How hurricanes replenish their vast supply of rain water

by Makarieva A.M., Gorshkov V.G., Nefiodov A.V., Chikunov A.V., Sheil D., Nobre A.D., Li B.-L.

New questions and ideas about hurricanes and their power.

Predicting the intensity of tropical cyclones, hurricanes and typhoons is a recognized challenge. We are grateful to Judith for this further opportunity to discuss our work with the Climate Etc. readers. (Some of you may remember previous posts about our work here, here, here and here). In this post we discuss how tropical cyclones fuel themselves by their motion, how this determines their intensity and we note some of the more general implications for atmospheric and land-cover sciences.

UPDATE: link to full paper

Hurricanes and their rainfall

Intense tropical cyclones — hurricanes and typhoons — involve violent winds, torrential rain and low atmospheric pressures. (Please note that hurricanes and typhoons reflect the same atmospheric phenomena — the label used depends only on where they occur.)

It is known that local evaporation accounts for less than a quarter of ongoing rainfall within the hurricane’s rainfall area (about 600-800 km in diameter and comprising the distinct vortex of clouds visible from space). Remarkably, despite the danger associated with hurricane rainfall, where the other three-quarters of the rain come from remains uncertain.

Fig. 1. An approximate water budget for a hurricane (square): mean evaporation 0.5 mm/h, mean rainfall 2 mm/h and imported moisture 1.5 mm/h within 400 km from the center. Mean tropical evaporation in a hurricane-free environment is about 0.2 mm/h. Also shown are relative humidity H and surface pressure ps at different radial distances r from the hurricane center.

In our recent study (in press in Atmospheric Research, accepted manuscript available from here, discussed in Physics World here) we argue, based on an analysis of available data, that hurricanes extract pre-existing moisture from the atmosphere as they move through it. Thus, the storm’s so-called propagation velocity — its velocity relative to the rest of the atmosphere — is key.

Our result has implications for understanding hurricane intensity too. It is widely believed that a hurricane derives its energy extracting heat from the ocean. Theory tells us that the power of such a steady-state process is constrained by Carnot efficiency (see multiplied by the oceanic heat flux. In contrast we argue that a hurricane derives its energy from the water vapor previously accumulated in the atmosphere (this vapor represents a major store of potential energy). The power of such a system is not constrained by Carnot efficiency: while the potential energy is limited to what is stored in the atmosphere, there is no thermodynamic limit on the rate that this can be released (as in an avalanche).

Before discussing the storm intensity in more detail, it is relevant to examine why water budgets have received such limited attention.

Why rainwater origins were not studied – our hypothesis

In 1960, in an influential paper, Malkus and Riehl (1960) [hereafter MR] proposed that rainfall does not matter. They wrote (our emphasis):

“… variations in the rate of import, condensation and export of normal tropical air will not lead to variations in surface pressure because the ascent path, and therewith the density of the vertical column, is entirely determined by the θE of the rising air. A storm will not deepen if simply more water is condensed at θE=350oA in the core; it can do so only if there is an additional heat source so that condensation will occur at θE greater than 350oA.”

For those unfamiliar with the meterological terminology, equivalent potential temperature θE is a measure reflecting, besides local temperature and pressure, the amount of water vapor in the air. Essentially, MR say that a surface pressure difference driving the hurricane-force winds can form only if the air rising in the hurricane core carries more water vapor than the ambient air. This excess water vapor — provided by oceanic evaporation as the air moves towards the hurricane core — represents the (main part of the) “additional heat source”.

In other words, rainfall does not matter, but evaporation does. This statement is somewhat puzzling. Indeed, for the surface pressure to fall, something must be removed from a hydrostatic atmospheric column, not added — meanwhile evaporation adds water vapor to the atmosphere.

We use our new approach to explain MR’s ideas as follows. Consider the mean tropical troposphere which we will here approximate as having a mean lapse rate of 6 K/km, surface temperature 26 oC and surface pressure 1015 hPa. We thus know the dependencies of pressure p and temperature T on altitude z. Relative humidity at the surface is about 80% (see, e.g., Table 5 of Jordan 1958 — the data used by MR).

Let’s compare this environmental pressure profile pe(z) with the pressure profile ph(z) the hurricane air would have if it were rising adiabatically from the surface with the same pressure and temperature, but with a higher relative humidity — 100%.

Fig. 2. Pressure Δp(z) = ph(z)-pe(z) and temperature ΔT(z) = Th(z)-Te(z) differences between hurricane air rising adiabatically and the mean tropical environment. The red square marks the altitude where air densities are equal, the blue circle marks the altitude where pressures are equal. (Cf. Fig. 1c in Makarieva et al. 2017b and Fig. 2 in Makarieva et al. 2015a).

We can see that the hurricane has a greater pressure in the troposphere. The reason is that as the air rises and cools, the water vapor condenses. The more water vapor condenses, the more latent heat is released. As there is more water vapor in the hurricane’s air, its temperature drops with altitude more slowly than in the surrounding air: or, to put it simply, the hurricane is warmer. Thus, since the scale height of the exponential pressure distribution is proportional to temperature, the air pressure drops with height more slowly in the hurricane than it does in the environment outside the storm.

So far we have not created (i.e., explained) any pressure drop at the surface. Now the key point: Let us imagine that this mid-altitude pressure surplus drives air away from the hurricane core. Since the surface pressure reflects the weight of air in the column, as soon as some air is removed, the surface pressure drops. But the pressure surplus diminishes as well, since the hurricane pressure at any altitude is proportional to surface pressure. Thus, gradually decreasing surface pressure in the hurricane we observe that at a certain moment the pressure surplus disappears altogether:

Fig. 3. Pressure difference between hurricane and environment versus altitude as dependent on the surface pressure drop.

Once this happens, we obtain an “unperturbed top” for our hurricane — an altitude where pressure, density and temperature in the hurricane and environment coincide.

This is the gist of the conventional hurricane intensity theory: pull the bottom of the pressure difference curve in Fig. 3 to the left until the pressure surplus disappears, and you get the maximum hurricane pressure drop at the surface. In this context “maximum” presumably refers to two things: (1) the fact that the rising air has 100% relative humidity at the surface and thus contains the maximum possible amount of water vapor and (2) the fact that once the unperturbed top is obtained, we, for some reason, cannot pull the curve any further to the left.

This approach ignores rainfall and other fluxes: it only requires a difference in the water vapor content between hurricane air and the wider environment. Since this difference is provided by evaporation, other factors such as rainfall are, this approach suggests, irrelevant.

Thus obtained surface pressure drop appears to be highly sensitive to minimal variations of atmospheric parameters in the vicinity of the unperturbed top. This sensitivity of the surface pressure estimates to parameters set at the top of the troposphere was discussed by Holland (1997) and, from a different perspective, by Makarieva et al. (2015a). However, the main problem with this approach is that it is not specified why an unperturbed point should exist at all in the presence of hurricanes. Why cannot we pull the pressure difference distribution even further to the left reaching greater surface pressure drops?

Maximum potential intensity and the Carnot cycle

In MR’s approach maximum potential intensity (MPI) is a unique function of the relative humidity H in the hurricane core (provided the environmental pressure profile and surface temperature Ts are known). The temperature and pressure of the unperturbed top is also set by H. Emanuel (1986) modified MR’s approach by adding one more free parameter to the MPI calculation. In his approach the environment is represented not by a fixed pressure profile, but by an isotherm and an adiabat (see curves DE and EF, respectively, in Fig. 1). Varying the altitude where the isotherm and the adiabat meet (i.e. point E), for a given H in the hurricane core it is possible to arrange an unperturbed top at any desirable altitude, pressure level and temperature. The temperature of the unperturbed top has become a free parameter called the outflow temperature To.

With two isotherms (one at the surface and another in the upper atmosphere, curves FB and DE in Fig. 1) and two adiabats (BD and EF) it became possible to interpret the hurricane as a Carnot cycle working on an isothermal oceanic surface and receiving heat and moisture from the ocean.

But it is a peculiar kind of Carnot cycle. Emanuel’s approach retained an essential property of MR’s approach: no mechanical work is performed in the upper atmosphere. Indeed, when an air parcel of a given mass rises from the surface in the hurricane core to reach the unperturbed top, then flows along the unperturbed top to the outer environment where it descends back to the surface, such an air parcel does not generate any mechanical work along its path (see Appendix A in Makarieva et al. 2017b for details). This is because the change of its potential energy along this path is zero, and no kinetic energy is generated either because at the unperturbed top there is no horizontal pressure gradient (by definition). Likewise, Emanuel’s hurricane is assumed to produce zero work in the upper atmosphere. Thus the total work produced by this Carnot cycle is equal to the work at the lower isotherm (surface); this mechanical work takes the form of the kinetic energy of the hurricane.

The rest is simple: since work W on the warmer isotherm is a function of the surface pressure difference Δps, while heat input Q is a function of Δps and ΔH, relating W = kQ via Carnot efficiency k=(TsTo)/Tsprovides an equation on Δps as a function of k and ΔH. The intensity of such a cycle can be considered a maximum in that sense that all kinetic energy is produced at the warmer isotherm – i.e. at the surface where the hurricane develops. Nothing is left for the upper atmosphere.

The sensitivity problem persists and the question why work in the upper atmosphere should be zero, lying at the heart of this approach, remains unanswered.

Before Holland (1997) exposed the high sensitivity of MPI to the outflow temperature, DeMaria and Kaplan (1994) had compiled intensity estimates of North Atlantic hurricanes to find that maximum intensity for each surface temperature agrees favorably with Emanuel’s MPI — provided some dependence is postulated between the surface and outflow temperatures. Since the outflow temperatures are defined and measured with far less certainty than surface temperatures, it was difficult to test this dependence empirically. Since then, MPI is considered as a plausible upper limit to hurricane intensity.

Reports of intensity beyond the MPI are rare but they do occur (see Montgomery et al. (2006)discussing Hurricane Isabel in 2003); to our knowledge, sporadic mentions of these intensity “over-achievers” are not systematized.

More recent developments: The gravitational power of precipitation

When in 2000 Pauluis, Balaji and Held proposed that the gravitational power of precipitation makes a significant contribution to the atmospheric power budget, nobody in the hurricane world seemed to notice. (The fact that it was the 21st century before the atmospheric sciences noticed rain as something beyond latent heat, is interesting in itself. Even now the global gravitational power of precipitation has only been estimated by only one group, ours — and we have recently submitted this estimate to publication.)

Another advance occurred in 2015 when a team of Japanese physicists estimated that in hurricanes, too, a significant part of the circulation power goes to raise the rainwater. They noted that hurricane intensity (i.e. their kinetic energy) must be significantly influenced by this drain on their energy substantially reducing estimates. Thus Sabuwala et al. (2015) published corrected intensity estimates for the 1999-2010 hurricane seasons — all by 10-30% lower than the conventional MPI. Since most hurricanes never reach their MPI, accounting for the gravitational power of precipitation has driven the corrected intensity estimates closer to observations. The authors interpreted this as a positive thing.

However, this achievement has raised a problem: what about those most intense hurricanes that have been previously shown, by DeMaria and Kaplan (1994) and others, to match the uncorrected (i.e. overestimated) MPI? Since those hurricanes do raise rainwater too, they are apparently over-achievers – i.e. total mechanical work performed by them goes beyond the Carnot cycle output.

Fig. 4. This is modified Fig. 1 of DeMaria and Kaplan (1994) (small black dots and thin curves) where we conservatively (and very approximately) applied the intensity corrections from Fig. 4a of Sabuwala et al. (2015) (large red dots and thick curve). Hurricanes above the red curve are potential “over-achievers” (1-5% of all observations).

Thus, now we do not just have hurricane Isabel possessing an apparently higher intensity than MPI (see Montgomery et al. 2006). We have a whole population of them.

The findings of Sabuwala et al. indicate conceptual problems with the MPI approach, which could be expected to have stirred a community of theorists. Yet, two years after publication in a high profile journal, this illuminating study has only one citation as reported by CrossRef — that was by our team.

To summarize, the problems with the current MPI approach are

  • High sensitivity to key parameters (outflow temperature), which makes possible easy tuning and hinders verification by observations
  • No theoretical rationale for the key dynamic proposition: the existence of unperturbed top in the approach of MR and zero mechanical work for z > 0 in the approach of Emanuel
  • Most intense hurricanes go beyond MPI (an explanation for this pattern is provided in Section 6 of our Atmos Res paper)

The use of numerical models to understand hurricanes deserves a comment. To generate a hurricane, we must remove air to reduce surface pressure and generate the center of the storm. This requires air flowing out from the hurricane center. In modern hurricane models this radial motion is governed by parameters of turbulent friction — these parameters are fitted empirically to provide a realistic pressure profile (e.g., Bryan and Rotunno 2009). Such models — by their construction — are unable to test whether (and to what degree) the pressure surplus associated with a higher water vapor content in the hurricane core can produce the pressure gradients required to drive an intense hurricane. Likewise, switching rainfall “on” and “off” in such fitted-parameter models sheds little light on how rainfall influences hurricane dynamics.

We thus argue that there are good grounds to revisit the imperatives set out half a century ago when the knowledge about the atmosphere, and the resources allocated to study it, were way poorer than they are now. The statement that the rain does not matter should be re-considered.

Way forward

Having established a linear correlation between rainfall rate and hurricane intensity Sabuwala et al. 2015 were apparently puzzled as to how to best account for what people actually think about rainfall in this field. In the Introduction, with a reference to Rodgers et al. 1994, Sabuwala et al. discussed the idea that rainfall can actually increase hurricane intensity: “latent heat is released which helps propel the updraft, which in turn increases the supply of water vapor and so forth.” However, this reasoning, as we have discussed, runs counter to the conventional paradigm, which denies any importance for rainfall intensity.Emanuel (1991) put it in this way: “Attempts to regard the condensation heat source as external lead to the oft-repeated statement that hurricanes are driven by condensation of water vapor, a view rather analogous to that of an engineer who proclaims that elevators are driven upward by the downward acceleration of counterweights.”

(It is of interest that in a closely related field monsoon scientists widely use the concept of “moisture advection feedback” – whereby the circulation intensity is assumed to be proportional to the (horizontal differences in) rainfall intensity – exactly because it is believed that latent heat release is proportional to rainfall rate and is what propels updrafts etc.)

Sabuwala et al. further noted that “from the positive correlation between P [precipitation] and V [hurricane wind speed] evinced in Figure 1d, it is tempting to argue that the effect of rainpower is to increase hurricane intensity. And yet positive correlation might not signify causality nor can the effect of P on V be understood in isolation from other aspects of a hurricane’s thermodynamics.”

However, the dependence between rainfall and hurricane intensity is not just a “positive correlation”. We have formulated a theoretical approach that quantitatively explains the empirical dependence between rainfall and hurricane intensity.

Fig. 5. Observations of Sabuwala et al. 2015 explained in the framework of condensation-induced hurricanes (Makarieva et al. 2015b).

In our approach, rather than being driven by latent heat, the hurricane is driven by condensation which releases potential energy accumulated in the form of atmospheric water vapor. As the water vapor condenses in the rising air, a non-equilibrium vertical pressure gradient forms that enhances the ascending motion. Once the hurricane air reaches the height where condensation ceases, it is propelled away by the centrifugal force — the centrifugal force overcomes the horizontal pressure gradient which diminishes with height. In other words, the air outflow can efficiently occur at the expense of the centrifugal force — it does not require any pre-existing pressure surplus shown in Fig. 2. Work output in the upper atmosphere can be negative (similar to what happens in Ferrel cells, see Makarieva et al. 2017b) — it does not have to be zero as currently assumed.

Hurricane power is determined by the work per unit time of the non-equilibrium pressure gradient of water vapor that formes during condensation. As water vapor fuels the storm, it is the availability of this vapor and the rate at which it can drawn into the cyclone that limits its intensity. Such processes are not steady-state Carnot cycles receiving heat from the ocean but rather deplete the potential energy of the pre-existing water vapor and can thus outperform a Carnot cycle. Key to hurricane intensity is the availability of water vapor in the surrounding atmosphere.

Thus hurricanes are not steady-state Carnot cycles receiving heat from the ocean – they deplete potential energy of the pre-existing water vapor as they move — as an avalanche. This explains why they can outperform a Carnot cycle.

Our view is that the same energy that powers hurricanes also drives many other air circulation patterns. This includes the main atmospheric transport of water vapor from the ocean to land. On land the store of water vapor in the atmosphere is largely created and maintained by plants. Thus forest and vegetation can ensure you a persistent flow of moist air from the ocean – e.g. the Californian drought could be eased by large-scale restoration of natural forests. Likewise, securing Amazon forests is crucial for ensuring reliable rainfall through South America, including in agricultural regions (Nobre 2014). Plants matter for climate much more than many of us are used to thinking (Ellison et al. 2017). We urge greater attention to the role and dynamics of water vapor condensation in hurricanes and in atmospheric sciences more generally.

Moderation note: As with all guest posts, please keep your comments civil and relevant.

72 responses to “How hurricanes replenish their vast supply of rain water

  1. Can oil on water, preventing evaporation, kill a tropical cyclone?

    • From our viewpoint, if you mean spreading oil on water immediately under the hurricane to prevent concurrent evaporation — it won’t kill a tropical cyclone (because the cyclone feeds on pre-existing atmospheric water vapor). Consider tornadoes — same violent vortices with no surface moisture input.
      If however we prevent evaporation completely such that the atmosphere gets dry, then hurricanes will not develop.


  2. Re restoration of natural forests easing the Californian drought. Historically, before the advent of Western civilization, California has suffered extreme and prolonged droughts. Obviously those droughts would have reduced biomass considerably, perhaps creating a feedback, but I’m not sure that the cause-effect relationship is all that clear.

    • Our Western civilization is by far not exceptional in disturbing and destroying the natural plant biomass.

      All big animals-herbivores are in a way similar to a hurricane. With a universal energy consumption by life of about 1 Watt/kg and a body mass of 100 kg large animals can consume about a thousand watts per square meter of their body projection to the Earth’s surface. This is a thousand of times greater energy flux than our biosphere is able to produce (global primary productivity of the order of 1 W/m2).

      Thus, like hurricanes devouring previously vaporized water and unable to sustain themselves by long-term mean evaporation, big animals must move consuming the biomass previously produced by plants on their way. In so doing, big herbivores invariably introduce dangerous disturbances to vegetation functioning. Any ecological imbalance accompanied by an exponential rise of population numbers of large herbivores can lead to a break down in native plant life — and, hence, to a drought and ecosystem collapse.

      Thus life on land in the presence of large herbivores is intrinsically unstable. We humans are unique only in that sense that we are presumably able to do science and then change our behavior depending on the obtained results. Thus, having known that forests bring rain, we can choose not to destroy them or to try to restore what has been lost.


      • “Thus life on land in the presence of large herbivores is intrinsically unstable.”

        Isn’t that were large carnivores come into it – to restore stability, at least in non human-engineered environments?

      • Isn’t that were large carnivores come into it – to restore stability, at least in non human-engineered environments?

        To a certain degree yes, and that’s an important function of carnivores — to stabilize plant life via their control of herbivores. However, the predator-prey system is itself stable only within a certain range of ecological parameters; i.e. it is itself prone to disintegration.

        In the ocean the situation is very different. There is very little live biomass (a thousand time less than on land). In consequence, the majority of herbivores are very tiny organisms unable to seriously disturb phytoplankton functioning. From this viewpoint oceanic ecosystems are more stable than terrestrial ones.


      • Restoring stability will be a re-occurring theme for humanity as it advances, necessitating change, necessitating opportunities of upsetting stability. We are curious monkeys in a china shop trying to stay handy at fixing stuff.

  3. Pingback: How hurricanes replenish their vast supply of rain water – Enjeux énergies et environnement

  4. That was very interesting!

    I seem to recall a paper about a fairly long term (decades) decrease in atmospheric water vapor (contrary to global warming theory), and I think this post’s new theory would say that hurricane intensity would also thereby decrease because of less available water vapor in the atmosphere.

  5. Much food for thought – thank you. It is refreshing old-fashioned science.

    CO2 influences evapotranspiration – and your work seems to introduce the potential for even broader impacts on terrestrial hydrology and ecology. To bring it back to the obsession de jour.

  6. Seems fair to me.

    Even has the appearance of scientific method.


  7. I think it was noticed by others before the 21st century (see Mazzarella’s concept of a ‘torque,’ below). The authors above write:

    (The fact that it was the 21st century before the atmospheric sciences noticed rain as something beyond latent heat, is interesting in itself. Even now the global gravitational power of precipitation has only been estimated by only one group, ours — and we have recently submitted this estimate to publication.)

    However, rather than simplifying reality with the GCMs that are now used to capture the complexity and interconnectedness of natural phenomena comprising global warming, Adriano Mazzarella noted that we need a better understanding of the concept of a ‘torque’ and additionally, the natural power of ‘swirling vortices’ as key elements to a better understanding of climate change.

  8. I sort of get this. My late father was a UCLA Masters meteorologist and commander of the 409th Typhoon Chasers off Guam before the Korean War. Instrumented B-29s. 24 hour missions. Very early days. Lots of dinner talk memories. Living now mostly in hurricane ally (Feet Lauderdale) we know intensification is the least resolved NHC prediction factor. So lets go get more data and check this new storm energy idea out. Whether we evacuate or ride out depends on just track and intensity. Track prediction has improved since movd here (narrowed cone of uncertainty). Intensity has not. More true science, please.

  9. David L. Hagen

    Thanks for your thought provoking model applying strong physical principles.
    PS I recommend referencing the CODATA value for the “molar gas constant” R = 8.314 4598(48) J mol-1 K-1
    I recommend replacing the popular phrase “the centrifugal force” with the technical term “centripetal acceleration“.

  10. From a previous posting on this blog ( re Makarieva et al.) –

    “We can now compare our theory with observations. First, we note that the mean global power of atmospheric circulation estimated from (5) is about 4 W m−2, which is in close agreement with the best observational estimates. We note that this is the first and only theoretical estimate of the power of global circulation currently available.”

    I confess to being only slightly surprised that nobody has previously addressed the global circulation power. It seems to me that this might play some role in climatological considerstions.

    More power to real scientists. Just because nobody seems to have done it before, doesn’t necessarily mean it’s irrelevant – consensus thinking notwithstanding.


  11. Thank you for the essay.

  12. Reblogged this on Climate Collections.

  13. Very enlightening. I had no idea that the state of knowledge about these storms was so undeveloped. That explains my inability to find any explanation of how the latent heat of condensation is transported from a cloud.

    One suggestion, though. The references to the Carnot cycle should be fixed. The Carnot cycle doesn’t exist in reality, and can’t, because it assumes that heat flow across boundary surfaces is reversible (it’s not). It was purely a pedagogical tool developed to put an absolute upper bound on the efficiency of a heat engine. No actual heat engine efficiency is of the form 1 – TL/TH. The Rankine cycle can come close, as can the Stirling cycle. It would interesting to see if hurricanes follow one of the classic cycles.

    • The Ericsson cycle (same engineer who invented the USS Monitor) has Carnot cycle efficiency, as does the Stirling cycle. Unlike the Stirling cycle, the Ericsson cycle might be quite useful, and an old RAND study recommended that all US turbine power plants switch to a modified version where the air is cooled between compressor stages (approximating isothermal compression), then run through a recuperator/regenerator heated by the engine exhaust, then combusted and run through multiple turbine stages with reheat in between them to approximate isothermal expansion.

      A true Ericsson cycle engine could be built with very slow pistons, which wouldn’t be practical for ship propulsion but might be practical in a power plant, where physical size isn’t much of an issue.

    • Carnot Cycle is an idealized case so of course it doesn’t exist as anything other than a reference. It is like planetary equilibrium, you just have to figure out how useful the concept might be.

    • The ideal reversible Carnot cycle does not produce power or work. The model requires equilibrium processes, ideal reversible processes require infinite time. If the driving potential is sufficiently small to approach reversibility, the work approaches zero, and the power approaches zero. If the processes take infinite time to approach reversibility, the power approaches zero.

      Real world finite time processes and real world finite driving potential processes will always involve irreversibility.

      I am basically unfamiliar with the Tropical Storm modelling literature. It is somewhat disconcerting to see the ideal Carnot cycle efficiency as a part of any discussion of power. If the modeling is based on the ideal reversible Carnot cycle, power cannot be the subject. And if the modelling is otherwise correctly posed, the “efficiency” cannot be greater than the Carnot efficiency. At maximum power the efficiency of a Carnot cycle engine is ( 1.0 – SQRT(Tc/Th) ). If the modeling is correctly posed relative to power the efficiency at maximum power cannot be greater than this value, which is less than the efficiency of the ideal reversible Carnot efficiency.

      All corrections will be appreciated.

      • If you use a Carnot Cycle model and the output exceeds the Carnot efficiency it is pretty obvious something is missing. Kerry Emanuel owns the first hurricane Carnot engine reference I found and I believe he is a heavy hitter in Climate Science :)

      • You are right. In 2010 we pointed this out. In their reply Bister, Renno, Pauluis and Emanuel (2011) appeared to have missed the point stating the following:
        “MGLN raise the separate and interesting issue of finite time thermodynamics, which we have not addressed in our previous work. This deserves a more extensive treatment than is practical in this comment, but we make two points about this here. First, the observed temperatures in the atmospheric boundary layer are usually only a degree or two less than those of the sea surface; as this is a small fraction of the temperature difference between the temperatures at which enthalpy flows in and out of the hurricane, we expect the finite time effects to be correspondingly small.”
        So, indeed, the maximum potential intensity theory, as it currently stands in atmospheric sciences, is based on Carnot efficiency which, as you rightly mentioned, is only valid in the limit of zero power.


      • captdallas2 0.8 +/- 0.3
        If you use a Carnot Cycle model and the output exceeds the Carnot efficiency it is pretty obvious something is missing.

        Carnot cycle describes a steady-state process. So, if one believes that a hurricane is a steady-state cycle which receives heat from the ocean, and then one observes an efficiency exceeding Carnot efficiency, this means that the hurricane is not a Carnot cycle.

        Consider an avalanche: here potential energy is transformed to kinetic energy with an efficiency close to unity. Once the potential energy is depleted, the process stops. We propose that the hurricane as it moves consumes the water vapor and transforms this potential energy to kinetic energy leaving a drier atmosphere in its wake.


      • Anitassia, ” We propose that the hurricane as it moves consumes the water vapor and transforms this potential energy to kinetic energy leaving a drier atmosphere in its wake.”

        I agree, Carnot Cycle is limited but was used by Kerry Emanuel among others to describe cyclones as heat engines. So for a given Th and Tc you may have a maximum amount of work done and anything over that would have to be the result of some other input. Carnot Cycle wouldn’t apply to the whole process but is could still be used as a reference.

  14. Geoff Sherrington

    Cyclones can exist for many days, often with heavy rainfall, after making landfall. For example, the highlighted track on this map covering years 2000-2010 (BOM acknowledged) was cyclone Steve, landfall 27 Feb 2000 near Cairns on the East Coast, exited land on the southern coast on 11 March 2000, some 13 days and about 5,000 km later, mostly travelling over historic low rainfall and desert areas, with an occasional brush with oceans.
    More information on TC Steve is here:
    The full recorded history of cyclone tracks shows many more tracks over dry land, cyclones that replenished their water from somewhere. For these, it is almost as if they collect rainwater at the tail of their weather system, after it has fallen at the head of the system, doing a continuous cycle from rear to front. (I have not done any rough maths on this yet).
    I do not know the details of replenishment, merely suggesting that West Australia could be a good study area.

    • Thank you for the interesting data.

      For these, it is almost as if they collect rainwater at the tail of their weather system, after it has fallen at the head of the system, doing a continuous cycle from rear to front.

      Evaporation is well-known to be significantly smaller than rainfall within the area of intense cyclones. This rules out any recycling of rainwater. I guess that if you consider the atmospheric moisture store ahead of the cyclone and estimate its propagation velocity, you will find that consuming this moisture store is probably enough to sustain rainfall.

      Without a detailed analysis, if asked for an opinion, I would suggest that TC Steve could be traveling in the way it did because the atmosphere where it traveled was (unusually) moist.


      • Geoff Sherrington

        Thank you, Anastassia.
        Another curious feature appears in these cyclone tracks. Many times the track intersects the land at about 90 degrees to the land, seldom at a shallow angle. This is seen when cyclone is in a strong phase, especially for East Coast of Australia. Maybe this gives some information on mechanisms, like the influence of what is ahead of the cyclone for the next 50 km or so before and as it crosses onto land. Maybe the physics of the system guides it towards a region with preferred properties, like humidity or evaporation rate or topography, but these are no more than guesses.

      • Hurricane Dennis 1999 had the unusual track of curling to a standstill off the coast and then complete a loopty-loop back itself as hit shore while weakening. (It just missed me.) This might have some good data for you, Anastassia.

  15. I don’t know what problem this paper is trying to solve. There was a paper by Trenberth on a similar topic in 2007. The implications of warming SSTs are discussed.

    • This paper is trying to solve a fundamental problem in dynamics/thermodynamics as applied to hurricanes. Bohr’s quadrant stuff. Trenberth’s paper is more edison’s quadrant to taxonomy quadrant

    • Commenting on our work Dr. Trenberth recognized that the moisture must come from somewhere (since evaporation within the hurricane’s rainfall area is by far insufficient to explain the observed rainfall). In our paper we propose a novel view on how hurricanes can get this remaining moisture — by motion.


  16. David Springer

    Can you confirm that hurricanes really are a Russian invention?

  17. Can someone explain “the gravitational power of precipitation?”

    • Pretty much self explained. Hurricanes create huge quantities of precipitation. The gravitational power should be negligibly small with respect to all the other factors, but new moon hurricanes do tend to be stronger that others, or at least that was the subject of previous papers.

    • Can someone explain “the gravitational power of precipitation?”

      It is the same as hydropower: a certain amount of water is falling per unit time from a given height. The formula is the same: gravitational power of precipitation is P g H, where P is precipitation (kg water/m2/sec), g is acceleration of gravity and H is the height from which the water precipitates. With P ~ 1 t/m2/year the global gravitational power of precipitation is about 1 W/m2 or about one fifth of total atmospheric power.

      To raise this rainwater, the atmosphere must do some work.


      • Re hydropower and rainfall

        I recall as a student in Leningrad Polytechnic Institute where Victor Gorshkov was then lecturing, during his course “Ecology of man” we were challenged to consider possible (and impossible) sources of renewable energy to fuel our civilization.

        Rainfall was one of them: imagine collecting rainfall with wide umbrellas spread across high masts high in the atmosphere once a storm is approaching – then using the potential energy of this water to do something useful, e.g. to generate electricity.

        With rainfall on land about 0.5 m/year = 0.5 tonn/m2/year and assuming that it falls from somewhere in the middle of the atmosphere (H = 5 km) the maximum power output available on land would be around 10^14 Watt (see Gorshkov and Dolnik 1980 Sov Phys Usp 23: 386, Table I) – compare this to the 2×10^13 Watt our civilization currently consumes.

        However, we also learnt that this renewable energy source, luxurious as it might seem, counts as “impossible”.


    • The energy required to raise water from the surface from which it evaporates to the level of the clouds. This energy is then released when the water falls as rain.

      (Since water vapour is buoyant in air no mechanical work is required to raise the water vapour up to the clouds, as would be needed if you wanted to raised a bucket of water to the same height. The gravitational energy comes from the internal energy of the water vapour, resulting in less latent heat being released when the water vapour condenses into rain (or ice) at cloud level.

      Gravitational energy = mass * height * g : where g = 9.81m/s^2
      Latent heat = mass * lhv : where lhv = 2.2×10^6 J/kg

      So for clouds at 4000m the gravitational energy is only about 1.7% of the latent heat)

  18. I believe that fierce winds make the water turbulent and it picks up water, as water drops, and transports them to produce much of the rainfall. This in addition to the evaporation.

  19. This is an exciting presentation and has all the makings of a recognized breakthrough. I did not know TCs thermodynamics were still not accounted for. It’s all the more fascinating that both the evaporation and condensation are combining in symbiosis to intensify and perpetuate TCs. Nature can be very cool by accident. The avalanche analogy makes sense except why is it so common for TCs to follow near the same path separated sometimes by only ~7 days if the air in the wake of TCs has lost so much moisture? Is humidity recovered that fast?

    Also can you clarify this?

    On land the store of water vapor in the atmosphere is largely created and maintained by plants. Thus forest and vegetation can ensure you a persistent flow of moist air from the ocean – e.g. the Californian drought could be eased by large-scale restoration of natural forests.

    This sounds like you are saying we need more surface water reservoirs on land so that we get more rain so that we can keep our reservoirs full. And, of course, that is circular so you can’t be meaning that.

    • The avalanche analogy makes sense except why is it so common for TCs to follow near the same path separated sometimes by only ~7 days if the air in the wake of TCs has lost so much moisture? Is humidity recovered that fast?

      Fig. 4a in our paper (PDF) shows that the atmospheric moisture content where hurricanes form is about 40 mm (40 kg water vapor/m2). With mean evaporation of about 0.2 mm/day, the turnover time is 20 days.

      Thus, in an idealized case — if the atmosphere was motionless and the hurricane was walking through it depleting all water vapor on its way – like a cow eats grass away on a pasture – then, sitting somewhere amidst this pasture, we could not expect one hurricane to follow another in less than 20 days.

      However, in reality we have estimated that the hurricane consumes around 70% of water vapor; and weaker cyclones could consume even less. This would reduce the minimal time interval to about ten days.

      Furthermore, the atmosphere moves itself – i.e. the hurricane is embedded into a so-called steering flow. Mean velocity of the hurricane’s center relative to the Earth’s surface is called translation velocity (it is about 5 m/sec). Mean velocity of the hurricane relative to the steering flow is called propagation velocity (it is about 0.7 of translation velocity, see Fig. 9c in our paper). It is this propagation velocity that matters for the cyclone’s water budget.

      Thus, how the local moisture stores are replenished is not uniquely determined by evaporation only — but also by lateral mixing. This makes the minimal return time for TC more fluctuating and seven days appear to be quite realistic.

      Note also that dry air does not sit exactly in the wake of the cyclone to meet the following one — it is brought away by air flows in the upper atmosphere — see Fig. 9a in the paper which shows the vertical distribution of radial velocity. The outflow of dry air is confined to the upper troposphere.

      • Anastassia: (If I understand correctly) under normal circumstances, the RATE of evaporation is proportional to wind speed and the undersaturation of the air over open water. (Wind speed is limiting because turbulent mixing is needed to promote vertical transport from the thin saturated layer of air adhering to the surface.) In the long run, the RATE of evaporation determines the RATE of precipitation, though the average global turnover time (9 days) is far too slow for hurricanes. The rate of exchange between the boundary layer and the free atmosphere produces undersaturation of about 20% thereby controlling evaporation. In the tropics, the trade winds sweep this moisture to the ITCZ, where the greatest precipitation falls. I’ve assumed hurricanes did something similar, except they concentrated the energy released into a small location. (And none of this depends directly on SST.) What I appear to be missing it is that hurricanes can’t be analyzed in such equilibrium terms. If they were, how big an area would they need to collect latent heat from to power themselves? Or do new physical principles come into play when winds are much stronger?

        The idea discussed by Ron above assumes that the dry air left behind by a hurricane remains in the same location for days or weeks. Perhaps in the doldrums, but even a trivial 1 mph wind brings in a new supply of air from 100 miles away (outside the area “harvested” by a hurricane?) in four days.

      • What I appear to be missing it is that hurricanes can’t be analyzed in such equilibrium terms. If they were, how big an area would they need to collect latent heat from to power themselves?

        We discuss this in Section 4.2 — an area with a radius of over 3000
        Meanwhile if they feed by motion 700 km is enough.

    • This sounds like you are saying we need more surface water reservoirs on land so that we get more rain so that we can keep our reservoirs full. And, of course, that is circular so you can’t be meaning that.

      It is not at all circular if you view your water store on land as an investment. If you invest (=give away) your money wisely, you get even more money in return.

      The same with the water vapor: if the forest evaporates the right amount of water at the right time, condensation can be locally initiated, local pressure drops and an inflow of moist air will come, governed by this pressure gradient, bringing even more water from the ocean. Several stages of this process were discussed in Douglas Sheil’s previous post at Climate Etc. (there were a few pictures there, too).

      However, if you do not invest wisely, you can lose everything. Thus replacing native vegetation, which, in the course of evolution, got to “know” how and when to invest, by some plants of our choice – will most probably undermine the local water cycle. E.g. planting poplars (they evaporate strongly) in an arid environment will just deplete the groundwater bringing no returns.


      • That moist, evaporating geographies promote more rainfall, and the opposite drought, should be provable statistically by the persistence of rainfall and/or drought in the face of similar circumstances (meteorological exposure). Or, has this been done already?

  20. Hi and thank you for this thought-provoking work on fundamentals. Regarding evaporation, I do wonder about the stated 0.5mm/hr. rate in the hurricane rainfall area. Does that 0.5mm/hr rate take into consideration evaporation from the very fine mist (= very large surface area) formed over the windy ocean? Also, does the broad tropical atmosphere show a drying trend as its preexisting moisture is drawn into the hurricane and condensed?

    • Also, does the broad tropical atmosphere show a drying trend as its preexisting moisture is drawn into the hurricane and condensed?

      This drying trend is shown in Fig. 4e and 4f in our paper. Figure 4e shows how the water vapor content differs between before and after the hurricane (blue triangles stand for three days before the hurricane, green squares — three days after the hurricane). Fig. 4f describes the corresponding differences when there are now hurricanes. (i.e. if a hurricane happened say 10 September 18.00 in 2007, Fig. 4f shows what happened at the same date and time in the same location in those years when there was no hurricane there).

      Of course because of lateral mixing and because of the steering flow itself moving away from the point of observation (see my reply to Ron Graf Ma href=”″>above ) we see nowhere a region which is completely dry. However, even despite these processes the dry footprint of the hurricane is visible across a very large area (6 000 km in diameter) .


  21. Does that 0.5mm/hr rate take into consideration evaporation from the very fine mist (= very large surface area) formed over the windy ocean?
    One cannot easily measure evaporation directly within the hurricane. What we can do: measure velocity and water vapor content of air that enters the hurricane. Integrating these over height we estimate the net inflow of moisture into the hurricane. Then we measure rainfall within the hurricane. The difference between imported moisture and rainfall equals evaporation within the hurricane. Thus, this measure includes all sources of moisture.

    Another relevant point is while the mist does have a very large surface area, the velocity of these tiny water droplets relative to the air is virtually zero. Thus, evaporation from these surfaces occurs by molecular diffusion, and that’s a slow process. Meanwhile there is a very big velocity difference between the sea surface and the hurricane air. This appears to be a stronger factor (despite the relatively small evaporating surface of the ocean relative to the mist).

    Also, take notice that while the estimate 0.2 mm/hour for a long-term mean evaporation in the absence of hurricanes is quite robust, within the hurricane local evaporation changes radically — it rises towards the hurricane’s center, see Table 1 in the paper (PDF). So 0.5 mm/hour is the approximate mean for the hurricane rainfall area (about 400 km).


  22. It would be great to have a model accurate enough to hint at how much directed power it would take to nudge a hurricane away from a coast or disrupt its formation. Then we could at least start to contemplate the cost of some kind of megaproject capable of such an intervention, which would undoubtedly be enormous but might have positive ROI given the massive destruction wrought by hurricanes.

  23. Since we are on the topic of hurricanes, could someone please enlighten me on the height of the top of a hurricane (the outflow)? Do they reach to the tropopause? Some think that rising SSTs will make the average hurricane stronger, but if they are powered by the temperature difference between the surface and the outflow, this conclusion isn’t obvious. The lapse rate between the surface and outflow is also important. Globally AGW should bring a lower average lapse rate.

  24. We can see that the hurricane has a greater pressure in the troposphere. The reason is that as the air rises and cools, the water vapor condenses. The more water vapor condenses, the more latent heat is released.

    This is what is happening here. The latent energy being released reduces how cool it gets at night. The amount of latent energy released is based on air temps and dew point temp. A temperature based regulation.

    This effect is the equivalent of a flow battery, they pump fresh electrolytic in, the atm has all of the local air mass to work with, but instead of electricity, it’s storing energy as water vapor during the day, condensing it out at night to keep the surface warm.

    • This process effectively eliminates most of the heat accumulated by co2 during the prior day, before the temperature drops low enough to increase the condensation rate and slow cooling.
      This is the basic function of a heat engine, and it operates at one cycle per day. over thousands of stations, and millions of station days, min temps follow dew point temps.

    • I am assuming your axis in in W/m2 and that it is surface radiation. Positive gives surface warming – negative cooling.

      Relative humidity is anti-correlated with temperature for the very good reason that saturation vapour content declines or increases with temperature. Ultimately water will condense out when the air gets cold enough. It has absolutely nothing to do with the energy content of the atmosphere – which depends on the how warm it is on average. This is influenced by the radiative properties of gases.

      Whatever the processes at the surface there will be more greenhouse gases – and more water vapour on average on both sides of the planet – and more energy will be retained in the atmosphere. These are not physics that you can get around.

  25. Hurricanes acting effectively as PAC-men of water vapor strongly reinforces the conclusion that control of atmospheric temperatures lies not in CO2 concentrations, but in the manifold manifestations of the hydrological cycle.

  26. Berényi Péter

    Moving a molecule of water 1 micron away from the surface of a droplet needs as much energy as raising it to a height of 230 km (144 miles). The energy released is the same for a reverse process. As thickness of the troposphere (where weather happens) is negligible compared to it, weather is absolutely dominated by evaporation/condensation of water.

  27. [W]eather is absolutely dominated by evaporation/condensation of water

    …and by pressure gradients!

  28. Thanks, Anastasia, for your replies above. Very interesting paper.

    One tendency of tropical cyclones is that, once they’ve reached hurricane intensity, they tend to expand (as defined by the outer closed isobar) only slowly or not at all. That is, small (areawise) cyclones tend to remain small while large cyclones tend to remain large. The reason for cyclones not appreciably growing in area (after reaching hurricane/typhoon intensity) is not well understood (as far as I know).

    I wonder, based on your group’s paper, if large-scale moisture availability controls the aerial extent of mature cyclones. Storms “born” in relatively dry regions tend to stay small while storms born in relatively moist environments tend to grow large areawise.

    • “… if large-scale moisture availability controls the aerial extent of mature cyclones…”

      The hypothesis, if validated by improvement in TC predictive skill, would be a great service to humanity, not only by better warning but by offering a possible angle for storm mitigation. If moisture could be condensed by artificial seeding prior to entering the TC it would act like a back-fire in controlling a wildfire.

  29. Pingback: Weekly Climate and Energy News Roundup #268 | Watts Up With That?

  30. Pingback: How hurricanes replenish their vast supply of rain water | privateclientweb


    Following the link above available till 22 June 2017 is the
    PDF of final published paper

  32. Warm sea water from under the eyewall is the heat source and the water source for cyclones. The heat and water transfer occur concurrently with the convection; there is no need for heat transfer from large radius (> 100 km) or for the moisture content of far distant air (<1000 km). High wind at the eyewall produces spray; the spray drops cool to the wet bulb temperature of the air. The drops come to equilibrium with the air almost immediately because of their small size and high surface to mass ratio, About 0.5% of the drops evaporates; the remaining 99.5% fall back in the sea at a temperature approximately 4 °C colder that the temperature at which they left the sea. The process transfers enormous quantities of water and energy from sea to air. Spraying surface air with warm sea water can increase its CAPE from 1500 to 4000 J/kg corresponding to an increase in wind speed from 50 to 80 m/s.

    Cyclone sea cooling is almost entirely due to heat removal from above and not from upwelling and mixing of cold water from below. The sea to air cooling required to produce the observed cooling in the cyclone’s wake is almost exactly equal to the heat required to produce the observed precipitation. The drops rise 10 to 100 m before falling back in the sea 1 to 100 km downwind. The sea cooling occurs slightly to the right of the hurricane track because they are carried by the cyclonic wind.

    Here are two links to a presentation entitled: “Hurricane Sea to Air Heat Transfer” which I succeeded in having accepted at the 2012 18th air sea interaction American Meteorological Society conference. The outsider presentation was not well received.

    Here is a link to an article entitled: “On Hurricane Energy” which was published in the journal Meteorology and Atmospheric Physics (MAP). The paper shows the effect of surface air temperature and humidity on hurricane maximum intensity. It shows that saturating surface air at 24.5 °C can increase CAPE from 2000 to 4000 J/kg. Saturated air at 24.5 °C can always be produced by spraying ambient with warmer sea water. The quantity of spray required decreases with increasing ambient air relative humidity and with increasing sea water temperature. The paper received little attention.