# Slope, in which direction?

I have a dilemma? I work with a slope terrain. Slope field is done by a percentage of 10%. My question is, in which direction is oriented this pixel, or any pixels? It is important to know to what direction, if you're designing roads. On image below I represented Slope image, and zoomed 10% slope pixel.  This is result from comments below. This is image made with Qgis2threejs. I still not sure that real slope of each pixel oriented to arrows, like those yellow pixels on top left corner, I mean diagonally. Sorry maybe my answer could be confused. • Possible duplicate of Rotating symbols per attribute value in QGIS? – Andre Silva Jan 5 '18 at 14:16
• You did not understand a question. – nagib Jan 5 '18 at 20:06
• Didn’t you ask how to show slope arrow/symbol per pixel according to aspect direction? How is it different? The answer in the other post goes beyond the accepted answer here; it explains how one can combine information of slope and aspect. – Andre Silva Jan 5 '18 at 20:15
• Since there was no proper answer, I simply accepted what was offered. My question was simple. On which side the pixel is tilted? – nagib Jan 6 '18 at 8:27
• Tks. In this case the answer here is 100% accurate (I thought you wanted to combine information of slope and aspect, as commented beneath the answer). Note I suggested to link “duplicate” questions so users can find the best answer quickly; this does not mean this is not a good question, etc. I upvoted it. – Andre Silva Jan 6 '18 at 11:56

## 2 Answers

With the back-and-forth comments, I am honestly not entirely clear as to what you are after here. In a quantitative sense there are metrics that provide an interaction of slope and aspect, that forest road engineers have commonly used.

One transformation is the Stage (1976) where; alpha=rad(aspect) and theta=percent(slope) which is an a priori assumption of a maximum in the NW quadrant (45 azimuth) and a minimum in the SW quadrant can be replaced by an empirically determined location of the optimum. An resulting value for 50% slope example aspects of 0(N) would be 0.50 at 60E=0.25 at 180S=-0.500 and at 270W=0. The metric ranges from [-1 - 1].

Another slope/aspect interaction is the Balice et al., (2000) site exposure index (SEI) where; alpha=rad(aspect) and theta=deg(slope), which rescales aspect to a north/south axis and weights it by steepness of the slope. The metric represents relative exposure ranging from -100 to 100.

You could also linearize aspect and multiply it by slope. Metrics such as Roberts and Cooper (1989) Topographic Radiation Index (TRASP) not only linearize aspect but recenter it around an expected. In the case of TRASP, aspect is re-centered around a north-northeast azimuth and has a range of [0-1].

These functions are all available in the ArcGIS Desktop/Pro Gradient Metrics Toolbox.

The direction of a Slope is known as its Aspect. It's usually defined as the direction the slope "faces", to me that's a little ambiguous and it's more intuitive to think of it as the "downhill" direction. Slope (the percentage you have already calculated) and Aspect will usually be two separate rasters. Depending on the tool you used to generate the Slope raster, generating an Aspect raster may have been an option, or it may be a separate tool. You can use r.slope.aspect in the GRASS GIS toolbox to generate both Slope and Aspect from the same input elevation raster.

• Ok, I know make Aspect image (I made it with SAGA) but is that solution? Is there way to sum both images to get useful image? Thanks for answer I will try. – nagib Apr 6 '17 at 18:55
• How would you visualize combination of slope and aspect on a flat map? Have you considered to use the profile tool plugins.qgis.org/plugins/profiletool or to create a 3D model with qgis2threejs plugins.qgis.org/plugins/Qgis2threejs? – user30184 Apr 6 '17 at 20:12
• @user30184 One way would be to convert your aspect raster to a point layer and then symbolize the points with an arrow pointing in the direction of the downslope. – Dan C Apr 6 '17 at 20:30
• @DanC, how one would symbolize the points with an arrow in the direction of the downslope? Is this an option in the symbology menu? Please, let me know if you decide to expand your answer. Tks. – Andre Silva Jan 3 '18 at 23:32
• @AndreSilva It's an option under the Style tab, these answers covers it: gis.stackexchange.com/questions/224032/…, gis.stackexchange.com/questions/216987/… – Dan C Jan 3 '18 at 23:40