Many problems in spatial analysis involve spatially extensive data - information on attributes that, in principle, can be measured at all locations within a defined region. Much of the research in this field stems from work on landscapes - modeling the form of surfaces from limited sample data using interpolation techniques, examining the flow of materials and water across surfaces, and evaluating sight lines and routes across landscapes. However, the same concepts apply to any set of data that has a single-valued (typically positive) attribute measurable at every location of a study area - temperature, pressure, humidity, trace elements in soil, and many other variables are of this type. In addition there are many instances where intensive variables (e.g. point event data, counts within zones etc) need to be set in the context of spatially extensive data for comparison purposes. Conversion of such intensive data to extensive form using kernel density (KDE) techniques has already been discussed. Note that a KDE surface provide a means of representation for intensive data and are not interpolation techniques as such.
In the sections that follow we commence by examining different approaches to modeling continuous or near-continuous surfaces and then proceed to address specific issues and applications relating to surface analysis. The discussion progresses from considerations of surface geometry and visibility to the way in which surface water flows can be modeled. The Chapter concludes with coverage of the main deterministic and statistical models currently used to construct surfaces from limited data.