Map algebra

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Map algebra is a simple and an elegant set-based algebra for manipulating geographic data.

Map algebra was proposed by Dr. C. Dana Tomlin in early 1980s. Tomlin proposed primitive operators for processing geographic data. Depending on the spatial neighborhood, operators are categorized into four groups: local, focal, zonal, and incremental. The input and output for each operator being map, the operators can be combined into a procedure to perform complex tasks.

Map algebra is a way to perform geographic analysis and processes on raster data sets using algebraic expressions. It can be used to manipulate geographic data to obtain desired information or results such as converting units, combining values, selecting data with specific ranges and much more.

The algebraic expressions generally have an input and operation and an output An example of this is

           (output)Raster_new = (Input)raster1 (+ raster2)

The expressions used can be very simple like the example above or they can be very complex and consist of many parts.

Arithmetic operators can be used to add subtract, multiply and divide. For example if you had raster data sets from 3 different years containing rainfall amount you could find the average of the three by using map algebra and adding them together and dividing by three.

Relational operators like equals, greater than, less than etc., allow you to return true or false results. For example if you were trying to find farms that grew corn you could have an expression like: crop = corn.

Boolean operators like AND, OR and NOT allow you to use multiple conditions is an expression, For example if you wanted to pick an area to put a farm you might want to find a place that had high average temperatures and high precipitation. The AND operator would allow you to enforce both of these conditions.

GIS software contain many map algebra functions already made to perform specific tasks so that you do not have to create them yourself. Some examples are functions that calculate slope or create a shaded relief from an elevation data set.

There are four basic function types:

• Local: this operates on and individual cell in the grid and the output comes from the corresponding input cell
• Global: this function take the input of every cell in the entire grid to create its output
• Focal: A target of focal cell is assigned a value coming from an analysis of the cells around it.
• Zonal: takes a group of cells that are classified by some common characteristic and then average measured values for those cells and assign that value to the output cell.

[edit] References

• Demers, Michael N., Fundamentals of Geographic Information Systems
• Map Algebra, ArcGIS Spatial Analyst, www.esri.com, Accessed 7 September, 2011.
• Huber, William A. Introduction to Map Algebra. Penn State - Great Valley, Accessed 7 September, 2011.
• Hurvitz, Phil, Raster Analysis & Map Algebra, FM 490, University of Washington, College of Forest Resources, Accessed 7 September, 2011.
• Grid function types in Raster Analysis I, ESRM 250, Introduction to Geographic Information Systems in Forest Resources, University of Washington. Accessed 7 September, 2011.
• Map Algebra, Department of Geography and Environmental Studies, Bar Ilan University. Accessed 7 September, 2011.