A geographic field is a geographic phenomenon that has a value “everywhere” in the study area. We can therefore think of a field as a mathematical function f that associates a specific value with any position in the study area. Hence if (x, y) is a position in the study area, then f(x, y) expresses the value of f at location (x, y). Fields can be discrete or continuous.
In a continuous field, the underlying function is assumed to be “mathematically smooth”, meaning that the field values along any path through the study area do not change abruptly, but only gradually. Good examples of continuous fields are air temperature, barometric pressure, soil salinity and elevation. A continuous field can even be differentiable, meaning that we can determine a measure of change in the field value per unit of distance anywhere and in any direction. For example, if the field is elevation, this measure would be slope, i.e. the change of elevation per metre distance; if the field is soil salinity, it would be salinity gradient, i.e. the change of salinity per metre distance.
Discrete fields divide the study space in mutually exclusive, bounded parts, with all locations in one part having the same field value. Discrete fields are intermediate between continuous fields and geographic objects: discrete fields and objects both use “bounded” features.
Discrete fields divide the study space in mutually exclusive, bounded parts, with all locations in one part having the same field value. Discrete fields are intermediate between continuous fields and geographic objects: discrete fields and objects both use “bounded” features.
Discrete fields divide the study space in mutually exclusive, bounded parts, with all locations in one part having the same field value. Typical examples are land classifications, for instance, using either geological classes, soil type, land use type, crop type or natural vegetation type.
Discrete fields are intermediate between continuous fields and geographic objects: discrete fields and objects both use “bounded” features. A discrete field, however, assigns a value to every location in the study area, which is not typically the case for geographic objects. These two types of fields differ in the type of cell values. A discrete field such as land use type will store cell values of the type “integer” and is therefore also called an integer raster. Discrete fields can be easily converted to polygons since it is relatively easy to draw a boundary line around a group of cells with the same value. A continuous raster is also called a “floating point” raster.
A field-based model consists of a finite collection of geographic fields: we may be interested in, for example, elevation, barometric pressure, mean annual rainfall and maximum daily evapotranspiration, and would therefore use four different fields to model the relevant phenomena within our study area.