How to calculate wind direction from U and V wind components in R
I have U and V wind component data and I would like to calculate wind direction from these values in R.
I would like to end up with wind direction data on a scale of 0-360 degrees, with 0° or 360° indicating a wind blowing to the north, 90° indicating a wind blowing to the east, 180° indicating a wind blowing to the south and 270° indicating a wind blowing to the west.
Below is some example data:
> dput(wind)
structure(list(u_ms = c(-3.711, -2.2417, -1.8188, -1.6164, -1.3941,
-1.0682, -0.57611, -1.5698, -1.4976, -1.3537, -1.0901, -0.60403,
-0.70812, -0.49045, -0.39849, 0.17875, 0.48356, 1.5082, 1.4219,
2.5881), v_ms = c(-1.471, -1.6118, -1.6613, -1.7037, -1.7388,
-1.8748, -1.8359, -1.6766, -1.6994, -1.7505, -1.4947, -0.96283,
-1.1194, -0.6849, -0.7847, -0.80349, -0.19352, -0.97815, -1.0835,
-0.81666), u_rad = c(-0.064769155, -0.039125038, -0.031744042,
-0.028211496, -0.02433163, -0.018643603, -0.010055014, -0.027398173,
-0.026138045, -0.023626517, -0.01902583, -0.01054231, -0.012359023,
-0.008559966, -0.006954961, 0.003119775, 0.008439712, 0.02632305,
0.024816831, 0.045170857), v_rad = c(-0.025673788, -0.028131211,
-0.028995149, -0.029735168, -0.030347779, -0.032721426, -0.032042493,
-0.029262184, -0.029660119, -0.030551982, -0.026087431, -0.01680455,
-0.019537212, -0.011953758, -0.013695596, -0.014023543, -0.00337756,
-0.017071935, -0.018910639, -0.014253403)), .Names = c("u_ms",
"v_ms", "u_rad", "v_rad"), class = "data.frame", row.names = c(NA,
-20L))
I have used the following code to try and obtain wind direction (column td ), but I am not convinced that the returned angles are those that I want (ie 0°/360° indicating a wind blowing to the north, 90° indicating a wind blowing to the east etc…).
u = wind$u_rad # u component in radians
v = wind$v_rad # v component in radians
d = (180/pi)*(atan2(u,v))
td = as.matrix(d + 180)
df = cbind(wind, d, td)
> df
u_ms v_ms u_rad v_rad d td
1 -3.71100 -1.47100 -0.064769155 -0.02567379 -111.6228 68.37716
2 -2.24170 -1.61180 -0.039125038 -0.02813121 -125.7164 54.28357
3 -1.81880 -1.66130 -0.031744042 -0.02899515 -132.4087 47.59129
4 -1.61640 -1.70370 -0.028211496 -0.02973517 -136.5062 43.49379
5 -1.39410 -1.73880 -0.024331630 -0.03034778 -141.2788 38.72124
6 -1.06820 -1.87480 -0.018643603 -0.03272143 -150.3269 29.67308
7 -0.57611 -1.83590 -0.010055014 -0.03204249 -162.5780 17.42199
8 -1.56980 -1.67660 -0.027398173 -0.02926218 -136.8842 43.11576
9 -1.49760 -1.69940 -0.026138045 -0.02966012 -138.6118 41.38819
10 -1.35370 -1.75050 -0.023626517 -0.03055198 -142.2844 37.71557
11 -1.09010 -1.49470 -0.019025830 -0.02608743 -143.8963 36.10365
12 -0.60403 -0.96283 -0.010542310 -0.01680455 -147.8980 32.10204
13 -0.70812 -1.11940 -0.012359023 -0.01953721 -147.6830 32.31699
14 -0.49045 -0.68490 -0.008559966 -0.01195376 -144.3939 35.60607
15 -0.39849 -0.78470 -0.006954961 -0.01369560 -153.0774 26.92258
16 0.17875 -0.80349 0.003119775 -0.01402354 167.4578 347.45783
17 0.48356 -0.19352 0.008439712 -0.00337756 111.8112 291.81121
18 1.50820 -0.97815 0.026323050 -0.01707193 122.9656 302.96561
19 1.42190 -1.08350 0.024816831 -0.01891064 127.3077 307.30771
20 2.58810 -0.81666 0.045170857 -0.01425340 107.5128 287.51279
I would appreciate any advice on whether my method is correct, and if not how I could correctly obtain the desired wind direction values. While Calculating wind direction from U and V components of the wind using lapply or ifelse was helpful, the code did work with my data, and I am sure that there is an easier away to obtain wind direction. Many thanks!
There are three problems with this:
atan2 , you must normalize them, but you don't do this by multiplying m/s by pi/180 (which you did to get u_rad and v_rad ). You should make a column of absolute windspeed ( sqrt(u_ms^2 + v_ms^2) ) and take atan2(u_ms/wind_abs, v_ms/wind_abs) . (also note that atan2 takes y component first - make sure that's what you want) atan2 will give you an answer in the unit circle coordinates, which increase counterclockwise and have a zero on the x-axis. You want an answer in cardinal coordinates which increase clockwise and have a zero on the y-axis. To convert unit circle to cardinal coordinates, you must subtract the unit circle angle from 90. If you are given u_ms = = -3.711 and v_ms = -1.471 (on the unit circle it is blowing down and slightly to the left, so it is coming from the northeast), then:
wind_abs = sqrt(u_ms^2 + v_ms^2)
wind_dir_trig_to = atan2(u_ms/wind_abs, v_ms/wind_abs)
wind_dir_trig_to_degrees = wind_dir_trig_to * 180/pi ## -111.6 degrees
Then you must convert this wind vector to the meteorological convention of the direction the wind is coming from:
wind_dir_trig_from_degrees = wind_dir_trig_to_degrees + 180 ## 68.38 degrees
Then you must convert that angle from "trig" coordinates to cardinal coordinates:
wind_dir_cardinal = 90 - wind_dir_trig_from_degrees
[1] 21.62284 #From the northeast.
While the accepted answer has the right idea it has a flaw. As mentioned in the comments one does not need to normalize the u and v component in order to use atan2 on them. The flaw comes when u == v == 0 and wind_abs becomes 0. In C# the two divisions will return infinity (in compliance to IEEE 754) and atan2 will return NaN. When not normalizing the components atan2(0,0) happily returns 0 . So not only is normalizing not necessary, it also introduces an error.
Please also be aware that the most common function signature of atan2 is atan2(y, x) -- Microsoft Excel being an exception.
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