30 Jan 2017

30 Jan 2017

Review status: this preprint was under review for the journal ACP but the revision was not accepted.

Quantifying the global atmospheric power budget

Anastassia M. Makarieva1,2, Victor G. Gorshkov1,2, Andrei V. Nefiodov1, Douglas Sheil3, Antonio Donato Nobre4, and Bai-Lian Li2 Anastassia M. Makarieva et al.
  • 1Theoretical Physics Division, Petersburg Nuclear Physics Institute, 188300 Gatchina, St. Petersburg, Russia
  • 2USDA-China MOST Joint Research Center for AgroEcology and Sustainability, University of California, Riverside 92521-0124, USA
  • 3Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Ås, Norway
  • 4Centro de Ciência do Sistema Terrestre INPE, São José dos Campos SP 12227-010, Brazil

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 modyfing 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.

Anastassia M. Makarieva et al.

Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
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Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement

Anastassia M. Makarieva et al.

Anastassia M. Makarieva et al.


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Short summary
Why the Earth's atmospheric power – the rate at which solar energy is converted to wind – takes the value it does has long challenged theorists. We identify distinct terms in the atmospheric power budget and highlight their meaning and implications. We note problems with past estimates of this global power and generate our own for 1979–2015 using available gridded data. Spatial changes in atmospheric moisture, such as those caused by forest loss, will impact wind power, circulation and climate.