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 present a formulation of the atmospheric power
budget, which distinguishes three components of $W$: the kinetic power
associated with horizontal pressure gradients ($W_K$), the gravitational power
of precipitation ($W_P$) and the condensate loading ($W_c$). We use MERRA and
NCAR/NCEP re-analyses to evaluate the atmospheric power budget at different
scales: $W_K$ increases with temporal resolution approaching our theoretical
estimate for condensation-induced circulation when all convective motion is
resolved.Comment: 55 pages, 14 figures; minor revisions after another discussion, see
https://doi.org/10.5194/acp-2017-17-AC7 and
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