(Fotheringham and Wong, 1991). Empirical studies may be the only possible ways to
explore the nature of MAUP (Fotheringham and Wong, 1991). Recently, there has
been an increase in using spatial autocorrelation indices to indicate geographical
patterns or geospatial data distributions. The underlying fundamental of spatial
autocorrelation is best explained by Tobler’s first law of geography—“everything
is related to everything else, but near things are more related than distance things” (Lo
and Yeung, 2002). The index is devised to measure the spatial ordering as well as the
spatial covariance structure of geospatial data and provides insights into the degree of
clustering, randomness, or fragmentation of a pattern (Read and Lam, 2002).
However, spatial autocorrelation is subject to the influence of scale, meaning that
at one scale its index may suggest a concentrated pattern while at another it may
suggest a scattered pattern (Cao and Lam, 1997).
4.5.1 Spatial Variations of Land Surface Temperature
at Multiple Census Scales
Liang and Weng (2008) conducted a multiscale analysis of census-based LST variations
and determinants in Indianapolis, Indiana. Urban temperatures have a close relationship
with many environmental, economic, and social issues in the urban areas. This study
utilized LST data, derived from a Landsat ETM+ image of Indianapolis, Indiana, to
examine census-based variations and to model their relationships with the parameters of
urban morphology. The NDVI, buildings, roads, and water bodies were selected as the
variables of the urban morphology. Correlation analysis and stepwise regression
modeling at each census level, that is, block, block group, and tract, were performed.
The sensitivity of the relationship to aggregation and thus the scale effect of MAUP were
examined. Their results showed that LST had a strongest positive correlation with
buildings but was negatively correlated with water at all scales. The correlation between
LST and the four variables tended to become stronger as the scale increased. Table 4.1
indicates that the adjusted R
2 value increased with the scale, suggesting that more
variations in LST could be explained by the regression models. The regression model
for the tract level possessed the closest goodness of fit in the population of LST with the
least estimation error. More independent variables are needed to predict LST at finer
scales. Meanwhile, when the analytical scale altered, the contribution of each independent variable to the models changed. For example, an increase of 10 in P bldg generated
an increase in LST of 2.95 K at the block level. The same increase at the block group and
tract levels generated increases of 5.21 and 5.95 K in the predicted LST values,
respectively. However, the strength of the correlation between LST and four biophysical
factors was not always consistent with their contributions to LST regression modeling.
For example, roads contributed the least to the LST estimation, although it correlated
stronger with LST than water. This is because in multivariate modeling regression
estimates attached to any single independent variable could become inflated or deflated,
since changes in the variable may be confused by variations in other independent
variables.
In order to validate the relationship between input data and LST models, a residual
map was produced for each model (Figure 4.2). The range of residuals decreased from
SCALE DEPENDENCY OF URBAN PHENOMENA
69
explore the nature of MAUP (Fotheringham and Wong, 1991). Recently, there has
been an increase in using spatial autocorrelation indices to indicate geographical
patterns or geospatial data distributions. The underlying fundamental of spatial
autocorrelation is best explained by Tobler’s first law of geography—“everything
is related to everything else, but near things are more related than distance things” (Lo
and Yeung, 2002). The index is devised to measure the spatial ordering as well as the
spatial covariance structure of geospatial data and provides insights into the degree of
clustering, randomness, or fragmentation of a pattern (Read and Lam, 2002).
However, spatial autocorrelation is subject to the influence of scale, meaning that
at one scale its index may suggest a concentrated pattern while at another it may
suggest a scattered pattern (Cao and Lam, 1997).
4.5.1 Spatial Variations of Land Surface Temperature
at Multiple Census Scales
Liang and Weng (2008) conducted a multiscale analysis of census-based LST variations
and determinants in Indianapolis, Indiana. Urban temperatures have a close relationship
with many environmental, economic, and social issues in the urban areas. This study
utilized LST data, derived from a Landsat ETM+ image of Indianapolis, Indiana, to
examine census-based variations and to model their relationships with the parameters of
urban morphology. The NDVI, buildings, roads, and water bodies were selected as the
variables of the urban morphology. Correlation analysis and stepwise regression
modeling at each census level, that is, block, block group, and tract, were performed.
The sensitivity of the relationship to aggregation and thus the scale effect of MAUP were
examined. Their results showed that LST had a strongest positive correlation with
buildings but was negatively correlated with water at all scales. The correlation between
LST and the four variables tended to become stronger as the scale increased. Table 4.1
indicates that the adjusted R
2 value increased with the scale, suggesting that more
variations in LST could be explained by the regression models. The regression model
for the tract level possessed the closest goodness of fit in the population of LST with the
least estimation error. More independent variables are needed to predict LST at finer
scales. Meanwhile, when the analytical scale altered, the contribution of each independent variable to the models changed. For example, an increase of 10 in P bldg generated
an increase in LST of 2.95 K at the block level. The same increase at the block group and
tract levels generated increases of 5.21 and 5.95 K in the predicted LST values,
respectively. However, the strength of the correlation between LST and four biophysical
factors was not always consistent with their contributions to LST regression modeling.
For example, roads contributed the least to the LST estimation, although it correlated
stronger with LST than water. This is because in multivariate modeling regression
estimates attached to any single independent variable could become inflated or deflated,
since changes in the variable may be confused by variations in other independent
variables.
In order to validate the relationship between input data and LST models, a residual
map was produced for each model (Figure 4.2). The range of residuals decreased from
SCALE DEPENDENCY OF URBAN PHENOMENA
69