seeking "Available Sky" implementations

Question

I'm looking for implementations of an algorithm called "Available Sky". ArcGIS (Spatial Analyst or GRID) is preferred, but solutions in GDAL, SAGA GIS or others are perfectly acceptable.

The description I have is "a method to quantify the influence of terrain on GPS radiocollar performance by creating a variable called "Available Sky" (Rodgers et al. 1997). ... AS is the proportion of sky available to GPS radiocollar through a direct line of site in all directions and at all angles without terrain obstructions (disregarding forest cover). ... locations on mountain tops have high AS values ... conversely locations in valley bottoms are low due to mountain ridges on either sides [lateral obstructions]" -- paraphrased from 'GPS radiotelemetry error and bias in mountainous terrain', Robert G. D'Eon, Robert Serrouya, Graham Smith, Christopher O. Kochanny; Wildlife Society Bulletin 2002.

The paper goes on to describe, in outline only, a process of comparing a base elevation model with a coarser "sky" raster set x100m higher than the highest point of the dem. The process is to calculate direct line of sight for each dem point to each Sky point, arriving at an AS value is the proportion of the total number of sky points visible from that location.

Answer 1

It seems like there should be a way to derive AS from a skyline graph created using the ArcGIS 10.0 3D analyst. If you have a skyline (3D polyline) that surrounds an observation point, it should be able to step through each vertex on the skyline and find some portion of a sphere that is visible.

Or, if you moved each vertex so that it is one unit distance from the observation point, but having same direction from it, it seems the shadow volume would correspond to the AS.

Answer 2

This is really a comment on Kirk Kuykendall's excellent answer (why has no one been perspicuous or generous enough to vote it up yet?), but I don't have the rep to post a comment.

Kirk suggests

It seems like there should be a way to derive AS from a skyline graph created using the ArcGIS 10.0 3D analyst.

I haven't seen that graph, but presumably it is a plot of horizon elevation (as an angle, or something equivalent to an angle) versus azimuth. OK: since you have a GIS, use it! Treat the azimuth as longitude and the angle (appropriately expressed) as latitude, project the plot using an equal-area projection, and compute the area of the polygon it encompasses: that's directly proportional to the solid angle subtended by the sky. (You have to take some care that you're not computing the area of the complementary polygon, which is the solid angle blocked by the earth.)

In the raster world, the AS calculation has been rediscovered many times (e.g., as "topographic openness" (1)). Unfortunately the obvious algorithm takes O(N^4) time where N is the number of rows or columns, making it prohibitive for precise work. Thus, having a vector horizon line is a real asset and it's a brilliant idea to exploit it.

Reference:

(1) Yokoyama R, Shirasawa M and Pike RJ, 2002, Visualizing topography by openness: A new application of image processing to digital elevation models. Photogrammetric Engineering and Remote Sensing, 68(3): 257-265. Scanned pdf available here.

Answer 3

Is this like the inverse of a Viewshed? Though, iteratively creating it would be the hard part, you might think about inverting the surface and using a Viewshed tool as a start.

Answer 4

You might look at GRASS and the r.horizon command. I have not used it, only the related r.sun for calculating solar irradiance, but for a given point you can calculate the horizon angle at whatever directions you specify.

http://grass.itc.it/gdp/html_grass64/r.horizon.html

Answer 5

Yes this is a somewhat commonly queried Q. for calculating min. required elevations of GPS Satellites for telemetry.

What you are seeking is the 'local' horizon created by terrain based on a 3D position.

Thre tools that come to mind are;

GRASS - r.horizon

MicroDEM

Trimble Planning Software

You can use the 'Obstruction Editor' in Trimble Planning Software (free download) and import the output .txt info from GRASS or MicroDEM in the format of (Azimuth, Horizon Angle) I believe... and that should give you your min. req. gps elevation telemetry.

Hope that helps,

Answer 6

In a similar fashion to Kirk's answer, considering the two ends of a skyline as a polyline will join, we can consider it a polygon. My taking the area of the polygon, we have an area of available sky. We can easily determine the area of a polygon where the edges lie on the horizon, thereby allowing us to calculate a percentage of the available sky to an optimal sky.

The other bonus with this method is that we can weight certain areas of the sky, boosting the real world usefulness. We generate a series of polygons in concentric circles, like that of an archery target, with the bulls eye directly above our current position. The outer circles having a higher value (as we know that satellites on the horizon provide better triangulation than those directly overhead). We can now simply work out what percentage of our sky is in high value areas (whether we have satellites in those areas though easily determined, is out of scope here).