> Chaotic variables stack over iterations, it's the entire basis for the butterfly effect, and yes, that does have follow on effect to the climate at large. Climate models themselves are VERY subject to initial state

I took a semester-long course in chaotic dynamical systems, and one of the insights I got from that is that initial state is most important at edges[1]. Attractors can pull fairly broad initial states to the same course, and the opposite of attractors[1] can cause huge divergences in trajectory[1] of some very close initial states. This makes it practically impossible to determine which deviations of initial states are important, without iterating the model, but it definitively does not mean that all deviations in initial states are important.

[1] - It's been over ten years and nomenclature has never been my strength, so pardon the names I'm using to refer to these technical ideas.

> > But chaos often doesn't affect long term predictions of characteristics like averages and periodic variation in a system.

> That's a very bold statement with no way to falsify it. I think it's better stated "we currently don't possess enough computing power to accurately predict climate long term".

Supporting evidence is gained by reanalyzing old models, and comparing them to each other and the current state. This can show that even old models run on much slower computers still often gave decent predictions within their limitations: https://eapsweb.mit.edu/news/2019/historical-climate-models-...

: the performance of these models could now be assessed for their accuracy. Enough time had likely passed since these historical projections were published that their warming signals would have emerged, and we could now evaluate them against several decades of global temperature measurements.

: The first result we found is that all of the 17 models correctly projected global warming (as opposed to either no warming or even cooling). While this is so unsurprising to climate scientists that it is not even mentioned in the paper, it may be surprising to non-experts. The second result is that most of the model projections (10 out of 17) published between 1970 and 2000 produced global average surface warming projections that were quantitatively consistent with the observed warming rate.

> Wouldn't it be a shame if compounded variables DID in fact have an effect on long term climate?

: simply comparing the warming rates between simulations and reality could be misleading, if the simulated emissions scenario and historical emissions were dramatically different. To account for differences in emissions between the simulations and reality, we calculated the warming rates with respect to anthropogenic radiative forcing, the rate at which human emissions trap energy at Earth’s surface, instead of calculating them with respect to time. Using this novel metric of the warming rate, we found that the model projections were even more consistent with reality (14 out of 17 models captured this).

(Emphasis mine, to address your point about initial states and stacking over iterations. While climate projections may be incorrect because human emissions aren't fully predictable over decades, the models themselves, when these variations are input, seem to do an okay job of modeling the basic physical parameters they incorporate, at least at the global scale.)

> Climate models themselves are VERY subject to initial state

: Additionally, climate science is based on more than just state-of-the-art computer models: measurements of the present climate, paleoproxy evidence from past climates, and fundamental theory provide additional constraints on future warming and bolster our confidence in the field’s findings. However, future climate change will not be experienced the same around the world—this is next frontier for climate researchers. Climate impacts are nuanced and are experienced at smaller, regional scales, for which different models often still disagree.