# The Atmosphere and the Ocean

## Integrating Mathematical Concepts in the Study of the Atmosphere and the Ocean

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## Mathematical Connections.

Many every day phenomena that pertain to the climate or the weather involve two or more quantities that related to each other by some rule of correspondence. Not all correspondences have simple mathematical relationships, but in most cases there is some rule of correspondence that matches each item from one set with an item from another set. This rule of correspondence is called a function.

Examples of function can be drawn from the following that affects the weather or climate.

Representing functions by sets of ordered pairs is a common practice in discrete mathematics. Example 1

- a) The amount of solar radiation is dependent on the latitude of the city and the position of the earth in its orbit in relationship to the sun.
- b) The seasonal variation in the altitude of the sun affects the amount of energy received by the earth’s surface.
- c) The temperature readings depend on the hour of the day.
- d) The climate of a region is dependent on the latitude, the altitude, and it’s position with respect to a continent or an island.
- e) Climate and weather with respect to the humidity
- f) The type of precipitin with respect to the type of clouds, ocean current, or the wind direction.
- g) Pressure with respect to the air flow.
- h) The wind direction with respect to the earth’s rotation.

Rule : Distance radiation must travel through the atmosphere.

Set A:( Altitude of the sun). | Set B (number of atmosphere) |

example 2 Length of daylight. set A set B latitude summer solstice.

It is sometimes necessary to represent a function by an equation. For example the relationship between pressure and density and pressure and altitude. The relationship between air pressure, temperature can be described as:

Pressure = density x temperature x constant mathematically this can be expressed as P (x) = mx + b ( where x is the variable)

Graphs: Most functions can be expressed geometrically. The Graph of a function ther