Comprehensive Operations:
Incremental Operations

Up to now, the operations have been limited by the spatial neighborhood (either by superposition/overlay or by a distance-based search). There is a set of operations that are not confined to any fixed neighborhood.

This is the list that critics want a GIS to perform to become more 'analytical'.

The first set of comprehensive operations are incremental operations - operations that use a series of neighborhood operations to move a local result into a global context.

Iterative operations:

• Viewshed radiate visual obstructions, determine visibility on a terrain
• Cost Accumulation propagate cost (plus) to neighbors
• Drainage accumulate flow downhill to sink
• Network Operations

• Shortest path (without capacity effects)

Viewshed

Intervisibility (what can be seen from where) can be computed based on a set of rays radiating outwards from a vantage point. In a complex 3D situation, there are many effects to calculate, but on a surface the surface can only obstruct a view by rising above the line of sight.

Intervisibility can be applied to human vision, hence issues like scenic beauty and property values, or to other forms of electromagnetic radiation, such as FM radios, cellular telephones and personal communication networks.

A diagram along a line of sight:



A viewshed is the area seen from a given vantage point (or points). It assembles all the areas where the line of sight is rising as the rays move outwards. The yes/no values can be summed to give a cumulative sense of how many times a place is seen.

A procedure to calculate viewshed operates incrementally, working outwards. A 'Horizon line' holds the highest vertical angle yet seen in each direction. A new location (such as a cell in a raster implementation) is tested against the horizon line to check if it is hidden (below) or visible (above). Locations must be visited in the order in which they might be seen, hence the iterative nature of the operation. Visible locations then can be marked as a part of the viewshed.

Some resources: The ESRI "white paper" about 3D analyst (has the visibility operations) | ArcObjectsOnline has some of the information in the ESRI Help |

Influencing the viewshed

Viewshed calculations depend upon an accurate model of the surface as seen. Topographic maps and topographic databases are constructed for highway engineers and artillery officers to give the ground surface. Vegetation screens the line of sight for many wavelengths (but not all). Vegetation effects are rarely measured, but often added to a surface by adding a constant for each land cover class (often a bit crude).



Viewer height can also influence the result.

USES OF VIEWSHEDS:

• Military applications (of course; an overview)
  • fields of fire, etc.
  • Border Patrol; cameras and infrared sensors
  • GPS signal availability
• Viewshed for Scenic Beauty (early usage)
  • Vista Scenic Beauty
  • Parkway siting
• Cell-phone towers
• Solar Input
• Wind Power Turbine Farms
  • Example from Wales; cumulative viewshed results
• Archeology
  Settlement visibility in Palestine

Error in the elevation data influences the viewshed, usually by reducing its size. See:

Fisher, Peter F. 1993: Algorithm and implementation uncertainty in viewshed analysis. International Journal of Geographical Information Systems 7(4): 331-347.

W. Randolph Franklin also has a large amount of material on simulations of viewsheds with a distinction of certainly viewed, probably viewed, possibly viewed, etc. (site may require modern browser...); NEW! automated observer siting...

Cost Accumulation

An incremental operation can work with a contributory rule to accumulate the total 'cost' outwards from a 'source'. This modifies a straight buffer analysis to some measure of "effort".

First, a realistic cost must be assigned to traverse each area. This thinking is easier in cells, but it could be done for any set of zones. The units of the cost can be in time, dollars or some other ratio measure. The various components of cost must be converted to this common measure.

Then, it may be necessary to convert the cost to traverse a cell into a rate (to handle diagonal movement properly).

An isolated object (point, or line or boundary line) provides the starting location.

A SPREAD operation, (similar to the buffer operator demonstrted with PostIt notes...) moves the cost outwards. Notice that the operation is not strictly geometrical. It is possible for a later 'message' arriving at a location to provide a cheaper cost (passing around a hill in the cost surface).

The result is an accumulated cost surface. (as in the Pipeline example; an example (abstract) for estimating flooded area; very explicit use of Arc/INFO cost-distance for channel habitat; archeological analysis of connection between Iron Age sites; a petroleum pipeline with added environmental costs; wolf habitat in Jasper Park; Wildlife Corridor Study (Montana))

More recent approaches

David Douglas has continued in the tradition of William Warntz (and Ernesto Lindgren) with some improvements to the cellular algorithms for accumulating cost. Sadly his web pages are offline following his retirement. (OK, Mike, this web strategy DOES eventually backfire.)

Drainage

Drainage is most easily visualized on a topographic surface. Water will flow from higher locations (cells, triangles, etc.) downwards. Erosion at one place creates deposition lower down.
Incremental operation works on a surface (such as an accumulated costs surface) to determine minimum cost routes. Uses a local interaction rule. Transmits a message downwards to the lowest cost neighbor. Called "COSTPATH" (or PATHDISTANCE) in Arc GRID (and in the Hydrology Operations group inside Spatial Analyst), this function can be used for a lot of analytical purposes: archeological analysis of settlements; sediment flow, the movie;

Network Operations

Incremental operations can find shortest path in a network and other results. (see next lecture).

Examples: Searching road networks for closure , USGS on what is special (scroll down to networks) | Amazon Basin Project