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# Section Four - Discrete and Continuous Data

The spatial distribution of raster and vector data can be placed into two descriptive categories: discrete data and continuous data. While both raster and vector data can contain data with either discrete or continuous, most often, vector data is described as discrete while raster is described as continuous.

### 3.4.1: Discrete Data

Discrete data is data that represents features which can exist independently with clear and definable boundaries, even when part of a larger data set. For example, a vector layer (a generic name for spatial data) showing the continental United States could be categorized as discrete data. The United States has a clear and definable administrative boundary, as does each state in the Union. The State of Colorado could continue to exist even if all the other states suddenly dissolved their boundaries; similarly, we can have a map of just Colorado. Discrete data can be any of the three geometries: points, polylines, or polygons, or one or many pixels of a raster layer.

### 3.4.2: Continuous Data

Continuous data is the opposite of discrete data, data which does not have clear and definable boundaries, but instead makes a "blanket" of data across a landscape, defined with interval-ratio of values. Continuous data will continue to exist even if you take away one portion of it (which is impossible). Even if you removed 75°F from the English language, 75°F will not cease to exist. Just because it doesn't have a label doesn't mean it doesn't exist or you have no comprehension of what it is. If Colorado, represented by discrete data, was absorbed by Kansas and a new border was drawn, future generations would not have experience with Colorado or Kansas - their reality might be Kansarado, a state with a clear and define boundary. They wouldn't have a comprehension of Colorado or Kansas as independent objects.

Data such as temperature, precipitation, elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface , slope, and aspect The direction the developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) faces in relation to the geographic coordinate system. Normal; transverse, oblique are all examples of continuous data. Each defined value on the scale of descriptive values must exist in order to arrive at the next one. Slopes (with the exception of cliffs) do not just change from 0% to 47% by taking one step forward on a hike. The slope must pass through all of the percentages to gradually rise (some places that rise is much more rapid, but the slope must still pass through all the values first).

Most often, classified raster data is continuous data, and from those continuous layers, we can extract the information we would need to create discrete data. For example, I might start with a DEM, which is a continuous expression of elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface , from which I can extract slope or aspect The direction the developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) faces in relation to the geographic coordinate system. Normal; transverse, oblique . From those layers, I can subset just the slopes between 10 and 40°, and define that discretely as the preferred area for a particular nesting bird.

Students sometimes have problems with the fact that continuous data appears to be discrete in the software. For example, in the "Geothermal Resource of the United States" map found in Figure 3.13, the swirled red, orange, yellow, and greens across the map show a continuous range of data classified between "Most Favorable" and "Least Favorable". Within these swirls, it appears that where the red stops, the orange begins. While this is true when looking at the map, it's not exactly how it is in real life. Since we know the definition of a map to be: a scale, symbolized, generalized model of reality, we need to both symbolize and generalize the data. In order for the data to coexist on the map and conform to the limitations of the software, computer monitor, and printer, each color needs to stop somewhere for the next to begin. If you keep continuous data in your mind as "data without defined boundaries covering a scale of values" and discrete data as "data with clear, defined, movable boundaries described with values which can be removed from a system without destroying the entire system", you will understand the difference.

Figure 3.10: An Example of Discrete and Continuous Data Displayed on a Single Map

Within the GIS, it's important to understand the difference between continuous and discrete data, as they are often referred to by name in geoprocessing and cartographic tools. Due to the properties of discrete and continuous data, the software processes and displays them differently, using totally different base calculus (which you don't need to know, just know it exists in the background).

### 3.4.3: Examples of Discrete and Continuous Data

Discrete data is fairly easy to image and understand - almost all vector data used in the GIS is discrete data. Below, we look at some examples of vector datasets that are continuous and raster data sets which are discrete (since we looked at continuous examples in Section Three: Raster Data).

Figure 3.11: Examples of Discrete Data
Three examples of discrete data - point, polyline, and polygon.

#### Triangulated Irregular Networks (TINs) and Contour Lines

Triangulated Irregular Networks (TINs) are a special kind of vector file which show continuous elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface over a landscape. Notice the TIN is a series of triangles, representing the landscape as a blanket while the contour lines show the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface in a decreasing manner. Notice the TIN is a series of triangles, representing the landscape as a blanket while the contour lines show the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface in a decreasing manner. TINs are used to create contour lines (described below), which is why you see contour lines on topographic maps and not TINs.

TINs are created from an input layer of either: a series of elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface points measured across the landscape or a DEM. When the input is a series of points, the tool connects each point to two other points around it, creating an irregular pattern (network) of triangles where each triangle represents a portion of the slope on a hill side. When the input is a DEM, each value associated with one pixel is connected to two other similar or same values in neighboring pixels, resulting in the same irregular network of triangles. TINs are not used in GIS 101, however, it's important to know they exist.

Figure 3.12: A TIN with Contour Lines Drawn Over
The TIN (shown with blue lines) can be seen below the contour lines (shown in red and white)

#### Contour Lines

Contour lines are another example of continuous vector data. Created from a TIN, a DEM, or a series of surveyed points stored in a vector point file, contour lines connect together all the points of equal elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface . While you can set the contour interval, or the equal gain or loss in elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface from one contour line to the next, the most common methods are by intervals of ten. The software creates the contour lines using a geoprocessing tool, with a user input of the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface -based file (TIN or DEM, usually) and a contour interval (often 10, 50, 100). The output file is a polyline file, which uses the polyline file icon , with a user-defined name.

Figure 3.13: A Very Close Up of Contour Lines Over an Elevation Point Layer
Contour lines, whether created from a TIN, a DEM, or a point layer, are all formed in the same way: point or pixels of equal elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface are determined by the software and then connected with lines. Each contour line represents one elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point on the Earth's surface , with the next having a