In Part Two we covered quite a bit of ground. At the end we looked at the first calculation of heating rates. The values calculated were a little different in magnitude from results in a textbook, but the model was still in a rudimentary phase.
After numerous improvements – outlined in Part Five – The Code, I got around to adding some “standard atmospheres” so we can see some comparisons and at least see where this model departs from other more accurate models.
First, what are heating rates? Within the context of this model we are currently thinking about the longwave radiative heating rates, which really means this:
If the only part of climate physics that was actually working was “longwave radiation” (terrestrial radiation) then how fast would different parts of the atmosphere heat up or cool down?
As we will see this mechanism (terrestrial radiation) mostly results in a net cooling for each part of the atmosphere.
The atmosphere also absorbs solar radiation – not shown in these graphs – which acts in the opposite direction and provides a heating.
Lastly, the sun warms the surface and convection transfers heat much more efficiently from the surface to the lower atmosphere – and this makes up the balance.
So, with longwave heating (cooling) curves, we are consider one mechanism of how heat is transferred.
Second, what is “longwave radiation”? This is a conventional description of the radiation emitted by the climate system, specifically the fact that its wavelength is almost all above 4 μm. The other significant radiation component in the climate system is “shortwave radiation”, which by convention means radiation below 4 μm. See The Sun and Max Planck Agree – Part Two for more.
Third, what is a “standard atmosphere”? It’s just a kind of average, useful for inter-comparisons, and for evaluation of various climate mechanisms around ideal cases. In this case, I used the AFGL (air force geophysics lab) models which are also used in the LBLTRM (line by line radiative transfer model).
Here is a graph for tropical conditions of heating rate vs height – and with a breakdown between the rates caused by water vapor, CO2 and O3:
Notice that the heating rate is mostly negative, so the atmosphere is cooling via radiation – which means for this atmospheric profile water vapor, CO2 and ozone have a net effect of emitting more terrestrial radiation out than they absorb via these gases.
Here is a textbook comparison:
And a set of graphs detailing the tropical condition for temperature, pressure, density and GHG concentrations:
Figure 3 – Click to enlarge
Now some comparisons of the overall heating rates for 3 different profiles:
Here is a textbook comparison:
So we can see that the MATLAB model created here from first principles and using the HITRAN database of absorption and emission lines is quite close to other calculated standards.
In fact, the differences are small except in the mid-stratosphere and we may find that this is due to slight differences in the model atmosphere used, or as a result of not using the Voigt profile (this is an important but technical area of atmospheric radiation – line shapes and how they change with pressure and temperature in the atmosphere – see for example Part Eight – CO2 Under Pressure).
Pekka Pirilä has been running this MATLAB model as well, has helped with numerous improvements and has just implemented the Voigt profile so we will shortly find out if the line shape is a contributor to any differences.
For reference, here are the profiles of the other two conditions shown in figure 4: Midlatitude summer & Subarctic summer:
Figure 6 – Click to enlarge
Figure 7 – Click to enlarge
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 Ten – “Back Radiation” – calculations and expectations for surface radiation as CO2 is increased
Part Eleven – Stratospheric Cooling – why the stratosphere is expected to cool as CO2 increases
Part Thirteen – Surface Emissivity – what happens when the earth’s surface is not a black body – useful to understand seeing as it isn’t..
AFGL atmospheric constituent profiles (0.120 km), by GP Anderson et al (1986)
A First Course in Atmospheric Radiation, Grant Petty, Sundog Publishing (2006)
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)