Example of mathematics used in meteorology

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

• 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

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.

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

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