# Seeking finer points of slope statistics within set of polygons?

I have a few questions related to finding slope statistics (min, max, mean, standard deviation) of slopes (1-meter LiDAR DEM derived) within a set of polygons (census blocks).

First; Is it valid to average slopes (degree or percent)? This is a big question I guess but could someone tell me if there is a way to use slope percent in the averages. Are there any other methods other than simply adding up the values of raster cells and dividing by the number of cells? (not addressed elsewhere)

Would it make more sense to present every slope value available (within each polygon) at the highest resolution (1-meter) and present the range within 1 or 2 standard deviations of the mean slope? One of the key statistics that I am looking for is the range of slopes within each polygon but perhaps presenting slope values within one standard deviation would suffice. Currently my method is to resample a 1-meter DEM to 10-meters to remove the extreme values and then use zonal stats to get the mean, min and max (this question is not addressed elsewhere) ...

Is there any other way to average the slope that takes into account partial cells? One method I thought of was to resample the raster down to a finer resolution.. e.g. 30-meters to 1-meter and then averaging the slope using zonal stats. This is kind of a rough integration.. is there a more elegant/perfect way to do this? (not addressed elsewhere)

I'm using ArcGIS 10.2 for Desktop.

## 1 Answer

I think the most appropriate way to average slope is using trend.

1. Clip LiDAR using individual meshblock geometry
2. Convert clipped raster to points
3. Interpolate point using TREND with polynomial order =1, i.e. linear. Specify output RMS file, say cba.txt
4. RMS file contains coefficients (C,B,A) for the flat sloped surface Z=C+BX+AY
5. The slope of above surface = sqr(B * B + A * A)