The atmosphere’s power budget may be hiding a whole extra watt

The atmosphere may be doing more mechanical work than the classic energy-cycle bookkeeping suggests. A new analysis argues that lifting the water that eventually becomes precipitation accounts for about 1 watt per square metre of Earth’s surface—an atmospheric power term that disappears if two widely used calculations are treated as interchangeable. The implication is not that the planet has discovered a new energy source. It is that scientists may have been comparing unlike quantities, and that the global power budget remains less settled than a single number suggests (Makarieva & Nefiodov, 2026).

Atmospheric power is the rate at which the atmosphere generates mechanical energy: the work that helps sustain winds and circulation. That circulation transports heat and moisture, steers storms and shapes rainfall. It is one of the links between the planet’s uneven heating and the weather people experience. To estimate it, climate scientists often use the Lorenz energy cycle, a framework that follows energy as heating creates available potential energy and atmospheric motion converts some of it into kinetic energy (Lorenz, 1955).

The trouble is that two standard ways of estimating that conversion are usually treated as equivalent. One uses pressure changes as air rises and sinks, in a formulation called alpha–omega. The other calculates how horizontal pressure gradients do work on the wind. Makarieva and Nefiodov say the equivalence holds only under conditions—especially dry-air continuity and hydrostatic balance—that a moist, precipitating atmosphere does not necessarily satisfy. Their paper is less a new measurement of global weather than a warning about what familiar measurements can and cannot tell us.

The Science

The distinction is easiest to see by asking what the two diagnostics count. The alpha–omega formulation uses specific volume—roughly, how much space a unit of air occupies—and pressure velocity, which describes how pressure changes as air moves. In a hydrostatic atmosphere, where vertical pressure changes balance the weight of the air above, this can be expressed as gas expansion power. The horizontal-wind formulation measures the work done by horizontal pressure gradients as they accelerate or resist the wind. In the paper, that quantity is called $W_K$; the alpha–omega estimate is $W_{\omega }$.

For a dry, hydrostatic atmosphere with consistent boundaries and no relevant mass sources or sinks, the two measures can be transformed into one another. This is why they have often been used as alternative ways to estimate the same Lorenz-cycle conversion. But water changes the accounting. Evaporation adds water molecules to the gas phase; condensation removes them. Rain and snow also have to be lifted before falling back down. The authors derive a relationship in which $W_{\omega }$ includes not only $W_K$, but also the power of lifting precipitating water, $W_P$, and a term for work associated with departures from gas-phase hydrostatic balance, $W_{\mathrm{nh}}$:

$$W_{\omega }=W_K+W_P+W_{\mathrm{nh}}.$$

Here, “nonhydrostatic” means that vertical pressure forces do not exactly balance the weight of gaseous air. The authors’ identity applies to a statistically stationary global atmosphere, meaning that, over the averaging period, energy and mass are not steadily accumulating inside the global accounting volume. It is a physical relationship, not a claim that current reanalyses can directly observe every term.

The precipitation term has an intuitive basis. Water evaporates near the surface, becomes part of the atmosphere, is transported upward, and later leaves the gas phase as precipitation. Lifting mass against gravity requires work. Makarieva and Nefiodov put this contribution at approximately $1\mathrm{W}{\mathrm{m}}^{-2}$ globally. If the two diagnostic estimates were equal despite this positive term, the nonhydrostatic term would have to offset it with negative work. That is a physical condition to investigate, not an outcome established by the reanalysis data.

To test the diagnostics in practice, the authors calculate them using six-hourly pressure-level fields for 2025 from three global reanalyses: ERA5, JRA-3Q and MERRA-2. Reanalyses combine observations with a weather model to produce a consistent, gridded account of the atmosphere through time. They are invaluable where direct measurements are sparse, but they are not three independent, perfect snapshots of reality: each uses its own model, data-assimilation system and rules for representing atmospheric mass and water.

The authors also examine how the bottom of the atmosphere is handled. Pressure-level datasets do not fully represent the thin layer between the lowest available pressure surface and the ground, even though the paper finds strong power generation near the surface. Two treatments of this omitted surface layer yield different cross-reanalysis means. The excerpt supplied for this digest does not include numbered figure captions, so the visuals below chart reported values rather than inventing references to paper figures.

What They Found

The main numerical contrast is in how much the two estimates vary from one reanalysis to another. Resolved $W_{\omega }$ runs from $1.9$ to $3.2\mathrm{W}{\mathrm{m}}^{-2}$, a factor of 1.7. Resolved $W_K$ spans $2.4$ to $2.8\mathrm{W}{\mathrm{m}}^{-2}$, a factor of 1.2. The reported endpoints are ranges across the three products, not individual values that can safely be assigned to a particular dataset (

Reported ranges for two atmospheric-power diagnostics

Label	Value
Alpha–omega, Wω	1.9 W m⁻²
Horizontal-pressure-gradient, WK	2.4 W m⁻²

Ranges reported by Makarieva and Nefiodov for ERA5, JRA-3Q and MERRA-2 2025 fields; no per-reanalysis values inferred.

).

That difference in stability matters because $W_{\omega }$ is not simply noisy around a robust global total. Its zonal-mean contributions—the averages around bands of latitude—reach area-weighted values near $+50$ and $-50\mathrm{W}{\mathrm{m}}^{-2}$. Those large, opposing contributions largely cancel when summed over the planet. The final global estimate is therefore a small residual of much larger terms. Small changes in the data or processing can shift that residual substantially, even if they barely change the large regional contributions.

This is one reason the paper argues that reanalysis-derived $W_{\omega }$ cannot serve as an independent constraint on atmospheric power. The difference between the two diagnostics, $W_{\omega }-W_K$, ranges from $-0.61$ to $+0.87\mathrm{W}{\mathrm{m}}^{-2}$ across the reported calculations (

The reported spread in Wω − WK

Label	Value
Reported minimum	-0.61 W m⁻²
Reported maximum	0.87 W m⁻²

Reported range: −0.61 to +0.87 W m⁻².

). That spread does not, by itself, measure the physical precipitation or nonhydrostatic terms. The pressure velocity in a reanalysis is tied to the model’s continuity equation, and that equation may not represent the physical sources and sinks of gaseous air in the way the authors’ derivation requires.

The horizontal-pressure-gradient estimate is steadier, but it is not automatically a complete account of atmospheric power either. Accounting for the omitted surface layer gives cross-reanalysis means of $2.8$ and $3.1\mathrm{W}{\mathrm{m}}^{-2}$ under two treatments. Corrected values span $2.6$ to $3.5\mathrm{W}{\mathrm{m}}^{-2}$. These estimates exceed the observation-based Lorenz-cycle estimate of available-potential-energy generation—about $1.2\mathrm{W}{\mathrm{m}}^{-2}$—reported by Romanski and Rossow (2013) (

Power estimates and the observation-based APE benchmark

Label	Value
WK mean, treatment 1	2.8 W m⁻²
WK mean, treatment 2	3.1 W m⁻²
APE generation estimate	1.2 W m⁻²
Corrected WK lower bound	2.6 W m⁻²
Corrected WK upper bound	3.5 W m⁻²

• WK mean, treatment 1 2.8 W m⁻²
• WK mean, treatment 2 3.1 W m⁻²
• APE generation estimate 1.2 W m⁻²
• Corrected WK lower bound 2.6 W m⁻²
• Corrected WK upper bound 3.5 W m⁻²

All values are reported in the paper; the corrected WK range is 2.6–3.5 W m⁻².

).

That mismatch is a question, not a verdict that the older estimate is wrong. The figures describe different sides of an energy budget and rely on different observations, definitions and processing choices. In a statistically stationary classical Lorenz cycle, available-potential-energy generation balances its net conversion to kinetic energy. If one side appears larger than the other, the discrepancy could point to omitted physical terms, diagnostic limitations, sampling and resolution problems, or a combination. The paper’s central contribution is to make that comparison harder to oversimplify.

Finally, the authors offer a conditional estimate of total atmospheric power. If nonhydrostatic work is nonnegative, then adding the approximately $1\mathrm{W}{\mathrm{m}}^{-2}$ precipitation-lifting term to corrected $W_K$ yields about $3.8$ to $4.1\mathrm{W}{\mathrm{m}}^{-2}$. The assumption is doing real work here: the reanalyses are hydrostatic and cannot independently diagnose the actual atmosphere’s $W_{\mathrm{nh}}$. So the figure is a motivated accounting scenario, not a direct observation or settled global constant.

Why This Changes Things

The stakes are about the reliability of the atmospheric energy budget, not a claim that a higher power estimate directly means stronger storms or more dangerous weather. Power describes energy converted into motion per unit time; it does not, by itself, say where that motion occurs, how it is distributed, or how it will change. But estimates of the budget help test whether our physical picture of the circulation is internally consistent—and whether models and observations leave important work unaccounted for.

A key implication is methodological: agreement between two calculations does not necessarily prove they measure the same physical process. A model may enforce a continuity equation that makes the diagnostics agree by construction. In the paper’s account, some systems conserve total atmospheric mass while water changes through precipitation and evaporation; others use different mass-budget conventions. Pressure velocity—the quantity used in $W_{\omega }$—is derived within those choices. Thus a clean-looking equality can reflect a model’s bookkeeping rather than a direct confirmation of physical equivalence in the real moist atmosphere.

That distinction also helps reinterpret earlier disagreements. Researchers have previously reported substantial differences between pressure-velocity and horizontal-wind estimates and often attributed them to data quality, particularly the difficulty of measuring vertical motion. Makarieva and Nefiodov do not deny those practical problems. They argue that data quality is only part of the story: the underlying physical identity includes precipitation and vertical-force work, while model continuity conventions determine which of those terms enter a resolved diagnostic (Li et al., 2007; Marques et al., 2009; Y.-H. Kim & Kim, 2013).

There is a broader lesson for climate science. Large-scale global totals often combine local processes that oppose one another. When the final number is a cancellation residual, precision in the inputs does not guarantee precision in the result. A result can look stable in one formulation and fragile in another, not because one is necessarily useless, but because they respond differently to the errors and assumptions built into the data. Showing the range and its physical meaning is more informative than presenting a single global value without its accounting rules.

For people beyond atmospheric physics, the consequence is indirect but important. Better energy accounting supports better tests of the models used to understand circulation, rainfall and climate change. This study does not revise a weather forecast, attribute a trend in extreme events, or establish that any particular region’s rain is changing. It identifies a basic uncertainty in the global machinery that redistributes heat and water—and a reason to be cautious when apparently equivalent model diagnostics disagree or happen to match.

What’s Next

The next step is to measure or constrain the terms separately. The precipitation-lifting contribution can be estimated from the water cycle and the effective heights at which water enters and leaves the gas phase. But the nonhydrostatic work term depends on vertical force imbalances and vertical motion—quantities that hydrostatic reanalyses cannot resolve as an independent physical measurement. High-resolution, nonhydrostatic models and observations that better constrain vertical structure could help test whether that term is positive, negative or small in the global mean.

Researchers also need to compare the diagnostics using a shared, explicit mass budget. That means tracing how each reanalysis defines atmospheric mass, handles evaporation and precipitation, computes pressure velocity, and fills or excludes the near-surface layer. Testing those choices across more years would show whether the reported ranges characterize a persistent issue or are unusually sensitive to the chosen 2025 fields. Independent estimates of available-potential-energy generation would help close the other side of the budget.

The paper’s case is therefore both provocative and deliberately unfinished. Its strongest conclusion is not that atmospheric power has been definitively measured at $3.8$ to $4.1\mathrm{W}{\mathrm{m}}^{-2}$, but that the two familiar diagnostics do not deserve to be treated as interchangeable evidence without checking what their mass and force assumptions imply. If further work confirms that the budget contains additional power-generation mechanisms, climate scientists will have a richer account of how the atmosphere sustains motion. If it instead identifies biases in current diagnostics, that too would sharpen the tools used to understand a changing planet.