Climates, seasons and cities of terraformed Mars

In a Earth-like planet, for a given distribution of land and sea, climate zones should be univocally determined. That is my hypothesis, it's pure physics! We find in the literature many fantasy worlds with deserts, rainforests, ice caps, volcanoes... however, are they in the right place?

I'm creating procedural worlds and, as a physicist, it's not just about 'looking real' but 'looking scientifically real'. I want to keep it simple and fast, so I came with a procedure to define climate areas based on simple grounds:

Average temperature depends on latitude and elevation.

Winds as the combination of prevailing ones and those due to pressure gradients.

Annual temperature range depends on latitude and distance downwind of the ocean.

The model still lacks ocean currents (definitely important, Europe is warm because ocean currents) and river neither (work in progress) but it looks enough for a nice estimation of climates. When I test it on Earth (taking elevation data from NASA for instance) I got something not too far from reality, with some deviations: