Huygens’s Principle for Dynamic Urban Growth

Successful management of urban areas requires continuous improvement in knowledge related to its underlying processes. The present study proposes a novel technique for analyzing urban boundary expansion. The analysis using remote sensing data at various sampled times of development shows that each point in the boundary has a forward flux outwardly from the developed region. Such behavior allows the use of Huygens's principle of wavefront propagation to study dynamic boundary expansion and its drivers. A simplified urban region near Mumbai city is taken to implement the method. The urban boundaries are extracted using Landsat satellite data for three periods—1999, 2009 and 2019. The extracted boundaries are smoothened and discretized into fifty equal sections. The discretized points act as the source of Huygen circles used to capture the rate of change in the magnitude and direction of urban boundaries. A regression analysis is used to relate the expansion rates to the potential driver variables. Results show that whereas the change in magnitude is likely to occur closer to highways and toward the nearby city center, it is expected to spread away from the railway stations due to the lack of space closer to them. The proposed technique opens up new avenues of research in urban studies.