I have noticed a correlation between the sun coming up and the night ending. I wonder if the sun coming up causes the end in night. [/snark]
I claim that a good correlation PLUS a convincing mechanism is enough to constitute 'proof' with the level of 'proof' increasing as the mechanism becomes more convincing.
There is a strong correlation between higher CO2 in the air and higher temps.
This is true for the time we have directly measured temps.
This is also true in the air bubbles trapped in icecap ice going back 800K years.
We are very sure that we know why the ice age has had 90K years of a lot of ice and 10K years of much less ice in cycles of about 100K years for all of the last 800K years. The reason is the way the Earth's orbit around the sun works to change the angle of the sunlight hitting the surface at different times during the year.
If this theory is correct, then we should be seeing the Earth cooling. We don't, why? Some say it is because for the last 8K to 10K humans have been adding CO2 and methane to the air. That is, instead of humans having zero ability to change the climate, humans have been changing the climate ever since it began farming and herding. That farming and herding was adding just the right amount of CO2 and methane to keep the temps very steady. Scientists can even explain the slight increases and decreases in the temps, like the "little ice age".
The 1st scientist to see that CO2 is a greenhouse gas did so in the mid 1800's. I have seen claims that one later scientist 'proved' that this is not so.
. . I claim that this theory is very easy to do an experiment on in a lab. I therefore conclude, that modern scientists have repeated the experiment and have found that CO2 does act as a greenhouse gas. I have never seen any climate science denier claim that an experiment has been done recently that proved that CO2 doesn't act as a greenhouse gas. I claim that because the experiment is easy and cheap to do, that *IF* some modern 'scientist' had done the experiment and show that CO2 is not a greenhouse gas, that you and I would have heard about this 'proof' that ACC, aka AGW, is not true. The deniers would be using this very strong evidence in every post or article they write.
Therefore, we do have a convincing mechanism to explain the correlation between high CO2 levels in the air and rising temps.
Now, are the computer models of climate change as CO2 levels are increased as data, accurate?
All the claims that they are *not*, are deeply flawed. Anyone can prove anything by distorting the data or lying about what others have said. This is how the deniers are able to show 'evidence' that the models are not accurate.
Recently a group of scientists did a study of the climate models that have been used sines the 1970s or 80s to see if they can accurately predict the relation between CO2 and temps. They found that yes, all the models used do accurately show that as CO2 increases so do temps at the right level of increase.
Before you reply you need to understand one key fact. It is that making predictions is always about the future. That therefore, if the author gets the increase in CO2 level in the future wrong, his prediction of the temps that are the result will also be wrong to/in a corresponding amount.
So, the new study fed the correct measured CO2 data into all the computer models, instead of the wrong data that the original authors used. When this is done, the accuracy of the resulting predicted temps improves a lot. That is, at each time interval the predicted temp is close to the actual measured temp.
In fact all the models had a predicted error bar and all the resulting new predictions with the now known CO2 levels fell within those error bars. I have even seen that you can run the models backwards by reversing the flow of time in the computer, and they still stay close to the new curve of decreasing temps. that results when CO2 levels fall.
Therefore, the correlation has been paired with a convincing mechanism to prove that the computer models are accurately predicting what will happen in the future at all levels of increasing CO2. That is, in the future (if no tipping point that are not in the models are tipped) as CO2's measured level changes the new temps the models predict will be close the the measured temp levels.