Guest essay by Jan Kjetil Andersen
As Willis describes in his article on December 21, the atmosphere can be seen as a gigantic heat engine, i.e. a machine which convert thermal energy, namely temperature, into mechanical energy, namely wind.
It may seem a bit strange to view the weather system as a kind of machine and compare it with engineered constructs like an automobile engine, but it is sound physics because all such systems are bound by the same fundamental physical laws and they utilizes the same basic phenomena to create movement from heat.
A heat engine cannot convert heat directly to mechanical energy since that would break the second law of thermodynamics. What are needed are temperature differences. The greater temperature difference the greater effect of the machine. The amount of the energy in the temperature difference that is converted to mechanical energy is called the machines efficiency.
And here we have a very interesting, but less known fact of heat engines; the maximum theoretical efficiency decreases with increasing temperatures. This is interesting because it negates the conventional wisdom and often cited myth that a warmer climate leads to
more storminess, like the claim in the Guardian “a warmer planet has more energy to power stronger storms”, see http://www.theguardian.com/environment/2011/jun/27/climate-change-extreme-weather-2010.
Let us therefore take a look at the theoretical foundation of this effect. This is described by Carnot’s theorem.
Carnot’s Theorem says that the maximum efficiency drawn from a heat engine is the temperature difference between the warmest element and the coldest element divided by the temperature of the highest element.
Expressed as a formula it says: Emax = (Th-Tc)/Th.
Emax is the maximum efficiency
Th is the high temperature element measured in Kelvin
Tc is the cold temperature element measured in Kelvin.
The Carnot cycle is an ideal reversible cyclic process involving the expansion and compression of an ideal gas, which enables us to evaluate the efficiency of an engine utilizing this cycle.
For an interactive demonstration of the Carnot heat engine cycle, courtesy of the University of Virginia, click on the image:
Three important effects can be seen from Carnot’s theorem. The first is that a temperature difference is a necessary condition for converting heat energy to mechanical energy such as wind.
The second effect is that even if we had a perfect heat engine with zero internal friction; it would not achieve anything close to 100% efficiency. The maximum theoretical efficiency for a heat engine operating between 300 K and 600K is for example 50%. The efficiency of a real machine would of cause be considerably lower.
This is why our car engines only operate at about 25% efficiency. The warm element for a car engine is the exploding fuel inside the cylinders and the cold element is the air intake.
The best coal fired power plants have about 40% efficiency and the best gas powered about 55%. The cold elements for those plants are the coolant water, and those with highest efficiency utilize cold seawater as coolant.
Warming gives less efficiency
The third effect is as mentioned above, that, for a given temperature difference between the warm element and the cold element, the efficiency will decrease if both elements heat equally much. On cold days one can see a discernible effect of this in car engines; because the air intake is colder, the engine gives somewhat more power and higher efficiency.
This is also why some turbo charged engines have intercoolers. The turbo gives higher effect, but a non-intentional side effect is that it also increases the temperature in the air intake which will reduce the efficiency. The intercooler reduces the temperature increase introduced by the turbo.
The same effect applies to the wind formations in the atmosphere. Consider the summer temperature in the northern hemisphere; the cold element is the Arctic with a temperature of approximately 0 Celsius and the warm element is in the tropics with approximately 35 Celsius.
The Carnot theorem gives a maximum efficiency in this temperature range of 11.36%. If the temperature increased with 1 Celsius all over the globe, i.e. the difference changed to 1 Celsius in the Arctic and 36 Celsius in the tropic, the maximum efficiency would sink to 11.32%.
This is a minuscule difference, but the point is that it is a decrease, not an increase as the conventional wisdom will have it.
Less temperature differences on the surface
In addition to the effect of higher overall temperatures, the temperature differences will also be smaller. It is quite uncontroversial that the largest effect of global warming is on the cold polar winters and the smallest on the hot tropical summers.
![GFDL_CM2p1_SfcTemp_JJA_DJF_A1B_wht3200x2000[1]](http://wattsupwiththat.files.wordpress.com/2013/12/gfdl_cm2p1_sfctemp_jja_djf_a1b_wht3200x20001.png?quality=75)
However, to be fair, this is not all there is to this. Some climate models tell that the temperature differences in the upper troposphere will increase and this may have larger effect than both the reduced differences on the surface and the higher temperatures.
No settled science there.
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Some climate models tell that the temperature differences in the upper troposphere will increase and this may have larger effect than both the reduced differences on the surface and the higher temperatures.
Models are not science until they have real measured data to base them on. After that, they need to compare the output of their models to what is really happening.
Have they done all this?
More models…..the climate is a convection system with a million variables including local thermodynamics. This complexity is immune to modeling. It would be refreshing to hear from quackitists and quackademics that we really dont have a clue about climate or weather and that most likely a trace chemical necessary for life mostly emitted by gaia has not much to do with anything….
As an engineer with some training in meteorology, the claim of increased strength and number of storms caused by global warming with more warming at the poles has always bothered me. Thank you for a well written article explaining thi issue.
Interesting article, thank you. You said;
‘And here we have a very interesting, but less known fact of heat engines; the maximum theoretical efficiency decreases with increasing temperatures. This is interesting because it negates the conventional wisdom and often cited myth that a warmer climate leads to more storminess, like the claim in the Guardian “a warmer planet has more energy to power stronger storms”
As one of the few who seems to be still carrying out primary historical climate research at such places as the Met office archives, I can confirm from reading tens of thousands of weather observations back to the 11th century that the most violent extremes occur during the periods of greatest cold during the intermittent Little Ice age. Whilst snow and ice feature, so do violent storms and especially very long periods of calamitous flooding brought about by prodigious amounts of rainfall.
The temperature gradient between the poles and the tropics is surely greatest during cold periods so more energy will be generated than when the temperatures are more equal, as during the current benign period and also during the MWP which appears to have experienced mostly settled weather.
tonyb
Don’t count on it. Why should they be willing to use measured data? Measured data can and will prove them wrong!
While the points of this post are correct, they left out one feature: The evaporation and condensation of water. Warmer air is capable of holding more water vapor, and the transport of energy by phase change is potentially capable of changing the energy driven dynamics of just pressure driven flow (wind). However, in fact the increase in moisture has not followed the expected level due to the temperature increase (it has not maintained average relative humidity as temperature increased, especially at higher altitudes), so the net result is even more unclear.
Some climate models tell that the temperature differences in the upper troposphere will increase…
Indeed, as evidenced by the infamous hotspot that was observed back in… oh wait.
Actual heat engines, to which Carnot’s physics apply, are artificial man-made technological systems that can be isolated and all input-connection-outputs be known; not so for a natural system in a reality that Mandelbrot called fractally complex. The essay is an interesting but microscopic examination of an open/un-isolable system.
The upper atmosphere might be cold, but it cannot be used to drive a convection cell. If you fill a balloon of air in the upper atmosphere and bring it down to ground level, the air in it will be warmer than the air at ground level. The increase in pressure would cause the warming.
Also, warmer air might be able to hold more moisture, but it is also unlikely to hold less. The portion of water vapor that does not condensate can be considered as a non-condensing gas. You need cold air to condensate water vapor, so water vapor might act less like a condensing gas on a planet with warmer poles.
What drives the jet streams? Are there any data collections on the velocity of jet streams over time?
Have they done all this?
I don’t think so. It would lead to inconvenient truths.
Let’s don’t forget another heat exchange engine operated by the oceans’ thermohaline circulation.
And here we have a very interesting, but less known fact of heat engines; the maximum theoretical efficiency decreases with increasing temperatures.
It does not seem to me that the efficiency is all that important compared with the amount of energy in the atmosphere?
Is it that the reduced efficiency simply results in more turbulent flows, thus diffusing that energy out more?
“If you fill a balloon of air in the upper atmosphere and bring it down to ground level, the air in it will be warmer than the air at ground level”
Assuming you mean the upper troposphere that would be because the air was originally humid and cooled during uplift at the moist lapse rate.
If you then capture dried out air and bring it down then it warms at the dry lapse rate which is faster and so it ends up warmer than the surface air.
I have argued elsewhere that the mechanical warming on the descent phase of the convective cycle is what warms the surface above the S-B prediction and not DWIR (Downward Infrared Radiation)
My understanding was that a car’s engine produces more power with a colder intake air because colder, denser air contains more oxygen and allows more gasoline to be completely burned during the cylinder explosion. Of course, it would make sense that thinner, warmer air cannot expand as much, thus produces less power.
Jan:
I know what you’re getting at.
But I feel the comparison of the Earth’s climate system with a Carnot engine is inappropriate.
A Carnot engine is a closed system – that is, it deals with an energy differential between two sources, these closed off from the outside. It acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work.
The Earth’s climate is an open system – with a constant input of energy from the Sun and a constant emission of that energy to space after conversion into terrestrial IR. Therefore the efficiency of the conversion does not matter.
To say that the earth will become “stormier” in a warmer world is (Meteorologically) correct. (supposing an unchanging LR). But there are exceptions.
A warmer world will have more evaporated water to release LH and therefore convective cells will have more power available to push up through the atmosphere to counter that LR.
In subtropical zones where Coriolis force can act on systems of thunderstorms, and in combination with westerly travelling waves in the upper air will make Hurricanes, Typhoons, Cyclones more powerful, as they derive their energy from SST’s, which will be higher in a warmer world.
The argument is applicable to tornadoes as well with, in the US, more moisture drawn up from the Gulf being overridden by dry Arctic sourced air – then the CAPE (convectively available energy) available will be greater. The spin will still be sourced from a backing/increasing wind with height over the top/through the Cumulonimbus cloud.
It is true though that if we accept that a warming world will not warm uniformly, and that the Arctic would warm more, then this would reduce the thermal contrast between Equator and Pole and so make less energy available to Earth’s “heat engine” via a weakening of the Polar jet-stream. However though this would serve to weaken the central pressure and hence wind gradients of mid-latitude Lows, due to the increased “waviness” of the jet then we will be more prone to “stuck” weather patterns giving regionally disparate flood/cooler and drought/hotter weather. These regional zones would shift around but would make rainfall patterns much less predictable.
Likewise Monsoon rains are likely to be disrupted via differences in ocean heating via current flow and they will contain more rain when they arrive.
• Concise overview of heat engines = p.433 [pdf p.10] here:
Sidorenkov, N.S. (2005). Physics of the Earth’s rotation instabilities. Astronomical and Astrophysical Transactions 24(5), 425-439.
• Elaboration on heat engines = section 8.7 (begins on p.175 [pdf p.189]) here:
Sidorenkov, N.S. (2009). The Interaction Between Earth’s Rotation and Geophysical Processes. Wiley.
• http://imageshack.us/a/img850/876/f0z.gif (credit: JRA-25 Atlas)
Your example leaves out one important element — the latent heat of the water vapor that “disappears” as the air dried out, is actually simply moving heat energy to a new location.
A practical example of this case is the issue with down slope winds like the chinook winds we have here in Colorado which can cause “local” warming on the front range. In the winter time these winds doming out of the west fall several thousand feet (about 7,000 – 8,000 ft) after crossing the continental divide dropping into the Denver basin, and can warm 20-30 degrees causing 40-50 degree days in the front range corridor while just 30-40 miles east of Denver temps are in the 20’s and 30’s.
From the local perspective the air has “warmed” but you are forgetting the cold side of the equation. The reason these winds warm on the down slope is that they had a significant moisture content as the were upslope winds on the western side of the continental divide and during that orographic lifting the moisture dropped out as snow. This released a lot of latent heat of freezing as the ice crystals formed and that is the heat that shows up on compression as dry air.
If the wind has low humidity or the temperatures on the western slope are not cold enough to cause rain or snow the winds in the lee of the mountains are bone chilling cold bora winds not warm Chinook winds. The warming is local there is an equal and opposite cooling captured in the snow pack on the western slope that will not be released back into the atmosphere until spring when the snows melt.
http://en.wikipedia.org/wiki/Orographic_lift
If that latent heat of condensation and freezing is radiated away from the cloud tops to deep space at the top of the convection column, and has left the the system and the down drafts will be much cooler than the air that went up. This happens every day in thunderstorms. You have 80+ deg F moist air rising int he updraft, and cold rain and hail falls out as the air is lifted, but much of that latent heat is released at high altitude as IR radiation to space. The resulting cold down drafts will be in the 50 deg F range and the combined result of the cool down draft and the chilling effect of the cold rain and melting hail is cooler (has less total heat content) than the original warm moist air that entered the storm in the updraft phase.
You have to consider the entire cycle and due to specific circumstances sometimes a drop in elevation can result in heating of the air and at other times a net cooling. It all comes back to the water cycle and where and under what conditions the moisture gains or loses energy as latent heat.
Interesting article for discussion, though I too think the car analogies are dubious. Combustion in the chamber is not really what Carnot cycle is about.
Also, efficiency dropping does not mean energy available is dropping. It could be less efficient while still producing more energy.
The equator / polar difference is probably dropping sufficiently to establish less energy available but that is not established by arguments shown here.
Warming gives less efficiency: doesn’t this classically describe a (temperature) negative feedback process?
Reduced efficiency would mean the working fluid has to circulate faster to achieve the same heat transport.
Probably a significant error in this simplistic analysis is that Hadley cell is not the only heat path to consider. Much of the heat transported from tropical surface to tropopause leaves the system by radiation.
Also strong negative feedbacks in the tropics cut down the heat entering the lower climate system.
considering the ‘heat engine’ aspects in isolation may not be informative, at least without further discussion.
Is it that the reduced efficiency simply results in more turbulent flows, thus diffusing that energy out more?
Turbulence requires energy. It is a part of the work done in the climate system. Less energy for work (Carnot) = less turbulence In a regular heat engine (turbine, diesel etc.) turbulence is counted as a loss from Carnot efficiency. In the case of the atmosphere it is counted as “useful” work.
When will the study of climate change ever yield results? We’ve spent hundreds of billions of tax payer dollars over decades studying climate change. The failure of scientists to prove any conclusive results pertaining to climate change science shows we should stop throwing good money after bad. The only objective conclusion that can be drawn is; We should stop giving quack and incompetent scientists our taxpayer money to study climate change.
” the maximum theoretical efficiency decreases with increasing temperatures. ”
This is a misleading statement. You get the math correct a paragraph or two later, but I can think of cases where your statement is wrong. Depending on the starting temperature differential, if Th is increasing at a higher rate then Tc, then efficiency can still go up. Ex. Th increasing at 3 times the rate of Tc: Th=100, Tc=50 e=50%, Th=400, Tc=150 e=62.5%.
I think what you meant to say is that if temperatures are increasing equally, then efficiency goes down. And for any case where Tc is increasing faster than Th efficiency goes down along with a fair number of cases where Th is increasing faster but not fast enough than Tc.
Efficiency also doesn’t tell the whole story. You should also state explicitly that the mechanical work is a function of the efficiency and the amount of heat transferred. But since the source for all of our heat is the sun and that is “constant” then a lower efficiency will result in less mechanical work done.
Finally, the cold sink in your car example is the air at the exhaust (and ambient air around the engine) and not the intake. They happen to come from the same pool but in principle they don’t have to. I could have a tank of hot air that I inject into the cylinders, expand, and exhaust and still get work from the system. Turbo’s have intercoolers because colder air is denser air, and Turbo’s are all about recovering some of the waste heat to better aspirate the engines.
p.s. You also have an “of cause” buried in there.
Don’t overlook the Coriolis force as a primary driver of large-scale wind. These rotational forces are huge and the energy put into driving the winds and ocean currents slow down the Earth’s rotation over time — the day was just 21-22 hours long in the time of the dinosaurs.