Hypotheses represent their subject matter by being true or false of that subject matter. Like most sorts of representation, this does not involve resemblance. But models are different: they do represent their subject matter by resembling it in some relevant way. For example, a model airplane might resemble a real airplane by having similar shape and colors, even though their sizes are different. Or it might mimic the real airplane’s flying behavior.
To keep things simple, I’ll talk about respective “behaviors” (of model and subject matter) over time, but bear it in mind that this mimicry can be along any dimension: for example, a Fourier series might model a function along the x-axis rather than over time. Here’s the important point: I think the behavior of both model and whatever it represents must be “lawlike” in the roughly the same way. (I include statistical laws here, by the way.) In respect of the relevant resemblance between them, it’s essential that “nature continues uniformly the same”.
I’ve used words associated with “Hume’s problem of induction”. Popper famously rejected all (enumerative) induction as problematic. I think that went far too far. As far as I’m concerned, induction is often fine, we just need to reflect in a piecemeal way on circumstances in which induction is reliable, and circumstances in which it isn’t. It’s reliable when it traces law-like connections in the real world (such as “these emeralds are green, so all emeralds are green”). It isn’t reliable when it doesn’t.
It seems to me that we have good reasons for thinking the climate doesn’t behave in a lawlike way, or at least not in any way useful for modelling in climate science. It may be deterministic, but that’s not the same as being predictable or capable of being modelled. Over time, or in response to various changes in initial conditions, the climate is very complicated and multiply chaotic. It seems to me that additional computing power will bring diminishing returns, so that attempts to model the climate will meet a “ceiling” like that of weather forecasting. We may get a bit better, but we probably can’t get all that much better. To put it bluntly, I think it’s a waste of time, brains and money.