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The Use of Areal Interpolation to Explore Long-Term Demographic Change

University of Portsmouth, United Kingdom

Key words: Areal Interpolation, Error, Long-Term Change, Census, Boundary Changes

The first British census was published in 1801 and, with the exception of 1941, it has been published every 10 years since that date. Although individual censuses have been analysed in detail, comparing censuses with each other has proved highly problematic. This is because every census has been published using different administrative units, in some cases a completely different system, or, more commonly, the same system, but with so many boundary changes that comparison becomes highly problematic. The traditional response to this problem has simply been to aggregate data to county level. This is highly unsatisfactory as it leads to a dramatic loss of detail and other modifiable areal unit related problems. This means that data on two centuries of demographic change in Britain has still to be properly explored at a statistically sensible spatial scale. In order to exploit these data properly, GIS-based spatial analytical techniques have been developed to enable the data to be compared at the level for which they were published: district level. This opens the door for a far better understanding of spatial and temporal change in British society.

The Great Britain Historical GIS has built a GIS database that contains the changing boundaries of the principal administrative units from 1840 to 1974 (Gregory and Southall, 1998). This is linked to a database that contains a large amount of data from nineteenth and twentieth century censuses. The remaining challenge, therefore, is to develop a technique that will interpolate these data onto a single, standardised administrative geography, and to evaluate the likely implications of error in the resulting data.

Areal interpolation has been defined as "the transfer of data from one set (source units) to a second set (target units) of overlapping, non-hierarchical areal units" (Langford et al., 1991: p. 56) and was identified by Fotheringham and Regression (1993) as one of the most pressing research areas for GIS-based spatial analysis. Although many techniques have been devised surprisingly little work has been done that attempts to evaluate the degree of error that they introduce (Cockiness et al. (1997) provide one obvious exception). A range of possible areal interpolation techniques could be used for interpolating data within the historical GIS including areal weighting (Godchild and Lam, 1980), asymmetric techniques (Gregory, in press), and the use of ancillary information about the target zones (Flowered and Green, 1994). Deciding which approach is the best is not always easy as this decision depends on many factors.

In order to test the reliability of the various possible techniques, 1991 Enumeration District level data were aggregated to form synthetic units that approximated to census districts from 1881, 1911, 1931 and 1971. 1911 was taken to be the target date and data from the other three sets of synthetic units were interpolated onto these using a variety of techniques. Several different variables were used to evaluate the effects of their differing distributions. The results of the interpolations were then compared to the target 1911 data to calculate the degree of error introduced. The errors reveal that the effectiveness of the interpolation depends on the variable being modelled and, in particular, its relationship with total population. The choice of target unit is also very important.

The impact of this work is that it will allow continuous time-series of nearly 200 years worth of data to be analysed at district level. Although this work is applied in a historical context, it has relevance to any work that is attempting to use areal interpolation techniques.


Flowerdew, R. and Green, M., 1994, Areal interpolation and types of data. In Fotheringham, S. and Rogerson, P. (Eds.), Spatial Analysis and GIS, London, Taylor and Francis, pp. 121-145.

Fotheringham, A. and Rogerson, P., 1993, GIS and spatial analytical problems. International Journal of Geographical Information Systems 7, pp. 3-19

Goodchild, M. and Lam, N., 1980), Areal interpolation: a variant of the traditional spatial problem. Geo-Processing, 1, pp. 297-312.

Gregory, I., Longitudinal analysis of age and gender specific migration patterns in England and Wales: A GIS-based approach. Social Science History, in press.

Gregory, I. and Southall, H., 1998, Putting the Past in its Place: The Great Britain Historical GIS. In Carver, S. (Ed.), Innovations in GIS 5, London, Taylor & Francis, pp. 210-221.

Langford, M., Maguire, D., and Unwin, D., 1991, The areal interpolation problem: Estimating population using remote sensing in a GIS framework. In Masser, I. and Blakemore, M. (Eds.), Handling Geographical Information: Methodology and Potential Applications, New York, Longman, pp. 55-77.