METEO 300
Fundamentals of Atmospheric Science

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

weathervane on top of building with moon and blue sky behind
Weathervane
Credit: Justin Otto via flickr

Meteorologists talk of 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 V = i u + j v + k w. The wind vector points to the direction the wind is going.

Using the subscript “H” to denote wind in the horizontal direction, VH = i u + j v and the magnitude of VH is Vh = (u2 + v2)1/2. The math wind angle, αThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , is the angle of the wind relative to the x-axis, so that tan( αThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. ) = v/u and the angle increases counterclockwise as the direction moves from the eastward x-axis ( αThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. = 0o) to the northward y-axis ( αThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. = 90o) .

Meteorology Wind Convention

typical weather station plot
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. The wind vector points to the direction the wind is coming from. The angle is denoted by delta, δThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , which has the following directions:

Wind Angles
direction wind is coming from angle δThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
north (northerlies or southward) 0o
east (easterlies or westward) 90o
south (southerlies or northward) 180o
west (westerlies or eastward) 270o

Meteorology angles, designated by δThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , increase clockwise from the north axis. We use the terms like “southward,” “eastward,” northwestward” to denote the direction the wind is going. Note that δ=θ+ 180 o This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. . Math angles, designated by αThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , are measured going counterclockwise from the x-axis.

Diagram for converting between meteorology and math wind directions for winds blowing from three different directions as described in the text below
Diagram for converting between meteorology and math wind directions for winds blowing from three different directions. Note that the barbs on the wind line point 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 this diagram, the wind is southwesterly, the meteorology angle (measured CW from N) δ =  180 o +Θ =  225 o This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. , and the math angle (measured CCW from the x axis) α =  45 o This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. . 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 This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. . If the wind is westerly (eastward), δ =  270 o , and α =  0 o This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. .

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

math angle = 27 0 o   meteorology angleThis equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

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

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.

Click here for a transcript for Wind Meteo Math Video

Quiz 8-2: Finding coordinates and wind directions.

  1. 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.
  2. When you feel you are ready, take Quiz 8-2. You will be allowed to take this quiz only once. Good luck!