Bivariate, Color Symbolization
With the addition of the color visual variables of hue and intensity, there are several more techniques available in ARC/INFO for the production of bivariate choropleth maps (for data that is continuous, and changes abruptly at polygon borders). These techniques include texture distinguished by hue, hue and intensity, dual-hue range and complementary-color maps.
Two Nominal Data Sets--Texture Distinguished by Hue
Figure 5.3c: CTH.aml Nominal data displayed with texture and a second nominal data set displayed with hue. This should be used for two separate variables, not data and meta-data.
This AML is a modification of the AML that generated Figure 5.3a; unlike that macro, this should be used for two nominal data sets, rather than data and meta-data. The AML requires a lookup table that specifies texture (in integers which are divided by 100) and a lookup table that specifies HLS hue. See Figure 5.3c and CTH.aml.
CTH <texture_lookup> <value_lookup>
{line_size} {value} {intensity}
<texture_lookup>- specifies line separation in hundredths of PAGEUNITS
<value_lookup>- specifies HLS lightness (from 0 to 100)
{line_size}- specifies a line width--defaults to 0.03 inches
{value} {intensity}- defaults of 50 and 100 (maximum intensity}.
Bivariate Legends--Lookup Table Based Displays
Figure 5.3d: CBL.aml A legend for figure 5.3c. This AML will also generate legends for the bivariate mapping techniques shown in figures 5.3a and 5.3b.
Along with the automation of polygon symbolization, the generation of legends can be automated. This AML (CBL.aml) creates bivariate legends for all of the area symbolization techniques that make use of two lookup tables. It automatically places labels on each of the axes, as well as the total number of occurrences in each column. See Figures 5.3d, 5.4b, 5.5b, 5.5d, 5.6b and 5.6d.
CBL <lookup_1> <lookup_2>
<start_x> <start_y> <size_x>
<size_y> <d|c|i|l|v|h|o>
{textset} {font} {point_size} {float_precision} {line_size}
{color_parameter_1} {color_parameter_2}
<lookup_1> <lookup_2>- the two lookup tables used in a bivariate mapping AML
<start_x> <start_y>- the lower left corner of the legend display
<size_x> <size_y>- the x and y sizes of the legend display
<d|c|i|l|v|h|o>- the bivariate method used: Dual hue range, Complementary color, hue and Intensity, intersecting Lines, texture and Value, texture and Hue, and texture and Orientation
{textset} {font} {point_size}- define the labeling text--defaults to a 10 point roman font
{float_precision}- the number of decimal places to be shown--the default is 2
{line_size}- for the texture methods, the fill line width
{color_[parameter_1} {color_parameter_2}- for the texture with hue or value methods, the additional two color parameters.
Two Nominal Data Sets--Dual Hue Ranges
Figure 5.5a: CDH.aml Two nominal data sets displayed with the dual hue range technique. This is best used to show the spatial replationship between two variables.
Figure 5.5b: CBL.aml A legend for figure 5.5a. Nominal data is displayed with the size of the column or row indicating the total number of items in that column/row.
To specify a hue, which can be used for mapping nominal or ordinal data, the SHADECOLOR command must be given with parameters that will establish a color. For dual hue range maps the shadecolors must be selected so that each data set uses one of the part-spectral color schemes (yellow to red, and yellow to green). See the table in the Dual Hue Range section in chapter three for a tables of possible color values. The lookup tables should set up to range from 0 to 100; one table will be used in the CMY color system to specify magenta (with yellow at 100, this controls the amount of red), and the other will specify cyan (with yellow at 100, this controls the amount of green). See Figure 5.5a and CDH.aml.
CDH <yellow-green_lookup>
<yellow-red_lookup>
<yellow-green_lookup>- specifies CMY cyan (from 0 to 100)
<yellow-red_lookup>- specifies CMY magenta (from 0 to 100);
Nominal Data, and Ordinal Data--Hue and Intensity
Figure 5.5c: CHI.aml Nominal data displayed with hue and ordinal meta-data displayed with color intensity; intense colors are used to display highly certain values.
Figure 5.5d: CBL.aml A legend for figure 5.5c. The AML separates nominal information and displays continuous (ordinal+) data as an unbroken column.
Color hue is best used for nominal data; intensity is best used for ordinal data (and generally only for meta-data, not a second data variable). The AML, CHI.aml, makes use of a lookup table that specifies HLS hue for a nominal data item, and HLS saturation (intensity) for an ordinal data item. See Figure 5.5c.
CHI <hue_lookup>
<intensity_lookup>
<hue_lookup>- specifies HLS hue (from 0 to 360) for a nominal data set
<intensity_lookup>- specifies HLS saturation (from 20 to 100) for an ordinal data set.
Two Ordinal Data Sets--Complementary Colors
Figure 5.6a: CCC.aml Two ordinal data sets displayed with the complementary color system. The large amount of red in the image can provoke a reaction of alarm.
Figure 5.6b: CBL.amlA legend for figure 5.6a. The use of two continuous variables is conveyed by using unbroken columns and rows, and placing labels at class breakpoints.
An alternative color scheme to the spectral encoding system given above is the complementary color scheme. This system is best for mapping two ordinal variables, because it highlights negative or positive correlation with a central gray zone (when classes are equal-interval or color specifications relate to data values). For example, to symbolize positive correlations, the following CMY color values generate an appropriate shading:
| Cyan | 100 | Cyan | 100 | Cyan | 100 | Cyan | 100 |
|---|---|---|---|---|---|---|---|
| Magenta | 0 | Magenta | 33 | Magenta | 67 | Magenta | 100 |
| Cyan | 67 | Cyan | 67 | Cyan | 67 | Cyan | 67
|
| Magenta | 0 | Magenta | 33 | Magenta | 67 | Magenta | 100 |
| Cyan | 33 | Cyan | 33 | Cyan | 33 | Cyan | 33
|
| Magenta | 0 | Magenta | 33 | Magenta | 67 | Magenta | 100 |
| Cyan | 0 | Cyan | 0 | Cyan | 0 | Cyan | 0
|
| Magenta | 0 | Magenta | 33 | Magenta | 67 | Magenta | 100 |
Figure 5.6c: CCC.aml The ordinal data sets from figure 5.6a with a reverse progression in the cyan lookup. This causes a change in overall tone of the map.
Figure 5.6d: CBL.aml A legend for figure 5.6c. Note that with this ordering of cyan, high values on both axes are displayed in red--the color of danger.
By reversing the values in either cyan or magenta/yellow, the direction of correlation that is highlighted is reversed. This AML requires two lookup tables, one of which has CMY values for cyan, and the other has values for red (magenta and yellow), like the table above. See Figure 5.6a (positive correlation) and 5.6c (the same data, but with negative correlation highlighting) and CCC.aml.
CCC <cyan_lookup>
<red_lookup>
<cyan_lookup>- specifies CMY cyan (from 10 to 100)
<red_lookup>- specifies CMY red (from 10 to 100).
Two Ratio Data Sets--Eyton's Ellipse
Figure 5.7a: CEE.aml Two ratio data sets displayed using the equiprobability ellipse method. Correlation between the two variables is determined to select a middle class.
Another technique for displaying correlations between two data sets is the equiprobability ellipse (Eyton 1984). This method uses four categories (a two by two matrix) to indicate the extreme values in the scatter plot of the two data sets, and a fifth category that indicates the central cluster of data. This method is effective at highlighting correlations between two data sets, but may not be effective in communicating uncertainty. See Figure 5.7a and CEE.aml.
CEE <ellipse_lookup>
<ellipse_lookup>- a lookup table for polygons generated by EYTON.aml.
Bivariate Legends--Eyton's Ellipse
Figure5.7b: EEL.aml A legend for figure 5.7a. A scatter plot show the location of each data pair, and the hues show the color used in the map.
Because of the uniqueness of the this bivariate representation system, a different AML must be used to generate the legend. EEL.aml generates a scatter plot of the two correlated data sets, and shades each marker with the color used to represent that data value. The AML works with all of the equiprobability ellipse displays (points, lines, and polygons). See Figure 5.7b and EEL.aml.
EEL <ellipse_lookup> <start_x>
<start_y> <size_x> <size_y> {markerset}
{markersymbol}
{markersize} {textset} {font} {point_size}
{float_precision}
<ellipse_lookup>- a lookup table generated by EYTON.aml
<start_x> <start_y>- the lower left corner of the scatter plot
<size_x> <size_y>- the size of the scatter plot in PAGEUNITS
{markerset} {markersymbol}- specify a marker to use in the scatter plot, the default is municipal.mrk, symbol 104
{markersize}- the size of the scatter plot marker--defaults to 0.15 inches
{textset} {font} {point_size}- define the labelling text--defaults to a 10 point roman font
{float_precision}- defines the number of decimal places that will be shown--defaults to 2.