What area of the country are you in?

Water conservation and environmental protection are probably your best available avenues into a climate science career of any sort. I've worked in environmental since 2012 when I got my master's. I specialize in hydrogeology, but there are lots of fields. The problem you will run into is they are gated by credential barriers at a certain point - specifically PE/PG requirements. If you have the math portion you are probably well capable of passing the PE exam, you just need the experience and recs, so you may want to tailor your class load to put you on that path. Engineer's also generally have higher pay brackets so there's that little carrot as well.

Most environmental based companies, regardless of their area of focus, have modelers and need engineers of various backgrounds. You typically don't get hired into modeling, but can sort of steer yourself that way once you're established. I'd recommend you avoid environmental consulting - it does not sound like the work environment you're looking for, and most clients end up being polluters. Water Purveyors could be a really interesting target to aim yourself at. They do SO MUCH more than water supply, and they are constantly looking into all kinds of interesting projects. When your job is to supply an ever increasing population with an ever dwindling supply of a crucial resource, creativity is very much necessitated.