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- Mathematics Used in Meteorology

You may ask, "what about the mathematics used in meteorology?" Many people have wondered how math relates to meteorology.

Do you need to be skillful in mathematics in meteorology? It can't hurt - that's for sure.

Technologies used in meteorology depend greatly on mathematical principles as well as physics. Examples include weather radar, chart usage and interpretation (such as the hodograph shown on the right) and numerical weather prediction.

Meteorologists study the atmosphere. They examine and attempt to predict the weather and the effects of air pollution, amongst other atmospheric wonders.

We also use instruments to measure wind speed and direction, temperature, pressure and humidity. Then, scientific theory helps us understand how these various quantities, sometimes called fields, interact with each other. And how the variables change in time and space.

A mathematical variable is an unspecified quantity able to accept different values under different conditions.

In math, we use the letters x and y for most problems. They are symbols representing variables, to which mathematicians use the circumstances of the problem either to determine or assign specific values.

Variables for the mathematics used in meteorology include:

- T for temperature, often qualified with subscripts to denote specific temperatures,
- P for pressure in millibars,
- θ (a Greek letter, theta), which looks like a zero with a horizontal dash dividing it in half, represents
potential temperature.
That is, the temperature a package of air would change to if it were suddenly compressed to 1000 millibars without gaining or losing any heat,
- u and v for horizontal velocities of varying types, expressed as vector quantities. Alternatively, they represent vector components of a single velocity and can be combined with w, vertical velocity, to give a three dimensional wind field,
- ρ (the Greek letter rho), which sometimes resembles a backwards 9, to mean density, a function of pressure, temperature and composition,
- the most varying component of composition is humidity. We often use RH for relative humidity and either a lower case r or q to represent the mixing ratio, a measure of absolute humidity.

Because meteorology is a three-dimensional science, four if you include time, the mathematics used in meteorology can require extensive use of partial derivatives. What's that? Partial derivatives allow you to look at how something such as wind speed changes when you move in one direction onlyonly, say, straight north. This could be important to pilots. They also let us determine the gradient of a field. That is, to identify what direction to move in order to see the greatest temperature increase, for instance. And even how much it increases after you go a certain distance in that direction.

The mathematics used in meteorology could, and does, fill textbooks quite extensively. A couple of good starter titles are *Atmospheric Science - An Introductory Survey* by Wallace and Hobbs as well as *An Introduction to Dynamic Meteorology* by James R. Holton. Go Nuts!

I just about did.

Many of the equations in the texts rely on balancing physical properties, such as in a centripetal force equation. Then each of the forces may be defined by products and derivatives of other parameters, usually. Then they are strung along as terms added together, each a component of the net force in this example. This is not always the case, but often enough.

Which other related fields of study borrow from the same set of mathematical principals? Atmospheric physics, climatology, hydrology and atmospheric chemistry.

What's math without a few computers? *Weather Prediction by Numerical Process*
by Lewis Fry Richardson came out in 1922. It said we could simplify the mathematics used in meteorology and, instead of these equations, look at small parametric changes with respect to small physical motions. We
could reduce the complex principles to simple algebra.

But it was labour intensive. He also predicted that 64000 people would be needed to make the calculations needed for predicting the world's weather using this primitive method. Also, his results were quite poor.

Little did he know about computers to be invented just a few decades later. They would really help with the mathematics used in meteorology. With these new machines and a few major refinements in the theory, numerical forecasts became a reality in the early 1950's.

And they have improved, believe it or not, in the several decades following that. We now rely on the models extensively. That's because they have incorporated things like chaos theory and can give ensemble forecasts, which allow for changing probabilities and small statistical variations giving very different results.

It just keeps getting better. Thanks to the mathematics used in meteorology.

At least that's what some people think. Do you think math helps us to understand our world? Succeed at work? Use a computer?

You bet. That reminds me, it can help make you a better gambler if you're so inclined.

What's the most important thing math helps you with?

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Examples of the mathematics used in meteorology.

Introduction to variables, equations and numerical weather prediction.

**Are you concerned about Air Pollution in your area?**

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