 | Techniques: Reclassifying and overlaying Maps |
Reclassifying Maps
The first, and in many ways the most fundamental class of analytical operations, involves the reclassification of map categories. Each operation involves the creation of a new map by assigning thematic values to the categories of an existing map. These values may be assigned as a function of the initial value, position, contiguity, size, or shape of the spatial configuration of the individual categories. Each of the reclassification operations involves the simple repackaging of information on a single map, and results in no new boundary delineation. Such operations can be thought of as the purposeful "re-coloring of maps.
Figure 5.2-1 shows the result of simply reclassifying a map as a function of its initial thematic values. For display, a unique symbol is associated with each value. In the figure, the Cover Type map has categories of Open Water, Meadow and Forest. These features are stored as thematic values 1, 2 and 3, respectively, and displayed as separate colors. A binary map that isolates the Open Water locations can be created by simply assigning 0 to the areas of Meadow and Forest. While the operation seems trivial by itself, it has map analysis implications far beyond simply re-coloring the map categories as well soon be apparent.
similar reclassification operation might involve the ranking or weighing of qualitative map categories to generate a new map with quantitative values. For example, a map of soil types might be assigned values that indicate the relative suitability of each soil type for residential development.
Quantitative values may also be reclassified to yield new quantitative values. This might involve a specified reordering of map categories (e.g., given a map of soil moisture content, generate a map of suitability levels for plant growth). Or, it could involve the application of a generalized reclassifying function, such as "level slicing," which splits a continuous range of map category values into discrete intervals (e.g., derivation of a contour map of just ten contour intervals from an elevation surface composed of thousands of specific elevation values).
Other quantitative reclassification functions include a variety of arithmetic operations involving map category values and a specified or computed constant. Among these operations are addition, subtraction, multiplication, division, exponentiation, maximization, minimization, normalization and other scalar mathematical and statistical operators. For example, an elevation surface expressed in feet might be converted to meters by multiplying each map value by the appropriate conversion factor of 3.28083 feet per meter.
Reclassification operations can also relate to location, as well as purely thematic attributes associated with a map. One such characteristic is position. An overlay category represented by a single location, for example, might be reclassified according to its latitude and longitude. Similarly, a line segment or area feature could be reassigned values indicating its center or general orientation.
A related operation, termed parceling, characterizes category contiguity. This procedure identifies individual clumps of one or more points having the same numerical value and spatially contiguous (e.g., generation of a map identifying each lake as a unique value from a generalized map of water representing all lakes as a single category).
Another location characteristic is size. In the case of map categories associated with linear features or point locations, overall length or number of points might be used as the basis for reclassifying those categories. Similarly, an overlay category associated with a planar area might be reclassified according to its total acreage or the length of its perimeter. For example, a map of water types might be reassigned values to indicate the area of individual lakes or the length of stream channels. The same sort of technique might also be used to deal with volume. Given a map of depth to bottom for a group of lakes, for example, each lake might be assigned a value indicating total water volume based on the area of each depth category.
Figure 5.2-2 identifies a similar processing sequence using the information derived in the previous figure 5.2-1. While your eye sees two distinct blobs of water on the open water map the computer only sees distinctions by different map category values. Since both water bodies are assigned the same value of 1 there isnt a categorical distinction and the computer cannot easily differentiate.
The Clump operation is used to identify the contiguous features as separate valuesclump #1, #2 and #3. The Size operation is used to calculate the size of each clumpclump #1= 78 hectares, clump #2= 543 ha and clump#3= 4 ha. The final step uses the Renumber operation to isolate the large water body in the northwest portion of the project area.
In addition to the initial value, position, contiguity, and size of features, shape characteristics also can be used as the basis for reclassifying map categories. Shape characteristics associated with linear forms identify the patterns formed by multiple line segments (e.g., dendritic stream pattern). The primary shape characteristics associated with polygonal forms include feature integrity, boundary convexity, and nature of edge.
Feature integrity relates to intact-ness of an area. A category that is broken into numerous fragments and/or contains several interior holes is said to have less spatial integrity than ones without such violations. Feature integrity can be summarized as the Euler Number that is computed as the number of holes within a feature less one short of the number of fragments which make up the entire feature. An Euler Number of zero indicates features that are spatially balanced, whereas larger negative or positive numbers indicate less spatial integrity.
Convexity and edge are other shape indices that relate to the configuration of boundaries of polygonal features. Convexity is the measure of the extent to which an area is enclosed by its background, relative to the extent to which the area encloses this background. The Convexity Index for a feature is computed by the ratio of its perimeter to its area. The most regular configuration is that of a circle which is totally convex and, therefore, not enclosed by the background at any point along its boundary.
Comparison of a feature''s computed convexity to a circle of the same area, results in a standard measure of boundary regularity. The nature of the boundary at each point can be used for a detailed description of boundary configuration. At some locations the boundary might be an entirely concave intrusion, whereas others might be at entirely convex protrusions. Depending on the "degree of edginess," each point can be assigned a value indicating the actual boundary convexity at that location.
This explicit use of cartographic shape as an analytic parameter is unfamiliar to most GIS users. However, a non‑quantitative consideration of shape is implicit in any visual assessment of mapped data. Particularly promising is the potential for applying quantitative shape analysis techniques in the areas of digital image classification and wildlife habitat modeling. A map of forest stands, for example, might be reclassified such that each stand is characterized according to the relative amount of forest edge with respect to total acreage and the frequency of interior forest canopy gaps. Those stands with a large proportion of edge and a high frequency of gaps will generally indicate better wildlife habitat for many species.
5.3 Overlaying Maps
The general class of overlay operations can be characterized as "light‑table gymnastics." These involve the creation of a new map where the value assigned to every point, or set of points, is a function of the independent values associated with that location on two or more existing map layers. In location‑specific overlaying, the value assigned is a function of the point‑by‑point coincidence of the existing maps. In category‑wide composites, values are assigned to entire thematic regions as a function of the values on other overlays that are associated with the categories. Whereas the first overlay approach conceptually involves the vertical spearing of a set of map layers, the latter approach uses one map to identify boundaries by which information is extracted from other maps.
Figure 5.3-1 shows an example of location‑specific overlaying. Here, maps of cover type and topographic slope classes are combined to create a new map identifying the particular cover/slope combination at each map location. A specific function used to compute new category values from those of existing maps being overlaid can vary according to the nature of the data being processed and the specific use of that data within a modeling context. Environmental analyses typically involve the manipulation of quantitative values to generate new values that are likewise quantitative in nature. Among these are the basic arithmetic operations such as addition, subtraction, multiplication, division, roots, and exponentials.
Functions that relate to simple statistical parameters such as maximum, minimum, median, mode, majority, standard deviation or weighted average also can be applied. The type of data being manipulated dictates the appropriateness of the mathematical or statistical procedure used. For example, the addition of qualitative maps such as soils and land use would result in mathematically meaningless sums, since their thematic values have no numerical relationship. Other map overlay techniques include several that might be used to process either quantitative or qualitative data and generate values which can likewise take either form. Among these are masking, comparison, calculation of diversity, and permutations of map categories.
More complex statistical techniques can be applied in this manner, assuming that the inherent interdependence among spatial observations can be taken into account. This approach treats each map as a variable, each point as a case, and each value as an observation. A predictive statistical model can then be evaluated for each location, resulting in a spatially continuous surface of predicted values. The mapped predictions contain additional information over traditional non‑spatial procedures, such as direct consideration of coincidence among regression variables and the ability to spatially locate areas of a given level of prediction. Sections 4.24 and 4.2.5 discussed considerations involved in spatial data mining derived by statistically overlaying mapped data.
An entirely different approach to overlaying maps involves category‑wide summarization of values. Rather than combining information on a point‑by‑point basis, this group summarizes the spatial coincidence of entire categories shown on one map with the values contained on another map(s). Figure 5.3-2 contains an example of a category‑wide overlay operation. In this example, the categories of the cover type map are used to define an area over which the coincidental values of the slope map are averaged. The computed values of average slope within each category area are then assigned to each of the cover type categories.
Summary statistics which can be used in this way include the total, average, maximum, minimum, median, mode, or minority value; the standard deviation, variance, or diversity of values; and the correlation, deviation, or uniqueness of particular value combinations. For example, a map indicating the proportion of undeveloped land within each of several counties could be generated by superimposing a map of county boundaries on a map of land use and computing the ratio of undeveloped land to the total land area for each county. Or a map of zip code boundaries could be superimposed over maps of demographic data to determine the average income, average age, and dominant ethnic group within each zip code.
As with location‑specific overlay techniques, data types must be consistent with the summary procedure used. Also of concern is the order of data processing. Operations such as addition and multiplication are independent of the order of processing. Other operations, such as subtraction and division, however, yield different results depending on the order in which a group of numbers is processed. This latter type of operations, termed non‑commutative, cannot be used for category‑wide summaries.
5.4 Establishing Distance and Connectivity
Measuring distance is one of the most basic map analysis techniques. Historically, distance is defined as the shortest straight-line between two points. While this three-part definition is both easily conceptualized and implemented with a ruler, it is frequently insufficient for decision-making. A straight-line route might indicate the distance as the crow flies, but offer little information for the walking crow or other flightless creature. It is equally important to most travelers to have the measurement of distance expressed in more relevant terms, such as time or cost.
Proximity establishes the distance to all locations surrounding a point the set of shortest straight-lines among groups of points. Rather than sequentially computing the distance between pairs of locations, concentric equidistance zones are established around a location or set of locations (figure 5.4-1). This procedure is similar to the wave pattern generated when a rock is thrown into a still pond. Each ring indicates one unit farther away increasing distance as the wave moves away. Another way to conceptualize the process is nailing one end of a ruler at a point and spinning it around. The result is a series of data zones emanating from a location and aligning with the rulers tic marks
However, nothing says proximity must be measured from a single point. A more complex proximity map would be generated if, for example, all locations with houses (set of points) are simultaneously considered target locations (left side of figure 5.4-2).
In effect, the procedure is like throwing a handful of rocks into pond. Each set of concentric rings grows until the wave fronts from other locations meet; then they stop. The result is a map indicating the shortest straight-line distance to the nearest target area (house) for each non-target area. In the figure, the red tones indicate locations that are close to a house, while the green tones identify a
