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For instance, the so-called butterfly effect implies that the number of hurricanes over a 30 year period (or whatever) will change primarily by butterflies.
Oh, it actually doesn't, though I understand why the idea is compelling. The reason it doesn't work that way has to do with weather vs. climate (attribution of single events to particular causes, vs. a statistical analysis of their probabilities), and on a deeper level, with concepts from perturbation theory.
The butterfly effect means that even the tiniest variations in the initial conditions of the state of the atmosphere will have effects that amplify with time. Indeed, the formation of a hurricane can depend on such small perturbations as a butterfly flapping its wings at a sufficiently earlier time. This is the essence of chaotic behavior in strongly nonlinear systems, and it is the reason we cannot predict weather very far in advance, no matter how well we understand the equations governing atmospheric motions. This is also the reason why increasing the resolution of model grids and input data helps improve the performance of weather forecasts.
You would be correct to use the principle of the Butterfly Effect to conclude that the occurrence of a particular event, like a given hurricane, cannot be determined with respect to small scale perturbations, like what the butterflies did.
However, this does not mean that the frequency of hurricanes will depend primarily on the behavior of butterflies. That is because butterflies are not the only things that can act to change the system. So does your breathing. So do birds, cars, chimneys, airplanes, forest fires, meteorites, exploding landmines, volcanic eruptions, and any number of other things across a variety of size and energy scales. All of these are perturbations, and what matters is how strongly they perturb the system. Butterflies do not perturb the system as strongly as the increasing thermal energy stored in the system due to global warming.
The other part of this is statistical in nature. We can't attribute single weather events to particular causes, but we can attribute the probabilities. We can run global climate models with and without the anthropogenic forcings and see what that does to the frequency that particular weather events occur.
The results of these kinds of analyses for hurricanes are somewhat unclear. Theory and models suggest that a warmer world will spawn stronger hurricanes. The frequency of hurricanes may be about the same or even a bit less, while the frequency of the strongest ones increases. However, this is very difficult to confirm from observations, because we don't have a sufficiently long record of consistent hurricane data. The satellite record is very good of course, but before then the record is not homogenous. Some studies that try to get around this have used reconstructions based on landfalling hurricane inundation zones, which do appear to agree with the expectations of models. But this is still very active research.
What we do know with high confidence is that global warming is changing other climate variables, such as the frequency and intensity of heat waves and droughts, average daily max/min temperatures, and the mean zonal wind and global circulation. The effect on storms is harder to determine, and so are general precipitation patterns, although in the last 5-10 years the use of regional, high resolution models has helped a lot in this area.