Cartographic modeling is a general methodology for the analysis and synthesis of geospatial data. It has been incorporated into a number of raster-oriented geographic information systems, and it can be used to address a variety of applications in a unified manner. This is done by decomposing both data and data processing tasks into elemental units that can then be clearly and flexibly recomposed. The result is an algebra- like language in which the variables are maps and the functions are map-transforming operations. The nature of this “map algebra” can be expressed in terms of three fundamental components: a body of data, a set of data processing capabilities, and a mechanism to control that data processing. To the extent that map algebra can be regarded as a language, these components can be, respectively, characterized as nouns, verbs, and expressions.

The primary unit of data employed in cartographic modeling is the layer. This can be envisioned as a single-factor map. Like any map, it is a bounded plane area depicting a geographic region such that every location within that area represents a corresponding location within the region. Formally, a location is that portion of the cartographic plane that is uniquely identified by a pair of planar coordinates. In the case of raster-encoded data, it is a grid cell or pixel. As a single-factor map, each layer is one on which every location is characterized in terms of exactly one of a related set of site conditions. Thus, one layer might depict every location’s soil type or its proximity to the nearest supermarket, while others might depict variations in characteristics such as population density or groundwater contamination. When multiple layers are used to represent a common region, all must be geometrically compatible with one another in terms of their spatial extent, orientation, and cartographic projection.

The set of all locations on a layer that share a common site condition is referred to as a zone, and each of a layer’s zones is represented by a numerical value. This is an integer or real number that identifies a zonal condition in terms that may be either qualitative or quantitative in nature. In the case of qualitative conditions (such as soil types or land uses), these values will be nominal and may be arbitrarily assigned. In the case of quantitative conditions (such as rankings, dates, distances, or directions), values may relate to ordinal, interval, ratio, or even cyclical scales of measurement. A special “NULL” value is also used to represent the absence of any recorded site condition.

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In more general settings, the term layer is sometimes used in reference to a multiple-factor map. A layer of soil types, for example, might be created such that each type is characterized not only by name but also in terms of its acidity, permeability, bearing capacity, and so on. From the perspective of cartographic modeling, each of those separate characteristics would constitute a separate layer.

If layers are the nouns, then the verbs of this cartographic modeling language are layer-transforming operations. Each of these operations generates output in a form (the map layer) that can then be accepted as input to any other operation. Since multiple operations can be combined in this manner, no one of those operations needs to be particularly complicated. Just as a small number of primitive algebraic functions (such as addition, subtraction, or multiplication) can be combined into an endless variety of mathematical equations, so can a concise vocabulary of elementary map algebraic operations be combined into an open-ended array of “cartographic models.

Each map algebraic operation is defined in terms of its effect on a single, typical location. This worm’s eye perspective gives rise to four major types of operation that are respectively referred to as local, zonal, focal, and incremental.