Functions of Spatial Analysis

What operations are typically used as spatial analysis functions in GIS? Chou (1997, p. 15) provides the most efficient description. Three different types are illustrated:

• Attribute query
• Spatial query
• Derive new data from existing data

Note that only some of these operations generate new data. The first two functions mentioned are simple queries, and the result consists of a selection of objects from the databases.
Spatial analysis functions can also be classified in regards to the data type involved in the spatial analysis (point, line, network, polygons/areas, surface), the data structure (vector vs. raster), or the conceptual model of space (discrete entity vs. continuous field (Burrough et al. 1998)).
Bailey et al. (1995) and Abler et al. (1971) propose another differentiation of the functionality of spatial analysis. They distinguish the functions by their level of dynamics: E.g. static data (point distribution, surface area etc.), interactions between objects in space (for example interactions between two economic centers), or analysis of spatio-temporal changes). Depending on the author's point of view and his knowledge, organization and classification of SA functions are defined differently.
The lesson of the module "Basic Spatial Analysis" is organized using a mixed approach. The module is composed of lessons dedicated to the different analysis and application functions such as terrain analysis, accessibility analysis, and suitability analysis, etc. Albrecht (1996) provides a nice classification of SA functions used in GIS (see also the illustration below). This classification was developed to deliver a universal interface for GIS. That is why this classification has two advantages: It gets the user's aspect (not the technical aspect), it is the briefest description, but it is a complete description of SA functions available in GIS (at least in commercial GIS). The term "spatial analysis" could be irritating. For this reason, a better description of SA would be "pattern analysis".

There is a very pragmatic approach in the following list provided by Goodchild (1990) based on Goodchild (1987). It provides the typical function range of commercial GIS and operation components in data analysis. Other books provide overviews and discussions on the topic of the typical SA functions used in GIS, such as Aronoff (1989), Bill (1999), Burrough et al. (1998), or Jones (1997).

Data analysis functions according to Goodchild (1990)

Counting and measuring:

• Measure number of items: The ability to count the number of objects in a class.
• Measure distances along straight and convoluted lines: The ability to measure distances along a prescribed line.
• Calculate bearings between points: The ability to calculate the bearing (with respect to True North) from a given point to another point.
• Measure length of perimeter of areas: The ability to measure the length of the perimeter of a polygon.
• Measure size of areas: The ability to measure the area of a polygon.
• Measure volume: The ability to compute the volume under a digital representation of a surface.

Function of spatial analysis:

• Point in polygon: The ability to superimpose a set of points on a set of polygons and determine which polygon (if any) contains each point.
• Line on polygon overlay: The ability to superimpose a set of lines on a set of polygons, breaking the lines at intersections with polygon boundaries.
• Polygon overlay: The ability to overlay digitally one set of polygons on another and form a topological intersection of the two, concatenating the attributes.
• Sliver polygon elimination: The ability to delete automatically the small sliver polygons which result from a polygon overlay operation when certain polygon lines on the two maps represent different versions of the same physical line.
• Nearest neighbor search: The ability to identify points, lines or polygons that are nearest to points, lines or polygons specified by location or attribute.
• Shortest route: The ability to determine the shortest or minimum cost route between two points or specified sets of points.
• Contiguity analysis: The ability to identify areas that have a common boundary or node.
• Connectivity analysis: The ability to identify areas or points that are (or are not) connected to other areas or points by linear features.
• Network analysis: Simple forms of network analysis are covered in shortest route and connectivity. More complex analyses are frequently carried out on network data by electrical and gas utilities, communications companies etc. These include the simulation of flows in complex networks, load balancing in electrical distribution, traffic analysis, and computation of pressure loss in gas pipes. In many cases these capabilities can be found in existing packages which can be interfaced to the GIS database.

Statistical analysis functions:

• Create lists and reports: This is the ability to create lists and reports on objects and their attributes in user-defined formats, and to include totals and subtotals.
• Calculate – arithmetic: The ability to perform arithmetic, algebraic and Boolean calculations separately and in combination.
• Complex correlation: The ability to compare maps representing different time periods, extracting differences or computing indices of change.

Terrain modeling:

• Spot heights: Given a digital elevation model, interpolate the height at any point.
• Heights along streams: Given a digital elevation model and a hydrology net, interpolate points along streams at fixed increments of height.
• Contours (isolines): Given a set of regularly or irregularly spaced point values, interpolate contours at user-specified intervals.
• Elevation polygons: Given a digital elevation model, interpolate contours of height at user-specified intervals.
• Watershed boundaries: Given a digital elevation model and a hydrology net, interpolate the position of the watershed between basins.
• View shed: Identification of the cells in an input raster that can be seen from one or more observation points.
• Generate view shed maps: Given a digital elevation model and the locations of one or more viewpoints, generate polygons enclosing the area visible from at least one viewpoint.
• Calculate slopes along lines (gradients): The ability to measure the slope between two points of known height and location or to calculate the gradient between any two points along a convoluted line which contains two or more points of known elevation.
• Calculate slopes of areas: Given a digital elevation model and the boundary of a specified region (e.g., a part of a watershed), calculate the average slope of the region.
• Calculate aspect of areas: Given a digital elevation model and the boundary of a specified region, calculate the average aspect of the region.
• Locations from traverses: Given a direction (one of eight radial directions) and distance from a given point, calculate the end point of the traverse.

Complex analysis:

• Combination of the analysis functions mentioned above.