I would argue that there was at least one famine that was incontrovertibly out of human control: the Year Without a Summer. Essentially, in 1816 a volcanic eruption threw enough ash into the sky to cause agricultural catastrophe and a relatively large temperature dip across most of Europe.

There is certainly evidence of several massive climate change events that would have caused extensive drought in the past, with one of these perhaps contributing significantly to the "Bronze Age Collapse".

Some of these events are called "Bond Events", and their origins are not always understood. However, many paleoclimatological studies incorporating coring samples, paleobotanical studies, isotope analysis, and other scientific methods have been able to reconstruct temperature and relative precipitation fluctuations over time.

For further reading, I really heartily recommend

Rosen, Arlene M. Civilizing Climate: Social Responses to Climate Change in the Ancient Near East. Lanham: Altamira Press, 2007

This is one of the best recent overviews of paleoclimatological studies in recent years.