocities w and u represent vertical and horizontal(along x-axis) velocities of the ascending air flow, respec-tively. Scale height h is defined in Eq. (25). A closely re-lated formula for horizontal pressure gradient can be appliedto an axis-symmetric stationary flow with p/x replaced byradial gradient p/r (Makarieva and Gorshkov, 2009b).

Equation (37) shows that the difference between the scaleheights hv and h (Eq. 25) of the vertical pressure distribu-tions for water vapor and moist air leads to the appearanceof a horizontal pressure gradient of moist air as a whole(Makarieva and Gorshkov, 2007; Gorshkov et al., 2012).This equation contains the ratio of vertical to horizontal ve-locity. Estimating this ratio it is possible to evaluate, fora given circulation, what sorts of horizontal pressure gradi-ents are produced by condensation and whether these gradi-ents are large enough to maintain the observed velocities viathe positive physical feedback described by Eq. (37).

For example, for Hadley cells at h=9 km, =0.03 anda typical ratio of w/u2103 (Rex, 1958) we obtain from

Eq. (37) a pressure gradient of 0.7 Pa km1. On a distance of1500 km such a gradient would correspond to a pressure dif-ference of around 10 hPa, which is close to the upper rangeof the actually observed pressure differences in the region(e.g., Murphree and Van den Dool, 1988, Fig. 1). Similarpressure differences and gradients, also comparable in mag-nitude to ps (Eq. 27) and p/r are observed within cy-clones, both tropical and extratropical, and persistent atmo-spheric patterns in the low latitudes (Holland, 1980; Zhouand Lau, 1998; Brummer et al., 2000; Nicholson, 2000; Sim-monds et al., 2008). For example, the mean depth of Arcticcyclones, 5 hPa (Simmonds et al., 2008), is about ten timessmaller than the mean depth of a typical tropical cyclone(Holland, 1980). This pattern agrees well with the Clausius-Clapeyron dependence of ps, Fig. 1b, which would pre-dict an 8 to 16-fold decrease with mean oceanic tempera-ture dropping by 3040 C. The exact magnitude of the pres-sure gradient and air velocities will depend on the horizon-tal size of the circulation pattern, the magnitude of frictionand degree of the radial symmetry (Makarieva and Gorshkov,2009a,b, 2011; Makarieva et al., 2011).

Our estimate of the horizontal pressure gradient in aHadley cell illustrates that our approach when coupled tofundamental atmospheric parameters, yields horizontal pres-sure gradients of magnitudes similar to those actually ob-served in large-scale circulation patterns. If we had obtaineda much smaller magnitude from Eq. (34) we could concludethat the impact of the vapor sink is negligible and cannot ex-plain the observations. This did not happen. Rather the resultadds credibility to our proposal that the vapor sink is a majorcause of atmospheric pressure gradients.

Difficulties in the understanding of atmospheric circula-tion relate to circumstances where uncertainty over the dy-namics of water vapor play a role even if the nature of thatrole remains debatable. For example, modern global circula-tion models do not satisfactorily account for the water cycleof the Amazon River Basin, with the estimated moisture con-vergence being half the actual amounts estimated from theobserved runoff values (Marengo, 2006). We note that cli-mate science offers no quantitative theory of Hadley circula-tion based on current theories and the effects of differentialheating alone (Held and Hou, 1980; Fang and Tung, 1999;Schneider, 2006). Efforts to address this challenge are on-going but progress is limited (e.g., Lindzen and Hou, 1988;Robinson, 2006; Walker and Schneider, 2005, 2006). In onerecent review concerning theories of general circulation theunderstanding of atmospheric moisture and its influences,particularly, lack of relevant theoretical concepts, were iden-tified as a persistent challenge (Schneider, 2006).

Furthermore, many climate researchers readily acknowl-edge that the current incomplete understanding of the gen-eral circulation precludes a theory-based analysis, from fun-damental physical principles, of the role of latitudinal at-mospheric mixing in stabilizing the Earths thermal regimeimportant this is not a minor and thus neglected detail



but is central in debates concerning climate sensitivity (e.g.,Lindzen and Choi, 2009; Trenberth et al., 2010). It wouldseem to many that new ideas are needed. If these ideas wereobvious, and followed directly from current paradigms, theywould have already been identified and accepted thus weshould not be surprised that the new ideas we all seek maychallenge conventional perspectives. We conclude that ourapproaches are a promising new avenue for further examina-tion.

4.2 Condensation rate and hydrostatic equilibrium

Let us dwell in greater detail on the physical meaning ofEq. (34) that specifies condensation rate in a unit volume.The second term in brackets, (Nv/N)N/z, describes howthe molar density of vapor would change during adiabaticascent if the water vapor were non-condensable and therewould be no condensation in the column. This referenceterm is needed to discriminate the density change caused bycondensation from the density change due to gravitationalexpansion. As we presume that moist air as a whole is inhydrostatic equilibrium, see Eq. (20), it is total molar den-sity N that must be used as such a reference. Indeed, totalmolar density remains in hydrostatic equilibrium in the ab-sence of condensation as well as in its presence. In the limitNv N Eq. (34) gives a physically meaningful result, S=0.Indeed, when atmosphere consists of water vapor only andis in hydrostatic equilibrium, no condensation takes place.Condensation occurs only when water vapor distribution isnon-equilibrium.

When condensation is absent, dry air is in hydrostatic equi-librium. But when water vapor condenses and its distributionis compressed several-fold compared to the hydrostatic dis-tribution, the dry air must be stretched compared to itshydrostatic distribution. Only in this case, when the non-equilibrium deficit of vapor in the upper atmosphere is com-pensated by the non-equilibrium excess of dry air, the moistair as a whole will remain in equilibrium. The distribution ofNd is non-equilibrium and cannot be used instead of N in thereference term in Eq. (34).

The horizontal pressure gradient produced by condensa-tion is therefore a direct consequence of hydrostatic adjust-ment. The air expands upwards to compensate for vapordeficit, thus its pressure at the surface diminishes in the re-gion of ascent. If no hydrostatic adjustment took place, thedry air would remain in hydrostatic equilibrium (while moistair as a whole would not). In this case dry air molar den-sity Nd could be used in the reference term in Eq. (34).Putting Nd instead of N in Eq. (34), i.e., replacing S bySdNv/z(Nv/Nd)Nd/z in Eq. (33), and performingall the derivations in Sect. 4.1, one obtains p/x=0. Thisresult is obvious: in the absence of hydrostatic adjustment,the dry air distribution is not affected by condensation andremains in equilibrium both in horizontal and vertical dimen-sions. The non-equilibrium gradient of total air pressure re-

mains located in the vertical dimension and is not translatedonto horizontal dimension. Such a situation could take placein an atmosphere that would be much higher than it is wide.In the real atmosphere which is effectively very thin, mostpart of the non-equilibrium pressure gradient is transferred tothe horizontal plane via rapid hydrostatic adjustment. Notethat SdS/(1 ) and SSd/(1+d), dNv/Nd. The ex-pressions for condensation rates in situations with or withouthydrostatic adjustment differ, respectively, by the absence orpresence of the multiplier 1/(1 ) in Eq. (34).

We emphasize that whether the hydrostatic adjustmenttakes place or not, the disequilibrium gradient of total airpressure persists, being located, respectively, either in thehorizontal or in the vertical dimension. Note that if S = Sdthen S Sd 0, condensation is absent and atmosphericpressure is in equilibrium in all directions (see Appendix A).

When asking for feedback on earlier versions of this textseveral readers assumed that Eq. (34) for condensation rate isan approximate form of the exact expression (Eq. 33). Herewe address this misunderstanding, see also Appendix A formore details. Equation (33) represents a general continuity(mass balance) equation for water vapor. It does not containany information about condensation indeed, it is equallyvalid for condensation S0 or absence ofphase transitions altogether, S=0. Also, it is equally validfor any dependence of S on spatial coordinates, velocities,temperature, pressure or any other variables. In other words,the continuity equation universally applies to all circulationevents. In the meantime, our task here is to study only thosecirculation patterns that are induced by condensation asso-ciated with adiabatic ascent. To do so, we need to specifyterm S in Eq. (33) so we can use this equation for the deter-mination of condensation-induced pressure gradients. Thisis done by means of Eq. (34), which says that: (1) in theconsidered volume the only source of phase transitions iscondensation; (2) this condensation is caused by the adia-batic ascent of moist saturated air (no condensation occursif the air moves horizontally because of isothermal surface)and (3) that the moist saturated air is in hydrostatic equilib-rium. We stress that none of these specific assumptions arecontained in the universal continuity equation (Eq. 33). (Incontrast to the generally applicable Eq. (33), Eq. (34) wouldnot be valid, for example, for the case of adiabatic descent,or for a horizontal motion along a non-isothermal surface.)We emphasize that S (Eq. 34) is based on specific physicalconsiderations, not on formal mathematical analogies.

4.3 Regarding previous oversight of the effect

For many readers a major barrier to acceptance of our propo-sitions may be to understand how such a fundamental physi-cal mechanism has been overlooked until now. Why has thistheory come to light only now in what is widely regarded asa mature field? We can offer a few thoughts based on ourreadings and discussions with colleagues.



The condensation-induced pressure gradients that we havebeen examining are associated with density gradients thathave been conventionally considered as minor and thus ig-nored in the continuity equation (e.g., Sabato, 2008). Forexample, a typical 1p=50 hPa pressure difference observedalong the horizontally isothermal surface between the outerenvironment and the hurricane center (e.g., Holland, 1980)is associated with a density difference of only around 5 %.This density difference can be safely neglected when esti-mating the resulting air velocity u from the known pres-sure differences 1p. Here the basic scale relation is givenby Bernoullis equation, u2/2=1p. The point is that a 5 %change in does not significantly impact the magnitude ofthe estimated air velocity at a given 1p. But, as we haveshown in the previous section, for the determination of thepressure gradient (Eq. 37) the density difference and gradi-ent (Eq. 36) are key.

Considering the equation of state (Eq. 5) for thehorizontally isothermal surface we have p=C, whereCRT/M=const. Irrespective of why the consideredpressure difference arises, from Bernoullis equationwe know that u2=21p/=2C1/, 1=0. Thus,if one puts 1/=1p/p equal to zero, no veloc-ity forms and there is no circulation. Indeed, wehave u2=21p/=2C1/=2C(1/0)(1+1/0+. . .).As one can see, discarding 1 compared to does indeedcorrespond to discarding the higher order term of the small-ness parameter 1/. But with respect to the pressure gradi-ent, the main effect is proportional to the smallness parameter1/0 itself. If the latter is assumed to be zero, the effect isoverlooked. We suggest that this dual aspect of the magnitudeof condensation-related density changes has not been recog-nized and this has contributed to the neglect of condensation-associated pressure gradients in the Earths atmosphere.

Furthermore, the consideration of air flows associated withphase transitions of water vapor has been conventionally re-duced to the consideration of the net fluxes of matter ignoringthe associated pressure gradients. Suppose we have a linearcirculation pattern divided into the ascending and descend-ing parts, with similar evaporation rates E (kg H2O m2 s1)in both regions. In the region of ascent the water vapor pre-cipitates at a rate P . This creates a mass sink EP , whichhas to be balanced by water vapor import from the region ofdescent. Approximating the two regions as boxes of heighth, length l and width d , the horizontal velocity ut associatedwith this mass transport can be estimated from the mass bal-ance equation

ld(P E)= uthd, ut = (P E)

l

h. (38)

Equation (38) says that the depletion of air mass in theregion of ascent at a total rate of ld(P E) is com-pensated for by the horizontal air influx from the re-gion of descent that goes with velocity ut via verticalcross-section of area hd. For typical values in the trop-

ics with PE5 mm d1=5.8105 kg H2O m2 s1 andl/h2103 we obtain ut1 cm s1. For regions where pre-cipitation and evaporation are smaller, the value of ut will besmaller too. For example, Lorenz (1967) estimated ut to be0.3 cm s1 for the air flow across latitude 40 S.

With d the value of ut can be understood as the mass-weighted horizontal velocity of the dry air+water vapor mix-ture, which is the so-called barycentric velocity, see, e.g.,(Wacker and Herbert, 2003; Wacker et al., 2006). There is nonet flux of dry air between the regions of ascent and descent,but there is a net flux of water vapor from the region of de-scent to the region of ascent. This leads to the appearance ofa non-zero horizontal velocity ut directed towards the regionof ascent. Similarly, vertical barycentric velocity at the sur-face is wt(EP)/ (Wacker and Herbert, 2003), whichreflects the fact that there is no net flux of dry air via theEarths surface, while water vapor is added via evaporationor removed through precipitation. The absolute magnitudeof vertical barycentric velocity wt for the calculated tropicalmeans is vanishingly small, wt +0.05 mm s1.

We speculate that the low magnitude of barycentric ve-locities has contributed to the judgement that waters phasetransitions cannot be a major driver of atmospheric dynamics.However, barycentric velocities should not be confused withthe actual air velocities (e.g., Meesters et al., 2009). Unlikethe former, the latter cannot be estimated without consideringatmospheric pressure gradients (Makarieva and Gorshkov,2009c). For example, in the absence of friction, the maxi-mum linear velocity uc that could be produced by conden-sation in a linear circulation pattern in the tropics constitutes

uc =

21p/ 40 m s1 ut . (39)Here 1p was taken equal to 10 hPa as estimated fromEq. (37) for Hadley cell in Sect. 4.1. As one can see, uc(Eq. 39) is much greater than ut (Eq. 38). As some part ofpotential energy associated with the condensation-inducedpressure gradient is lost to friction (Makarieva and Gorshkov,2009a), real air velocities observed in large-scale circulationare an order of magnitude smaller than uc, but still nearlythree orders of magnitude greater than ut .

4.4 The dynamic efficiency of the atmosphere

We will now present another line of evidence for the im-portance of condensation-induced dynamics: we shall showthat it offers an improved understanding of the efficiencywith which the Earths atmosphere can convert solar energyinto kinetic energy of air circulation. While the Earth onaverage absorbs about I2.402 W m2 of solar radiation(Raval and Ramanathan, 1989), only a minor part 102of this energy is converted to the kinetic power of atmo-spheric and oceanic movement. Lorenz (1967, p. 97) notes,the determination and explanation of efficiency constitutethe fundamental observational and theoretical problems of



atmospheric energetics. Here the condensation-induced dy-namics yields a relationship that is quantitative in nature andcan be estimated directly from fundamental atmospheric pa-rameters.

A pressure gradient is associated with a store of poten-tial energy. The physical dimension of pressure gradient co-incides with the dimension of force per unit air volume,i.e. 1 Pa m1=1 N m3. When an air parcel moves alongthe pressure gradient, the potential energy of the pressurefield is converted to the kinetic energy. The dimension ofpressure is identical to the dimension of energy density:1 Pa=1 N m2=1 J m3. As the moist air in the lower part ofthe atmospheric column rises to height h where most partof its water vapor condenses, the potential energy releasedamounts to approximately ps (Eq. 27). The potential energyreleased piv per unit mass of water vapor condensed, dimen-sion J (kg H2O)1, thus becomes

piv(Ts)= psv

= RTsMv

(1 MvgTs

L0s

). (40)

The global mean precipitation rate isP103 kg H2O m2 yr1 (Lvovitch, 1979), global meansurface temperature is Ts=288 K and the observed meantropospheric lapse rate 0o=6.5 K km1 (Glickman, 2000).Using these values and putting 0o instead of the moist adi-abatic lapse rate 0s in Eq. (40), we can estimate the globalmean rate 5v=Ppiv at which the condensation-related po-tential energy is available for conversion into kinetic energy.At the same time we also estimate the efficiency =5v/Iof atmospheric circulation that can be generated by solarenergy via the condensation-induced pressure gradients:

5v = Ppiv 3.5Wm2, 0.015. (41)Thus, the proposed approach not only clarifies the dynamicsof solar energy conversion to the kinetic power of air move-ment (solar power spent on evaporation condensation-related release of potential power kinetic power gener-ation), but it does so in a quantiatively tractable manner,explaining the magnitude of the dissipative power associ-ated with maintaining the kinetic energy of the Earths at-mosphere.

Our estimate of atmospheric efficiency differs fundamen-tally from a thermodynamic approach based on calculatingthe entropy budgets under the assumption that the atmo-sphere works as a heat engine, e.g. Pauluis et al. (2000);Pauluis and Held (2002a,b), see also Makarieva et al. (2010).The principal limitation of the entropy-budget approach isthat while the upper bounds on the amount of work that couldbe produced are clarified, there is no indication regarding thedegree to which such work is actually performed. In otherwords, the presence of an atmospheric temperature gradientis insufficient to guarantee that mechanical work is produced.In contrast, our estimate (Eq. 41) is based on an explicit cal-culation of mechanical work derived from a defined atmo-spheric pressure gradient. It is, to our knowledge, the only

available estimate of efficiency made from the basic phys-ical parameters that characterize the atmosphere.

4.5 Evaporation and condensation

While condensation releases the potential energy of atmo-spheric water vapor, evaporation, conversely, replenishes it.Here we briefly dwell on some salient differences betweenevaporation and condensation to complete our picture regard-ing how the phase transitions of water vapor generate pres-sure gradients.

Evaporation requires an input of energy to overcome theintermolecular forces of attraction in the liquid water to freethe water molecule to the gaseous phase, as well as to com-press the air. That is, work is performed against local atmo-spheric pressure to make space for vapor molecules that arebeing added to the atmosphere via evaporation. This work,associated with evaporation, is the source of potential energyfor the condensation-induced air circulation. Upon conden-sation, two distinct forms of potential energy arise. One isassociated with the potential energy of raised liquid drops this potential energy dissipates to friction as the drops fall.The second form of potential energy is associated with theformation of a non-equilibrium pressure gradient, as the re-moval of vapor from the gas phase creates a pressure short-age of moist air aloft. This pressure gradient produces airmovement. In the stationary case total frictional dissipationin the resulting circulation is balanced by the fraction of solarpower spent on the work associated with evaporation.

Evaporation is, fundamentally, a surface-specific processbecause it represents a flux of water molecules via the sur-face of liquid. In contrast, condensation is a volume-specificprocess that affects vapor molecules distributed in a certainvolume. The balance between condensation and evaporationdemands that to compensate for the amount of moisture con-densed in a certain volume vapor must be transported tothat local volume via its borders. Adding more gas to a gasvolume where condensation has occurred is associated withcompression of the gas in the volume and, hence, with per-forming work on the gas.

In the stationary case, as long there is a supply of en-ergy and the relative humidity is less than unity, evaporationfrom the planetary surface is adding water vapor to the atmo-spheric column without changing its temperature. The rate ofevaporation is affected by turbulent mixing and is usually re-lated to the horizontal wind speed at the surface. The globalmean power of evaporation cannot exceed the power of solarradiation.

The primary cause of condensation is the cooling of airmasses as the moist air ascends and its temperature drops.Provided there is enough water vapor in the ascending air, ata local and short-term scale, condensation is not governed bysolar power but by stored energy and can occur at an arbitrar-ily high rate dictated by the vertical velocity of the ascendingflow, see Eq. (34).



Any circulation pattern includes areas of lower pressurewhere air ascends, as well as higher pressure areas where itdescends. Condensation rates are non-uniform across theseareas being greater in areas of ascent. Importantly, in suchareas of ascent condensation involves water vapor that is lo-cally evaporated along with often substantial amounts of ad-ditional water vapor transported from elsewhere. Therefore,the mean rate of condensation in the ascending region ofany circulation pattern is always higher than the local rateof evaporation. This inherent spatial non-uniformity of thecondensation process determines horizontal pressure gradi-ents.

Consider a large-scale stationary circulation where the re-gions of ascent and descent are of comparable size. A rel-evant example would be the annually averaged circulationbetween the Amazon River Basin (the area of ascent) andthe region of Atlantic ocean where the air returns from theAmazon to descend depleted of moisture. Assuming thatthe relative humidity at the surface, horizontal wind speedand solar power are approximately the same in the two re-gions, mean evaporation rates should be roughly similar aswell (i.e., coincide at least in the order of magnitude). How-ever, the condensation (and precipitation) rates in the two re-gions will be consistently different. In accordance with thepicture outlined above, the average precipitation rate Pa inthe area of ascent should be approximately double the av-erage value of regional evaporation rate Ea. The pressuredrop caused by condensation cannot be compensated by lo-cal evaporation so as to produce a net zero effect on air pres-sure. This is because in the region of ascent both the localwater vapor evaporated from the forest canopy of the Ama-zon forest at a rate EaEd as well as imported water vaporevaporated from the ocean surface at a rate Ed precipitate,Pa=Ed+Ea. This is confirmed by observations: precipita-tion in the Amazon river basin is approximately double theregional evaporation, Pa2Ea (Marengo, 2004). The differ-ence between regional rates of precipitation and evaporationon land, R=PaEaEa, is equal to regional runoff aerialor liquid. In the region of descent the runoff thus defined isnegative and corresponds to the flux of water vapor that isexported away from the region with the air flow. Where R ispositive, it represents the flux of imported atmospheric watervapor and the equal flux of liquid water that leaves the regionof ascent to the ocean.

The fact that the climatological means of evaporation andprecipitation are seldom observed to be equal has been rec-ognized in the literature (e.g., Wacker and Herbert, 2003), ashas the fact that local mean precipitation values are consis-tently larger than those for evaporation (e.g., Trenberth et al.,2003).

The inherent spatial non-uniformity of the condensationprocess explains why it is condensation that principally de-termines the pressure gradients associated with water vapor.So, while evaporation is adding vapor to the atmosphereand thus increasing local air pressure, while condensation

in contrast decreases it, the evaporation process is signifi-cantly more even and uniform spatially than is condensation.Roughly speaking, in the considered example evaporation in-creases pressure near equally in the regions of ascent anddescent, while condensation decreases pressure only in theregion of ascent. Moreover, as discussed above, the rate atwhich the air pressure is decreased by condensation in theregion of ascent is always higher than the rate at which lo-cal evaporation would increase air pressure. The differencebetween the two rates is particularly marked in heavily pre-cipitating systems like hurricanes, where precipitation ratesassociated with strong updrafts can exceed local evaporationrates by more than an order of magnitude (e.g., Trenberth andFasullo, 2007).

We have so far discussed the magnitude of pressure gradi-ents that are produced and maintained by condensation in theregions where the moist air ascends. This analysis is applica-ble to observed condensation processes that occur on differ-ent spatial scales, as we illustrated on the example of Hadleycell. We emphasize that to determine where the ascendingair flow and condensation predominantly occur is a separatephysical problem. For example, why the updrafts are locatedover the Amazon and the downdrafts are located over theAtlantic ocean and not vice versa. Here regional evapora-tion patterns play a crucial role. In Sect. 4.1 we have shownthat constant relative humidity associated with surface evap-oration, which ensures that Nv/x=0, is necessary for thecondensation to take place. Using the definition of (Eq. 2)Eq. (37) can be re-written as follows: lnx

=wu

z. (42)

This equation shows that the decrease of with height and,hence, condensation is only possible when grows in thehorizontal direction, ln /x>0. Indeed, surface pressureis lower in the region of ascent. As the air moves towards theregion of low pressure, it expands. In the absence of evapo-ration, this expansion would make the water vapor containedin the converging air unsaturated. Condensation at a givenheight would stop.

Evaporation adds water vapor to the moving air to keepwater vapor saturated and sustain condensation. The higherthe rate of evaporation, the larger the ratio w/u at a given /z and, hence, the larger the pressure gradient (Eq. 37)that can be maintained between the regions of ascent anddescent. A small, but persistent difference in mean evapo-ration 1E


spatial and temporal localization of condensation events islikely to fluctuate in a random fashion.

5 Discussion: condensation dynamics versusdifferential heating in the generation ofatmospheric circulation

In Sect. 2 we argued that condensation cannot occur adia-batically at constant volume but is always accompanied bya pressure drop in the local air volume where it occurs. Weconcluded that the statement that the pressure drop by adi-abatic condensation is overcompensated by latent heat in-duced pressure rise of the air (Poschl, 2009, p. S12437) wasnot correct. In Sect. 3 we quantified the pressure change pro-duced by condensation as dependent on altitude in a columnin hydrostatic balance, to show that in such a column thepressure drops upon condensation everywhere in the loweratmosphere up to several kilometers altitude, Fig. 1c. Theestimated pressure drop at the surface increases exponen-tially with growing temperature and amounts to over 20 hPaat 300 K, Fig. 1b.

In Sect. 4 we discussed the implications of thecondensation-induced pressure drop for atmospheric dynam-ics. We calculated the horizontal pressure gradients producedby condensation and the efficiency of the atmosphere as a dy-namic machine driven by condensation. Our aim throughouthas been to persuade the reader that these implications aresignificant in numerical terms and deserve a serious discus-sion and further analysis. We will conclude by discussingcondensation in contrast to differential heating, the latter con-ventionally considered the major driver dominating atmo-spheric dynamics.

Atmospheric circulation is only maintained if, in agree-ment with the energy conservation law, there is a pressuregradient to accelerate the air masses and sustain the existingkinetic energy of air motion against dissipative losses. Forcenturies, starting from the works of Hadley and his prede-cessors, the air pressure gradient has been qualitatively as-sociated with the differential heating of the Earths surfaceand the Archimedes force (buoyancy) which makes the warmand light air rise, and the cold and heavy air sink (e.g., Gill,1982, p. 24). This idea can be illustrated by Fig. 1c, wherethe warmer atmospheric column appears to have higher airpressure at some heights than the colder column. In the con-ventional paradigm, this is expected to cause air divergencealoft away from the warmer column, which, in its turn, willcause a drop of air pressure at the surface and the resultingsurface flow from the cold to the warm areas. Despite thephysics of this differential heating effect being straightfor-ward in qualitative terms, the quantitative problem of pre-dicting observed wind velocities from the fundamental phys-ical parameters has posed enduring difficulties. Slightly morethan a decade before the first significant efforts in computerclimate modelling, Brunt (1944) as cited by Lewis (1998)wrote:

It has been pointed out by many writers that it isimpossible to derive a theory of the general circu-lation based on the known value of the solar con-stant, the constitution of the atmosphere, and thedistribution of land and sea . . . It is only possibleto begin by assuming the known temperature dis-tribution, then deriving the corresponding pressuredistribution, and finally the corresponding windcirculation.

Brunts difficulty relates to the realization that pressuredifferences associated with atmospheric temperature gradi-ents cannot be fully transformed into kinetic energy. Someenergy is lost to thermal conductivity without generating me-chanical work. This fraction could not be easily estimated bytheory in his era and thus it has remained to the present.The development of computers and appearance of rich satel-lite observations have facilitated empirical parameterizationsto replicate circulation in numerical models. However, whilethese models provide reasonable replication of the quantita-tive features of the general circulation they do not constitutea quantitative physical proof that the the observed circulationis driven by pressure gradients associated with differentialheating. As Lorenz (1967, p. 48) emphasized, although itis sometimes possible to evaluate the long-term influence ofeach process affecting some feature of the circulation by re-course to the observational data, such knowledge will notby itself constitute an explanation of the circulation, since itwill not reveal why each process assumes the value which itdoes.

In comparison to temperature-associated pressure differ-ence, the pressure difference associated with water vaporremoval from the gas phase can develop over a surface ofuniform temperature. In addition, this pressure differenceis physically anchored to the lower atmosphere. Unlike thetemperature-related pressure difference, it does not demandthe existence of some downward transport of the pressuregradient from the upper to the lower atmosphere (i.e., thedivergence aloft from the warmer to the colder column asdiscussed above) to explain the appearance of low altitudepressure gradients and the generation of surface winds.

Furthermore, as the condensation-related pressure differ-ence ps is not associated with a temperature difference,the potential energy stored in the pressure gradient can benearly fully converted to the kinetic energy of air massesin the lower atmosphere without losses to heat conductivity.This fundamental difference between the two mechanisms ofpressure fall generation can be traced in hurricanes. Withinthe hurricane there is a marked pressure gradient at the sur-face. This difference is quantitatively accountable by the con-densation process (Makarieva and Gorshkov, 2009b, 2011).In the meantime, the possible temperature difference in theupper atmosphere that might have been caused by the dif-ference in moist versus dry lapse rates between the regionsof ascent and descent is cancelled by the strong horizontal



mixing (Montgomery et al., 2006). Above approximately1.5 km the atmosphere within and outside the hurricane isapproximately isothermal in the horizontal direction (Mont-gomery et al., 2006, Fig. 4), see also Knaff et al. (2000).Therefore, while the temperature-associated pressure differ-ence above height zc, Fig. 1c, is not realized in the atmo-sphere, the condensation-associated pressure difference be-low height zc apparently is.

Some hints on the relative strengths of the circulationdriven by differential heating compared to condensation-induced circulation can be gained from evaluating wind ve-locities in those real processes that develop in the lower at-mosphere without condensation. These are represented bydry (precipitation-free) breezes (such as diurnal wind pat-terns driven by the differential heating of land versus sea sur-faces) and dust devils. While both demand very large temper-ature gradients (vertical or horizontal) to arise as comparedto the global mean values, both circulation types are of com-paratively low intensity and have negligible significance tothe global circulation. For example, dust devils do not in-volve precipitation and are typically characterized by windvelocities of several meters per second (Sinclair, 1973). Theother type of similarly compact rotating vortexes tornadoes that are always accompanied by phase transitions of water develop wind velocities that are at least an order of magni-tude higher (Wurman et al., 1996). More refined analyses ofHadley circulation (Held and Hou, 1980) point towards thesame conclusion: theoretically described Hadley cells drivenby differential heating appear to be one order of magnitudeweaker than the observed circulation (Held and Hou, 1980;Schneider, 2006), see also Caballero et al. (2008). While thetheoretical description of the general atmospheric circulationremains unresolved, condensation-induced dynamics offersa possible solution (as shown in Sect. 4.1).

Our approach and theory have other significant impli-cations. Some have been discussed in previous papers,for example with regard to the development of hurricanes(Makarieva and Gorshkov, 2009a,b) and the significance ofvegetation and terrestrial evaporation fluxes in determininglarge scale continental weather patterns (Makarieva et al.,2006, 2009; Makarieva and Gorshkov, 2007; Sheil and Mur-diyarso, 2009). Recently accumulated evidence directly doc-uments air flows induced by the phase transitions of water va-por (Chikoore and Jury, 2010). Other implications are likelyto be important in predicting the global and local nature ofclimate change a subject of considerable concern and de-bate at the present time (Pielke et al., 2009; Schiermeier,2010).

In summary, although the formation of air pressure gra-dients via condensation has not received adequate theoreti-cal attention in climatological and meteorological sciences,here we have argued that this lack of attention has been un-deserved. Condensation-induced dynamics emerges as a newfield of investigations that can significantly enrich our under-standing of atmospheric processes and climate change. We

very much hope that our present account will provide a spurfor further investigations both theoretical and empirical intothese important, but as yet imperfectly characterized, phe-nomena.

Appendix A

On the physical meaning of Eq. (34) for condensation rate

Equation (34) expresses condensation rate as the differencebetween (a) the total change of vapor density with height and(b) the density change caused by adiabatic expansion. Herewe explore the physical meaning of this expression from adifferent perspective. We shall show that Eq. (34) followsdirectly from the condition that the vertical distribution ofmoist air remains in equilibrium under the assumption thatcondensation rate S is linear over the amount of vapor (i.e.,condensable gas) in the atmosphere.

A1 Linearity of condensation rate over the molardensity Nv of water vapor

The linearity assumption is justified by the particular physi-cal nature and stoichiometry of condensation, with gas turn-ing to liquid: condensation is a first-order reaction over satu-rated molar density Nv of the condensing gas. This can beexperimentally tested by considering condensation of wa-ter with different isotopic composition (e.g., Fluckiger andRossi, 2003). (Note, for example, that the reverse process(evaporation) is a zero-order reaction over Nv.)

The rate of first-order reactions is directly proportionalto the molar density of the reagent, with the proportional-ity constant having the dimension of inverse time: S = CNv,where C (dimension s1) is in the general case independentof Nv. In chemical kinetics C depends on temperature andthe molecular properties of the reagent as follows from thelaw of mass action. Since the saturated concentration Nv ofcondensable gas depends on temperature as dictated by theClausius-Clapeyron law, we can ask what the proportionalitycoefficient C physically means in this case. Different sub-stances have different partial pressures of saturated vapor atany given temperature this is controlled by the vaporizationconstant L and the molecular properties of the substance.Note too that for any given substance (like water) the satu-rated concentration depends on various additional parametersincluding the curvature of the the liquid surface and availabil-ity of condensation nuclei. Therefore, a range of saturatedconcentrations is possible at any given temperature. This al-lows one to consider C and Nv as independent variables inthe space of all possible combinations of C and Nv.

A2 The equilibrium

The notions of equilibrium and deviation from it are key todetermining the rate of any reaction. For example, in the case



of evaporation the deviation from equilibrium is measuredby the water vapor deficit: the deviation of relative humidityfrom the (equilibrium) unity value. Atmospheric condensa-tion is peculiar in being physically associated with air move-ment in a particular direction water vapor condenses as theair moves vertically towards a lower temperature.

Here, in the context of this derivation, by invoking the con-cept of equilibrium we mean the vertical distribution that thewater vapor would locally take in the absence of condensa-tion, all other conditions being equal. Let us denote the in-verse scale height of such an equilibrium distribution for kE.Condensation rate S is then proportional to the first order de-viation kv of the observed vertical distribution of water vaporfrom the equilibrium:

kv = 1Nv

Nv

z kE. (A1)

The physics of Eq. (A1) consists of the fact that the characterof the considered equilibrium distribution is not affected bycondensation. For example, for the case of hydrostatic equi-librium any gas having molar mass M , temperature T andfinding itself on a planet with acceleration of gravity g in thepresence of a temperature gradient T /z will have a distri-bution of its molar density followingN/z= kEN , wherekE =Mg/RT + (1/T )T /z. (But note that Eq. (A1) canalso be applied to describe physical equilibria of a differentnature. For example, in a vertically isothermal atmosphere inthe absence of gravity kE = 0.)

Such a formulation (proportionality of condensation rateto kv) presumes that the deviation kv of the vertical distribu-tion of water vapor from equilibrium is due to condensationalone. (This premise is empirically testable: where conden-sation is absent, the vertical water vapor distribution shouldhave the same scale height as the non-condensable gases andmoist air as a whole.) This removes the need to consider Nvas the saturated vapor concentration. When kv = 0, the con-densation rate is zero independent of whether water vapor issaturated or not. When kv 6= 0, Nv is saturated water vaporby formulation.

A3 Distribution of vapor, dry air and moist air asa whole

We write the condition that moist air with molar density N isin equilibrium in the vertical dimension as:

1N

N

z k = kE, N =Nv+Nd. (A2)

Condensation causes the distribution of vapor Nv to de-viate from the equilibrium distribution. The condition thatmoist air as a whole nevertheless remains in equilibriumcauses dry air Nd to also deviate from the equilibrium butin the opposite direction to the vapor:

Nvz

= (k+ kv)Nv, Ndz

= (k+ kd)Nd, (A3)

kvNv+ kdNd = 0, (A4)

kv = 1Nv

Nv

z k, kd 1

Nd

Ndz

k. (A5)

The value of kv describes the intensity of the mass sink.In the case of water vapor kv > 0 is caused by a steep ver-tical temperature gradient that causes vapor to condense(Makarieva and Gorshkov, 2007; Gorshkov et al., 2012,Sect. 3). From consideration of the Clausius-Clapeyron lawand hydrostatic equilibrium one can see that

kv = L0RT 2

MgRT

, (A6)

where L is molar vaporization constant, 0 T /z is tem-perature lapse rate, and M is molar mass of air.

The value of kv is controlled by temperature lapse rate 0 keeping all other variables constant, changing 0 it is possiblefor kv to take any value, < kv


including cases where all other variables in Eq. (A10) are in-dependent of Nv. From this condition we obtain C =wkvand

S =wkvNv, (A11)which is Eq. (34). An experiment to test this relationshipwould be to consider a circulation with given vertical andhorizontal velocities w and u, set kv and Nd and change thesaturated molar density Nv by either changing the condens-able gas or the amount of condensation nuclei in the atmo-sphere or temperature (see below) or both. One will observethat as the condensable gas disappears from the atmosphere,the horizontal pressure gradients vanish. (It is interesting tonote the following. Given that the spatial distribution of Nvis exponential, Nv(z)=N0 exp(z/hN ), the local conditionNv 0 corresponds to complete disappearance of the con-densable component from the atmosphere and restoration ofequilibrium in the horizontal plane. In comparison, the localcondition kv 0 does not presume that condensation is ab-sent everywhere else in the atmosphere (it is plausible thatkv changes stepwise at the point where condensation com-mences).)

In Eq. (A11) condensation rate S is a linear functionof three independent variables: vertical velocity w, localamount of vapor Nv and deviation kv of vapor from the equi-librium distribution (kv can be characterized as the condens-ability strength of atmospheric vapor). Note an interestingrelationship: with S given by Eq. (A11) and Nv/N wehave SdS Sd Sd . When S = Sd we have S Sd 0:condensation is absent.

A5 Appendix summary

Equations (32) and (33), taken together, contain the infor-mation that it is water vapor and not dry air that undergoescondensation. Equation (34) contains information about themagnitude of deviation from equilibrium that causes conden-sation. Jointly considered, these facts are sufficient to deter-mine the horizontal pressure gradient produced by the vaporsink.

Note that in Eq. (A7) any small difference of the orderof d between S and Sd is multiplied by a large magnitude1/d 1 and thus has a profound influence on the magni-tude of the horizontal gradient Nd/z. We emphasize thepoint we made in Sect. 4.2: if it were dry air to be in equi-librium, i.e. kE =(1/Nd)Nd/z, the same considerationof the same equations would give Nd/x = 0 instead ofNd/x = S/u as in the case when it is moist air that is inequilibrium. The impact of this physical process on atmo-spheric dynamics remains unexplored.

Acknowledgements. We thank D. R. Rosenfeld and H. H. G.Savenije for disclosing their names as referees in the ACPD dis-cussion of the work of Makarieva et al. (2008) and D. R. Rosenfeldfor providing clarifications regarding the derivation of the estimateof condensation-related pressure change as given by Poschl (2009,p. S12436). We acknowledge helpful comments of K. E. Trenberthtowards a greater clarity of the presentation of our approach.The authors benefited greatly from an exciting discussion ofcondensation-related dynamics with J. I. Belanger, J. A. Curry,G. M. Lackmann, M. Nicholls, R. A. Pielke, G. A. Schmidt, A. Sei-mon and R. M. Yablonsky. We thank all people who discussedour work, both in the ACPD discussion and in the blogosphere,in particular, J. Condon, J. A. Curry, L. Liljegren, N. Stokesand A. Watts for hosting the discussions on their blogs. We aregrateful to P. Restrepo for his interest and help in finding potentialreviewers for our work. AMM acknowledges the essential role ofS. McIntyres blog where she came in contact with J. A. Curry.We sincerely thank our two referees, J. A. Curry and I. Held, fortheir valuable input. We gratefully acknowledge the commitmentand insight of A. Nenes and the entire ACP Executive Committeein handling our contribution. BLL thanks the US National ScienceFoundation and UC Agricultural Experiment Station for theirpartial support.

Edited by: A. Nenes

Editor Comment. The authors have presented an entirely newview of what may be driving dynamics in the atmosphere. Thisnew theory has been subject to considerable criticism which anyreader can see in the public review and interactive discussion of themanuscript in ACPD (http://www.atmos-chem-phys-discuss.net/10/24015/2010/acpd-10-24015-2010-discussion.html). Normally,the negative reviewer comments would not lead to final acceptanceand publication of a manuscript in ACP. After extensive deliber-ation however, the editor concluded that the revised manuscriptstill should be published despite the strong criticism from theesteemed reviewers to promote continuation of the scientificdialogue on the controversial theory. This is not an endorsement orconfirmation of the theory, but rather a call for further developmentof the arguments presented in the paper that shall lead to conclusivedisproof or validation by the scientific community. In additionto the above manuscript-specific comment from the handlingeditor, the following lines from the ACP executive committee shallprovide a general explanation for the exceptional approach taken inthis case and the precedent set for potentially similar future cases:(1) The paper is highly controversial, proposing a fundamentallynew view that seems to be in contradiction to common textbookknowledge. (2) The majority of reviewers and experts in the fieldseem to disagree, whereas some colleagues provide support, andthe handling editor (and the executive committee) are not convincedthat the new view presented in the controversial paper is wrong.(3) The handling editor (and the executive committee) concludedto allow final publication of the manuscript in ACP, in order tofacilitate further development of the presented arguments, whichmay lead to disproof or validation by the scientific community.



References

Bolton, D.: The computation of equivalent potential temperature,Mon. Weather Rev., 108, 10461053, 1980.

Brunt, D.: Physical and Dynamical Meteorology, 2nd Edn., Cam-bridge University Press, 428 pp., London, UK, 1944.

Brummer, B., Thiemann, S., and Kirchganer, A.: A cyclone statis-tics for the Arctic based on European centre re-analysis data, Me-teorol. Atmos. Phys., 75, 233250, 2000.

Caballero, R., Pierrehumbert, R. T., and Mitchell, J. L.: Axisym-metric, nearly inviscid circulations in non-condensing radiative-convective atmospheres, Q. J. Roy. Meteor. Soc., 134, 12691285, 2008.

Chikoore, H. and Jury, M. R.: Intraseasonal variability of satellite-derived rainfall and vegetation over Southern Africa, Earth Inter-act., 14, 126, 2010.

Curry, J. A. and Webster, P. J.: Thermodynamics of Atmospheresand Oceans, Academic Press, San Diego, 471 pp., 1999.

Deluc, J. A.: Einige meteorologische Erscheinungen, zu derengenauern Kenntniss die electrische Saule als Luft-Electroscopfuhren kann, Gilberts Ann. d. Phys., 41, 162194, 1812.

Gill, A. E.: Atmosphere-Ocean Dynamics, Academic Press, NewYork, 1982.

Fang, M. and Tung, K. K.: Time-dependent nonlinear Hadley circu-lation, J. Atmos. Sci., 56, 17971807, 1999.

Fluckiger, B. and Rossi, M. J.: Common precursor mechanism forthe heterogeneous reaction of D2O, HCl, HBr, and HOBr withwater ice in the range 170230 K: Mass accommodation coeffi-cients on ice, J. Phys. Chem. A, 107, 41034115, 2003.

Glickman, T. S. (Ed.): Glossary of Meteorology, 2nd Edn., Amer.Meteor. Soc., Boston, 855 pp., 2000.

Gorshkov, V. G., Makarieva, A. M., and Nefiodov, A. V.: Condensa-tion of water vapor in the gravitational field, J. Exp. Theor. Phys.,115, 723728, 2012.

Gu, H. and Qian, Z.: A discussion about the role of the water va-por source/sink term in continuity equation of numerical models,Chin. Sci. Bull., 36, 1621, 1991.

Haynes, P. (Ed.): Interactive comment on On the validity of rep-resenting hurricanes as Carnot heat engine by A. M. Makarievaet al., Atmos. Chem. Phys. Discuss., 8, S12168S12178, 2009.

Held, I. M. and Hou, A. Y.: Nonlinear axially symmetric circula-tions in a nearly inviscid atmosphere, J. Atmos. Sci., 37, 515533, 1980.

Holland, G. J.: An analytic model of the wind and pressure profilesin hurricanes, Mon. Weather Rev., 108, 12121218, 1980.

Kis, A. K. and Straka, J. M.: Nocturnal tornado climatology,Weather Forecast., 25, 545561, 2010.

Knaff, J. A., Zehr, R. M., Goldberg, M. D., and Kidder, S. Q.:An example of temperature structure differences in two cyclonesystems derived from the Advanced Microwave Sounder Unit,Weather Forecast., 15, 476483, 2000.

Lvovitch, M. I.: World Water Resources and Their Future, Ameri-can Geological Union, Washington, 1979.

Lackmann, G. M. and Yablonsky, R. M.: The importance of the pre-cipitation mass sink in tropical cyclones and other heavily precip-itating systems, J. Atmos. Sci., 61, 16741692, 2004.

Lewis, J. M.: Clarifying the dynamics of the general circulation:Phillipss 1956 experiment, B. Am. Meteorol. Soc., 79, 3960,1998.

Lindzen, R. S. and Hou, A. Y.: Hadley circulations for zonally aver-aged heating centered off the equator, J. Atmos. Sci., 45, 24162427, 1988.

Lindzen, R. S. and Choi, Y.-S.: On the determination of climatefeedbacks from ERBE data, Geophys. Res. Lett., 36, L16705,doi:10.1029/2009GL039628, 2009.

Lorenz, E. N.: The Nature and Theory of the General Circulationof the Atmosphere, World Meteorological Organization, Geneva,1967.

Lorenz, E. N.: A history of prevailing ideas about the general cir-culation of the atmosphere, B. Am. Meteorol. Soc., 64, 730734,1983.

Makarieva, A. M. and Gorshkov, V. G.: Biotic pump of atmo-spheric moisture as driver of the hydrological cycle on land, Hy-drol. Earth Syst. Sci., 11, 10131033, doi:10.5194/hess-11-1013-2007, 2007.

Makarieva, A. M. and Gorshkov, V. G.: Condensation-induceddynamic gas fluxes in a mixture of condensable and non-condensable gases, Phys. Lett. A, 373, 28012804, 2009a.

Makarieva, A. M. and Gorshkov, V. G.: Condensation-induced kine-matics and dynamics of cyclones, hurricanes and tornadoes,Phys. Lett. A, 373, 42014205, 2009b.

Makarieva, A. M. and Gorshkov, V. G.: Reply to A. G. C. A.Meesters et al.s comment on Biotic pump of atmosphericmoisture as driver of the hydrological cycle on land, Hy-drol. Earth Syst. Sci., 13, 13071311, doi:10.5194/hess-13-1307-2009, 2009c.

Makarieva, A. M. and Gorshkov, V. G.: The biotic pump: Conden-sation, atmospheric dynamics and climate, Inter. Jour. Water, 5,365385, 2010.

Makarieva, A. M. and Gorshkov, V. G.: Radial profiles of velocityand pressure for condensation-induced hurricanes, Phys. Lett. A.,375, 10531058, 2011.

Makarieva, A. M., Gorshkov, V. G., and Li, B.-L.: Conservationof water cycle on land via restoration of natural closed-canopyforests: implications for regional landscape planning, Ecol. Res.,21, 897906, 2006.

Makarieva, A. M., Gorshkov, V. G., and Li, B.-L.: On the va-lidity of representing hurricanes as Carnot heat engine, At-mos. Chem. Phys. Discuss., 8, 1742317437, doi:10.5194/acpd-8-17423-2008, 2008.

Makarieva, A. M., Gorshkov, V. G., and Li, B.-L.: Precipitation onland versus distance from the ocean: evidence for a forest pumpof atmospheric moisture, Ecol. Complex., 6, 302307, 2009.

Makarieva, A. M., Gorshkov, V. G., Li, B.-L., and Nobre, A. D.:A critique of some modern applications of the Carnot heat engineconcept: the dissipative heat engine cannot exist, P. R. Soc. A,466, 18931902, 2010.

Makarieva, A. M., Gorshkov, V. G., and Nefiodov, A. V.: Condensa-tional theory of stationary tornadoes, Phys. Lett. A., 375, 22592261, 2011.

Makarieva, A. M., Gorshkov, V. G., and Li, B.-L.: Revisiting for-est impact on atmospheric water vapor transport and precipita-tion, Theor. Appl. Climatol., 111, 7996, doi:10.1007/s00704-012-0643-9, 2013.

Mapes, B. E.: Waters two height scales: the moist adiabat and theradiative troposphere, Q. J. Roy. Meteor. Soc., 127, 22532266,2001.



Marengo, J. A.: Interdecadal variability and trends of rainfall acrossthe Amazon basin, Theor. Appl. Climatol., 78, 7996, 2004.

Marengo, J. A.: On the hydrological cycle of the Amazon basin: Ahistorical review and current state-of-the-art, Rev. Bras. Meteo-rol., 21, 119, 2006.

Meesters, A. G. C. A., Dolman, A. J., and Bruijnzeel, L. A.: Com-ment on Biotic pump of atmospheric moisture as driver ofthe hydrological cycle on land by A. M. Makarieva and V. G.Gorshkov, Hydrol. Earth Syst. Sci., 11, 10131033, 2007, Hy-drol. Earth Syst. Sci., 13, 12991305, doi:10.5194/hess-13-1299-2009, 2009.

Montgomery, M. T., Bell, M. M., Aberson, S. D., and Black, M. L.:Hurricane Isabel (2003): New insights into the physics of intensestorms. Part I: Mean vortex structure and maximum intensity es-timates, B. Am. Meteorol. Soc., 87, 12251347, 2006.

Murphree, T. and Van den Dool, H.: Calculating tropical winds fromtime mean sea level pressure fields, J. Atmos. Sci., 45, 32693282, 1988.

Nicholson, S. E.: The nature of rainfall variability over Africa ontime scales of decades to millenia, Global Planet. Change, 26,137158, 2000.

Ooyama, K. V.: A dynamic and thermodynamic foundation formodeling the moist atmosphere with parameterized micro-physics, J. Atmos. Sci., 58, 20732102, 2001.

Pauluis, O. P., Balaji, V., a

Documents

Trabajo de los rusos.pdf