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Map algebra

Algebra for manipulating geographic data

  • 8 min read
  • 3 chapters

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History

Prior to the advent of GIS, the overlay principle had developed as a method of literally superimposing different thematic maps (typically an isarithmic map or a chorochromatic map) drawn on transparent film (e.g., cellulose acetate) to see the interactions and find locations with specific combinations of characteristics. The technique was largely developed by landscape architects and city planners, starting with Warren Manning and further refined and popularized by Jaqueline Tyrwhitt, Ian McHarg and others during the 1950s and 1960s.

In the mid-1970s, landscape architecture student C. Dana Tomlin developed some of the first tools for overlay analysis in raster as part of the IMGRID project at the Harvard Laboratory for Computer Graphics and Spatial Analysis, which he eventually transformed into the Map Analysis Package (MAP), a popular raster GIS during the 1980s. While a graduate student at Yale University, Tomlin and Joseph K. Berry re-conceptualized these tools as a mathematical model, which by 1983 they were calling "map algebra." This effort was part of Tomlin's development of cartographic modeling, a technique for using these raster operations to implement the manual overlay procedures of McHarg. Although the basic operations were defined in his 1983 PhD dissertation, Tomlin had refined the principles of map algebra and cartographic modeling into their current form by 1990. Although the term cartographic modeling has not gained as wide an acceptance as synonyms such as suitability analysis, suitability modeling and multi-criteria decision making, "map algebra" became a core part of GIS. Because Tomlin released the source code to MAP, its algorithms were implemented (with varying degrees of modification) as the analysis toolkit of almost every raster GIS software package starting in the 1980s, including GRASS, IDRISI (now TerrSet), and the GRID module of ARC/INFO (later incorporated into the Spatial Analyst module of ArcGIS).

This widespread implementation further led to the development of many extensions to map algebra, following efforts to extend the raster data model, such as adding new functionality for analyzing spatiotemporal and three-dimensional grids.

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