Revisiting thematic map theory

There has been a long standing view that choropleth maps (from the Greek words choros - space, and pleth – value, or simply thematic maps) should not be used to present absolute values like, for example, counts of persons per postcode, unless mapped areas are of similar size. Ideally, only normalised values should be mapped (for example, proportions such as density of people per postcode area). People have been conditioned to perceive that “bigger means more” so, when we present information in a spatial content the effect of size of spatial units should be eliminated for a meaningful comparison.

For example, two postcodes may have exactly the same number of people residing in them, so both would be coloured the same way on an thematic map, but if one polygon is significantly larger than the other, it would give an impression of a greater importance (ie. larger size = more important). The argument goes that using ratios rather than absolute values eliminates the influence of area, so that the map becomes meaningful by portraying accurately the distribution of features within each area. In our example, if we use ratio of counts to area size, larger polygon would have a smaller density value hance would be coloured in a lighter shade, “demoting” the importance of that area in relation to the other.

[Source: Wikipedia]

There are all sorts of other concerns about inadequacy of thematic mapping for presentation of spatial information, including the more recent one that maps in Mercator projection, ie Google and other online maps, are particularly bad because they introduce extra distortion of areas the further you move from the equator. Not to mention there is a general concern that since users “get clues” as to hierarchical importance from both, the value attached to a polygon (shown with colour intensity) AND the size of respective polygon, they may not be able to interpret correctly the “hierarchy” of information being presented. That is, users are potentially unable to rank the order from “the smallest” to “the largest” because of conflicting messages presented on a map: large polygons with small absolute values (light colours) and small polygons with large absolute values (dark colours), or vice versa. Yet, many novice cartographers are either unaware of these issues or are totally ignoring “experts”, happily mapping absolute values on Google maps. 

However, as it turns out, there is some validity in this non-expert approach to thematic mapping. In particular, “…psychological studies have shown that size and color (or at least, size/value and size/hue) are a ‘separable’ combination: that is, variations in the size of graphic elements do not considerably interfere with our ability to determine their color [sequence], or vise-versa. So, theoretically, there should be no problem with using choropleths on a Mercator projection: the distorted areas shouldn’t mess up our ability to determine a region’s color, which is what choropleth mapping is all about.”

So, there you go – since only colour counts in thematic mapping and users are able to distinguish colour hierarchy independent of size of polygons,  it should ok to use absolute values with unequal polygons after all! Happy mapping!

Map Basics: Map reading guide

In one of my recent posts I tried to explain basic concepts behind map projections, coordinate systems and geodetic datum and outline characteristics of the ones used in Australia. Today just as short note about another handy resource that explains the concept of a topographic map and provides comprehensive instructions on how to use such maps with a magnetic compass or GPS navigation tools.



The booklet has been published by Geoscience Australia and is an excellent introduction for anyone interested in maps, orienteering or GPS navigation. National Mapping Agency within Geoscience Australia produces topographic maps that cover entire country at different scales. They are available for online use from aus-emaps.com:

• NATMAP Topo 250K (1 : 250 000 scale map)
• Topo 1M (1 : 1 000 000 sclale map)
• Topo 5M (1 : 5 000 000 scale map)
  

Map basics: datum, coordinate system, projection

Map projections, coordinate systems and geodetic datums are not the most exciting topics to discuss in reference to maps but any user of geographic information should have at least a basic understanding of the concepts.

In a nutshell, Earth is an oblate spheroid an in order to represent its surface as a flat map, complex mathematical transformations are required.

[oblate spheroid - image courtesy of Wikipedia]

Geodetic datum defines reference points on the Earth's surface against which position measurements are made. Central to this concept is an associated model of the shape of the Earth (that is, reference spheroid) to define a coordinate system.

Map coordinates are usually shown in one of two ways, as geographical coordinates (ie latitude and longitude values, in degrees) or grid coordinates, (as easting and northing values, in metres).

Map projection is a method of representing the surface of a sphere on a plane. By definition, all map projections show a distorted representation of the Earth surface therefore different map projections exist in order to preserve some properties of the sphere-like body (ie. either area, shape, direction, bearing, distance and/or scale) at the expense of other properties.

What does it all mean? The key point is that commonly quoted “geographic coordinates” (eg Sydney Opera House: lat, lng) are only meaningful in reference to a specific datum (eg. that point is shifted approximately 200m on AGD66 datum as compared to GDA94 datum). And to represent that point properly on a map you will also need to know projection of the map, otherwise the point may be depicted in a wrong place.


[example of mismatch resulting from source data being in geographic projection and the underlying map in Mercator projection]


More examples to illustrate the point. Satellite based navigation systems (the Global Positioning System or GPS) are becoming more and more popular in Australia so users should be aware that GPS coordinates are based on WGS84 datum, which is different from official Australian datum GDA94 (different spheroid definitions were used). All current official maps and data in Australia are based on GDA94. However, luckily, the difference between WGS84 and GDA94 is negligible and for most common uses both datums can be used interchangeably.

As to map projections, when you have a map showing just a few streets, projections don’t really matter. Similarly, if you view small scale maps in atlases or on wall posters, projection rarely comes to mind simply because it has already been determined by the author to best represent the phenomenon and also to “look nice”. However, when you deal with raw geographic data (whether vector – points, lines and polygons, or raster - images) and need to compile them into a map, projections of source data and final map are of outmost importance. Similarly, if you need to take a reliable measure of distance or area on the map you have to know which projections preserve those properties and therefore are the most appropriate to use.

The following is an illustration of the “distortions” in representation of shapes on a map due to different projections. The first image was generated by applying a common projection to input data and the second shows the result of not applying any projection at all.

[image courtesy of Statistics Canada]

Projections that you are most likely to encounter in Australia are:

1. Geographic/Equirectangular projection: a de-facto standard for computer applications because of the connection between an image pixel and its geographic position.

The following are the international reference codes to precise definitions of the transformation: EPSG:4326 (WGS84 datum) and Australian specific EPSG:4283 (GDA94 datum) – for all common purposes, they are interchangeable, unless you require a sub-meter accuracy.

[image courtesy of spatialreference.org]

2. Transverse Mercator projection used with Universal Transverse Mercator coordination system (UTM zones 49 to 56) - suitable for measuring distances and areas; mostly used for medium scale printed maps.


3. Lambert Conformal Conic projection (EPSG:3112) - well approximates distance between two points; often used for aeronautical charts, small scale maps or road maps.

[image courtesy of spatialreference.org]

4. Mercator projection (EPSG:3395) - used for Google Map, Virtual Earth/ Bing Map, and all tile based online maps – distance between two points on the map is distorted, the more the further you move from the equator.

Individual States in Australia also define their own local projections for variety of purposes so it is always wise to check metadata before putting the data to any use.