climate models are already “low-level physics” except that “low-level” means coarse aggregates of climate/weather measurements that are so big that they don’t include tropical cyclones!
Just as as aside, a typical modern climate model will simulate tropical cyclones as emergent phenomena from the coarse-scale fluid dynamics, albeit not enough of the most intense ones. Though, much smaller tropical thunderstorm-like systems are much more crudely represented.
Tangential, but now I’m curious… do you know what discretization methods are typically used for the fluid dynamics? I ask because insufficiently-intense cyclones sound like exactly the sort of thing APIC methods were made to fix, but those are relatively recent and I don’t have a sense for how much adoption they’ve had outside of graphics.
do you know what discretization methods are typically used for the fluid dynamics?
There’s a mixture—finite differencing used to be used a lot but seems to be less common now, semi-Lagrangian advection seems to have taken over from that in models that used it, then some work by doing most of the computations in spectral space and neglecting the smallest spatial scales. Recently newer methods have been developed to work better on massively parallel computers. It’s not my area, though, so I can’t give a very expert answer—but I’m pretty sure the people working on it think hard about trying to not smooth out intense structures (though, that has to be balanced against maintaining numerical stability).
How much are ‘graphical’ methods like APIC incorporated elsewhere in general?
My intuition has certainly been pumped to the effect that models that mimic visual behavior are likely to be useful more generally, but maybe that’s not a widely shared intuition.
I would have hoped that was the case, but that’s interesting that both large and small ones are apparently not so easily emergent.
I wonder whether the models are so coarse that the cyclones that do emerge are in a sense the minimum size. That would readily explain the lack of smaller emergent cyclones. Maybe larger ones don’t emerge because the ‘next larger size’ is too big for the models. I’d think ‘scaling’ of eddies in fluids might be informative: What’s the smallest eddy possibly in some fluid? What other eddy sizes are observed (or can be modeled)?
Not sure if this was intended to be rhetorical, but a big part of what makes turbulence difficult is that we see eddies at many scales, including very small eddies (at least down to the scale that Navier-Stokes holds). I remember a striking graphic about the onset of turbulence in a pot of boiling water, in which the eddies repeatedly halve in size as certain parameter cutoffs are passed, and the number of eddies eventually diverges—that’s the onset of turbulence.
Sorry for being unclear – it was definitely not intended to be rhetorical!
Yes, turbulence was exactly what I was thinking about. At some small enough scale, we probably wouldn’t expect to ‘find’ or be able to distinguish eddies. So there’s probably some minimum size. But then is there any pattern or structure to the larger sizes of eddies? For (an almost certainly incorrect) example, maybe all eddies are always a multiple of the minimum size and the multiple is always an integer power of two. Or maybe there is no such ‘discrete quantization’ of eddy sizes, tho eddies always ‘split’ into nested halves (under certain conditions).
It certainly seems the case tho that eddies aren’t possible as emergent phenomena at a scale smaller than the discretization of the approximation itself.
I wonder whether the models are so coarse that the cyclones that do emerge are in a sense the minimum size.
It’s not my area, but I don’t think that’s the case. My impression is that part of what drives very high wind speeds in the strongest hurricanes is convection on the scale of a few km in the eyewall, so models with that sort of spatial resolution can generate realistically strong systems, but that’s ~20x finer than typical climate model resolutions at the moment, so it will be a while before we can simulate those systems routinely (though, some argue we could do it if we had a computer costing a few billion dollars).
It seems like it might be an example of relatively small structures having potentially arbitrarily large long-term effects on the state of the entire system.
It could be the case tho that the overall effects of cyclones are still statistical at the scale of the entire planet’s climate.
Regardless, it’s a great example of the kind of thing for which we don’t yet have good general learning algorithms.
Just as as aside, a typical modern climate model will simulate tropical cyclones as emergent phenomena from the coarse-scale fluid dynamics, albeit not enough of the most intense ones. Though, much smaller tropical thunderstorm-like systems are much more crudely represented.
Tangential, but now I’m curious… do you know what discretization methods are typically used for the fluid dynamics? I ask because insufficiently-intense cyclones sound like exactly the sort of thing APIC methods were made to fix, but those are relatively recent and I don’t have a sense for how much adoption they’ve had outside of graphics.
There’s a mixture—finite differencing used to be used a lot but seems to be less common now, semi-Lagrangian advection seems to have taken over from that in models that used it, then some work by doing most of the computations in spectral space and neglecting the smallest spatial scales. Recently newer methods have been developed to work better on massively parallel computers. It’s not my area, though, so I can’t give a very expert answer—but I’m pretty sure the people working on it think hard about trying to not smooth out intense structures (though, that has to be balanced against maintaining numerical stability).
How much are ‘graphical’ methods like APIC incorporated elsewhere in general?
My intuition has certainly been pumped to the effect that models that mimic visual behavior are likely to be useful more generally, but maybe that’s not a widely shared intuition.
I would have hoped that was the case, but that’s interesting that both large and small ones are apparently not so easily emergent.
I wonder whether the models are so coarse that the cyclones that do emerge are in a sense the minimum size. That would readily explain the lack of smaller emergent cyclones. Maybe larger ones don’t emerge because the ‘next larger size’ is too big for the models. I’d think ‘scaling’ of eddies in fluids might be informative: What’s the smallest eddy possibly in some fluid? What other eddy sizes are observed (or can be modeled)?
Not sure if this was intended to be rhetorical, but a big part of what makes turbulence difficult is that we see eddies at many scales, including very small eddies (at least down to the scale that Navier-Stokes holds). I remember a striking graphic about the onset of turbulence in a pot of boiling water, in which the eddies repeatedly halve in size as certain parameter cutoffs are passed, and the number of eddies eventually diverges—that’s the onset of turbulence.
Sorry for being unclear – it was definitely not intended to be rhetorical!
Yes, turbulence was exactly what I was thinking about. At some small enough scale, we probably wouldn’t expect to ‘find’ or be able to distinguish eddies. So there’s probably some minimum size. But then is there any pattern or structure to the larger sizes of eddies? For (an almost certainly incorrect) example, maybe all eddies are always a multiple of the minimum size and the multiple is always an integer power of two. Or maybe there is no such ‘discrete quantization’ of eddy sizes, tho eddies always ‘split’ into nested halves (under certain conditions).
It certainly seems the case tho that eddies aren’t possible as emergent phenomena at a scale smaller than the discretization of the approximation itself.
It’s not my area, but I don’t think that’s the case. My impression is that part of what drives very high wind speeds in the strongest hurricanes is convection on the scale of a few km in the eyewall, so models with that sort of spatial resolution can generate realistically strong systems, but that’s ~20x finer than typical climate model resolutions at the moment, so it will be a while before we can simulate those systems routinely (though, some argue we could do it if we had a computer costing a few billion dollars).
Thanks! That’s very interesting to me.
It seems like it might be an example of relatively small structures having potentially arbitrarily large long-term effects on the state of the entire system.
It could be the case tho that the overall effects of cyclones are still statistical at the scale of the entire planet’s climate.
Regardless, it’s a great example of the kind of thing for which we don’t yet have good general learning algorithms.