I'll make it a little bit more accurate. If I poor water into a bucket at a set rate, it takes incredible computing power to simulate the hydrodynamics and understand how the water is splashing, the patterns of ripples, and the turbulence in the water, but I can tell you that when I've poured in 2 gallon, the bucket will be full.
I'll make it even better.
I'm spraying water at my dog. Weather is predicting where the hose spray will fly, and how much make it on the dog at any moment. Climate is predicting how wet the dog will be in the end and what will get wet if dog goes in the house.
My (blue) wife claims she can predict the exact amount of water on my dog, and says if I let the mutt in, 1.4 cups of mud will get on the stairs, and I shouldn't do it.
I (red) correctly say that's nonsense, and that she can't predict that with any accuracy. I keep spraying the dog, and let the muddy dog in the house.
Dog doesn't go for the stairs, but heads for the $5000 sofa, staining it to where it's a $100 Goodwill sofa, and shaking mud onto the AV system. Stairs are clean, though.
TL;DR: We can't predict shit will get f-ed up to nearly the degree Democrats say they can. We know shit will get f-ed up, though, with pretty good certainty.
(My own opinion is we've badly underestimated the impact of chemical effects, like ocean acidification, and overestimated the effects of temperature change; but the dog might go for the pantry instead)
All that being said, with regards to this particular study at the scale of 500 years it's likely our climate models nearly completely break down, as we've yet to successfully create one without significant divergence even a few decades out (although maybe that has changed as by definition the best ones we can test against only include those made before the year ~2000)
It's easier to deal with these distributions because you don't need to predict the next year of weather to predict what global temperature properties keep the earth in equilibrium with incoming solar energy, for example.
By contrast climate is "simple" in that it can have fewer variables. The most basic climate model is literally zero-dimensional: it treats the earth as a homogeneous gas mixture and that's it. It can be reported in a single variable, the temperature.
The zero-dimensional model won't tell you all of the things that happen: some places get more rain, some less, some even get cooler. There are more complicated models that do that, and to make specific policy recommendations you need those. But there is a crucial discussion that comes from that single number: yes, the world is getting warmer, because of humans turning carbon in the ground into CO2 in the atmosphere, and it's bad enough that action needs to be taken.
The model is still unstable, but much more tightly constrained, to within a fraction of a degree C per year. That's because the atmosphere is so large, and the sheer mass of it means it has to change slowly, but predictably. Over very long scales (tens of thousands of years) additional factors create more instability, but they're not pressing problems the way highly predictable century-scale changes are.
Take the math out of it for a second. I’m not nearly smart enough to predict which room you’ll be in during a specific minute of a specific day. Predicting that you’re going to be hungry at exactly 12:42 and you’ll go to the store this Sunday at 9:21 is well beyond me.
But I could be much more accurate if I abstract it a bit to a few important properties. During shelter in place, you probably spend 25-35% of the time asleep, maybe 0.1-0.5% at the store (once every 1-3 weeks maybe), etc. I can even confidently predict that as shelter in place relaxes, you’ll likely go out more often, but probably still very rarely to the grocery store more than twice per week.
Your precise movements are impossible to accurately predict more than a few moments out, but their distribution from one day to the next during shelter in place is pretty stable. On a longer timescale, that distribution will shift once shelter in place lifts, and it’s even reasonable to predict how it’ll change.
Another timely analogy might be modeling specifically who has COVID-19 at a point in time versus modeling the distribution. The percent of people in a place who have it is the distribution in question here: the probability that any given person there has it is a simple distribution over true or false. There’s no question of stability over time here because it’s a distribution over people instead of time. You can model how that spreads over time and location so much more easily than predicting the specific individuals who will get it and transmit it.
- weather is mostly about complex local interactions between air pressure / surface temperature / air flow (convection) / humidity etc. these are described by differential equations with very chaotic behaviour (small changes in inputs may have extreme effects on the outputs the further you run the model)
- climate is more about long-time effects of the energy input/output of the whole planetary surface and atmosphere. Mostly solar radiation (input) vs. black-body radiation (output). There are also some complex interactions and feedback cycles e.g. change of albedo (cloud cover), and changes of atmospheric composition (i.e. methane due to permafrost melting), but local weather patterns may cancel out when looking at the sum-total of surface thermal energy.
Imagine Oxygen molecules in a box. The individual movements are complex and unpredictable but at a very high level macro view we can see all of these movements in aggregate as temperature.
Temperature is not only much more stable then the chaotic movements of individual atoms but it is predictable and controllable. I can heat a kettle of water to a very specific temperature and I can accurately predict the rate in which it will cool down when I stop heating it. I cannot however control or predict the actions of specific molecules within the kettle.
The lower level you go the more chaotic things become. The higher you go the more deterministic things appear to be.
Plenty of others if you care to look. Weather is a chaotic system whereas climate is not.
Climate involves long term trends which are quite stable and predictable.
It’s kinda like the stock market. There may be lots of fluctuations in a given day, but most traders are interested in long term trends which tend to be more stable and predictable.
Perhaps you mean macro vs. micro as in economics. Even there micro is far more predictable than macro. Macro is almost voodoo when it comes to prediction of any sort on any timescale.
tldw: weather is like a dog on walk, running around, climate like the owner, bounding what weather is possible