Map algebra
Dr. Amy Griffin
Masaryk University, Brno
25 April 2018
Learning objectives
• Define map algebra.
• Explain the differences between and provide
examples of local, focal, zonal and global map
algebra operations.
• Construct a model diagram that captures the
steps of a map algebra analysis.
Inventors of
the concept
C. Dana Tomlin
Joseph Berry
(mapematics)
The general idea
• Layers
Input(s)
Output(s)
• Operators
• Functions
More complex
combinations of
operators & layers
Layer
Function
Operator
4 kinds of map algebra operations
•Local
•Focal
•Zonal
•Global
Decreasing scale
(increasing size)
of area required
for the operation
Local Operations
Operates on a cell-wise
basis (pixel by pixel).
Arithmetic, Statistics, Relations, Trigonometric,
Exponential/logarithmic, Reclassify
Focal Operations
Operates on a cell using
information from
neighbours (window)
Examples: low-pass filter, slope, aspect
Zonal Operations
Performs an
operation on a
cell based on cells
within a zone that
contains that cell. Example: calculate the
maximum value in that zone.
Global operations
An operation on an
individual cell depends upon
the values of ALL cells
example:
Euclidean
Distance
operation
Prerequisites for Map Algebra
• Raster pixels need to line up across layers
• Map projection needs to be the same
• Spatial resolution needs to be the same
• Handling No Data values:
• No Data + 1 = No Data
• 0 + 1 = 0
Examples
(from Berry’s Tutorial Map Analysis Package)
1 * 1 * 1 = 1 0 * 1 * 1 = 0
Still working with binary data, but
adding instead of multiplying
Rankings instead of binaries
Adding in proximity analysis (buffers)
And make those buffer sizes depend
on slope
Map Algebra Inputs
Find ‘best’ campground location
1) Gentle slope
2) Near roads
3) Near water
4) Good views of water
5) Westerly aspect
Derive criteria from inputs
Derive criteria from inputs
Derive criteria from inputs
Derive
preferences
from criteria
Combine
preferences
ConstraintsNot too close to the road
Not on slopes over 50%
Combine
constraints with
preference map
Final
suitability
map
Summary
• Map algebra takes multiple map layers and
combines them using mathematical and logical
operations.
• Pay attention to raster data requirements
(same map projection, same spatial resolution).
• Multistep analysis with map algebra can build
powerful models to solve multicriteria spatial
problems.
References
• Berry, J., Reed, K.L. (2008). MapCalc Learner software.
http://www.innovativegis.com/basis/MA_Workshop/MapCalc_download.
htm Last accessed 24 April 2018.