A Method to Model Neighborhood Interactions in Geo-simulation of Urban Dynamics

Yaolong Zhao and Yuji Murayama

Division of Spatial Information Science, University of Tsukuba, Japan. Email: yaolongzhao@gmail.com

Importance of neighborhood interactions in urban dynamics

Fig. 3 Scheme of impact gradient

Fig. 1 Effect of neighborhood on location decision at micro-scale

Fig. 2 An extended neighborhood

Tab. 1 Results of model Calibration ( from 1984 to 1994 )

Fig. 4 Simulated urban area in 1994

To propose a unified method for the analysis of neighborhood interactions in geo-simulation of urban dynamics

Darling, how about we construct our

house in this parcel?

Methodology• Tobler’s First Law of Geography: theoretical fundamentals• Modificatory Reilly’s Law of Retail Gravity: theory expression • Logistic Regression Approach: model constitution

Distance from developable cells: far

Modificatory Reilly’s Model

Impact index: great

2ji

jkhkh d

AGf

Where, fkh: constribution of one cell with land use k in the neighborhood to the conversion of the developable cell to land use h for next stage, Aj: area of the cell j, dji: the distance between the cell j and the developable cell i, Gkh: constant of the effect of land use k on the transition to land use h, Fkh: aggregated contribution of all the cells in the neighborhood, and m: number of the cells in the neighborhood.

For one developable cell, there are just two statuses could be transformed to: conversion and no conversion. Therefore, in logistic regression, potential ph of the conversion of the cell to land use h derived from the effect of neighborhood can be expressed as:

m

khkh fF

k

khkhhh

h Fp

pLog 0)

1(

βoh and βkh are the coefficients to be calibrated with maximum likelihood estimation.

A Case of the Tokyo metropolitan area

Factors (k)

Active land use types (h)

Vacant Industrial Residential Commercial

βkh Vacant 1.108   0.179 0.127

βkh Industrial 0.359 1.417 0.220 0.457

βkh Residential 0.160 0.570 0.197

βkh Commercial 0.367 0.642 0.274 1.811

βkh Road 0.287   0.388 0.517

βkh Public 0.234 0.164** 0.229 0.264

β0h Constant -2.592 -1.979 -3.064 -2.816

Test:

PCP (%) 84.1 87.0 84.8 86.6

ROC 0.924 0.931 0.914 0.938PCP: percentage correctly predicted. ROC: relative operating characteristic. **: significant at p<0.05. Others significant at p<0.001.

Fig. 5 Visual comparison of simulation

with reality

Fig. 6 Area-radius plots of comparison between simulation and reality of built-up area

Concluding remarks Local spatial interactions between neighborhood land-use types play an important role in urban dynamics. Tobler’s First Law of Geography is suitable as theoretical fundamental for understanding the neighborhood interactions. The relative differences of the radial dimensions between the simulation and reality indicate that other factors influence the allocation decisions as well, such as policy considerations, tenure status etc. The model proposed in this research provides a alternative approach to effectively explore and quantify the neighborhood interactions for geo-simulation of urban dynamics.

Neighborhood interactions are often addressed as the main factors deciding urban dynamics as other factors like natural constraints and institutional controls (land-use policies) which are comparatively stable in certain period.

Objective of this study

We assume that in cellular environment all the cells in the neighborhood contribute to the conversion of developable cell. The contribution of one cell is associated with the state of it and the distance to the developable cell based on Tobler‘s First Law of Geography and modificatory Reilly‘s Gravity function in which no unit problem exists.

Impact of one cell: Aggregated impact:

We simulate urban growth of the Tokyo metropolitan area from 1984 to 1994 using this model constrained by land condition, land use zoning plan and transportation network, and assess the validation of the simulation via visual comparison and fractal dimension index.

1

100

10,000

1,000,000

1 10 100Radius (km)

Are

a (n

umbe

r of

cel

ls)

Tokyo (fractal dimension:1.60)

Simulation (fractal dimension:1.62)