<p>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.)</p>

<p>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 :-)</p>

CC BY-SA 4.0
2019-02-04T02:25:58.730Z
@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 :-)
jamesqf
CC BY-SA 4.0
2019-02-04T18:08:47.797Z
@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.
jamesqf
CC BY-SA 4.0
2019-02-05T19:39:39.673Z
@gansub: Err... Because that's the way the universe works?    Chaos is not pure randomness: the ensemble solutions cluster around attractors.  So if you put in a varying range of initial conditions, and they all cluster around say "major snowstorm next week", then you can be pretty confident that it will snow.  (And you can only do practical ensemble forecasting because of increased compute power.)
jamesqf
CC BY-SA 4.0
2019-02-06T00:43:28.560Z
Are you suggesting that there is no limit? That the forecasts will extend further and further indefinitely as long as we get more accurate initial conditions and finer grids?
That shouldn't be the case If the atmosphere is really a chaotic systems. Also, nobody have mention that in addition of uncertainties in initial conditions there are unpredictable perturbations that can happen after the forecast was issue, like me waving my hand or doing a BBQ. So even perfect initial conditions might not be enough to make a perfect forecast years ahead of time.
Camilo Rada
CC BY-SA 4.0
2019-02-03T18:15:25.423Z
2019-02-03T18:15:25.423Z
jamesqf
<p>Refer to a report <a href="https://www.theatlantic.com/science/archive/2019/01/polar-vortex-weather-forecasting-good-now/581605/" rel="nofollow noreferrer">here</a> that mentions the huge advancement in weather forecasting models since the 1980s:</p>

<blockquote>
  <p>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.”</p>
</blockquote>

<p>But weather forecasting cannot be indefinitely accurate, one fundamental limitation is Chaos Theory:</p>

<blockquote>
  <p>Chaos: When the present determines the future, but the approximate
  present does not approximately determine the future. (<a href="https://en.wikipedia.org/wiki/Chaos_theory" rel="nofollow noreferrer">Wikipedia</a>)</p>
</blockquote>

<p>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. </p>

<p>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? </p>

CC BY-SA 4.0
2019-02-02T10:58:17.833Z
@gansub , I afraid no. Not relevant
Graviton
CC BY-SA 4.0
2019-02-03T08:33:05.223Z
@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
Graviton
CC BY-SA 4.0
2019-02-03T23:09:44.253Z
I'm no expert on how chaos works with such things... but my instinct is that while chaos theory means that models cannot be perfectly accurate, there may not be any limit to *how* accurate they can be at more than linearly increasing levels of computational expense. (well, unless we're simulating things at the molecular level)
Semidiurnal Simon
<meteorology><weather-forecasting><chaos>
How much further can weather forecasting models go before the limits of Chaos Theory set in?
Graviton
# How much further can weather forecasting models go before the limits of Chaos Theory set in?

(Asked by: username_0 on 2019-02-02)

Refer to a report [here](https://www.theatlantic.com/science/archive/2019/01/polar-vortex-weather-forecasting-good-now/581605/) 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](https://en.wikipedia.org/wiki/Chaos_theory))

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?

**Tags:** meteorology, weather-forecasting, chaos

> **Comments:**
> **username_0**: @gansub , I afraid no. Not relevant  
> **username_0**: @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  
> **username_1**: I'm no expert on how chaos works with such things... but my instinct is that while chaos theory means that models cannot be perfectly accurate, there may not be any limit to *how* accurate they can be at more than linearly increasing levels of computational expense. (well, unless we're simulating things at the molecular level)  

---

## 1 answers

### Answer by username_2 on 2019-02-03. Score: 1

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 :-)

> **Comments:**
> **username_2**: @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 :-)  
> **username_2**: @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.  
> **username_2**: @gansub: Err... Because that's the way the universe works?    Chaos is not pure randomness: the ensemble solutions cluster around attractors.  So if you put in a varying range of initial conditions, and they all cluster around say "major snowstorm next week", then you can be pretty confident that it will snow.  (And you can only do practical ensemble forecasting because of increased compute power.)  
> **username_3**: Are you suggesting that there is no limit? That the forecasts will extend further and further indefinitely as long as we get more accurate initial conditions and finer grids? That shouldn't be the case If the atmosphere is really a chaotic systems. Also, nobody have mention that in addition of uncertainties in initial conditions there are unpredictable perturbations that can happen after the forecast was issue, like me waving my hand or doing a BBQ. So even perfect initial conditions might not be enough to make a perfect forecast years ahead of time.  

---

