{
  "abstract": "Atmospheric power is commonly assessed with two Lorenz-cycle formulations treated as equivalent: the $αω$ formulation, yielding gas expansion power $W_ω$, and the $\\mathbf{v}\\cdot\\nabla z$ formulation, yielding kinetic-energy generation by horizontal pressure gradients, $W_K$. We show that, for a statistically stationary global moist atmosphere, $W_ω=W_K+W_P+W_{\\rm nh}$, where $W_P$ is the power of lifting precipitating water and $W_{\\rm nh}$ is power associated with departures from gas-phase hydrostatic balance. Since $W_P\\simeq1$ W m$^{-2}$ globally, equality would require $W_{\\rm nh}\\simeq-W_P<0$, 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 $\\pm50$ W m$^{-2}$, making global $W_ω$ a cancellation residual, whereas $\\mathbf{v}\\cdot\\nabla z$ 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 $W_{\\rm nh}\\geq0$, adding $W_P\\simeq1$ W m$^{-2}$ gives total atmospheric power of about 3.8--4.1 W m$^{-2}$, motivating investigation of additional power-generation mechanisms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38522",
  "author_total": 2,
  "authors": [
    {
      "name": "Anastassia M. Makarieva"
    },
    {
      "name": "Andrei V. Nefiodov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97vxbwpyrn157.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38522",
  "fulltext_url": null,
  "id": "97vxbwpyrn157",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38522",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.ao-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38522",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/97vxbwpyrn157.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38522",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38522"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.ao-ph",
      "subfield": "atmospheric"
    }
  ],
  "title": "The Alpha--Omega Problem in the Assessments of Atmospheric Power",
  "title_text": "The Alpha--Omega Problem in the Assessments of Atmospheric Power",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/97vxbwpyrn157",
  "venue": "arXiv",
  "versions": []
}