The Science of Doom

We have mostly looked at the upward spectra at the top of atmosphere (TOA) as various conditions are changed. There’s a good reason for this focus – the outgoing longwave radiation (OLR) determines how much the climate system cools to space.

Over a given timescale this either matches absorbed solar radiation or the planet is heating or cooling. So it is changes in OLR (or absorbed solar) that really affect the heat balance in the climate.

By comparison, the trend in downward longwave radiation (DLR) at the surface is more a result of overall planetary heating and cooling. But of course, the climate is a lot more complex than indicated by that last statement.

Let’s take a look. Note that Part Four – Water Vapor already has some graphs of how the DLR or “back radiation” changes with water vapor concentration.

Here is the DLR for 4 different surface temperatures. In each case there is a lapse rate of 6.5 K/km, the boundary layer humidity (BLH) = 100%, the free tropospheric humidity (FTH) = 40% and there were 10 atmospheric layers in the model with a top of atmosphere at 50 hPa. More about the model in Part Two and Part Five – The Code.

The top graph is the real case, the bottom graph is without the effect of the water vapor continuum:

Figure 1

The continuum operates over the whole range of terrestrial wavelengths of interest, but its main impact is in the “atmospheric window region” between 800-1200 cm^-1. This window region doesn’t have many strong absorption lines so absorption from any other cause has a big effect.

As we can see, the “window” is very dependent on temperature – which is mainly a result of the amount of water vapor. It’s clearer when we look at the spectral difference between the two cases for each of the temperatures:

Figure 2

Notice that the 273 K (0 °C) condition is almost unaffected by the continuum. This is because the effect is dependent on the amount of water vapor squared. And the amount of water vapor is strongly dependent on temperature.

Let’s look at the total flux for both cases and compare with a reference of blackbody emission from the bottom layer of atmosphere (in this case 400m above the surface so about 2.6°C cooler than the surface, and see note 1):

Figure 3

This shows that once we are above a surface temperature of 300 K (27 °C) with high boundary layer humidity the radiation from atmosphere to surface is getting close to blackbody emission. The graph also demonstrates that most of that change is due to the continuum.

Now good emitters are also good absorbers. So here is another way of looking at the same effect - the % of surface radiation in the 800-1200 cm^-1 window region that makes it to the top of atmosphere (without being absorbed anywhere along the way):

Figure 4

These were all with CO2 at 360ppm (and N2O at 319 ppbv, CH4 at 1775 ppbv and no ozone).

Let’s look at how changing CO2 concentration affects these results.

Figure 5

This is a very important graph – what does it show?

• while different surface temperatures have quite different TOA radiation to space – the change in CO2 causes a fairly constant change in this radiation
• changing CO2 has much less effect on the DLR (radiation from the atmosphere to the surface), and as the temperature increases this effect is even more reduced

Let’s look at the “delta”:

Figure 6 – [Corrected Jan 23]

This shows clearly how the change in atmospheric DLR due to doubling CO2 is very much a function of surface temperature. And at the same time, the change in TOA radiation (“OLR”) is almost independent of surface temperature.

From the information presented in this article on how DLR is affected by water vapor at high temperatures the first point shouldn’t be surprising. And from the explanation in Part Four – Water Vapor both points shouldn’t be surprising.

For interest, here are the two DLR spectrum for 280 ppm & 560 ppm at 288 K, and below, the difference:

Figure 7

Conclusion

The surface energy balance is very important for determining the dynamics of surface heat transfer, including initiating convection. As the temperature gets up to 30°C the ability of the surface to radiate to space is reduced to a very low value.

“Deep convection” which drives the tropical circulation is mostly initiated in these very hot surface conditions.

The effect of changing CO2 on atmospheric radiation to the surface (DLR) is small. With high boundary layer relative humidity, water vapor masks out most of the effect of changing CO2 in hotter surface conditions.

But the effect of increasing CO2 on the TOA radiation balance is completely different. High surface humidities have little or no effect on this TOA balance. And there, doubling CO2 has a significant impact (all other things being equal) as shown in figure 12 of Part Seven – CO2 increases.

Working out radiation balance through the atmosphere in your head is difficult. Most people attempting it don’t have the right “calibration points”.

The fundamental physics is straightforward, at least in terms of the values of absorption and emission of radiation (not the “why”). But calculating the result requires computing effort and an integration (summation) across:

• multiple layers at different temperatures and concentrations
• the hundreds of thousands of absorption/emission lines of multiple GHGs
• a large range of wavenumbers

Related Articles

Part One - some background and basics

Part Two - some early results from a model with absorption and emission from basic physics and the HITRAN database

Part Three – Average Height of Emission - the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions

Part Four – Water Vapor - results of surface (downward) radiation and upward radiation at TOA as water vapor is changed

Part Five – The Code - code can be downloaded, includes some notes on each release

Part Six – Technical on Line Shapes - absorption lines get thineer as we move up through the atmosphere..

Part Seven – CO2 increases - changes to TOA in flux and spectrum as CO2 concentration is increased

Part Eight – CO2 Under Pressure - how the line width reduces (as we go up through the atmosphere) and what impact that has on CO2 increases

Part Nine – Reaching Equilibrium - when we start from some arbitrary point, how the climate model brings us back to equilibrium (for that case), and how the energy moves through the system

Part Eleven – Stratospheric Cooling - why the stratosphere is expected to cool as CO2 increases

Part Twelve – Heating Rates - heating rate (‘C/day) for various levels in the atmosphere – especially useful for comparisons with other models.

References

The data used to create these graphs comes from the HITRAN database.

The HITRAN 2008 molecular spectroscopic database, by L.S. Rothman et al, Journal of Quantitative Spectroscopy & Radiative Transfer (2009)

The HITRAN 2004 molecular spectroscopic database, by L.S. Rothman et al., Journal of Quantitative Spectroscopy & Radiative Transfer (2005)

Notes

Note 1: This model looks at the range of wavenumbers 200-2,500 cm^-1, which equates to 4-50μm, to ease up the calculation effort required. This means that when we sum up the contribution from all calculated wavelengths we are missing some bits. So for example, if we calculate the emission of thermal radiation by a surface at 288K with an emissivity of 1.0 we calculate 390 W/m² – the “blackbody flux”.

But with our “restricted view” of the spectrum we will instead calculate 376 W/m².

Almost all of the “missing spectrum” is in the far infra-red (longer wavelengths/lower wavenumbers), and is subject to relatively high absorption from water vapor.