Monthly Archives: April 2011

Text that was not included in our reply 2 to Dr. Isaac Held

by Anastassia Makarieva

See context here.

On pp.~C14691-C14692 of the review several suggestions are provided on how we could write a paper that would be easier to read (and review). This advice joins the many constructive recommendations that we have received while trying to communicate our ideas and findings to the meteorological community. While convinced that the text they comment upon should be rejected, some have been kind enough to suggest ingredients required for success somewhere in the future. Some believe that we should present simple thought experiments and focus on basic physical concepts. Others, including Dr.~Held, expect that our message could rather be clarified with use of explicit simulation models. Some critics discourage our use of the continuity equation as a source of information on pressure gradients. One private comment was that we might highlight our ideas as a comment on an existing related paper in the literature. Others, on the other hand, suggested that if the authors have a theory of their own they should present that rather than a critique of other people’s work.

We have appreciated all these comments and can claim some progress and efforts with almost every suggestion: we worked on a unified theory of hurricanes and tornadoes, criticized others, clarified the broader environmental implications of our findings (here is a list of our publications on the topic). However, all these recent developments occurred either in physics, environmental or ecological journals. Our success with the meteorological literature is very limited. Why is that? We have some ideas that we offer here as we hope to clarify some challenges arising in the review process.

The common practice in the meteorological literature is that the authors have to satisfy the expectations of all referees. Indeed, one editor of a high-profile journal explicitly admitted that papers are published if only all referees are in agreement. But when the authors’ findings are unexpected and, using Dr.~Held’s words, extraordinary, it is not straightforward to decide how such findings could be shaped, if at all, to meet the publicability standards. There are not many grounds either to expect that an account of paradigm-challenging findings would constitute an easy reading. In such a case the reviewers’ recommendations while expectedly diverse are likely to agree at one point: the authors should present something different to what they are presenting. The practical outcome of this process is that publication of such findings becomes impossible. In his review Dr.~Held provides evidence of this. He explains (p.~C14688) that a study that goes against the standard perspective or aims to overturn the conventional wisdom has to pass a high bar.

Condensation Rate: Devil in a Detail

When gas disappears somewhere in the atmosphere, local pressure is lowered and a compensating air inflow from the surrounding areas is initiated. In our paper “Where do winds come from?” (M10) we derive the magnitude of a stationary horizontal pressure gradient \partial p/\partial x that is associated with water vapor condensation — the process by which the vapor gas molecules are packed into a thousand of times smaller liquid volume and thus effectively disappear from the atmosphere.

There has been much critical discussion in the blogosphere and further on the ACPD web site of our Equation 34 for condensation rate S that is key to the presented derivation. At various times and places, including Section 4.2 of our paper, it was pointed out that if one formulates S in terms of water vapor mixing ratio \gamma_d \equiv N_v/N_d = p_v/p_d one obtains \partial p/\partial x = 0. If one instead uses the relative partial pressure of water vapor, \gamma \equiv N_v/N = p_v/p, a horizontal pressure gradient is obtained that appears to be so significant as to substantiate the claim for a dominant role in the whole planetary dynamics. (Here N_v, N_d, N = N_v + N_d, p_v, p_d, p = p_v + p_d are molar density and pressure of water vapor, dry air and air as a whole, respectively.)

A typical value of water vapor partial pressure p_v in the lower atmosphere is around 1-3 per cent. This means that the mixing ratio and relative partial pressure \gamma_d and \gamma differ very insignificantly. Reckoning up the preceding criticisms, our second referee Dr. Isaac Held referred to this difference as to “a detail”. It is the purpose of this note to show that the \gamma/\gamma_d dichotomy is precisely the devilish detail that, as it increasingly appears, is responsible for the fact that the condensation-induced dynamics has not received the attention it deserves.

Consider the stationary continuity (mass conservation) equations written for dry air and water vapor (Eqs. 32 and 33 in M10): \nabla N_d \mathbf{v} = 0,      \nabla N_v \mathbf{v} = S.      These equations only tell us that the dry air mass is conserved, while the vapor mass may be conserved or it may be not: there can be a local source or sink of vapor S. Irrespective of the existence/nature/magnitude of the vapor sink/source S, the above equations can be combined with use of elementary algebra such that their left-hand parts take various forms. In his review Dr. Held chose N_d \mathbf{v} \nabla (N_v/N_d) = S, which is equivalent to

\mathbf{v} (\nabla N_v - \gamma_d \nabla N_d) = S.    [1]

In the two-dimensional circulation considered in M10 the velocity vector is the sum of the horizontal and vertical components, \mathbf{v} = \mathbf{u} + \mathbf{w}. We also consider a horizontally uniform surface temperature, which dictates a constant saturated pressure of water vapor, such that \mathbf{u} \nabla N_v = 0.     [2] (If water vapor is not saturated, this assumption corresponds to a horizontally uniform surface temperature and constant relative humidity.) Combining [1] and [2] we obtain

\displaystyle \mathbf{u} \nabla N_d = \left(S - S_d\right)\frac{1}{\gamma_d},     where S_d \equiv \mathbf{w} \left(\nabla N_v - \gamma_d \nabla N_d \right).    [3]

Equation [3] has two important implications for any given horizontal velocity u \ne 0. First, it shows that when S = S_d, the horizontal density gradient \partial N/\partial x = \partial N/\partial x = 0. Second, it shows that if S and S_d differ by a small relative magnitude of the order of \gamma_d \ll 1, this magnitude is multiplied by a large relative magnitude 1/\gamma_d \gg 1 to determine the horizontal density gradient \partial N/\partial x.

We should emphasize that the two above conclusions are unrelated to any ideas about what the condensation rate could look like. The value of S in [3] is unknown. Equation [3] shows that any minor difference of the order of \gamma_d in the theoretical formulation of S — whatever the latter might be — is not a detail but is the zeroth order term in determining the horizontal density and pressure gradients associated with vapor condensation.