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Refer to a report here that mentions the huge advancement in weather forecasting models since the 1980s:

How much better? “A modern five-day forecast is as accurate as a one-day forecast was in 1980,” says a new paper, published last week in the journal Science. “Useful forecasts now reach nine to 10 days into the future.”

But weather forecasting cannot be indefinitely accurate, one fundamental limitation is Chaos Theory:

Chaos: When the present determines the future, but the approximate present does not approximately determine the future. (Wikipedia)

I used to think some ten or twenty years ago that the accuracy level of 3 day weather forecasts was due to Chaos Theory, but apparently it wasn't.

Are there studies where weather forecasting models are subjected to sensitivities of initial conditions, investigating how Chaos Theory puts an upper limit on the accuracies of such models? Also, based on current models, how much further can weather forecasting models go before the limits of Chaos Theory set in?

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  • $\begingroup$ earthscience.stackexchange.com/questions/14597/…. Does it help ? $\endgroup$
    – user1066
    Feb 2, 2019 at 7:45
  • $\begingroup$ in the tropics what is most difficult to capture is the intraseasonal variability. So on scales of 3-5 days we can be reasonably accurate and even that is only possible if we have accurate observations feeding the model. I think skill is a little more over the mid latitudes(maybe 7 days) but beyond that it is questionable. $\endgroup$
    – user1066
    Feb 2, 2019 at 7:52
  • $\begingroup$ @gansub , I afraid no. Not relevant $\endgroup$
    – Graviton
    Feb 2, 2019 at 10:58
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    $\begingroup$ -journals.ametsoc.org/doi/pdf/10.1175/MWR-D-13-00222.1 - "The lead time at which tropical weather becomes in-herently unpredictable is not well known, but is generallythought to be shorter than that for extratropical weather" $\endgroup$
    – user1066
    Feb 3, 2019 at 5:24
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    $\begingroup$ @gansub , why can't put the two conditions in one answer ? I think the current question is good for the site as it is more Google friendly $\endgroup$
    – Graviton
    Feb 3, 2019 at 8:33

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There are (at least) two factors involved here, before we even get to questions of chaos theory. First, thanks to weather satellites and other sensor improvements, we can measure the initial conditions much more accurately. (One can do a halfway decent 3-day forecast for the West Coast just by eyeballing the GOES West images.)

Second, we have greatly increased computing power. Forecast models (simplisticaly) work by dividing the world, or part of it, into a 3D grid, applying a set of differential equations in the grid, propagating the changes to neighbors, and then stepping forward in time to repeat the process. The finer you can make the grid, the more accurate the forecast can be. However, if you cut the size of a cell in half, you need to do 8 times as much computing. And if it takes longer to do your computation than the actual weather, it's not much use as a forecast :-)

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    $\begingroup$ works for the mid latitudes I agree . In the tropics global model skill is still very poor. I can give instance after instance with ECMWF(supposedly the best model out there) but that would be another question in it's own right. $\endgroup$
    – user1066
    Feb 4, 2019 at 0:54
  • $\begingroup$ @gansub: That may well be a different issue, one of how well the theory & equations of the model actually describe reality. I just do the modelling :-) $\endgroup$
    – jamesqf
    Feb 4, 2019 at 2:25
  • $\begingroup$ it is part of OP's question. How long into the future before chaos sets in ? $\endgroup$
    – user1066
    Feb 4, 2019 at 2:26
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    $\begingroup$ @gansub: But the onset of "chaos" is a different matter from not implementing the correct models. It's not really something you can calculate, at least AFAIK. You can always push the limits back by measuring your initial conditions more accurately, and working on a finer grid, but that doesn't help if the model itself is incorrect. For instance, consider how the Newtonian gravity model couldn't explain the precession of Mercury, no matter how accurate the observations & calculations. $\endgroup$
    – jamesqf
    Feb 4, 2019 at 18:08
  • $\begingroup$ why should a finite set of ensemble members(no matter how accurately sampled) be representative of reality ? $\endgroup$
    – user1066
    Feb 5, 2019 at 1:50

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