Chris Budd is one mathematician who has made a career in numerical weather prediction. He describes some of the challenges in The Mathematics of Climate Change. He explains the need for ‘simple’ mathematical models of climate, which can explain what comes out of the massive computer simulation of the Navier-Stokes equations that the IPCC uses to make its predictions. There is room for mathematical and physical ingenuity there. Some examples:
One challenge for experts in dynamical systems is to investigate tipping points, rapid and irreversible changes when parameters are changed only slightly.
Extreme event attribution is a particularly urgent area of research where experts in statistical inference and inverse problems can make influential contributions: How to combine data and models to link cause and effect.
More generally mathematicians can make a difference in educating the public on the meaning of statistical predictions. What do error bars in climate change models mean? Some in the general public dismiss the IPCC predictions because they are "uncertain". For more on this see Climatology needs Mathematics.
A similar question can be asked about physics. One of our former students in theoretical physics, an expert in the analysis of the massive data produced by particle accelerators, switched his career to climatology and became co-founder of the World Weather Attribution initiative. I find his life story inspirational.
