Atmosphere as a Steam Engine: New Results

I love my work!

I would like to communicate and share a very special mood I am now in — we have just completed a one-year job, finalized and submitted our paper, “Atmosphere as a Steam Engine.” It sheds so much light on the physics of the biotic pump, on condensation-induced atmospheric dynamics, and ultimately on how plants, by creating vapor, literally make the atmosphere do work. It is an accomplishment, a milestone. I am quietly proud and exceptionally satisfied.

When it rains, think that it is the atmosphere at work!

How does a new idea come into your head? I honestly do not know, but perhaps one of the ways is to reach calmness. In this calmness, you begin to see the invisible surface of the Universe, which sometimes has small wrinkles. These wrinkles are pre-ideas: they appear and disappear, but if you are attentive, you may see a pattern and catch one of them mentally, capture it into being — and then, voilà, you have a new idea. Which can also be wrong — meaning that it belonged to a different Universe.

The idea for this paper, new then but accomplished now, came almost exactly one year ago, when we were in Siberia, in a small cabin in the taiga, already one week disconnected from civilization. The brain was still running at full force in an analytical mode, but calmness was already setting in — and then it came.

Now, over the course of this one year, it has matured into a full-fledged work, which we were able to submit two days before we depart for Siberia again, to disappear once more into the green. It feels so bizarre to be free to go, having done what you felt you had to do. Fais ce que dois, advienne que pourra.

So this post shares a mixture of emotions and scientific content from the new paper, which you can find on arXiv here, with the codes for all calculations available at Zenodo:

http://arxiv.org/abs/2605.23875

https://doi.org/10.5281/zenodo.20371682

I am posting this from the airport. The next four posts will come as scheduled posts, as I will be offline until the second week of July.

The Last Day of Pompeii

The Last Day of Pompeii by Karl Bryullov

This is a very large painting in the State Russian Museum in St. Petersburg, where I live. It has a bench nearby, so when we, as schoolchildren, were guided through the museum, one could always rest on this bench and at the same time contemplate the tragedy.

Meanwhile, the guide would explain that the painting tells many stories at once, stories of different people and their small groups. There are sons saving their elderly father; a wounded mother parting with her son; a young family trying to escape with a child. Together, these separate stories create the joint impression of a great drama — which I did not quite experience as tragic when I was a small girl, because the negativity and angst of the painting were softened by the opportunity to rest on the bench.

But I loved the colors.

Our scientific paper, “Atmosphere as a Steam Engine,” is similar in that sense: it weaves together several stories that, especially if you know the context, are quite dramatic. Since our restless minds sometimes have difficulty synthesizing things, we created a sort of painting in the Discussion section, bringing all these stories together for a comprehensive evaluation.

Here it is — let me share three of those stories with you. Please allow me a little drama in the telling: the dry scientific prose is in the arXiv version.

Abstract of “Atmosphere as a steam engine”

Earth’s atmosphere operates a steam cycle in which water vapor evaporates from the surface, expands, condenses in colder air, and returns as precipitation. The Clausius–Clapeyron law relates the incremental expansion work of saturated water vapor to latent heat converted at a Carnot efficiency corresponding to the temperature difference between evaporation and condensation. We generalize this relation to an atmospheric column in which condensation occurs over a range of heights and derive the expansion work per mole of precipitated water. This includes the gravitational work associated with lifting moist air to the mean condensation height, the expansion work generated by condensation, and a correction for incomplete condensation.

Using GPCP v3.3 precipitation and observational constraints on condensation height, we estimate the global steam-engine power as W_v = 4.4 ± 0.9 W m⁻². This is close to an independent estimate of total atmospheric power, W = W_P + W_K ≃ 4.3 ± 0.6 W m⁻², obtained from the gravitational power of precipitation and kinetic energy generation by horizontal pressure gradients diagnosed from MERRA-2. Kinetic energy generation is W_K ≃ 3.2 ± 0.3 W m⁻², of which at least two thirds is generated in the lower atmosphere. The smaller upper-atmospheric contribution is dominated by temperature-related pressure gradients and is comparable to Lorenz available potential energy generation.

We argue that the agreement between steam-engine and atmospheric power is physically linked to condensation and precipitation fallout. By removing water from the atmospheric gas phase and enabling column-mass redistribution, precipitation can maintain surface pressure gradients that drive cross-isobaric flow in the frictional lower atmosphere. The steam-engine framework thus provides a thermodynamic basis for condensation-induced atmospheric dynamics and identifies a major lower-atmospheric power pathway associated with water phase transitions.

First story: A Major Gain in Credibility for Biotic Pump Physics

The biotic pump came into being as a physical concept based on the following consideration: the distribution of water vapor in the atmosphere is strongly compressed relative to that of other gases. This non-equilibrium pressure distribution, caused by water vapor disappearing from the gas phase, allows air to expand and perform work at a rate proportional to condensation. Thus, wind power is proportional to condensation rate.

This formula expresses local kinetic energy generation, σ_CIAD, in the framework of condensation-induced atmospheric dynamics (CIAD, the physical basis of the biotic pump). Here, w is vertical velocity, p_v is water vapor partial pressure, p is air pressure, z is altitude, and γ = p_v/p reflects the relative water vapor content of air. The formula says that kinetic energy is generated in proportion to the decline in this relative water vapor content in rising air as condensation proceeds.

However, this idea, and the corresponding formulations, were kind of an orphan in the community of meteorological truths. It seemingly did not have any connections, yet claimed big things — predicting the magnitude of the atmospheric power of Earth as well as hurricane power. In a way, it could be compared to Kikuchiyo, the “incorrect” samurai from the Seven Samurai by Akira Kurosawa.

Kikuchiyo was not a samurai by birth. He arrived with a false genealogy, noisy manners and an impossible sword.

Orphans do not have the family protection and external attacks are more difficult to handle for them than for others.

For the biotic pump concept, a major line of criticism has always been that the effect is “small.” The controversy here is that the main formulation of the biotic pump correctly predicts the observed magnitude of wind power, so its effect is demonstrably not small. But since the origins of this formulation remained unclear, one could argue that it simply could not be so — while there was nothing carved in stone that ruled out a significant role for atmospheric water vapor pressure differences.

For example, Axel Kleidon wrote the following, with my emphasis:

While it is well known and established that water vapor pressure differences can perform physical work and thus generate motion, the conditions that are associated with this are very different to the Earth’s atmosphere. One practical example of work done by water vapor is the steam engine. Yet, to perform work, the operating temperature and vapor pressure differences of steam engines are substantial. They operate with temperatures above the boiling point of water, for which the saturation vapor pressure is greater than the mean sea level pressure. Such water vapor pressure differences (and temperature differences) are much greater than what is observed anywhere in the Earth’s atmosphere, which at best amount to 3% of the air pressure. Because water vapor pressure differences on Earth are much smaller, the effect on buoyancy can be neglected. Hence, the BP hypothesis is, in principle, not unphysical, but simply focuses on an irrelevant effect and does not explain why convective motion takes place.

That is to say, the criticism did not address how the conclusion about the significant role of water vapor pressure differences had been reached — because this remained obscure. Rather, it argued that the effect must be small because atmospheric water vapor pressure differences are small. There was no common thermodynamic ground on which this dispute could be settled.

And such a battle was difficult for either side to win. As Fred Pearce wrote in Science in 2020:

Since then, there has been neither validation nor disproof, but largely a standoff.

In this paper, we explicitly consider the steam-engine power of the terrestrial atmosphere. The physical picture is relatively straightforward: water vapor evaporates, rises, expands, condenses and precipitates. But the calculation requires accounting for different heights and temperatures, since droplets form at different heights.

After all, why should a huge temperature difference be needed to produce significant power? Significant power can be generated even at a small temperature difference, provided that there is a lot of rain. This is what happens on Earth.

By the way, a pressure difference amounting to 3% of atmospheric pressure — about 30 hPa — corresponds energetically to a wind velocity exceeding 50 m s⁻¹.

During these derivations, we showed that the CIAD formulation represents a part of the steam-engine work: the part related to water vapor expansion caused by condensation. The total work of Earth’s atmospheric steam engine

includes:

[a] the gravitational work associated with lifting moist air to the mean condensation height;
[b] the expansion work generated by condensation;
[c] a correction for incomplete condensation in rising air.

We showed that CIAD represents contribution [b], with contribution [c] assumed to be zero — corresponding to complete condensation.

In the measured and delicate language of a scientific paper, the summary of this story reads as follows:

…since 2007, condensation-induced atmospheric dynamics (CIAD) has suggested that condensation and precipitation contribute substantially to atmospheric power by generating surface pressure gradients. These ideas have given rise to extensive discussion. In particular, the relationship between condensation rate and power generation, while yielding meaningful predictions across diverse meteorological contexts, has remained largely heuristic. The steam-engine formulation developed here provides a thermodynamic framework in which this relationship can be reconsidered.

To give an analogy, it is as if, after Kikuchiyo had already fought courageously and proved through his actions that he was a true samurai, an authentic ancient genealogy were suddenly found showing that he was, after all, of samurai descent.

To summarize, in the paper we calculate the steam-engine power, estimate its magnitude under terrestrial conditions, and then compare it with an independent estimate of wind power, finding close correspondence. We also show that the earlier CIAD relation is a major part of the steam-engine power, thus providing it with solid thermodynamic grounding.

Second story: What Is Bigger?

A subspecies of the narrative “the effect is small,” which has accompanied the biotic pump since its birth, was the idea that this effect is smaller than the effect of latent heat release during condensation — whatever these “effects” may represent in measurable terms.

Condensation does two things at once. It removes water vapor from the gas phase, such that there is less gas around. When the condensed water precipitates, mass is also removed from the atmospheric column. But condensation also releases the energy that was spent on evaporation — the energy required for water molecules to break free from the liquid and enter the vapor phase.

The argument goes like this. Suppose precipitation removes a certain amount of water from an atmospheric column, reducing its weight and hence reducing air pressure at the surface. But the same condensation releases latent heat and warms the air. Since warmer air expands, this warming is assumed to produce a pressure effect larger than the pressure decrease associated with the removed water.

There are two problems with this argument.

The first is that, for condensation and precipitation to occur, rising air must cool, not warm. Thus, when speaking of latent heat “warming,” one is actually comparing condensing air that cools less with some reference air that would cool more in the absence of condensation. Depending on how this comparison is made, the conclusion can differ.

The second point is that, for a column of fixed mass, warming of the air aloft does not by itself increase air pressure at the surface. Surface pressure is determined by the weight of the atmospheric column. Warming changes how pressure differences are distributed with height; removal of mass changes pressure in the lower atmosphere and at the surface.

Therefore, latent heat release and removal of gas by condensation and precipitation do not simply produce two opposing effects that can be compared by asking which one is “bigger.” They create pressure gradients in different spatial domains, with different dynamical consequences.

There is also a more sophisticated historical parallel related to the same problem.

More than a century ago, Max Margules evaluated how much work could be produced by surface pressure perturbations if the atmosphere relaxed from a given state to a static, horizontally isothermal state. He found that the available work associated with surface pressure perturbations was small compared with the kinetic energy of observed hurricane winds.

This reasoning later became part of the background against which atmospheric available potential energy was understood. In a static formulation, the available energy associated with pressure perturbations is proportional to their square. Therefore, if surface pressure perturbations are several times smaller than temperature-related pressure perturbations aloft, their static available energy can indeed be much smaller.

Height-latitude plot of kinetic energy generation. Note the large areas with negative generation in the upper atmosphere: here the air must move against an adverse pressure gradient. Source: http://arxiv.org/abs/2605.23875

But here is the key point: small static available energy does not imply small kinetic energy generation. And vice versa, large static available energy does not imply large kinetic energy generation.

Near the surface, friction makes air cross the isobars, and a surface pressure gradient can therefore continuously generate kinetic energy. Aloft, pressure gradients can be larger, but fast air motion may proceed largely along the isobars — or even against an adverse pressure gradient, as the negative areas in the figure show.

In this sense, the historical argument was important, but it became a distraction when static available energy was taken as a measure of the importance of a pressure gradient in a dynamically maintained circulation. The biotic pump is not a proposal that a disturbed atmosphere quietly relaxes to a static state. It is about a continuously operating moist circulation, in which condensation and precipitation can maintain surface pressure gradients, and friction allows these gradients to generate wind.

So, if you are a biotic pump supporter and are confronted with the argument that the effect must be small compared with latent heat release, you can respond:

Latent heat release shapes pressure gradients primarily through temperature differences aloft, while condensation and precipitation alter column mass and surface pressure in the lower atmosphere. These effects act in different parts of the circulation and are not directly comparable by saying that one is bigger than the other.

And if the dialogue continues, your position becomes even stronger when the logic of our third story is brought in: rain-driven kinetic energy generation in the lower atmosphere and temperature-related pressure gradients aloft do not compete, but work together.

Third story: The Beauty of Rain-Driven Winds

When I look at the colors in old paintings — like this masterpiece by Piero di Cosimo, which filled me with awe when I saw it in the Uffizi Gallery in Florence with Ugo Bardi — I feel that these colors were as deep and solid as the earth herself, nourishing body and soul. There was beauty around, and at least some of our ancestors had time to contemplate it, perhaps without knowing how transient it was.

Much of this beauty is now being lost.

The physical processes that shape our climate are not beautiful in the same direct way: pressure, condensation, motion and work do not nourish the eye and soul like a living landscape. But caught in clean and elegant physical laws, they open to the human mind, and beauty can be seen in them too.

Through this lens, the available data tell us something beautiful: the steam-engine power approximately coincides with the total atmospheric power on Earth — water lifting and wind generation combined. At the same time, our analysis shows, in agreement with CIAD, that precipitation-driven kinetic energy generation occurs predominantly in the lower atmosphere.

How can this happen?

Let me tell an imaginary story about three planets.

First, imagine a planet with a dry atmosphere. The Sun heats this planet mercilessly along the equator. The air there is much warmer than over the poles, and the warm atmospheric columns have higher pressure aloft. This surplus pressure pushes the air toward the poles.

But the planet rotates. Air moving toward the poles, toward the axis of rotation, acquires a fast motion around this axis, and the associated centrifugal force opposes further poleward motion. Instead of freely running from high to low pressure, much of the flow proceeds along the isobars.

The temperature gradients are there. The store of potential energy is there. Some kinetic energy generation is possible. But there is no reason to expect it to reach the power of our moist and raining Earth, where water itself enters the game.

As Heinrich Hertz wrote more than a century ago:

If the atmosphere were dry, the temperature differences existing in it would by themselves give rise merely to movements of minor significance.

Now imagine a second planet. This one has an ocean and rain, but no horizontal temperature differences. Such a planet is far more imaginary: to keep her equally warm everywhere, we would probably need to surround her with several suns.

On this strangely warmed planet, rain removes water vapor from the atmospheric gas phase and decreases pressure in the lower atmosphere. Near the surface, where there is friction and the flow cannot simply follow the isobars, air moves from high to low pressure — toward the rain. This motion brings more moisture into the precipitation area and sustains the pattern.

Down below, the atmosphere is working vigorously. Kinetic energy generation in the lower branch can be large.

Then the air aloft has no other choice but to close the circulation initiated by precipitation below. Since there are no temperature differences, the pressure difference created near the surface remains adverse for the returning air in the upper atmosphere. To complete the circulation, the air must move against this adverse pressure gradient, consuming almost all the kinetic energy that was generated below.

Thus this rainy but horizontally isothermal planet can have strong rain-driven kinetic energy generation in the lower atmosphere and still have little total kinetic energy generation. What she makes below, she loses aloft.

By the way, tropical cyclones provide a very real analogue. They develop over a nearly uniform warm ocean surface, with enormous kinetic energy generation in the low-level inflow. But in their upper-level outflow, rapidly moving air proceeds against an adverse pressure gradient, producing negative kinetic energy generation and offsetting part of the work generated below.

And now let us return to our Earth.

She has both: the temperature contrasts of the first planet, and the oceans and rain of the second. Precipitation decreases pressure in the frictional lower atmosphere and generates air motion from high to low pressure. But now temperature differences change how this pressure difference varies with height.

Here the temperature gradients that were largely locked on the dry planet acquire a new role. They do not have to provide the main kinetic energy generation in the lower atmosphere: precipitation does this. Their role is to prevent this lower-atmospheric work from being undone aloft.

The air rising from the lower branch has already lost much of its newly generated kinetic energy to friction. It cannot sustain an extensive upper-level return flow against a comparable adverse pressure difference. For the circulation to continue, this adverse pressure difference aloft must become small or reverse sign. This is what the temperature contrast makes possible.

The pressure gradient can remain strong near the surface, where rain drives kinetic energy generation, while becoming very small or slightly favorable aloft. In our analysis, the upper-atmospheric contribution to kinetic energy generation just barely exceeds zero. But it does exceed zero: it no longer cancels the large positive generation below.

Thus the two mechanisms meet. On the dry planet, differential heating creates a store of potential energy, but without the moist power pathway much of it remains locked. On the isothermal rainy planet, precipitation generates kinetic energy below, but nearly all of it is taken back aloft. On our living, thriving Earth, precipitation makes the lower atmosphere work, while temperature differences prevent this work from being undone above.

The result is that total atmospheric power — the power of lifting water and generating wind combined — is approximately equal to the power of Earth’s atmospheric steam engine.

So rain does not merely fall from an atmosphere already set in motion by something else. Rain itself is part of what makes the atmosphere move.

And when you look at a tree, think of this as well: it is an enabler of the atmospheric engine over land, feeding it with its working fluid — water vapor.

We need to respect trees.

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