Quantifying the global atmospheric power budget

TL;DR

This paper reviews and refines the definition of atmospheric power, clarifies previous formulations, and presents a scale-aware power budget model using reanalysis data to better understand Earth's climate dynamics.

Contribution

It provides a new, comprehensive formulation of atmospheric power accounting for moist atmosphere effects and clarifies the dependence on boundary conditions and scale.

Findings

W_K increases with temporal resolution.

The new formulation distinguishes three components of atmospheric power.

Reanalysis data helps evaluate power contributions at different scales.

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 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.