Макарьева А.М., Горшков В.Г., Нефёдов А.В., Шейл Д., Нобре А.Д., Ли Б.-Л. (2016) К расчёту мощности глобальной циркуляции. arXiv:1603.03706v4 [physics.ao-ph] [на англ. яз.]
Аннотация
The power of atmospheric circulation is a key measure of the Earth's climate system. The mismatch between predictions and observations under a warming climate calls for a reassessment of how atmospheric power W is defined, estimated and constrained. Here we review published formulations for W and show how they differ when applied to a moist atmosphere. Three factors, a non-zero source/sink in the continuity equation, the difference between velocities of gaseous air and condensate, and interaction between the gas and condensate modifying the equations of motion, affect the formulation of W. Starting from the thermodynamic definition of mechanical work, we derive an expression for W from an explicit consideration of the equations of motion and continuity. Our analyses clarify how some past formulations are incomplete or invalid. Three caveats are identified. First, W critically depends on the boundary condition for gaseous air velocity at the Earth's surface. Second, confusion between gaseous air velocity and mean velocity of air and condensate in the expression for W results in gross errors despite the observed magnitudes of these velocities are very close. Third, W expressed in terms of measurable atmospheric parameters, air pressure and velocity, is scale-specific; this must be taken into account when adding contributions to W from different processes. We further present a formulation of the atmospheric power budget, which distinguishes three components of W: the kinetic power associated with horizontal pressure gradients (WK), the gravitational power of precipitation (WP) and the condensate loading (Wc). This formulation is valid with an accuracy of the squared ratio of the vertical to horizontal air velocities. Unlike previous approaches, it allows evaluation of WP + Wc without knowledge of atmospheric moisture or precipitation. This formulation also highlights that WP and Wc are the least certain terms in the power budget as they depend on vertical velocity; WK depending on horizontal velocity is more robust. We use MERRA and NCAR/NCEP re-analyses to evaluate the atmospheric power budget at different scales. Estimates of WK are found to be consistent across the re-analyses, while estimates for W and WP drastically differ. We then estimate independent precipitation-based values of WP and discuss how such estimates could reduce uncertainties. Our analyses indicate that WK increases with temporal resolution approaching our theoretical estimate for condensation-induced circulation when all convective motion is resolved. Implications of these findings for constraining global atmospheric power are discussed.

Примечания

This paper stemmed from a short Technical Comment on the work of Laliberte et al. (2015) in Science (it was not published). Here is the review that we received.
Then there were some other developments, then it was submitted to Atmospheric Chemistry and Physics Discussions, endured two discussions but was not accepted. The Editor's decision and our response will be available here soon. In our opinion, it is a good paper which disentangles a lot of confusions surrounding the definition of atmospheric power, we recommend it for any student of atmospheric circulation.

Makarieva A.M., Gorshkov V.G., Nefiodov A.V., Sheil D., Nobre A.D., Li B.-L. (2016) Quantifying the global atmospheric power budget. arXiv:1603.03706v4 [physics.ao-ph]
Abstract
The power of atmospheric circulation is a key measure of the Earth's climate system. The mismatch between predictions and observations under a warming climate calls for a reassessment of how atmospheric power W is defined, estimated and constrained. Here we review published formulations for W and show how they differ when applied to a moist atmosphere. Three factors, a non-zero source/sink in the continuity equation, the difference between velocities of gaseous air and condensate, and interaction between the gas and condensate modifying the equations of motion, affect the formulation of W. Starting from the thermodynamic definition of mechanical work, we derive an expression for W from an explicit consideration of the equations of motion and continuity. Our analyses clarify how some past formulations are incomplete or invalid. Three caveats are identified. First, W critically depends on the boundary condition for gaseous air velocity at the Earth's surface. Second, confusion between gaseous air velocity and mean velocity of air and condensate in the expression for W results in gross errors despite the observed magnitudes of these velocities are very close. Third, W expressed in terms of measurable atmospheric parameters, air pressure and velocity, is scale-specific; this must be taken into account when adding contributions to W from different processes. We further present a formulation of the atmospheric power budget, which distinguishes three components of W: the kinetic power associated with horizontal pressure gradients (WK), the gravitational power of precipitation (WP) and the condensate loading (Wc). This formulation is valid with an accuracy of the squared ratio of the vertical to horizontal air velocities. Unlike previous approaches, it allows evaluation of WP + Wc without knowledge of atmospheric moisture or precipitation. This formulation also highlights that WP and Wc are the least certain terms in the power budget as they depend on vertical velocity; WK depending on horizontal velocity is more robust. We use MERRA and NCAR/NCEP re-analyses to evaluate the atmospheric power budget at different scales. Estimates of WK are found to be consistent across the re-analyses, while estimates for W and WP drastically differ. We then estimate independent precipitation-based values of WP and discuss how such estimates could reduce uncertainties. Our analyses indicate that WK increases with temporal resolution approaching our theoretical estimate for condensation-induced circulation when all convective motion is resolved. Implications of these findings for constraining global atmospheric power are discussed.

Notes

This paper stemmed from a short Technical Comment on the work of Laliberte et al. (2015) in Science (it was not published). Here is the review that we received.
Then there were some other developments, then it was submitted to Atmospheric Chemistry and Physics Discussions, endured two discussions but was not accepted. The Editor's decision and our response will be available here soon. In our opinion, it is a good paper which disentangles a lot of confusions surrounding the definition of atmospheric power, we recommend it for any student of atmospheric circulation.