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Data Classroom

Cartographic Symbology

Symbol Basics:

In general, data depicted on maps, and in fact maps themselves, are symbolic representations of geographic phenomena and the Earth's surface on a sheet of paper, or on a computer monitor. Only at a scale of 1:1 could physical data be depicted at its true size and in complete detail. As use of this scale is rarely practical, all features and thematic data shown on a map must undergo a process of simplification, generalization (sometimes exaggeration), and finally symbolization. In effect, maps are complex tools for visualizing and communicating scaled-down geospatial data, and graphic symbology is their language of communication.

Geographic phenomena: Cartographers and geographers use symbols on maps to represent various geographic phenomena involving location, distance, volume, movement, function, process, correlation, etc. These phenomena can be classified into four basic categories: point (non-dimensional data), line (one-dimensional data), area (two-dimensional data), and volume (three-dimensional data), (Wright, 1955). The challenge in cartographic symbol design is that four categories of data must be represented on maps by only three basic symbol types: point, line, and area. Therefore, considerable imagination must be used to design map symbols that portray more than one data characteristic, at the same time.

A point symbol represents a geographic feature or event characterized by location and attributes. Its location can be represented by a single "x,y" coordinate pair, while attributes can be many. For example, a populated place or a mine site can be represented by a point symbol.

A line symbol represents a geographic feature characterized by linear dimension, but not area. In digital technology, a line is a sequence or stream of point coordinates with a node at each end (vector data) that symbolizes a linear feature such as a road, river, or boundary.

An area symbol represents a closed geographic surface feature, two-dimensional geometric region, or a polygon. A census division, a lake, or a province (any geographically defined surface) are examples of area features.

The text above describes how each of the three symbol types represents different basic geographic features, such as those shown on topographic or reference maps. However, in thematic cartography these symbols may also be used to represent geo-statistical data, such as volume, or density.

Symbology typically found on a topographic map:

(From Topographic Maps...The Basics, Centre for Topographic Information, Natural Resources Canada).

Symbol design: Once the purpose of a map has been established, it is necessary to select which geographical features are to be depicted on the map, and in what manner. Map scale is an important factor in determining which features can be shown and how. Some data are not suitable for depiction at all scales. If displayed at the wrong scale, data may appear too congested or too sparse.

In general, there are two basic symbol designs that may be used to portray information on maps, pictorial and abstract.

Symbols that are pictorial look like the features that they represent. These symbols tend to reflect the shape and colour of the feature. For example, the symbol for a picnic site may be a picnic table, or the symbol for a vegetated area may be a green polygon.

Symbols described as abstract may be any geometric shape assigned to represent a feature. For example, a series of graduated dots and/or squares could represent populated places on a reference map. On the other hand, coloured or patterned polygons could represent varying concentrations of people, on a population density map.

There is little difference in the way symbols are designed for display in the computer environment and for the traditional paper map. The main concerns with the computer mapping environment are screen resolution, map scale, and colour.

With regard to screen resolution, the smallest size for displaying a symbol is determined by the size of a physical pixel on the monitor. For example, a line symbol representing a road with a line weight (thickness) of 0.007 inches typically used in conventional cartography, is not a suitable size specification for computer display. This small line weight cannot be displayed on a computer monitor at its true size. The minimum size for displaying a line, point, or area on a computer monitor is the height and width of one pixel. Pixel sizes are as follows: on a PC there are approximately 96 PPI (Pixels Per Inch), on a Mac there are about 72 PPI. As fractions of pixels cannot be displayed, symbol size specification must be based on multiples of whole pixels. Please note that this limitation only applies to graphics and text displayed on a monitor. When symbols and graphics created on a PC or Mac are sent to a printer, symbols on the printout are at the correct size specified in the application.

In regard to map scale and Web mapping tools, problems can arise in the sizing of symbols. A symbol designed to be legible on a small scale map may appear too small when the map is viewed at a larger scale. On the other hand, a symbol sized to look correct at a large scale may appear exaggerated at a smaller scale.

Thought and experimentation in the selection of symbol size are required so that the symbols are suitable for the range of scales at which a map may be viewed. Sometimes the best size selection may be a compromise.

For a complete discussion on the use of colour in computer graphics, see the section entitled Colour Design and Tools, included in this Guide.

Please note that on any map, regardless of symbol design or the media used, all symbols must be clearly explained in the map legend.

Data Evaluation and Classification:

Before assigning map symbology, it is important to have a good understanding of the data set to be mapped. The distribution of a data set can be explored by calculating descriptive statistics such as mean, mode, median, range, and standard deviation. Plotting a scattergram or histogram of the data can determine the shape of the distribution. A good knowledge of these basic statistical concepts is useful in classifying any data. It may be necessary to process data coming from different sources, into a standardized form. This will compensate for differences in the way data are collected, or expressed. For example, when making comparisons between, or combining data from, different sources, the data should be in comparable units of measurement, and at the same level of measurement (nominal, ordinal, interval, ratio). (Level of measurement is also referred to as scale of measurement.)

Data classification: When a data set is large, it is not practical to assign a unique symbol to each data record. Therefore, for mapping it is essential that data is classified or grouped. There are several methods of classifying data. In choosing the right method, the level of measurement and the underlying distribution of the data set must both be considered. The classification method chosen should adequately describe the phenomenon being mapped, and at the same time facilitate the cartographic display of spatial patterns. All classification methods depend on exhaustive and mutually exclusive classes. Exhaustive classes contain all values in a given data range, no values are omitted. Mutually exclusive classes do not overlap; no value can fall into two classes.

Before classifying or grouping data, it is necessary to determine whether the data are qualitative or quantitative and the level of measurement. This is important to know so that if required, the proper analyses may be applied to the data set. Certain analyses can only be applied on particular types of data.

Data may be described and/or mapped as either qualitative or quantitative.

Qualitative data are data that are grouped in classes according to differences in type or quality. Qualitative data have no numerical values attached. Nominal data comes under this category. (Ordinal data may also be considered qualitative, if no numerical values are involved).

Quantitative data are data that contain attributes indicating differences in amount and can be expressed as numerical values. Included in this category are ordinal, interval, and ratio.

Data can also be described by the level of measurement and there are usually four levels of measurement to consider: nominal, ordinal, interval, and ratio. In some literature and statistical computer programs, no distinction is made between interval and ratio data, calling them both continuous. However, this is not technically correct because interval data does not have a natural zero *, while ratio data does.

Nominal data are discrete (i.e., mutually exclusive) and are classed according to type or quality. For example, a line could represent either a road or river, and a land use polygon could be residential, commercial, or a recreational area. Nominal data are often labelled with numbers or letters, but these labels do not imply ranking. A nominal datum can only be examined for its physical similarity to, or its difference from, other occurrences, or for the frequency of its occurrence.

Ordinal data provide information about rank or hierarchy, in other words, relative values. Therefore, it is possible to describe one item as larger or smaller than another, or as low, medium, or high. However, it is not possible to measure the differences between ordinal data, because there are no specific numerical values attached to them. An example of ordinal data is roads ranked as expressway, main thoroughfare, and secondary road.

Interval data, in addition to being ranked, include numerical values. The information can be arranged along a scale using a standard unit. Therefore, it is possible to calculate the distance or difference between ranks, which must be expressed in terms of a standard unit. For example, a temperature scale uses degrees (F or C) as a standard unit of measurement; between 20 and 35 there is a difference of 15. As shown by this example of interval data, it cannot be said that 35 is 1.75 times warmer than 20, because the scale on which temperature is measured is arbitrary. For example, in C the freezing point of water is set at 0, while in F it is 32. Interval data, as illustrated, have no natural zero *.

Ratio data are the same as interval data, except there is a natural zero; therefore, it is possible to express data as ratios. Physical measurements of height, weight, and length are examples of ratio variables. With this type of data it is meaningful to state that a measurement is twice that of another. This ratio remains true no matter what the unit of measurement (e.g., metres or feet) because this type of data has a natural zero *.

* A natural zero is a non-arbitrary starting point for data. For example, a measurement of distance at zero units has no length; furthermore, it makes sense to state that two metres are twice as long as one metre. Whereas, with the measurement of time, the year zero is arbitrary, so it is not sensible to state that the year 2000 is twice as old as the year 1000.

Constructing class intervals: The assignment of class intervals or cutpoints for nominal and ordinal data sets is fairly straightforward. However, because of the more complex nature of interval/ratio data, more exploration of the data set is required. First, it is necessary to understand the underlying distribution of the data. For thematic mapping, different classification (or ranging) methods are used to generalize different types of data distributions. Each method is suited to a particular shape of distribution. Plotting a scattergram or histogram that employs basic descriptive statistics (such as mean, mode, median, range, or standard deviation) will reveal the shape of the distribution. This shape will aid in the selection of the most appropriate classification method.

There are many statistical methods for the classification or ranging of interval/ratio data. In cartography, the four most common are: equal steps, quantiles, standard deviation, and natural breaks.

The equal steps method divides the data set into classes with equal intervals between them. The data may be arranged from high to low, or low to high values. In this method the difference between the high and low values of the distribution is divided into a number of equally spaced steps. This technique of classification is useful for mapping rectangular distributions, and when enumeration areas are of equal size.

In quantile classifications the data are arranged in sequence from low to high values and the number of individual observations are counted. The observations are then divided into the selected number of classes, each class containing the same number of observations. The term quartiles is used when the data are divided into four classes, quintiles for five, and sextiles for six, and so on. This method is useful for mapping rectangular distributions.

In the standard deviation method the mean or central point of the data distribution must first be calculated. The standard deviation is then used to set the classes. The observations are grouped based on how they are positioned on the plot in relation to the number of standard deviations from the mean. This method is useful if the data distribution is a normal curve.

The natural breaks method of classification is based on the subjective recognition of gaps in the distribution, where there are significantly fewer observations. Plotting a histogram of the data can identify these gaps. This method, developed by George Jenks, minimizes variation within classes and maximizes variation between classes. This technique is most useful when the data set has more than one modal value.

Data Symbolization: Once geographic features and data have been selected, generalized and classified for the map, it is necessary to choose the appropriate graphic representation or symbols for the information. Symbols have characteristics that can be manipulated to suit the category of data being mapped. These characteristics are referred to as visual variables or visual resources. Visual variables include symbol size, shape, orientation, pattern (texture), hue (colour), and colour value (brightness and lightness), (Bertin, 1983).

These variables, individually or in combination, may be applied to map symbol design. However, not all variables apply equally well to the symbolization of all types of geographic phenomena or data sets.

The symbolization of nominal or qualitative data is usually the least difficult. In this case, the symbol design should only indicate difference in class, and not imply ranking. The variables of shape, pattern, and hue may be used for qualitative data. The symbolization of quantitative data is more complex, often there is a need to show data as a logical progression. Here, the variables of size and colour value are more important.

Nominal data: The design of Point symbology on maps depicting nominal data should use distinctly different shapes and/or hues, and not different sizes. (This rule can also apply to line symbology portraying nominal data.)

Line symbols used to show nominal data should vary only in pattern and/or hue, not in thickness. Line symbols can also be used to indicate connectivity (e.g., roads) and separation (e.g., boundaries).

For area symbology on maps depicting nominal data, such as chorochromatic maps, only different area hues or patterns should be used, and not different values of selected hues.

Ordinal data: Point symbols on a map depicting ordinal data may use an abstract geometric shape or a pictorial symbol, classified according to size. Another method for depicting ordinal data is using the same point symbol in different colour values. Size and colour value may be combined for emphasis.

Line symbols can rank data by line weight, style, or hue. Any combination of these methods is possible, and will help the user distinguish more readily the data classes on the map.

Areas can show quantitative differences in data by different hue/colour value, and pattern fills. For further emphasis, patterns can also be in different colours.

Interval and ratio data: Point symbols to depict interval and ratio data can be designed in various colours, shapes and sizes; including graduated dots, circles, squares, bars, block piles, pie charts, etc.

Line symbols depicting interval data can be graduated, as in the symbolization of commodity flows. An isopleth is a line symbol connecting points of equal value. Contours (lines joining points of equal elevation) are the most common form of this line symbol. Contours graphically indicate elevation value and position, and also allow for the calculation of slope data.

Area symbology depicting interval and ratio data can use variations in colour value and pattern to show a gradual progression of data values.

Colour progressions in a single hue have data values increasing as the colour value increases from white to the pure colour. This is particularly suited to monochrome maps, with data classes displayed as a gradual change, for example, from light to dark grey.

Partial hue spectral progressions blend one colour with another.

Bipolar progressions display data that range from positive to negative. For example, hypsometric tints showing elevation above and below sea level.

Please note that all information provided here is deemed reliable, but is not guaranteed and should be independently verified.

References and Other Resources: Bertin, J. 1983. Semiology of Graphics, The University of Wisconsin Press, Translated by W. J. Berg.

Fisher, Dr. Peter (Project Manager). 1996. Project Argus. (Interactive computer visualization of spatially distributed data). Available at: URL. Leicester, U.K.: University of Leicester. (Accessed Dec. 1998).

Gillespie, Joe. 1997. Web Page Design for Designers. Available at: URL. London: Pixel Productions. (Accessed Sept. 1998).

Horton, Sarah and Lynch, Patrick. 1997. Yale Center for Advanced Instructional Media (C/AIM) Web Style Guide. Available at: URL. New Haven: Yale University. (Accessed Sept. 1998).

Owen, G. Scott (Project Director). 1998. HyperVis - Teaching Scientific Visualization Using Hypermedia. ACM (Association for Computing Machinery) SIGGRAPH (Special Interest Group on Computer Graphics), Education Committee and the Hypermedia and Visualization Laboratory. Available at: URL. Atlanta: Georgia State University. (Accessed Dec. 1998).

Robinson, Arthur H. and Sale, Randall D. 1969. Elements of Cartography. Third edition. Toronto: John Wiley & Sons, Inc.

McNeney, Brad. 2001. Stat-201: Statistics for the life sciences. Available at: URL. Burnaby, B.C.: Simon Fraser University, Department of Statistics and Mathematics. (Accessed Dec. 2001).

Statistics Canada. 1998. Statistical Profile of Canadian Communities. Available at: URL. Ottawa. (Accessed Dec. 1998).

Wright, John K. 1955. 'Crossbreeding' Geographical Quantities, Geographical Review, 45, 52-65

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