Update: see further discussion here
NOAA has a webpage on radiative forcing here, which includes a list of equations relating GHG concentrations to radiative forcing, substantially identical to the expressions in TAR.
Below is a figure showing, on the left, the graphic at NOAA illustrating their calculation and, on the right, my emulation of this graphic from original GHG concentration data using the radiative forcing equations summarized at NOAA – so I’ve obviously got this calculation down pretty well. My text for generating this graphic is online here http://data.climateaudit.org/scripts/forcing/forcing.noaa_graphic.txt.
The calculation uses my collation of GISS GHG concentration data which I’ve posted up at http://data.climateaudit.org/data/hansen/giss_ghg.2007.dat . I’ve done my own collation because the GISS information is maintained (messily) in several different files:
1850-2000 from http://data.giss.nasa.gov/modelforce/ghgases/GHGs.1850-2000.txt
2001-2004 from http://data.giss.nasa.gov/modelforce/ghgases/GHGs.Obsv.2001-2004.txt
2005-2006 from individual files for each gas, estimating 2005-2006 for two trace gases where data not shown
The function to calculate forcing provides for implementing different sets of equations, not all of which are tested yet.
Whlie NOAA implementation was straightforward, this is not the case for Hansen et al 1988 and other articles. Sometimes the problems are units: Hansen et al 1988 Appendix B expressed forcing in terms of global temperature change and not in terms of wm-2. Unlike the original article, Gavin Schmidt’s Hansen et al 1988 scenario data is expressed in wm-2 (a unit not yielded by the equations of the original article.) IPCC 1990 discusses the conversion to wm-2 as follows (p 52):
“Values derived from Hansen et al have been multiplied by 3.35 (Lacis, pers comm) to convert forcing as a temperature change to forcing as a change in net flux at the tropopaus after allowing for stratospheric temperature change. These expressions should be considered as global mean forcings; they implicitly include the radiative effects of global mean cloud cover.
Using this conversion, the equations for CFC11 and CFC12 immediately translate. However, the translation for other equations is not as easy.
IPCC 1990 Table 2.2 says that, fr CO2, CH4 and N2O, they say that the “functional form [was derived] from Wigley 1987; coefficient derived from Hansen et al 1988″. I can confirm the functional form from Wigley 1987, but Hansen et al 1988 set out coefficients for different functional forms. I’ve been unable to locate any of the IPCC 1990 coefficients in original articles – I wonder where they came from.
The same problem occurs for the overlap equation for CH$ and N2O in IPCC 1990. Although the overlap term is attributed to Hansen et al 1988, the expression in IPCC Table 2.2 does not occur in either Hansen et al 1988 or Wigley 1987 – where did it come from?
I can get the IPCC 1990 overlap expression to yield sensible values, but I can’t get the Hansen et al 1988 expression to yield sensible values so far – if anybody else can, I’d appreciate the info. IPCC 1990 also mentions (also on p 52) a typographical error in Hansen et al 1988 (“0.014 should be 0.14″).
In summer 2007, Gavin Schmidt reported the GHG concentrations for the three Hansen 1988 scenarios at and the total radiative forcing (wm-2) for the three Hansen scenarios here .
I’m hoping that I will be able to replicate the Hansen radiative forcing total (at RC here http://www.realclimate.org/data/H88_scenarios_eff.dat) from the GHG concentration data (http://www.realclimate.org/data/H88_scenarios.dat) using contemporary equations and then compare this to the observed radiative forcing. In passing, I note that the structural links between Hansen et al 1988 and IPCC 1990 are quite close and provide some mutual clarification.