Can you become a climatologist with a math degree and physics master's?

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So, I was wondering what is the best possible way to become a climatologist. Having to deal with all that data concerning climate seems like a fun idea to me.

Is becoming a specialist in climate science an option after getting bachelor's degree in mathematics? If yes, what should one be doing next? Would master's degree in physics be suficcient?
 
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I know of a climatologist who was at first pursuing studies in pure mathematics. Climatology seems to be an interdisciplinary field but I suspect they use mathematics the most. Heard of chaos theory and butterfly effect? Mathematical concepts that had origins in climatology.
 
You didn't state your current situation, but applied math and computer science are obviously important, and also have very wide application. You might take some introductory courses in climatology or related sciences (meteorology, atmospheric science) to see if you like this area and to gauge career opportunities.
 
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And a lot of thermodynamics and quite a bit of chemistry too.