The things that I trust add up to evidence beyond a reasonable doubt include:
1] changes in planting zones over decades;
2] earlier spring arrival, about 2 weeks earlier over the past 100 years;
3] later fall arrival;
4] peak flow changes in various river basins, like the Columbia;
5] migrations of insects into new ranges;
6] the changing migratory patterns of birds, including extending ranges into formerly too cool areas, and overwintering in northerly areas without migrating [see Canada geese];
7] the changes in boreal forests and the greening of the tundra;
8] the change in the ratio of record high-temp days to record low-temp days, as it is on the order of 10:1 hot:cold;
9] the increasing acidity of the oceans at the same time their temps are going up and the levels of CO2 in the air are going up;
10] that quantum mechanics works so well;
11] the isotopic signature of the CO2 in the air;
12] the measured increase in storm intensity over the past 3 decades;
13] the patterns of temperature change correlated with aerosols and greenhouse forcings for the globe, based on world-wide acceptable temperature data dating back to 1880 and earlier.
There's a baker's dozen of reasons that taken together add up to pretty convincing proof of AGW. All of these things I can understand, or understand well enough; basic quantum mechanics I managed the math for back in school, but I could not do it now. I'd probably need 2-3 years to relearn the math adequately to play with the Schrodinger Equation again, and I admit it wasn't all that much fun the first time, but I did it - passed the math, physics, and physical chemistry courses well enough to get a bachelor's in chemistry. For everything I've listed, I understand it well enough to be satisfied the information is good and shows human-caused global warming.
Most of what I've listed is pretty obvious stuff, and doesn't depend on computer models or even the temperature record - when everything that flies, walks, buzzes or greens does its best to head toward cooler climes, you don't need a really sophisticated computer model to tell you what's going on. It seems to me that basic observations and logic greatly favor the AGW theory [not even hypothesis, but theory at this point.]
If you wish, I could add more. I certainly have more evidence of various kinds. But I like this evidence because it's rather simple and easy to understand. It's actually the sort of evidence that you can use common sense on. You don't need to be a climate scientist to understand most of these things, much less a rocket scientist. Any reasonably intelligent person with decent general knowledge can certainly discuss at least most of the items and come away with a good understanding of the basic positions, if not complete agreement with the AGW positions.
And now it's getting late, so I'll post this and follow up later.
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Just told "too many sources", so I'll add the rest here:
7] http://adsabs.harvard.edu/abs/2010AGUFM.B23C0401W
8] http://www.mherrera.org/temp.htm
9] http://www.economist.com/node/16479264
9] http://www.sciencedaily.com/releases/2007/10/071017102133.htm
10] http://www.mtnmath.com/faq/meas-qm-1.html
11] http://ossfoundation.us/projects/environment/global-warming/human-caused
12] http://www.nature.com/nature/journal/v436/n7051/full/nature03906.html
13] http://www.cru.uea.ac.uk/cru/info/warming/
I could add more, but just looking up the references in what is already there should be adequate.