Computing the Greenhouse Effect and Delta T

COMPUTATION OF EARTH SURFACE TEMPERATURE CHANGE
USING MODTRAN ANALYSIS

ModTran is a computer program available free online at  http://forecast.uchicago.edu/modtran.html . It has been used for many years by climatologists and aerospace scientists/engineers, and has been verified quite well. It is used here to compute the earth’s infrared radiation (heat loss) to space, computed at 70 km altitude looking down, near the upper limit of the atmosphere.   The use of Modtran is described here.

Atmospheric conditions used for ModTran is the 1976 U.S. Standard Atmosphere, and a choice of cloud conditions. See sample ModTran baseline input at the bottom of this page.

Summary

Two methods, A & B, are given to compute the temperature change due to change in atmospheric CO2.  Method A is simple but less accurate, Method B is more accurate.  For example for doubling CO2 (400 ppm) without water vapor feedback, Method A gives δT of 0.75C, where as Method B gives 0.83C.

Method A is simple

  • ΔT = -0.30 * ΔH, where ΔH is the change in infrared radiated to space (H) by changing CO2, as determined by Modtran.  Units: T in centigrade, H in watts/m2.
  • Green House Effect is 139 w/m2  or 36.7% or 31C.   The development of Method A is presented here.

Method B is computed within Modtran using the Temperature Offset feature, where H is determined before and after change in CO2, and the temperature offset required to make one equal the other is determined by trial and error.  The procedure for using Method B is here.

NOTE: This method does not allow for variation in sunlight reflected from the earth’s surface; i.e. albedo.   The total temperature change is the sum of the δT’s for each independent variable:

δT = ∑ (òT/òxi)*δxi + òT/òA)*δA,

where xi are components of the atmosphere, whose effect on surface temperature can be computed via ModTran.  A is albedo.  The value of òT/òA*δA must be calculated separately and added to the effect of changing concentrations of atmospheric components (primarily CO2).  The Albedo Effect is analyzed here.

 

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