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Fields

The idea that the Earth’s surface is a space littered with various kinds of objects certainly matches the ways humans tend to think about the world around them. Scenes perceived by the eye are immediately parsed by the brain into “tree”, “car”, “house”, and other discrete objects. But in other cases the world may appear more continuous than discrete. Ground elevation (or ocean depth), for example, is in broad terms a continuously varying property that can be measured anywhere on the Earth’s surface, as is atmospheric temperature, or, within an urbanized area, average level of noise or pollution (Figure 2‑5, below — each pixel of this image indicates the measured or modeled level of traffic-related noise in decibels – reds are the highest levels, gray indicates buildings).

In essence there are two ways of thinking about phenomena on the Earth’s surface. In the first, the discrete-object view, reality is like an empty table-top littered with discrete, countable objects that can be assigned to different classes. In the second, the continuous-field view, reality is a collection of continuous surfaces, each representing the variation of one property, such as elevation, over the Earth’s surface (Figure 2‑4, layer 3). When it is necessary to differentiate by height, the field becomes three-dimensional rather than two-dimensional, and time may add a fourth dimension. Mathematically, a field is a continuous function mapping every location to the value of some property of interest.

Figure 2‑5 Noise level raster

The distinction between continuous fields and discrete objects is merely conceptual, and there is no test that can be applied to the contents of a database to determine which view is operative. But it is a very important distinction that underlies the choices that analysts make in selecting appropriate techniques. Points, polylines, and polygons arise in both cases, and yet their meanings are very different. For example, points might represent the locations where a continuous field of temperature is measured, or they might represent isolated instances of a disease — in the latter case, which falls within the discrete-object view, there is no implication that anything happens in between the cases, whereas in the former case one would expect temperature to vary smoothly between measurement sites. Polylines might represent the connected pieces of a stream network (as in Figure 2‑4, uppermost layer), or they might represent the contours of an elevation surface — in the latter case, the polylines would collectively represent a field, and would consequently not be allowed to cross each other. If filled contours rather than separate contour lines are generated then polygons rather than polylines define the field values (Figure 2‑6, source as per Figure 2‑4).

Figure 2‑6 Filled contour view of field data