Q:

Spatially joining large raster to polygon shapefile

I have a large raster file with elevation data. From this raster, I would like to infer the average ruggedness for different geographic zones (like countries). I have the "countries shapefile" as a separate polygon shapefile. 
I was able to get a raster file with a ruggedness measure. 
However, this raster is still very large. It is therefore not possible to convert it to a shapefile to do a spatial join of the two shapefiles. 
Since I do not need very precise data, is it possible to either: 

convert my raster to a shapefile with an output that has larger cells than the default (I did not find this option)
directly spatially join the raster to the polygon shapefile

Do you have any advice?
I use ArcGis10, Gdal, and Qgis 1.8

A:

This is what zonal raster functions are for. You can obtain zonal variance by using the ArcGIS "Zonal Statistics as Table" tool and then taking the square-root of the standard deviation. Variance is a simple and common measure of roughness. 
Your polygon feature-class of countries would be your zone data and your elevation raster would be the value raster. It is quite easy to then join the resulting zonal statistics back to your polygon feature-class based on the FID.    

