theory, certainty factors (Bloch, 1996), and neural networks (Foody, 1999; Mannan
and Ray, 2003). Nevertheless, as Mather (1999) suggested, neither hard nor soft
classification was an appropriate tool for the analysis of heterogeneous landscapes. To
provide a better understanding of the compositions and processes of urban landscapes,
Ridd (1995) proposed an interesting conceptual model for remote sensing analysis of
urban landscapes, that is, the vegetation–impervious surface–soil (VIS) model. It
assumes that land cover in urban environments is a linear combination of three
components, namely, vegetation, impervious surface, and soil. Ridd suggested that
this model can be applied to spatial–temporal analyses of urban morphology,
biophysical, and human systems. While urban land use information may be more
useful in socioeconomic and planning applications, biophysical information that can
be directly derived from satellite data is more suitable for describing and quantifying
urban structures and processes (Ridd, 1995). The VIS model was developed for Salt
Lake City, Utah, but has been tested in other cities (Ward et al., 2000; Madhavan et al.,
2001; Setiawan et al., 2006). All of these studies employed the VIS model as the
conceptual framework to relate urban morphology to medium-resolution satellite
imagery, but hard classification algorithms were applied. Therefore, the problem of
mixed pixels cannot be addressed, and the analysis of urban landscapes was still based
on “pixels” or “pixel groups.” Weng and Lu (2009) suggested that linear spectral
mixture analysis (LSMA) provided a suitable technique to detect and map urban
materials and VIS component surfaces in repetitive and consistent ways and to solve
the spectral mixing of medium-spatial-resolution imagery. The reconciliation
between the VIS model and LSMA provided a continuum field model which offered
an alternative, effective approach for characterizing and quantifying the spatial and
temporal changes of the urban landscape compositions. However, Weng and Lu
(2009) warned that the applicability of this continuum model must be further
examined in terms of its spectral, spatial, and temporal variability.
4.4 OPERATIONAL SCALE
Urban landscape processes appear to be hierarchical in pattern and structure. A study
of the relationship between the patterns at different levels in the hierarchy may help in
obtaining a better understanding of the scale and resolution problem (Cao and Lam,
1997; Weng et al., 2004) and in finding the optimal scale for examining the
relationship, that is, the operational scale (Frohn, 1998; Liu and Weng, 2009). Lo
et al. (1997) suggested that the urban surface characteristics required a minimum
thermal mapping resolution of 5–10 m based on a study in Huntsville, Alabama.
Nichol (1996) confirmed that satellite-derived land surface temperature (LST) image
data at the scale of 10
2 m was adequate for depicting most of the intraurban LST
variations related to urban morphology based on a study in Singapore. The length of
spatial scale that characterizes the overall distribution of scales of all objects in a
collection may be compared among different cities. Small (2009) suggested that the
modal scale length was 10–20 m based on a comparative analysis of 14 cities in the
world.
OPERATIONAL SCALE
67
and Ray, 2003). Nevertheless, as Mather (1999) suggested, neither hard nor soft
classification was an appropriate tool for the analysis of heterogeneous landscapes. To
provide a better understanding of the compositions and processes of urban landscapes,
Ridd (1995) proposed an interesting conceptual model for remote sensing analysis of
urban landscapes, that is, the vegetation–impervious surface–soil (VIS) model. It
assumes that land cover in urban environments is a linear combination of three
components, namely, vegetation, impervious surface, and soil. Ridd suggested that
this model can be applied to spatial–temporal analyses of urban morphology,
biophysical, and human systems. While urban land use information may be more
useful in socioeconomic and planning applications, biophysical information that can
be directly derived from satellite data is more suitable for describing and quantifying
urban structures and processes (Ridd, 1995). The VIS model was developed for Salt
Lake City, Utah, but has been tested in other cities (Ward et al., 2000; Madhavan et al.,
2001; Setiawan et al., 2006). All of these studies employed the VIS model as the
conceptual framework to relate urban morphology to medium-resolution satellite
imagery, but hard classification algorithms were applied. Therefore, the problem of
mixed pixels cannot be addressed, and the analysis of urban landscapes was still based
on “pixels” or “pixel groups.” Weng and Lu (2009) suggested that linear spectral
mixture analysis (LSMA) provided a suitable technique to detect and map urban
materials and VIS component surfaces in repetitive and consistent ways and to solve
the spectral mixing of medium-spatial-resolution imagery. The reconciliation
between the VIS model and LSMA provided a continuum field model which offered
an alternative, effective approach for characterizing and quantifying the spatial and
temporal changes of the urban landscape compositions. However, Weng and Lu
(2009) warned that the applicability of this continuum model must be further
examined in terms of its spectral, spatial, and temporal variability.
4.4 OPERATIONAL SCALE
Urban landscape processes appear to be hierarchical in pattern and structure. A study
of the relationship between the patterns at different levels in the hierarchy may help in
obtaining a better understanding of the scale and resolution problem (Cao and Lam,
1997; Weng et al., 2004) and in finding the optimal scale for examining the
relationship, that is, the operational scale (Frohn, 1998; Liu and Weng, 2009). Lo
et al. (1997) suggested that the urban surface characteristics required a minimum
thermal mapping resolution of 5–10 m based on a study in Huntsville, Alabama.
Nichol (1996) confirmed that satellite-derived land surface temperature (LST) image
data at the scale of 10
2 m was adequate for depicting most of the intraurban LST
variations related to urban morphology based on a study in Singapore. The length of
spatial scale that characterizes the overall distribution of scales of all objects in a
collection may be compared among different cities. Small (2009) suggested that the
modal scale length was 10–20 m based on a comparative analysis of 14 cities in the
world.
OPERATIONAL SCALE
67