[cjbillington]

No doubt they are using floats (well, doubles) - these models are usually coupled partial differential equations, propagated forward through time over the earth's surface using finite-difference or finite-element methods.

It's unlikely IMHO that floating point rounding oddities would cause catastrophically erroneous results. In my experience from other physics simulations, you usually validate some known behaviour you're not trying to predict, e.g. that energy is conserved, or that total mass of fluid is conserved. Bad numerics will usually violate these conservation laws, so you can use the fact that they are conserved as some evidence that your numerics are actually solving the differential equation relatively correctly.

Basically, people would notice broken numerics in this case.

There are situations where it is harder to validate numerics (e.g. if your numerics inherently conserve some quantity by construction, then you can't use it to validate the behaviour of the numerics), and to be sure, a concerning fraction of all publications with numerical results contain mistakes.

But I don't think floating point rounding is near the top of the list of issues to go looking for in these models.