Spatial Analysis


Technical Issues
Topological Overlay

Putting one map over another to reveal relationships between spatial distributions of different phenomena has a long history. Keeble (1952) detailed the process of Sieve Mapping as a planning tool, indicating that it 'constituted a most valuable means of summarising and analysing survey data'. The sieve map is a composite map showing characteristics of land which render it unsuitable for a particular purpose; such characteristics are termed constraints. The composite map is formed from a series of maps showing single constraints which are drawn on transparent paper. These maps are overlain on a base map and on each other to reveal areas not subject to any constraints and thus deemed suitable for use for the purpose in question. Keeble notes that using overlays rather than redrawing all the constraints on a single composite map has the advantage that overlays can be used in any combination. The disadvantages are the difficulty of securing and maintaining a perfect register between overlays and the difficulty of reading the lower layers when overlays are placed on top of each other. Keeble notes a further difficulty inherent in all paper maps when he comments that in drawing a complicated sieve map, if a mistake is made 'amendment is usually impossible'. In a computer based GIS amendment is relatively easy and perfection of registration is only limited by the accuracy of digitising for each overlay.

In the United States of America sieve mapping developed under the title of Land Suitability Analysis, particularly in the field of landscape architecture. McHarg's (1969) book Design with Nature was especially influential in advocating the identification of physical factors affecting development, the mapping of spatial variations in each factor and the overlaying of the maps to produce a land suitability map.

The sequence of maps below shows the principle of overlaying. Each of the first three constraint maps are themselves composites made from overlaying other maps. The three constraint maps are then combined to form a fourth composite map.

Map 1. Conservation Constraint - the darker the tone the more suitable the land for conservation purposes.

Map 2. Recreation Constraint - the darker the tone the better the area for recreation.

Map 3. Urbanisation Constraint - the darker the area the more suitable for urbanisation.

Map 4. A composite map made up from the three previous maps.

Areas on the composite map shown in their original colours are exclusively suitable for the use associated with the colour. Other areas where constraints overlap have combinations of colours which can be used to interpret the best use, given the constraints.

In the late nineteen sixties the growing power and availability of computers was used to develop overlaying techniques through the introduction of Development Potential Analysis (sometimes referred to as Potential Surface Analysis). Wannop (1972) described Development Potential Analysis (DPA) as 'essentially a systematic and comprehensive development of traditional sieve map procedures'. As implemented at the time, it was a primitive raster based GIS in which the study area is first divided into a set of grid squares. These vary in size depending on the scale and purpose of the DPA; a one kilometre square was common for structure planning.

As with Land Suitability Analysis, DPA requires a set of factors affecting the potential of land for development to be defined. DPA, however, recognises opportunities as well as constraints; factors positively attractive to development may be included and are balanced against the constraints. DPA also recognises the importance of economic and social factors in determining land suitability. For example, accessibility to employment opportunities may be an important factor in determining land suitability for residential development. The amount of each factor in each grid square is measured and recorded, thereby creating a series of raster maps. Rather than cartographically overlaying the individual maps to produce a composite, DPA adds the values for all the factors for each grid square and maps the resulting total values. For examples of DPA see LeHeron and Heerdegen (1978), Staffordshire County Council (1974) and Wannop (1972).

Overlay analysis in the Keeble and McHarg mould is deterministic. It can identify sites that meet inclusion criteria, those criteria that a site must have, and exclusionary criteria, those criteria that a site must not have (Carver 1991). This allows decision makers to narrow a wide range of sites. But it does not allow identification of the best site amongst those that meet the criteria. To achieve this one must add multi-criteria evaluation procedures that provide a relative measure of the suitability of sites (Carver 1991). DPA is one method of multi-criteria evaluation.

Technical Issues
Sieve Mapping, Land Suitability Analysis and Development Potential Analysis all involve overlaying polygons (raster maps are maps with a fixed polygon size and shape). In principle overlaying can be an operation involving any combination of point, line or polygon objects i.e. a point map may be overlain on another point map, or on a line map, or on a polygon map and so on. The diagram below shows the nine possible combinations.

Source: adapted from Martin (1991), p104.

Whether overlaying is carried out with paper maps or in a computer based GIS, there are a number of issues that must be considered. Some of these are clearly set out by Hopkins (1977). Overlaying maps of separate factors to build up a composite map implies that the whole (the composite map) is the sum of the parts (the factor maps). It could be argued, however, that an assessment of land suitability based on some overall consideration of the land might reach different conclusions to an assessment based on overlaying. In this case the whole is not represented adequately by the sum of the parts.

Assuming overlaying might in fact represent the whole adequately, there are other issues. Different factors are measured in different units. Some measures are simple presence or absence measures (either land is privately owned or it is not). Other measures have a limited range of values but each factor has a different range. Aspect measured in degrees may range from 0 to 360, frost free days in a year may range from 0 to 366, and the probability of land flooding annually may range from 0 to 1. Some factors have undefined ranges; accessibility to shops may range from 0 to an undefined maximum. Factors measured in different units cannot simply be added together in a meaningful way, they have to be converted to a common unit; a process known as standardisation. Standardisation is generally achieved by equating the highest and lowest values in data sets to common numbers e.g. 0 for the lowest and 100 for the highest. All other values are then converted to an appropriate point on the 0 to 100 scale. Another method of standardisation is to use a simple ordinal scale, with the highest value given an ordinal of 1, the next highest value becomes 2 and so on. Standardisation can also be done by colour shading or grey scale shading of overlays (Hopkins 1977).

Overlaying several factors for which data has been standardised assumes that each factor has equal value in the resulting composite map. This assumption may not be correct. For some purposes such as residential development more weight might be given to factors such as freedom from flooding, access to shops, schools etc. and landscape quality, and less importance to factors such as soil type, flatness of contour and density of subdivision. Such differences in the importance of factors should be reflected by weighting overlays differently. A minor illustration of weighting overlays can be found in Wang Shu-Quiang and Unwin (1992).

A further issue in overlaying is the increasing number of errors in the final composite map as each overlay is added. Overlays may contain positional and/or classification errors, all of which are transferred to the composite map. Chrisman (1987) describes typical sources of error and assesses the impact of cumulative error on the final map. He concludes that, while combining information from different sources can strengthen the value of information, it is necessary to be aware of possible map errors and to be prepared to reject data sources that are too inaccurate.

The so called ecological fallacy is a further issue in overlaying of polygons. Frequently polygons are considered to have some attribute that is constant over the whole polygon. A polygon contains one soil type or one slope angle or one class of vegetation or one density of population. In practice the constant is an average for the polygon and there may be considerable variation from the average in some parts of the polygon. A population density for a polygon may be 6 per hectare, but there may be some parts of the polygon with no people and a true density of 0 per hectare. An overlaying process may result in the polygon being subdivided; each subdivision carries with it the average density for the whole polygon. The average was correct for the original polygon but it is unlikely to be correct for the subdivisions. Where attributes are not in fact constant over the whole of a polygon it may be necessary to recalculate attributes for any new subdivision which arises as the result of overlaying (Martin 1991 p105). Pickle(2002, pp3/4, para 2.4.1) illustrates the influence of the ecological fallacy in assessing the relationship between cancer rates and possible environmental causes of cancer.

Topological Overlay
The process of topological overlay is the combining of two or more coverages into a single coverage and the creation of topology for the single coverage. Line intersections in the single coverage are detected, all polygons are identified and attributes for the new polygons are carried over from the previous coverages. Planar enforcement is required for topological overlay; planar enforcement requires the coverages being overlaid to lie on the same plane. To take an extreme example, it makes no sense to overlay a cross section through the Southern Alps of New Zealand onto a map of the South Island. The cross section lies in the vertical plane and the map in the horizontal plane and the overlaying would at best result in a straight line drawn across the map.

When topological overlaying occurs it is likely that some of the new polygons will be sliver polygons. These tend to occur when two lines are overlaid that are slightly different versions of the same line. For example, the same road may be digitised as a vegetation boundary on one map and an administrative boundary on another map; slight variations in digitising will result in sliver polygons after the lines are overlaid. Software may allow tolerance values to be set, within which lines will be considered the same and only one line will be created on the new map. Care needs to be exercised in setting the tolerance value to avoid eliminating genuine polygons through too high a setting or not eliminating all sliver polygons through too low a setting (Rybaczuk 1993).

There are several ways that polygons can be overlaid to give differing outcomes on the resulting single map. The following diagram (Laurini and Thompson 1992) shows the types of polygon overlay.

Clip, erase and split are self explanatory operations. Identity overlaying produces a combined map that includes all the areas on the primary map and all the areas on the overlay map that are within the area of the primary map. Union overlaying produces a combined map that shows all the areas on both the primary and overlay maps. Intersect overlay produces a combined map showing only the area that is common to both the primary and the overlay maps. In boolean logic identity overlay is the equivalent of 'and/or', union overlay is the equivalent of 'or' and intersect overlay is the equivalent of 'and'.

Other forms of overlaying commonly used are point-in-polygon and line-on-polygon. Point-in-polygon searches overlay a polygon on a set of points and the output shows those points contained in the polygon. The 'is contained in' relationship is computed between the points and the polygon. An 'is contained in' relationship is also computed for line on polygon searches. Lines are broken at the boundaries of overlaid polygons and the containing polygon becomes an attribute of the line segment contained in the polygon. These overlays are shown diagrammatically below.

The use of overlaying is illustrated in a study of watershed management and ecological balance in the Berchtesgaden area in southern Germany (Schaller 1994). The process is illustrated in the diagram below.

At the top of the diagram, two maps, geology and site mapping, are overlaid to produce a composite map showing site data. Three maps, altitude, exposure and drainage, are then overlaid on each other to produce another combined map showing topographic data. The two combined maps and two other maps, linear structures and real use type, are then overlaid to produce the final combined map called evaluation geometry. Each overlay process produces what Schaller terms smallest common geometry. These are the smallest polygons that have the same attributes for all the factors in the overlay maps. They are also referred to as smallest common unit or smallest common area.

The size of the smallest common geometry depends on the size of area for which data is available in each map. There are many cases where the data is only available in rather large units that do not necessarily reflect the underlying characteristics of the data. Census data is particularly difficult in this regard because it is published in arbitrarily defined units. The extent to which the smallest common geometry really represents areas with common attributes should be carefully considered in relation to the quality of data in the maps from which they are formed.