Cartographic
Methods
Alan Brenne*
The U. S. Environmental Protection Agency
Office of Information Resources.Management
National Geographic Information Systems Program
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The ARC Macro Language^ and C programs discussed in this guideline are
available by anonymous ftp from sdcdg01.sdc.epa.gov and are in the files:
/pub/readme.cart
/pub/map_amls.tar.Z
/pub/map_design.tar.Z
/pub/map_post.Z
/pub/color_post.tar.Z
For users not on the Internet, the programs can be obtained on hardcppy,
3.5 inch disks or QIC 150 by contacting the National CIS Program at 703^235-5600,
or:
401MST.SW,MS3405R
Washington, DC 20460.
AML, ARC/GRID, ARC/TIN and ARC Macro Language are trademarks
and ARC/INFO is a registered trademark of Environmental Systems Research
Institute. AViiON is a trademark of Data General Corporation. Sun and
SPARCstation are trademarks of Sun Microsystems, Inc. PostScript is a trademark
of Adobe Systems, Inc. Use of these trademarks does not constitute an
endorsement by the United States Government.
In no event shall the United States Government have any responsibility or
liability for any consequences of any use, misuse, inability to use, or reliance upon
the information contained herein, nor warrant or otherwise represent in any way
the accuracy, adequacy, efficacy, or applicability of the contents hereof. :
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Table of Contents
Chapter One
The Utility of Maps and Graphics 1
The Principles of Data 1
Meta-Data and Uncertainty 4
Uncertainties of the Physical World 6
Uncertainties of the Computer World 7
Uncertainties of the Human World 10
The Idea of Visual Communication 11
The Means of Visual Communication 13
Methods for Visually Communicating Data and Meta-Data 17
Chapter Two
Producing Displays 24
Classifying Space 24
Projections 25
Scale and Generalization 27
Space and Time 27
Classifying Data 28
Manual Classification 28
Natural Breakpoints 29
Eyton's Equiprobability Ellipse Bivariate Classification 30
Symbol Value Update 31
Unclassed Maps 31
Page Layout 32
Titles and Type 34
Insets and Legends 35
ARC/INFO Hints 36
Chapter Three
Point Symbolization in ARC/INFO 38
Monovariate Symbolization 38
Nominal Data-Hue 38
Nominal Data-Orientation 38
Nominal Data-Shape 38
Ordinal to Ratio Data—Orientation 40
Ordinal to Ratio Data-Value 40
Ordinal to Ratio Data—Size 40
Ordinal to Ratio Data-Graduated Circle Size 42
Bivariate, Monochrome Symbolization 42
Two Nominal Data Sets—Shape and Orientation 42
Nominal Data, and Ordinal Data—Shape and Value 44
Nominal Data, and Ratio Data—Shape and Size 44
Ratio Data, and Ordinal Data-Size and Value 44
Bivariate, Color Symbolization 45
Two Nominal Data Sets—Shape and Hue 45
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Two Nominal Data Sets—Dual Hue Ranges 45
Two Ordinal Data Sets—Complementary Colors 47
Point Legend Creation 47
Nominal Data, and Ordinal Data-Hue and Intensity 47
Two Ratio Data Sets-Equiprobability Ellipse 49
Ratio Data, and Nominal Data—Size and Hue 49
Multivariate Symbolization 49
Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization 49
Nominal Data, Ratio Data and Ordinal Data—Shape, Size and Value 51
Ratio Data, Nominal Data, and Ordinal Data—Size, Hue and Intensity 51
Ratio Data-Point Pie Graphs 51
Chapter Four
Line Symbolization in ARC/INFO 53
Monovariate Symbolization 53
Nominal Data—Hue 53
Nominal Data—Shape or Texture 53
Ordinal Data-Value 55
Ratio Data-Size 55
Bivariate, Monochrome Symbolization 56
Two Nominal Data Sets—Shape and Texture 56
Nominal Data, and Ordinal Data—Shape and Value 56
Nominal Data, and Ratio Data—Shape and Size 58
Ratio Data, and Ordinal Data—Size and Value 58
Bivariate, Color Symbolization 58
Two Nominal Data Sets—Texture or Shape, and Hue 58
Two Nominal Data Sets-Dual Hue Ranges 60
Two Ordinal Data Sets—Complementary Colors 60
Bivariate Color Legends 60
Two Ratio Data Sets-Eyton's Ellipse for Lines 62
Ratio Data, and Nominal Data-Size and Hue 62
Nominal Data and Ordinal Meta-Data—Hue and Intensity 62
Multivariate Symbolization 62
Three Ordinal to Ratio Data Sets—Red, Green and Blue Symbolization 62
Nominal Data, Ratio Data, and Nominal Data-Shape, Size and Hue 64
Nominal Data, Ratio Data, and Ordinal Data-Shape, Size and Value 64
Ratio Data, Nominal Data, and Ordinal Data-Size, Hue and Intensity 64
Chapter Five
Choropleth Symbolization in ARC/INFO 66
Monovariate Symbolization 66
Nominal Data-Hue 66
Monovariate Legends—Filled Polygons 66
Nominal Data—Orientation 68
Nominal Data—Shape 68
Ordinal Data-Value 68
Ordinal to Ratio Data—Orientation 68
Monovariate Legends—Orientation 70
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Bivariate, Monochrome Symbolization 70
Two Nominal Data Sets-Texture and Orientation 70
Nominal Data, and Ordinal Data—Texture Distinguished by Value 72
Nominal Data-1 and 2—Texture as Intersecting Lines 72
Two Ordinal to Ratio Data Sets-Texture as Intersecting Lines 72
Bivariate Legends—Unclassed Texture 74
Bivariate, Color Symbolization 74
Two Nominal Data Sets—Texture Distinguished by Hue 74
Bivariate Legends—Lookup Table Based Displays 74
Two Nominal Data Sets—Dual Hue Ranges 76
Nominal Data, and Ordinal Data—Hue and Intensity 76
Two Ordinal Data Sets—Complementary Colors 76
Two Ratio Data Sets-Eyton's Ellipse 78
Bivariate Legends—Eyton's Ellipse 78
Multivariate Symbolization 80
Two Nominal or Ordinal Data Sets, Ordinal Data Sets-Texture with Value 80
Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization 80
Multivariate Legends—RGB Space 80
Chapter Six
Graduated Symbol Symbolization in ARC/INFO 83
Monovariate Maps 83
Ordinal to Ratio Data—Graduated Circles 83
Ordinal to Ratio Data—Cartograms 83
Monochrome, Bivariate Symbolization 83
Ordinal to Ratio Data, and Ordinal Data-Graduated Circles and Value 85
Ordinal to Ratio Data, and Ordinal Data-Cartograms Shaded by Value 85
Color, Bivariate Symbolization 85
Ordinal to Ratio Data, and Nominal Data-Graduated Circles and Hue 85
Graduated Circle Legends 85
Ordinal to Ratio Data, and Nominal Data—Cartograms with Hue 87
Cartogram Legends 87
Multivariate Symbolization 87
Ratio Data, Nominal Data, and Ordinal Data—Graduated Circles, Hue and Intensity 87
Ratio Data, Nominal Data, and Ordinal Data—Cartograms, Hue and Intensity 89
Ratio Data-Polygon Pie Graphs 89
Graduated Pie Legends 89
Chapter Seven
Grid-Cell Symbolization in ARC/INFO 90
Conversion of Polygons to Grids 90
Lookup Tables for Ratio Grids 90
Monovariate Symbolization 90
Nominal Data-Hue 92
Ordinal to Ratio Data-Value 92
Bivariate and Multivariate Symbolization 92
Nominal Data, and Ordinal Data-Hue and Intensity 92
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Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization 92
Chapter Eight
Dot Density Symbolization in ARC/INFO 93
Conversion of Polygons to Dot Density 93
Monovariate Symbolization 93
Ordinal to Ratio Data-Texture 93
Monovariate Dot Density Legends. 93
Monochrome, Bivariate Symbolization 95
Ratio Data, and Ordinal Data-Texture and Value 95
Bivariate Dot Density Legends 95
Color, Bivariate, and Multivariate Symbolization 95
Ratio Data, and Nominal Data—Texture and Hue 97
Ratio Data, Nominal Data and Ordinal Data—Texture, Hue and Intensity 97
Three Ordinal to Ratio Data Sets—Red, Green and Blue Symbolization 97
Chapter Nine
Isopleth and Fishnet Symbolization in ARC/INFO 98
Polygon to Isoline Conversion 98
Polygon to Surface Conversion 98
Monovariate Symbolization 98
Ratio Data—Isoline Location 98
Ratio Data-Fishnet Height 100
Isoline and Fishnet Legends 100
Bivariate Symbolization 100
Ratio Data and Ordinal Data-Surface Shaded with Value 100
Ratio Data and Nominal Data—Surface Shaded with Hue 102
Multivariate Symbolization 102
Ratio Data, Nominal Data and Ordinal Data-Surface with Hue and Intensity 102
Four Ratio Data Sets—Surface Shaded with Red, Green and Blue 103
Chapter Ten
Thematic Mapping in ARC/INFO 104
Summary of Presented Methods 104
Areas of Possible Continued Research 104
Acknowledgments 104
References 105
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Table of Figures
Chapter One
Figure 1.1 2
Table 1.1 3
Figure 1.2 6
Figure 1.3 7
Figure 1.4 8
Figure 1.5 10
Figure 1.6 11
Figure 1.7 14
Figure 1.8 15
Figure 1.9 18
Figure 1.10 20
Chapter Two
Figure 2.1 24
Figure 2.2 25
Figure 2.3 25
Figure 2.4 26
Figure 2.5 26
Figure 2.6 27
Figure 2.7 28
Figure 2.8 32
Figure 2.9 33
Figure 2.10 34
Figure 2.11 35
Chapter Three
Figure 3.1 39
Figure 3.2 41
Figure 3.3 43
Figure 3.4 46
Figure 3.5 48
Figure 3.6 50
Chapter Four
Figure 4.1 54
Figure 4.2 57
Figure 4.3 59
Figure 4.4 61
Figure 4.5 63
Chapter Five
Figure 5.1 67
Figure 5.2 69
Figure 5.3 71
Figure 5.4 73
Figure 5.5 75
Figure 5.6 77
Figure 5.7 79
Figure 5.8 81
Chapter Six
Figure 6.1 84
Figure 6.2 86
Figure 6.3 88
Chapter Seven
Figure 7.1 91
Chapter Eight
Figure 8.1 94
Figure 8.2 96
Chapter Nine
Figure 9.1 99
Figure 9.2 101
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Chapter One
The Utility of Maps and Graphics
Maps have a wide variety of uses, ranging from the recording of
information (such as cadastral maps) to aiding navigation (such as road maps and
naval charts). Two of the main uses of maps (and graphics) in environmental
analysis, particularly as assisted by geographic information systems, are the
analysis of data and the presentation of data. Neither of these uses precludes the
other, and both can be aided by good graphic design techniques. Graphic design
requires an understanding of the data (and the information represented by the
data), an understanding of the methods of visual communication, and the ability
to make use of the available means of communication. Although each of these
components is described in other places (such as statistics books for data analysis,
cartographic texts for visualization of spatial data, and software manuals for the
actual production of maps), this guideline integrates these three areas in the
context of the Environmental Systems Research Institute's geographic information
system, ARC/INFO revision 6, as the available means of communication.
As such, chapter one contains a brief discussion of data and meta-data
issues, and visualization and communication theory; chapter two consists of a
discussion of issues involved in the design of maps, such as projections and data
classification, as accomplished in ARC/INFO; and chapters three through nine
present ARC Macro Language programs for specific symbolization techniques for
point, line and area data. Chapter ten provides a brief conclusion.
The Principles of Data
For geographic phenomena, there are two types of data that comprise
information about a phenomena: attribute data (the measured characteristic of a
location), and location data (the measured location of a characteristic). This
pairing of information types is reflected in the two major approaches of geographic
information systems: vector systems, which emphasize the attribute; and raster
systems, which emphasize the location. ARC/INFO now combines both of these,
allowing a wide variety of analysis and mapping, but the appropriate use of this
information is still dependent on the analyst/cartographer.
Attribute data can be grouped into several categories-empirical levels-
which influence the design requirements for representing information. Each
empirical level contains all of the information of lower levels (and thus can be
simplified) while adding additional information (see Figure 1.1 on page 2 for a
comparison of attribute data levels with spatial characteristics and Visual
variables' for area data). The lowest empirical level is nominal data; this data only
indicates that something is different than something else. Names of states are an
example of nominal categorization. The next level of empirical data is ordinal
data; this data indicates that something is more (or less) than something else, but
no quantity can be given to that distance. The terms high, medium and low reflect
ordinal differences. The third level of empirical data is interval data; a linear
measurement of distance can be used to gauge the differences between instances.
The highest level of empirical data is ratio data; this data indicates that something
is more (or less) than something else (and thus different), that a linear distance can
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Abrupt character of Inter-regional change SmOOth
Discrete
Interval/Ratio
Data
Graduated
Symbol
character
of Intra-
reglonal
change
Graduated
Symbol
Continuous
Ordinal
Data
Continuous
Circle/Dot
Combination
Dot
Density
Unit-Vector
Density
/ Dosymetrtc
Unclassed
Choropleth
Isoline
[Fishnet}
Classed
Graduated
Symbol
Dot
Density
Multip
^ Classed
Graduated
Classed
Choropleth
Stepped
Surface
Visual Variables
location
value
Intensity
orientation
shape
size
hue
texture
arrangement
focus
Discrete
^ Arbitrary ^
Nominal
Data
Continuous
Visual Order
established by the
Visual Variables
Ca Visual Isolation
(differences)
EZ Visual Levels
(standing out)
CD poor order control
Representation of Data Variables
•1 good/primary representation
^ good as an additional variable In multlvarlate
maps
ES fair representation
E3 fair as an additional variable In mulovartate
maps
O poor representational method
Figure 1.1 Spatial data models for area data and their cartographic representa-
tions; developed from MacEachren and DiBiase (1991) and DiBiase, Krygier,
Reeves, MacEachren and Brenner (1991). In a thematic map, the information to be
displayed can be categorized by its empirical level (nominal to ratio), how the data
changes within any region it is aggregated into, and how the data changes between
adjacent regions. Once this categorization is done, visual variables can be selected
on the basis of the ability to represent the information so categorized.
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be used to gauge differences and that ratio comparisons (such as: this is twice that)
can also be done. The essential difference between ratio and interval data is that
for ratio data, a non-arbitrary zero point is intrinsic in the measurement; this
difference is small enough that, for visualization, the methods used for
representing both types of data are the same. An example of the difference
between interval and ratio measurement is the difference between temperature
measured in degrees Celsius and degrees Kelvin; the Celsius system has an
arbitrary zero (the freezing point of water) but the Kelvin system's zero is not
arbitrary (absolute zero: point at which the particle motion that is 'temperature,'
stops).
Because of these differences in attribute data, care must be taken when
comparisons between different levels of data area made (see Table 1.1 for the types
of comparisons that can be performed on data of given levels). For example,
ordinal data may be stored as integers that represent the order, but the values of
these integers do not indicate any measurement of the variability of the data. This
lack of measurement does not, however, preclude a software system from acting
on the data as if it were ratio data and thereby calculating essentially meaningless
statistics (or spatial patterns). If comparisons of data of different levels must be
done, either the higher level of data must be reduced to the lower, or a
transformation (an addition of information) must be done to raise the lower level
to the higher. For nominal or ordinal data, the procedures of psychometrics can be
used to recast ordinal information into interval or ratio data. Essentially this
involves assigning utility values (such as money) to data levels that do not
normally have this type of information associated with it (such as aesthetic values).
This can be accomplished by conducting a survey to get individual assignments of
value, and then using the collected data to assign overall values to the data.
Nominal Ordinal Interval Ratio
Rank Comparison Invalid Valid Valid Valid
Addition, Subtraction Invalid Invalid Valid Valid
Multiplication, Division Invalid Invalid Invalid Valid
Statistics:
Parametric Invalid Invalid Valid Valid
Nonparametric Invalid Valid Valid Valid
Table 1.1 Valid data comparisons. Because of the varying degree of numerical
precision associated with different data levels (nominal through ratio) only certain
operations can be applied to comparisons between two data sets; comparisons
between data of two different levels must occur at the lower of the two classes
(ESRI Grid Class Notes 1992,11-22).
Although all information is classified due to the nature of measurement
uncertainty in the recording of data (MacEachren 1992, 48), attribute data can be
further classed into groups for both presentation and analysis (see Classifying
Data on page 28 for a discussion of data classification in ARC/INFO).
Classification involves the creation of range categories that individual instances fit
into and thus take on that value range. This results in a loss of information and can
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be a reduction in the empirical level of a measurement (interval/ratio data is
reduced to ordinal, for example). This loss of precision is offset by the
simplification of the presentation of information. These classifications are
accomplished by representing ranges of data as categories on the display medium,
through the use of symbolization that is appropriate to the level of measurement
(see Figure 1.1 on page 2).
Spatial data can be grouped into four categories. The first type of data
represents point specific information. The second type of data represents linear
information. The third type of data represents area information. The fourth type
of data represents volume information. Each of these categories is scale specific;
an area feature such as stream may require mapping as a linear feature if the total
area under consideration is small enough that displaying the stream as having
both length and breadth becomes too tedious or difficult to represent in the
available media, for the additional information retained. Volumetric information
is also dependant on the means of display-the appearance of three dimensions can
only be approximated on a two dimensional surface. Although the visual
variables that best represent different levels of information do not change for each
of the types of spatial data, the ARC/INFO methods for accomplishing those
representations change.
For environmental data, Mark Monmonier and Branden Johnson (1990,5-7)
have characterized spatial data into: single location; single location and affected
area; and multiple locations and the pattern of distribution. Single location
answers not only 'what' but 'where'; this can be applied to all of the basic types of
spatial data and allows the map user to relate environmental information to his or
her own experience (this is what Edward Tufte (1990) calls micro/macro
readings). Building on single location, single location and affected area adds
information concerning how a 'what' influences its surroundings (because
'influence' may be more subject to interpretation than a measurement, presentation
of meta-data can become very important in the presentation of data). Finally,
multiple locations and the pattern of distribution integrates more than one
instance of single location and affected area into one map.
Area phenomena can also be categorized on the basis of its spatial grouping
and how it changes over space (MacEachren and DiBiase 1991) (see Figure 1.1).
Grouping ranges from continuous (no grouping) to discrete (complete grouping):
This reflects the degree of spatial autocorrelation within areas. Changes over space
can be smooth to abrupt. This reflects the degree of spatial autocorrelation
between areas. These changes suggest that appropriate symbolization choices be
made that accurately reflect the nature of the data. The possible symbolization
choices include, but are not limited to: graduated symbols for abrupt, discrete data;
dot density for smooth, discrete data; isopleth (or the '3-D' equivalent fishnet) for
smooth, continuous data; and choropleth for abrupt, continuous data; this is in
contradiction with the all-to-common practice of making choropleth maps for all
types of area data.
Meta-Data and Uncertainty
The uncertainty of information is becoming an important topic with the
increased use of computers for data processing, presentation and analysis. This is
being addressed with position statements such as the Environmental Protection
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Agency's Locational Data Policy (1991) and the National Center for Geographic
Information and Analysis' Visualization of Data Quality initiative (MacEachren
1992, 47). Yet, these cannot eliminate uncertainty, which exists at the most basic
levels of measurement according to Heisenberg's Uncertainty Principle (Capra
1983). Because of this, David Rejeski (1991) suggests that uncertainties should be
addressed openly in order to ensure that decisions have both utility and
believability. He, as well as Granger Morgan and Max Henrion, recognize that
uncertainty can be valuable information. Morgan and Henrion (1990,3) give three
specific reasons for the inclusion of uncertainty in policy oriented research:
1. A central purpose of policy research and policy analysis is to help
identify important factors and the sources of disagreement in a
problem, and to help anticipate the unexpected. An explicit
treatment of uncertainty forces us to think more carefully aoout
such matters, helps us identify which factors are most and least
important, and helps us plan for contingencies or hedge our bets.
2. Increasingly we must rely on experts when we make decisions. It is
often hard to be sure we understand exactly what they are telling
us. It is harder still to know what to do when different experts
appear to be telling us different things. If we insist they tell us
about the uncertainty of their judgments, we will be clearer about
how much they think they know and whether they really
disagree.
3. Rarely is any problem solved once and for all. Problems have a way
of resurfacing. The details may change but the basic problems
keep coming oack again and again. Sometimes we would like to
be aole to use, or adapt, policy analyses that have been done in the
past to help with the proolems of the moment. This is much easier
to do when the uncertainties of the past work have been carefully
described, because then we can have greater confidence that we
are using the earlier work in an appropriate way.
Uncertainty has dictionary definitions such as, "uncertain in respect of
duration, continuance, occurrence, etc.," "liability to chance," "indeterminate as to
magnitude or value" (Simpson and Weiner, Oxford English Dictionary, 1989, 899).1
A more useful interpretation for use in environmental risk analysis would be that
uncertainty is the information contained in the data about data (that is, meta-data).
By defining uncertainty this way, meta-data can be used as another piece of
information in the analysis and presentation of data, including risk-based policy
making.
Uncertainty has a taxonomy that should be useful in delimiting the origins
of uncertainty and the reliability of data at any given point in an analysis (see
Figure 1.2 on page 6). Although Morgan and Henrion (1990) discuss 'The Nature
and Sources of Uncertainty" as chapter 4 of Uncertainty: A Guide to Dealing with
Uncertainty in Quantitative Risk and Policy Analysis in detail, this presentation is a
distillation based on several sources, which include Morgan and Henrion and
others sources, as noted. The taxonomy can be broken down into three groups:
uncertainties of the physical world; uncertainties of the computer world; and
'•Uncertainty begins as the vagueness of duration, etc with Wyclif in 1382. By 1982, Oxford
(1989,900) reports: "What the uncertainty principle asserts is that for no state of any system
can all dynamical variables be arbitrarily well-determined."
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uncertainties of the human world. Problems of the measurement of natural
phenomena constitute the first category; Alan MacEachren (1992, 48) reports that
the National Center for Geographic Information and Analysis calls this "data
quality". The uncertainty of the physical world can be further split into
measurement uncertainty and parameter uncertainty.
Uncertainty
Physical World ' Computer World ' Human World
Measurement
Location
Attribute
Parameter
Aggregation
Generalization
Time
Consistency
Descriptive
I Numeric
1 Spatial Delineation
Computational
Sending Meanings
I Open Presentation
of Data and Meta-Data
Receiving Meaning
Rounding Ignoring Meta-Data
Significant Digit Shift I Misunderstanding
Over/Underflow Meta-Data
Propagational
Compounded Computational
1 Polygon Overlay
Modeling
I Robustness
1 Validity
Figure 1.2 A taxonomy of uncertainty.
Uncertainties of the Physical World
Measurement uncertainty for geographic data includes both location and
attribute uncertainties. Location uncertainties (Rejeski and Kapuscinski 1990,10)
can be considered the accuracy (closeness to a 'true' value) of the instruments and
the reliability, or precision, (repeatability of a measurement) of the methods used
to calculate a site's position (see Figure 1.3 on page 7). For example a location of a
phenomenon can be determined by use of many methods, such as a professional
surveyor's analysis, use of a global positioning system, or terrain analysis
estimation. Each of these methods is of varying accuracy and precision, and the
meta-data that should be recorded includes the manner in which a site location
was first defined, the method use to derive its location, the time it was derived,
and an estimate of its accuracy.
Attribute uncertainty can be considered the accuracy and reliability of the
instruments used to take a measurement of the environment. For example, an
instrument may be set up to measure atmospheric concentrations of carbon
monoxide, measuring levels in parts per million and with an accuracy of plus or
minus one part per million. The data in this situation is the part per million
measurement and the meta-data includes the plus or minus one part per million
accuracy of the instrument.
Parameter uncertainty (Rejeski and Kapuscinski 1990,11; MacEachren 1992,
47-8) involves the problem of the aggregation and generalization of point samples
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to areas for spatial data, or trend lines Reliable, but not Accurate.
for linear data; the temporal variability (/^
between data items and between _ Arrurate, but
measurement times and data usage; /^ ^\ not reliable.
and the logical consistency and
completeness of data. This is the
question of whether the measurements
that are recorded and then used for
analysis are adequate measurements
of what was intended to be measured;
it entails the consequences of the True Value'
assumption of autocorrelation. Before Figure 1.3 An example of the
a model is constructed to provide an difference between accuracy and
explanation or a projection of reliability in spatial location measure-
environmental phenomena, it must be ments.
recognized that there are few (if any)
phenomena that can be precisely defined and measured for all possible
occurrences. Because of this, interpolation and extrapolation-whether linear (as
in a measurement), spatial (as in an area generalization), or temporal (as in data
from one time as estimates for some other time)-must be done even though the
process introduces uncertainty into the analysis.
There have been suggestions made for reducing and representing
parameter uncertainty. For generalizing spatial data, Cort, Rowe and Philpot
(1985; in MacEachren 1992,44) suggest that interpolation in spherical, rather than
planar, coordinates will introduce less uncertainty in the creation of area
information from point samples (particularly for large areas). MacEachren and
Davidson (1987; in MacEachren 1992, 46) demonstrate that increasing sampling
frequency will also reduce (but not eliminate) the uncertainty of interpolation; this
should also be true for linear and temporal data as well. For, representing
parameter uncertainty, Rejeski and Kapuscinski (1990, 10) suggest the use of
transitional buffer zones to represent "fuzzy" boundaries, rather than one line
demarcating "hard edges" (see Figure 1.4 on page 8).
Uncertainties of the Computer World
Problems of the use of computers for storing and manipulating data
constitute the second category of uncertainty. This can be subdivided into four
groups: descriptive uncertainty, computational uncertainty, propagational
uncertainty and modeling uncertainty. Thoughtful use of programs and
programming techniques can reduce the amount of uncertainty introduced to data
by computer manipulation. Herman Knoble (1990, 2) states that correct and
accurate computer programs must be an ethical responsibility when dealing with
numerical algorithms, all of which, "at the bottom line...affect people."
Descriptive uncertainty deals with the representation of data in computers,
including both numeric and spatial problems. Numeric uncertainty arises from
the method computers use to store data. For example, the binary number system
does not have an exact representation of some common decimal numbers, such as
1/100. Another type of numeric uncertainty arising from number storage is the
shifting of significant digits. If a number is input into a computer that has the
ability to store a longer number than is input, the computer will 'pad1 the extra
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Mean Sea Level
Mean Spring High Tide
Mean Neap High Tide
Mean Sea Level
Mean Neap Low Tide
Mean Spring Low Tide
Figure 1.4 An example of a change from a hard to a 'fuzzy' boundary.
space with zeros. These digits will be available for computation in numeric
modeling even though they add no information and are meaningless. Significant
digit shift can occur in the other direction as well. If a number is input into a
computer that stores fewer digits than is input, the computer will round or
truncate the number to fit its numeric scheme. These problems can be controlled,
but not eliminated, by specifically programming the computer for the required
operations (Knoble 1990), but for generally available software this is not possible.
Spatially, data is generally stored as either a table of vectors that define
sharp boundaries between regions, or in regular tessellations (square, 'raster'
grids) that force a predefined spatial pattern on an area (Rejeski and Kapuscinski
1990,10). Both of these methods introduce uncertainty: the vector representation
forces boundary lines where transition zones may be; and tessellations assume the
entire grid cell is homogenous. These problems can be reduced, but again not
eliminated, by using smaller polygons or grid cells, but this forces a trade off
between data file size and computational time, and decreased uncertainty, which
may not be pragmatically feasible.
Computational uncertainty deals with the problems of numeric modelling
by using computers (Knoble 1990; Rejeski and Kapuscinski 1990,13). Once data
are stored in a digital format, any further processing can introduce uncertainty.
Type shifting (such as from an integer format to a real number format, or from
reals to integers) can introduce uncertainty by forcing rounding to occur. More
commonly, rounding occurs within real numbers when numbers that are not
similar in value are arithmetically joined. Knoble (1990,4-5) gives an example of
the results of this type of rounding: an IBM 3090 Model 600, VS FORTRAN 2.4
program that for the formula:
P=((A+X)**2-A"2-2.*A*X)/X**2
generates an answer of -4999.99609 when A is equal to 1000.0 and X is equal to 0.01,
despite the fact that the formula simplifies to P equalling one for all X's not equal
to zero.
Significant digit shift can also occur in arithmetic operations, particularly in
operations involving subtraction of similar values. Subtracting 1.23456787 * 107
from 1.23456789 * 107 yields 0.2, but a computer can store this value as 2.00000000
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* 10'1, and as with data input, will allow computation on all of the digits to the right
of the 2, which is the only meaningful digit in the number.
Two additional, similar problems that may occur are overflow and
underflow. These result when a number is incremented, or decremented beyond
the storage type's ability to represent numbers. Depending on the operating
system this may cause an error or may be ignored with the value remaining the
same or drastically changing. Borland's Turbo C++ 2.0, running under MS-DOS
5.0 on an IBM AT, compiles programs that allow adding one to the thirty-two bit,
'unsigned long' integer 4294967295 (which is equal to 232 - 1, and is the largest
integer that can be represented in thirty-two bits), changing the value of the
variable to 0. Turbo C++ compiled programs will give an overflow error when
thirty-two bit real numbers (type 'float') are incremented outside of type float's
range. When these computational uncertainty errors occur in a program, and are
not handled well, the program could continue and generate an apparently correct
answer purely by chance (Knoble 1990,2).
Propagational uncertainty deals with the problem of how uncertainty from
a physical world measurement or another computer-related uncertainty moves
through successive iterations of a model. It can be tested by varying the input to a
numeric model in small steps to see if small changes can make large differences in
the output of a computation, which in principle should not occur. For example, by
making the value of A equal to 100.0 and X equal to 0.01, Knoble's (1990, 5)
program generates a value for P equal to -39.0624847; by changing X to 0.0078125,
the program generates a value of P equal to 0.0000000. Propagational uncertainty
can also be tested if the computer program can be rewritten to an algebraically
equivalent, but computationally different manner, which would allow comparison
between programs that should generate the same output. By simplifying the
formula in Knoble's example to a command line such as:
if X not equal to 0 then P = 1 else print "DIVISION BY ZERO"
the problems of floating point arithmetic can be avoided.
Propagational uncertainty not only involves the accuracy of real number
computations for numeric data, but also the generation of polygon overlay slivers
within vector spatial data, such as that used by ARC/INFO (see Figure 1.5 on page
10). The slivers that may be handled by "fuzzy tolerances" (ARC Command
References, Commands J-Z, 1991, UNION 1), which would allow the shifting of
close lines so that they merged in the output. This could cause the shifting of data
from one layer of a known high accuracy (such as a surveyor's cadastral data) to
correspond with a layer of lower or unknown accuracy (such as information
digitized from a medium or small scale paper map). All future use of the merged
data layer would include the uncertainty created by the overlaying of two data
layers of varying accuracy, and the meta-data that should be attached to the new
data layer would have to reflect an estimate of how much shifting occurred. This
type of shifting can be eliminated by avoiding fuzzy overlays, although this can
cause the generation of sliver regions along boundaries that will cause increased
storage and processing time for use of the new layer, and may not hold any useful
information other than the indication of the difference between the two layers used
to create the new layer.
Modeling uncertainty culminates the types of uncertainty associated with
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Boundary 1\ 11 Boundary 2
Fuzzy Tolerance
Boundary Shift
..Polygon Merge
Sliver
Figure 1.5 Polygon overlay can
cause shifting in boundary lines, or can
create boundary slivers.
10
computers. Although there are several
types of modelling (verbal, graphic,
physical, and mathematical), each of
which is subject to questions of
robustness and validity versus the goal
of the model (such as description or
prediction), it is only mathematical
models that tend to be dependent on
computers for execution and are thus
subject to the other computer
uncertainties. The robustness of a
model is reflected in a model's ability to
handle all appropriate input and
produce a reasonable output. It is thus
tied to propagational uncertainty, but
robustness also entails that not only do
small changes in input not cause
inappropriate changes in output, but
that the model's output, in practice, is
also within the expected range of the
mathematical model, in principle. The
validity of a model is the question of whether a model, in practice, actually
represents the phenomena being modeled, in principle. This questions the
methods used to operationalize a numerical model, such as the validity of using
'if.. .then' statements to ensure the apparent robustness of a procedure that would
otherwise produce non-robust output, when no such statements are apparent in
the 'real world' phenomena.
Uncertainties of the Human World
Problems of the human communication of information and meanings
constitutes the third area of uncertainty (Rejeski and Kapuscinski 1990, 12). In
attempting to communicate information meta-data can be lost in two ways: the
sender of information can give data without the meta-data information, or the
receiver of information does not understand that part of the message. The first
way, not giving meta-data with data, can be the result of restrictions of space
within publication materials, the desire for the appearance of greater accuracy
(Star 1985), and until recently a lack of awareness of the potential importance of
uncertainty information, particularly in the areas of human and environmental
risk analysis (Rejeski and Kapuscinski 1990). The second way that meta-data can
be lost is when the receiver of information not does receive that part of a message.
This can result from the ignoring of meta-data or the inability to interpret the
meta-data through lack of experience in dealing with the way it is conveyed. This
type of failed effective communication can be the result of the variable
interpretations of both words and images. The meaning of words constitutes one
of the major problems the U. S. Environmental Protection Agency has had to deal
with in risk analysis (Rejeski and Kapuscinski 1990,12). Effective communication
of meta-data has been studied in a strictly human realm (body language, etc.), but
little has been done in the area of communication of uncertainty within the realm
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11
of scientific communication, particularly with spatial data (Rejeski and
Kapuscinski 1990, MacEachren 1992).
This taxonomy should prove useful, particularly for reducing human
communication uncertainties. By recognizing that uncertainty exists in
measurement and is propagated in computer manipulation of data, these
uncertainties can be dealt with openly and honestly, as Rejeski (1991) suggests.
This, aided by visual communication techniques, should reduce human
uncertainty by increasing the amount of information (by communicating
meta-data) given in the presentation of data.
The Idea of Visual Communication
The effective communication of environmental data and uncertainty as
meta-data requires an understanding of the principles of visual communication
and map design. David DiBiase (1990) has developed a model of information
display, in a research setting, as a means of communication in a continuum from
communication to self through communication to others (see Figure 1.6).
Communication to self can be thought of as "visual thinking", and includes data
exploration, hypothesis generation and confirmation. At this level of data
visualization, maps and other graphics are used to "prompt insight, reveal patterns
in data, and highlight anomalies" (MacEachren 1992,1). The goal in the creation
of these images should be to assist these goals. Because of these goals, it is with
this type of visual communication that the possibility of visualization error is
greatest. MacEachren and Ganter (1990) describe these errors as seeing wrong
(similar to the type I error in hypothesis testing—identifying a pattern that is not
there) and not seeing (similar to the type II error—not identifying a pattern that is
there). But, since these graphics are generally rough and intended only for
viewing by the researcher(s), searching for one 'optimal' display is less important;
more views on the same data may be more helpful and reduce the chances of not
seeing or seeing wrong.
Communication to
others can be thought of as
"visual communication" and
is the realm of presentation
graphics. At this level of
data visualization, maps and
other graphics are used to
synthesize data into an
"abstract statement
concerning patterns and
relationships" (MacEachren
1992,6) and finally to present
the information to others to
persuade them of the
accuracy of the data
assessment (MacEachren
1992, 7). Edward Tufte's
(1983, 77) principles of
graphic excellence can help
Visual
Communication
Synthesis
Presentation
Figure 1.6 DiBiase's (1990) model of the function
of graphics in research. Visualization begins with
exploring an idea. The idea then moves through
confirmation and synthesis in a larger group of
both ideas and people, and ends with presentation
(although each stage can spawn new ideas).
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12
ensure the most information is presented in a minimum of space, and that this
information is conveyed ethically:
The representation of numbers, as physically measured on the surface
of the graphic itself, should be directly proportional to the
numerical quantities represented.
Clear, detailed, and thorough labeling should be used to defeat
graphical distortion and ambiguity. Write out explanations of the
data on the graphic itself. Label important events in the data.
Show data variation, not design variation.
In time-series displays of money, deflated and standardized units of
monetary measurement are nearly always better than nominal
units.
The number of information-carrying (variable) dimensions depicted
should not exceed the number of dimensions in the data.
Graphics must not quote data out of context.
Tufte also discusses the concept of data-carrying ink—that is, don't put more ink on
the page than is necessary to convey the information. These principles are similar
to those that Morgan and Henrion (1990) propose for designing graphics for the
presentation of uncertainty information. Judy Olson (1981) also suggests the need
for clear and accurate legends in her guidelines for the production of bivariate
maps.
Monmonier and Johnson (199077) have proposed a guideline for the
communication of environmental risk, which can aid in the making of maps for
visual communication. Their multistep process is not a waterfall type model
(when one level is completed it cannot be returned to), but rather a guideline for
iterative refinement for the presentation of data. The steps they include are:
setting up the design team; identifying the communication goal; the issue profile;
the audience; the messages of environmental maps; methods; and evaluation.
Setting up the design team acknowledges that one person may not have all of the
knowledge necessary to adequately design a graphic, and that, as necessary, each
of the following steps should involve each person who has or can contribute to the
map. Identifying the communication goal is simply that a focus should be selected
for the map; this will facilitate inclusion of important information and removal of
extraneous data. The issue profile deals with the history of the problem to be
mapped and the constraints on producing the map; that is, the 'environment' of
the map and map design process.
The audience must also be considered when designing a graphic. This
includes consideration of who will be viewing the map (politicians, scientists, the
public, etc.). These different audiences will generally have varying degrees of
map-interpretation skills; this influences the amount of explanatory information
that should be included, the appropriateness of bi- or multivariate maps, and the
appropriateness of 'eye catchers' such as bright colors. Consideration of the
audience should also include an acknowledgment of how the map will be
presented; this is part of the issue profile and influences the choices of methods.
Monmonier and Johnson (1990) present a list of several categories of
messages that environmental maps generally present. The first of these is "What
we found/What we know/What we think we know" (p!2). This is the
presentation of information at its most basic level, but even at this level meta-data
can be presented-'what we think we know.' The second of these messages is
"What you can do/What you should do" (p!3). This is very dependent on the
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13
choice of audience—a lawmaker's set of choices of what to do can be quite distant
from a concerned citizen's, for example. The third message is "What we're doing/
What we want to do" (p!3). For this type of message Monmonier and Johnson
suggest that an overview map with several smaller maps of detail maps may aid
the presentation. The last category is "Why we're doing what we're doing/Why
you should do what we're asking you to do" (p!3). This type of map should
present the reasoning behind a choice or plan of action; this can include the
presentation of the history side of the issue profile.
The final two steps of Monmonier and Johnson's strategy are methods and
evaluation. Methods need to address questions such as the need for one or several
maps, how these maps will be presented (large size color maps, 8.5x11 black and
white maps, slides, video, etc.) and whether or not additional information such as
non-map graphics should be included. Although evaluation is presented as the
last step in map design, it is a part of each of the earlier steps. It is the last step as
a review of the, possible, final design. Evaluation can be formal (a survey) or
informal (a telephone call to someone who has seen the map and can suggest any
possible improvements).
The Means of Visual Communication
Jacques Bertin proposed a group of 'visual variables' that has since been
added on to by other cartographers (such as: Morrison (1974), McCleary (1983),
and Woodward (1991)). This group of variables constitutes those representational
techniques that a cartographer or illustration designer has in the creation of an
image. The list includes: location, size, value, hue, intensity, orientation, shape,
texture, arrangement, and focus (see Figure 1.7 on page 14). This list is not
necessarily all inclusive, but the list is useful in the design of maps and graphics.
Each of the variables can be used to establish visual isolation (difference from
surroundings) and visual levels (greater noticeability) (see Figure 1.1 on page 2),
and according to Bertin, these visual variables have certain levels of measurement
that are commonly associated with them, and thus allow representations that
convey the character of the data.
In a static map, the use of location is limited to the signification of the spatial
place of an item, although in orthogonal displays, location is a flexible tool because
of the possibility of specifying the viewpoint on a simulated three-dimensional
surface. In multiple maps, or dynamic mapping, change in position can be used to
show movement of a feature. It is inherently an interval/ratio variable, but can be
used to depict all levels of measurement.
Size is most often used to depict an ordinal variable, although interval/ratio
variables can also be depicted using size. Because a larger symbol is almost always
associated with 'more,' this is the context that it should generally be used in.
Of the 'color' variables, Bertin (1983, 42) only identified value and hue.
Value, like size, has a distinct range from more to less and is therefore good for
mapping ordinal data and can also be used for interval/ratio data. ARC/INFO
refers to value as lightness. Hue can be used to depict ordinal or interval/ratio
data because the frequencies that constitute hue are ordered, but these orders are
not always readily remembered and used; hue (at a constant value and intensity)
is therefore best used for nominal data. Intensity, which is also called saturation,
has a distinct range from more to less and is therefore good for ordinal data.
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14
Point
Line
Area
Location
Size
*
Value /.;•.
• •
£ -^ j
& £
, , -tl'-
± Xt v A
©
Hue
Intensity
Orientation
Shape
Texture
Arrangement
Focus
Figure 1.7 The visual variables as presented by DiBiase, Krygier, Reeves,
MacEachren, and Brenner (1991). All have been done in ARC/INFO 6.0, but some
(such as texture for point symbols, orientation for line symbols, and arrangement
for area symbols) are more difficult and, thus, less useful than others.
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15
As availability increases for the means of creation of high resolution color
displays, use of the color visual variables will become an even greater part of
cartography. Color can be specified in several ways (Dent 1985). One common
and useful way is the Munsell color system (see Figure 1.8); it is based on the
human perception of color (and is similar to the Tektronix color cone, and a color
specification system in ARC/INFO, Hue-Lightness-Saturation). This system
divides color into the three visual variable categories value, hue and intensity.
Value is the measure of the lightness or darkness of a surface; it is the total
amount of light that is reflecting or emitting from a surface measured relative to
the human ability to discriminate black from gray up to white. It is the only
measure of light along the white-gray-black continuum, because all frequencies of
light should be equally present.
Hue is the term most often meant when the word 'color1 is used. The
Munsell color system records hue as an angular measure around a color space. It
represents the modal value of the frequency of light that is reflecting or being
emitted from a surface. When a light has no modal frequency, the perceived light
is along the white-gray-black
continuum, which constitutes the Value —'W*1116
central axis of the Munsell color
space.
Intensity is a measure of the
purity of the spectral frequency of
light. It represents the variance of the
frequency of light; greater variance
means that a larger range of
frequencies of light are being emitted
or reflected from a surface—that the
surface has more gray in it. A feature
of intense colors is that they tend to be
more noticeable (stand out more)
than less intense colors, even when
the total amount of light reflected or
emitted may be the same, which
Hue
Intensity
2/
I/
Black
Figure 1.8 The Munsell color system;
makes intensity good for establishing for example, an intense yellow could be
J C7 O • f • j ^N/F"f / *1 J
visual hierarchies. Because of the specified as 5Y7/14.
human visual system, the value of the
most intense color of different hues varies, with yellow having the highest value
for its maximum intensity. This change is accounted for in the Munsell color
system; the Tektronix color cone assumes that maximum intensity for any color
occurs at the midpoint of the value scale.
For cartographic use in displaying ordered data, color hues are generally
arranged to allow ease of interpretation. There are many possible color schemes,
many having been suggested for terrain shading. For other data, the spectral
ordering of hues may be the most obvious for use in mapping ordered data, but
because colors can shift in intensity and value, this may lead to misleading
maps—yellow will stand out in the spectral pattern. Two suggestions are of note
for remedying this problem. The first is the use of a part-spectral scheme: yellow
through orange to red; or, yellow through green to blue. This can allow
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16
redundancy in the visual variables of intensity and value, which reinforces the hue
progression. The second is the use of hues ordered on the basis of value. This may
be a viable alternative, but could prove confusing to those who know the spectral
sequence of hues.
The ability to discriminate colors has received some study, particularly in
the discrimination of values. The Munsell color system divides the range from
black to white into eleven steps, as does the system for black and white
photography developed by Ansel Adams (Upton and Upton 1989,313). For most
cartographic use, eleven steps would be both difficult to create and difficult to
interpret; most cartographic research indicates that the use of half that range (five
or six) is better for map design. If value gives is an indication for the amount of
discriminability that can be expected for intensities, four intensity values is
probably the most that should be used. Discrimination of hues for cartographic
use is affected by the apparent changes in intensity and value that occur as hue is
changed, but for univariate symbolization, five steps should be easily
discriminable in one of the part-spectral sequences.
Colors are produced by two methods: color addition and color subtraction.
The color addition process is most commonly seen in color monitors for computer
displays and television. It involves the mixture for red, green and blue to create
colors on a black surface with all three being used for white. The color subtractive
process is used for the production of printed material, such as paper maps. It
involves the use of cyan, yellow and magenta (and black) to subtract colors that
would reflect from the surface of white paper. Because the overprinting of cyan,
yellow, and magenta generally leaves muddy brown, black is often used as a
fourth color in the printing process. Colors are obtained by overprinting the four
separates, with each offset slightly in order to allow the apparent mixing of colors
in a dither pattern.
The production processes must be kept in mind when choosing color
schemes on a color monitor that will be printed on a paper output device. Colors
on a computer display may not appear the same on a printed sheet, because of the
change in creation method. In addition, on a computer monitor, a point can take
on any of the possible colors generatable by the graphics system, and resolution is
independent of color. On paper output, the dither patterns that are used to create
the appearance of many colors may cause a change in apparent color and, more
significantly, output resolution. ARC/INFO allows the use of color lookup tables
in commands such as HPGL2 (ESRI ARC Command References, 1991) to enable
redefining screen colors to pretested printer colors to help compensate for changes
in color; changes is resolution must be accounted for by the cartographer.
A final consideration for color (particularly hue) is its social interpretation.
Colors can have meanings that must be taken in to consideration when designing
maps and graphics, for example: red as stop; yellow as caution; green as go. For
environmental maps, use of red (particularly, intense red) can indicate imminent
danger, and with dark shades of other colors (blues, grays and browns, for
example) can evoke a sense of foreboding or futility (this is demonstrated in The
Nuclear War Atlas and movies such as Blade Runner). Other color schemes can
invoke other reaction: pastels (colors of low intensity and high value) can indicate
serenity (unclassified maps by the Central Intelligence Agency often make use of
pastels); intense colors such as yellow and cyan grab attention, and can indicate
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17
happiness—they are often used in maps for children.
The final three variables that Berlin identified are orientation, shape and
texture. Orientation is readily discriminated by the human visual system and is
therefore good for indication of nominal data, although by using common symbols
such as clock faces, ordinal and interval/ratio data can be displayed with
orientation. Shape should be used for nominal data categories, because shapes in
general do not have an apparent order and are not as readily distinguished as
other visual variables. Texture is the relative coarseness of an area fill, and because
rough textures appear closer than fine textures, texture is good for establishing
visual hierarchies. Texture should generally be used for nominal data, but it can
also be used for ordinal and interval/ratio data.
Unlike orientation and texture, shape has a continuum of possible
representations: from mimetic to abstract (see Classifying Space on page 24).
Mimetic symbols convey the appearance of what they represent (an animal's
outline represents sightings of that animal). Abstract symbols must be defined (a
legend indicates that triangles represent sightings). ARC/INFO provides many
abstract symbols, a few that are less abstract (for example, an anchor that might be
used to represent a marina), and the ability to define new symbols (see Map Display
and Query). Selection of appropriate levels of abstractness must be considered in
designing a display—use of mimetic symbols may allow less dependence on the
legend, but too many mimetic symbols may give the appearance of a map oriented
toward children.
Two additional visual variables that have been identified since Bertin
proposed his list are arrangement and focus. Arrangement is the order of symbols
in an area fill (from regular to random to clustered), and nominal and ordinal data
can be represented by changes in arrangement. Focus is the last visual variable; it
is the crispness of the edges of symbols. Because this has an apparent order, focus
can be used to display ordinal data and could be used for interval/ratio data,
although too much variability of focus may make a map hard to read.
Methods for Visually Communicating Data and Meta-Data
The communication of uncertainty has been studied by Morgan and
Henrion (1990) with Harold Ibrekk, although their concern was the
communication of the uncertainty of linear data. Because of this, the methods they
present cannot be readily used in the communication of mapped geographic data,
except for point symbolization (even this is difficult in ARC/INFO), but their
study highlights some of the difficulties that can be encountered in the visual
communication of uncertainty and their conclusion are useful.
Their study analyzed nine methods for displaying uncertainty in linear
data: a point estimate with an error bar; a discrete density function); a pie chart; a
probability density function; a half-height probability density function mirrored
on the x-axis; a dot density horizontal bar a vertical line density horizontal bar; a
modified Tukey box plot (minimum and maximum points are not included, and a
mean point is included); and a cumulative density function (see Figure 1.9 on page
18). Their recommendations include using displays that specifically show the
information that is to be extracted (such as a point for a mean value, if mean values
are important), and using multiple displays (particularly, display the cumulative
density function and the probability density function one over the other, with a
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18
Point Estimate with Error Bar Mirrored Probability Density
I • 1
0 2 4 6 8 1012141618
Discrete Density Function
0.20-i
0.16-
0.12-
0.08-
0.04-
0
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19
common horizontal axis).
For two- and multidimensional uncertainty in non-spatial displays, Morgan
and Henrion give several examples of methods that can be used for graphing (see
Figure 1.10 on page 20). These include: multiple lines in a probability density/
cumulative density pair; multiple Tukey box plots; linear graphs with error bars;
orthogonal displays; and triangle plots alone and in multiples.
They conclude with a list of factors that should go in to design of
uncertainty displays (Morgan and Henrion 1990,252):
finding a clear, uncluttered graphic style and an easily understood
format,
making decisions about what information to display,
making decisions about what information to treat in a deterministic
form and what to treat in a probabilistic form,
making decisions about what kind of parametric sensitivities will
provide key insights.
They also suggest that display design often involves the reduction of a multi-
dimensional model into the two dimensions of a paper or monitor display (as does
Tufte 1991), and that the intended audience's experience in interpreting graphs
must be considered when creating a display.
For the representation of uncertainty for spatial variables, there are two
possible cartographic routes. The first of these is the creation of two maps, one for
displaying the data, and one for displaying the meta-data. Olson (1981) and
Laurence Carstensen (1986) have tested this choropleth map arrangement against
two bivariate mapping techniques (Olson: spectral encoding; Carstensen:
intersecting lines) in the representation of statistical correlation.
Olson finds that map readers can initially interpret value shaded,
monovariate maps pairs more readily than bivariate maps. On the other hand, she
reports that over half of those who could interpret bivariate maps at a significantly
better than guessing level, did better with a bivariate map than two separate maps.
She then suggests that the bivariate maps may be more readily interpreted once the
"cognitive hurdle" (Olson 1981, 269) of the bivariate mapping technique is
overcome.
Carstensen also finds that map readers find interpreting value shaded,
monovariate map pairs easier than bivariate maps. Because his test compared a
classed map pair and unclassed bivariate maps, the problem he notes with the use
of map pairs (poorer statistical residual scores) would not be as likely to occur if
map pairs are compared with classed bivariate maps.
The map pair technique should be a useful tool for communication of two
variables, when the data must be classed (as is done for pragmatic reasons in
ARC/INFO). Since meta-data values may not be correlated with data values, the
use of two monovariate maps should be an effective tool for communicating
uncertainty versus techniques that were designed to highlight spatial correlation.
The second cartographic route for the visual representation of uncertainty
is bivariate mapping (the mapping of two variables onto the same map). This
would ensure that meta-data is presented to the map reader with the data, but this
mapping method generally increases the difficulty with which data can be
extracted from a map. Because of the variety of visual variables, there are several
possible methods of bivariate mapping, some of which have been tested for
communication effectiveness; most of these have been oriented toward the
-------
Probability/Cumulative Density
20
Orthogonal Display
1.0-,
iiiiirn
2 4 6 8 1012141618
XI (first uncertain variable)
Multiple Tukey Box Plots
8g
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21
representation of spatial correlation. This includes the testing of the intersecting
lines method (which uses texture), color maps made by the U. S. Census Bureau
(which uses a full hue range to achieve bivariate representations—spectral
encoding), color maps that rely on two complementary hues, and the
equiprobability ellipse (which also uses the complementary hues).
In a technique that allows for bivariate mapping in monochrome displays,
Carstensen (1982) has tested the communication effectiveness of the intersecting
lines method of bivariate mapping (see Figure 5.4b on page 73). These maps use
horizontal and vertical lines for representing two variables. Carstensen suggests
that this scheme be used in an unclassed map, but this scheme can be used for
classed representations of data and meta-data. Although this technique can be
used in monochrome displays, colored lines can be used to distinguish the two
variables (this has not been tested for communication effectiveness, though).
This technique has one disadvantage: the method of producing the area
symbolization may lead to a conflict between two visual variables. Both texture
and value change with the mixing of the lines; both establish visual hierarchies
with coarse textures and dark values standing out in the display. This is a problem
because in the representation scheme these two points (coarseness and darkness)
are at opposite ends of the data ranges. This can cause value to be used for
identifying relationships even though squareness in the texture is the intended
visual variable (Carstensen 1986).
The U. S. Census products, originally published for 1970 census data, that
show two variables were studied for communication effectiveness by Olson (1981)
(see Figure 5.5c and d on page 75). These maps use two hue patterns for
representing two variables, with the part-spectral ranges of yellow to blue and
yellow to red being used on the x and y axes, respectively. Olson reports that some
of these maps (such as education and income) convey information well, especially
for homogeneous regions. She also indicates that these maps are thought to be
more authoritative and more innovative than two separate maps showing the
same information. In concluding, she suggests that prominent and clear legends
are necessary for accurate interpretation of bivariate maps; that both the
monovariate map pair and the bivariate map be shown, with the monovariate map
pair in a monochrome format; and explanatory notes should be include to the
types of information presented. These guidelines are in keeping with both Morgan
and Henrion, and Tufte, and are feasible with ARC/INFO's ability to rapidly
generate small, monovariate maps.
As a response to the problems of interpreting a spectrally encoded bivariate
maps, Steiner (1979, in Eyton 1984) has proposed a complementary color scheme
(see Figure 5.6 on page 77). This color system makes use of the mixing of
complementary colors (such as red and cyan) to produce a central gray region that
highlights the diagonal that represents correlation in a bivariate map. This can be
done for unclassed or classed representations of data, and by flipping the order of
one tint, negative correlations can be shown as well as positive correlations.
Building on Steiner's proposal, J. Ronald Eyton (1984) developed the
complimentary color bivariate map with an equiprobability ellipse (see Figure 5.7a
and b on page 79). These maps use a modified, 2x2 complimentary color range,
with an additional class that occurs in the middle of the matrix and represents the
central cluster of data. By plotting the two variables to be mapped on a scatter
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diagram, linearly correlated data will have an ellipse-shaped central cluster. By
selecting a percentage of the total number of observation to be included in the
central ellipse, a category for the central cluster can be created with the formula
(Eyton 1984,488):
(X-X )2 (Y-Y )2
m m
o2 -2
X2 =
a2 a2 2r(X-X )(Y-Y )
x y v m/x rrv
1 -r2 a »a
x y
X2 = chi-square (1.386 for 50%)
X, Y = the X and Y observations
X , Y = the means of X and Y
m m
a , a = the variances of X and Y
r = coefficient of correlation (Pearson's r)
When this ellipse is displayed in gray, surrounded by the four corners of the data
set in white, black, rea and cyan, a bivariate map that portrays the central data
cluster explicitly (without haying a staircase effect) can be created.
There are other possible methods of bivariate mapping that have been
postulated as effective communicators of (un)certainty. Two of these, which have
not been tested, are color intensity and focus. Neither of these methods place
emphasis on a correlation of the data and meta-data variables, but rather use visual
variables to highlight portions of the data set, as determined by the meta-data
information.
Use of color intensity may prove useful for the cartographic representation
of uncertainty, because it allows the highlighting of certain (or uncertain) areas by
specifying intense shades for those areas, and less intense for others (see Figure
5.5b on page 75). Because intense colors stand out in an image, this technique
would allow the creation of a distinct visual hierarchy that emphasizes certain (or
uncertain) values. Generally, for maps that will be used for data communication
(as in the DiBiase model), intense colors should represent certain areas and less
intense (that is, more gray) colors should represent uncertain areas.
Focus is potentially a useful means of representing uncertainty.
MacEachren (1992) presents several possible variations on focus: edge crispness
(for external boundaries of points, lines and areas), fill clarity (for internal
boundaries within point, line or area symbols), fog (by imposition of an
interposing, translucent layer over another symbol), and resolution (point
thinning for vector databases or aggregation in to larger area units for raster
databases). All of these involve the blending of a symbol with the surrounding
parts of the image, thereby eliminating clearly defined regions. In ARC/INFO
edge crispness can be accomplished by buffering regions and careful assignment
of color in the buffer areas; resolution can be accomplished by thinning points
manually or with the ARCEDIT command GENERALIZE.
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Another method of bivariate mapping is the use of a fishnet, orthogonal,
view to display one data set, with another data set used to color the display (see
Figure 9.2 on page 101). This is commonly used as a technique for displaying
terrain elevation (with land use/land cover draped over the net by specifying the
net's color with the land use symbolization scheme), although there is no
restriction on its use for other types of data. When a data layer represents
information that is known to be continuous and smoothly changing (such as
elevation, air temperature, or air pressure), this type of representation is
appropriate. If the uncertainty of a spatial data layer can be shown or assumed to
be continuous and smoothly changing, a fishnet representation of that statistical
surface (with data values used to specify the color of the net) should be an effective
method of conveying meta-data.
Finally, another representation of continuous and smoothly changing data
that could be used to display data and meta-data is the use of isoiines (see Figure
9.1a on page 99). With this technique data and/or meta-data can be represented,
with the use of another display technique if only one is to be displayed with
isoiines. Like fishnets, isoiines are often used for displaying terrain information (as
in topographic maps), but isoiines can also be used to show data and meta-data.
This could be accomplished by using different hues, values, intensities, sizes, or
textures to indicate which lines represent data and which represent meta-data.
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Chapter Two
Producing Displays
As Monmonier and Johnson indicate, the process of designing and creating
maps and graphics is a multistep process. There are many things that must be
considered in the design process, including the classification of both space and
data, and issues such as page layout. This chapter addresses these issues in the
context of ARC/INFO and leads into the methods of representing data that are
presented in later chapters.
Classifying Space
A fundamental process in the classification of space is the abstraction of
data. MacEachren and Ganter (1990) have describe this as a shifting along a
continuum ranging from images to graphics. At one end of this continuum is
information in its rawest form: for spatial data, aerial photographs and other
remote sensing products (see Figure 2.1, left). Further along the continuum, maps
provide an abstraction of images (Figure 2.1, middle). Some of the information
that is present in an image is dropped in order to allow symbolization of
information that may not be directly perceivable in the image. For example,
replacing a dark line through a green area with symbols for a road and a forested
area; the road can then be given a label, as well as provide an indication of the
number of lanes and access. At the other end of the continuum, graphics allow the
use of position in the display to symbolize any variable (Figure 2.1, right). For
example, a distance decay graph uses the X axis to indicate distance from a point
in any direction, and the point may not be tied to any one geographic location.
A similar continuum is the range of symbols that can be used in maps and
graphics (see Figure 2.2 on page 25). At the end of the continuum most similar to
images are mimetic symbols. At the end of the continuum most similar to graphics
are abstract symbols. Except for a few symbols that are toward the mimetic end of
this continuum, most of the symbols that are provided with ARC/INFO are
Distance from site.
Figure 2.1 The Image to Graphic continuum. Images approximate what we see,
graphics provide abstract representations of, possibly, invisible relations
(MacEachren and Ganter, 1990).
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25
abstract-these tend not
to have commonly
accepted meanings, and
thus can be defined by
the cartographer as
needed.
The degree of
abstraction that should
be used is dependent on
several factors. Most
mimetic
abstract
Figure 2.2 The Image to Graphic continuum
applied to symbolization. Symbols can vary from
mimetic to abstract. All of these symbols could be
used to represent a marina—the audience must be
importantly, the data that considered in selecting which to use.
needs to be mapped must
be effectively shown, with a degree of abstraction that is appropriate to the data.
For example, if a distance decay model is developed from a set of sample sites,
showing the values measured at individual sites may not convey the distance
decay as clearly as a graph. If the site locations are important, a map can be
generated with the data and an inset showing the graph can be made using
ARCPLOT's graphing tools. As mentioned in Chapter One, the audience must also
be considered when determining symbolization abstractness. Highly mimetic
symbols can convey a sense of simpleness, which may need to be avoided in order
to project an image of authority. A third consideration is the means of display;
mimetic symbols can be used to minimize the need for/use of a legend. This can
be helpful for slides and overhead displays.
Projections
There are several classes of projections, each with strong points. Equal area
projections show the same amount of space on the earth's surface for any given
area of the map. Equidistant projections show true distance from a point or along
given lines. Conformal projections have a constant scale in every direction from
any given point, and because of this latitude and longitude lines meet at right
angles. Some projections, such as Robinson's, are not mathematical
transformations, but rather, tabular. These projections have been designed for
specific purposes (Arthur
Robinson developed his
projection for world maps that are
more visually appealing than
others, like the Mercator
projection). Other projections
include the Mercator and gnomic
projections; the Mercator
projection shows lines of constant
compass directions as straight,
and the gnomic projection shows
all great circles as straight lines.
These two projections are best
used for navigation and not for
general reference
environmental maps.
or
Figure 2.3 EPA Region Six shown in
Alber's conic equal area projection.
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For environmental maps, in general,
equal area projections should be used. This
insures that symbols, especially those based on
size, are not distorted on the basis of the base
cartographic data (such as county, or state
outlines). For the 48 contiguous states, Alber's
conic equal area projection should be used;
Alber's conic should also be used for smaller
regions that are east-west oriented, such as EPA
Region Six (see Figure 2.3). The sinusoidal
equal area projection should be used for regions
that are north-south in extent, such as EPA
Region One (see Figure 2.4). Lambert's
azimuthal equal area should be used for areas
that have the same extent in all directions from
a center point (see Figure 2.5).
Because the distortions of any given
projection are scale dependant, the use of any
specific projection becomes less critical as the
map's scale increases (and thus the area shown
becomes smaller). For example, a map of a
hazardous waste site may need the Universal
Transverse Mercator grid for locations within
the site; at this large a scale (1:50,000 or larger)
use of the UTM projection is more appropriate
than an equal-area projection-there will be
little, if any, perceivable distortion of areas
regardless of the projection used, as long as the
projection is centered on the site.
The ARC command PROJECT allows
transformation of coverages between
projections, as well as realignment of
projections. If data is obtained from a national
database, the projection (if not included with
the database) may be:
Project: projection albers
Project: units meters
Project: parameters
1st standard parallel: 29 30 0
2nd standard parallel: 45 30 0
central meridian: -96 0 0
latitude of projections origin: 23 0 0
false easting (meters): 0
false northing (meters): 0
Figure 2.4 EPA Region One
shown in the sinusoidal equal
area projection.
Figure 2.5 EPA Region
Four shown in Lambert's
azimuthal equal area
projection.
Because this is designed for the contiguous 48 states, any subset of this data should
be reprojected for the subset, even if the output projection is Alber's. In particular,
the standard parallels should be chosen such that the new parallels divide the re-
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27
gion into three equal east-west bands,
and the central meridian select bisects
the region. This minimizes distortion
away from the parallels and prevents
an appearance of the whole map lean-
ing in one direction, which results
from an off-center central meridian.
Scale and Generalization
As noted above, selection of
scale is critical in the selection of an
appropriate projection. Scale is also
important in the selection of total area
to be mapped, and the relation of the
area to the data to be mapped. By
using a smaller scale, and thus
showing more area, the apparent
seriousness of a problem will be
reduced. This is because the apparent
extent of a problem is reduced by
showing more of the surrounding
area. Zooming in on a site has the
opposition effect~the appearance of
Figure 2.6 Insets allow focusing on
detail and give a 'big picture.' When
possible, place them in otherwise
unused space.
symbolization over a large part of the display conveys the idea that the problem is
everywhere. Use of zoomed in areas, which allow presentation of detail, with a
locator map can combine these two extremes (see Figure 2.6 on page 27). The
locator map allows a wide perspective, which, when combined with the large-
scale, detailed map, conveys both a micro and a macro reading, as Tufte (1990)
suggests is a key component of good presentation graphics.
Space and Time
With the increased processing speed of single user workstations, and the
increased flexibility of ARC/INFO, animation of data—both for analysis and
presentation—is becoming feasible. Animation has several possible approaches.
Change in time can be used to depict existence, attributes, or change in existence
or attributes. Change can also be broken into: looking at different parts of a data
set, one after the other; looking at a data set that shows variation in time, in time
sequence; or use of progression in time to show another data variable (this is
comparable to use of an axis of a graph to indicate change in time rather than
change in space).
There are two primary methods of creating animations in ARC/INFO, and
both require AML programming. The most flexible method is the use of AML
driven interactive map composition. This allows the display of an object (for
example a point location, such as the population center of the United States) that
changes over time. The object can be drawn at one location, erased with the
MDELETE command, and redrawn at a new location. The other method of
animation is the use of GRID to display changes in area data. The cliche 'Raster is
Faster' is still true enough to make a difference. Separate grid layers can be
generate, each of which shows the change in areal extent of a phenomenon. Each
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layer can then be draw with successive calls to a display routine.
Classifying Data
Data to be mapped for presentation should generally be classified (into five
or six groups) in order to aid ease of interpretation. When drawing features in
ARCPLOT, the commands: ARCLINES, LABELMARKERS, POINTMARKERS,
and POLYGONSHADES, as well as AML driven RESELECT's, allow the use of
lookup tables to define a data to symbol relationship for feature display (the
CLASS command also allows grouping of data). These tables allow user defined
ranges for cartographic products, rather than the default of directly relating the
data item identifications with the symbol set identifications. These ranges must be
determined by the cartographer and range types include: quantiles, equal
intervals, geometric progressions, mean and standard deviation intervals, and
natural breaks (the Jenks' Optimal classification) (see Figure 2.7). Certain data sets
may need to be classified on the basis of predetermined breaks (such as maximum
allowable concentration of a pollutant). This can be accomplished by manually
specifying all breakpoints, or by use of another classification scheme, with the
externally defined break added in. For example: run the Jenks' optimal AML for
five classes, note the breakpoints, then run the manual specification AML on a new
lookup table and specify the Jenks' breakpoints plus the predefined point.
Manual Classification
For both the CLASS command and lookup tables, break points can be
chosen manually, by exporting the data to a statistical package, or with the
assistance of the ARCPLOT command STATISTICS. The command syntax is:
STATISTICS
- contains the items to be classed;
- includes POINTS, ARCS and POLYS.
Jenks' Equal Interval Quantile Mean and Standard Deviation Exponential
www w f-
I1LL
CN
rH
IT)
Figure 2.7 Breakpoints set by different classification schemes. Equal Interval is
close to the statistically optimal (Jenk's), for this example. Quantile separates
relatively similar values at the extremes of the distribution. Mean and Standard
Deviations fail because the distribution is bimodal, not normal; Exponential fails
by grouping all of the items greater than 256 into one category.
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STATISTICS has several subcommands:
SUM -
MEAN
-
MINIMUM
-
MAXIMUM
-
STANDARDDEVIATION
-
- is a field in the attribute table of .
END - indicates all subcommands have been entered.
These values can be used to calculate mean and standard deviation break points,
as well as quantiles and geometric progressions.
There are several methods of defining classes within ARC/INFO, as well as
several methods of determining class breaks. As MacEachren (1992) notes,
interval and quantile classification systems, which are automated parts of the
CLASS command, generally are not the best methods for grouping data and
therefore will not be discussed here. The syntax for manually specifying intervals
with the ARCPLOT command CLASS is:
CLASS MANUAL <#classes>
<#classes> - the number of classes that will be generated;
- the numeric class breaks. There must be <#classes> -1 values.
CLASS NONE - turns off the classification scheme.
Until the CLASS NONE command is given the classification remains in effect, and
will cause all subsequent uses of ARCLINES, LABELMARKERS, POINT-
MARKERS, and POLYGONSHADES to be classified.
Another method of classifying data is to use lookup tables. These are INFO
files that perform a similar function as the CLASS MANUAL command. A manual
procedure from ARC for the creation of a lookup tables is:
1) Use PULLITEM to extract the attribute table item that holds the data values;
2) Use ADDITEM to add a numeric field called SYMBOL;
3) Enter INFO, SELECT the table and PURGE the old data;
4) ADD records to the lookup table;
a) Specify the breakpoint value for numeric data, or the alphanumeric for text data;
b) Specify the symbol number;
5) SORT on the data field (not the SYMBOL field).
It is possible to automate the creation and specification of lookup tables
within ARCPLOT. SETMAN.aml allows the manual update of symbol values
within a lookup table, as well as creation a new table. The AML handles both
nominal and numeric data. The syntax is:
SETMAN
will be created if it does not exist, existing tables will be selected for update.
Natural Breakpoints
Because the Jenks' Optimal classification scheme is generally considered to
provide the best classification of numeric data (MacEachren 1992), it should be
included in ARC/INFO (and with any mapping program). Unfortunately it is not,
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but ARC/INFO's does provide a macro language, commands to export data, and
a method for calling system programs. These can be combined to allow the
automated generation of the breakpoints for Jenks' optimal classification. The
AML, JENKS.ami, exports the data to be classified, calls the C program, jenks
(which must be in the executable search path), that calculates the breakpoints, and
constructs a lookup table. The cartographer must still specify symbol matches
though. Please note that the routine generates a lookup table that contains more
information than is required for ARCPLOT's use (although ARCPLOT can still use
it); this additional information is included for use by the AML's presented in later
chapters. The additional information is: an initial line that is one smaller than the
smallest data value (this is included only in non-nominal lookup tables, including
the output from Jenk's); a column that contains the number of values in the
associated coverage in the first record, and the number of values in each category
in the following records; and a column that contains the coverage name in the first
record, an 'n' (for nominal data), an 'o' (for ordinal data) or an 'r' (for interval/ratio
data), the coverage type in the third record (point, arc, etc), and for route and
section lookup tables, the route name in the forth record. This additional
information allows these AMLs to select the coverage it is based on and, for
legends, provide category totals and appropriate symbolization.
The C program jenks.C can be compiled on a workstation with an ANSI C
compiler (including Data General's DG/UX 5.4) by using the command line:
cc -ansi -o jenks jenks.c -Im
The command syntax for using JENKS.aml is:
JENKS
- the coverage that the lookup table will be created for;
- the feature type (point, line, poly, etc) of ;
- an interval or ratio level data field in the attribute table of ;
- the name of the lookup table to be generated;
- the number of data classes in the output lookup table.
Eyton's Equiprobability Ellipse Bivariate Classification
The uniqueness of Eyton's ellipse as a bivariate mapping scheme requires
that a column be added to the attribute table of the data to be mapped. As with the
calculation of Jenks1 optimal classifications this is best done with a combination of
macro and C program. EYTON.aml requires two ratio data items—the
classification system is based on the parametric statistic, Pearson's r. It also
requires that the system program, eyton, be in the executable search path. Like
jenks.c, the eyton.c program can be compiled on a workstation with an ANSI C
compiler by using the command line:
cc -ansi -o eyton eyton.c -Im
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31
The command line syntax for using EYTON.aml is:
EYTON
{classes} {chi_square_value}
- the coverage that the lookup table will be created for;
- the feature type (point, line, poly, etc.) of ;
- interval or ratio data fields in the attribute table of < cover>;
- the output lookup table;
{classes} - the number of classes on each axis, valid codes are 2 (default) or 3;
{chi_square_value} - a value for the selecting the number of points in the central ellipse,
defaults to 1.386, which is 50% of the observations.
Symbol Value Update
The lookup tables generated by these commands may require the
modification of the symbol numbers. There are several ways this can be
accomplished: use of '&SYS ARC INFO' to enter INFO from ARCPLOT; manually
declaring a cursor and using it to update the lookup table; using the AML given
above for manually changing values; or use of the AML, SETAUTO.aml. This
AML updates a lookup table by replacing the SYMBOL values with an ordered set
of numbers. It requires a starting value, a step value, and can optionally be given
two other values. Nonlinear progressions can be specified by including a 'scale'
value, and decreasing numbers can be obtained by specifying a
'subtraction_value.' These non-linear progressions should be used when a
SYMBOL value is used for specifying something other than a predefined symbol,
such as symbol value. In this case value should range from black to very light grey
with a greater change in the black/dark-gray values (value differences are easier
to discriminate for lighter values). For five classes, the use of 0 50 0.8 and, if
necessary, 69 as the subtraction value, will set up an appropriate value
progression.
SETAUTO {scale} {subtraction_value}
- the lookup table to be updated;
- the beginning value of the progression;
- the value used to change the beginning value;
{scale} - an exponent that is applied to --defaults to 1;
{subtraction_value} - value that a symbol value will be subtracted from in order to generate
decreasing progressions
Unclassed Maps
Unclassified maps (those that are continuously symbolized) can be created
in ARC/INFO, but the symbolization schemes available can be limiting and the
potential improvement in the ability to depict data (as suggested by Monmonier,
1976) may not justify the effort for presentation of data. For exploration and
analysis however, unclassified maps are an approach that may be worthwhile,
although software/hardware limitations can impinge on truly unclassified
displays. Eight bit plane graphic displays can only display 256 colors at once,
thereby preventing unclassed display of data sets with more than 256 values. This
can be partially circumvented by using the Jenks' optimal classification system to
create a lookup table with 256 classes. For data sets with less than 256 data values
or for systems with 'true color' (24 bit plane) displays, use the manual lookup table
definition AML (SETMAN.aml) to define a nominal lookup table. A limitation of
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'true color' displays is that 24 bit graphics systems can only generate 256 shades of
gray. So, in general, for 'unclassed' maps, create a lookup table with 256 categories
(or fewer if there are not 256 data values); once a lookup table is created, symbol
values must be assign on the basis of the lookup table's item value. SETUNCL.aml
accomplishes this. The command syntax is:
SETUNCL {scale_factor} {subtraction_value}
- the table with symbol values to be updated;
{scalejactor} - an exponent for generating non-linear scaling, defaults to 1;
{subtraction_value} - allows creation of descending scales.
Page Layout
Once the information to be displayed is classified, the data must be
displayed. This is the process of page layout, which can be broken into: layout
within parts and layout within the whole. Layout within parts of a display
involves the selected use of visual variables to highlight a part or parts of a data set
or display. This is the establishment of graphic hierarchies and involves two
techniques: visual isolation, and visual levels (MacEachren 1992, 27) (see Figures
1.1 on page 2 and 1.7 on page 14).
Visual isolation is the use of visual variables to give the appearance of the
separateness of part of a display. The visual variables that can accomplish this
include location, size, focus, value, hue, saturation, texture and orientation.
Location is the most obvious control-display items that are not close together will
not generally be associated (see Figure 2.8). Size can influence isolation because
any feature that is drawn smaller than the area allocated to it, will appear separate
from the surroundings (this is done in cartograms). Focus influences isolation
because unfocused, fuzzy symbols blend into the surrounding, reducing isolation.
Value, hue, saturation, texture and orientation influence isolation by enabling one
item to be displayed in a manner that is noticeably different than its surroundings
(dark blue surround by yellow, for example) and thus isolating it.
Like visual isolation, visual levels are used to separate an item from its
surroundings, but whereas visual isolation seeks to accomplish that in the x-y
space of the page, visual levels give
the appearance of separation in the
third dimension. The visual variable Isolation as Separateness
that control visual levels are: size,
value, saturation, texture, focus and
hue. These visual variables all play
a part in depth perception. Size
controls visual levels because things
that appear larger, appear to be
closer. Value controls visual levels by
control of contrast from the display
background—objects with high —— —1 mlle
contrast will appear above the 1 ldlometer
background (see Figure 2.9 on page Figure 2.8 Visual isolation. The letters
32). Saturation controls contrast in each word 'go together,' as do the lines
because intense colors appear to be and their labels, but not the lines and the
closer than less-intense colors, display title.
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Texture influences visual levels
because coarse textures appear to be
closer to the observer. Focus
influences visual levels because
sharply focused objects appear to be
closer than fuzzy objects. Hue
influences visual levels because, at a
constant value and saturation,
yellow is more noticeable than
other colors, but the influence of
hue can be hard to predict and
control.
In designing a page, the Figure 2.9 Visual levels. Darker value
layout within the whole page usually is a foreground (at a higher level)
involves the use of space (and for than lighter values, particularly on white
animation, time) to present backgrounds.
different parts of a message. The
type of display has an influence on what can, and should, be said on an image.
Paper displays can be of any size, but two are of more importance: 8.5 by 11 inch
paper, and full size electrostatic plotters. 8.5 by 11 inch paper is probably the most
common format for graphic publication. Its small size restricts the amount of
information than can be shown on one page, but generally high resolution and the
ability of the reader to study the graphic at length permit a great deal of
information communication. The portrait orientation, which is normally used
with text, limits the left-right extent of a display, so graphics that have a large left-
right extent should be displayed as landscape, when the graphic cannot be
redesigned to take advantage of the more common reading orientation. Generally
the primary part of the display should be shown with a maximum left-right extent.
Titles can then be placed above, and additional information such as legends and
locator diagrams can be placed below the primary part of the display.
Large size paper products, such as posters, can be created with less
emphasis on the orientation of the page, and more emphasis on the size and shape
of the area of interest. Orientation of the page should follow the larger axis of the
data set. Additional information should then be placed around the main part of
the graphic, in order to take advantage of 'dead space/
Slides and overheads limit the amount of data that can be displayed because
of the distance that they force on the viewer (see Figure 2.10 on page 34). The
farther a viewer is from the display, the smaller the display will appear, limiting
the visibility of detail. This implies that the page layout decisions for slides and
overheads require greater generalization in both space and data. Only the most
important information needed to support a point should be included on the
display. As such, additional information such as legends and locator diagrams
should not be included. This allows the maximization of the available space for
data display, and like posters, the orientation of the display should be aligned with
the larger axis of the data area. This loss of data on the graphic is offset by the
explanations of the presenter of the slide, overhead or video.
Video involves both high resolution computer monitors, and lower
resolution National Television Standards Committee displays. Video displays
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34
must, like slides, take into account the distance from the viewer, as well as lower
resolutions and display flicker. Minimize the amount of ancillary information, in
order to maximize the amount of space available for the primary data. Like slides,
this loss of visual information must be offset by audio explanations.
Titles and Type
The text that is used to label a map or graphic should be selected carefully.
This involves the determination of what should be labeled, how it should be
labeled, where the labeling should be placed, and what type of lettering to use.
Which items must be labeled should be identified during the planning phases of
the map design, particularly in identification of the communication goal—label
those things that are necessary to accomplish the goal. Additional labeling may be
necessary for locational reference, etc., but this ancillary labelling should be kept
to a minimum in order to emphasize the new information.
As with the amount of features that get labelled, the amount of text in each
label should be kept to a minimum. Often leading 'a,' 'an' and 'the's can be dropped
from labels. Phrases such as 'the city of,' 'plot of or 'Legend' can also be dropped
without loss of information and result in an improvement in communication by
getting rid of the clutter.
Labels should be placed on or near the object they label. Locations for titles
can include prominent positions such as top center, but may also include making
use of otherwise empty space (such as using the Gulf of Mexico's space in a map
of Florida). Labels of point features should, when possible, be put at the upper left
of the feature. Labels of linear features should be placed on straight sections of the
feature, or if necessary fit along a smooth curve, and be oriented for maximum
readability (top up, whenever possible). Area features should be labeled inside
their boundaries, when possible. Although it is not entirely unavoidable, text
should not be broken up by linear features or area boundaries; it may be preferable
to have a break in the line, although this can be difficult to accomplish in ARC/
INFO.
There are two general classes of fonts that are used for cartographic
displays, roman and sans-serif, both of which can be italicized, underlined, etc.
Roman fonts, such as the font used for this text, have 'serifs'-the small extension
at the end of the strokes that make up the character. These fonts usually are more
legible than fonts without (sans) serifs, particularly for small text. Sans-serif fonts
are simpler, but are generally best used only for titles and other large text. For
either type of font that may be used to label a body of water, it is cartographic
tradition to use an italic font. This may connotate a sense of flowing.
The size of text influences legibility, particularly when the speed of a
presentation is controlled by the
presenter, rather than the reader.
For paper displays that the reader PoStGr Title
will be able to study at length, text
as small as 5 points (0.07 inches) can Po*t8r ™*
b Ud Dif!erenCfLin^\ |iZ6S R9"re 2.10 The apparent size of 16 point
3n 6oaxSo 35% (0\°^5 Pt' text from 8 feet away (top) is the same as 6
tf 0.13\9 pt e^c.)(Kea^ int letterm fr/m £- feet (bottom)
1982). For paper displays which are [MacEachren ?992f 71).
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35
not available in depth study (such as flip charts and posters) the following
suggestion for slides and overhead are more appropriate, although detail
information could be included in posters.
For slides and overheads, not only must there be less text, but the text
should be larger (see Figure 2.10 on page 34). As a general rule text should be at
least 18 point with larger differences than paper (50%) (MacEachren 1992, 71).
Video displays also need to make use of large points sizes, because of lower
resolution and with some systems, flicker.
Insets and Legends
There are two main types of insets: locator diagrams and additional
graphics. Locator diagrams show the location of a smaller area, in relation to a
larger and presumably
more well known area ..^ |
(seeFigure 2.11). When C "j ""; iI YI \"\ .
multiple graphics are i i [ I I \ i \ ';
generated for the same L /" \ i : "\ i ••• :"\ / •; ; A.....
region, only one locator i
diagram should be !--•
needed, and it may be i
advisable simply to ;
i J : : :.. / . .' "• .-• ; ;-.— . /
make the locator i / f\ "••./' / ,/ \ ( *""'"" :'
diagram a separate I
graphic. For displays i
which need integrated |
location diagrams, they i
should be visually
isolated—the diagram Figure 2.11 A simple locator diagram.
should be secondary to
the main display. Therefore avoid bright colors, if not colors entirely, but ensure
the area of the main display is readily discernible.
Other graphics include legends, north arrows, scales and, for bi- or
multivariate displays, monovariate maps. Legends must convey the information
necessary to extract information from the main display. North arrows assist in
orientation when north is not at the top, which it does not have to be. For maps to
be presented to an international audience, include a north arrow, because south
may be expected at the top (as is the Chinese custom). For maps where a large and
hopefully well-known area is displayed (the United States or a subset of them, for
example), a north arrow is not needed. Map scales, like north arrows, are not
necessary for maps of well known areas and generally are not needed, unless the
map may be used for measurement of extent. As suggested by Olson (1980),
monovariate maps may be helpful in assisting readers who are not familiar with
bi- or multivariate maps. These single variable maps should be designed to be
both isolated and at a lower level in the visual hierarchy than the main display.
Monochrome displays may be the most appropriate technique for all but nominal
data.
Because of the requirements of different media, the amount of information
that should be carried in a legend varies, as does the need for a legend. Because of
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36
the generalization that goes into slides and video displays, the need for legends
should be minimal, particularly when the presenter is available to answer
questions. A slide for a legend may be a waste, because it cannot be referred back
to, and handing out a legend before a presentation may only serve to focus
attention on the legend, not on the data that is being presented.
Paper displays, particularly those where the author is not available to
answer questions, require the most thoughtful use of additional graphics.
Explanations of data must be written out on the graphic. For bi- and multivariate
displays, the mapping technique should be explained, and monovariate maps
should be included. Legends should present the character of the data (data level,
continuous or discontinuous, classification system used). This can, in part, be
accomplished by defining discreet variable symbols separately with a label on
each symbol, and by defining continuous variables as a continuum with
breakpoints, rather than midpoints, labeled (see the legends in Figures 5.1 on page
67 and 5.2 on page 69, for example).
An approach to legend design that may be most helpful to inexperienced
map readers is natural legends (see Figures 6.2 on page 86 and 9.1 on page 99).
Natural legend design is particularly helpful with abstract symbolization, such as
isolines, which can be difficult to interpret by a novice (especially when only given
a contour interval). By providing a legend that shows isolines on a surface and
spot values, the concept of a continuous surface and how data values are shown
can be communicated. Isoline data, particularly when several data items are
shown together, can be displayed as a single-variable, fishnet inset; this will
convey the concept of a continuous surface and allow analysis of individual data
sets, in addition to the presentation of the interplay of multiple data sets in the
main display.
ARC/INFO Hints
There are two lines that should be added to the $HOME/app-defaults/
Mwm file. These lines allow ARC to automatically place popup windows:
'clientAuloPlace: FALSE
*interactivePlacement: FALSE
There are a few general tools available in ARCPLOT that may assist in the
design or production of maps and graphics. When using 'DISPLAY 9999,'
ARCPLOT defaults to a black background; this is a problem with the 'true color1
display of value-black objects will be visible on paper, but invisible on the display,
and vice-versa for white. The remedy for this is to include the following line in
either a .cshrc or .login file:
setenv CANVASCOLOR WHITE
When using nineteen inch monitors, it is possible to specify a display
canvas size that has (as far as ARC is concerned) the same dimensions as an 8.5 by
11 sheet of paper. The dimension for portrait layout are 691 by 930. The
dimensions for landscape layout are 896 by 727.
All AMLs can be executed in two ways: specifying an AML path and
running with the &RUN directive; or by placing the AMLs in an atool directory
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37
and running them as a standard command. The $ARCHOME/atool directory can
be used, or the AMLs can be placed in another directory and linked into
$ARCHOME/atool subdirectories. The AMLs can also be placed in any other
directory, with subdirectories for each module (arc and arcplot), and use the
&ATOOL directive to specify the directory path (see the &ATOOL page in the
AMI User's Guide).
The AMLs discussed in this document, for the most part, follow a naming
convention. For the first character:
P = point or node displays.
L = line, route or section displays.
C = choropleth area displays.
G = graduated symbol area displays.
D = dot density area displays.
R = raster (grid) area displays.
S = surface displays.
For each additional character (one for each variable displayed):
H =hue.
V = value.
I = intensity.
O = orientation
S = shape.
T = texture.
Z = size.
B = box (used with points only).
C = circle (used with points and graduated symbols only).
G = cartoGram (used with graduated symbols only).
D = density (used with dot density only-all are DD).
F = fishnet (used with surfaces only).
AO = angle (for single variable displays only: cao, pao)
ISO = isoline (used with surfaces only).
Other codes include:
P = pie (graduated circles with subdivisions).
L = legend (gel, ggl, gpl, sfl; al - single variable; ol - orientation)
BL = bivariate legend.
CC= complementary colors.
DH= dual hue colors.
EE = equiprobability ellipse (and eel - legends).
IL = choropleth area intersecting lines with PAT data (and cill - legends).
TL = choropleth area intersecting lines with lookup tables.
RGB = red, green and blue (and rgbl - legends).
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38
Chapter Three
Point Symbolization in ARC/INFO
For point symbolization, the visual variables of hue, orientation and shape
can be changed by the use of an INFO lookup table that relates nominal
distinctions to different symbols; the visual variables of size and value can be used
to symbolize ordinal and interval/ratio data either with a lookup table or with
data from the file attribute table. For lookup tables use, one of the methods
discussed in Chapter Two should be used to generate a lookup table. The AMLs
discussed in this chapter generally require some of the additional information that
the lookup table generating AMLs in Chapter Two provide.
Monovariate Symbolization
The macros in this chapter demonstrate the use of AML to accomplish map
design. The AMLs become progressively more complex in order to set the stage
for bi- and multivariate mapping, which, for all intensive purposes, must be done
with AMLs (most of which also require the use of cursors).
Each of the examples makes use of the markers that are provided with
ARC/INFO: a default set of markers in the markerset file, PLOTTER.MRK; and
several other available markersets: BW.MRK, COLOR.MRK, MINERAL.MRK,
MUNICIPAL.MRK, OILGAS.MRK, USGS.MRK, and WATER.MRK. Most of these
are displayed in the Map Display and Query guide's Appendix B, and the ability to
create new symbols sets is discussed in Chapter Three of Map Display and Query.
Nominal Data-Hue
Hue is best used for nominal data, and the COLOR.MRK markerset
provides fifteen symbols of the same shape, but each with a different color. All of
the other markersets, except BW.MRK, have the same symbol in black, red, green
and blue. An appropriate markerset can be selected with the MARKERSET
command, and used with a lookup table that relates changes in data values to
changes in hue. POINTMARKERS can then be used in conjunction with the
lookup table to plot the points. This is the method used in PH.ami; see Figure 3.1a.
PH
- the coverage to be displayed;
- an item in the point attribute table of ;
- an info table that relates values to markers;
- a markerset file.
Nominal Data-Orientation
Orientation is best used for nominal data, and the MINERAL.MRK
markerset provides some ready-to-use symbols that vary in orientation (such as
markers 143 through 149). PH.ami (above) uses command line arguments to select
this markerset and draw these symbols; see Figure 3.1b.
Nominal Data-Shape
Shape should only be used for nominal data. All of the markersets, except
COLOR.MRK, have symbols that change in shape. The macro PS.aml uses cursors
to extract the coverage name and type (point or node) from the lookup table (which
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39
Figure 3.1a: PH.aml Figure 3.1b: PH.aml
Nominal data displayed with hue Nominal data displayed with orien-
using the color.mrk markerset. tation by using symbols from
mineral.mrk.
o
t
o
o
Figure 3.1c: PS.aml Figure 3.1d: PAO.aml
Nominal data displayed with shape. Ratio data displayed with symbol
orientation.
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40
must be in the format generated by the lookup table AMLs discussed in Chapter
Two), and then draws the points with the lookup table; see Figure 3.1c.
PS {markerset}
- a lookup table generated by SETMAN;
{markerset} - a markerset file-the current markerset is the default.
Ordinal to Ratio Data-Orientation
Orientation is best used for nominal data, but ARC/INFO allows the
specification of orientation that can be used with higher data levels. For point
symbols, the MARKERANGLE command allows specification of the drawing
angle of the current symbol. The macro, PAO.aml, uses cursors to determine the
minimum and maximum data values to be displayed, and then uses these values
to adjust the drawing angle of the selected marker; see Figure 3.Id.
PAO {markerset} {markersymbol} {markersize}
{max_angle} {pointlnode}
- the coverage to be displayed;
- a numeric data field in the attribute table of ;
{markerset} {markersymbol} - specify a marker-the current marker is the default;
{markersize} - drawing size of the marker-the default is 0.15 inches;
{max_angle} - angle of the maximum data value-the default is 179 degrees;
{pointlnode} - symbolize point (the default) or node feature.
Ordinal to Ratio Data-Value
Color value is best used for ordinal data. For point symbols, the
MARKERCOLOR command allows specification of the drawing color of the
current symbol. ARC/INFO has a Munsell-like color specification: the HLS color
model; the parameters for the HLS model are .
Hue is an integer from 0 to 360 (red = 0, green = 120, blue = 240). Lightness is an
integer from 0 to 100 (black = 0, white = 100). Saturation is an integer from 0 to 100
(gray = 0, fully saturated = 100). Specification of changes in value are
accomplished by: setting hue to any valid number; adjusting lightness to control
the grayness (for output on white paper, generally use a percentage less than 90);
saturation must be set to 0. The macro, PV.aml, uses MARKERCOLOR to control
value; see Figure 3.2a.
PV {markerset} {markersymbol} {markersize} {hue} {intensity}
- a lookup table generated by SETMAN or JENKS:
{markerset} {markersymbol} - specify a marker-the current marker is the default;
{hue} {intensity} - specify a color that will be value shaded:.
Ordinal to Ratio Data-Size
Size can be used in point symbols for ordinal and interval/ratio data, and
within ARC/INFO changes in size can be achieved in two ways: for circles and
boxes, ARC/INFO provides the SPOTSIZE/POINTSPOT command pair to
generate circle or box point symbols; for other symbol shapes, size is changed by
changing the drawing size of point symbols. The MARKERSIZE command allows
the specification of the size of the current point symbol. This macro, PZ.aml, uses
markersize to display a ratio data set; see Figure 3.2b.
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41
Figure 3.2a: PV.aml
Classed ratio (ordinal)
displayed with color value.
Figure 3.2b: PZ.aml
data Ratio data displayed with symbol
size.
Figure 3.2c: PC.aml Figure 3.2d: PB.aml
Ratio data displayed with graduated Ratio data displayed with graduated
circles. boxes.
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42
PZ {size_exponent} {size_factor} {minimum_size}
{markerset} {markersymbol} {pointlnode}
- the coverage to be displayed;
- a numeric data field in the attribute table of ;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches.
All of the size symbolization AMLs use the formula:
size = size_factor (normalized_data_value s|ze-exP°nent) + minimum_size
This is just a formula for a line in x (normalized_data) and y (symbol size)
space (with size_exponent set to one), with the ability to create non-linear
progressions (with size_exponent not equal to one). The slope of the line is
determined by size_factor, and the y-intercept of the line is minimum_size. The
data is normalized prior to calculating the size in order to set the minimum data
value to minimum_size; data values are normalized by:
normalized_data_value = (actual - minimum) / (maximum - minimum)
Ordinal to Ratio Data-Graduated Circle Size
Symbol size is good for either ordinal or interval/ratio data. For the
generation of graduated circle (or box) symbols, ARC/INFO provides two
commands that allow rapid generation of these maps: SPOTSIZE and
POINTSPOT. SPOTSIZE must be given before POINTSPOT can be used.
SPOTSIZE allows the creation of point symbols that can be linearly or
exponentially scaled; of the two, exponential scaling is generally preferred,
although the command line syntax is more complicated. Once SPOTSIZE has been
given, POINTSPOT can be used to create graduated symbol maps, with either
circle or box symbols. These two macros generate circle (PC.ami) and box (PB.aml)
symbols (see Figures 3.2c and d).
PC {minimum_size} {maximum_size} {pointlnode}
PB {minimum_size} {maximum_size} {pointlnode}
- the coverage to be displayed;
- an interval or ratio data field in the attribute table of ;
{minimum_size} - size of the smallest symbol-defaults to 0.05 inches;
{maximum_size} - size of the largest symbol-defaults to 0.5 inches;
{pointlnode} - the type of to be displayed-defaults to point.
Bivariate, Monochrome Symbolization
Most of the AML's presented in this section make use of shape to indicate a
nominal distinction. An appropriate symbol set should be selected (or created)
and one of the bivariate methods should be selected on the basis of the second
variable's type.
Two Nominal Data Sets-Shape and Orientation
For nominal data and meta-data, shape and orientation can be combined to
create bivariate point symbolization. Shape should generally be used for the
primary data, and orientation for the less important data, or meta-data (varying
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43
Figure 3.3a: PSO.aml Figure 3.3b: PSV.aml
Two nominal data sets displayed A nominal data set displayed with
with shape (primary data) and orien- shape and an ordinal data set displayed
tation (secondary data). with value. This is better for meta-data
than a second data set.
o
H
O
Figure 3.3c: PSZ.aml Figure 3.3d: PCV.aml
A nominal data set displayed with Interval/Ratio data displayed with
shape and a ratio data set displayed graduated circles that are value shaded
with size. This is more effective than on the basis on an ordinal data set.
value for a second data set.
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44
orientations of the same shape seem to 'go together' more than the same
orientation of varying shapes). PSO.aml, uses lookup tables for both shape and
orientation to generate a bivariate display; see Figure 3.3a. Note that this AML (as
with all that follow) require that any necessary lookup tables be set up in the
format generated by SETMAN.aml and JENKS.aml prior to running this routine.
PSO {markerset} {markersize}
- specifies marker symbol numbers;
- specifies angles in degrees;
{markerset} - a markerset for shapes-defaults to the current markerset;
{markersize} - a size for the markers-defaults to 0.15 inches.
Nominal Data, and Ordinal Data-Shape and Value
As with the next AML, this routine uses nominal primary data and ordinal
secondary data, but the visual hierarchy established by value makes it more
appropriate for display of meta-data than size. With value, uncertain values of the
primary data can be faded into the background; see Figure 3.3b and PSV.aml.
PSV {markerset} {markersize} {hue} {intensity}
- specifies marker symbol numbers;
- specifies HLS lightness data (0 to 100);
{markerset} - a markerset for shapes-defaults to the current markerset;
{markersize} - a size for the markers-defaults to 0.15 inches;
{hue} {intensity} - specify a color that will be value shaded.
Nominal Data, and Ratio Data-Shape and Size
For nominal primary data, shape can be used in conjunction with size to
create bivariate point symbols. This seems to work better for two data sets rather
than data and meta-data, which should be shown with shape and value; see Figure
3.3c and PSZ.aml (and the size discussion on page 39).
PSZ {markerset} {size_exponent} {size_factor} {minimum_size}
- specifies marker symbol numbers;
- an interval or ratio data item in the coverage named by ;
{markerset} - a markerset for shapes-defaults to the current markerset;
{size_exponent} {sizejactor} {minimum_size} - define the scaling of sizes,
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches.
Ratio Data, and Ordinal Data-Size and Value
Symbol size and value are good for either ordinal or interval/ratio data.
The AML PCV.aml combines the two; see Figure 3.3d. Because symbol size is
calculated directly from the Point Attribute Table, only one lookup table is needed,
but rather than containing point symbol numbers, it should contain color value (0-
-100) numbers. This system can be used to represent a ratio data value with size,
and a meta-data estimate of accuracy with value.
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45
PCV {minimum_size} {maximum_size} {hue} {intensity}
- a numeric item in the coverage referenced by ;
- specifies HLS lightness data;
{minimum_size} - graduated circle size for the smallest data value-default = 0.05 inches;
{maximum_size} - graduated circle size for the largest data value-default = 0.5 inches;
{hue} {intensity} - specify a color that will be value shaded.
Bivariate, Color Symbolization
For color (hue or hue/intensity) based bivariate mapping, a point symbol
should be selected from the available marker sets (PLOTTER, COLOR, MINERAL,
MUNICIPAL, OILGAS, TEMPLATE, USGS, or WATER); these markersets are
displayed in Appendix B of the Map Display and Query guide. The color
specification of that point symbol will then be changed to show variations in data
and meta-data. For size and hue based maps, only a sets of hues must be chosen;
symbol size and shape is calculated by ARC/INFO.
Two Nominal Data Sets-Shape and Hue
This macro (PSH.aml) uses two lookup tables for symbolizing two nominal
data sets. Unlike shape and orientation, neither shape or hue is, in general, the
dominant visual variable. Visual hierarchies can be established by selecting
intense color and similar shapes—this will make color hue the more prominent of
the two nominal visual variables. See Figure 3.4a.
PSH {markerset} {markersize} {value} {saturation}
- specifies marker symbol numbers;
- specifies HLS hue data (values of 0 to 360);
{markerset} - a markerset for shapes-defaults to the current markerset;
{markersize} - a size for the markers-defaults to 0.15 inches:
{value} {saturation} -defaults of 50 and 100 (maximum intensity).
Two Nominal Data Sets-Dual Hue Ranges
Color hue is best used for nominal data, although with well selected colors,
hue can be used with ordinal data. Use of the spectral encoding bivariate mapping
scheme requires careful selection of colors. For the specification of colors for dual-
hue range mapping, the CMY (Cyan, Yellow, Magenta) color scheme is most
useful. A color chart for this color specification system is in Appendix J of the Map
Display and Query manual. For a four by four color matrix, color specifications like
the following can be used:
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:
Magenta:
33 Cyan:
0 Magenta:
33 Cyan:
33 Magenta:
33 Cyan: 33
67 Magenta: 100
Cyan:
Magenta:
0 Cyan:
0 Magenta:
0 Cyan:
33 Magenta:
0 Cyan: 0
67 Magenta: 100
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46
*>
o
Figure 3.4a: PSH.aml Figure 3.4b: PDH.aml
Two nominal data sets displayed Two nominal data sets displayed
with shape and hue. with the dual-hue ranges. Note the
lack of discernible order in color
changes—this necessitates a legend
.
Figure 3.4d: PBL.aml
The AML that
generates these
legends automati-
cally places the
labelling text and the
total number of
occurrences in each
column or row.
11.11 ->
5.42->
6
6
7
7
i 5
11.11* *••• 9
-> 5.420 * * • • 6
I 5
I 1
0.82 ->
0.11 -> 0.82
Figure 3.4c: PCCaml
Two ordinal data sets displayed with comple-
mentary colors. This technique highlights corre-
lation better than dual-hue range maps—the central
gray diagonal could indicate a linear relation.
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47
This pattern can be generated with SETAUTO.aml with the command line 0 33.
Yellow should be held constant for each of the sixteen positions—generally, 100
should be good. Even with this control of changes in color, dual-hue range maps
should generally be used only for nominal data—the complementary-color system
tends to present ordinal data better. See Figure 3.4b and PDH.aml.
PDH {markerset} {markersymbol} {markersize}
- specifies changes in cyan (values of 0 to 100);
- specifies changes in magenta (values of 0 to 100);
{markerset} {markersymbol} - specify which symbol will be drawn with-defaults to current;
{markersize} - silicifies the size of the marker-defaults to 0.15 inches.
Two Ordinal Data Sets-Complementary Colors
This AML is a variation on the previous macro. The change is in the colors
used to symbolize data; complementary colors are hues that are on opposite sides
of the Munsell or Tektronix color spaces and mix to form grey. This mixing allows
highlighting of data that is not highly correlated, because these areas will appear
in color, whereas the central axis of correlated data will appear in grey. This
method allows the representation of both positive and negative correlations;
negative correlations should be represented by reversing the values in one of the
lookup tables—this changes the direction of the slope of the central axis. Note that
white should be avoided because the entire symbol will disappear on a white sheet
of paper; use a range from 5 to 100 for percent area inked. See Figure 3.4c and
PCC.aml.
PCC {markerset} {markersymbol} {markersize}
- specifies changes in cyan (values from 0 to 100);
- specifies changes in red (values from 0 to 100);
{markerset} {markersymbol} - specify which symbol will be drawn wrth-defaurts to current;
{markersize} - specifies the size of the marker-defaults to 0.15 inches.
Point Legend Creation
Although the usage of this AML (PBL.aml) is lengthy, it allows one macro
to generate a bivariate legend for three different types of point symbolization
schemes: dual hue, complementary colors, and hue and intensity. See Figure 3.4d
for both dual-hue and complementary-color legends and Figure 3.5b for a hue and
intensity legend.
PBL
{markerset} {markersymbol} {markersize} {textset} {font} {point} {decimaLprecision}
- the first lookup given in one of the bivariate AMLs;
- the second lookup given in one of the bivariate AMLs;
- the lower left corner of the legend matrix, in PAGEUNITS;
- the separation of symbols on the x and y axes, in PAGEUNITS;
{markerset} {markersymbol} - specify which symbol will be drawn wrth-defauKs to current;
{markersize} - specifies the size of the marker-defaults to 0.15 inches;
{textset} {font} {point} - specify a textset for legend labels-defaults to a roman, 10 point;
{decimaLprecision} - number of decimal places shown for ratio data labels-defaults to 2.
Nominal Data, and Ordinal Data-Hue and Intensity
Color hue is best used for nominal data; color intensity, on the other hand,
is best used for ordinal data (and generally only for meta-data, not a second data
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48
rs
5
9
Figure 3.5a: PHI.aml
A nominal data set displayed with
hue and an ordinal data set used to
display meta-data. Intense (bright)
colors tend to be more noticeable and are
used to present more certain values.
Figure 3.5b: PBL.aml
A hue and intensity legend. Not the
lack of a diagonal, as in the comple-
mentary color system. This makes hue
and intensity better suited to display of
meta-data than two correlated data sets.
• I
0
Figure 3.5c: PEE.aml Figure 3.5d: PCFLaml
Two ratio data sets displayed with Interval/Ratio data displayed with
the Eyton's equiprobability ellipse graduated circles that are hue shaded,
system. This should be used to highlight displaying nominal data.
correlated data.
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49
variable). This color scheme represents meta-data better than the dual-hue and
complementary-color bivariate systems, because the data variable is clearly
displayed in a constant hue, unlike the other color bivariate methods. See Figure
3.5a and PHI.aml.
PHI {markerset} {markersymbol} {markersize}
- specifies changes in HLS hue (from 0 to 360)
- specifies changes in HLS saturation (from 0 to 100)
{markerset} {markersymbol} - specify which symbol will be drawn wrth-defaults to current;
{markersize} - specifies the size of the marker-defaults to 0.15 inches.
Two Ratio Data Sets-Equiprobability Ellipse
Eyton's ellipse is a variation on the complementary color system. The colors
that are used are the same, but the linear correlation between the two variables is
used to determine a central category, which specifically highlights correlation.
This AML requires that the EYTON.aml, presented in chapter two, be run first. See
Figures 3.5c and 5.7b on page 79 for a legend display, and PEE.ami.
PEE {markerset} {markersymbol} {markersize}
- a lookup table generated by EYTON.aml;
{markerset} {markersymbol} - specify which symbol will be drawn with-defaults to current;
{markersize} - specifies the size of the marker-defaults to 0.15 inches.
Ratio Data, and Nominal Data-Size and Hue
This macro is the color equivalent of the one that generated Figure 3.3d.
Unlike that AML though, this should be used for one nominal data variable and
one ratio data variable. See Figure 3.5d and PCH.aml.
PCH {minimum_size} {maximum_size} {value} {intensity}
- a numeric data item of the coverage reference by ;
- specifies changes in HLS hue (from 0 to 360);
{minimum_size} - graduated circle size for the smallest data value-default = 0.05 inches;
{maximum_size} - graduated circle size for the largest data value-default = 0.5 inches;
{value} {intensity} -default to 50 and 100 (maximum intensity).
Multivariate Symbolization
Multivariate point symbolization can be accomplished by several means,
each of which is suited to various combinations of data levels. Because of the
increased complexity involved in multivariate mapping, care must be taken to
insure legends are well designed and convey the methods that should be used in
interpreting map symbols.
Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization
The 'false color' images that are often generated with satellite derived data
use red, green and blue to symbolize data values from three spectral bands. This
technique is applied here to allow display of three data values. See Figures 3.6a
and 5.8b on page 82 for a legend. Note that the AML (PRGB.aml) performs a
linear-stretch on the items in the Point Attribute Table. This AML also allows color
specification as cyan, magenta, and yellow. This can be helpful because this color
scheme tends to allow numbers in the low end of the data range to be
distinguished more readily than the RGB scheme.
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50
«•.«
D
Figure 3.6a: PRGB.aml Figure 3.6b: PSZV.aml
Three ratio data sets displayed by A nominal data set displayed with
linearly stretching the data sets from 0 to shape, a ratio data set displayed with
255 and using data set one for red, two size, and an ordinal data set (size
for green and three for blue. meta-data) displayed with color value.
Figure 3.6c: PCHLaml Figure 3.6d: PP.aml
A nominal data set displayed with Ratio data displayed with size; each
color hue, ratio data displayed with size, pie slice is a nominal difference within
and an ordinal data set (size meta-data) the ratio whole—pie slice values are
displayed with color intensity. percentages of the whole.
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PRGB
{markerset} {markersymbol} {markersize} {pointlnode} {rlc}
- the coverage to be displayed;
- numeric items in the attribute table of ;
{markerset} {markersymbol} - specify which symbol will be drawn wrth-defaults to current;
{markersize} - specifies the size of the marker-defaults to 0.15 inches;
{pointlnode} - symbolize point (the default) or node features;
{rlc} - display with the RGB (default) or CMY color system.
Nominal Data, Ratio Data and Ordinal Data-Shape, Size and Value
Shape can be used to display nominal data, and size can be used to display
ratio data. This AML (PSZV.aml) adds to this bivariate representation by allowing
color value to be used to display an ordinal data set. Color value can be used to
display uncertainty on monochrome output devices, such as laser printers. The
calculation of symbol size is discussed on page 39; see Figure 3.6b.
PSZV {markerset}
{size_exponent} {sizejactor} {minimum_size} {hue} {intensity}
- specifies marker symbol numbers;
- a numeric data item in the coverage referred to by ;
- specifies HLS lightness data (from 0 to 100);
{markerset} - a markerset for shapes-defaults to the current markerset;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches;
{hue} {intensity} - define a color that will be value shaded.
Ratio Data, Nominal Data, and Ordinal Data-Size, Hue and Intensity
Like the previous AML, size, hue and intensity should be used to display a
nominal data variable, a ratio data variable, and an ordinal data variable
(meta-data for the ratio data variable would be appropriate). This AML however
uses color hue and intensity, and therefore requires full color displays. See Figure
3.6c and PHIZ.aml.
PHIZ
{markerset} {markersymbol} {size_exponent} {sizejactor} {minimum_size}
- specifies HLS hue data (from 0 to 360);
- specifies HLS saturation data (from 0 to 100);
- a numeric data item in the coverage referred to by the lookup tables:
{markerset} {markersymbol} - specify a marker-the current marker is the default;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches.
Ratio Data-Point Pie Graphs
This AML generates pie symbols for point data by use of the POINTSPOT
command. The type of data that should be used in the creation of this type of map
is a size value that represents a sum of several other values; these other values
should have nominal distinctions. POINTSPOT uses the sum value to calculate the
size of the circle, and it calculates the pie slice size that will be drawn as a function
of the ratio a sub-value to the whole. Colors for each slice are calculated by the
AML. See Figures 3.6d and 6.3d on page 88 for a legend, and PP.aml.
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PP
- the coverage to be displayed;
- symbolize points or nodes;
- a numeric item in that specifies the size of the circle;
- the smallest and largest circle sizes;
- the number of pie slice data rtems~the value of n, next;
- names of numeric items in that specify the size of pie slices.
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Chapter Four
Line Symbolization in ARC/INFO
For line symbolization, the visual variables of hue, shape, and texture can
be controlled by the use of lookup tables, which relate nominal difference to
symbolization. Value and size can be used either by means of lookup tables, or by
referencing Arc Attribute Table values. Lookup tables should be generated with
one of the lookup table AMLs presented in Chapter Two.
Monovariate Symbolization
As with point symbolization, the AMLs discussed in this chapter start out
relatively simply, and the output could be accomplished almost as readily by
hand. Like the monovariate point AMLs, these AMLs are primarily background
for the bi- and multivariate AMLs of later sections.
ARC/INFO provides a default set of lines in the lineset file, PLOTTER.LIN;
there are several other available linesets: 50.LIN, BW.LIN, CALCOMP2.LIN,
CARTO.LIN, COLOR.LIN, HP.LIN, and OILGAS.LIN. These are displayed in the
Map Display and Query guide's Appendix A, and the ability to create new symbols
sets is discussed in chapter three of Map Display and Query.
Nominal Data-Hue
Hue is best used for nominal data, and the COLOR.LIN lineset provides
fifteen symbols of the same shape, but each with a different color. All of the other
linesets, except BW.LIN, have the same symbol in black, red, green and blue. This
AML (LH.aml) uses the COLOR.LIN lineset for generating a display for arcs-see
the next section for display of routes, and Figure 4.1a.
LH
- the arc coverage to be displayed;
- the data item in referenced by ;
- an info table that relates to ;
- a lineset.
Nominal Data-Shape or Texture
Shape should be used for nominal data, and a line's shape can be changed
in several ways in ARC/INFO. The linesets PLOTTER.LIN, TEMPLATE.LIN and
OILGAS.LIN have symbols that change in shape. LINESET can be used to select
one of these, and LINESYMBOL can be used to change the shape of the current line
type, as well as change the line color and width (although the selection is limited).
This allows the selecting of several different shapes; the LINETYPE command
allows the generation of nine other types of shapes.
Texture is best used for nominal data, and the CARTO.LIN lineset provides
many ready-to-use symbols that vary in texture (such as lines 106, 110,114 and
118). These symbols can be selected by using LINESET to select this symbol set,
and LINESYMBOL to select the individual symbols. A line's texture can also be
directly varied; LINEINTERVAL and LINETEMPLATE can be used to control
texture. LINEINTERVAL determines the space between successive parts of a line
symbol; it defaults to 0 (no space). LINETEMPLATE requires that a lineinterval be
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54
K. .
Figure 4.1a: LH.aml Figure 4.1b: LS.aml
Nominal data in an arc coverage A nominal data set in a route system
distinguished by hue with the color.Un distinguished by shape using symbols
lineset. from plotter.lin.
Figure 4.1c: LV.arnl Figure 4.1d: L/.aml
Classed ratio (ordinal) data Ratio data displayed with size; sizes
displayed with color value by using a are calculated by scaling the data in the
lookup table. coverage Arc Attribute Table.
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55
set. The LINETEMPLATE command then allows control over both the length of
the mark and the length of the space between marks. The digits are
used to scale the lineinterval, with the first digit used for a line length, the second
for a space size, the third for a line, etc. For example, if the lineinterval is set to 0.25
inches and linetemplate is set to 2122, a line pattern of: a line 0.5 inches long,
followed by a space 0.25 inches long, followed by a line 0.5 inches long, followed
by a 0.5 inches long space is used to draw new lines. LS.aml uses a preset lookup
table to select line symbols for routes (see Figure 4.1b).
LS
- the route coverage to be displayed;
- the data item in referenced by ;
- an info table that relates to ;
- a lineset.
Ordinal Data-Value
Color value is best used for ordinal data, and the application of lookup
tables to a ratio data set, provides this data level. This AML (LV.aml) requires an
ordinal or ratio lookup table that specifies HLS color value (0 to 80) in its symbol
column. So the AML can control line value, any LINETYPE except hardware can
be used. The AML uses LINETYPE WIDE; this allows control of the width of a
solid line, which should be wide enough that dithering will not cause the line to
appear broken (a line width of at least 0.02 inches on a 300 dpi printer). See Figure
4.1c.
LV {size} {hue} {intensity}
- a lookup table generated by SETMAN or JENKS;
{size} - a line width-the default is 0.1 inches:
{hue} {intensity} - specify a color that will be value shaded.
Ratio Data-Size
Size can be used for ordinal data, and the PLOTTER.LIN, CARTO.LIN and
OILGAS.LIN linesets provide symbols that vary in size. An appropriate lineset
can be selected with the LINESET command, and used with a lookup table that
relates changes in data values to changes in size. For interval/ratio level data, the
LINESIZE command allows direct control of a line's width. Prior to using the
LINESIZE command however, the LINETYPE command must be given with a
type not equal to HARDWARE. A LINETYPE such as WIDE can be used. Once
this is done, the line's width can be controlled to represent data. This AML uses
the interval/ratio method to control width (see Figure 4.1d and LZ.aml).
LZ {size_exponent} {sizejactor} {minimum_size} {linetype}
- the arc coverage to be displayed;
- an interval/ratio data item in the Arc Attribute Table of ;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes,
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches.
All of the size symbolization AMLs use the formula:
size = sizejactor (normalized_data_value size_exponentj + mjnjmum_size
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56
This is just a formula for a line in x (normalized_data) and y (symbol size) space
(with size_exponent set to one), with the ability to create non-linear progressions
(with size_exponent not equal to one). The slope of the line is determined by
size_factor, and the y-intercept of the line is minimum_size. The data is normal-
ized prior to calculating the size in order to set the minimum data value to
minimum_size; data values are normalized by:
normalized_data_value = (actual - minimum) / (maximum - minimum)
Bivariate, Monochrome Symbolization
The visual variables of shape, texture, value and size can be combined to
allow monochrome bivariate mapping of linear features. This can be used to
present two data sets, or data and meta-data.
Two Nominal Data Sets-Shape and Texture
This AML (LST.aml) uses two lookup tables to determine symbolization.
Because the selection of predefined shape/texture symbols is limited, LINETYPE
can be combined with LINETEMPLATE. This is assisted by assigning numeric
codes in the shape lookup table:
1000= WIDE
1001 = DIAMOND
1002 = DOTS
1003 = HASH
1004 = SCALLOP
1005 = SCRUB
1006 = SLANT
1007 = ZIGZAG
These codes do not interfere with the Agfa Compugraphic glyph numbers,
which this AML will use for LINETYPE MARKER. The second (texture) lookup
table requires an integer value that specifies texture (see the texture discussion in
Nominal Data-Shape or Texture, above). See Figure 4.2a.
LST {interval} {size}
- specifies either Agfa Compugraphic glyphs or the above codes;
- specifies an integer code for the LINETEMPLATE;
{interval} - a ratio size in PAGEUNITS-the default is 0.1 inches:
{size} - specifies a line size-the default is 0.1 inches.
Nominal Data, and Ordinal Data-Shape and Value
Shape should be used to specify nominal differences and value should be
used to specify ordinal differences. Generally, value should be used for meta-data
and size (the next AML) should be used for a second data set. This AML (LSV.aml)
requires a lookup table that relates nominal distinctions to line symbols in a lineset,
and a second lookup table that specifies HLS values. See Figure 4.2b.
LSV {lineset} {linesize} {hue} {intensity}
- specifies line symbol numbers;
- specifies HLS lightness data (from 0 to 80);
{lineset} - specifies a lineset for shapes-defaults to the current lineset;
{linesize} - specifies a line width-defaults to 0.1 inches;
{hue} {intensity} - specify a color that will be value shaded.
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57
~"W 9"
,/p
^f^:
m / i \>
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*v,'
cr*^
AA^V' . :
r*^ AT^^J
rT^^ />J> ^**H
Figure 4.2a: LST.aml Figure 4.2b: LSV.aml
Two nominal data sets displayed A nominal data set displayed with
with shape (primary data) and texture, shape and an ordinal data set displayed
with value. This is more effective with
meta-data than a second data set.
rff\
Figure 4.2c: LSZ.aml Figure 4.2d: LVZ.aml
A nominal data set displayed with Ratio data displayed with size,
texture and a ratio data set displayed which is value shaded on the basis of
with size. Size is more effective than meta-data.
value in conveying a second data set.
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58
Nominal Data, and Ratio Data-Shape and Size
The AML, LSZ.aml, should be used for two data sets-one of nominal
information (shape or texture) and one of ordinal to ratio information (size). Like
the shape and value AML, this AML requires a lookup table that relates nominal
categories to line symbols, but requires the specification of a ratio data item in the
line coverage's attribute table. See the discussion of size specification on page 50
and Figure 4.2d.
LSZ {lineset} {scale_factor} {size_factor} {minimum_size}
- specifies line symbol numbers;
- an ratio data item in the attribute table referenced by ;
{lineset} - specifies a lineset for shapes-defaults to the current lineset;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes,
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches.
Ratio Data, and Ordinal Data-Size and Value
This AML uses size to indicate a ratio data set, and value to represent a
second data set. Because of the establishment of visual levels by both size and
value, this combination is good for conveying data and meta-data. The AML
requires a numeric attribute item for size, and a lookup table for HLS value
specification. See Figure 4.2d and LVZ.aml.
LVZ {size_exponent} {size_factor} {minimum_size} {hue} {intensity}
- specifies HLS lightness data (from 0 to 80);
- a ratio data item in the attribute table referenced by ;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes,
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches;
{hue} {intensity} - specify a color that will be value shaded.
Bivariate, Color Symbolization
Color hue and intensity add two important visual variables to the
representational techniques possible in ARC/INFO. Hue allows better
specification of nominal variables than texture (particularly in monochrome,
bivariate mapping) and can also be used for ordinal data. Intensity is useful for
display of uncertainty meta-data.
Two Nominal Data Sets-Texture or Shape, and Hue
This AML (LSH.aml) takes advantage of the ability of shape to convey
nominal data, and it uses color hue to specify a second nominal category. The
AML requires a lookup table that specifies line symbols for the shape (or texture)
variable, and a second AML that specifies HLS hue values (0 to 300). See Figure
4.3a.
LSH {lineset} {linesize} {value} {intensity}
- specifies line symbol numbers;
- specifies HLS hue data;
{lineset} - select a lineset for shapes-defaults to the current lineset;
{linesize} - specifies a line width-defaults to 0.1 inches;
{value} {intensity} - defaults: 50,100 (maximum brightness).
-------
Figure 4.3a: LSH.aml
Figure 4.3b: LDH.aml
Two nominal data sets displayed Two nominal data sets displayed
with shape and hue. with the dual-hue range technique.
Note the lack of discernible order in
color changes—this necessitates a legend
(below).
\c o vo
10135 -> 143.7
455 -> 10135
2435 -> 453
8.1 -> 2435
VO
S
R
M
A
15
10
14
IS
15
12
Figure 4.3c: LCC.aml Figure 4.3d: LBL.aml
Two ordinal data sets displayed with Dual-hue (top) and complementary
the complementary color technique, color legends. Note the central gray
This method highlights correlation diagonal in the complementary color
better than dual-hue mapping. legend.
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Two Nominal Data Sets-Dual Hue Ranges
Another method of displaying two nominal data sets is the dual-hue range
technique. This uses two hue ranges (yellow to red and yellow to green) to specify
data values. The combination of the two color ranges results in unique colors for
each combination of data values. The AML requires two lookup tables, which
specify color for the CMY color model (ranges of 0 to 100). See Figure 4.3b and
LDH.aml.
LDH {linesize}
- specifies changes in cyan (from 0 to 100);
- specifies changes in magenta (from Oto 100);
{linesize} - specifies a line width-defaults to 0.1 inches.
Two Ordinal Data Sets-Complementary Colors
The use of color to specify ordinal data requires careful selection of colors.
By use of color intensity in two complementary colors (equal amounts of each yield
gray), it is possible to specify a color system that represents ordinal information
well. This AML (LCC.aml) accomplishes this with two lookup tables for the CMY
color system (color numbers of 10 to 100), one of which is used for cyan and the
other is used for magenta and yellow, together (this yields red). A central diagonal
results, which is gray. With color values based directly on data values, this gray
line would represent linear correlation between the two variables. See Figure 4.3c.
LCC {linesize}
- specifies changes in cyan;
- specifies changes in red;
{linesize} - specifies a line width-defaults to 0.1 inches.
Bivariate Color Legends
Legends should present the map reader with as much information as
possible. This AML not only generates a line symbol for each color bivariate
scheme, but also labels the rows and columns with the appropriate name or data
range and provides the total number of items in each row or column. See Figure
4.3d, Figure 4.4d and LBL.aml.
LBL
{linesize} {textset} {font} {point} {floating_point_precision}
- the first lookup specified in LDH, LHI or LCC;
- the second lookup table from on of the display AMLs;
- the lower left corner of the legend;
- the size of each row and column;
- the symbolization method: Dual hue, Complementary color, or Hue and intensity;
{linesize} - specifies a line width-defaults to 0.1 inches;
{textset} {font} {point} - define the labelling text-defaults to a 10 point roman font;
{floating_point_precision} - the number of decimal places to be shown-the default is 2.
Two Ratio Data Sets-Eyton's Ellipse for Lines
A development of the complementary color system that specifically
highlights correlation is Eyton's equiprobability ellipse. This system calculates the
correlation between two ratio variables and specifies a complementary color shade
to each data pair. The central category contains the central cluster of correlated
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61
Figure 4.4a: LEE.aml Figure 4.4b: LHZ.aml
Two ratio data sets displayed with A nominal data set displayed with
an equiprobability ellipse. This selects hue and a ratio data set displayed with
the central cluster of correlated data as a size.
fifth category in a 2x2 matrix.
132.6 -> 190.5
59.7 -> 132.6
33.6 -> 59.7
-> 33.6
1
24
13
7
Figure 4.4c: LHLaml Figure 4.4d: LBL.aml
A nominal data set displayed with Hue and intensity legend. Note the
hue and an ordinal data set displayed lack of a diagonal, as in the comple-
with intensity. Intense colors tend to mentary color system; hue and intensity is
stand out in an image, highlighting data, better suited to data and meta-data.
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62
data. This system requires that the AML described in chapter two be run to
determine the classification. Once this is done, this AML (LEE.aml) displays linear
data. See Figure 4.4a.
LEE {lineset} {linesymbol} {linesize}
- a lookup table for linear data created by EYTON.aml;
{lineset} {linesymbol} - define a line to use for shading-defaults to the current line;
{linesize} - specifies a line width-defaults to 0.1 inches.
Ratio Data, and Nominal Data-Size and Hue
For combinations of nominal and ratio data, shape (which can be used in
monochrome maps) or hue can be used to specify the nominal data and size can be
used to display the ratio information. This AML uses a lookup table that relates
nominal data to HLS color hue (0 to 300) and a numeric item in the coverage's
attribute table. See Figure 4.4b and LHZ.aml.
LHZ {size_exponent} {size_factor} {minimum_size} {value} {intensity}
- specifies HLS hues;
- a numeric data item in the attribute table referred to be ;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes,
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches;
{value} {intensity} - default to 50 and 100--maximum intensity.
Nominal Data and Ordinal Meta-Data-Hue and Intensity
For display of a nominal data and meta-data, color hue can be used for the
nominal information and color intensity can be used for the meta-data. This AML
(LHI.aml) requires a lookup table for relating nominal data to HLS hue (0 to 300)
and a second table for relating meta-data to HLS saturation (20 to 100). See Figure
4.4c.
LHI {linesize}
- specifies HLS hue;
- specifies HLS saturation;
{linesize} - specifies a line width-default is 0.1 inches.
Multivariate Symbolization
Multivariate line symbolization allows the representation of three or more
variables about the same line segment on the same map. This is useful for the
communication of spatial patterns, but—as with all bi- and multivariate maps-
legends should include explanations of the data representation technique.
Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization
For representing three ratio data values, line color can be specified by
control of the red, green and blue (or cyan, magenta and yellow) components of
the color additive (or subtractive) process. This use of RGB color is similar to that
used to display satellite imagery. As such, the AML LRGB.aml requires three
numeric data items, which are linearly stretched from 0 to 250 (this prevents white
lines on white paper). See Figure 4.5a.
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63
Figure 4.5a: LRGB.aml Figure 4.5b: LSHZ.aml
Three ratio data sets displayed by A nominal data set displayed with
linearly stretching each data set from 0 shape, a second nominal data set
to 250 and using data set one for red, displayed with color hue, and a ratio
data set two for green and data set three data set displayed with size.
for blue.
Figure 4.5c: LSZV.aml Figure 4.5d: LHIZ.aml
A nominal data set displayed with A nominal data set displayed with
shape, a ratio data set displayed with color hue, a ratio data set displayed with
size, and an ordinal data set (possibly size, and an ordinal data set displayed
ratio meta-data) displayed with value, with color intensity.
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64
LRGB {linesize} {rlc}
{arclroutelsection} {subclass}
- the coverage to be displayed;
- three numeric data fields in ;
{linesize} - specifies a line width-default is 0.1 inches;
{rlc} - specifies the RGB or CMY color model;
{arclroutelsection} {subclass} - specifies arcs (default) or route/section and subclass.
Nominal Data, Ratio Data, and Nominal Data-Shape, Size and Hue
By adding a ratio variable to the bivariate representation shown in Figure
4.3a, a trivariate representation results. This allow communication of two nominal
variables, and a third, ratio, variable. The AML requires two lookup tables: one
that relates nominal data to line symbols; the other relating nominal data to HLS
hue (0 to 300). The size information is generated directly from a numeric item in
the arc (or route or section) attribute table. See Figure 4.5b, the discussion of size
on page 50 and LHSZ.aml.
LSHZ {lineset}
{size_exponent} {size_factor} {minimum_size} {value} {intensity}
- specifies line symbol numbers;
- specifies HLS hues;
- a ratio data field in the attribute table referenced by ;
{lineset} - specifies a lineset for shapes-defaults to current lineset;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes,
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches;
{value} {intensity} - default to 50 and 100-maximum intensity.
Nominal Data, Ratio Data, and Ordinal Data-Shape, Size and Value
This AML is addition of the bivariate representation techniques shown in
Figure 4.2b, Figure 4.2c and Figure 4.2d. This monochrome, trivariate mapping
system allows representation of nominal data and ratio data, along with an ordinal
data set, which can be used for representing the ratio data set's meta-data. The
AML requires the two lookup tables: one for relating nominal data to line symbols;
the other for relating ordinal data to HLS value (0—black to 80—almost white). The
size of the line symbol is generated from a numeric data item in an attribute table.
See Figure 4.5c and LSZV.amI.
LSZV {lineset}
{size_exponent} {size_factor} {minimum_size} {hue} {intensity}
- specifies line symbol numbers;
- a ratio data field in the attribute table referenced by ;
- specifies HLS lightness;
{lineset} - specifies a lineset for shapes-defaults to current lineset;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes;
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches;
{hue} {intensity} - specify a color to be value shaded.
Ratio Data, Nominal Data, and Ordinal Data-Size, Hue and Intensity
As with the previous AML, this macro is displays a nominal data set (with
hue instead of shape) and a ratio data set, along with an ordinal data set, which can
be used for representing the ratio data's meta-data. The AML requires two lookup
tables: for nominal data, a table of HLS hues (0 to 300); for ordinal data, a table of
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65
HLS saturation (20--off gray to 100-maximum intensity). The line symbol size is
calculated from a numeric item in the attribute table specified in the second lookup
table. See Figure 4.5d and LHIZ.aml.
LHIZ {size_exponent} {size_factor} {minimum_size}
- specifies HLS hue;
- specifies HLS saturation;
- a ratio data field in the attribute table referenced by ;
{size_exponent} {size_factor} {minimum_size} - define the scaling of sizes;
defaults: size_exponent = 1; size_factor = 0.15; minimum_size = 0.02 inches.
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66
Chapter Five
Choropieth Symbolization in ARC/INFO
There are several techniques available in ARC/INFO for the production of
choropleth maps (for area data that is continuous, and changes abruptly at
polygon borders). These techniques include hue, texture, orientation and shape
for nominal data, and size for ordinal to ratio data. As with the other monovariate
sections, the AML's start off simply in order to build a base for bi- and multivariate
mapping. Also these techniques tend to make use of lookup tables, which should
be generated prior to executing the display AML's.
ARC/INFO provides a default set of area fills in the shadeset file,
PLOTTER.SHD; there are several other available shadesets: CARTO.SHD,
COLOR.SHD and COLORNAMES.SHD. These are displayed in the Map Display
and Query guide's Appendix C, and the ability to create new symbols sets is
discussed in chapter three of Map Display and Query.
Monovariate Symbolization
Monovariate Symbolization techniques for area data involve the use of hue,
value, orientation and shape to represent data. This can be done when only one
variable needs to be shown, or as an inset for bi- or multivariate maps.
Nominal Data-Hue
Hue is best for representations of nominal data. In ARC/INFO's default
shadeset, there are only three colors (red, green and blue) available—shade
patterns 2, 3 and 4, and white—shade pattern 1. Rather than using the limited
default colors, SHADECOLOR can be used to specify the output color.
SHADECOLOR requires that the shadetype be set to a type other than the default
HARDWARE, such as COLOR. When this is done, hues can be specified directly;
an alternate method is to use one of ARC/INFO's color shadesets: COLOR.SHD
and COLORNAMES.SHD. This AML (CH.aml) accomplishes the display of a data
set with the shadeset method; see Figure 5.la.
CH
- a polygon coverage;
- the item in Polygon Attribute Table of referred to in ;
- relates data item to shades in ;
- a shadeset file.
Monovariate Legends-Filled Polygons
In keeping with the idea of presenting as much information as possible in
legends, AL.aml generates monovariate legends for area data that include the
number of polygons in each category as well as defining the category
Symbolization. The AML automatically labels each category, as well as adjusting
the display for nominal (discreet symbols) and ordinal (or better) data (continuous
symbols). See Figure 5.1b for nominal data, and Figure 5.2b for ratio data.
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METALS
METAL-OCMPOUNDS
HYDROCARBONS
HALOCARBONS
ACIDS
Figure 5.1a: CH.aml Figure 5.1b: AL.aml
Nominal data displayed with hue, A legend for figure a. This legend
using the color.shd shadeset. design gives the names associated with
hues as well as the total number of
regions in each class.
¥ * *,*,•»* * *,© © 0 •
¥ '. A ***** A • ^
» « « « » '. * A * '.A ******** f V <
« » « « « (V * * * * *\,.*. *******,»¥<
• , A * * * * A V ***** *: ¥ ¥ <
» « « « » «A***********4 ¥¥<
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Figure 5.1c: CH.aml Figure 5.1d: CS.aml
A nominal data set displayed with A nominal data set displayed with
orientation, using symbols from shape by using the Agfa Compugraphic
plotter.shd. glyphs. This symbolization is best for
areas that will not have specific borders.
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68
AL {color_parameter_1}
{color_parameter_2} {line_size} {textset} {font} {point_size} {floating_point_precision}
- the lookup table that a legend will be based on;
- the lower left corner of the legend area;
- the size of the legend-all locations are in PAGEUNITS;
- the symbolization method: Hue, Value, Texture, orientation (Angle), or
shadeset symbols;
{color_parameter_1} {color_paramter_2} - Hue: value and saturation (default: 50 and 100)
for Value: hue and saturation (default 0 and 0), no effect for other symbolization;
{linesize} - for Texture and Angle line width-defaults to 0 (minimum displayable width);
{textset} {font} {point_size} - define the labelling text-defaults to a 10 point roman font;
{floating_point_precision} - the number of decimal places to be shown--the default is 2.
Nominal Data-Orientation
Orientation is best used for nominal data. There are three ways of achieving
changes in area fill orientation: selecting a subset of a shadeset that has a pattern
that changes in orientation, the POLYGONSHADES command (see Ordinal to
Ratio Data-Orientation), and the SHADEANGLE command. The AML, CH.aml,
uses the PLOTTER.SHD shadeset's symbols; see the above discussion of the AML
and Figure 5.1c.
Nominal Data-Shape
Shape is best used for nominal data. The SHADETYPE command allows
the specification of a marker to be used for the area fill. The macro, CS.aml, makes
use of the Agfa Compugraphic font set to change area fill shape; see Figure 5.Id.
Note the use of a loop to set up area fills.
CS
- contains Agfa Compugraphic glyph numbers (font 94021);
- a size for the glyph symbols in PAGEUNITS;
- the separation of the glyphs in X and Y in PAGEUNITS.
Ordinal Data-Value
Color value is best used for ordinal data. A new command in ARC/INFO
release 6.0 allows the rapid generation of ordinal maps based on color value. The
command SHADECOLOR allows a 'true color' specification of area fills. Prior to
using SHADECOLOR, the shadetype must be set to color. Once this is done, colors
can be specified by one of several color models (such as HLS, RGB and CMY). This
macro uses lookup table symbols to specify value (lightness) in the HLS color
model; see Figure 5.2a and CV.aml.
CV {hue} {intensity}
- specifies HLS lightness (values from 0 to 100);
{hue} {intensity} - specify a color that will be value shaded.
Ordinal to Ratio Data-Orientation
For interval/ratio data that should not be classed and is continuous with
abrupt spatial changes (that is, it should be displayed as a choropleth map), ARC/
INFO provides one automated way of generating an unclassed choropleth map. It
uses changes in the orientation of area fills to vary the symbolization. The
POLYGONSHADES command is used with an area fill pattern that will show
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69
Figure 5.2a: CV.aml Figure 5.2b: AL.aml
An ordinal data set displayed with A legend for figure a. The
color value. This data set was classified continuous data is displayed as an
with the Jenk's optimal classification unbroken column.
system.
Figure 5.2c: CAO.aml Figure 5.2d: OL.aml
A ratio data set displayed with A legend for figure c. This AML
symbol orientation. The original data generates angled lines and labels (the
was scaled in INFO to range from 0 to labels are the original data range). It
179 degrees. also labels the minimum and maximum.
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70
angular changes (not a solid color fill, for example), such as shade 5 of
PLOTTER.SHD, and an angle item (preset to a range from 0 to 180 degrees) in the
Polygon Attribute Table. This AML displays this kind of data; see Figure 5.2c and
CAO.aml.
CAO {shadeset} {shadesymbol}
- the polygon coverage to be displayed;
- a numeric data item in the Polygon Attribute Table of ;
- select a shade to be oriented--defaults to plotter.shd 5.
Monovariate Legends-Orientation
Because orientation can be used in point symbols as well as area symbols,
the AML that follows is designed to work with either coverage type. It is also
allows specification of a data variable that is not the same as the item that
determined the drawing angle—an attribute item can be rescaled in INFO, for
example, into another item and the second item can be used to draw area fills. The
original item still holds the data values that the angles represent. By assuming a
linear transformation between data values and angles, this AML can label the
angles with an interpolated data value. See Figure 5.2d and OL.aml.
OL
{textset} {font} {point_size} {float_precision}
-the point or polygon coverage with angle data;
- the coverage type;
- the original data field;
- the data field used to display rotated symbols;
- the location of the center point of the legend;
- the length of each radiating line, in PAGEUNITS;
{textset} {font} {point_size} - define the label test-defaults to a 10 point roman font;
{float_precisionj - the number of decimal places to be shown-the default is 2.
Bivariate, Monochrome Symbolization
For area symbolization, the visual variables of texture, orientation and
value can be combined to represent to variables. This set of macros is designed for
continuous and abruptly changing spatial data of nominal to ratio attribute levels.
Two Nominal Data Sets-Texture and Orientation
Texture is best for showing nominal data. With the default ARC/INFO
shadeset, texture involves the selection of polygon shade patterns such as 5,9 and
13. A more flexible approach to texture involves using the SHADETYPE and
SHADESEPARATION commands. In this method the SHADETYPE must be set
to type HATCH, first. Then the shadesize should be set; because of the dithering
necessary to create gray shades on paper maps, the shadesize should be set to at
least 0.02 inches. The SHADESEPARATION value is then varied to change the
texture of the area fill. Because the general ARCPLOT commands require an
integer in the SYMBOL column of a lookup table and this how the lookup table
generation AMLs are set up, the AML, CTO.aml, scales each of the texture values
by dividing by 100. SHADE ANGLE is used to control the drawing angle of each
shade; the SYMBOL values in the angle lookup table should be values from 0 to
180 degrees. See Figure 5.3a.
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71
Figure 5.3a: CTO.aml Figure 5.3b: CTV.aml
Nominal data displayed with texture Nominal data displayed with texture
and a second nominal data set displayed and ordinal data displayed with value.
with orientation. This can be used to display a data set
with its meta-data.
6
6
6
6
Figure 5.3c: CTH.aml Figure 5.3d: CBL.aml
Nominal data displayed with texture A legend for figure c. This AML will
and a second nominal data set displayed also generate legends for the bivariate
with hue. This should be used for two mapping techniques shown in figures a
separate variables. and b.
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72
CTO {line_size}
- specifies line separation in hundredths of PAGEUNITS;
- specifies drawing angles;
{line_size} - specifies the width of the fill lines-defaults to 0 (minimum displayable width).
Nominal Data, and Ordinal Data-Texture Distinguished by Value
This AML makes use of two lookup tables to display texture and value; the
first lookup table's symbol column should contain values for line separation,
which will be divided by 100, and the second lookup table's symbol column should
contain values for value (0 to 80). This method should be used when presenting
data with meta-data, rather than texture, and orientation or hue, which are
intended to show spatial correlation. See Figure 5.3b and CTV.aml.
CTV {line_size} {angle} {hue} {intensity}
- specifies line separation in hundredths of PAGEUNITS;
- specifies HLS lightness;
{line_size} - specifies fill line width-defaults to 0.03 inches;
{angle} - specifies a drawing angle-defaults to horizontal;
{hue} {intensity} - specify a color to be value shaded.
Nominal Data-1 and 2-Texture as Intersecting Lines
One method of bivariate mapping that has been studied (by Carstensen) for
communication of two correlated variables is intersecting lines. This involves use
of texture as a visual variable by the controlled mixing of horizontal and vertical
lines. This AML uses the SYMBOL value in both of the lookup tables to determine
the texture of the vertical (the first lookup table) and horizontal (the second lookup
table) lines; see Figure 5.4a and CTL.aml (the legend AML is presented in the
Bivariate, Color Symbolization section).
CTL {line_size}
- specifies line separation in hundredths of PAGEUNITS for vertical
lines;
- specifies line separation for horizontal lines;
{line_size} - specifies line width-defaults to 0 (minimum displayable width).
Two Ordinal to Ratio Data Sets-Texture as Intersecting Lines
A variation of the previous AML allows the display of unclassed, ratio data.
This AML (CIL.aml) makes use of the values in two columns of the Polygon
Attribute Table to determine the spacing of the vertical and horizontal lines; see
Figure 5.4c.
CIL {maximum_separation}
{minimum_separation} {separation_scale} {line_size}
- the polygon coverage to be displayed;
- a numeric data item in for vertical line spacing;
- a numeric data item in for horizontal line spacing;
{maximum_separation} - the maximum width between lines-defaults to 0.3 inches;
{minimum_separation} - the minimum width between lines-defaults to 0.05 inches;
|separation_scale} - a real number to control exponential scaling of data to separation,
the default is 1 -linear scaling;
{line_size} - specifies a fill line width-defaults to 0 (minimum displayable width).
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6
6
6
6
73
Figure 5.4a: CTL.aml Figure 5.4b: CBL.aml
Two nominal data sets displayed A legend for figure a. The shape of
with texture. This AML can also be used the boxes formed by the intersecting
to display ordinal data. lines designates the values shown.
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Figure 5.4c: CIL.aml Figure 5.4d: CILL.aml
This intersecting lines map is an A legend for figure c. As with the
unclassed representation of two ratio classed map in figure a, the shape of the
data sets. boxes designates the values repre-
sented.
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74
Bivariate Legends-Unclassed Texture
Because the previous AML uses Polygon Attribute Table to determine
polygon texture, the AML that generates bivariate legends with lookup tables will
not work. This AML only creates an unclassed texture legend, specifically for the
maps generated with the previous AML. See Figure 5.4d and CILLaml.
CILL
{maximum_separation} {minimum_separation} {separation_scale} {line_size}
{textset} {font} {point_size} {floating_point_precision}
- the polygon coverage displayed with CIL.aml;
- a numeric data item in for vertical line spacing;
- a numeric data item in for horizontal line spacing;
- the lower left corner of the legend's location;
- the size of the legend diagram;
{maximum_separation} - the maximum width between lines-defaults to 0.3 inches;
{minimum_separation} - the minimum width between lines-defaults to 0.05 inches;
{separation_scale} - a real number to control exponential scaling of data to separation,
the default is 1 -linear scaling;
{line_size} - specifies a fill line width-defaults to 0 (minimum displayable width);
{textset} {font} {point_size} - define the labeling text-defaults to a 10 point roman font;
ffloating_point_precision} - the number of decimal places to be shown-the default is 2.
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
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 {line_size} {value} {intensity}
- specifies line separation in hundredths of PAGEUNITS;
- 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
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.
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75
Figure 5.5a: CDH.aml Figure 5.5b: CBLuiml
Two nominal data sets displayed A legend for figure a. Nominal data
with the dual hue range technique. This is displayed with the size of the column
is best used to show the spatial or row indicating the total number of
relationship between two variables. items in that column/row.
4
3
Figure 5.5c: CHI.aml Figure 5.5d: CBL.aml
Nominal data displayed with hue A legend for figure c. The AML
and ordinal meta-data displayed with separates nominal information and
color intensity; intense colors are used to displays continuous (ordinal+) data as
display highly certain values. an unbroken column.
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76
CBL
{textset} {font} {point_size} {float_precision} {line_size}
{color_parameter_1} {color_parameter_2}
- the two lookup tables used in a bivariate mapping AML;
- the tower left corner of the legend display;
- the x and y sizes of the legend display;
- 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
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
- specifies CMY cyan (from 0 to 100);
- specifies CMY magenta (from 0 to 100);
Nominal Data, and Ordinal Data-Hue and Intensity
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.ami, 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
-specifies HLS hue (from 0 to 360) for a nominal data set;
- specifies HLS saturation (from 20 to 100) for an ordinal data set.
Two Ordinal Data Sets-Complementary Colors
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:
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77
Figure 5.6a: CCC.aml Figure 5.6b: CBL.aml
Two ordinal data sets displayed with A legend for figure a. The use of two
the complementary color system. The continuous variables is conveyed by
large amount of red in the image can using unbroken columns and rows, and
provoke a reaction of alarm. placing labels at class breakpoints.
14.95
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6.81
Figure 5.6c: CCC.aml Figure 5.6d: CBL.aml
The ordinal data sets from figure c A legend for figure c. Note that with
with a reverse progression in the cyan this ordering of cyan, high data values
lookup. This causes a change in overall on both axes are displayed in red—the
tone of the map. color of danger.
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Cyan: 100 Cyan: 100 Cyan: 100 Cyan: 100
Magenta: 10 Magenta: 40 Magenta: 70 Magenta: 100
Yellow: 10 Yellow: 40 Yellow: 70 Yellow: 100
Cyan: 70 Cyan: 70 Cyan: 70 Cyan: 70
Magenta: 10 Magenta: 40 Magenta: 70 Magenta: 100
Yellow: 10 Yellow: 40 Yellow: 70 Yellow: 100
Cyan: 40 Cyan: 40 Cyan: 40 Cyan: 40
Magenta: 10 Magenta: 40 Magenta: 70 Magenta: 100
Yellow: 10 Yellow: 40 Yellow: 70 Yellow: 100
Cyan: 10 Cyan: 10 Cyan: 10 Cyan: 10
Magenta: 10 Magenta: 40 Magenta: 70 Magenta: 100
Yellow: 10 Yellow: 40 Yellow: 70 Yellow: 100
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
- specifies CMY cyan (from 10 to 100);
- specifies CMY red (from 10 to 100).
Two Ratio Data Sets-Eyton's Ellipse
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
- a lookup table for polygons generated by EYTON.aml.
Bivariate Legends-Eyton's Ellipse
Because of the uniqueness of the this bivariate representation system, a
different AML must be used to generate the legend. EELaml 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.
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Figure 5.7a: CEE.aml Figure 5.7b: EEL.aml
Two ratio data sets displayed using A legend for figure a. A scatter plot
the equiprobability ellipse method, shows the location of each data pair, and
Correlation between the two variables is the hues show the color used in the map.
determined to select a middle class.
14.95
11.69
6.81
Figure 5.7c: CTLW.aml
Two classed ratio (ordinal) data sets
displayed using texture with meta-data
for each data set displayed by using
color value; a legend is on the right.
0.14
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80
EEL {markerset} {markersymbol}
{markersize} {textset} {font} {point_size} {float_precision}
- a lookup table generated by EYTON.aml;
- the lower left corner of the scatter plot;
- 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.
Multivariate Symbolization
Multivariate choropleth maps can expand on some of the bivariate
mapping techniques in order to allow meta-data to be presented with data, in an
otherwise bivariate map. Multivariate maps can also be used to present more than
two data sets to the map reader.
Two Nominal or Ordinal Data Sets, Ordinal Data Sets-Texture with Value
For monochrome displays, intersecting lines allow control of texture to
convey a data value. By adding control of line value, meta-data can be presented
along with the two primary data sets. This AML requires two lookup tables with
values that will be divided by 100 to set texture and two lookup tables with HLS
value data (0 to 80). See Figure 5.7c and CTLVV.aml. (The legends are generated
with CBL.aml and AL.aml).
CTLW
{hue} {intensity} {line_size}
- specifies line separation in hundredths of PAGEUNITS:
- specifies HLS lightness (from 0 to 80);
- specifies line separation i hundredths of PAGEUNITS;
- specifies HLS lightness (from 0 to 80);
{hue} {intensity} - specify a hue to be value shaded;
{line_size} - specifies line width-defaults to 0.03 inches.
Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization
Three ratio data sets can be displayed by scaling the data to the range of the
RGB color system (0 to 255) and then using the data values to specify color. This
AML requires three numeric data items in the polygon attribute table; a switch can
be specified to direct the AML to use the CMY color system, which can represent
data values at the low end of each range better than the RGB system. See Figures
5.8a and 5.8c, and CRGB.aml.
CRGB {rlc}
- the polygon coverage to be displayed;
- three numeric data fields in the Polygon
Attribute Table of ;
{rlc} - Rgb or Cmy color space.
Multivariate Legends-RGB Space
Because the specification of color requires three dimensions, development
of a legend is difficult—it must appear to be three dimensional. This AML takes the
same three numeric data items used for the previous AML and displays the colors
-------
0 0 768704
0 843473 768704
-«k
000
0 843473 768704
670875 00
670875 843473 0
Figure 5.8a: CRGB.aml Figure 5.8b: RGBL.aml
Three ratio data sets displayed with A legend for figure a. The AML
red, green and blue color ranges. This is finds the minimum and maximum data
the 'false color' imagery often used with values, and displays these along with
satellite data. the colors at the corners of the color
cube.
0 0 768704 0 843473 768704
000
670875 00
670875 843473 0
The AML
Figure 5.8c: CRGB.aml Figure 5.8d: RGBL.aml
Three ratio data sets displayed with A legend for figure c.
cyan, magenta and yellow color ranges, increases the size of the front of the cube
This color model shows variability at the and the front four circles, in order to
low end of the data better than RGB. enhance the legend's '3-D' appearance.
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82
and data values associated with the corners of the color cube. The AML will also
work with points, lines and grids. See Figures 5.8b and 5.8d, and RGBL.aml.
RGBL
{rlc} {textset} {font} {point} {floating_point_precision}
- the coverage that contains the data;
- the type of ;
- numeric fields in the attribute table of ;
- the lower left corner of the back plane of the legend;
- the size of the back plane, in PAGEUNITS;
{rlc} - Rgb or Cmy color space;
{textset} {font} {point} - define the labelling text-defaults to a 10 point roman font;
{floating_point_precision} - the number of decimal places to be shown-defaults to 2.
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83
Chapter Six
Graduated Symbol Symbolization in ARC/INFO
For the generation of graduated symbol maps (which should be used for
discrete, abruptly changing, ordinal to ratio area data), ARC/INFO provides two
commands that allow rapid generation of these maps: SPOTSIZE and
POLYGONSPOT. SPOTSIZE controls the scaling of data to circle size, and
POLYGONSPOT does the plotting of the circles. A second method of graduated
symbol mapping is cartograms. These maps scale individual polygons on the basis
of a data value. Cartogram creation requires interactive map composition, both for
the scaling of polygons and the repositioning of scaled polygons.
Monovariate Maps
Monovariate symbolization for graduated symbols is based on the
manipulation of size to specify data. This makes graduated symbols appropriate
for ordinal to ratio data.
Ordinal to Ratio Data-Graduated Circles
This AML (GC.aml) uses the commands SPOTSIZE and POLYGONSPOT to
generate a graduated circle map. Because SPOTSIZE requires the minimum and
maximum data values, the AML searches the data set for the extremes, and then
displays the data. See Figure 6.1a.
GC {minimum_size} {maximum_size}
- the polygon coverage to be displayed;
- a numeric data field in the attribute table of ;
{minimum_size} - the circle representing the smallest data value-defaults to 0.05 inches;
{maximum_size} - the circle representing the largest data value-defaults to 0.5 inches.
Ordinal to Ratio Data-Cartograms
There are several varieties of cartograms; this AML simply scales a polygon
be a data value, and places the scaled polygon in the center of the original
polygon's extents. Because this does not handle unusually shaped polygons well,
the AML allows the scaled polygons to be repositioned. Since the representation
of data in cartograms is done with the polygon outline, cartograms are best used
to display density data (the AML calculates density from the data item and the
polygon size). See Figure 6.1b and GG.aml.
GG {scale_factor}
- the polygon coverage to be displayed;
- a numeric data field in the attribute table of ;
{scale_factor} - specifies the exponent used to calculate cartogram size-defaults to 1.
Monochrome, Bivariate Symbolization
Symbol size is good for either ordinal or interval/ratio data. For the
generation of value-shaded, graduated symbol maps (which should be used for
discrete, abruptly changing, ordinal to ratio area data and meta-data), size must
be used in conjunction with SHADECOLOR. This combination allows the display
of either data and meta-data, or two data variables.
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84
Figure 6.1a: GCaml Figure 6.1b: GG.aml
Discontinuous and abruptly Ratio area data displayed with carto-
changing, ratio area data displayed with grams. This shows the AML's defaults;
graduated circles. note the extremely small sizes and the
misplaced polygons.
Figure 6.1c: GCV.aml Figure 6.1d: GGV.aml
Graduated circles that are value Value shaded cartograms. The size
shaded with an ordinal data set. This is data is the same as figure b, but the scale
best used for meta-data, although a exponent is 0.5--representing smaller
second data set can be displayed as well, data values with larger polygons.
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Ordinal to Ratio Data, and Ordinal Data-Graduated Circles and Value
This AML (GCV.aml) develops the display of graduated circles to include
the value shading of the circle. The value_lookup must specify lightness data in
the HLS color model, with value ranging from 0 black to no more than 90 (light
gray), in order to avoid white symbols on a white background. See Figure 6.1c.
GCV {minimum_size} {maximum_size} {hue} {saturation}
- a numeric data field in the attribute table referred to by ;
- specifies HLS lightness data;
{minimum_size} {maximum_size} - the minimum and maximum circle sizes,
the defaults are 0.05 and 0.5 inches;
{hue} {saturation} - specify a color that will be value shaded.
Ordinal to Ratio Data, and Ordinal Data-Cartograms Shaded by Value
By using interactive map composition, cartograms (use of scaled areas to
represent a data value) can be drawn in ARC/INFO. Value is used to represent a
second variable; this can be used for a second variable when color is not an
available option, or meta-data. See Figure 6.1d and GGV.aml.
GGV {scale_factor} {hue} {intensity}
- a numeric data field in the attribute table referred to by ;
- specifies HLS lightness data;
{scale_factor} - specifies the exponent used to calculated cartogram size-defaults to 1;
{hue} {intensity} - specify a color that will be value shaded.
Color, Bivariate Symbolization
Symbol size is good for either ordinal or interval/ratio data. Graduated
symbol maps should be used for discrete, abruptly changing, ordinal to ratio area
data. Color hue can be used to display a second, nominal data set.
Ordinal to Ratio Data, and Nominal Data-Graduated Circles and Hue
Unlike the macro used to generate Figure 6.1c, this AML should be used for
two data sets—one ratio and one nominal, rather than data and meta-data. See
Figure 6.2a and GCH.aml.
GCH {minimum_size} {maximum_size} {value} {intensity}
- a numeric data field in attribute table referred to by ;
- specifies HLS hue data (from 0 to 360);
{minimum_size} - the size of the smallest data value's circle-defaults to 0.05 inches;
{maximum_size} - the size of the largest data value's circle-defaults to 0.5 inches;
{value} {intensity} --default to 50 and 100 (maximum intensity).
Graduated Circle Legends
This AML (GCL.aml) generates a series of circles that are labeled with the
data value represented by that size, and filled with the polygon fill in shadesymbol
1. It works for all of the graduated symbol AMLs (point and area). It should be
supplemented by an additional figure if the circles are hue or value shaded (see
Figure 6.2b).
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10027800
7525350
5022900
2520450
18000
METALS |
METALrOCMPOUNDS |
HYMIOCARBONS
HALOCARBON5
AOES
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ooo
Figure 6.2a: GCH.aml Figure 6.2b: GCL.aml
Discontinuous and abruptly A legend for figure a. The
changing, ratio area data displayed with graduated circle legend identifies size
graduated circles that are hue shaded (to data, and the hue data is displayed with
represent a nominal data set). AL.aml.
0.014
i 0.0112
0.0084
0.0056
0.0028
t
METALS |
METALrOCMPOUNDS |
HYKIOCARBONS
HALOCARBONS
ACIDS
I I I I I I I I I I I
O fN ^t ^O 00 O
Figure 6.2c: GGH.aml Figure 6.2d: GGL.aml
Hue shaded cartograms. These can A legend for figure c. Cartogram
be used to represent a nominal data set size data is displayed with reference to
and a ratio (density) data set. an unsealed polygon, indicating that the
symbols are based on polygon size.
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GCL
{minimum_size} {maximum_size} {textset} {font} {point} {float_precision}
- the coverage that was displayed with graduated circles;
- the type of ;
- the numeric data item in the attribute table of ;
- lower center of the column of circles;
- the number of circle to be drawn for the legend;
{minimum_size} - the size used to display the smallest data value-defaults to 0.05 inches;
{maximum_size} - the size used to display the largest data value-defaults to 0.5 inches;
{textset} {font} {point} - define the labelling text-defaults to a 10 point roman font;
{float_precisionj - the number of decimal places to be shown-defaufts to 2.
Ordinal to Ratio Data, and Nominal Data--Cartograms with Hue
This AML should be used to display a nominal data set, along with density
data. See Figure 6.2c and GGH.aml.
GGH {value} {intensity} {size_scale}
- a numeric data field in the attribute table referred to by ;
- specifies HLS hue (from 0 to 300);
{value} {intensity} - default to 50 and 100 (maximum intensity);
{size_scale} - specifies the exponent used to calculate cartogram size-defaults to 1.
Cartogram Legends
This AML, like the graduated circle legend AML, generates a series of
polygons that represent data values. Each polygon is placed inside an unsealed
outline of the polygon, and labeled. The polygon is drawn with the current
polygon shade fill. This legend must also be supplemented by a legend specifying
hue, value, or hue and intensity, if more than one variable is shown on the map (see
Figure 6.2d).
GGL - the polygon coverage displayed with cartograms;
- a numeric data field in the attribute table of ;
- the lower left corner of the legend area;
- the drawing size of each polygon;
- the total number of legend symbols;
{scale} - the exponent used to calculate cartogram size-defaults to 1;
{polygon} - the record number of an example polygon-defaults to the middle record;
{textset} {font} {point} - define the labelling text-defaults to a 10 point roman font;
{precision} - the number of decimal places to be shown-defaufts to 4.
Multivariate Symbolization
Two multivariate symbolization methods are presented here. Hue,
intensity and size is a development of hue and size. Graduated pie symbols allow
the display of a total value and a set of components of that value.
Ratio Data, Nominal Data, and Ordinal Data-Circles, Hue and Intensity
Like all graduated symbols, size should be used to represent a ratio variable
(that is discrete and abruptly changing). Hue can be used to represent a second,
nominal variable, and intensity can be used to represent an ordinal data—including
ratio meta-data. See Figure 6.3a and GCHI.aml.
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Figure 6.3a: GCHLaml Figure 6.3b: GGHLaml
Graduated circles shaded with color Cartograms shaded with hue and
hue (a nominal data set) and intensity intensity. Cartograms should be used
(an ordinal data set). to represent density data.
Figure 6.3c: GP.aml Figure 6.3d: GPL.aml
Graduated pie symbols. These show A legend for figure c. The size data
a total value (size) and the components can is displayed with the graduated
of the total (each pie wedge). circle legend AML. Pie slices are
shaded and labeled by this AML.
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89
GCHI {minimum_size} {maximum_size}
- a numeric data field in the cover referred to by ;
- specifies HLS hue (from 0 to 300);
- specifies HLS saturation (from 20 to 100);
{minimum_size} - the size representing the smallest data value-defaults to 0.05 inches;
{maximum_size} - the size representing the largest data value-defaults to 0.5 inches.
Ratio Data, Nominal Data, and Ordinal Data-Cartograms, Hue and Intensity
Like the previous AML, this macro should be used to represent a ratio data
set, a nominal data set, and an ordinal data set (which can be ratio meta-data). Like
the other cartogram AML's this should be used to display density information.
See Figure 6.3b and GGHI.aml.
GGHI {size_scale}
- a numeric data filed in the coverage referred to by ;
- specifies HLS hue data (from 0 to 300);
- specifies HLS saturation (from 20 to 100);
{size_scale} - specifies the exponent used to calculate cartogram size-defaults to 1.
Ratio Data-Polygon Pie Graphs
In addition to the appropriate spatial characteristics, graduated pie maps
should also have a data value that represents a total of multiple elements (this total
determines circle size). Each element displayed a fraction (pie wedge) of the
whole. The AML automatically determines hues for each element. See Figure 6.3c
and GP.aml.
GP
- a polygon coverage with data that is discontinuous and abruptly changing;
- a numeric field in the attribute table of , which is a total of ;
- the size of the smallest data value's circle (0.05 may be good);
- the size of the largest data value's circle (0.5 may be good);
- the total number of items given in ;
- numeric fields in that represent elements of .
Graduated Pie Legends
Legends for graduated pie can be generated by using the graduated circle
legend AML for displaying size data, and using GPL.aml to display the hues used
to shade pie slices. This AML uses the same hue selection routine as the graduated
pie mapping AMLs, but it only draws one circle with equally sized pie slices. See
Figure 6.3d.
GPL {textset} {font} {point_size}
{data_item_names}
- a numeric value in PAGEUNITS for the circle radius;
- the center location of the circle;
- the used in the mapping AML;
{textset} {font} {point_size} - define 1he labelling text-defaults to a 10 point roman font;
{data_ttem_names} - the labelling text-if used, there should be
separated by spaces.
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90
Chapter Seven
Grid-Cell Symbolization in ARC/INFO
For data that falls in the middle of the Continuous-Discrete range and in
the middle of the Abrupt-Smooth range (see Figure 1.1), a grid cell representation
should be used. This is accomplished by converting a polygon coverage into a grid
data layer; if necessary, smoothing the resulting grid; then displaying the grid.
POLYGRID is an ARC command that converts a polygon coverage into the GRID
cell format.
Conversion of Polygons to Grids
POLYGRID is an ARC command that converts polygon coverages into
GRID cell format. This is best for nominal data, or other polygon data that needs
to retain the shape of the original polygon. For ratio data, the GRID operators:
IDW, SPLINE and TREND allow conversion of polygons to grids. These operators
take a point file (polygon centers can be used) which also have a 'Z' value and
calculate intermediate values, in order to populate the resulting grid. IDW is the
inverse distance weighted routine; this is quick, but it may smooth the data by
eliminate extreme values. SPLINE retains extremes, but requires more processing
time. TREND calculates an overall trend for the input data. POLYGRID.aml links
the ARC command to ARCPLOT. An ARC version of the ARCPLOT AML is called
POLYGRID.
POLYGRID {resolution} {plllilslt}
- the input polygon coverage;
- a numeric data field in the attribute table of ;
- the resulting grid;
{resolution} - cell resolution-defaults to one hundredth of the smaller axis;
{plllilslt} - the method used to generate the grid-defaults to p: Polygon, point, Idw,
.Spline, Trend.
Lookup Tables for Ratio Grids
Because of the impracticality of calculating optimal breakpoints for ratio
grid layers, this AML (GRIDLUT.aml) only generates equal interval, or mean and
standard deviation classifications. These are based on the grid statistics table,
rather than calculated directly from the data set. Lookup tables for nominal grids
can be generated with SETMAN.aml.
GRIDLUT {intervallstandard_deviation}
- the name of the grid layer;
- a name for the resulting lookup table;
- the number of classes in the resulting lookup table;
{intervallstandard_deviation} - the classification method: equal Interval (the default) or
Standard deviation.
Monovariate Symbolization
Because of the limitations of ARC/INFO, which reflect the nature of the
raster data model, single grid layers can only be displayed with hue, value or
intensity (not used here). A grid cell is generally represented by a single pixel,
which prevents use of area fills based on shape, texture, etc.
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91
Figure 7.1a: RH.am I
Grided (raster) nominal
displayed with color hue.
Figure 7.1b: RV.aml
data Grided ratio data displayed with
value. Like the color hue display,
legends for this type of data can be
displayed with AL.aml.
Figure 7.1c: RHI.aml Figure 7.1d: RRGB.aml
Nominal data displayed with hue Three ratio data sets displayed with
and ordinal data displayed with the RGB (false color) system (compare
intensity (compare Figure 5.5a). Figure 5.8a).
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92
Nominal Data-Hue
Color hue is best used for nominal data. Because of this, RH.aml takes a
lookup table generated by SETMAN.aml--the method for creating nominal, grid
lookup tables. Legends for hue and value based displays can be generated with
ALaml. See Figure 7.la.
RH {value} {intensity}
- specifies HLS hue (from 0 to 300);
{value} {intensity} --default to 50 and 100 (maximum intensity).
Ordinal to Ratio Data-Value
Because color value is best for ordinal data, this AML requires a lookup
table generated by GRIDLUT.aml. For grid layers in which the middle value is
important, the lookup table should be generated with the mean and standard
deviation method, otherwise equal intervals is probably better. See Figure 7.1b
and RV.aml.
RV {hue} {intensity}
- specifies HLS lightness (from 0 to 100);
{hue} {intensity} - specify a color to be value shaded-defaufts to 0 and 0.
Bivariate and Multivariate Symbolization
As with single variable displays, bivariate displays are limited to the control
of color. This is best accomplished by use of hue and intensity. Three variables can
be represented in grid cell format by use of Red, Green and Blue encoding. This is
the method used to generate color satellite images, for example.
Nominal Data, and Ordinal Data-Hue and Intensity
Hue should be used for nominal data (with a lookup table generated by
SETMAN.aml). Intensity should be used for ordinal data (with a lookup table
generated by GRIDLUT.aml). Legends can be created with CBLaml. See Figure
7.1candRHI.aml.
RHI {nominal_vat_rtem} {ordinal_vat_item}
- specifies HLS hue (from 0 to 300);
- specifies HLS saturation (from 20 to 100);
{nominal_vat_item} - specifies an item in the hue grid attribute table other than VALUE;
{ordinal_vat_item} - specifies an item in the intensity grid attribute table other than VALUE.
Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization
This AML takes three grids, assigns the first to red, the second to green, and
the third to blue. Each grid is linearly stretched from 0 (no color) to 255 (maximum
color), and displayed. Legends can be created with RGBL.aml. See Figure 7.1d and
RRGB.aml.
RRGB
- a grid that will be displayed in shades of red;
- a grid that will be displayed in shades of green;
- a grid that will be displayed in shades of blue.
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Chapter Eight
Dot Density Symbolization in ARC/INFO
Production of dot density maps, which should be used for discrete,
smoothly changing area data, in ARC/INFO requires the use of GRID and TIN for
the creation. This is accomplished by converting a polygon coverage to a grid data
layer; if necessary, smoothing the resulting grid; then converting the grid into a
stepped surface polygon coverage. ARCPLOT then fills the polygons with dots.
Conversion of Polygons to Dot Density
POLYDOT.aml performs the conversion from polygons based on
choropleth boundaries to polygons based on stepped surface boundaries. A
lookup table for the input coverage is used to determine the steps. The lookup
table can be based on Jenks optimal, or some other classification method. The
AML modifies this input lookup table, in order to make it the lookup table for the
output coverage. See the discussion of surface generation on page 84.
POLYDOT {resolution} {ilslt}
- specifies a stepped surface classification for ;
- the resulting stepped surface coverage;
{resolution} - the grid cell size for creating a surface,
defaults to one hundredth of the smallest axis of the coverage;
{ilslt} - the method of creating the surface: Idw, Spline, or Trend.
Monovariate Symbolization
For single variable dot density maps, the visual variable of texture is used
to show changes in data value. By controlling the number of dots placed in an area,
data that is discrete, but smoothly changing can be represented.
Ordinal to Ratio Data-Texture
Texture can be controlled by using SHADESEPARATION with shadetype
RANDOMDOTS. Higher values should be represented with a small separation—
this will increase the dot density. Because of ARCPLOT's dot placement routine,
the shade separation for dots of 0 size must not be greater than 4/100 of an inch.
For four classes, SETAUTO.aml can be run with the arguments 0 100 0.5 22. See
Figure 8.1a and DD.aml.
DD {dot_size}
- specifies dot separation in hundredths of PAGEUNITS;
{dot_size} - the size of individual dots-defaults to 0.02 inches.
Monovariate Dot Density Legends.
Legends for dot density maps must convey the idea of a continuous range
of data values. To accomplish this, DDL.aml generates a column that is
subdivided, and labeled, at the surface breakpoints, and filled with dots of the
appropriate density. See Figure 8.1b.
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Figure 8.1a: DD.aml Figure 8.1b: DDL.aml
Discontinuous and smoothly A legend for figure a. The
changing data displayed with dot continuous nature of the data is
density. This use of texture is accom- displayed by the unbroken column and
plished by converting polygons in labels at transition points.
stepped surfaces.
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Ratio data displayed with dot A legend for figure b. This AML can
density texture and ordinal data also be used to generate a legend for dot
displayed with color value. This can be density and hue maps.
used to show ratio meta-data.
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DDL {dot_size} {textset} {font} {point_size}
{float_precisiont}
- the lookup table that specifies shade separations;
- the lower left corner of the legend column;
- the x and y sizes of the legend;
{dot_size} - the size of dot used in the map-defaults to 0.02 inches;
{textset} {font} {point_size} - define the labelling text-defaults to a 10 point roman font;
{float_precision} - the number of decimal places shown in the legend-defaults to 2.
Monochrome, Bivariate Symbolization
Monochrome bivariate maps are limited to dot density texture and color
value. This can be used to display two data values, or data (texture) and meta-data
(value).
Ratio Data, and Ordinal Data-Texture and Value
Dot density maps that show more than texture must use a dot size larger
than that needed for texture alone. This is because specification of halftone shades
(such as those used by printers) requires more than one pixel (which can only be
on or off). The macro, DDV.aml, adjusts for this by using a larger dot size. See
Figure 8. Ic.
DDV {dot_size} {hue} {intensity}
- specifies dot density in hundredths of PAGEUNITS;
- specifies HLS lightness (from 10 to 100);
{dot_size} - the size of a dot-defaults to 0.03 inches;
{hue} {intensity} - specify a color to be value shaded.
Bivariate Dot Density Legends
Like single variable legends, bivariate legends must convey the idea of
continuity in dot density, as well as display the character of the second variable.
The macro will display hue (nominal) data in separate rows, and value (ordinal)
data as continuous. See DDBL.aml and Figure 8.1d.
DDBL {dot_size}
{textset} {font} {text_size} {float_precision} {color_parameter_1} {color_parameter_2}
- the lookup table used to specify dot density;
- the lookup used to specify hue or value;
- the lower left corner of the legend box;
- the size of the legend box;
- Hue or Value symbolization;
{dot_size} - the size of dot used in the map-defaults to 0.03 inches;
{textset} {font} {text_size} - define the labelling text-defaults to a 10 point roman font;
{float_precision} - the number of decimal places shown-defauhs to 2;
{color_parameter_1} - for Hue, value; for Value, hue;
{color_parameter_2} - intensity-defaults are the same as the mapping AMLs.
Color, Bivariate, and Multivariate Symbolization
Color bivariate maps use texture and hue to display data. Texture should
be used for numeric data, and hue should be used for nominal data. More than two
variables can be shown in a dot-density map by making use of two or three of the
dimensions used to specify color. Hue and intensity allow three variables to be
shown and RGB symbolization allow four variable to be shown.
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Figure 8.2a: DDH.aml Figure 8.2b: DDHI.aml
Ratio data displayed with dot Ratio data displayed with dot
density texture and nominal data density texture, nominal data displayed
displayed with color hue. with hue and ordinal data (ratio
meta-data) displayed with intensity.
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Figure 8.2c: DDRGB.aml Figure 8.2d: DDL.aml and RGBL.aml
Four ratio data sets, one displayed A legend for figure c. These two
with dot density texture, one with red, AMLs display all of the data shown,
one with green and one with blue. Color without creating a four dimensional
data values are linearly stretched. display.
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Ratio Data, and Nominal Data-Texture and Hue
This AML is a variate of the monochrome macro. Like that one, shade
separation must not be specified lower than 0.04 inches, or ARCPLOT will hang.
See DDH.aml and Figure 8.2a.
DDH (dot_size) {value} {intensity}
- specifies dot density in hundredths of PAGEUNITS;
- specifies HLS hue (from 0 to 300);
{value} {intensity} -default to 50 and 100 (maximum intensity}
Ratio Data, Nominal Data and Ordinal Data-Texture, Hue and Intensity
The use of color intensity can be used to display an ordinal data set, such as
meta-data. This can be accomplished by adding intensity to the dot density and
hue AML. See DDHI.aml and Figure 8.2b.
DDHI {dot_size}
- specifies shade separation in hundredths of PAGEUNITS;
- specifies HLS hue (from 0 to 300);
- specifies HLS saturation (from 20 to 100);
{dot_size} - specifies the size of a dot-defaults to 0.03 inches.
Three Ordinal to Ratio Data Sets-Red, Green and Blue Symbolization
Three numeric data sets can be displayed by assigning each to one of the
color primaries (red, green and blue). In order to ensure that all data values are
represented, DDRGB.aml linearly stretches each of the color data sets, so that each
value ranges from 0 to 250, or 0 to 100 for the CMY color model (this may show
changes at the lower ranges of the data better than RGB). See Figures 8.2c and d.
DDRGB {rlc} {dot_size}
- specifies shade separation in hundredths of PAGEUNITS;
- numeric data fields in the coverage referred to by
{rlc} - selects the Rgb (the default) or the Cmy color model;
{dot_size} - specifies the size of a dot-defaults to 0.03 inches.
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Chapter Nine
Isopleth and Fishnet Symbolization in ARC/INFO
Isopleth maps, or the three-dimensional equivalent, fishnet displays,
should be used for data that is continuous and smoothly changing. Both of these
can be displayed within ARCPLOT, but first a surface must be generated from a
coverage. The result of this conversion, or any grid layer, can be turned into a
isoline coverage and displayed as arcs, or displayed as a fishnet. All of the surface
display routines can be used for both grids (lattices) and TINs (Triangulated
Irregular Networks).
Polygon to Isoline Conversion
Contours can be used to show continuous, constantly changing data, but if
the data is summarized to polygons, isolines must be generated before they can be
displayed. POLYCONT.aml accomplishes this. See the discussion of surface
calculation on page 84.
POLYCONT {contourjnterval} {resolution} {ilslt}
- the coverage to be converted;
- a numeric data field in that specifies 'Z values;
- the output line coverage;
{contour interval} - the contour interval of the output coverage-default is 1/10 of the range;
{resolution} - resolution of the surface grid-defaults is 1/100 of the small axis in ;
{ilslt} -surface calculation method: Idw (default), Spline, or Trend surface.
Polygon to Surface Conversion
The generation of a surface can be accomplished by creating a grid or a TIN.
Creation of grids is discussed on page 84. In general, grids may be the better
method, unless full use is made of the TIN surface generation capabilities. A
simple TIN can be created from ARCPLOT with POLYTIN.aml.
POLYTIN {polysllabels}
- the coverage to be converted;
- a numeric item in that specifies 'Z' values;
- the output surface;
{polysllabels} - whether polygon bounds or label points should be used as the Z reference.
Monovariate Symbolization
The two primary methods of surface display, isolines and fishnets, display
a single variable by control of location. This should only be used for interval or
ratio data.
Ratio Data-lsoline Location
Isoline coverages are arc coverages that can be labeled with a surface height
(although elevation is a common use, it is not the only use of isolines and fishnets).
SISO.amI draws arcs with the current line type and labels the arcs. Because the
current line type is used multivariate maps can be created by changing line hue,
value, shape, etc. See Figure 9.1 a.
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Figure 9.1a: SISO.amI Figure 9.1b: SF.aml
A continuous, smoothly changing Ratio area data displayed with a
ratio surface displayed with isolines. fishnet. This display shows the default
The AML attempts to place contour options of SURFACEDEFAULTS and
labels along the lines. the AML.
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Figure 9.1c: SFV.aml Figure 9.1d: SFL.aml
Value shaded surface. This can be A legend for the surface in figure c.
used for hypsometric tinting, as well as Because of the comparative abstractness
the display of meta-data. of isolines, legends for both fishnets and
isolines should show a labeled surface.
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SISO {contour_item} {textset} {font} {point_size} {float_precision}
- a coverage generated by POLYCONT;
{contour_item} - defaults to the item generated by POLYCONT (contour);
{textset} {font} {point_size} - define labelling text-defaults to a 10 point roman font;
{float.precision} - the number of decimal places shown in contour labels-defaults to 0.
Ratio Data-Fishnet Height
The macro, SF.aml, simply automates the default setup of a surface display,
calculates a better 'Z' expansion value than ARCPLOT, and displays the surface.
The expansion value relates the data values used to describe X and Y locations with
the value used to describe the height at a location. For example, the default view
for a surface could appear absolutely flat, if the X and Y coordinates have a much
larger range than the Z values. See Figure 9.1b.
SF {zfactor} {latticeltin} {resolution}
- a grid layer or a TIN;
{zfactor} - 'Z expansion factor-defaults to range_of_z / the larger of x_range and y_range;
{latticeltin} - the type of --defaults to lattice (grid);
{resolution} - the density of fishnet lines-defaults to the SURFACEDEFAULTS value.
Isoline and Fishnet Legends
Isoline and fishnet legends can be generated by specifying a small area for
the display of a fishnet that has isolines drawn on it, and labeled. This is most
beneficial for isoline maps, which can be greatly enhance by the inclusion of the
less abstract fishnet as the legend. See SFLaml and Figure 9.1d.
SFL {zscale} {latticeltin}
{textset} {font} {point} {precision}
- a grid layer or a TIN~not an isoline (arc) coverage;
- the lower left corner of the legend;
- the size of the legend drawing area;
- the separation distance in Z of isolines;
{zscale} - a 'Z expansion factor;
{latticeltin} - the type of -defaults to lattice;
{textset} {font} {point} - define the labelling text-defaults to a 10 point roman font;
{precision} - the number of decimal places to be shown in the legend-defaults to 2.
Bivariate Symbolization
Monochrome bivariate isoline maps can be generated by changing the line
shape, texture, size, value, etc of the current line and using the monovariate line
AML to draw a second isoline coverage. Monochrome, bivariate fishnet maps can
be generated by value shading a surface. Like monochrome, color bivariate
isolines can be created by changing the current line's color and drawing a second
isoline coverage. Color, bivariate fishnets can be generated by hue shading a
surface.
Ratio Data and Ordinal Data-Surface Shaded with Value
Both polygon coverages and grid layers can be used to value shade a
surface. In either case, the data should be ordinal. The ARCPLOT draping routine
seems to work better with grids than with polygons. See SFV.aml and Figure 9.1c.
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101
Figure 9.2a: SFH.aml Figure 9.2b: SFHLaml
Continuous, smoothly changing Hue and intensity shaded fishnet
ratio data displayed as a surface. The surface. This AML can use either a
surface is hue shaded with a nominal polygon coverage, or two grids; this
data set (the AML supports polygons image is polygon based (compare
and grids).
Figure 5.5a).
Figure 9.2c: SFHLaml Figure 9.2d: SFRGB.aml
Hue and intensity shaded fishnet. A red, green and blue shaded
This is the same AML as figure b, but fishnet. This AML only works with
this figure is based on two grids grids; polygon data must be converted
(compare Figure 7.1c). prior to display with this AML.
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102
SFV {zfactor} {latticeltin} {resolution} {hue} {intensity}
- a grid layer of a TIN;
- specifies HLS lightness (0 to 100) for a polygon coverage or a grid;
{zfactor} - 'Z expansion factor-defaults to z-range / the larger of x-range and y-range;
{latticeltin} - the type of --defaults to lattice;
{resolution} - the density of fishnet lines-defaults to the smaller of x-range and y-range / 25;
{hue} {intensity} - define a color to be value shaded.
Ratio Data and Nominal Data-Surface Shaded with Hue
A prime example of the appropriate use of hue shaded surfaces is the
display of land use/land cover data over a digital terrain model. Although this is
a common use, hue can be used for any nominal data (this AML supports both
choropleth and grid cell data). The surface can be any continuous, smoothly
changing ratio data set. See SFH.aml and Figure 9.2a.
SFH {zfactor} {latticeltin} {resolution} {value} {intensity}
- a grid layer or TIN;
- specifies HLS hue (from 0 to 300);
{zfactor} - 'Z' expansion factor-defaults to z-range / the larger of x-range and y-range;
{latticeltin} - the type of ~defaults to lattice;
{resolution} - the density of fishnet lines-defaults to the smaller of x-range and y-range / 25;
{value} {intensity} - defaults to 50 and 100 (maximum intensity);.
Multivariate Symbolization
Multivariate isoline maps can be created by display of multiple isoline
coverages, with each coverage drawn with a different current line setting. These
difference should reflect either the differences in the coverages (nominal
differences by differences in hue or shape, for example), or differences in
importance (the main data can be drawn last and in a large, black line—with less
important data drawn in smaller lines or grays, for example). For fishnets,
multivariate maps can be created by use of hue and intensity, or by RGB encoding.
Ratio Data, Nominal Data and Ordinal Data-Surface with Hue and Intensity
Surfaces can be shaded with hue and intensity to show nominal distinctions
with meta-data, or another ordinal data set. This AML can display hue and
intensity from a polygon coverage, or from two grid layers. See SFHI.aml and
Figures 9.2b and c.
SFHI {zfactor} {latticeltin} {resolution}
{nominal_vat_item} {ordinal_vat_item}
- a grid layer or TIN;
- specifies HLS hue (from 0 to 300);
- specifies HLS saturation (from 20 to 100);
{zfactor} - 'Z' expansion factor-defaults to z-range / the larger of x-range and y-range;
{latticeltin} - the type of --defaults to lattice;
{resolution} - the density of fishnet lines-defaults to the smaller of x-range and y-range / 25;
{nominal_vat_item} - specifies an item in the hue grid attribute table other than VALUE;
{ordinal_vat_item} - specifies an item in the intensity grid attribute table other than VALUE.
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Four Ratio Data Sets-Surface Shaded with Red, Green and Blue
Unlike the other surface draping AMLs, SFRGB.aml only drapes grid
layers, which are linearly stretched. If polygons need to be shown with this
method, use the polygon to grid conversion AML discussed on page 84. See
SFRGB.aml and Figure 9.2d.
SFRGB {zfactor} {latticeltin} {mesh_resolution}
- a grid layer or TIN;
- three numeric grid layers;
{zfactor} - 'Z' expansion factor-defaults to z-range / the larger of x-range and y-range;
{latticeltin} - the type of ~defaults to lattice;
{mesh_resolution} - the density of fishnet lines-defaults to the smaller of x-range and
y-range divided by 25 (half of the default resolution);
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104
Chapter Ten
Thematic Mapping in ARC/INFO
Because of the great flexibility of ARC/INFO, a wide variety of maps can be
generated within the system. This guide's focus has been on the design of
environmental maps. These maps include maps of point data (Toxic Release
Inventory sites, for example), linear data (STORET information), and area data
(demographic/Census data). With the GRID and TIN modules, ARC/INFO has
the ability to show area data with grid cell, dot density, isoline and fishnets, as well
as the choropleth and graduated circles methods that are part of ARCPLOT.
Summary of Presented Methods
The methods presented in this guide have been based on the theoretical
construct, 'visual variables.' Use of this construct allows the specification of rules
for matching data to symbolization types. Each of these rules is indicated in the
subsection headings in Chapters Three through Nine. For point and line data,
select the number of variables that need to be represented with one symbol, then
match the appropriate data levels to the symbolization method by following the
headings (Ratio Data—Size, etc.). For area data, the character of the data must be
considered. Data that is continuous and changes abruptly at boundaries should be
displayed with choropleth maps (for example, sales tax rates). Data that is
continuous and smoothly changing should be displayed with isoline of fishnet
maps (for example, elevation). Data that is discrete and smoothly changing should
be displayed with dot density maps (for example, population density). Data that is
discrete and abruptly changing should be displayed with graduated symbols (for
example, TRI point source emissions).
Areas of Possible Continued Research
As a simple continuation of these AMLs, there are many possibilities of
combinations of data types (particularly for area data) and visual variables that are
not presented here. This expanded set of AMLs, could be developed on an as
needed basis.
A potentially valuable addition to the ARC/INFO repertoire is the
development of animation. Time can be used to show temporal changes in data,
for touring a data set, or for display of some other variable. These abilities can be
used to both impress (as in visual communication) and highlight otherwise
obscure relations (as in visual thinking).
Acknowledgments
I would like to thank my colleagues at the National GIS Program: Tommy
Dewald, Jeff Booth, Dave Wolf, and Ed Partington for seeing the need for an ARC/
INFO cartographic guideline and reviewing the text. Dave Rejeski originally
foresaw the need for a guideline, from which this has developed.
At the Pennsylvania State University, Deryck Holdsworth has provided
valuable guidance, for the version of this guideline that is my master's thesis.
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105
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Subject Index
Agfa Compugraphic glyphs 56
AMLs
naming 36
running 36
Animation 27,33,104
Area symbolization
choropleths 4,19,66
color bivariate 74,85,92,95,100
dot density 4,93
fishnet 4,23,98
graduated symbols 4,83
grid cells 90
isolines 4,23,98
monochrome bivariate 70,83,95,100
multivariate so, 87,95,102
single variable 66,83,90,93,98
Audiences 12
color selection 16
symbol selectction 25
symbol selection n
B
Bivariate mapping 19
choropleths 70.74
dot density 95
fishnets 100
graduated circles 83,85
grid cells 92
lines 56,58
points 42,45
Boot files 36
Cartograms 83
Classifying data 4,28
Eyton's ellipse 30
Jenks' optimal 28,30
optimal breakpoints 30
unclassed maps 31
Classifying Space 24
Color production 16
Communication of environmental
risk 12
messages 12
Complementary colors 21,47,60,76
Data i
attribute i
classification 4
empirical levels i
location i
spatial categories 4
spatial grouping 4
valid comparisons 3
Design of uncertainty displays 19
Discrimination of hues 16
Discrimination of values 16
Dual hue ranges 19,21,45,60,76
Eyton's equiprobability ellipse 21,30,
49, 62, 78
H
Heisenberg's Uncertainty Principle 5
Hue and intensity 22,47,62,76,92
I
Image to Graphic continuum 24
Insets
legends 35,36
locator diagrams 27,35
Intersecting lines 19,21
Interval data i
Legends 35,36
areas 66,74
cartograms 87
dot density 93
graduated circles 85
isolines and fishnets 100
lines 60
points 47
Line symbolization 53
color bivariate 58
monochrome bivariate 56
multivariate 62
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109
single variable 53
M
Map scale
generalization 27
projections 26
Meta-Data 10,19
definition 5
Micro and a macro reading 27
Multivariate mapping
choropleths so
dot density 95
graduated circles 87
lines 62
points 49
Munsell color system is, 16
N
Nominal data i
Ordinal data i
Page layout 32
paper 33,36
posters 33
slides 33,35
video 33
visual isolation 32
visual levels 32
Point symbolization 38
color bivariate 45
monochrome bivariate 42
multivariate 49
single variable 38
Presentation graphics n
Principles of graphic excellence 12
Projections 25
Alber's conic 26
equal area 26
Lambert's azimuthal 26
sinusoidal 26
Universal Transverse Mercator 26
Ratio data 3
Slides 33,35
Spatial data 4
autocorrelation 4
grouping 4
models 2
raster systems i, 8
vector systems i, 8
Spectral encoding 19,21,45,60,76
STORET 104
Text
fonts 34
labels 34
size 34
titles 34
verbiage in labels 34
Toxic Release Inventory 104
u
Uncertainty 4
attribute 6
computational 8
computer 7
definition 5
descriptive 7
graphic communication is, 20
human communication 10
location 6
measurement 6
modeling 10
overflow 9
parameter 7
policy oriented research 5
propagational 9
raster systems s
robustness 10
rounding 8
significant digit shift 8,9
spatial display 19
taxonomy 5, n
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underflow 9 W
validity 10 Workstation environment 36
vector systems 8
visual communication n
Updating lookup tables
numeric progressions 31
unclassed maps 31
V
Video 33
Visual isolation 32
Visual levels 32
Visualization n
arrangement n
bivariate maps 19
color addition 16
color schemes 15
color selection 16
color subtraction 16
complementary colors 21,47,60,76
equiprobability ellipse 21,49,62,78
focUS 17,22
hue 13,15,16,38,53,66,92
hue and intensity 22,47,62,76,92
image to graphic continuum n
intensity is, 16,22
intersecting lines 19,21
location 13,98
orientation n, 38,40,68
risk communication 12
saturation is
Shape 17,38,53,68
Size 13,40,42,55,83
spectral encoding 19,21,45,60,76
texture 17,53,93
uncertainty n, 19
value 13, 15, 16, 55, 68,92
visual communication n
visual isolation 32
visual levels 32
visual thinking n
visual variables 2,13,21,104
visualization
value 40
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Ill
ARC/INFO Commands and AML Programs
Symbols
&RUN36
ADDITEM 29
AL.aml 66,80,92
ARCLINES 28,29
CAO.aml 70
CBL.aml 74,80,92
CCC.aml 78
CDH.aml 76
CEE.aml 78
CH.aml 66,68
CHI.aml 76
CIL.aml 72
CILL.aml 74
CLASS 28,29
CRGB.aml 80
CS.aml 68
CTH.aml 74
CTL.aml 72
CTLW.aml 80
CTO.aml 70
CTV.aml 72
CV.aml 68
DD.aml 93
DDBL.aml 95
DDH.aml 97
DDHI.aml 97
DDL.aml 93
DDRGB.aml 97
DDV.aml 95
EEL.aml 78
EYTON.aml 30,49,78
GCaml 83
GCH.aml 85
GCHI.aml 87
GCL.aml 85
GCP.aml 89
GCV.aml 85
GENERALIZE 23
GG.aml 83
GGH.aml 87
GGHI.aml 89
GGV.aml 85
GPL.aml 89
GRID 90,93,104
GRIDLUT.aml 90,92
H
I
HPGL2 16
IDW90
INFO 29,70
I
JENKS.aml 30,44
LABELMARKERS 28,29
LBL.aml 60
LCCaml'60
LDH.aml 60
LEE.aml 62
LH.aml 53
LHI.aml 62
LHIZ.aml 65
LHSZ.aml 64
LHZ.aml 62
LINEINTERVAL 53
LINESET 53,55
LINESIZE 55
LINESYMBOL 53
LINETEMPLATE 55,56
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112
LINETYPE 53,55,56
LRGB.aml 62
LS.aml 55
LSH.aml 58
LST.aml 56
LSV.aml 56
LSZ.aml 58
LSZV.aml 64
LV.aml 55
LVZ.aml 58
LZ.aml 55
M
MARKERANGLE 40
MARKERCOLOR40
MARKERSET 38
MARKERSIZE 40
MDELETE 27
OL.aml 70
POLYTIN.aml 98
PP.aml 51
PRGB.aml 49
PROJECT 26
PS.aml 38
PSH.aml 45
PSO.aml44
PSV.aml 44
PSZ.aml 44
PSZV.aml 51
PULLITEM 29
PV.aml 40
PZ.aml 40
RESELECT 28
RGBL.aml 81,92
RH.aml 92
RHI.aml 92
RRGB.aml 92
RV.aml 92
PAO.aml 40
PB.aml 42
PBL.aml 47
PC.aml 42
PCC.aml 47
PCH.aml 49
PCV.aml 44
PDH.aml 47
PEE.aml 49
PRaml 38
Pffl.aml 49
PHIZ.aml 51
POINTMARKERS 28, 29,38
POINTSPOT 42
POLYCONT.aml 98
POLYDOT.aml 93
POLYGONSHADES 28,29,68
POLYGONSPOT 83
POLYGRID.aml 90
SETAUTO.aml 31,47,93
SETMAN.aml 29, 31,44,90, 92
SETUNCL.aml 32
SF.aml 100
SFH.aml 102
SFHI.aml 102
SFL.aml 100
SFRGB.aml 103
SFV.aml 100
SHADEANGLE 68,70
SHADECOLOR 66,68,76,83
SHADESEPARATION 70,93
SHADETYPE 68,70
SISO.amI 98
SPLINE 90
SPOTSIZE 42,83
STATISTICS 28
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113
T
TIN 93,98,104
TREND 90
u
UNION 9
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114
Author Index
B
Berlin 13,17
c
Capra 5
Carstensen 19
Cort, Rowe and Philpot 7
D
01613562,4,11,14,22
E
Eyton 21,30,49,62,78
K
Kapuscinski 6,7,8,10
Keats 34
Knoble 7,8,9
M
MacEachren 2,3,4,5, 6,7,11,14,22,24,29,32,34,35
Monmonier 4,12,24,31
Morgan and Henrion 5,12,17,18,20,21
o
Olson 12,19,21,35
R
Rejeski 5,6,7,8,10
Robinson 25
T
Tufte 4,12,19,21
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