As you can see, only in the driest desert on earth will increasing CO2 increase the back radiation. Water vapor is by far the strongest greenhouse gas, but it is nearly saturated at 10% humidity. At 10% humidity and above, no amount of CO2 does anything. Most of the humidity on earth is in that area on the right where doubling CO2 will do nothing to increase the long-wave radiation from the sky. Yet another CAGW fail.
Fallacy: misrepresentation