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Statistical distribution of building lot depth: Theoretical and empirical investigation of downtown districts in Tokyo

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  • Hiroyuki Usui

Abstract

A building lot represents one of the most important basic spatial objects of urban form because building lots are basically adjacent to road networks and combine to make an exact whole with no leftover space. Thus, it is important to understand the relationship between the sizes and shapes of building lots and the density of buildings and road networks at a district scale. While building lot sizes and frontages are known to follow a log-normal distribution, respectively, the probability density function that building lot depths follow remains uncertain. Therefore, the research objective is to answer the following research question: What types of statistical distribution of building lot depths are found if the values of building density (the number of buildings per unit area) and road network density (total lengths of road networks per unit area) are given at a district scale? Assuming that (A1) one building lot has one building; (A2) building lot depth is defined as the ratio of building lot size to frontage; and (A3) building lot frontages and depths are independently distributed, I derived the probability density function of rectangular building lot depths as a log-normal distribution. As the result of theoretical investigations, it was found that (1) the probability density function of building lot depths depends not on the building density but on road network density; and (2) it depends not only on road network density but also on the variation in building lot sizes and frontages. For the empirical study of 20 downtown districts of the Tokyo metropolitan region, I tested (A3) and the log-normality of building lot depths and applied the derived function. At a 5% significance level, it was found that the hypothesis of log-normality of building lot depths was accepted in 12 of the 20 selected districts. These findings imply that when we discuss the criteria of the variation in building lot sizes and frontages, we must take into consideration the variation in building lot depths and vice versa. I also derived the probability density function of building setbacks, whose parameters include road network density and building coverage ratio. These findings are expected to provide urban planners with a theoretical basis to not only reconsider the validity of the present road network density and building coverage ratio (form-based codes) but to additionally discuss the relationship between building-lot-scale and district-scale urban physical planning.

Suggested Citation

  • Hiroyuki Usui, 2019. "Statistical distribution of building lot depth: Theoretical and empirical investigation of downtown districts in Tokyo," Environment and Planning B, , vol. 46(8), pages 1499-1516, October.
    • Handle: RePEc:sae:envirb:v:46:y:2019:i:8:p:1499-1516
    DOI: 10.1177/2399808319840366
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    References listed on IDEAS

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    1. Hiroyuki Usui, 2018. "Statistical distribution of building lot frontage: application for Tokyo downtown districts," Journal of Geographical Systems, Springer, vol. 20(3), pages 295-316, July.
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    10. Hiroyuki Usui & Yasushi Asami, 2020. "Size Distribution of Building Lots and Density of Buildings and Road Networks: Theoretical Derivation Based on Gibrat’s Law and Empirical Study of Downtown Districts in Tokyo," International Regional Science Review, , vol. 43(3), pages 229-253, May.
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    2. Hiroyuki Usui, 2021. "Optimisation of building and road network densities in terms of variation in plot sizes and shapes," Environment and Planning B, , vol. 48(5), pages 1263-1278, June.

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