Last Wednesday I attended a meeting of the Royal Met Society on Perfecting Imperfect Models.
During the panel discussion we spent time dicussing the relative importance of spending effort on
- improving the physical parameterisations in climate models
- increasing the number and breadth of ensembles, and
- improving model resolution
In a somewhat provocative manner, we were charged to think about whether, if we could achieve 1 km horizontal resolution (in climate models for climate length integrations) in 10-15 years time, we would put less effort into improving the physical parameterisations in our models?
Leaving aside the obvious response that some physical parameterisation will always be needed, there was little discussion about the reality of the proposition. Let’s consider the facts:
- Recent state of the art climate models (HadCM3 in 2000, HadGEM in 2005) have moved resolutions from order 300 to order 150 km (implying a factor of two was achievable in those five years).
- The next generation of models (e.g. HiGEM) are aiming for a doubling again, but it is a three year project (again, e.g. HIGEM) to do the work required to double the resolution (this is not the computing work, it’s about producing ancillary datasets, understanding the coupling of the components at higher resolution, and indeed, addressing changes to the physical parameterisations).
So, in fifteen years from a scientific point of view, we might be able to sustain at best doubling five times (although I suspect it ought to be less than that to get better mileage out of the better models at each step). That implies, scientifically the absolute best we might be able to get to for climate is around 150/(25) = 32, i.e. about 3 km. More realistically it will be necessary to do some science along the way too, so we can imagine a process of resolution enhancement, scientific consolidation, and further enhancement. This process of model evolution could be called punctuated equilibrium (with obvious apologies for appropriating the name). So, with punctuated equilibrium, scientifically the best we could do is probably going to be more like 10 km … (for climate, obviously NWP etc will be at higher resolution).
What about from a computing point of view?
Remembering that a factor n horizontal resolution increase requires n squared calculations, and that in practice we would need to increase the vertical resolution and decrease the time step, means that we are talking about somewhere between n3 and n4 more calculations (anything less than 4 implies some smart improvements in numerics). In reality as we increase the resolution, we will undoubtedly find that we needmore parameters to be advected on a global scale, and/or additional complexity (e.g. new chemistry/aerosol schemes) so there is an additional factor p to be included which will also scale in the same way.
Moores Law implies a doubling in computing capacity every 2 years, which needs to be compared with the increase in computations of (at best) (pn)3 If m is the number of years required to support p and n, we have (at best) 2n/2 = (pm)3 or m=11.5 log(pn). For p=1.2 and n = 10 (a guess, and from the example above), we would have m=28 years from Moores Law … so it seems that computing will limit development (and allow time for punctuated equilibrium in model resolution improvement).
Another way of thinking about it would be: what if we spent all our computing capacity improvement on resolution enhancement for the next ten years? In that case, we would have 25 = 32 times more capacity available (from Moores Law) which neglecting p would support, a resolution increase of just over two! This seems to be evidence that the 2000-2005 increase was only possible because there had been a rest period in the punctuated equilibrium of model development.
Of course, Moore’s Law isn’t the whole story because as the computing capacity has gone up, we have also been able to apply massive parallelisation as well … this is an example of a technical improvement in the way we do things. However, we’ve done that, so without a new way of doing our modelling (or a new cost model for the hardware), the bottom line here is that a resolution increase of much more than 2-4 for climate models in the next decade is very unlikely.
One of the factors that impacts on all this will be how much effort we put into increasing our ensemble sizes. We carry out ensembles in two main ways:
- initial condition ensembles and
- parameter ensembles.
In general these are targeted at understanding the uncertainties in predictions on shorter and longer timescales respectively. In general the larger the ensemble, the more likely the predictions are to sample a wider range of possible futures, and the better the accompanying prediction of the various likelihoods. However, one thing that ensembles can never do is sample possible futures that are not predictable by the models involved. That means the probability distribution and accompanying likelihoods must be biased by all the things that we didn’t or couldn’t include in our models. While that seems obvious, what it means is that spending our increasing computer resources on increasing ensemble sample size will not necessarily result in better or more accurate climate predictions. However, without ensembles, predictions are not accompanied by any uncertainty at all, and as someone said, a prediction without a quantification of uncertainty is no better than no prediction at all (tarot cards anyone?). The question is, how big is an adequate ensemble size for most work? We don’t yet know!
What about the physics improvements? I think there are three classes of physics parameterisations in our models:
- parameterisations which represent scales which are a long way from ever being resolved (e.g. radiation, cloud nucleation)
- parameterisations of the ensemble effects of complete systems which we may be able to resolve to a “suitable” scale (e.g mid-latitude storm systems, some classes of clouds).
- parameterisations which represent the sub-grid scale effects of processes which occur on a range of scales, some of which are resolved (e.g. the gravity wave spectrum and associated effects of flow over orography).
I believe we need to think about each of these rather differently, and weigh the effort required against predicted resolution at the time a particular round of parameterisation improvements may be complete.
Things that we didn’t spend time thinking about include:
- What about the effort improving the complete systems which we need to address as separate component models (ice, the land surface etc)?
- What about the problems handling the datasets that are produced by enormous ensembles and high resolution? (Indeed, IO limits may in fact be a bigger problem than CPU limits in the near future).
Another thing we never spend enough time on in climate science is thinking about how best to exploit adaptive grid techniques, e.g. the material discussed at Cambridge in December 2004.
Using more computer power, revisited. (from “Bryan’s Blog” on (on Wednesday 23 January, 2008))
In the comments to my post on why climate modelling is so hard, Michael Tobis made a few points that need a more elaborate response (in time and text) …
hpc futures - part one (from “Bryan’s Blog” on (on Monday 02 August, 2010)
… By way of organising my thinking about increased resolution, and in some ways, following up on an even older discourse, I’ve spent a bit of time thinking about computing capacity …