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Comment by jetrink | Hacker News Reader

One interesting fact that I learned from Nate Silver's book, The Signal and the Noise, is that weather forecasting is a four-dimensional problem (space + time), so to produce a forecast that is twice as detailed requires approximately 16x the computing resources. Historically, the resolution of weather forecasts has doubled roughly every eight years, in line with with Moore's Law.

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I heard that it's twelve dimensional. Used to work with a guy who's PHD thesis was on the diffeq of weather predictions.

'if twelve cows are lying down it's gonna rain'

QED

The time-spatial discretization is 4D. There are many different state variables within each grid cell.

Vorticity patterns are often treated as an additional set of 3 dimensions, because they require continuous differentiation. Modern weather forecasting software is a beast.

I've done some reading through the literature on the dynamical cores of weather models. It isn't really true that vorticity is modeled as an additional set of dimensions.

Vorticity and divergence are an alternative description of the fluid velocity. They are the curl and div of the fluid velocity, respectively.

Just as the fluid velocity may be discretized in 3 spatial and one time dimension, the fluid's vorticity and divergence may be discretized in three spatial and one time dimension.

Is there a similar rule of thumb for how accuracy tracks with the added resolution?

Do you mean added resolution of input data, or improved resolution at which the models are run? Input data is frankly very limited - IMO we are barely measuring the atmosphere. Model runs are higher resolutions are only good if there is sufficient input data to seed the models.

It's my lifelong passion to increase the usable input data (live atmosphere measurements) that models can assimilate. My latest attempt is to use the barometers in phones to create billions of new 'virtual weather stations'. My US-only Android app (iOS and international coming soon) is

https://play.google.com/store/apps/details?id=com.allclearwe...

You can see an animation of the data recorded in the Orlando, FL area when Dorian was churning off the coast: https://www.allclearweather.com/hurricane-dorian

The data requires significant QA and bias correction to use, but it is possible (see Cliff Mass research papers) and the trends in the data are already clear and usable, regardless of actual pressure value recorded.

Let's add a source code link for Android background/foreground sensor access that I wrote to further these goals: https://github.com/JacobSheehy/AllClearSensorLibrary

so 32 years ago they could forecast an hour into the future?

It's more like the ranges of uncertainty for given time horizons were much larger 32 years ago then they are now. Take a look at https://www.globalweatherclimatecenter.com/tropical-cyclone-... for hurricanes in particular: the 5-day forecast is now more accurate than the 2-day forecast was in 1990.

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