|San José State University|
& Tornado Alley
the Greenhouse Effect in the Atmosphere
The difference in temperature for a cloudless winter night compared with one with cloud cover can be as much as 20°F. The problem investigated here is what can account for this extreme temperature difference. The argument being presented is that the effect of greenhouse gases alone cannot account for that temperature difference. The greenhouse effect is where molecules in the atmosphere absorb infrared radiation and radiate it in all directions. This means that that about one half is radiated downward toward Earth's surface. The term cloud blanket effect is used to denote phenomenon in which the underside of a cloud reflects back down the infrared radiation that the Earth's surface is radiating upward.
The greenhouse effect from a thin layer of the atmosphere can result in at most 50 percent of the thermal radiation absorbed from the surface being returned to the surface. The amount of radiation absorbed even from a thick layer of the atmosphere is quite small. The amount returning due to reflection from the underside of clouds can be higher. The albedo of cumulus clouds for the visible light range can be as high as 90 percent and that for the infrared range is of the same order of magnitude.
Reflection of electromagnetic radiation generally occurs at the interface between two types or two densities of a conducting media. This means that when a cloud is resting on the land surface as a fog there is no reflection of infrared radiation. Instead the effect of fog on surface temperature would be entirely through the greenhouse effect. This would mean that all other conditions being equal the surface temperature on a foggy night would be noticeably cooler than when there are clouds but no fog. The foggy night, however, would be warmer than a clear night.
Clouds are an overwhelming influence on the climate of the Earth. Despite this the focus of climate modelers on the greenhouse effect of carbon dioxide has resulted in a neglect of cloud phenomena. The climate models fail to adequately represent the matter of clouds and cloudiness. Consider the following graph
The usual focus of this display is that the climate modelers, one and all, do not know much about cloud coverage. But another salient element is the difference between actual cloud coverage in the Arctic compared with the Antarctic. At the North Pole it is 70 percent; at the South Pole it is about 3 percent. Since carbon dioxide is supposedly well mixed in the atmosphere the greenhouse effect of carbon dioxide should be the same at both poles. But consider the record for temperature by latitude.
Robert C. Balling, Jr. gives a graph relevant to comparing a model prediction with the actual record. It is given in his article, "Observational Surface Temperature Records versus Model Prediction," which is published in Shattered Consensus: The True State of Global Warming (page 53). A facsimile of Balling's graph is given below.
Here we have the real world in all its complexity. Over the period 1970 to 2001 the Arctic region did have a greater temperature increase than the tropical region. It was not a five to one ratio however. The north polar region increased in temperature about 83 percent more than the tropic region. However in the south polar region there was no larger increase than the tropics, If anything the south polar region increased less in temperature than the tropics with Antarctica actually decreasing in temperature. If the increase in temperature in the north polar region is taken as a verification of the theory and global warming model then the record in the south polar regions is a denial of the validity of the theory and model. This is the real world in all its complexity and the climate models definitely do not capture that complexity. In particular, the models, driven as they are simply by the level of carbon dioxide in the atmosphere, cannot account for the discrepancy in temperature change in the two polar regions. The cloud blanket effect does account for that difference.
At the first level of analysis the greenhouse effect can be estimated using Beer's Law. Beer's Law implies that the proportion P of radiation absorbed in passing through a medium is
where D is the optical depth of the medium and this is given by
where α is the absorption coefficient of the material of the medium, ρ is the molecular density and L is the physical depth of the medium. If there are two or more absorbing substances in the medium the optical depth for each is determined and their sum is the overall optical depth.
The absorption coefficient for a substance may vary with the wavelength of the radiation. There may be certain critical wavelengths at which the medium absorbs. For example, the absorption spectra for water vapor and for carbon dioxide are given in Radiative Efficiencies. What is needed is an average absorption coefficient over a range of wavelengths. It would be a weighted average based upon the distribution of radiation of different wavelengths. The radiation from a body depends upon its temperature. The total energy in that radiation is proportional to the fourth power of the absolute temperature. The wavelength distribution of that radiation looks something like the following.
In this graph the frequency scale runs from left to right whereas the wavelength scale runs from right to left.
There does not appear to be available simple absorption coefficients for water vapor and carbon dioxide averaged over the range of infrared radiation relevant for Earth's emissions. In lieu of and while continuing to pursue the technical information needed to carryout an estimation of the absorption of infrared radiation using Beer's Law some ballpark estimates will be made using the bits and pieces of relevant information that is available.
One datum that appears to be relevant is the estimate that 90 percent of the infrared radiation emitted by the Earth's surface does not go out into Space. This 90 percent would be made up of several components, which include:
Let α be the proportion absorbed by greenhouses gases in a clear sky. The amount reradiated downward would then be (1/2)(0.4)α. Suppose the proportion absorbed by greenhouses gases before the infrared radiation reaches the undersides of the clouds is one half of that for traversing the full atmosphere; i.e., ½α. This would then be 0.6(½α). The infrared radiation reaching the clouds would be 1-0.6(½α). If the reflectivity of the clouds to infrared radiation is 70 percent (as opposed to 90 percent for visible light) then infrared reflection accounts for 0.7[1-0.6(½α)]. The rest would be absorbed in the clouds and half radiated back down to the surface. The other half would heat the cloud and eventually that heat would find its way to the top surface of the cloud and half be radiated out into Space. In terms of that which does not going into Space it is [0.7+0.3(0.5+0.25)][1-0.6(½α)] . Thus
This would mean that the cloud blanket effect (reflection of infrared radiation from the undersides of clouds) accounts for about 63 percent of the return of energy to the Earth's surface and the greenhouse effect accounts for only about 37 percent. In an area without clouds there would be only 16 percent of the infrared radiation returned to the surface instead of the 86 percent returned to the surface under clouds. This 86 percent is made up of 59 percent from the cloud reflectivity, 8 percent from the effect of the greenhouse gases below the clouds and 19 percent from the greenhouse effect in the clouds. This is compatible with the experience of the cold clear winter night compared with a cloud-covered night.
A proportion absorbed of 0.322 means that 0.618 is transmitted. Thus the optical depth of the atmosphere due to the greenhouse gases is -ln(0.618)=0.48. At an altitude that included one half of the greenhouse gases the transmission would be exp(-0.48/2)=0.8055 and thus the absorption would be 0.1945.
Some insights may be gained by looking at equilibrium temperatures. However the nighttime temperatures are not equilibrium temperatures. At night the temperature is decreasing roughly according to a negative exponential curve.
Without greenhouse gases or clouds the equilibrium temperature of a planet's surface would be given by
where T is the equilibrium absolute temperature, R is the planet radius, ψ is the intensity of the solar radiation, ε is the surface emissivity, α is the planet surface albedo and σ is the Stefan-Boltzmann constant.
If the greenhouse gases in the atmosphere absorb a proportion β and radiate half of it back to the surface then the equilibrium temperature satisfies the condition:
Now clouds can be brought into the picture. Let α0 be the albedo of the surface, α1 the albedo of the top of the clouds to short wave radiation and let α2 be the albedo of the bottom of clouds to long wave radiation. Let β0 be the proportion of short wave radiation absorbed by atmospheric greenhouses gases below the clouds and β1 be proportion absorbed by those gases in the atmosphere above the lower level of the clouds. Let β2 be the proportion absorbed by the greenhouse substances in the clouds.
Then for a clear sky
For the case of the cloud cover
Ratio of the clear and cloudy equilibrium temperatures is then:
As seen above the common factors like the solar intensity and short wave surface albedo are eliminated.
The equation for the dynamics of temperature is
where C is the heat capacity of the body, T is its absolute temperature, S0 is the surface over which the body receives solar radiation, S1 is the surface area over which the body emits thermal radiation. The heat capacity is proportional to the body volume; say C=γV, where γ is the heat capacity per unit volume.
The net inflow of radiant energy ψ(t) is a cyclic function of time. Let ψmean and Tmean be the mean energy inflow and temperature, respectively. Then
This equation may be subtracted from the dynamic equation to give:
where ΔT and Δψ are (T-Tmean) and (ψ-ψmean), respectively.
The term (T4-T4mean) on the right can be approximated by 4T3meanΔT. Thus the equation for the dynamics of diurnal temperature is of the form
For material on the solution to this type of equation see Diurnal Temperature.
(To be continued.)
On November 22, 2008 John Bryant of the WMCTV Weather Team in Memphis, Tennessee noted that the temperature at the airport under cloud cover was about 42°F whereas at Dyersburg, a small city near Memphis, sky was clear and the temperature at midnight was almost twenty degrees colder.
Comparing night time temperatures is not a matter of comparing equilibria. After the sun goes down the temperature is in disequilibrium and it decreases approximately like a negative exponential function; i.e.,
Suppose the temperature under the clear sky at sunset was 45°F and at midnight seven hours later it was 22°F. In absolute temperature these were 505°R and 482°R, respectively. The value of the coefficient in a negative exponential function for these two temperatures is
According to the case data the value of γ for the cloud covered situation was 0.
Let β1 be the proportion of the thermal radiation absorbed in a clear sky. The value of γ1 for the clear sky case is
where K is a coefficient depending upon all of the other factors besides the greenhouse gas absorption.
Let β2 be the proportion of the thermal radiation absorbed by the atmosphere under the cloud layer and α2 the proportion of thermal radiation returned to Earth from the underside of the clouds or the greenhouse effect in the clouds. Then the γ2 for the cloud cover case is
Since for the case under examination γ2=0, this means α2 must equal 1.0. This can occur only with reflection of the thermal radiation. Since β2 can be at most 1.0 and thus the proportion of radiation returned to Earth can be at most 0.5 this means at the extreme 0.5 of the thermal radiation would be returned to Earth by the greenhouse effect of the atmosphere and 0.5 by the reflectivity of the clouds and their greenhouse effect. If β2 is 0.3 then 15 percent of the thermal radiation would be returned by the greenhouse effect of the atmosphere and 85 percent by the reflectivity and greenhouse effect of the clouds. The overwhelming proportion of the effect of the clouds has to come from their reflectivity of infrared radiation.
Most of the effect of clouds in moderating the night temperatures is from their reflectivity of infrared radiation.
(To be continued.)
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