GIS-based computational models are explored. While models vary immensely across disciplines and specialties, the focus is on models that simulate and forecast geographical systems and processes in time and space. The degree and means of integration of the many different models with GIS are covered, and the critical phases of modeling: design, implementation, calibration, sensitivity analysis, validation and error analysis are introduced. The use of models in simulations, an important purpose for implementing models within or outside of GIS, is discussed and the context of scenario-based planning explained. To conclude, a survey of model types is presented, with their application methods and some examples, and the goals of modeling are discussed.

Kernel density estimation is an important nonparametric technique to estimate density from point-based or line-based data. It has been widely used for various purposes, such as point or line data smoothing, risk mapping, and hot spot detection. It applies a kernel function on each observation (point or line) and spreads the observation over the kernel window. The kernel density estimate at a location will be the sum of the fractions of all observations at that location. In a GIS environment, kernel density estimation usually results in a density surface where each cell is rendered based on the kernel density estimated at the cell center. The result of kernel density estimation could vary substantially depending on the choice of kernel function or kernel bandwidth, with the latter having a greater impact. When applying a fixed kernel bandwidth over all of the observations, undersmoothing of density may occur in areas with only sparse observation while oversmoothing may be found in other areas. To solve this issue, adaptive or variable bandwidth approaches have been suggested.

Location-allocation models involve two principal elements: 1) multiple facility location; and 2) the allocation of the services or products provided by those facilities to places of demand. Such models are used in the design of logistic systems like supply chains, especially warehouse and factory location, as well as in the location of public services. Public service location models involve objectives that often maximize access and levels of service, while private sector applications usually attempt to minimize cost. Such models are often hard to solve and involve the use of integer-linear programming software or sophisticated heuristics. Some models can be solved with functionality provided in GIS packages and other models are applied, loosely coupled, with GIS. We provide a short description of formulating two different models as well as discuss how they are solved.

Uncertainty and error are integral parts of science and technology, including GIS&T, as they are of most human endeavors. They are important characteristics of knowledge, which is very seldom perfect. Error and uncertainty both affect our understanding of the present and the past, and our expectations from the future. ‘Uncertainty’ is sometimes used as the umbrella term for a number of related concepts, of which ‘error’ is the most important in GIS and in most other data-intensive fields. Very often, uncertainty is the result of error (or suspected error).  As concepts, both uncertainty and error are complex, each having several different versions, interpretations, and kinds of impacts on the quality of GIS products, and on the uses and decisions that users may make on their basis. This section provides an overview of the kinds of uncertainty and common sources of error in GIS&T, the role of a number of additional related concepts in refining our understanding of different forms of imperfect knowledge, the problems of uncertainty and error in the context of decision-making, especially regarding actions with important future consequences, and some standard as well as more exploratory approaches to handling uncertainties about the future. While uncertainty and error are in general undesirable, they may also point to unsuspected aspects of an issue and thus help generate new insights.