Here we go
Incorrect.
There is no question that this poses
challenges, and some of them can be quite perplexing. For example, one issue is that the more factors you include in the models (which makes it more realistic) also introduce new sources of uncertainty. This can make the models less accurate overall. In some cases, a model that is more simplified can in fact produce better predictions. I.e. "unavoidable systemic errors" -- which, unsurprisingly, you did not even discuss -- do not always mean that the models are doomed to wild inaccuracies.
It's routine to test the accuracy of models, by checking their predictions against historical data. At this point, we can also compare past predictions with more recent results. We should note that these models are not merely using past data to develop predictions; rather, they apply the laws of physics to known conditions to develop the predictions. Past data loses its viability to predict the future when conditions change too much, and can be of limited value.
There are some things we can't predict well at this time, such as whether the frequency of hurricanes will increase or decrease because of climate change. That doesn't stop us from knowing that the
intensity of hurricanes will increase because of climate change.
Scientific modeling is hardly limited to climatology. Physics, chemistry, biology, epidemiology, satellite paths, interstellar travel, short-term weather predictions, hurricane predictions, fluid dynamics, protein folding, the list goes on. And yet, for
some reason, the only form of scientific modeling that comes under scrutiny is.... yep, climate change. Hmmmmmmmm
Last but not least, we know enough about the various mechanisms involved to know the basics of the causality, and the basic trend we're facing. We know CO2 is a greenhouse gas. We know that adding more CO2 to the atmosphere generates a feedback loop, which results in more water vapor (the biggest component in trapping heat on the planet) in the atmosphere. We know that higher atmospheric and ocean temperatures is melting land ice, which results in higher sea levels, which makes storms more damaging for coastal areas. I.e. the predictions we've seen should not surprise anyone.
Oh? Which models don't account for it? What is a "proper" accounting?
Jim Milks gives an example of using a statistical function to compensate for autocorrelation on his blog. It makes very little difference. I'd also assume that other models do take this into account, though we'd need to inquire about the specific models in question.
Compensating for autocorrelation in global temperature data