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I assumed hillshades output percent shaded (scaled to 255) at the given azimuth and altitude but this is incorrect. A flat raster at 80 degrees altitude has a maximum value of 251 instead of 255. How can I go from a hillshade to percent shaded and can I simply divide by the cosine of the 10 degrees in this case to get the correct value or is it more complicated?

Here is some R code with gdaldem that may help you see what I'm seeing:

library(raster)
r <- raster(ncol=100,nrow=100)
values(r) <- rep(1,ncell(r))
writeRaster(r,"flatelevation.tif")
system("gdaldem hillshade -az 180 -alt 80 flatelevation.tif hillshade_flat.tif")
hs <- raster("hillshade_flat.tif")
summary(values(hs))
summary(values(hs)/cos((90.0-80.0)*pi/180.0))

I will try to parse the source code but it's been ten years since I've used C++.

Can someone with general knowledge about hillshades point me the right direction?


I thought I could get a "percent of the tile that is shaded" from running a hillshade. Upon further reading a hillshade outputs the illuminance of each tile. So, the cosine is only part of the equation, I would need to pull in the slope and aspect as well for additional trigonometric readjustments, and maybe more.

Turns out there are tools that are functionally equivalent for that I need called "shadow masks" that only output 1 or 0, indicating whether the tile is shaded.

This nail biting article referenced in gdal's source code helped enlighten me, in addition to this question on cloud shading, this question on solar maps, and this question on r.sun where a contributor indicates that r.sunmask is slow. A couple available tools:

GRASS r.sunmask

RSGISLib Elevation Module: shadowmask

USGS ISIS Shadow

Of course I need the speed of gdal's hillshading so I'll keep this question up until I or others come up with a solution that can process a 1000 square mile area in a second.

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    Please tell us what you mean by "percent shaded". For the flat raster case the value of 251 looks correct, because sin(80 degrees)*255 = 251 when rounded. – whuber Aug 22 '14 at 0:51
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So I think the answer is effectively no. You can't get a percent shaded from a hillshade. You can get an estimated shadowed mask. The confusing bit here is that unlike the description here gdaldem hillshade outputs 1 instead of 0 for shaded tiles. Postgis's ST_Hillshade outputs 0 but takes around 20 seconds on my system version 0.5 seconds.

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