The newer estimates of radiative forcing due to a doubling of CO2 are between 3.5 and 4.1 Wm-2 with the relevant species and various overlaps between greenhouse gases included.
As regards the forcing issue, again the number used it is merely to force inadequate models to approximate temperature of the troposphere by changing a coefficient, and is not based or derived from fundamental physics and science of CO2 thermal activity.
Adjusting a polynomial coeffecient to make its curve match a dataset range does not in any way imply a physical basis in interpolating a dataset's values. Likewise adjusting a coefficient to make a GCM fit a dataset does not imply the coefficient has a physical reality unless the entire model is truly an accurate representation of the real world. The GCMs "assessed" by IPCC do not have that fundamental characteristic. They have gross inadequecies, which is why the coefficient are changed. If IPCC GCM CO2 forcing coefficients were based in science & physics the coefficient would not be changing. There would be no "newer estimates".
The atmospheric CO2 concentration is known, the number applied for forcing should be a fixed value if it were derived from basic science, as opposed to making a model fit.
Please comment on:
6.5.3. deltaF-deltaC relationships
and
IPCC Observations of Greenhouse Gas and Radiative Forcing Changes since 1750
In the latter, particularly note the summary entitled "Radiative Forcing".