The most informative measurements have come from bubbles of air trapped in Antarctic ice dating back to preindustrial times. These show that for at least the past 160 000 years, CO2 levels in the atmosphere have almost exactly matched the record of temperatures, as revealed in ice cores, tree rings and elsewhere.
If it's all so precise, why is there so much confusion and uncertainty about global warming?
Surely if we know how much CO2 is entering the atmosphere and how much energy each molecule can trap, we ought to be able to calculate the overall warming effect?
It's not that simple. For example there is no easy formula for predicting what future increases in CO2 levels will do to the average global temperature. While we can calculate that a doubling of CO2 in the atmosphere will produce a "forcing" of roughly 1 °C warming, the planet is more complex than that.
In particular, it will respond in ways that will probably magnify, but could conceivably damp down, the warming. These "feedbacks" involve essential planetary processes, such as the formation of ice, clouds, the circulation of the oceans and biological activity.