Giving 110 Per Cent: The Diminishing Returns of Increased Greenhouse Gas Emissions
CO2 is more evenly distributed than water, so if CO2 caused warming it would have a proportionately greater effect in areas where there is little water vapor (such as deserts and in very cold regions), while in areas with a lot of water, the effect of CO2 may be insignificant compared to the effect of water vapor. This is one of many factors that mitigate against the idea of a "climate catastrophe."
Fig.2. Absorption of ultraviolet, visible, and infrared radiation by various gases in the atmosphere. Most of the ultraviolet light (below 0.3 microns) is absorbed by ozone (O3) and oxygen (O2). Carbon dioxide has three large absorption bands in the infrared region at about 2.7, 4.3, and 15 microns. Water has several absorption bands in the infrared, and even has some absorption well into the microwave region. There is already sufficient CO2 in the atmosphere to absorb almost all of the radiation from the sun or from the surface of the earth in the principal CO2 absorption bands. (Data from ref. [1], page 93).
The net effect of all these processes is that doubling carbon dioxide would not double the amount of global warming. In fact, the effect of carbon dioxide is roughly logarithmic. Each time carbon dioxide (or some other greenhouse gas) is doubled, the increase in temperature is less than the previous increase. The reason for this is that, eventually, all the longwave radiation that can be absorbed has already been absorbed. It would be analogous to closing more and more shades over the windows of your house on a sunny day -- it soon reaches the point where doubling the number of shades can't make it any darker.