# Using Spherical Standard Deviation to identify ledges on steep cliffs? [closed]

I have been implementing the approach highlighted here: Finding regions or zones in raster DEM of similar slope or aspect values in ArcGIS for Desktop?

to calculate firstly the "spherical variance" and then the "spherical standard deviation (SD)" on a 50 cm DEM of an island.

My intention is to identify the ledges that may exist on the cliffs of the island and the relatively flat areas.

However, I have found it difficult to identify and justify how to classify the resulted spherical SD values. In particular, I understand that the closer the values are to zero, the more likely the variation of slopes in these areas is smaller (i.e. gentle and flat areas). In my understanding, I could classify such areas as the ledges I am looking for. However, I am unsure up to what values of spherical SD ledges can be classified (i.e. SD=0.1 or SD=0.2 and so on).

I seek answers pointing me to the threshold that I could set in my pursuit of classifying spherical SD values as flat areas and ledges. Ideally, a book or a scientific paper that has done something similar would be perfect.

• You don't need the full information supplied by the spherical variance (or, really, the normal vector field to the surface). If by "relatively flat" you mean nearly horizontal, then you can identify those regions by their low slopes. The cliff areas have extremely high slopes. Aspect appears irrelevant to your query. Please check out related threads at gis.stackexchange.com/questions/325, gis.stackexchange.com/questions/79490, and perhaps even gis.stackexchange.com/questions/53274. May 16, 2018 at 11:07
• My simple mind was thinking something similar, nothing as fancy as spherical variance. Compute a slope raster, the ledges on your cliffs will have low slope values with steep values on either side. You can identify these "slivers" of low slope due to their proximity to the edge of the island, or if you buffered out from the sea inland. My only concern is that ledges on cliffs tend not to be very wide and would the resolution of the DEM be sufficient, you might need to move to the resolution of lidar to identify such features? May 16, 2018 at 11:17
• Were the comments by whuber and Hornbydd useful to you? If so, can you update your question with where you are now still stuck, please? Or if you are no longer stuck perhaps you can post a self-answer?
– PolyGeo
Jun 25, 2018 at 22:59
• Hi all, first of all, thank you so much for your comments and efforts to help me. To be honest, I did not have enough time to work on this project yet, but so far I am using the simple results of the "slope" tool to identify relative flat areas on the cliffs. However, I believe that the particular links that @whuber has shared with us will be proved very useful in the near future. I will update this thread as soon as I have made more progress. Thank you for your interest and support. Jul 2, 2018 at 9:47
• OK - since you are not actively working to get your question answered I'll put it on hold, pending you editing your question (which will put it into the review queue) or when you or anyone is ready to answer it just flag us to do so.
– PolyGeo
Jul 4, 2018 at 5:20