Visualization of the spatial patterns of inter-urban income disparities using coordinate transformations

Inter-urban income disparities reflect differences between individual urban localities in the average incomes of their residents. The present paper discusses different ways of visualizing such disparities on thematic maps. The approach we propose is based on the transformation of distances between individual localities and a reference city (e.g. a major population centre of a country) in proportion to the actual differences in the income levels. The general principle of such a transformation is to bring closer to the reference city places with higher incomes, while moving away localities with low income levels. Three alternative approaches to the implementation of this transformation technique are discussed. According to the 'actual distance' method, the spatial 'shift' of a locality on the map is set proportional to both the relative difference in incomes and the aerial distance between a locality and the reference city. In the 'proportional increment' transformation, the distance between a locality and the reference city is adjusted by a parameter whose values are proportional to income disparities between the two. Lastly, according to the 'concentric circle' transformation, localities with identical levels of incomes are positioned at a certain distance from the reference city, forming concentric circles around it. Both advantages and disadvantages of these transformation techniques are discussed, and the 'proportional increment' method is chosen as the best-performing visualization technique. The performance of this technique is demonstrated using income data for urban localities in Israel in 1991 and 1999. As analysis indicates, the proposed method helps to illustrate both the existing patterns of inter-urban income disparities and their dynamics over time.