Infrared radiation emitted by the earth needs to balance the incoming solar energy to keep the climate in equilibrium.  Radiation is emitted by the surface.  However, before it reaches space, it is absorbed within the atmosphere by carbon dioxide and water vapor.  The amounts of energy absorbed depends on the concentration of CO2 and water vapor, often called greenhouse gases.  The absorption results in a temperature increase with IR energy emitted in both upward and downward directions or converted into other forms of energy.  The radiation calculations are well defined and many models have been developed for the calculations.  Here we will use an early model developed by the author that were used in early meteorological mesoscale models (Atwater, 1971).  More recent models may use line by line calculations.

The ground is the input source of IR to the atmosphere.   There is very little that is written on the vertical absorption regarding the surface flux which is dependent on the path length of the absorber.  The emission of IR and conversion to other energy forms at the various levels will not be examined here.

The results for the surface transmission (1-absorption) are shown in the following graph for total CO2 and water vapor transmittance (CO2=280ppm) and for carbon dioxide transmittance at 280ppm and 560ppm for the lowest 300 m..  It is assumed that the carbon dioxide absorbs 18.5% if the total spectrum.

 

The results show that about half of the surface IR radiation is absorbed within 150m (about 20 mb) of the ground, both for the total spectrum and the CO2 portion of the spectrum.  With the increase CO2 concentration, half of the energy in the CO2 spectrum is absorbed within 50m of the surface and 2/3 are absorbed by 300 m .  More than 99% of the CO2 spectrum is absorbed by 7000m.

The amount of radiation absorbed in each of the lowest layers is shown in the following table.

Layer Thickness  mb	Layer Thickness  m	Top of Layer m	Radiation Differential W/m2
1	8	8	3.2
2	18	26	.5
3	26	52	.2
4	34	87	.07
4	35	121	.04
4	35	156	.01
5	44	200	-.01

Most of the increase in absorbed radiation is in the first 8 meters of the ground with much of the remaining radiation in the next layer.  About 90% of the increased absorption due to a doubling of the carbon dioxide occurs within 26 m (about 3 mb) of the ground.  Above about 175 meters, the absorption of the ground flux is reduced due to reduction of infrared flux reaching the levels.

In most climate models the lowest layer is often 10mb thick with the increased absorption assumed to occur in a much deeper layer.  In an earlier paper, Raisanen (1996) did a study of the vertical resolution needed to minimized errors in climate models for radiation calculations and found a number of systematic errors near the surface when the layers were thickened.  He attributed this to sharp differences in temperature in the region rather than the rapid absorption near the surface of both water vapor and carbon dioxide.  Models with layers too thick may not properly account for conversion of radiant energy to convective energy.  The impact on climate models should be further investigated.

Atwater, M.A., 197l:  The Radiation Budget for Polluted Layers of the Urban Environment.  J. Appl. Meteor., 10, 205-14.

Raisanen, P, 1996: The effect of vertical, resolution on clear sky radiation calculations: tests with two schemes.  Tellus, 48A,403-423.

 

 

 

 

 

Carbon dioxide saturation is the fact that most of the infrared radiation emitted at the surface that will be absorbed by the atmosphere is done in the lowest atmospheric layers. Computations show that one third of the absorption occurs within 25 feet of the surface, 80 % occurs within 800 feet and 99% within the first mile of the surface. Any radiation that is emitted in the wavelength of absorption by CO2 has to be reradiated at higher levels. Thus the amount emitted depends on the carbon dioxide in the upper atmosphere and its temperature.

With increased CO2, the radiation at the surface will be absorbed closer to the surface. With the atmospheric reradiation, there will be a small increase during the day and a slight decrease, due to temperature inversion conditions, at night. This is the opposite of what is observed in the past 50 years with nighttime temperatures rising more than the day time temperature.

One question that is widely known is that the climate models are predicting temperatures higher than observed. I have not seen any mathematical analyses that are concerned with the large amount of radiation observed by the carbon dioxide within 1000 feet of the surface. Most of the vertical layers in the atmospheric models have 30 to 50 layers for the atmosphere with the lowest layer being 400 to 1000 feet in thickness.