Meteorology

[RationalBiker]

Does anyone familiar with Meteorology know how "weathermen" can determine a 27% chance of rain? (I ask this because my local weather tomorrow includes that particular percentage during one portion of the day

In a broader sense, I'm serious. How accurate is the science of weather forecasting?

Edited October 5, 2005 by RationalCop

[xavier]

I'm not an expert in this area, but I've had it explained to me once.

Our understanding of the laws of nature (pressure, temperature, moisture, etc) are good enough, it is our computation limitations that are the roadblock.

To compute the weather for tomorrow, we cut up the area we are interested in, into a bunch of cubes, measure things like pressure and temperature at each cube, then apply our equations, then use the brute force of computers to calculate pressure and temperature at some time in the future, of each cube. I suppose the cubes will be squares, if you only want a 2-D, top-down view.

This discretized method has some inherent problems. How fine a resolution do you want? If you want accuracy, you need tiny cubes, and you have to take measurement at each cube to start the calculation. Tiny cubes means more cubes, so the computation time goes up. This could easily mean computation times of several decades, just to find tomorrow's weather.

So you have to make a trade off, you want a timely computation, which means poor resolution, which means poor accuracy.

Of course, all measurements or computations based on measurements have an uncertainty. They should be expressed as Average +/- Error. They leave out the error because it would confuse people.

If someone knows of a different way to forecast the weather, let us know!

[RationalBiker]

Of course, all measurements or computations based on measurements have an uncertainty. They should be expressed as Average +/- Error. They leave out the error because it would confuse people.

Thanks for the explanation.

I figured they were generally averages, or at least rough guides, given that you usually see them expressed in 5 or 10% intervals, as opposed to figures like 27%.

[jrs]

How accurate is the science of weather forecasting?

Weather forecasting can be rather good over short periods of time, if you collect enough data and have enough computer power.

A 27% chance of rain might mean that rain WILL FALL in 27% of the viewing area of the TV station (the other 73% remaining dry). So it does not necessarily represent uncertainty in the model.

After several days, the forecasts breakdown because the equations used are chaotic, i.e. small initial errors grow exponentially over time until the forecast becomes useless.

[xavier]

There's another way that 27% might come about. To use a computer, space is discretized, but time is as well, so you have to pick a time step, and iterate the computation through all the time steps, until you get to the time you want. There are math theorems that say that the final error is no greater than a certain value, which means the error is bounded, and you know this bound.

So is it raining?

[Robin Schenck]

After several days, the forecasts breakdown because the equations used are chaotic, i.e. small initial errors grow exponentially over time until the forecast becomes useless.

If it's possible, could you elaborate on this?

[jrs]

After several days, the forecasts breakdown because the equations used are chaotic, i.e. small initial errors grow exponentially over time until the forecast becomes useless.

If it's possible, could you elaborate on this?

If you mean that you want an explanation of chaos theory, then you could start with the wikipedia:

http://en.wikipedia.org/wiki/Chaos_theory

Roughly speaking, a system of equations is chaotic, if it acts like shuffling a deck of cards (imperfectly). Each time it is shuffled, the arrangement of the deck becomes less predictable, until any sequence is equally likely.

[Robin Schenck]

If you mean that you want an explanation of chaos theory, then you could start with the wikipedia:

http://en.wikipedia.org/wiki/Chaos_theory

Roughly speaking, a system of equations is chaotic, if it acts like shuffling a deck of cards (imperfectly). Each time it is shuffled, the arrangement of the deck becomes less predictable, until any sequence is equally likely.

I'm already familiar with chaos theory, as I'm currently doing research into its application in networks - I haven't looked into the weather aspect of it yet however, but I was just wondering if there was a noticeable critical point in weather forecasting where the weather goes from somewhat predictable to not predicatable. Is it something that can be expressed by a power law?

[jrs]

I'm already familiar with chaos theory, as I'm currently doing research into its application in networks - I haven't looked into the weather aspect of it yet however, but I was just wondering if there was a noticeable critical point in weather forecasting where the weather goes from somewhat predictable to not predictable. Is it something that can be expressed by a power law?

Sorry, I do not know that much about it. I would guess that the transition is gradual as you try to predict further into the future.

All I know is that the troposphere (the lowest part of the atmosphere where the temperature decreases with altitude) is unstable. The Sun heats the surface of the Earth and this causes heat and moisture to move into the atmosphere in contact with the surface. The warmer and moister air expands and becomes less dense. Then it rises (a low-pressure area). As it rises to regions with lower pressure, it expands further and cools. Water condenses and falls as rain or snow. The condensation prevents the temperature from falling much until the air has become dry. Once dry, the air begins to cool again and continues rising until it crosses the tropopause and finds the level at its temperature in the stratosphere. Cold dense and dry air sinks to the surface (a high-pressure area) to replace the hot moist air.

I have read that the weather in the troposphere was one of the first systems to have been shown to be chaotic. Someone was doing simulations of the equations, trying to figure out why they breakdown. He discovered that even though the equations are nominally deterministic and he started with the same initial conditions, after awhile, the results diverged in different runs of the simulation.

[Jay P]

If it's a matter of the weather being a chaotic system, then my experience is that it's chaotic enough that after 3 or 4 days, a precise forecast isn't worth much.

If I look at a 2 or 3 day forecast, typically it ends up being good enough to be useful. If it predicts rain, it's likely that it really will rain. But a 10 day forecast is another matter. These often end up getting modified radically - i.e. going from "clear and 65" to "rainy and 55" - so are practically useless.

In any event, saying there's a "27% chance" of rain seems pretty lame, unless the data really are good enough to predict the probability to within 1%. But given the uncertainties in prediction, rounding it to 30% would be more honest.