Have we historical evidence?
Maybe. Many historians believe that the Mexican drought of 1906-10 played an important role in setting off the Mexican Revolution. Melissa Dell set out to test that hypothesis, combining one dataset of pre-1910 precipitation and another one of Revolutionary violence. She found that drought-affected counties were more likely to experience violent mobilization during the revolution.
I think she is right ... but I am not sure that her data is good enough to show it. The data on revolutionary mobilization were not the best. They came from the Encyclopedia of Mexican Counties, taking on a value of zero or one depending on whether the authors of the Encyclopedia noted spontaneous violent mobilizations. The data are summarized in this map:
The counties singled out on the map are few of the ones where the coding is unclear. Tlahualilo, for example, produced few local leaders or organized revolt, but there were not a few complaints of banditry in 1911 and when Pancho Villa did roll in, the locals supported him. In Camargo, the Loyal Camargo Brigades formed an important part of the Villista army. (Inasmuch as they were no violent mobilizations in Camargo, it appears to be because the Revolution took over the state quickly enough to let Villa use it as a place for serious R&R as early as 1913.) If you go through all the possible switchers (and note that there might be something special about Yucatán) the results are weaker. Contagion models could weaken it further.
This does not mean that the argument is wrong! Just that more data is necessary.
Which brings us back to Syria. The report from the Center for American Progress (see page 25) is damnably vague. But data on precipitation, internal displacement, and the pace of revolutionary mobilization in the country should exist. (Doug? Carlos?) If they do, then it should be possible to see if climactic stress is linked to unrest or violence, at least in the modern Levant.