The problem with such an arbitrary climate system is that it is, well, arbitrary. Random flipping almost simultaneously taking effect? I mean, sure, have some variation in tiles outputs and a general trend towards tundra in one period, or desert in another, but having simultaneous change of climate at random would just be too arbitrary and annoying.
Also, where would pollution fit into your model? Would these changes be sparked by the amount of pollution (health levels) of the world, or your civ in particular?
As far as being arbitary, I would perhaps envisage these changes occuring close to different biomes. These are in the game already, snow, tundra, grassland, desert, rainforest, desert, grassland, tundra, snow. These ecotones are where climate change would be felt the strongest.
And the flipping could be over a prolonged period of time, say 30 turns, so it wouldnt happen all at once, but over a long time you would see the potential of a city change, and you would also then be aware that at some point it may turn back. When these changes did occur would be kind of arbitrary though yes, but I would simply limit them to a handful of times at most in the game, perhaps randomly assigned to between 2 and 8 a game.
Pollution is another interesting one... and I guess if you do have some even vague representation of climatic change then why not go for anthropogenic change as well?
You could go a number of ways... a climate change route or a pollution route.
Perhaps if a city gets too polluted, beyond a certain point, then the tiles around it start to degrade, produce 1 less food for instance. If pollution then got back under control then the tile would revert to normal.
For climate change, perhaps if the total pollution of the map got beyond a certain point then change would happen. It could simply be the same as now, random squares changing to deserts, or it could be something more complex, random tiles losing some capacity, or changing to another terrain type. With climate change though, this would be irreversible (on civ timescales it certainly is), once it got kicked in you would be stuck with it for the rest of the game. It may get worse/stronger/more frequent as pollution then got higher, and so once it started all you could do would be to try to cut down on pollution levels so it didnt get worse.
There could even be a UN option to do something about this, like adopting Environmentalism I guess, but different, like Kyoto or Copenhagen (wishful thinking there mind you), maybe banning building of any more polluting buildings until you've first reduced the pollution in that city or something. Not sure if that specifically would work very well. And maybe this UN idea is a bit too complicated anyway.
You could also combine the climate and pollution models as well now i think of it.
Also, an unrelated point. It annoys me that if you build a coal plant, then a damn or nuclear plant, you still get the unhealthiness from the coal. I would prefer it if when you built one powerplant it overwrote another, so people would build coal plants initially, but if some cities had a major pollution/unhealthiness you may then choose to build a cleaner power plant. This would fit in rather well with climate/pollution as well.