northerness, easterness and slope - some proxies if a cell is "sunny"

In (plant) ecology the importance of solar radiation has been recognized for a long time.

Northerness, easterness and slope may be some of the simpler proxies for solar radiation which can be calculated by GIS.

As aspect is a circular land-surface parameter, a sine (eastness) or cosine (northness) transformation can be used to obtain a continuous gradient, stressing the north-south or east-west gradient.

In the northern hemisphere for instance, slopes facing south receive more potential insolation than those facing north; a relation between northerness and slope can also be established.

Let's do some calculations with

Open Data

• Digital terrain model of Tyrol (10m x 10m)

and

Open Source

• GDAL - Geospatial Data Abstraction Library 
• GRASS GIS
• r.northerness.easterness

The commands are as simple as

# build a VRT from a list of datasets
gdalbuildvrt -input_file_list dem_tiles.txt dem.vrt

# r.external - Links GDAL supported raster data as a pseudo GRASS raster map
r.external input=C:\data\dem.vrt output=dem10m

# calculation of northerness, easterness and the interaction between northerness and slope
r.northerness.easterness --verbose elevation=dem10m

 The result maps of r.northerness.easterness are

• northerness: cos(aspect)
• easterness: sin(aspect)
• interaction between northerness and slope: northerness*slope

DEM 10m x 10m

DEM 10m x 10m (zoomed)

easterness

easterness (zoomed)

northerness

northerness (zoomed)

northerness*slope

northerness*slope (zoomed)

 Let's do some checks in the field.