Guest Post by Willis Eschenbach
One of the best parts of new tools is new discoveries. So the tools to calculate the heat constants of the ocean and land as described in my last post, Lags and Leads, reveal unknown things to me.
A while back I wrote a post called “Wrong Again”, about a crucial mistake I’d made that was pointed out by a commenter, might have been Mosher. In any case, what I’m wrong about this time is that I always thought that over the course of a year, much more energy per square metre of surface was stored in and subsequently released from the ocean than was stored in the land. I figured that in part this was a result of the difference in heat capacities (specific heats) of water and soil, which are in a proportion of about three to one per cubic metre. That is to say, it takes about three times the energy to warm a cubic metre of ocean by one degree C that it takes to warm a cubic metre of soil. I also figured that because the heat can penetrate the ocean more deeply, it would store more of the heat than the land would. Finally, I figured that the differences in albedo would favor the ocean over the land.
One of the joys of writing for the web is that commenters set off whole trains of thought about what I’m investigating. It’s like having a set of global colleagues. Sometimes rambunctious colleagues, to be sure, but well worth it. In this case a comment from Bruce Ploetz led me to look into the question of the implied heat storage in the thermally lagged system.
In my last post I used the example of putting an aluminum pan on the fire versus putting a cast-iron pan on the fire. The aluminum pan has a small heat constant “tau”, while the cast-iron pan has a large heat constant tau.
An oddity of this is that we can calculate the relationship between tau and the actual size of the thermal mass. For the earth system, it works out to a thermal mass per square metre of 7.9 metres depth of water. This is the amount of thermal mass that is involved in the annual temperature swings. I usually call that 8 metres for quick first-cut calculations. (I’m not sure where I got that number, 7.9 metres thermal mass per month of tau in the earth system, although it was from a trusted source of some kind. Any assistance in backing up that number would be appreciated.)
As a result of my newly-gained ability to calculate the time constants tau for the ocean and the land (on the order of 3+ months and 1 month respectively), we get about 24+ metres and 8 metres of thermal mass for the ocean and land respectively.
So … given that we have that much thermal mass for the land and the ocean, how much energy goes into and out of the thermal mass per year?
Now, I’m a great fan of rules of thumb, which I keep in my head for back-of-the-envelope calculations. One such rule of thumb is that a watt per square metre of incoming energy applied over a year (1 W-yr/m2) will raise a cubic metre of seawater by 8°C.
This means that for the land, with an involved thermal mass of 8 metres depth, 1 W-yr/m2 changes the temperature of the thermal mass by 1°C. And similarly, for the ocean’s involved thermal mass of 24+ metres depth, it takes about 3+ times that or 3+ W/m2 to change the temperature by 1°C.
Here’s the key graph, from my last post:
Figure 1. A comparison of the annual temperature swings of the northern hemisphere ocean and land. Solar variation in both cases is the same.
The land is easy, because the involved thermal mass warms and cools at one degree C per watt-year/m2. It swings 28°C, but remember that is in half a year. So the rate is 56°C per year. And conveniently, this is also 56 watts/m2. So every year, in back-of-the-envelope terms, there is a flux of about half a hundred watts first into and then out of the land.
Next, the ocean. The swing of the ocean temperatures is 7.7°C per half-year, or a rate of about 15°C per year. The involved thermal mass of the ocean requires 3+ watts per square metre per degree. How nice, the thermal flux in W-yr/m2/°C is equal to tau. That works out to 45+ watts/m2. Now, the “+” I carried through the calculations was plus 10%, as the true tau for the ocean is 3.3. So we need to add an additional 10% to the 45+ watts, giving us 50 watts first into and then out of the ocean … versus 56 watts for the land. Half a hundred either way.
Of course, now that I think about it, it makes perfect sense. The smaller involved thermal mass will heat up more, the larger involved thermal mass will heat up less, and they both actually store about the same amount of energy per square metre. Of course, in global terms, the 70:30 ratio of the sizes of ocean and land comes into play … but per square metre, they each have a flux of about fifty watts per square metre, first into and then out of the thermal mass each year. Good to know.
Always more to learn,
w.
My Usual Request: If you disagree, do us all the favor of telling us exactly what you disagree with. There’s only one way to do this, which is to quote the exact words you disagree with. Anything else is your interpretation. We can only be clear what you think is incorrect if you quote the precise words they actually used.
Math Note:
Here’s the actual calculations in comma separated format.
Type, time constant tau, depth heat mass, W-yr/m2/°C, Swing °C, Equiv W/m2
Land, 1, 7.9, 1.0, 28.3, 55.8
Ocean, 3.3, 26.1, 3.3, 7.7, 50.3
Note that this is only valid with tau expressed in months.
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No worries, Willis. I too made a mistake once.. I think it was in 1964.
I used to think I made mistakes until I learnt about modelling. Now I just tweak my data!
Great line!
Do you mind if I use it on other web sites?
I thought I made a mistake once back in 1998 (it must of been the heat), but it later became apparent that I was wrong.
Now, vary clouds over that.
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You can get anything you like, Aunt Gaia’s Restaurant.
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Excepting Gaia. Just as well, because our concerns are trivial to her. As George Carlin said, we are just a surface nuisance like a bad case of fleas.
Now vary the incidence angles of solar radiation on the wrinkled land masses and variation of vegetation cover and consider the churning action of ocean waves to bring cooler water into the solar radiation and so on. Very complex and not easily measured.
Evaporation, condensation, atmospheric circulation, storms….
Oh, and if you want anything close to a realistic solution, do all of that to a spatial resolution of 1mm.
And photosynthesis involves more than just heat transfer, it is doing work.
Hmmm, in fact what Willis says – if I understand correctly – is that the amount of energy he specifies moves in and out of the respective thermal masses each year. He does not specify how. How would include radiation, conduction, evaporation, etc. All of those are routes the outgoing energy can take in their convoluted paths away from the planet.
Matt, Michael, Kim,
And so on, etc., etc. The complexity boggles the imagination. Like many, though, I believe the oceans have much more to do with long term climate and its changes on our 70% water covered world than any other single variable. However it is made up of and impacted by a multitude of other intervening variables not the least of which is TSI from which it stores and circulates and disperses heat in unknown ways. Add to this the unknown amount of geothermal energy it absorbs and the clouds mentioned above and it is questionable if the equation to describe the system could even be written were the values of the variables known quantities.
Jim G
Absolutely.
The problem is very complex.
Our data – especially over the oceans (which are big) – is sparse.
This blog once listed a shed-load of variables.
Auto
The details are mind boggling! Wow!
One difference between ocean and land is that heat transport from the surface to below the surface is done almost solely by conduction in land, where convection dominates in the ocean for all but the shortest time sales.
Another difference is that radiant energy at optical wavelengths (sunlight) will penetrate a fair distance into the ocean as opposed to being stopped at the surface on land.
Having said that, knowing the Tau for land and water does give some nice information.
“…the shortest time sales.” Would that be an instant discount, or as we say in Asia, “For you, special price”?
Convection does not transfer enthalpy from the surface to depth in the ocean. Quite the reverse. Convection insures that enthalpy at depth from the deep penetration of light quickly moves to the surface.
Willis, a man who admits his error makes me think on Burns:
(The whole can be ).
Willis, you are a king o’ men for a’ that. Would any other Mann admit to a’ that?
The whole can be seen here: http://www.robertburns.org/works/496.shtml
Willis, how does this affect your impression of Dr. S’s research?
Or doesn’t it?
“One such rule of thumb is that a watt per square metre of incoming energy applied over a year (1 W-yr/m2) will raise a cubic metre of seawater by 8°C.”
A watt is a power unit, not an energy unit, i.e. Btu/h. 3.412 Btu/h per W.
The heat capacity of air is 0.24 Btu.lb – F, water, 1.0 Btu/lb-F. No watts involved.
Three Legged Stool of CAGW: 1) Anthropogenic 2) Radiative Forcing 3) GCMs
Leg the 2nd
Radiative forcing of CO2 warming the atmosphere, oceans, etc.
If the solar constant is 1,366 +/- 0.5 W/m^2 why is ToA 340 (+10.7/- 11.2)1 W/m^2 as shown on the plethora of popular heat balances/budgets? Collect an assortment of these global energy budgets/balances graphics. The variations between some of these is unsettling. Some use W/m^2, some use calories/m^2, some show simple %s, some a combination. So much for consensus. What they all seem to have in common is some kind of perpetual motion heat loop with back radiation ranging from 333 to 340.3 W/m^2 without a defined source. BTW additional RF due to CO2 1750-2011, about 2 W/m^2 spherical, 0.6%.
Consider the earth/atmosphere as a disc.
Radius of earth is 6,371 km, effective height of atmosphere 15.8 km, total radius 6,387 km.
Area of 6,387 km disc: PI()*r^2 = 1.28E14 m^2
Solar Constant……………1,366 W/m^2
Total power delivered: 1,366 W/m^2 * 1.28E14 m^2 = 1.74E17 W
Consider the earth/atmosphere as a sphere.
Surface area of 6,387 km sphere: 4*PI()*r^2 = 5.13E14 m^2
Total power above spread over spherical surface: 1.74E17/5.13E14 = 339.8 W/m^2
One fourth. How about that! What a coincidence! However, the total power remains the same.
1,366 * 1.28E14 = 339.8 * 5.13E14 = 1.74E17 W
Big power flow times small area = lesser power flow over bigger area. Same same.
(Watt is a power unit, i.e. energy over time. I’m going English units now.)
In 24 hours the entire globe rotates through the ToA W/m^2 flux. Disc, sphere, same total result. Total power flow over 24 hours at 3.41 Btu/h per W delivers heat load of:
1.74E17 W * 3.41 Btu/h /W * 24 h = 1.43E19 Btu/day
Suppose this heat load were absorbed entirely by the air.
Mass of atmosphere: 1.13E+19 lb
Sensible heat capacity of air: 0.24 Btu/lb-°F
Daily temperature rise: 1.43E19 Btu/day/ (0.24*1.13E19) = 5.25 °F / day
Additional temperature due to RF of CO2: 0.03 °F, 0.6%.
Obviously the atmospheric temperature is not increasing 5.25 °F per day (1,916 °F per year). There are absorbtions, reflections, upwellers, downwellers, LWIR, SWIR, losses during the night, clouds, clear, yadda, yadda.
Suppose this heat load were absorbed entirely by the oceans.
Mass of ocean: 3.09E21 lb
Sensible heat capacity: 1.0 Btu/lb °F
Daily temperature rise: 1.43E19 Btu/day / (1.0 * 3.09E21 lb) = 0.00462 °F / day (1.69 °F per year)
How would anybody notice?
Suppose this heat load were absorbed entirely by evaporation from the surface of the ocean w/ no temperature change. How much of the ocean’s water would have to evaporate?
Latent heat capacity: 970 Btu/lb
Amount of water required: 1.43E19 Btu/day / 970 Btu/lb = 1.47E+16 lb/day
Portion of ocean evaporated: 1.47E16 lb/day / 3.09E21 lb = 4.76 ppm/day (1,737 ppm, 0.174%, per year)
More clouds, rain, snow, etc.
The point of this exercise is to illustrate and compare the enormous difference in heat handling capabilities between the atmosphere and the water vapor cycle. Oceans, clouds and water vapor soak up heat several orders of magnitude greater than GHGs put it out. CO2’s RF of 2 W/m^2 is inconsequential in comparison, completely lost in the natural ebb and flow of atmospheric heat. More clouds, rain, snow, no temperature rise.
Second leg disrupted.
Footnote 1: Journal of Geophysical Research, Vol 83, No C4, 4/20/78
Are you not joining their (false) assumption that you can “average” heat transfer energy over the entire year by “averaging” the insolation at the equator, mid-latitudes, and poles into a single “flat earth” value valid for both day and night?
Although it’s a bit of a bass ackwards sentence ” . . . watt per square metre of incoming energy applied over a year . . . ” But W-yr is an energy unit and a W-yr/m2 is an energy flux across an area. That was my understanding of the sentence.
Cheers, Mark
<i?“One such rule of thumb is that a watt per square metre of incoming energy applied over a year (1 W-yr/m2) will raise a cubic metre of seawater by 8°C.”
A watt is a power unit, not an energy unit
But a watt-year is.
Please read carefully before jumping in feet first.
as stated above by other, a Watt-year is energy ; 31.5 MJoules. Which indeed will rise a cubic meter of water by (a little less than) 8K.
I one saw a greeny very proud of his energy conservation system for his house : a huge pool in the cellar. The poor guy had no physical ideas of how few energy his costly and inconvenient (thanks to humidity everywhere) system actually contained.
“before jumping in feet first”… also before inserting feet into mouth.
The land is easy, because the involved thermal mass warms and cools at one degree C per watt-year/m2. It swings 28°C,
Are you saying the ground temperature swings 28°C (82 F). Or are you getting air temperatures above the ground? How deep do you have the 28 C going into the mass of the earth?
I live in the state of Wisconsin. The frost line here is 6ft, which means over the course of the winter the ground will freeze to a depth of 6 feet and will thaw to that depth over the spring/summer. My understanding is that summer ground temp averages somewhere around 68 F, and since if will freeze to 6 ft in the winter, an 82 F swing over the course of a year is not that unbelievable.
P.S. This is why most buildings here have full basements, since you have to sink the foundation below the frost line anyway, once you are below 6feet, there isn’t that much extra cost to putting in a full basement.
Rockford, Il, just 15 miles South of the Wisconsin border had, according to It’s Water Department, 6 feet of ground freeze this year. This is near a record as it froze mains that had not previously frozen and residential pipes more than they could remember. The City issued a warning on pipe freezing and offered to reduce water bills for those who left water trickling to prevent mains freezing. Here water mains are under the streets and the ground density and lack of sod covering would allow deeper cooling and freezing. Grave diggers generally found frost just below 4 feet under grass.
I wonder how deep the temperature difference goes? Does ground cover make a big difference everywhere? In heavily wooded areas would both increase and decrease be reduced? Has paving changed the heat exchange with the atmosphere much? Finally, is the estimate for heat gain and loss pretty close?
Our well water is way colder than 68 degrees from a 130 feet deep well in the yard. Doesn’t change much by season. Mighty cool watering the garden in August. Does not freeze quickly if the hose supply system is opened and used in March, something I have done.
Clear sky
Grass
Concrete (slope from moving shadow as sun moves)
Asphalt
Plus air temps
“swings 28degrees C” = delta C. 28C delta = 50F delta.
Average daily range since the 50’s is ~17.8F (specifically 17.83143F rising temp, 17.83556F falling temp).
Cooling slightly more than warming.
if the surface of the water and the surface of the land had radically different rates wouldn’t we have expected to see very distinct and unusual weather patterns at the shorelines of every ocean ? you would have had a very distinct line of demarcation of differing thermal behaviors that would have led to interesting weather patterns everywhere the oceans touched the land …
KaiserDerden, You do get that. In the day, heated air is greater over land and rises causing onshore breezes from the cooler ocean. At night, after the land has cooled, the warmed air over the sea rises and offshore breezes are generated.
https://ca.search.yahoo.com/search?fr=mcafee&type=C111CA662D20141029&p=onshore+breeze+diagram
Gary,
Not just the oceans. The Great Lakes, or at least Michigan and Superior are large enough to experience the same effect.
It sure makes the weather near the coast of southern California very nice. Cool summers and not so cold winters. But you have to be pretty close to the coast, maybe 5 miles.
This seems to imply there’s a significant difference between the Northern and Southern Hemispheres.
There’s far more water down under.
So these lags ought to cause systematic differences between the N and S temperatures. But the Jet stream and the Gulf Stream both cross the Equator,
If that’s right, there ought to be repeated patterns in accelerations and decelerations of the Jet stream and the Gulf Stream.
It may not be periodic in frequency. But, if this is right, it should be repeated in sequence.
And that would be a useful thing to learn.
It’s interesting that despite the large difference in NH and SH land:water, that their albedo is the same.
”This symmetry is achieved by increased reflection from SH clouds offsetting precisely the greater refl
ection from the NH land masses. (ii) The albedo of Earth appears to be highly buffered on hemispheric and global scales as highlighted by both the hemispheric symmetry and a remarkably small interannual variability of reflected solar flux (~0.2% of the annual mean flux). We show how clouds provide the necessary degrees of freedom to modulate the Earth’s albedo setting the hemispheric symmetry. We also show that current climate models lack this same degree of hemispheric symmetry and regulation by clouds. The relevance of this hemispheric symmetry to the heat transport across the equator is discussed.”
http://webster.eas.gatech.edu/Papers/albedo2015.pdf
The jet streams are normally restricted to northern and southern hemispheres and do not cross the equator. There are polar jets and subtropical jets in each hemisphere. Also, I doubt that any part of the Gulf Stream is considered to be from south of the equator. I know there is a flow of water from off the coast of Africa near the Congo that feeds into the Caribbean Sea but that is not normally considered part of the Gulf Stream.
Don’t forget oceanic currents that transport the solar energy imparted in the tropics and transport it in 3 directions, particularly pole words.
For example, the reason why the ocean off Iceland or the West coast of Norway does not freeze, but the Baltic Sea at the same latitude does freeze, is down to oceanic currents. One cannot look at how much solar is being received at any one location at any given moment in time, because energy is being transported through the system to different places by different means and at different rates. The energy budget at any one location is made up of a number of different factors.
I explained this to Willis in his Radiating the Oceans article. There is so much solar being inputted into the tropical oceans that the tropical oceans never freeze. The excess energy is transported in 3 directions (some being distributed to depth, and some polewards) at different speeds. Some seas in some places are the recipient of this warm water currents and they do not freeze; other areas are not and they gradually freeze when the input from their direct local solar insolation falls below critical levels, and thaw, once direct local solar insolation picks up.
To err is human, to arrrr is pirate.
Hi, your post got me wondering about the heat curves of temperature of soil and water over depth.
i would love to see that posted on the skeptical science site.even if it did not last long,it may even provoke some proper thought among he worlds leading warmists.
This is O/T but I hope everyone has a chance to look at this latest report from the OZ Climate Council. That’s Flannery, Steffen etc. Just unbelievable, let’s hope Anthony has the time to ponder their nonsense.
http://www.climatecouncil.org.au/climate-change-2015-growing-risks-critical-choices
Not all Australians are liars with their snouts snuffling in the public money trough..
A very strong and rapid decarbonisation of the global economy could stabilise the climate system below 2°C,
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It would sure as shooting destabilize the global economy. The stock market swings of the past week would be remembered as the “good old days”.
Funny how we are told that fossil fuels are not sustainable, yet every time prices rise there is a huge glut of oil on the market and prices fall. This suggests that supply is a function of price, not fundamental scarcity.
Abe
Thank you.
michael
Yeah I’d say that this reference pretty much settles it for the climastrologists science background:
http://wattsupwiththat.com/2015/02/24/are-climate-modelers-scientists/
Willis – I’m not at all sure about this, but you may have a logic error. It looks to me like the way in which you have calculated the relative thermal mass for land and water necessarily means that you will find the same stored energy per square metre. IOW your conclusion was initially assumed. For example, does your relative thermal mass calc cater for possible difference in albedo? I repeat : I am not at all sure about this, you are much more likely than me to be correct, but I would appreciate it if you could check.
Willis, logical slip it seems:
Accepting your 3:1 ratio that should be 3°C.
I would just add that you need to keep in mind the internal heat that comes from radioactive decay from within the earth, (mainly U, K and Th) which in this solar system is unusual, and which ultimately and largely drives plate tectonics and volcanoes. The mid ocean ridge system is quite extensive and certainly effects chemistry within the deep oceans.
It might not be much of a percentage in terms of heat in the discussion above, but over long periods of time and in terms of chemistry and other effects in can be quite significant. Many scientists have made the mistake of ignoring internal earth processes, such as ascribing the origin of the ocean water from comets (when magma solidifies it expels water, which is more than enough to explain the origin of the ocean water), ignoring the buffering capacity of ocean sea floor with ocean acidity, and mistaking the age of the earth by not taking into account the effect of radioactive decay with heat loss calculations. I’m sure there are other examples.
Willis
Have you taken into account that the temperature gradient between land and ocean is fundamentally different, and that they are heated in different ways from different sources?
As one descends through the oceans the temperature at 24 metres is considerably cooler than the temperature at the surface (the SST is very slightly cooler than the top mm,) Also there is a fundamental difference between day and night temperature profiles due to the lack of solar input.
During the night, a typical ocean has much the same temperature extending over a depth of between about 1mm and say about 8 metres (although anyone who has dived/snorkelled will be aware of how there can be significant temperature fluctuations over very small distances), but during the day, the temperature drops off significantly from 1mm and below. Most of the solar is absorbed within the first few metres. See generally (where (a) is the night time profile and (b) is the day time profile):
http://disc.sci.gsfc.nasa.gov/oceans/additional/science-focus/modis/MODIS_and_AIRS_SST_comp_fig2.i.jpg
However with land the temperature at 8 metre depth is higher than that at say a few centimetres. This is why in Northern countries, plumbing has to be buried below the perma frost depth.
There is a fundamental difference between how the oceans are heated (top down by solar which can penetrate to a depth of about 100 metres, although most is absorbed within 3 to 5 metres). On land the vertical penetration of solar is negligible. Obviously solar heats the very top surface, but below that it is geothermal heat that is heating the ground below the very top surface, ie., it is being heated from below by a different heat source. And there is no equivalence of ocean overturning inland. Heat is transferred by conduction, not by physical mixing.
Incidentally, if you look at the NASA plot (a) of the ocean temperature profile, you will note the steady temperature profile between about 1mm and 8 metres. This suggests that ocean overturning does not effectively mix the very top layer of the ocean. This, of course, has a bearing on whether DWLWIR which is fully absorbed in the top microns, can effectively be mixed and dispersed/dissipated into the bulk ocean below and hence whether it plays an effective role in keeping the oceans warm and preventing their freezing.
.
Great comment. Why would geothermal heat warm the continents and not the oceans?
Good question. Temperature increases by ~30°C per kilometer below the sediments.
Thermal mass is one parameter, thermal conductivity is another. Experiment with a stainless steel teaspoon and with a Silver, Aluminum or Copper one. In a hot cup of tea or coffee, the handle of the SS one will stay very cool, compared to the others. Little to do with thermal mass. What is the temp profile in degrees difference vs. depth for seawater and for land (whatever that is)? In my quick skim, I didn’t trip over this relationship, so pls accept my apologies if it’s covered. / mark F
And thermal diffusivity is yet another.
It’s a good point. I wonder what percentage of so called climate scientists ever read Verhoogen “Energetics of the Earth.”
This should be a Guest Post on its own. /Mr Lynn
Willis,
You state:
“As a result of my newly-gained ability to calculate the time constants tau for the ocean and the land (on the order of 3+ months and 1 month respectively), we get about 24+ metres and 8 metres of thermal mass for the ocean and land respectively.”
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It is nearly 3 am and it may be that I am not thinking straight, but is this a comparison without real meaning?
The ocean is uniform in its nature and characteristics but the land is not, having vastly different albedos and varying heat capacities. For example how much of the of the land surface of the planet is covered by forest? There is all but no solar reaching the land/forest floor. The trees are more than 8 metres high. In (tropical rain) forests, it is the high humidity (water vapour) that is keeping the temperature stable, nothing to do with the land. And where is the distribution of these forest, since over the equatorial area, there is far less seasonal variation in solar insolation (indeed, they have less seasons)
PS. Per Wikipedia: “According to the widely-used[5][6] United Nations Food and Agriculture Organization definition, forests covered an area of four billion hectares (15 million square miles) or approximately 30 percent of the world’s land area in 2006.[4]”
Richard, I think you are on the right track.
The vegetation prevents warming in two ways: evaporation, which is how it grows, and absorbing solar energy and converting CO2 into biomass, which is how it grows.
In the oceans, incoming energy evaporates water, lots of it. There is also a considerable amount of biomass growing in the ocean which converts energy into chemical stored energy.
The emissivity of water is higher than nearly everything on land, as well as more reflective. The idea that water is a powerful emitter of IR is not easily apprehended because we see it as transparent. Water looks clear and reflective, but in IR it is jet black. Irradiate it, it evaporates. Leave it alone, it sheds heat.
Willis, in a comment above replying to another commenter, I mentioned the fact of equal albedo between NH and SH modulated by clouds. I think your work here and your climate governor work could connect with this finely tuned phenomenon.
http://wattsupwiththat.com/2015/08/24/wrong-again-again/#comment-2014616
Should have added that the difference in heat capacities of the land and ocean end up being equalized in the NH and SH because clouds are generated that reduce the insolation that other wise would have seen vast differences and probably killer currents and winds from the difference in land:ocean ratio. A remarkable balance that I hadn’t even heard about until I read it in one of your articles as a passing thought.