2. The Fireworks atmospheric simulation

Once absorbed by a GHG molecule, the GhIR energy will be re-radiated and absorbed very many times before it will be radiated out into space or be absorbed by the surface.

Describing this process quantitatively in formulas seemed to be impossible, at least for my mathematics skills. And as far as I know, even very skilled mathematicians have never been able to describe more than 7 layers in a mathematical model of the atmosphere. So I invented another way to calculate a large number of layers accurately, using an iteration approach.

Let me first show the layer definition image of the first chapter:


Layer definition

If I tilt the blue arrows a bit, a new image appears, that can clarify the formulas that I based my simulation on:

Iteration scheme

You see that Su is divided equally in Ed1 and Eu1.
Ed1 looses 50% to the surface, and Eu1 looses 50% to layer 3, so half of Ed1 and Eu1 (twice 25% of Su) will be re-radiated back to the top of layer 1. (more…)

By |May 14th, 2012|Climate|1 Comment

3. The Fireworks simulation: Layer determination

I mentioned earlier that the simulation is extremely rational and accurate, but that all problems have been shifted to the determination of the number of layers.

First we have to address a basic problem: I am simulating the earth’s atmosphere by averaging very different situations. In the humid tropical regions, water vapour will be dominant, and present up to quite high in the atmosphere. In arctic regions or in deserts, there will be hardly any water vapour.  The number of layers in a humid environment is several times higher than in dry regions. Averaging it all is an interesting exercise, which can help understand the way the greenhouse effect works, but cannot do more than that, unless proper adjustments are made (see chapter 10 about the Hadley cell).
Understanding was my goal at first, so I was happy that I managed to construct an average calculation which worked nicely and certainly provided great insight.

But if we use a method that is able to determine the number of layers accurately at a certain place, for instance by using pyrgiometer measurements, it is possible to differentiate in different regions, or use the same approach as the existing climate models, i.c. divide the world into quadrants, calculate the radiation in each one of them, and just add up the results. I will leave that up to the real experts, if they agree that the Fireworks simulation might be a good tool.

I managed to do a first, data based calculation to establish a number of layers. But I welcome any effort by experts to increase the accuracy of this calculation.

Basic assumptions

First assumption:
Due to the rather homogeneous distribution of GHG in the atmosphere, and the many different sensitivities of the different wavelengths of GhIR for different GHG molecules, it is reasonable to assume that the height at which the GhIR is in average absorbed, coincides with the height where 50% of the GhIR has actually been absorbed.

Second assumption:
The absorption is a statistic process, in which the absorption rate is linearly correlated with the number of GHG molecules.

First layer assessment based on GAT data
With these assumptions, it is easy to determine the layer thickness from measurements (pyrgiometer), or from simulations like HARTCODE from GAT data, as in this graph:


By |May 13th, 2012|Climate|1 Comment

4. The Fireworks simulation: Climate sensitivity

All this is of course intended for the purpose of establishing the climate sensitivity of CO2.

So let’s assume that we managed to get an accurate representation of the number of layers, by using physics or empirical data, and that the number of layers is determined by the number of greenhouse gas molecules. Then it is easy to double the number of layers that are attributed to CO2, and see what happens with the radiation, and hence with the energy balance of the earth.

In the third chapter we calculated that the number of layers is app. 100.
Numbers about the share of CO2 in the greenhouse effect I found on internet varied widely and had a huge inaccuracy, but averaged on 14%.
Assuming that CO2 contributes app. 14% to the greenhouse effect, it provides app 14 layers of the 100. So a doubling of CO2 would increase the number of layers to 114.

First the 100 layer simulation with Surface Upward radiation (Su), and rather randomly Latent Heat (LH), convection and solar IR (SIR) included (double click to enlarge):

100 layers 3000 it
It turns out that with 100 layers, the downwards radiation Ed is 369,19 W/m2  (72.1%) vs a radiation to space of 142.81 W/m2  (27.9%)

Enjoy playing with the 100 layers simulation here!


By |May 12th, 2012|Climate|1 Comment