Urbanization between compactness and dispersion: designing a spatial model for measuring 2D binary settlement landscape configurations

Measuring spatial patterns is a crucial task in spatial sciences. Multiple indicators have been developed to measure patterns in a quantitative manner. However, most comparative studies rely on relative comparisons, limiting their explanatory power to specific case studies. Motivated by advancements in earth observation providing unprecedented resolutions of settlement patterns, this paper suggests a measurement technique for spatial patterns to overcome the limits of relative comparisons. We design a model spanning a feature space based on two metrics – largest patch index and number of patches. The feature space is defined as ‘dispersion index’ and covers the entire spectrum of possible two-dimensional binary (settlement) patterns. The model configuration allows for an unambiguous ranking of each possible pattern with respect to spatial dispersion. As spatial resolutions of input data as well as selected areas of interest influence measurement results, we test dependencies within the model. Beyond, common other spatial metrics are selected for testing whether they allow unambiguous rankings. For scenarios, we apply the model to artificially generated patterns representing all possible configurations as well as to real-world settlement classifications differing in growth dynamics and patterns.