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I'm working on a DEM in the Arctic region (initially in a NAD83 coordinate system) and I projected it into a North Pole Stereographic Cartesian coordinate system to compute slope and aspect. Now, because of the distortions, slope and aspect have to be corrected.

I corrected the slope without much trouble (Using SRTM Global DEM for Slope calculation?) but I'm stuck with the aspect correction.

I carefully read the suggestion made in How to use SRTM Global DEM for Aspect calculation? to add the longitude of the location + 90 degrees to the computed aspect value but it doesn't work as expected in my case (some values are negative as far as -87 degrees). I am not sure that the person was speaking about the same polar projection I'm using (he spoke about a Northern Stereographic projection while I use a North Pole Stereographic with Greenwich as prime meridian: 0.0).

Here are the characteristics of the projection I use:

Prime Meridian Greenwich   0.0
False Northing             0.0
Central Meridian           0.0
False Easting              0.0
Linear Unit Meter          1.0
Latitude of Origin        90.0

After much trial and error, I am looking now for any general formula for this aspect correction, taking into account the characteristics of the projection I use (or any other projection if it exists).

EDIT:

I have tried the method mentioned in my comment and I still have doubts about the results. I still have an offset of more or less 70 degrees between the aspects produced using Mercator (which are correct) and the aspects produced with a North Pole projection which are corrected by subtracting the longitude and then adding or subtracting 360 if the obtained result is < 0 or > 360 respectively. Any further ideas welcome...

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Marc
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    I think you mean that the central meridian / longitude of origin was at Greenwich / 0.0. Prime meridian is used to identify the origin of longitude values. Meanwhile, why didn't or why don't you use a custom stereographic projection with the CM set to the center of your data? Wouldn't that reduce any distortions in the slope and aspect values? – mkennedy Dec 28 '16 at 18:39
  • I have no experience with custom projections, so I didn't even think about this possibility. Will dig a little bit, thanks for the idea. My data spans from Western Alaska to Eastern Canada so I guess there will be distortions anyway. In fact I started the correction procedure using Mercator which worked very well for Alaska and Western Canada, but part of my DEM is located in the northern part of Nunavut and Mercator produced lots of artifacts there. – Marc Dec 28 '16 at 19:12
  • So I switched for a North Pole Stereographic projection. I can use something else though, I use it because it's conformal so I thought it would be easier to correct the aspect afterward... – Marc Dec 28 '16 at 19:12
  • In fact I think the solution is not far from the aspect + longitude + a X value (90, 180, 270), but I can't figure out how to be 100% sure of what I'm doing, that's why I would like some sort of formula that is valid for any location on the map.. – Marc Dec 28 '16 at 20:03
  • Found an "short note" for correcting aspect in Antarctica here: https://www.researchgate.net/publication/248620369_Correcting_GIS-based_slope_aspect_calculations_for_the_Polar_Regions. If applied to the Arctic, one apparently has to subtract the longitude to the calculated aspect. Then if the result is < 0 then add 360. If the result is > 360 then subtract 360... – Marc Dec 29 '16 at 09:12
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    If you don't use a Polar stereographic projection, then the aspect correction becomes next to impossible, so please ignore any suggestions to customize the projection to a different center. The procedure I gave for correction works, but there's nothing I can do to diagnose your problem because you haven't provided any actionable information about what is actually going wrong. – whuber Dec 30 '16 at 21:46
  • I think it's in part because the projection I use is not centered on North America, but on Greenwish so in my case I think I don't need to add the 90 degrees you suggest in the other post. Also, as longitudes go from -180 to +180, I get negative results for some aspect values if I don't correct for the negative longitudes (e.g. aspect = 10, lon = -170 -> even +90 you get -70). – Marc Dec 31 '16 at 08:23
  • The method I found in the document posted above seems to answer this two things as well. However, I systematiclly get different values for the corrected aspects compared to the aspects I computed using Mercator (which serves as a reference when I compare both results in Alaska where Mercator still works well). But visually, I don't have any mean to check if the aspects I get in the Arctic are correct or not, as far as I know... – Marc Dec 31 '16 at 08:25

1 Answers1

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So. I think I found a solution.

  1. Compute the aspect as usual using the North Pole Stereographic projection.
  2. For each cell, add the longitude of the cell to the aspect.
  3. Add 360 if the obtained result is less than 0, subtract 360 if the result is more than 360, do nothing otherwise.

It seems to work. Now the values I get are similar to the ones I obtained using Mercator. Visually, the northern facing slopes seem well oriented as well. Thanks whuber for his above mentioned, informative related posts!

Marc
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