The climate model approximation that could fundamentally change the climate movement

Carbon warming, water cooling

Is an approximation made in one of the world’s first climate models the reason that today we believe global warming is solely due to greenhouse gases?

This is a story of how the ‘Global Warming = Greenhouse Gases’ narrative came to be, and an inquiry into whether the real climate narrative should really be

‘Global Warming = Greenhouse Gases + Land Degradation affects Water Cycle’ .

This story involves the characters of Jule Charney, Syukoro Manabe, and Richard Wetherald, who we followed in the previous essay “The quest to figure out the origin of rain part II: Weather in digitial worlds” as they discover that a significant amount of our rain comes from the small water cycle, that land use change affects the rain, and that evapotranspiration cools the surface of the earth. Jule Charney headed the world’s first numerical weather predication effort. Syukoro Manabe, who would later win the Nobel prize for his greenhouse model, made the first climate model that could simulate the water cycle. You can read that essay for backstory, or you can simply jump into this story.

The inquiry into which narrative above is correct is significant inquiry because if the second narrative is correct, what we need do to lessen global warming will require a lot more actions in addition to reducing carbon emissions.

1979: The world awakens to climate change

The scientific voices proclaiming climate change was man-made were increasing in number. Concern was rising. In 1979 the World Meteorological Organization organized the first World Climate Conference, bringing together representatives from 53 countries, encompassing a range of disciplines that included agriculture, fisheries, ecology, climate science, economics, environment, and medicine. They release a report at the conference which describes how humans are creating climate change - one, through greenhouse emissions, two, through changing land use.

Later that year, the US National Research Council convenes a scientific committee, headed by the meteorologist ring-leader Jule Charney, to look into the carbon emissions greenhouse effect. The scientists meet and compare their global climate models - Manabe and Wetherald’s, Akio Arakawa’s, and James Hansen’s. The models differ in quite a bit in how they think carbon dioxide affects global warming, so there is a debate about how to proceed. Finally they decide to average their results, and release a report that says if carbon dioxide doubled, “global temperatures would increase between 1.5 and 4.5 degrees Celsius with the most likely outcome a warming of three degrees”. The global warming threat, now finally quantified and publicized, makes a big impact in the cultural dialogue of the day, and leads to the first US congressional hearing on the greenhouse effect the following year, and many ensuing climate policy discussions. The report, which later became known as the Charney report, thus plays a key role in birthing the modern climate movement.

The three global climate models that were discussed in the report base their methodology on a calculation that Manabe and Wetherald did in 1967 to see how carbon emissions might have led to the measured global temperature rise. In this calculation as more carbon dioxide enters the atmosphere, more radiation gets trapped, raising the global temperature. An increased global temperature means more water vapor is held in the atmosphere. That extra water vapor traps extra radiation, heating up the atmosphere even more. In the model, carbon and water combine to heat up the atmosphere, in contrast to previous models which only had carbon heating up the atmosphere. The calculation is written up in a paper, a paper that decades later is proclaimed by climate scientists as the most influential climate paper ever.

The Manabe and Wetherald approximation. Is it correct?

To do this calculation Manabe and Wetherald have to figure out how to model convection and the water cycle. Convection is the movement of heated air upwards, and cooler air downwards. Convection carries water vapor. It is difficult to simulate convection because it happens at a much smaller scale than the grids in a global climate model allow. It is hard to model because water undergoes a phase change from vapor to liquid at the cloud level. So Manabe and Wetherald make an approximation, called a convective adjustment, or a convective parametrization. It is an approximation that will propagate into many climate models down the line, for decades to come.

Making approximations though can lead to problems. If you leave out friction when you are modelling billiard ball dynamics, you get the result that everything keeps bouncing around without ever slowing down. If you model nonlinear dynamics with linear equations you might neglect lots of interesting behavior. You would miss out on chaos theory. Small perturbations can turn into large phenomena. Nonlinear equations have strange attractors, linear equations do not. For many years, economists left out small perturbations in their linear models. Then Brian Arthur came along and said a small difference can morph into something larger. He gave the example of how if there were slightly more people using Beta instead of VHS video tapes earlier on, Beta might have come to dominate over VHS, instead of what eventually happened, with VHS taking over the market. Economists linear approximations had caused them to miss understanding real world phenomena.

Would Manabe and Wetherald’s approximations lead to problems? Is the approximation they make, called the convective parametrization, the reason our climate movement today is so focused on carbon, rather than on both carbon and water? Is their approximation the reason we have discounted the impact of the destruction of forests and wetlands in causing climate change?

Anastasia Makarieva, the co-founder of the biotic pump theory, points out there is problem with Manabe and Wetherald’s model. She says they have simplified the situation too much. The approximation is off.

Convection is the movement of heated air upwards, and cooler air downwards. It is difficult to calculate because convection is a nonlinear phenomena. To simply the situation, Manabe and Wetherald model convection as a linear phenomena. They use a hydrostatic model rather than a hydrodynamic model. The hydrostatic model uses what is called a convective adjustment, which Manabe and Wetherald keep constant even as forests and wetlands are destroyed.

Makarieva says the way they do their approximations, the way they use what is called a convective adjustment is problematical. The way they keep it constant is problematical. She says it ignores the important role forests and wetland evapotranspiration have in cooling the earth, which should change the convective adjustment. Last year she gives a talk about it, which you can see it in this video and in this one. (I noticed a lot of people have trouble understanding her talk, so I try to simplify her explanation in this little video I made last year. But even my video is still probably too geeky for half the people watching it to understand.) Anastasia Makarieva works with Andre Nefiokov, Antonio Nobre and Anja Rammig to write up a paper on this, and publish it earlier this year. [Makarieva 2023]. There is a potential bombshell impact as the world begins to understand what is going on in these approximations.

I continued to ponder how to explain Makarieva’s results in a more easily understandable way, and recently came up with the following example. It still requires a bit of study, and I still suggest reading it a couple of times to digest properly. (If you don’t want to dive into this, you can jump several sections ahead to the “Climate model tuning” section or the “The eco-crowd’s ‘alternative’ understanding of evapotranspirational cooling” section)

What we are going to do is follow the water as it is transported up by convection carrying latent heat that it then dumps at higher altitudes to radiate into space. What we are going to do is try and figure out under what conditions the water will move upwards, because if it doesn’t move up then the water won’t be able to cool the earth. To understand how the water vapor rises we will first try and understand how balloons can rise. We will show that balloons with more water vapor inside can rise more often, technically expressed as having a lower critical lapse rate. The balloons with more water vapor will be analagous to forests and wetlands evapotranspiring more water vapor. The balloons can transport the water vapor higher into atmosphere where infrared radiation coming from latent heat of the water condensing, can then radiate more efficiently into space, thus cooling the earth. When we deforest and drain wetlands, we are metaphorically taking the water vapor out of the balloons so they cannot rise as well.

Imagine a balloon with hot air. Release it, and the balloon will start rising if the air is hot enough. As the balloon rises, the balloon will keep expanding (we assume the balloon is made of a special material that allows it to keep stretching without popping), while the air inside cools. If the air inside the balloon is ever cooler than the air around it, it will not rise anymore. So we can say if, as the ballooon rises, the air inside the balloon cools off at a faster rate than the air outside cools, then the balloon will stop rising. If the air inside the balloon cools off at a slower than the air outside cools, it will keep rising. This temperature decrease rate as one moves to higher altitudes is called the lapse rate. The temperature decrease rate for which the balloon no longer will rise is called the critical lapse rate.

Now imagine we also have some water vapor in the balloon. As the balloon rises the water vapor will condense and give up latent heat, which heats up the air inside the balloon. The balloon can thus rise even more because its now hotter. So the temperature outside the balloon can decrease at a slower rate vertically and the balloon will still rise. The critical rate at which the atmospheric temperature decreases so that the balloon stops rising, the critical lapse rate, will thus be less. This is a key point - balloons with more water vapor in them will have a lower critical lapse rate which allows them to keep rising when compared to balloons with less water vapor in them.

Now imagine that we get rid of the balloon, because in the real world the atmosphere is not full of balloons, and we are left with just an air parcel containing water vapor. Imagine initially this air parcel is quite a bit warmer than the surrounding air, causing it to rise. As it rises, it expands and cools. The water vapor in the parcel condenses and releases latent heat which heats up the atmosphere.

[diagram from MS meteorology. Heres a video of their’s explaining this diagram . Looking at some meteorology 101 videos about this effect may be useful]

Now imagine if we had thousands and thousands of these air parcels rising. At some point they will warm the atmosphere enough, that more air parcels will not be able to rise, as the vertical temperature gradient is now not steep enough.

Meanwhile the atmosphere is also continually radiating infrared radiation heat to space, so it will cool down over time, the top of the atmosphere cooling faster because the infrared radiation there has less greenhouse gases to go through before entering the atmosphere.

As it cools down over time, the vertical temperature gradient, the lapse rate, becomes greater, and so air parcels can once again rise. The air parcels rise until the critical lapse rate is reached and then it stops again. (This type of behavior which involves radiation and convection is why Manabe and Wetheralds model is called a radiative-convective model). Because the cooling via radiation is slower than the convection rise, on average the atmosphere spends most of its time at the critical vertical temperature gradient, at the critical lapse rate.

This physical explanation is a simplified view of what is really happening in the atmosphere, and is the one Manabe and Wetherald use in their climate model. For their model to run they need a critical lapse rate. So they looked at the earths average vertical temperature gradient, which is about 6.7 K km^-1, and put that into their model.

The problem is that they assumed in their model that the critical vertical temperature gradient, the critical lapse rate, was the same in their present as it was in their past. But that’s not the case if forests had been chopped down, grasslands paved over, and wetlands degraded. There would have been more water evapotranspiration in the past. Which means that the actual critical vertical temperature gradient then would have been less. The problem with Manabe and Wetheralds model is that they don’t allow this critical lapse rate to vary over time and the critical lapse rate plays a big role in what global temperature is reached. So the model fails to take into land degradation as being a key factor in climate change. And most climate models after this, basing their models on the convective adjustment/parametrization idea, also have this same problem.

Climate model tuning

As Manabe and Wetherald’s convective parametrization is integrated into climate models, and models built on top those models over the decades after that 1967 year, the convective approximation becomes forgotten about. Its analogous to when someone writes some underlying computer code, and then people later build on top of that computer code, but forget about the approximations that went into it.

A review of tuning and parametrization by many climate scientists in 2017, write “Although the need for parameter tuning was recognized in pioneering modeling work (e.g., Manabe and Wetherald 1975) and discussed as an important aspect in epistemological studies of climate modeling (Edwards 2001), the importance of tuning is probably not advertised as it should be. It is often ignored when discussing the performances of climate models in multimodel analyses. Why such a lack of transparency? This may be because tuning is often seen as an unavoidable but dirty part of climate modeling, more engineering than science, an act of tinkering that does not merit recording in the scientific literature. There may also be some concern that explaining that models are tuned may strengthen the arguments of those claiming to question the validity of climate change projections.” [Hourdin 2017]

Many later climate models also adjust their results so they can get the same result of global warming of 1 degree from the carbon dioxide addition that Manabe and Wetherald got. So the climate models already assumed carbon emissions were the only global warming cause. Hourdin et all write “some models may have been inadvertently or intentionally tuned to the twentieth-century warming [as being only caused by greenhouse emissions].” In which case they defacto they already have vanished the water-cycle-disruption-through-land-degradation effect.

So what we have here is a situation where we have a worldwide climate movement based on an approximation which gets the carbon part right, but probably leaves out half (or more) of the cause.

The eco-crowd’s ‘alternative’ understanding of evapotranspirational cooling

Intuitively, many people in the eco-crowd ‘alternative’ water paradigm have felt that land degradation disrupting evaporatranspiration is an additional cause of global warming. But a significant section of this crowd often simplifies the situation too much (as an example see this video by Walter Jehne). The water takes away the surface heat when it evaporates is the basic argument. Its definitely true that when water evapotranspires it cools the land, in a similar way to how sweat cools the body. But that’s not the whole story. Manabe, Wetherald, in conjunction with Yeh, after all, found that surface evapotranspiration can cool the surface of the earth by several degrees [Yeh 1982], and yet this effect does not influence the temperature in Manabe and Wetherald’s global warming model. What many climate scientists and many in the IPCC claim is that the water vapor transports the surface heat into the atmosphere, and then that heat redistributes itself around the whole earth. They argue the situation is similar to that of a fridge with its door open. The fridge will cool the room in certain areas, but the heat coming out the back of the fridge will also heat up the room.

But their argument is based on Manabe and Wetherald’s approximation, where an increase in vegetation and wetlands and its accompanying increase in evapotranspiration does not change the critical lapse rate (the critical vertical temperture profile) which would allowing more water vapor to ascend to higher parts of the atmosphere, where it would more easily radiate into space.

A better explanation of what is happening is illustrated in the diagram below.

The evapotranspiration of the water cools the surface of the earth, in a similar way to how sweating cools the body. The water vapor ascends to the cloud level, where it then condenses, releasing heat (technically called releasing latent heat). That heat can then radiate in the form of infrared radiation into space. Because that infrared radiation does not have to go through greenhouse gases below, it more efficiently cools the earth. If there was no evapotranspiration, the heat at the surface would heat up the atmsophere just above it, in the form of whats called sensible heat. This heat would then radiate infrared raditation, but the radiation would get absorbed by the greenhouse gases, and so most of it would not reach outer space and cool the earth.

An analogy can be made here. Imagine you have a heater heating a house on a cold winters day, and you leave the front door open. If the heater is in a back room, less heat will escape to the outside. But if the heater is right by the front door in the entrance hall, a lot more heat will escape to the outside. The analogy to make here is the house is the earth, outside the house is outer space, the back room is the surface of the earth, the latent heat of the condensing water vapor is the heat coming from the heater in the entrance hall, and the sensible heat (which is the felt sense of heat, the vibration of air molecules) when there is no evapotranspiration is the heater in the back room.

“For want of a nail, the horseshoe was lost. For want of a horseshoe, the steed was lost. For want of a steed, the message was not delivered. For want of an undelivered message, the …..” climate movement lost some of its way? Is a proper way to approximate convection the nail we need to get back on track?

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If you want a slightly more technical explanation of the above discussion in this essay, check out the excerpts from Makerieva et al’s paper, and also from Lindzen et al’s paper below….

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Excerpts from “Re-appraisal of the global climatic role of natural forests for improved climate projections and policies” by Makerieva, Nefiodov, Rammig, and Nobre, 2023

'“We argue that deforestation-induced global cooling results from the models’ limited capacity to account for the global effect of cooling from evapotranspiration of intact forests. Transpiration of trees can change the greenhouse effect via small modifications of the vertical temperature profile. Due to their convective parameterization (which postulates a certain critical temperature profile), global climate models do not properly capture this effect. This parameterization may lead to underestimation of warming from the loss of evapotranspiration in both high and low latitidues, and therefore, conclusions about deforestation-induced global cooling are not robust.

An exact estimate of what happens when the evapotranspiration and the latent heat flux are suppressed on a certain part of land area requires solving the problem simultatenously for the radiative-convective transfer [a radiative-convective transfer means that the infrared radiation heats up air which then leads to convection] and the temperature profile. This problem is too complicated for modern global climate models, which therefore apply the so-called convective parameterization. The idea is to postulate the (generally unknown) value of a critical temperature lapse rate instead of solving for it. While the numerical simulation is run, ‘whenever the radiative equilibrium lapse rate is greater than the critical lapse rate, the lapse rate is set equal to the critical lapse rate’.

We have seen that, for a given amount of absorbers [absorbers means the greenhouse gas at lower levels that absorbs the infrared radiation], surface temperature is determined by the vertical distribution of the non-radiative heat fluxes [non-radiative fluxes is the water vapor transporting the latent heat upward]. But these fluxes themselves depend on the vertical temperature gradient: if the air temperature declines with height faster than a certain critical lapse rate, the atmosphere is unstable to convection. The non-radiative heat fluxes originate proportional to the difference between the actual and the critical temperature lapse rates. Therefore, strictly speaking, it is not justified to freely vary where and how the non-radiative heat fluxes dissipate to thermal radiation, not paying attention to whether the resulting vertical temperature profile is consistent with their specified values.”

An exact estimate of what happens when the evapotranspiration and the latent heat flux are suppressed on a certain part of land area requires solving the problem simultatenously for the radiative-convective transfer and the temperature profile. This problem is too complicated for modern global climate models, which therefore apply the so-called convective parameterization. The idea is to postulate the (generally unknown) value of a critical temperature lapse rate instead of solving for it. While the numerical simulation is run, ‘whenever the radiative equilibrium lapse rate is greater than the critical lapse rate, the lapse rate is set equal to the critical lapse rate’

Therefore, by construction, global climate models cannot provide any independent information about the climatic effect of evapotranspirational cooling – that should be manifested as the change in the global mean lapse rate – besides what was fed into them a priori via convective parameterization.”

Excerpt from “The Role of Convective Model Choice in Calculating the Climate Impact of Doubling CO₂ " by R. S. Lindzen, A. Y. Hou, and B. F. Farrell

[ Editor note: In their model they allow for a variable lapse rate, which they call a cumulus model. They are comparing it to Manabe and Wetherald’s model which is a fixed lapse rate, meaning the temperature gradient is constant.]

“The freedom of a variable lapse rate allows radiative perturbations to be accommodated locally near the tropopause, without being carried through a fixed lapse rate to the surface. As a result, the perturbation response of a cumulus model tends to concentrate at the cloud-top levels rather than the uniform response of a fixed-lapse rate model; this would then lead to a smaller greenhouse feedback.”

References

To read these papers, get the doi number from scholar.google.com, then type that doi number into sci-hub.ru

Jeevanjee, N., I. Held, and V. Ramaswamy, 2022: Manabe’s Radiative–Convective Equilibrium. Bull. Amer. Meteor. Soc., 103, E2559–E2569, https://doi.org/10.1175/BAMS-D-21-0351.1.

Hourdin, F., and Coauthors, 2017: The Art and Science of Climate Model Tuning. Bull. Amer. Meteor. Soc., 98, 589–602, https://doi.org/10.1175/BAMS-D-15-00135.1

Lindzen, R. S., A. Y. Hou, and B. F. Farrell, 1982: The Role of Convective Model Choice in Calculating the Climate Impact of Doubling CO2. J. Atmos. Sci., 39, 1189–1205, https://doi.org/10.1175/1520-0469(1982)039<1189:TROCMC>2.0.CO;2

Makarieva, Anastassia M., Andrei V. Nefiodov, Anja Rammig, and Antonio Donato Nobre. "Re-appraisal of the global climatic role of natural forests for improved climate projections and policies." arXiv preprint arXiv:2301.09998 (2023).

Ramanathan, V., and James A. Coakley Jr. "Climate modeling through radiative‐convective models." Reviews of geophysics 16, no. 4 (1978)

Yeh, T. C., R. To Wetherald, and S1 Manabe. "The effect of soil moisture on the short-term climate and hydrology change—A numerical experiment." Monthly Weather Review 112, no. 3 (1984): 474-490.