First let me say that “know” is not quite right. No scientific fact is actually known. It is just a belief based, however, on strong evidence.
First it is “known” that CO2 is a greenhouse gas. This means that it is transparent to visible wavelenghts of light, but opaque in the infrared (or a large part of the infrared regions at any rate). It is no accident that the visible wavelengths of light are those to which the major constituents of the atmosphere are transparent. (They are N2, 78%; O2, 21%; CO2, 1%–the rest are in trace amounts.)
The result is that incoming radation comes right through the atmosphere. Actually, that’s not entirely true since there is plenty of infrared and ultraviolet in the incoming radiation, but we don’t see them. But the heat of the earth is reradiated, especially at night, mostly in the infrared band. The night earth is pretty much black in the visible light band and certainly in the UV. More CO2, then less reradiation is expected. I believe that it is mainly the CO2 in the upper atmosphere that is responsible.
Anyway, the result is that one would predict that more radiation = less reradiation = higher temperatures. Ok, that is a prediction and not every prediction comes true. Maybe the theory was wrong, maybe there are confounding factors (for example if more CO2 meant less cloud that would be a confounding factor). So now you look to see, has the temperature actually risen? It would seem that it has. Is the weather different? It would seem to be. But weather is so variable that it takes a long time to establish that it really is different. For example, in Montreal last winter had much less snow than historical records show is normal, but this winter we are well above average for accumulation till Dec. 23 (but it is raining right now and a lot will disappear tonight). So there is always wiggle room for claims that the greenhouse effect has been exaggerated.
Then there are some disturbing facts. Like that the northwest passage seems to be opening during the summer. This has not happened, certainly since 1492. And the arctic ice is at historic lows. The Greeland ice cap and the West Antartic ice are melting at unprecedented speeds. Forty years ago, a friend who skis in Switzerland told me that the Rhone glacier had come down to 2000 meters altitude 100 years earlier and was now only at 3000.
On the other side, I was on a cruise to Glacier Bay a year and a half ago and we went right in and saw the remaining glaciers. In 1800, the entire bay was ice locked. But they told us that the native tribes claimed that they had had settlements there in earlier centuries. They weren’t believed until they actually could study the interior when they discovered remains of settlements from several centuries earlier. So the bay had frozen and then unfrozen. Which illustrates how hard it is to draw firm conclusions.
When all is said and done it seems to me that the weight of evidence is that there is global warming and it is man made. Incidentally, if there is global warming and it is not man made, it still behooves us to act to avert it, since it is to our long-term interest to do so. The idea that if we didn’t cause it, then we don’t have to act would imply, for example, that we should not bother to build especially carefully in earthquake zones since no one claims that human activities cause earthquakes.