# How do I represent wind direction on a UTM (Universal Transverse Mercator) map projection?

What does it mean when I say "the wind direction is 50o" on a UTM map? Which direction is the 0o reference?

For example, if I draw a wind vector V as seen in the image below, what degrees does it correspond to for the UTM map?

Meteorological winds are referenced from North being 0$^{\circ}$ increasing in a clockwise direction. Additionally, they are named for the direction the wind is coming from. Your vector on the map, which is mathematically 45$^{\circ}$ is meteorologically 225$^{\circ}$ aka a southwesterly wind.

• A 0$^{\circ}$ wind is a wind from the north (math vector 270$^{\circ}$).
• A 180$^{\circ}$ wind is wind from the south (math vector 90$^{\circ}$).
• A 50$^{\circ}$ wind is from the northeast (math vector 220$^{\circ}$).

In general if $\alpha$ is the mathematical angle and $\beta$ is the meteorological angle, then the relation between the two conventions is given by $$\alpha = 270^{\circ} - \beta$$ where angles are specified in degrees.

Image from https://www.e-education.psu.edu/meteo300/node/719 from Penn State available under CC-by-nc-sa-3.0

This answer was initially wrong. Thank you to mkennedy for pointing this out. I have now corrected it.

Casey's answer is a good one with respect to interpreting a wind direction in general. However, you specifically asked about doing so on a UTM projected map, which implies that you're aware that in some projections, the direction of North on the page varies from point to point.

This is indeed true for UTM. UTM is a transverse Mercator projection, which means that most lines of longitude follow curved paths on the projected map.

However, UTM is used in narrow zones, as shown in the image in the question. The central meridian of each zone (the line running from north to south in its centre, which has an easting of 500,000m) aligns with a line of longitude, so "up" on the grid corresponds to north. Either side of this the angle of north will diverge, but so long as you are using the correct UTM zone, this divergence should be small (a maximum of about 3 degrees at high latitude at the edge of a zone, less otherwise). Therefore, for many purposes it is still useful to consider a wind direction as an angle on a UTM map.

If greater precision is needed, then some calculation will be necessary - searching for "UTM grid declination" provides a few explanations of how to do this, although I think many are simplified. (I'm not qualified to go into detail on the maths)

• That is true for the wind direction at a point, but be aware that you won't be able to show the path of the wind flow lines across the globe unless you correct for the distortion in the projection. Edit: um, thinking about it, I'm not sure my comment is correct so please correct me if I'm mistaken. – haresfur Dec 7 '15 at 2:17
• UTM (universal transverse Mercator) does not maintain "true" or geodetic North. This is the north along a line of longitude. While TM is a conformal projection that maintains shapes/angles, it does not maintain direction. "North" or "up" on a UTM map is grid north, not true north. Some info here. – mkennedy Dec 7 '15 at 21:51
• @mkennedy ach, thank you, you're quite right. For some reason I had been thinking that vertical grid lines would align to lines of longitude, which is obviously silly - IIRC that's Mercator rather than Transverse Mercator. Am I right that within a given UTM zone, grid north and true north will align at the (east-west) centre of the zone? Let's make sure I actually understand, then I'll update the answer... – Semidiurnal Simon Dec 7 '15 at 23:59
• @SimonW Yes, that's true about the central meridian/longitude of center. – mkennedy Dec 8 '15 at 0:00
• @mkennedy thanks - answer now edited to actually be right (I hope) – Semidiurnal Simon Dec 8 '15 at 0:29