### 8.4 Do you need a weathervane to see which way the wind blows?

Meteorologists use terms such as northeasterlies and southerlies when they describe winds. These terms designate directions that the winds *come from*. But when we think about the dynamic processes that cause the wind, we use the conventions for direction that are common in mathematics and in coordinate systems like the Cartesian coordinate system. The conversion between the two conventions—math and meteorology—is not simple. However, we will show you a simple way to do the conversion (see the second figure below).

### Math Wind Convention

The wind vector is given by **U** = **i **u + **j **v + **k **w**. **The wind vector points to the direction the wind *is going*.

The subscript “H” will be used to denote horizontal vectors, such as the horizontal velocity, *U**_{H} = i u + j v * (though note that sometimes the symbols

*,*

**V**

**v**_{H}, and

*will be used to denote the horizontal velocity). The magnitude of*

**v****is**

*U*_{H}*U*(

_{H}=*u*

^{2}

*+ v*

^{2})

^{1/2}. The

**$\alpha $, is the angle of the wind relative to the**

*math wind angle,**x*-axis, so that tan($\alpha $)

*= v/u*and the angle increases counterclockwise as the direction moves from the eastward

*x*-axis ($\alpha $ = 0

^{o}) to the northward

*y*-axis ($\alpha $ = 90

^{o}) .

### Meteorology Wind Convention

The meteorology wind convention is often used in meteorology, including station weather plots. The wind vector points to the direction the wind *is coming from*. The angle is denoted by delta, $\delta $, which has the following directions:

direction wind is coming from | angle $\delta $ |
---|---|

north (northerlies or southward) | 0^{o} |

east (easterlies or westward) | 90^{o} |

south (southerlies or northward) | 180^{o} |

west (westerlies or eastward) | 270^{o} |

### Relationship Between Math and Meteorology Wind Conventions

Meteorology angles, designated by $\delta $, increase clockwise from the north (*y*) axis. Math angles, designated by $\alpha $ , increase counterclockwise from the east (*x*) axis.

In the diagram on the left, the wind is southwesterly, the meteorology angle (measured clockwise from the north or y-axis) $\delta \text{}=\text{}{225}^{o}$, and the math angle (measured counterclockwise from the east or x-axis) $\alpha \text{}=\text{}{45}^{o}$. If the wind is northerly (southward), the wind vane points to the north, the wind blows to the south, $\delta \text{}=\text{}{0}^{o},\text{}and\text{}\alpha \text{}=\text{}{270}^{o}$. If the wind is westerly (eastward), $\delta \text{}=\text{}{270}^{o},\text{}and\text{}\alpha \text{}=\text{}{0}^{o}$.

Note that in all cases, we can describe the relationship between the math and the meteorology angles as:

$$math\text{}angle\text{}=\text{}27{0}^{o}-\text{}meteorology\text{}angle$$

When the meteorology angle is greater than 270^{o}, the math angle will be negative but correct. However, to make the math angle positive, simply add 360^{o}.

Drawing a figure like those shown in the figure above often helps when you are trying to do the conversion. The following video (2:17) explains the conversion between meteorology and math wind angles using the figure above.

#### Quiz 8-2: Finding coordinates and wind directions.

- Find
**Practice Quiz 8-2**in Canvas. You may complete this practice quiz as many times as you want. It is not graded, but it allows you to check your level of preparedness before taking the graded quiz. - When you feel you are ready, take
**Quiz 8-2**. You will be allowed to take this quiz only**once**. Good luck!