Map Algebra

Overview Map algebra is a framework for performing spatial analysis on raster dataRaster DataRaster data represents geographic information as a grid of cells or pixels, where each cell holds a value representin... through cell-by-cell mathematical operations. Originally formalized by C. Dana Tomlin in the 1980s, map algebra treats each raster layer as a variable in an equation, enabling analysts to combine, transform, and analyze gridded data using arithmetic, logical, statistical, and conditional operations to produce new raster outputs.

Map algebra operations are classified by the spatial scope of their computation. Local operations compute output values from corresponding cells in one or more input rasters, such as adding two elevation surfaces or applying a threshold to NDVINDVIThe Normalized Difference Vegetation Index (NDVI) is a widely used spectral index that quantifies vegetation health a... values. Focal (neighborhood) operations calculate output values based on a cell and its surrounding neighbors, enabling smoothing, edge detection, and slope calculation. Zonal operations summarize cell values within defined zones, such as calculating the average elevation within each watershed. Global operations consider all cells in the raster, such as computing flow directionFlow DirectionFlow direction analysis determines the downhill direction of water flow from each cell in a digital elevation model, ... across an entire elevation surface or calculating Euclidean distanceEuclidean DistanceEuclidean distance is the straight-line distance between two points in a plane, computed using the Pythagorean theore... from source cells.

Map algebra is essential for environmental modeling, enabling calculations of terrain derivatives (slope, aspect, curvature), hydrological analysis (flow accumulationFlow AccumulationFlow accumulation counts the number of upslope cells that drain through each cell in a raster, creating a surface tha..., watershed delineation), and habitat suitability modeling through weighted overlayWeighted OverlayWeighted overlay is a raster analysis technique that combines multiple reclassified layers by assigning each a relati... of environmental variables. Climate studies use map algebra to compute temperature anomalies and precipitation trends from gridded climate data. Agricultural applications combine soil, slope, and climate rasters to model crop suitability. Urban heat islandUrban Heat IslandThe Urban Heat Island (UHI) effect occurs when cities experience significantly higher temperatures than surrounding r... analysis uses map algebra to compare surface temperatures across land cover types.

Map algebra is implemented in all major GISGISGeographic Information Systems (GIS) enable users to analyze and visualize spatial data to uncover patterns, relation... platforms. ArcGISArcGISArcGIS is a leading GIS platform offering tools for spatial analysis, mapping, and data visualization. It serves a wi... provides the Spatial Analyst extension with a raster calculator. QGISQGISQGIS is a user-friendly, open-source GIS platform that provides tools for geospatial data analysis, mapping, and inte... offers the raster calculator and GRASS GISGRASS GISGRASS GIS is a free, open-source geographic information system used for geospatial data management, analysis, image p... integration. Python libraries like rasterioRasterioRasterio is a Python library for reading and writing geospatial raster data. Built on GDAL, it provides a Pythonic AP... and xarray support programmatic map algebra operations. The GDALGDALGDAL (Geospatial Data Abstraction Library) is an open-source translator library for raster and vector geospatial data... library provides command-line tools for raster computation across formats.