[?] Subscribe To This Site

Example of mathematics used in meteorology

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

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

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

We use instruments to measure wind speed and direction, temperature, pressure and humidity. The 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 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.

meteorology math

Variables for mathematics used in meteorology include:

T for temperature, often qualified with subscripts to denote specific temperatures,
theta, which looks like a zero with a horizontal dash dividing it in half, for potential temperature. That is, the temperature a package of air would change to if it were suddenly compressed to 1000 millibars
P for pressure in millibars
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, give a three dimensional wind field
The Greek letter rho, which resembles a backwards 9, to mean density, a function of pressure, temperature and composition
the most variable 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 only. 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.

The mathematics used in meteorology could, and do, 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 quite often.

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

Meteorology Computers

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 parameter 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 them 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 small statistical variations giving very different results.

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

Math rules!

At least that's what some people think. Do you think it helps us 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?

Give it a title

Here's where you tell me the story. [ ? ]

Got a Diagram, or a photo? [ ? ]

Add Picture Caption (optional)

Author Information (optional)

To receive credit as the author, enter your information below.

Your Name	(first or full name)
Your Location	(ex. City, State, Country)

Submit Your Contribution

Check box to agree to these submission guidelines.

(You can preview and edit on the next page)

What Other Visitors Have Said

Click below to see contributions from other visitors to this page...

wind diagrams
HOW DO ONE DRAW A WIND ROS AND what is the function of these wind diagrams?

Barry's Response - Kelvin:

A wind rose is a plot that shows a breakdown ...

Hydrology Consulting
I have a new hydrology consulting idea. I am a civil engineer specializing in computer modeling of hydrologic phenomena. My primary interest is in finding ...

School
Math is very helpful in school. Of course it helps me in Algebra, but it also helps me in other classes. Like in Science.

The teacher tells us the ...

Search this site for more information now.