Vandelay is an expert in this field i recall, ill email him.
I´m pretty good at Carthaginian religion, but Nort African post-Roman climate change...
Anyway, my two cents:
As in many cases there are probably a lot of factors involved (rather than Blame the Vandals or Blame the Mongols):
Warefare, certainly. In most time-periods endemic. Systematic destruction of the enemys economical foundation is traditional...
Political disintegration - irrigation systems demand a lot of maintenance (e.g. to counter rising salt-levels in the water) and is in archaeological interpretation closely linked to the development of the state and its requisite beurocracy.
Deforestation and overgrazing - adversely affects humidity on the micro-level and lack of trees or shrubs causes soil to literally blow away.
Agricultaral technique and system - single-crop dependent systems (e.g. cereal growing Roman Africa or cotton growing Soviet Central Asia) are fragile not only ecologically but economically compared to multi-crop systems.
AFAIK macro-climate has not changed much in the last 2500 years and I think the human factor in desertification is much more decisive than climatological factors.
/Vandelay