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

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

Weathervane

Credit: Justin Otto(link is external) via flickr

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 v will be used to denote the horizontal velocity). The magnitude of U_H is U_H = (u² + v²)^1/2. The math wind angle, $\alpha$, is the angle of the wind relative to the 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

In this station weather plot, the wind is blowing from the southwest.

Credit: NOAA National Weather Service

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

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.

Diagram for converting between meteorology and math wind directions for winds blowing from three different directions. Note that the part of the wind line that has the barbs points toward the direction the wind is blowing from. In this diagram, we have extended the line past the center of the axis to indicate the direction that the wind is blowing to because this is the line needed for the math angle.

Credit: W. Brune

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

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

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.