MapAlgebra

Map algebra is a formal framework for analyzing raster geographic data by combining the values of corresponding cells across one or more raster layers using mathematical expressions. Each raster is viewed as a grid of cells, with the value in each cell representing a geographic variable such as elevation, temperature, or land cover. The core idea is to produce new raster surfaces by applying algebraic, logical, and statistical operations to input layers.

Operations in map algebra are commonly categorized as local, focal (neighborhood), and global (zonal). Local operations apply cell-by-cell, such as adding two rasters or applying a conditional expression. Focal operations use a moving window around each cell to compute statistics like mean or maximum. Global or zonal operations summarize values across regions defined by another layer or by the entire raster, such as calculating the mean within a polygon.

Beyond arithmetic, map algebra supports reclassification, thresholding, boolean logic, and conditional expressions, enabling complex suitability analyses, habitat models, and change detection. It is often used to derive terrain attributes (e.g., slope, aspect) from elevation data and to create integrated indices by combining multiple layers.

Historically, map algebra emerged with raster GIS in the 1980s and 1990s and was popularized by researchers and software developers in the GIS community. It remains a foundational concept in spatial analysis, implemented in major platforms such as ArcGIS Spatial Analyst, GRASS GIS, and SAGA GIS, as well as in programming environments like Python and R.

See also: raster data, geographic information systems, spatial analysis.