10. Analysing the Hadley Cell

One of the assumptions about the way latent heat is radiated into space, is “deep convection”. Like the standard greenhouse theory that was described in chapter 9, this suggests that the main radiation into space is from high in the atmosphere, near or even above the tropopause.

I have always had my doubts about that. There is hardly any water vapour and a very low concentration of CO2 at that height, so how can so much energy be disposed of, with so few GHG molecules?
I expected that lower parts of the atmosphere would be more important, even for the emission of the energy from deep convection to space. But it was not easy to quantify that without modelling the Hadley Cycle, which is powering most of the latent heat transport (LHT). I have been postponing that for months now.
But I decided to give it a try, two days before my flight to ICCC7, as a showcase of what my Fireworks simulation could do, if provided with the right data by experts. So here is a long night’s work.

Caution: since the model still lacks good data, the results of this chapter are not solid at all.
But I think that they will be inspiring nevertheless!

The Hadley Cells: the worlds cooling engine
As Willis Eschenbach explained so clearly in his presentation in ICCC4 in 2010, the world has a powerful thermostat, consisting of the tenthousands of daily tropical storms in the intertropical conversion zone.

They are part of the Hadley cells and transport enormous amounts of latent heat to the tropopause. They are able to compensate the radiative effects of greenhouse gas concentration changes, and probably have done so for billons of years. But how does this Hadley cell actually work? What really drives it, and how does that relate to the standard explanation of the greenhouse effect?   

Convection cells analysed
Tropical convection always appears above sea or rainforest, with moist air at the surface, so the rising air will follow the saturated adiabatic lapse rate (SALR) until the tropopause. Tropical storms will even break through the tropopause locally and transport energy to up to 18 km high.

Then the air is trapped between the cooler troposphere beneath it and the hotter stratosphere above it. Before it can descend it has to cool down until it can follow the dry adiabatic lapse rate.

In the mean time it is not hanging still, but drifting away to the subtropical regions. During this journey the air looses energy by radiating to space:

Hadley Cell caught in a diagram

In the diagram you can see how the upward flow ends at 14,5 km high and a temperature of –65 C, following the SALR.

Then it has to stay in the tropopause to loose energy and cool down.
Moving away from the equator, there is less convection, so the tropopause drops (in this case to 11,5 km, and a temperature of –80C). While moving from 14 to 11 km height, it is assumed by some that the latent heat is radiated into space.

Calculating the emissions of the Hadley Cell
Actually, now we have enough information to (roughly) calculate where the cell radiates it’s energy to space, and how much. Because, during the whole cycle, we know:
- from the diagram: the temperature and the height
- from the simulation: the part of the energy that is radiated to space at any layer, and the height of the layers.

So let’s assume a certain amount of energy being radiated in all directions, by a mol of air at the surface. When at an other temperature, it will radiate more or less, with the 4^th power.  This gives us a measure of the amount of radiation at any temperature.

At the same time we can calculate with the Fireworks simulation how much of the radiation at any height is radiated to space. In order to do that, I calculated what the ratio was for the SALR and the DALR, for every 500m between the surface and the tropopause, in 30 steps.

I assumed 100 layers in the saturated tropics, and 30 layers in the dry deserts of the subtropics where the main GHG, water vapour, is missing, and tried to find layers that matched the 500 m steps. That gave quite a few mismatches, so there is a lot of “noise” if you look closely at the data. But the general picture is very smooth:

Hadley emission to space

This picture shows the radiation per time unit to space of the greenhouse gases at a specific height.
It has the surface at the right and the tropopause at the left, with 30 steps of 500m.

The rising air (dark blue line) first emits almost everything to the surface (steps 30 to 28), but at 1 km (step 28) it begins  to radiate to space, reaching a peak at 4 km (step 22).

Of course a larger part of the radiation will be emitted to space at greater height, but the dropping temperature decreases the radiation itself more, so from 4 km on you see a decrease in emissions to space.
When CO2 doubles, a 114 layer atmosphere is assumed here, resulting in the purple line giving radiation to space.

From now on, we assume that the air has lost almost all its water vapour, and will behave as in an atmosphere of 30 layers.

Once trapped at the tropopause, the air has to cool down and descend slowly, following the green line, in steps 1 to 7. This is during the journey to the subtropics.

Then, at 11.5 km,  it is cool enough to descend with the DALR and heat up fast, increasing radiation to space, even though a smaller part of the radiation will reach space. Because there are less layers, the peak is at 2 km high (step 26) this time.

When doubling CO2, the influence is much larger now, since the 30 layers are mainly based on CO2. So for the CO2 influence I chose an increase to 40 layers here (the red line).

Time
This picture needs another factor though. The radiation per time has to be multiplied with the real time that the radiation took place in order to get the amount of energy that is radiated out. So I chose “1” for the very fast rising of air in the tropical storms, a factor 4 for the much slower descent in the subtropics, and a factor 12 for the period that the air is moving through the tropopause. These factors are not completely random, but I welcome all suggestions for improvement.
If we make a picture with the values multiplied with time, this result appears:

Hadley emission to space x time

This gives a clear view on where the Hadley cell looses it’s energy to space. And as I expected, only a small part is radiated from the tropopause! Most is radiated from 1 to 10 km, since both blue lines have to be added.

Clouds  in the fireworks model
The obvious error in this calculation is the complete omission of clouds.
In the general energy balance in chapter 5, clouds are primitively accounted for by a general percentage of sky coverage, but in this Hadley cell analysis, this would not work.

Let’s first look at clouds from the Fireworks Theory point of view.

Translated into its layer definition, clouds represent a part of the atmosphere with an infinite number of layers. So, in an equilibrium situation, only an infinitely small part of the surface upward radiation will be emitted to space after absorption, and all energy will be emitted back to the surface.

Since water or ice particles are no greenhouse gases but behave like black bodies (BB), they absorb the complete IR spectrum (visible light is reflected though), and also the emitted radiation will have a normal BB spectrum. Part of it will pass through the IR window and reach the earth surface without being absorbed.

This results in the effect that we all know: at night, under a cloudy sky, the surface stays much warmer than under a clear sky.

Clouds in the Hadley Cell analysis
Let’s see what the influence of clouds could be on our analysis.

In the downwards part of the cell, there are no clouds, so this part is accurate.

In horizontal movement part of the cell in the tropopause, there are hardly any clouds, and as far as there are, they are very thin cirrus clouds. I don’t know if they are increasing the emission into space or decreasing it: whatever energy they contain or whatever IR they absorb, they will emit as a black body, so the IR window part of the energy will be radiated straight to the earth surface and into space. At the same time they will not absorb visible light, because they reflect it. This will cool down the clouds a lot, thus reducing their emission capacity.
Without suggesting to have any expert knowledge about this complex subject, I don’t expect a considerable influence of clouds on the emission to space in this part of the cell.

Tropical storm

Finally: the rising part of the cell.
This part is heavily influenced by clouds. In fact, the latent heat transport over the saturated adiabatic lapse rate is by definition a done by clouds.
Since a vertical column of clouds as in a tropical storm is impenetrable for radiation, the only direct emission into space will be from the top of the anvil. But this has an extremely low temperature. Even with a BB spectrum, it will only emit more energy than a last layer in our theory, as far as there is extra emission through the IR window, ic 15%.
What about the emission during the upward movement, in our graph represented by the low bent curve, representing app. 30% of the total emission into space according to that graph?
It is obvious that at the location of a tropical storm, there will not be any radiation into space, apart from the anvil, ic the last layer.

There are a number of reasons why there still is emission into space at lower levels:
- The tropical storms only cover a part of the surface
- The tropical storms only form during the day, finally producing the anvil. Until that moment, there is radiation from lower levels, and that is substantial because of the higher temperature and the BB spectrum of clouds.
- The vertical column of clouds of a tropical storm emits its energy to the air around it. This air will behave like a normal moist atmosphere and emit its energy into space.

Considering all this, it is, in my opinion, likely that omitting clouds in the analysis, results in a too high estimation of the emission during the upwards part of the cell. If this error is 20 or 80% is hard to tell. My guess is between 40 and 60%.
This would not affect my conclusion.

Greenhouse effect
Now let’s see what CO2 is doing, by subtracting the two curves:

Decrease of latent heat, radiated into space in the Hadley cell, caused by CO2 doubling

Conclusion
Here the noise on the data shows clearly, but the conclusion is obvious: the influence of CO2 doubling on the radiation to space from the Hadley cell is mainly found between 3 and 7 km high, peaking at 5km, during the descending part of it, in the subtropics.

Actual measurement data check
These findings should not be a surprise: when you look at the latent heat and outgoing long wave radiation (OLR) maps, it is obvious that where the Latent heat is transported upwards, it is not radiated into space.

First the LHT, which is mainly found above the oceans and the rainforests, but not at all at the rest of the continents:

Latent heat flux

In the deserts however, where there is absolutely no LHT, but the downward part of the Hadley cells, there you find the maximum OLR:

OLR

The standard greenhouse theory would suggest that both have to occur at the same place, since the DALR, which is supposed to be pushed up by the tropopause, is a local phenomenon.
It seems to me that my calculations, although still based on very weak data, are much more convincing.

Is CO2 increase heating up the atmosphere after all?
In this chapter we established an influence of CO2 increase on the radiation during the Hadley cycle, which lead to a decrease of emission to space over the whole loop. This seems to contradict the thermostat theory of Willis Eschenbach, and chapter 7, where I suggested that doubling CO2 has (also) a direct cooling influence by increasing convection.

But it should be noted that, for the purpose of analysis, I calculated the radiative aspect of a Hadley Cell that was assumed to be unaffected by the CO2 content itself. That way the results could be compared. However, the cell itself is of course also influenced by the heating and cooling aspects of the GHG.

What powers the Hadley Cells?
According to Eschenbach, an increased radiation to the surface (by what reason whatsoever) will increase evaporation, power more tropical storms, which have an overshoot, which means that they create their own positive feedback, leading to more cooling of the atmosphere than the heat that they were caused by. This turns them into a working thermostat.
For the Hadley Cell, more storms clearly mean an increase in LHT, and a powering of the low heat source, as was discussed in chapters 6 an 7 about convection theory.

Considering the heat sink part of the Hadley cell, we now established that it is mainly the descending phase, in the subtropics, where most of the heat is radiated out to space. This is the second power source of the cell.

According to chapter 7, an increase in GHG concentration should increase convection, ic. increase the heat sink in the Hadley cell. Important was the second law, which stated that the convection will be trapped between the low heat source and the high heat sink. For the Hadley Cell that means that with an incresed CO2 content, the heat sink wil be higher, increasing the height of the tropopause.
This enables a longer time to emit during the ascending and descending. It would also lead to a longer path in the tropopause, either by descending at higher latitude (which could be the result of a higher tropopause), or by a change in the portion of the air that descends next to the storm versus the air that descends in the subtropics. These options can be studied in the way I calculated the emissions in this chapter.

Anyway, so far I have not yet been able to quantify the factors powering the Hadley calls. A lot of good thinking will be required before I will.

Still I think that this exercise has been helpful in understanding the way the greenhouse effect works in the Hadley Cells, and that this is a lot more complex than the standard theory suggests.