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Spatial analysis encompasses the quantitative techniques for examining the locations, attributes, and relationships of geographic features. Core operations include overlay (combining layers to find areas meeting multiple criteria), buffering (creating distance zones around features), proximity analysis (measuring distances and identifying nearest neighbors), map algebra (cell-by-cell raster calculations), and spatial statistics (identifying clusters, hotspots, and spatial patterns). These operations exploit the fundamental property of geographic data -- that location matters, and nearby things tend to be more related than distant things (Tobler's First Law of Geography).
Spatial analysis is what separates a GIS from a digital map. While a map shows where things are, spatial analysis answers questions about why they are there, what is nearby, where conditions overlap, and how patterns vary across space.
Overlay operations are the workhorses of spatial analysis. Vector overlay (intersection, union, identity, erase) combines the geometry and attributes of two or more layers, producing new features where inputs overlap. Raster overlay (map algebra) performs cell-by-cell calculations -- adding, multiplying, or applying conditional logic to grid layers. A classic suitability analysis might weight and combine slope, soil type, proximity to roads, and land cover rasters to produce a composite suitability score for each cell.
Proximity analysis measures spatial relationships. Buffering creates distance zones. Near analysis finds the closest feature. Point-in-polygon determines which polygon contains each point. Distance matrices compute all pairwise distances. These operations answer questions like "how far is each house from the nearest fire station?" or "how many schools are within 2 km of each park?"
Spatial statistics move beyond simple description to inference. Point pattern analysis tests whether features are clustered, dispersed, or random. Hotspot analysis (Getis-Ord Gi*) identifies statistically significant concentrations of high or low values. Spatial autocorrelation (Moran's I) quantifies the degree to which nearby locations have similar values. These tools reveal patterns that visual inspection might miss and provide statistical rigor for spatial decision-making.