What equations do meteorologists use to predict weather patterns?

[Q_Goest]

I wonder how meteorologists 'calculate' weather in order to predict weather patterns. I know they use computational models, but after looking around the net, I haven't figured out what equations they use. Do they go with the typical Navier Stokes equations? I'd think meteorology, especially before the time of computational models, must have used something else. Just like piping engineers use the Darcy Weisbach equation, Bernoulli's and mix that with thermodynamics as the primary equations for piping networks (as oposed to the NS equations) I wonder if meteorologists use equations that move up a level, so to speak. Some equations that are broader or more general and easy to use.

 

[klimatos]

I wonder how meteorologists 'calculate' weather in order to predict weather patterns. I know they use computational models, but after looking around the net, I haven't figured out what equations they use. Do they go with the typical Navier Stokes equations? I'd think meteorology, especially before the time of computational models, must have used something else. Just like piping engineers use the Darcy Weisbach equation, Bernoulli's and mix that with thermodynamics as the primary equations for piping networks (as oposed to the NS equations) I wonder if meteorologists use equations that move up a level, so to speak. Some equations that are broader or more general and easy to use.

There are three basic ways of forecasting weather, and modern meteorologists use a combination of all three:

1. Seeing what's happening "upstream" and assuming that you will have something similar when the system gets to you. Pretty much the standard nowadays.

2. Computer forecasts based on thermodynamics and fluid mechanics and established meteorological techniques. This is basically what you were talking about. It's hard to get all the variables in time to make a forecast. Subject to the GIGO rule.

3. Statistical analyses of similar conditions in the past. This is the "old-timers" tried and true methodology. Works more often than not, but that's about the best that can be said for it.

Put them all together and you get excellent forecasts for tomorrow, pretty good for the day after tomorrow, and fair for the third day. By the time you get to five days out, you might as well flip a coin.

 

[Studiot]

By the time you get to five days out, you might as well flip a coin.

Funny you should say that.

Some years back a very well known fuel gas supply company did exactly that.

They use(d) meteorological forcasting to determine the storage and distribution of gas supplies, particularly for the winter because gas demand is strongly related to the weather.

Since they were commited to supply, regardless of the existence of meteorological forcasts, they tasked their maths department with providing a statistically based alternative in case of loss of forcasts.

 

[SW VandeCarr]

Here's an outline of methods used from the simplest (tomorrow will be like today) to the most complex where the weather patterns are evolving rapidly and small changes in temperature, storm tracks and upper atmosphere wind patterns can make very big differences.

Typically, 5 day forecasts in the US in 2010 were about as accurate as 2 day forecasts were in 1980. However, it depends very much on the location and time of year. Forecasting snowfall amounts along the US east coast can be very difficult even for 12 or 24 hours. Temperatures close to freezing and a slight shift of the storm track to the east or west can be the difference between two inches or two feet (5-60cm) of snow in New York City.

Also you have to define what a correct forecast is. If the forecast is for a foot of snow (30cm) and you get two feet, is that wrong? If you forecast a high temperature of 35 F (2 C) an it actually is 33 F (1 C) at ground level, is that wrong? It could be the difference between one or two feet of snow where some rain gets mixed in at the higher temperature. However, no one will complain if you forecast partly cloudy and mild with a high of 50 F (10 C) and the actual weather is clear with a high of 59 F (15 C).

http://www.csun.edu/~hcgeg004/forecast.html

 

[Q_Goest]

Thanks klimatos, Studiot, SW VandeCarr. After some more research on the web, I found an interesting book by Jackobson, "Fundamentals of Atmosopheric Modeling" that goes through all sorts of models. It seems like the models are differentiated by the number of simplifying assumptions made, such as whether or not the air has a vertical component of velocity. Anyway, I think I have what I was looking for. Thanks again.