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I did my doctorate in the Met Office.

Weather forecasting is two separate problems. The first of these is physics - given the state of the atmosphere right now, what will it do. And this is hard, because there are so many different effects, combined with the fact that our computational models have a limited resolution. There's a huge amount of work that goes into making the simulation behave like a real atmosphere does, and a lot of that is faking what is going on at a smaller scale than the model grid.

The second part is to work out what the current state of the atmosphere is. This is what takes vast amounts of computing power. We don't have an observation station at every grid point and at every altitude in the atmospheric model, so we need to find some other way to infer what the atmospheric state is from the observations that we can from it. Many of these observations are limited in locality, like weather stations, or are a complex function of the atmospheric state, like satellite imagery. The light reaching a satellite has been affected by all the layers of the atmosphere it passes through, and sometimes in a highly nonlinear way. In order to calculate the atmospheric state, we need to take the previous forecast of the current atmospheric state, compare it to the observations, then find the first derivative (as in calculus) of the observation function so that we can adjust the atmospheric state estimate to the new best estimate. This is then complicated by the fact that the observations were not all taken at a single time snapshot - for instance polar orbiting satellites will be taking observations spread out in time. So, we need to use the physics model to wind the atmospheric state back in time to when the observation was taken, find the first derivative of that too, and use it to reconcile the observations with the atmospheric state.

It's a massive minimisation/optimisation problem with millions of free variables, and in some cases we need the second derivative of all these functions too in order to make the whole thing converge correctly and within a reasonable amount of time. It takes a reasonable number of iterations of the minimisation algorithm to get it settle on a solution. The problem is that these minimisation methods often assume that the function being minimised is reasonably linear, which certain atmospheric phenomena are not (such as clouds), so certain observations have to be left out of the analysis to avoid the whole thing blowing up.

My doctorate was looking to see if the nonlinearity involved in a cloud forming as air was moving upwards could be used to translate a time-series of satellite infra-red observations into a measurement of vertical air velocity. The answer was that this single form of nonlinearity made the whole minimisation process fairly dire. I implemented a fairly simple not-quite-machine-learning approach, and it was able to find a solution that was almost as accurate but much more reliable than the traditional minimisation method.

Also, to answer the dead sibling comment asking whether weather is really a chaotic system - yes it is. The definition of a chaotic system is that a small change in current state results in a very large change in outcome, and that's definitely the case. The improvements in weather forecasting over the last few decades have been due to improvements in solving both of the above problems - the physics has been pinned down better, but we're also better as working out the current atmospheric state fairly accurately, and that has added something like a day of forecasting accuracy each decade we have been working on it.



Seems like you know what you are talking about!

What's your take on GraphCast - do you see it as a step forward?


It looks interesting. It's different. It's clearly able to find patterns linking what was happening to what will happen in some ways better than our current physics-based modelling, which is really neat. That's because it has been trained on what the real world actually does, rather than on what our physics models (which are incomplete) say it should do. I think there's definitely a place for this system in our forecasting, and I think it'll sit alongside the current physics-based systems. Forecasters regularly look at what multiple different models say, to get a feel for the level of uncertainty, and they'll temper that with experience about what sort of circumstances certain models are better than others in, so this is another one to add to the list. It appears that this model is better at predicting certain extreme events, so it is likely that a forecaster will pay special attention to it for that in particular.

The system does have some problems. As mentioned in the article, it is a black box, so we can't look at what it has worked out and see why it differs from our physics models. It doesn't build an internal physical model of the atmosphere, so it may not be able to forecast as far into the future as a physics based model. It also seems limited in scope - it makes one particular type of forecast quite well, but not others such as local forecasts (limited area higher resolution).

What might be very interesting is to see if this system can be integrated into a physics-model-based forecasting system. At the moment, the local models get extra data from the global models, which helps them know what weather is going to blow in through the boundaries of the local model. If this system can improve the global model, then that might be able to help the local models, even if the system isn't good at doing local forecasts itself.

Weather forecasting has for a long time been a mixture of methods, usually depending on the range of the forecast. If you want to know if it's going to rain in the next five minutes, looking out the window is more accurate than going to the forecast. Within the next few hours, a very simple model that just looks at the weather radar and the wind direction to predict where the rain will fall is more accurate than a physics model (but less accurate for the next five minutes than looking out the window) - that's called "nowcasting". So it may be that this new system can slot in somewhere in-between nowcasting and physics-based forecasting.

I think it'll be a very interesting development over the next few years. I think it's particularly interesting that the system uses so little compute time, which implies to me that maybe it could be made even better with more resources dedicated to it. I'm not in this field of study any more, but I'll be watching the news.




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