Mitigating the zonal effect in modeling urban population density functions by Monte Carlo simulation

Most empirical studies indicate that the pattern of declining urban population density with distance from the city center is best captured by a negative exponential function. Such studies usually use aggregated data in census area units that are subject to several criticisms such as modifiable areal unit problem, unfair sampling, and uncertainty in distance measure. In order to mitigate these concerns associated, this paper uses Monte Carlo simulation to generate individual residents that are consistent with known patterns of population distribution. By doing so, we are able to aggregate population back to various uniform area units to examine the scale and zonal effects explicitly. The case study in Chicago area indicates that the best fitting density function remains exponential for data in census tracts or block groups, however, the logarithmic function becomes a better fit when uniform area units such as squares, triangles or hexagons are used. The study also suggests that the scale effect remain to some extent in all area units, and the zonal effect be largely mitigated by uniform area units of regular shape.