The Alpha--Omega Problem in the Assessments of Atmospheric Power
Abstract
Atmospheric power is commonly assessed with two Lorenz-cycle formulations treated as equivalent: the αω formulation, yielding gas expansion power Wω, and the v·∇ z formulation, yielding kinetic-energy generation by horizontal pressure gradients, WK. We show that, for a statistically stationary global moist atmosphere, Wω=WK+WP+Wnh, where WP is the power of lifting precipitating water and Wnh is power associated with departures from gas-phase hydrostatic balance. Since WP≃1 W m−2 globally, equality would require Wnh≃−WP<0, so the associated vertical force imbalance would have to do negative work globally. Using six-hourly ERA5, JRA-3Q, and MERRA-2 fields for 2025, we find that resolved Wω varies by a factor of 1.7 (1.9--3.2 W m−2), versus 1.2 for WK (2.4--2.8 W m−2). Zonal-mean αω profiles have area-weighted contributions near ±50 W m−2, making global Wω a cancellation residual, whereas v·∇ z profiles vary much less with latitude. The difference Wω−WK ranges from −0.61 to +0.87 W m−2. Thus reanalysis-derived Wω cannot provide an independent constraint on atmospheric power. Two treatments of the omitted surface layer give cross-reanalysis mean WK of 2.8 and 3.1 W m−2, with corrected values spanning 2.6--3.5 W m−2. Both exceed the observation-based Lorenz available-potential-energy generation estimate of 1.2 W m−2. Assuming Wnh≥0, adding WP≃1 W m−2 gives total atmospheric power of about 3.8--4.1 W m−2, motivating investigation of additional power-generation mechanisms.
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BibTeX
@misc{makarieva2026alphaomega,
title = {{The Alpha--Omega Problem in the Assessments of Atmospheric Power}},
author = {Anastassia M. Makarieva and Andrei V. Nefiodov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38522},
eprint = {2610.38522},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38522},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Alpha--Omega Problem in the Assessments of Atmospheric Power
AU - Anastassia M. Makarieva
AU - Andrei V. Nefiodov
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38522
UR - https://arxiv.org/abs/2610.38522
AB - Atmospheric power is commonly assessed with two Lorenz-cycle formulations treated as equivalent: the αω formulation, yielding gas expansion power W_ω, and the v·∇ z formulation, yielding kinetic-energy generation by horizontal pressure gradients, W_K. We show that, for a statistically stationary global moist atmosphere, W_ω=W_K+W_P+W_nh, where W_P is the power of lifting precipitating water and W_nh is power associated with departures from gas-phase hydrostatic balance. Since W_P≃1 W m^−2 globally, equality would require W_nh≃−W_P<0, so the associated vertical force imbalance would have to do negative work globally. Using six-hourly ERA5, JRA-3Q, and MERRA-2 fields for 2025, we find that resolved W_ω varies by a factor of 1.7 (1.9--3.2 W m^−2), versus 1.2 for W_K (2.4--2.8 W m^−2). Zonal-mean αω profiles have area-weighted contributions near ±50 W m^−2, making global W_ω a cancellation residual, whereas v·∇ z profiles vary much less with latitude. The difference W_ω−W_K ranges from −0.61 to +0.87 W m^−2. Thus reanalysis-derived W_ω cannot provide an independent constraint on atmospheric power. Two treatments of the omitted surface layer give cross-reanalysis mean W_K of 2.8 and 3.1 W m^−2, with corrected values spanning 2.6--3.5 W m^−2. Both exceed the observation-based Lorenz available-potential-energy generation estimate of 1.2 W m^−2. Assuming W_nh≥0, adding W_P≃1 W m^−2 gives total atmospheric power of about 3.8--4.1 W m^−2, motivating investigation of additional power-generation mechanisms.
ER -