A simplified toy-model to simulate radiative transfer in the atmosphere and compute the radiative forcing as a function of CO2 amount.
Using only one simplified absorption band for CO2 (around 15 microns), the model output a radiative forcing of 4.8W/m2 for CO2 going from pre-industrial 280ppm to 560ppm (doubling). The currently best estimate by scientists (with a better code and richer input data) is about 3.7 W/m2.