Map Algebra

Map algebra manipulates geographic raster data sets to produce new map layers.  They can work on a single layer (grid), or combine multiple layers.  Tomlinson is credited with the concept.  In many ways map algebra works like matrix manipulations in Matlab.

The map algebra transformations can use different spatial neighborhoods:

Single layer operations can add a constant, take a log or sin, filter the raster, or compute the slope.  This can operate on the grid in question in memory, provided you take care not to the overwrite the original layer unless you want to do that.

Multiple layer operations can include addition/subtraction, multiplication/division, ratios, or statistics like mean or standard deviation. This often requires creating a new grid, because if you replace values in the original grid, that will affect the computation of its neighbors not yet done. Focal operations must create a new grid, since the values depend on the neighborhood which cannot be overwritten.

Some operations may require several steps in succession.  For example, with a noisy DEM, it might be best to Filter before computing Curvature because as a second derivative, curvature can be very sensitive to minor noise in the input DEM.

You can often combine many operations into one step, but often the intermediate grids will be helpful to help you see the effects of each layer.  If you have five criteria and their result is no acceptable locations, it helps to look at each layer so you can decide which one to change, or to know why there are no acceptable locations.  The ability of the analyst to see the spatial patterns can provide insights the software cannot.


In MICRODEM, map algebra operations are available:

Last revision 11/23/2017