"Although the hydrological cycle may increase in intensity, it does so at the expense of its ability to do work, such as powering large-scale atmospheric circulation or fueling more very intense storms."The paper adds to many others demonstrating that a warmer climate is a more benign climate with fewer extreme weather events, opposite the claims of climate alarmists. Claims of global warming producing more extreme weather due to "more energy in the system" are refuted by the paper which finds the atmosphere will become "less energetic" and the atmospheric "Carnot engine" will become less efficient at performing Work (such as generating intense winds and storms) due to global warming and a decrease of temperature differentials.
Note also the great physicist and engineer Carnot, who was the first to describe the atmosphere as a heat engine, agreed in his writings with both Maxwell and Clausius that the atmospheric temperature gradient, aka now called the "greenhouse effect," is a consequence of atmospheric mass/gravity/pressure rather than irradiance.
The global engine that could
It has been widely accepted since Carnot's seminal work (1) that the atmosphere acts as a thermodynamic heat engine: Air motions redistribute the energy gained from the Sun in the warm part of the globe to colder regions where it is lost through the emission of infrared radiation to space (facilitated by greenhouse gases). Through this process, some internal energy is converted into the kinetic energy needed to maintain the atmospheric circulation against dissipation. The analogy to a heat engine has been applied to explain various atmospheric phenomena, such as the global circulation (2), hurricanes (3), and dust devils (4). On page 540 of this issue, Laliberté et al. (5) show that the hydrological cycle reduces the efficiency of the global atmospheric heat engine.
Fine weather machine.
Nice, sunny weather occurs when dry air from the upper troposphere sinks and is mixed with moist air near Earth's surface. Laliberté et al. show that such mixing weakens the atmospheric heat engine.
Although the atmosphere acts overall as a heat engine, it may not be a very efficient one. The distribution of energy sources and sinks around Earth implies a maximum work of ~10 W·m−2 when averaged globally, yet estimates for the rate of kinetic energy production by atmospheric motions are about half this figure. The difference is very likely due to Earth's hydrological cycle, which reduces the production of kinetic energy in two ways. First, as rain droplets, hail pellets, or snowflakes fall through the atmosphere, they generate microphysical shear zones in which a substantial amount of dissipation occurs. Satellite data yield an estimated dissipation rate from precipitation of ~1.2 W·m−2 in the tropics (6). Second, water mostly evaporates in unsaturated air, and this evaporation is thus thermodynamically irreversible. Such irreversibility reduces the work produced by a heat engine compared to a Carnot cycle. In particular, when the energy source of the Carnot cycle is replaced by evaporation, the mechanical work of the cycle is reduced and strongly depends on the relative humidity (7).
Idealized cycles such as the Carnot cycle are useful theoretical models for understanding how much wind can be sustained around the globe. However, the atmosphere is highly turbulent, and extracting a single cycle from the complex motions that make up the global circulation is not straightforward. Thermodynamic studies of the climate system have typically required detailed knowledge of all thermodynamic transformations and have involved a complex analysis of numerical simulations (8–10). These intensive data requirements explain why there have been relatively few thermodynamic studies of the global climate.
Laliberté et al. offer an elegant way to address this problem. Meteorologists have studied air flow on surfaces of constant entropy since the 1930s. Atmospheric scientists and oceanographers have extended this approach to study how air and water move around the planet on various thermodynamic surfaces, such as surfaces of constant temperature or salinity (11, 12). Laliberté et al. push this idea even further by averaging the circulation in a three-dimensional thermodynamic space (pressure, entropy, and water content). Dalton's law, however, states that all thermodynamic properties of moist air can be determined from the knowledge of these three state variables. This means that the circulation computed by Laliberte et al. can be used to infer all thermodynamic transformations in the atmosphere, based solely on standard meteorological measurements.
The authors apply their methodology to the global thermodynamic cycle using data from meteorological reanalysis and from a global climate model. The results confirm that the hydrological cycle reduces the amount of kinetic energy generated by the large-scale atmospheric flow by about one-third. As much as we may associate the hydrological cycle with severe weather and heavy precipitation, it is also responsible for nice, sunny weather, which occurs when air masses gradually regain some of the water vapor lost during an earlier rainfall (see the figure). The hydrological cycle reduces the average intensity of the winds around Earth mostly by generating pleasant weather around large portions of the globe.
The study by Laliberté et al. offers a blue-print for the systematic analysis of the thermodynamic transformations in the climate system. The method can be applied based solely on the standard output of numerical models and can easily be used to compare the thermodynamic cycles simulated by different global climate models. It also opens up two important questions.
First, what are the contributions of convection and other atmospheric motions at small scales in the atmospheric heat engine? The approach presented by Laliberté et al. is limited to motions resolved by their data set, which excludes anything with a horizontal scale of less than 100 km. Yet, many thermodynamic transformations occur within clouds, at scales that are not typically resolved in an atmospheric or climate model. Second, how are the thermodynamic processes affected by climate change? As Earth's climate warms, the air will be able to contain more water vapor on average. Laliberté et al. indicate that this would lead to a slight reduction in the work done by the atmospheric circulation. This result, if confirmed, could offer important insights into what Earth's global engine could do in the future.
References
Excerpts from main article:
Constrained work output of the moist atmospheric heat engine in a warming climate
EDITOR'S SUMMARY:
Because the rain falls and the wind blows
Global warming is expected to intensify the hydrological cycle, but it might also make the atmosphere less energetic. Laliberté et al. modeled the atmosphere as a classical heat engine in order to evaluate how much energy it contains and how much work it can do (see the Perspective by Pauluis). They then used a global climate model to project how that might change as climate warms. Although the hydrological cycle may increase in intensity, it does so at the expense of its ability to do work, such as powering large-scale atmospheric circulation or fueling more very intense storms.
Incoming and outgoing solar radiation couple with heat exchange at Earth’s surface to drive weather patterns that redistribute heat and moisture around the globe, creating an atmospheric heat engine. Here, we investigate the engine’s work output using thermodynamic diagrams computed from reanalyzed observations and from a climate model simulation with anthropogenic forcing. We show that the work output is always less than that of an equivalent Carnot cycle and that it is constrained by the power necessary to maintain the hydrological cycle. In the climate simulation, the hydrological cycle increases more rapidly than the equivalent Carnot cycle. We conclude that the intensification of the hydrological cycle in warmer climates might limit the heat engine’s ability to generate work.
As a reflection of the seminal work of Carnot, atmospheric motions have been described as an important component of the planetary heat engine (1). The concept of a heat engine is closely associated with the idea of work: For two cycles that transport the same amount of heat between the same two reservoirs, the one that generates the least irreversible entropy will produce the most work (2). We quantify the atmosphere’s work output through a budget of its entropy production. Previous attempts at obtaining such a budget either resulted in gross estimates (3, 4) or required highly specific data from climate models for a precise analysis (5–8). Some of these studies showed that the hydrological cycle was an important contributor to the generation of irreversible entropy (6, 9, 10), suggesting that moist processes, including the frictional dissipation associated with falling hydrometeors (11, 12), tend to limit the work output of the atmospheric heat engine. On a warming Earth, the increase in precipitable water (13) has been identified as a reason for the tropical overturning to slow down (14), and studies over a wide range of climates suggest that global atmospheric motions are reduced in extremely warm climates (15–17). Models forced according to a climate change scenario also exhibit this behavior in their tropical circulation (18). Here, we employ a method that uses high-frequency and high-resolution data to obtain an atmospheric entropy budget from climate models and reanalyses. This method does not depend on specialized model output, making the diagnostic applicable to the suite of models produced for the Climate Model Intercomparison Project phase 5 (CMIP5) and paving the way to a systematic analysis of the entropy budget in climate models, as proposed by some authors (8).
We base our analysis on the first law of thermodynamics describing moist air (19, 20).
The material derivatives of moist enthalpy h and moist entropy s (19–21) are given by 
and 
, respectively.
The material derivatives of moist enthalpy h and moist entropy s (19–21) are given by and , respectively.
The equation of state used here provides a comprehensive treatment of moist thermodynamics, including the effect of the latent heat of fusion on 
and 
(19, 20). The specific ratio 
represents the total mass of water divided by the total mass of wet air (humid air plus water condensate). The work output 
is given by the product of the specific volume 
with the vertical velocity in pressure coordinates 
. The chemical potential μquantifies the effect of adding or removing moisture; it is equal to the sum of two terms with different physical meanings (see the supplementary text). The first of these terms accounts for the moistening inefficiencies that accompany the irreversible entropy production associated with the addition of water vapor to unsaturated air (9,10). The second term accounts for the enthalpy changes associated with the drying and moistening of air. For the atmospheric thermodynamic cycle, we will show that when 
is positive, 
primarily quantifies the moistening inefficiencies accounted for by the first term, and when 
is negative 
primarily quantifies how much power is associated with combined moisture and dry air fluxes between the surface and the precipitation level accounted for by the second term.
and (19, 20). The specific ratio represents the total mass of water divided by the total mass of wet air (humid air plus water condensate). The work output is given by the product of the specific volume with the vertical velocity in pressure coordinates . The chemical potential μquantifies the effect of adding or removing moisture; it is equal to the sum of two terms with different physical meanings (see the supplementary text). The first of these terms accounts for the moistening inefficiencies that accompany the irreversible entropy production associated with the addition of water vapor to unsaturated air (9,10). The second term accounts for the enthalpy changes associated with the drying and moistening of air. For the atmospheric thermodynamic cycle, we will show that when is positive, primarily quantifies the moistening inefficiencies accounted for by the first term, and when is negative primarily quantifies how much power is associated with combined moisture and dry air fluxes between the surface and the precipitation level accounted for by the second term.
Averaging the first law using a mass-weighted annual and global spatial mean [denoted as {□}] results in simplification. First, 
equals the difference between interior moist enthalpy sinks and the moist enthalpy sources at Earth’s surface stemming from diffusive fluxes. If we assume that the atmospheric system is in steady state (and therefore approximately yearly periodic), the sinks cancel the sources and 
vanishes. Moreover, under this averaging, 
is positive because it quantifies the power necessary to maintain the hydrological cycle and accounts for the moistening inefficiencies (10), and 
is also positive because it is associated with the dissipation of kinetic energy at the viscous scale (22). Writing 
, then, the first law reads [equation 4 in (10)]
is thus reduced by the moistening inefficiencies accounted for by 
. In the following sections, we obtain a diagnostic for 
and 
based on the area occupied by the atmospheric thermodynamic cycle in a temperature-entropy diagram (hereafter 
diagram) and in a specific humidity-chemical potential diagram (hereafter 
diagram), respectively.
equals the difference between interior moist enthalpy sinks and the moist enthalpy sources at Earth’s surface stemming from diffusive fluxes. If we assume that the atmospheric system is in steady state (and therefore approximately yearly periodic), the sinks cancel the sources and vanishes. Moreover, under this averaging, is positive because it quantifies the power necessary to maintain the hydrological cycle and accounts for the moistening inefficiencies (10), and is also positive because it is associated with the dissipation of kinetic energy at the viscous scale (22). Writing , then, the first law reads [equation 4 in (10)] is thus reduced by the moistening inefficiencies accounted for by . In the following sections, we obtain a diagnostic for and based on the area occupied by the atmospheric thermodynamic cycle in a temperature-entropy diagram (hereafter diagram) and in a specific humidity-chemical potential diagram (hereafter diagram), respectively.
We analyze two different data sources. The first source is a coupled climate model simulation using the Community Earth System Model (CESM) version 1.0.2 (23). The time period 1981 to 2098 is simulated using a combination of historical radiative forcing estimates and the Representative Concentration Pathway 4.5 (24) future scenario (hereafter historical RCP45). The second source is the period 1981 to 2012 of the Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis (25). For these two data sets, we use a recently developed method (20) to project the material derivative 
from eulerian space to 
, its representation in the 
diagram. We use the same method to project 
to 
, its representation in the 
diagram. Each of these quantities is associated with a closed, uniquely defined mass flux stream function in its respective coordinate system.
, ,
,Each stream function describes a separate aspect of the large-scale atmospheric thermodynamic cycle. This approach is similar to a method that has been previously used to study the atmospheric and oceanic circulations in thermodynamic coordinates (26–29).
from eulerian space to , its representation in the diagram. We use the same method to project to , its representation in the diagram. Each of these quantities is associated with a closed, uniquely defined mass flux stream function in its respective coordinate system., ,,Each stream function describes a separate aspect of the large-scale atmospheric thermodynamic cycle. This approach is similar to a method that has been previously used to study the atmospheric and oceanic circulations in thermodynamic coordinates (26–29).
In a 
diagram, the quantity 
describes a clockwise cycle (Fig. 1, A and B) with three main branches. In the lower branch, a large fraction of air is transported along the surface saturation curve (1000 hPa, 100% relative humidity) and, as it moves toward warmer temperatures, picks up heat through exchanges at Earth’s surface. In the tropical branch, air is transported from warm temperatures to colder temperatures at almost constant moist entropy along the zonal-mean tropical (15°S to 15°N) profile. The zonal-mean tropical profile thus represents the transformations that tropical air masses undergo when they convect, detrain, and mix with environmental midtropospheric air masses (30). In the third branch, radiative cooling acts to reduce entropy as air is transported from high moist entropy and cold temperatures to low moist entropy and warmer temperatures. The thermodynamic cycles in CESM and MERRA have a similar shape, but MERRA’s is stronger (larger maximum stream function value). In the region of the 
diagram rightward of the zonal-mean subtropical profile (25°N to 35°N) and at temperatures lower than 280 K, the saturation specific humidity is small, so that pressure is approximately a function of temperature and moist entropy. In this region, thermodynamic transformations that occur along discrete pressure levels [diagnosed by 
, 
, and 
(20) but not explicitly demonstrated here] yield the prominent sawtooth patterns seen in the CESM cycle. Although the same patterns appear in the MERRA cycle, they are not as prominent because the vertical resolution is finer by a factor of three, so that a smaller portion of the thermodynamic cycle is sampled along a given pressure level.
diagram, the quantity describes a clockwise cycle (Fig. 1, A and B) with three main branches. In the lower branch, a large fraction of air is transported along the surface saturation curve (1000 hPa, 100% relative humidity) and, as it moves toward warmer temperatures, picks up heat through exchanges at Earth’s surface. In the tropical branch, air is transported from warm temperatures to colder temperatures at almost constant moist entropy along the zonal-mean tropical (15°S to 15°N) profile. The zonal-mean tropical profile thus represents the transformations that tropical air masses undergo when they convect, detrain, and mix with environmental midtropospheric air masses (30). In the third branch, radiative cooling acts to reduce entropy as air is transported from high moist entropy and cold temperatures to low moist entropy and warmer temperatures. The thermodynamic cycles in CESM and MERRA have a similar shape, but MERRA’s is stronger (larger maximum stream function value). In the region of the diagram rightward of the zonal-mean subtropical profile (25°N to 35°N) and at temperatures lower than 280 K, the saturation specific humidity is small, so that pressure is approximately a function of temperature and moist entropy. In this region, thermodynamic transformations that occur along discrete pressure levels [diagnosed by , , and (20) but not explicitly demonstrated here] yield the prominent sawtooth patterns seen in the CESM cycle. Although the same patterns appear in the MERRA cycle, they are not as prominent because the vertical resolution is finer by a factor of three, so that a smaller portion of the thermodynamic cycle is sampled along a given pressure level.
Fig. 1Thermodynamic diagrams for years 1981–2012.
(A and C) CESM. (B and D) MERRA. [(A) and (B)] 
diagram. 
in color shading and gray contours (–75, –225, –375, and –525 Sv). Thick dashed lines represents the zonal-mean vertical profile in different latitude bands. Dotted lines give the 100% relative humidity curves at 1000 hPa, 500 hPa, and 200 hPa. Axes are oriented so that the lower left corner is closest to typical tropical surface 
values, the upper left corner is closest to typical tropical upper tropospheric 
values, and the right side of the graph is closest to typical polar 
values. The correspondence between the equivalent potential temperature 
and 
(21) is indicated on the top abscissa. [(C) and (D)] 
diagram. 
in color shading and gray contours (–333, –667, –1000, and –1333 Sv). The thick dashed line represents the zonal-mean vertical profile in the tropics. Pressure levels are indicated along this profile. Axes are oriented so that the lower left corner is closest to typical tropical surface 
values. [(A) to (D)] Thin black curves indicate where 
= –1 Sv or 
= –1 Sv. They indicate the small-magnitude cutoff over which 
or 
were computed to avoid floating-point errors.
diagram. in color shading and gray contours (–75, –225, –375, and –525 Sv). Thick dashed lines represents the zonal-mean vertical profile in different latitude bands. Dotted lines give the 100% relative humidity curves at 1000 hPa, 500 hPa, and 200 hPa. Axes are oriented so that the lower left corner is closest to typical tropical surface values, the upper left corner is closest to typical tropical upper tropospheric values, and the right side of the graph is closest to typical polar values. The correspondence between the equivalent potential temperature and (21) is indicated on the top abscissa. [(C) and (D)] diagram. in color shading and gray contours (–333, –667, –1000, and –1333 Sv). The thick dashed line represents the zonal-mean vertical profile in the tropics. Pressure levels are indicated along this profile. Axes are oriented so that the lower left corner is closest to typical tropical surface values. [(A) to (D)] Thin black curves indicate where = –1 Sv or = –1 Sv. They indicate the small-magnitude cutoff over which or were computed to avoid floating-point errors.
...
The evolution of 
in response to anthropogenic forcing indicates a trend of –0.038 ± 0.08 Wm−2 [one-sided ttest, 95% confidence interval (CI)] per 100 years for the 10-year running mean (Fig. 4B). Over the 21st century, this amounts to a small reduction in 
(≈–1%). In an 
diagram, the 
response at the end of the 21st century exhibits a reduction of –0.102 Wm−2 per 100 years below 300 hPa and an increase of 0.073 Wm−2 per 100 years above 300 hPa (fig. S4); at 500 hPa, it is reduced by more than 5% per 100 years. This response is compatible with a general weakening of tropospheric motions accompanied with a strengthening of deep convective motions that have enough energy to reach the upper troposphere.
in response to anthropogenic forcing indicates a trend of –0.038 ± 0.08 Wm−2 [one-sided ttest, 95% confidence interval (CI)] per 100 years for the 10-year running mean (Fig. 4B). Over the 21st century, this amounts to a small reduction in (≈–1%). In an diagram, the response at the end of the 21st century exhibits a reduction of –0.102 Wm−2 per 100 years below 300 hPa and an increase of 0.073 Wm−2 per 100 years above 300 hPa (fig. S4); at 500 hPa, it is reduced by more than 5% per 100 years. This response is compatible with a general weakening of tropospheric motions accompanied with a strengthening of deep convective motions that have enough energy to reach the upper troposphere.
Because 
is proportional to the material derivative 
, we might expect its response to scale like the near-surface specific humidity and therefore be directly related to changes in global surface temperature through a surface Clausius-Clapeyron scaling. Indeed, the specific humidity on the model level nearest to the surface explains 94% of the variance of 
over the entire 1981 to 2099 period (Fig. 4A). Both the near-surface specific humidity and 
increase by 5.4% per K global surface warming, which is slightly less than the 7% per K surface warming increase associated with a tropical Clausius-Clapeyron scaling (14). In fact, most of the increase in 
can be attributed to an increase in the moistening inefficiencies (fig. S5A). Moreover, this increase alone compensates for the increase in 
(fig. S5B) and is therefore sufficient to constrain the atmospheric heat engine’s work output.
is proportional to the material derivative , we might expect its response to scale like the near-surface specific humidity and therefore be directly related to changes in global surface temperature through a surface Clausius-Clapeyron scaling. Indeed, the specific humidity on the model level nearest to the surface explains 94% of the variance of over the entire 1981 to 2099 period (Fig. 4A). Both the near-surface specific humidity and increase by 5.4% per K global surface warming, which is slightly less than the 7% per K surface warming increase associated with a tropical Clausius-Clapeyron scaling (14). In fact, most of the increase in can be attributed to an increase in the moistening inefficiencies (fig. S5A). Moreover, this increase alone compensates for the increase in (fig. S5B) and is therefore sufficient to constrain the atmospheric heat engine’s work output.
Previous theoretical analyses of the entropy cycle (6, 31) suggest that 
should scale like 
, where 
is the outgoing long-wave radiation and 
, 
, and 
are the mean temperature of atmospheric heat input, output, and dissipation, respectively. Observations of recent tropospheric warming [figures 2.26 and 2.27 in (32)] show that temperature trends are somewhat uniform in the vertical, which suggests that the difference 
might increase more slowly than either 
or 
. This slower increase may explain why 
does not follow a surface Clausius-Clapeyron scaling and why one would expect moist processes to limit the work output in simulations with anthropogenic forcing. Simulations over a wider range of climates would help verify this hypothesis.
should scale like , where is the outgoing long-wave radiation and , , and are the mean temperature of atmospheric heat input, output, and dissipation, respectively. Observations of recent tropospheric warming [figures 2.26 and 2.27 in (32)] show that temperature trends are somewhat uniform in the vertical, which suggests that the difference might increase more slowly than either or . This slower increase may explain why does not follow a surface Clausius-Clapeyron scaling and why one would expect moist processes to limit the work output in simulations with anthropogenic forcing. Simulations over a wider range of climates would help verify this hypothesis.
Our comparison of thermodynamic cycles in CESM and MERRA show many similarities; however, we find that CESM requires less power to maintain its hydrological cycle than the reanalysis, due to the smaller amplitude of its moistening inefficiencies. We suggest that this difference might be a consequence of the idealized nature of parameterized convection schemes, and it is likely that it might also influence the response of CESM to anthropogenic forcing. Typically, convection schemes artificially transport moisture along a moist adiabat without accounting for the work needed to lift this moisture, but in the real world, this work is necessary to sustain precipitation. Any increase in global precipitation therefore requires an increase in work output; otherwise, precipitation would have to become more efficient, for example, by reducing the frictional dissipation of falling hydrometeors (11, 12). This is one reason we should interpret the constraint in work output in CESM as a constraint on the large-scale motions and not on the unresolved subgrid-scale convective events.
Our work illustrates a major constraint on the large-scale global atmospheric engine: As the climate warms, the system may be unable to increase its total entropy production enough to offset the moistening inefficiencies associated with phase transitions. This suggests that in a future climate, the global atmospheric circulation might comprise highly energetic storms due to explosive latent heat release, but in such a case, the constraint on work output identified here will result in fewer numbers of such events. Earth’s atmospheric circulation thus suffers from the “water in gas problem” observed in simulations of tropical convection (6), where its ability to produce work is constrained by the need to convert liquid water into water vapor and back again to tap its fuel.
