Quantitative evidence for leapfrogging in urban growth

Urban growth can take different forms, such as infill, expansion and leapfrog development. Here we focus on leapfrogging, which is characterised as new urban development bypassing vacant land. Analysing a sample of 100 global locations, we study the probability that land cover is converted from non-urban to urban as a function of the minimum distance to existing urban cells. The probability decreases with the distance but in many of the considered real-world samples it increases again just before the maximum possible distance. Comparing these empirical findings with numerical ones from a gravitational model, we discover that the characteristic increase can be found in both. Our results indicate that the conversion probability as a function of the distance to urban land cover includes three urban growth domains. (i) Expansion of existing settlements, (ii) discontinuous development of coincidental new settlements rather close to existing ones and (iii) leapfrogging of new settlements far away from existing ones. We conclude that gravitational effects can explain discontinuous development but leapfrogging can be attributed to a scarcity of developable land at long distances to settlements.