by Anastassia Makarieva, Victor Gorshkov, Douglas Sheil, Antonio Nobre, Larry Li
It’s official: our controversial paper has been published. After a burst of intense attention (some of you may remember discussions at Climate Etc., the Air Vent and the Blackboard), followed by nearly two years of waiting, our paper describing a new mechanism driving atmospheric motion has been published in Atmospheric Chemistry and Physics.
It’s been an epic process – most papers get published (or rejected) in less than a tenth of that time. The paper is accompanied by an unusual Editor Comment (p. 1054) stating that in the paper we have presented a view on atmospheric dynamics that is both “completely new” and “highly controversial”. They accept that we have made a case to be answered: they clarify that “the handling editor (and the executive committee) are not convinced that the new view presented in the controversial paper is wrong.” That’s not exactly an endorsement but it is progress.
We have not been simply waiting the last two years. Arguments and ideas have matured. We want to give you an update. In Section 1 of this post we discuss the novelty of our propositions. In Section 2 we address three of the most common objections. In doing so, we draw on all the recent work by our group thus providing an updated view on our theory.
What is new?
We have described a new and significant source of potential energy governing atmospheric motion. Previously, the only such recognised energy source was the buoyancy associated with temperature gradients.
Unlike the buoyancy mechanism, that applies to both liquids and gases, our new mechanism applies only to gases. Water vapor condenses and disappears from the gas phase when moist air ascends and cools. For this reason the water vapor pressure declines with height much faster than the other (non-condensable) atmospheric gases. As a result the exponential scale height hv of water vapor is markedly smaller than the scale height h of the air as a whole, hv << h. What are the implications of these two different scales for atmospheric dynamics?
In hydrostatic equilibrium the vertical pressure gradient force -∂p/∂z balances the gas weight in a unit atmospheric volume –ρg: -∂p/∂z – ρg = 0, where p is air pressure, ρ (kg m−3) is air density, and g is acceleration of gravity. In the absence of condensation in a circulating atmosphere the relative partial pressure γi ≡ pi/p of the non-condensable atmospheric gases, including the unsaturated water vapor, is independent of height. In hydrostatic equilibrium for such gases we have:
where pi and Ni (mol m−3) are partial pressure and molar density of the i-th gas, respectively, R = 8.3 J mol−1K−1 is the universal gas constant, and N and M are the molar density and mean molar mass of air as a whole.
This relationship determines that in hydrostatic equilibrium any work –w∂pi/∂z performed by the vertical partial pressure gradient per unit time per unit atmospheric volume is compensated exactly by the work –wγiρg performed by the force of gravity that acts on a corresponding molar share γi of the air mass (here w is vertical velocity). In other words, all work performed by the non-condensable gases as they ascend and expand is fully spent on elevating their respective molar shares of total air mass in the gravitational field. Nothing is left to generate kinetic energy.
By contrast, if we consider the saturated water vapor, condensation means that we have
That is, the work of the partial pressure gradient of water vapor greatly exceeds what is needed to overcome gravity. The main physical statement behind our new view is that this net remaining power q (W m−3)
is available to generate kinetic energy and drive the Earth’s atmospheric dynamics. Roughly speaking it is the power that remains after the water vapor has “lifted itself”. The value of q represents the volume-specific power of the “motor” that drives the atmospheric circulation.
The formation of strong vertical winds is directly inhibited by the atmosphere’s condition of hydrostatic equilibrium. For that reason the dynamic power of condensation is mostly translated into the power of horizontal pressure gradients and winds:
Here v = u + w is air velocity, u is horizontal and w is vertical air velocity, and ∇p is the pressure gradient, all measured on the circulation largest spatial scale. The kinetic energy generated by horizontal pressure gradients dissipates in smaller-scale eddies and ultimately converts to heat.
By integrating (3) over height z and noting that wN = wp/(RT) is independent of z to the accuracy of γ (e.g., see Appendix here), we obtain a relationship indicating that the driving power Q per unit area is proportional to precipitation P (mol m−2 s−1):
where T is the mean temperature in the air column, and P ≡ wNγ(0) = wNv(0) is the upwelling flux of water vapor (mol m−2 s−1), which, in the stationary state and assuming complete condensation, is equal to the downward flux of precipitating water. As discussed in our paper, this equation is exact for a horizontally isothermal atmosphere. In the general case it may be imprecise by about 10% (Makarieva, Gorshkov, 2010).
We can now compare our theory with observations. First, we note that the mean global power of atmospheric circulation estimated from (5) is about 4 W m−2, which is in close agreement with the best observational estimates. We note that this is the first and only theoretical estimate of the power of global circulation currently available. We return to this in the next section.
We then observe that the above physical relationships apply to circulation phenomena characterized by notably different spatial and temporal scales. For a steady-state global-scale pattern (e.g., Hadley cells) the mean value of precipitation P is determined by solar power I. About one third of solar power is spent on evaporation. Given that evaporation and precipitation must be nearly equal (in a steady state) we can see that P ∼ I/Lv, where Lv (J mol−1) is the heat of vaporization. In a much smaller and short-lived circulation system, like a hurricane or tornado, that moves as a whole with velocity V, precipitation within the circulation area is determined by the flux of water vapor imported. It thus depends on the height hh and radius r of the circulation, velocity V and the ambient amount of water wapor: P ∼ (hh/r)VNv (here Nv is the mean ambient molar density of water vapor).
As we can see, the physical determinants of precipitation are very different. E.g., hurricane P can be several orders of magnitude higher than the mean global P. The horizontal scale of Hadley cells is several times larger than that of hurricanes. Despite such different scales, physical determinants of condensation intensity and drastically varying P values theoretical estimates (3) and (5) successfully describe the Hadley cell as well as much more compact and transient circulation phenomena (see (Makarieva, Gorshkov, 2011) and (Makarieva et al., 2011) for details). Our approach thus provides a unified physical explanation to atmospheric circulation phenomena previously considered unrelated.
Thanks to help from blog readers, those who visited the ACPD site and many others who we have communicated with, our paper has received considerable feedback. Some were supportive and many were critical. Some have accepted that the physical mechanism is valid, though some (such as JC) question its magnitude and some are certain it is incorrect (but cannot find the error). Setting aside these specific issues, most of the more general critical comments can be classified as variations on, and combinations of, three basic statements:
1. Current weather and climate models (a) are already based on physical laws and (b) satisfactorily reproduce observed patterns and behaviour. By inference, it is unlikely that they miss any major processes.
2. You should produce a working model more effective than current models.
3. Current models are comprehensive: your effect is already there.
Let’s consider these claims one by one.
Models and physical laws
The physical laws behind all existing atmospheric circulation models are Newton’s second law, conservation of mass, the ideal gas law and the first law of thermodynamics. Here the first law of thermodynamics is assigned the role of the energy conservation equation (see, e.g., McGuffie and Henderson-Sellers 2001, p. 1084). However, while equilibrium thermodynamics allow the estimation of the maximum possible mechanical work from heat it provides neither information about the actual efficiency of converting heat to work (kinetic energy) nor whether such conversion to motion actually occurs. In practice, this means that models do not define these factors from physical principles but through adjusting model parameters in order to force it to fit observations (i.e., to produce the observed wind speeds). Mostly this pertains to the determination of the turbulent diffusion parameters. An
interested reader see p. 1776 of Bryan and Rotunno (2009) for a simple example (see also here for a discussion). The principle remains the same even in the most complex models.
Thus, while there are physical laws in existing models, their outputs (including apparent circulation power) reflect an empirical process of calibration and fitting. In this sense models are not based on physical laws. This is the reason why no theoretical estimate of the power of the global atmospheric circulation system has been available until now.
The models reproduce the observations satisfactorily
As we have discussed in our paper (p. 1046) current models fail when it comes to describing many water-related phenomena. But perhaps a more important point to make here is that even where behaviours are satisfactorily reproduced it would not mean that the physical basis of the model are correct. Indeed, any phenomenon that repeats itself can be formally described or “predicted” completely without understanding its physical nature. We just need our experience to predict that in winter the days will be shorter than they were in summer. Thus, improvements in performance may be caused not by the correct physics but by an ever more refined description of the probability distributions characterizing persistent, regular behaviours. Consider for example how satellite data have made it possible to better analyze hurricane tracks allowing to judge about hurricane motion with some certainty a few days in advance, something entirely unavailable for the ancient weather forecasters. Such information is definitely valuable and useful. But it does not provide any insight concerning outcomes when the underlying system undergoes changes. For example, a climate model empirically fitted for a forest-covered continent cannot inform us about the climatic consequences of deforestation if we do not correctly understand the underlying physical mechanisms.
You should produce a better model than the existing ones
Modern numerical models of weather and climate are over half a century old. They contain huge numbers of parameterizations that summarize the work of thousands of researchers working for decades. As already mentioned, these parameterizations include the many adjustments needed to match the behaviour of the model to reality. If the physical core of the model is changed (e.g. from buoyancy- to condensation-driven), all these parameterizations will require revision. To expect a few theorists, however keen, can achieve that is neither reasonable nor realistic. We have invested our efforts to show, using suitable physical estimates, that the effect we describe is sufficient to justify a wider and deeper scrutiny. (At the same time we are also developing a number of texts to show how current models in fact contain erroneous physical relationships (see, e.g., here)).
Your effect is already present in existing models
Many commentators believe that the physics we are talking about is already included in models. There is no omission. This argument assumes that if the processes of condensation and precipitation are reproduced in models, then the models account for all the related phenomena, including pressure gradients and dynamics. This is, however, not so. Indeed this is not merely an oversight but an impossibility. The explanation is interesting and deserves recognition – so we shall use this opportunity to explain.
The circulation “motor” q unambiguously defines condensation intensity S that enters the continuity equation (see also Gorshkov et al., 2012). In a horizontally isothermal atmosphere for an arbitrary unknown condensation rate S the continuity equation has the form (see (A7) on p. 1053 in the paper)
where S and Sd are in mol m−3 s−1, Nd and γd are the molar density and the relative partial pressure of the dry air constituents. Recalling that in hydrostatic equilibrium q = –u∇p = RT(u∇N) (4) and using (3) we obtain from (6)
which the reader may recognize as the (in some quarters, notorious) Equation 34 in the paper. The main message from the above derivation is that the relative difference between S and Sd is itself of the order of γ: (S – Sd)/γd = S = q/(RT).
In current models in the absence of a theoretical stipulation on the circulation power, a reverse logic is followed. The horizontal pressure gradients are determined from the continuity equation, with the condensation rate calculated from the Clausius-Clapeyron law using temperature derived from the first law of thermodynamics with empirically fitted turbulence. However, as we have seen, to correctly reproduce condensation-induced dynamics, condensation rate requires an accuracy much greater than γ << 1. Meanwhile the imprecision of the first law of thermodynamics as applied to describe the non-equilibrium atmospheric dynamics is precisely of the same order of γ. The kinetic energy of the gas is not accounted for in equilibrium thermodynamics.
It is an interesting situation. The precision of the first law of thermodynamics is sufficient to determine condensation rate to the accuracy of γ. This accuracy is more than sufficient to allow existing models to be fitted to reproduce realistic precipitation rates. But at the same time the precision provided by the first law of thermodynamics is in principle insufficient to quantify our condensation-induced dynamics. This two-faced result is striking and has implications for models: Suppose that a modeller develops a model of atmospheric circulation that assumes that heating rate gradients are the only driver. If this model presents some unrealistically high wind velocities (due to some unanticipated effect) then this behaviour can readily be suppressed with only minor modifications. The model can thus accommodate phenomena for which it lacks any intrinsic relationships without any red-flags being raised.
We showed in our paper that following this route (i.e., reproducing condensation dynamics from condensation rate) requires a thorough theoretical analysis of the condensation rate behavior (see Section 4.2 and Appendix in the paper). As we discussed, no adequate theory for condensation rate exists in the current models. Therefore, as the fitting process cannot anticipate all situations (combinations and/or values of key variables etc.) there must be occasions when the omission of the relevant physical processes is revealed. The pertinent example here is in the analyses of alternative parameterizations of condensation rate: applying different cloud microphysical parameterizations in hurricane models produces systems that differ from each by over 40 mb in their central drop of pressure (with 55 mb being the mean figure for the pressure drop in hurricanes) (e.g., Deshpande et al. 2012). Generally, the situation is such that condensation-induced dynamics are neither present in modern models nor have their impacts been studied in an adequate manner.
Summary and outlook
The Editor’s comment on our paper ends with a call to further evaluate our proposals. We second this call. The reason we wrote this paper was to ensure it entered the main-stream and gained recognition. For us the key implication of our theory is the major importance of vegetation cover in sustaining regional climates. If condensation drives atmospheric circulation as we claim, then forests determine much of the Earth’s hydrological cycle (see here for details). Forest cover is crucial for the terrestrial biosphere and the well-being of many millions of people. If you acknowledge, as the editors of ACP have, any chance – however large or small – that our proposals are correct, then we hope you concede that there is some urgency that these ideas gain clear objective assessment from those best placed to assess them.
JC comment: This is an invited guest post, which follows up on Makarieva et al.’s previous blog post at Climate Etc. Comments will be strictly moderated for relevance and for civility.