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Beyond the difficulty of running calculations (or even accurately measuring the current state), is there a reason to believe weather is unpredictable? I would

by brap 3y ago

Beyond the difficulty of running calculations (or even accurately measuring the current state), is there a reason to believe weather is unpredictable? I would imagine we probably have a solid mathematical model of how weather behaves, so given enough resources to measure and calculate, could you, in theory, predict the daily weather going 10 years into the future? Or is there something inherently “random” there?

danbrooks 3y ago
Small changes in initial state can lead to huge changes down the line. See: the butterfly effect or chaos theory. https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory
deleted 3y ago
[deleted]
ethanbond 3y ago
AFAIK there's nothing random anywhere except near atomic/subatomic scale. Everything else is just highly chaotic/hard-to-forecast deterministic causal chains.
- mesoman 3y ago
  Cloud formation is affected by cosmic ray flux. It's effectively random. But the real problem is chaos - which says that even with perfect data, unless you also have computations with infinite precision and time/spatial/temperature/pressure/etc resolution, eventually you wind up far from reality. The use of ensembles reduces the effect of chaos a bit, although they tend to smooth it out - so your broad pattern 12 days out might be more accurately forecast than without them, but the weather at your house may not be. Iterative DL models tend to smooth it faster, according to a recent paper.
counters 3y ago
What you're describing is effectively how climate models work; we run a physical model which solves the equations that govern how the atmosphere works out forward in time for very long time integrations. You get "daily weather" out as far as you choose to run the model. But this isn't a "weather forecast." Weather forecasting is an initial value problem - you care a great deal about how the weather will evolve from the current atmospheric conditions. Precisely because weather is a result of what happens in this complex, 3D fluid atmosphere surrounding the Earth, it happens that small changes in those initial conditions can have a very big impact on the forecast on relatively short time-periods - as little as 6-12 hours. Small perturbations grow into larger ones and feedback across spatial scales. Ultimately, by day ~3-7, you wind up with a very different atmospheric state than what you'd have if you undid those small changes in the initial conditions. This is the essence of what "chaos" means in the context of weather prediction; we can't perfectly know the initial conditions we feed into the model, so over some relatively short time, the "model world" will start to look very different than the "real world." Even if we had perfect models - capable of representing all the physics in the atmosphere - we'd still have this issue as long as we had to imperfectly sample the atmosphere for our initial conditions. So weather isn't inherently "unpredictable." And in fact, by running lots of weather models simultaneously with slightly perturbed initial conditions, we can suss out this uncertainty and improve our estimate of the forecast weather. In fact, this is what's so exciting to meteorologists about the new AI models - they're so much cheaper to run that we can much more effectively explore this uncertainty in initial conditions, which will indirectly lead to improved forecasts.
- willsmith72 3y ago
  is it possible to self-correct, looking at initial value errors in the past? Is it too hard to prescribe the error in the initial value?
  - counters 3y ago
    Yes, this is effectively what 4DVar data assimilation is [1]. But it's very, very expensive to continually run new forecasts with re-assimilated state estimates. Actually, one of the _biggest_ impacts that models like GraphCast might have is providing a way to do exactly this - rapidly re-running the forecast in response to updated initial conditions. By tracking changes in the model evolution over subsequent re-initializations like this, one could might be able to better quantify expected forecast uncertainty, even moreso than just by running large ensembles. Expect lots of R&D in this area over the next two years... [1]: https://www.ecmwf.int/en/about/media-centre/news/2022/25-years-4d-var-how-machine-learning-can-improve-use-observations https://www.ecmwf.int/en/about/media-centre/news/2022/25-yea...
- brap 3y ago
  So isn’t it just a problem of measurement then? Say you had a massive array of billions of perfect sensors in different locations, and had all the computing power to process this data, would an N year daily forecast then be a solved problem? For the sake of the argument I’m ignoring ”external” factors that could affect the weather (e.g meteors hitting earth, changes in man-made pollution, etc)
  - counters 3y ago
    At that point you're slipping into Laplace's Demon. In practical terms, we see predictability horizons get _shorter_ when we increase observation density and spatial resolution of our models, because more, small errors from slightly imperfect observations and models still cascade to larger scales.
_visgean 3y ago
See https://en.wikipedia.org/wiki/Numerical_weather_prediction https://en.wikipedia.org/wiki/Numerical_weather_prediction > Present understanding is that this chaotic behavior limits accurate forecasts to about 14 days even with accurate input data and a flawless model. In addition, the partial differential equations used in the model need to be supplemented with parameterizations for solar radiation, moist processes (clouds and precipitation), heat exchange, soil, vegetation, surface water, and the effects of terrain. I think there is a hope that DL models wont have this problem.

by brap 3y ago

danbrooks 3y ago

Small changes in initial state can lead to huge changes down the line. See: the butterfly effect or chaos theory. https://en.wikipedia.org/wiki/Chaos_theory https://en.wikipedia.org/wiki/Chaos_theory

deleted 3y ago

[deleted]

ethanbond 3y ago

AFAIK there's nothing random anywhere except near atomic/subatomic scale. Everything else is just highly chaotic/hard-to-forecast deterministic causal chains.

mesoman 3y ago
Cloud formation is affected by cosmic ray flux. It's effectively random. But the real problem is chaos - which says that even with perfect data, unless you also have computations with infinite precision and time/spatial/temperature/pressure/etc resolution, eventually you wind up far from reality. The use of ensembles reduces the effect of chaos a bit, although they tend to smooth it out - so your broad pattern 12 days out might be more accurately forecast than without them, but the weather at your house may not be. Iterative DL models tend to smooth it faster, according to a recent paper.

counters 3y ago

What you're describing is effectively how climate models work; we run a physical model which solves the equations that govern how the atmosphere works out forward in time for very long time integrations. You get "daily weather" out as far as you choose to run the model. But this isn't a "weather forecast." Weather forecasting is an initial value problem - you care a great deal about how the weather will evolve from the current atmospheric conditions. Precisely because weather is a result of what happens in this complex, 3D fluid atmosphere surrounding the Earth, it happens that small changes in those initial conditions can have a very big impact on the forecast on relatively short time-periods - as little as 6-12 hours. Small perturbations grow into larger ones and feedback across spatial scales. Ultimately, by day ~3-7, you wind up with a very different atmospheric state than what you'd have if you undid those small changes in the initial conditions. This is the essence of what "chaos" means in the context of weather prediction; we can't perfectly know the initial conditions we feed into the model, so over some relatively short time, the "model world" will start to look very different than the "real world." Even if we had perfect models - capable of representing all the physics in the atmosphere - we'd still have this issue as long as we had to imperfectly sample the atmosphere for our initial conditions. So weather isn't inherently "unpredictable." And in fact, by running lots of weather models simultaneously with slightly perturbed initial conditions, we can suss out this uncertainty and improve our estimate of the forecast weather. In fact, this is what's so exciting to meteorologists about the new AI models - they're so much cheaper to run that we can much more effectively explore this uncertainty in initial conditions, which will indirectly lead to improved forecasts.

willsmith72 3y ago
is it possible to self-correct, looking at initial value errors in the past? Is it too hard to prescribe the error in the initial value?
- counters 3y ago
  Yes, this is effectively what 4DVar data assimilation is [1]. But it's very, very expensive to continually run new forecasts with re-assimilated state estimates. Actually, one of the _biggest_ impacts that models like GraphCast might have is providing a way to do exactly this - rapidly re-running the forecast in response to updated initial conditions. By tracking changes in the model evolution over subsequent re-initializations like this, one could might be able to better quantify expected forecast uncertainty, even moreso than just by running large ensembles. Expect lots of R&D in this area over the next two years... [1]: https://www.ecmwf.int/en/about/media-centre/news/2022/25-years-4d-var-how-machine-learning-can-improve-use-observations https://www.ecmwf.int/en/about/media-centre/news/2022/25-yea...
brap 3y ago
So isn’t it just a problem of measurement then? Say you had a massive array of billions of perfect sensors in different locations, and had all the computing power to process this data, would an N year daily forecast then be a solved problem? For the sake of the argument I’m ignoring ”external” factors that could affect the weather (e.g meteors hitting earth, changes in man-made pollution, etc)
- counters 3y ago
  At that point you're slipping into Laplace's Demon. In practical terms, we see predictability horizons get _shorter_ when we increase observation density and spatial resolution of our models, because more, small errors from slightly imperfect observations and models still cascade to larger scales.

_visgean 3y ago

See https://en.wikipedia.org/wiki/Numerical_weather_prediction https://en.wikipedia.org/wiki/Numerical_weather_prediction > Present understanding is that this chaotic behavior limits accurate forecasts to about 14 days even with accurate input data and a flawless model. In addition, the partial differential equations used in the model need to be supplemented with parameterizations for solar radiation, moist processes (clouds and precipitation), heat exchange, soil, vegetation, surface water, and the effects of terrain. I think there is a hope that DL models wont have this problem.