# Discrete and continuous data

Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. A lake is a discrete object within the surrounding landscape. Where the water’s edge meets the land can be definitively established. Other examples of discrete objects include buildings, roads, and parcels. Discrete objects are usually nouns.

A continuous surface represents phenomena in which each location on the surface is a measure of the concentration level or its relationship from a fixed point in space or from an emitting source. Continuous data is also referred to as field, nondiscrete, or surface data. One type of continuous surface is derived from those characteristics that define a surface, in which each location is measured from a fixed registration point. These include elevation (the fixed point being sea level) and aspect (the fixed point being direction: north, east, south, and west).

Another type of continuous surface includes phenomena that progressively vary as they move across a surface from a source. Illustrations of progressively varying continuous data are fluid and air movement. These surfaces are characterized by the type or manner in which the phenomenon moves. The first type of movement is through diffusion or any other locomotion in which the phenomenon moves from areas with high concentration to those with less concentration until the concentration level evens out. Surface characteristics of this type of movement include salt concentration moving through either the ground or water, contamination level moving away from a hazardous spill or a nuclear reactor, and heat from a forest fire. In this type of continuous surface, there has to be a source. The concentration is always greater near the source and diminishes as a function of distance and the medium the substance is moving through.

In the source-concentration surface above, the concentration of the phenomenon at any location is a function of the capability of the event to move through the medium. Another type of concentration surface is governed by the inherent characteristics of the moving phenomenon. For example, the movement of the noise from a bomb blast is governed by the inherent characteristics of noise and the medium it moves through. Mode of locomotion can also limit and directly affect the surface concentration of a feature, as is the case with seed dispersal from a plant. The means of locomotion, whether it be bees, man, wind, or water, all affect the surface concentration of seed dispersal for the plant. Other locomotion surfaces include dispersal of animal populations, potential customers of a store (cars being the means of locomotion and time being the limiting factor), and the spread of a disease.

For many objects, their boundaries can be represented and modeled as either continuous or discrete. A continuum is created in representing geographic features, with the extremes being pure discrete and pure continuous features. Most features fall somewhere between the extremes. Illustrations of features that fall along the continuum are soil types, edges of forests, boundaries of wetlands, and geographic markets influenced by a television advertising campaign.

The determining factor for where a feature falls on the continuous-to-discrete continuum is the ease of defining the feature’s boundaries. No matter where on the continuum the feature falls, the grid-cell storage can represent it to a greater or lesser accuracy.

It is important to understand the type of data you are modeling, whether it be continuous or discrete, when making decisions based on the resulting values. The exact site for a building should not be based solely on the soils map. The square area of a forest cannot be the primary factor when determining available deer habitat. A sales campaign should not be based only on the geographic market influence of a television advertising spree. The validity and accuracy of boundaries of the input data must be understood.

9/10/2014