Characterizing urban subpixel composition using spectral mixture analysis - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 113

and the degree of human impact on the landscape. Model
complexity for the settlement of Seringueiras is presented for
four dates: 1986 (Fig. 8.5a), 1990 (Fig. 8.5b), 1995 (Fig. 8.5c),
and 2000 (Fig. 8.5d). Four-endmember models correspond to
urban land cover, i.e., spectrally the most complex land-cover
type, while three-endmember models correspond to cleared land
and regenerating vegetation. Two-endmember models corre-
spond to primary forest, spectrally the least complex land cover
in this landscape at this spatial resolution. The population of
Seringueiras remained low, but increased almost 15-fold dur-
ing this period. Population was estimated as approximately 260
inhabitants in 1986 and reported as approximately 3800 inhabi-
tants in the 2000 Brazilian Census (IBGE, 2000). The increase in
population was accompanied by an increase in both extent and
density of built-up land cover. Areas along roads and adjacent
to the settlement center were cleared first (i.e., two-endmember
models are replaced with three-endmember models, indicat-
ing human alteration of the landscape), and through time, the
areas of disturbance expanded outward from the settlement
and the roads. Because maps of model complexity clearly sep-
arate built-up from non-built-up land cover, this methodology
could be further explored to facilitate semi-automated map-
ping of urban extent at regional to global scales (Powell and
Roberts, 2008).
Fraction images through time not only capture change in
urban extent (i.e., land-cover transitions), but also quantify
change in urban composition (i.e., land-cover modifications)
(Rashed et al ., 2005). To compare urban composition through
time, a fixedurbanboundarywas definedbasedonurban extent in
the year 2000. Mean fraction values within each urban boundary
were calculated, corresponding to percent area covered by each
material type. In a tropical frontier environment, an idealized
trajectory of urban land-cover change might be imagined as
follows: (i) settlers move into a tropical forest (sub-pixel fractions
dominated by vegetation); (ii) initial clearing occurs (sub-pixel
fractions are dominated by soil, with small fractions of GV or
NPV); and (iii) a settlement emerges (soil fraction diminishes and
impervious fraction increases). The trajectories of the settlements
of Seringueiras (Fig. 8.6a) and Buritis (Fig. 8.6b), illustrate this
pattern, though change occurs at different rates in each case. In
Seringueiras, conversion to urban land cover followed a gradual,
consistent trend, as indicated by the steady increase of impervious
and soil fractions and corresponding decrease of vegetation
fractions (Fig. 8.6a). In contrast, the location where Buritis
emerged was dominated by natural land cover (100%vegetation)
until 1995, and then experienced explosive conversion to urban
land cover, as indicatedby the steep slopes associatedwith changes
in impervious and soil fractions (Fig. 8.6b), and concurrent loss
of vegetation fractions.
The physical composition and structure of urban areas repre-
sent a complex interaction between physical and social processes
(Rashed et al ., 2005; Sanchez-Rodriguez et al ., 2005). A logical
extension of the research presented here, therefore, is to compare
urban land-cover change with socio-economic characteristics
of settlements through time, both at inter-urban and intra-
urban scales (Boucek and Moran, 2004; Rashed et al ., 2005).
Linking physical descriptions of development trajectories to
socio-economic drivers of urban expansion in the Amazon could
contribute to assessment of the role of urbanization in regional
land-cover change and global environmental change (Lambin
et al ., 2003).

TABLE 8.2 Summary measures for accuracy assessment for three
validation sites in Rondonia. A total of 41 samples were included;
average sample size was 2 × 2pixels.

Vegetation Impervious Soil

Slope 0.787 0.814 0.704

Intercept 10.75 5.99 5.99

Pearson's r 0.93 0.87 0.84

MAE 7.71 5.55 8.59

Bias 1.71 2.99 −6.20

''Pearson's r '' refers to the Pearson correlation coefficient between modeled
and measured fractions; ''MAE'' refers to mean absolute error; ''Bias'' refers to
mean error.

are also an important component of the built-up landscape and
dominate roadways in this scene, indicating that the roads are
either unpaved or dust-covered. The soil component is also high
in pasture areas, but remains low in forested land cover.
Correlation between reference fractions and modeled frac-
tions was assessed for the three 2000 sub-scenes for which
reference data were available (Table 8.2). Correlation between
reference and modeled fractions was highest for impervious frac-
tions, with a slope of 0.814 and a Pearson's correlation coefficient
( r ) of 0.87, and lowest for soil fractions, with slope equal to
0.704 and Pearson's r equal to 0.84. The vegetation fraction,
representing the sum of GV and NPV fractions, had a relatively
high slope (0.787) and the highest correlation ( r = 0 . 93). For all
classes, the intercept was approximately 10% or lower, and the
MAE was also less than 10%, within the uncertainty expected due
to the MTF of Landsat TM (Townshend et al ., 2000).
The biases (i.e., mean residuals) for all classes were quite
low (Table 8.2). The impervious and vegetation fractions had
very small, positive biases (below 3%), indicating a slight over-
estimation of the modeled fractions relative to the reference
fractions. The soil fractions had a slightly larger negative bias
(approximately 6%), indicating a general trend of underesti-
mation of the soil fractions. The overestimation of impervious
and vegetation fractions was approximately equal to the under-
estimation of the soil fractions, a result of the SMA constraint
that requires the fractions of any pixel to sum to 1.0. Much
of the uncertainty of fraction estimation is due to spectral
ambiguity between soil, NPV, and/or bright impervious spec-
tra. Unfortunately, comparing reference and modeled fractions
does not allow the specific nature of spectral confusion to be
quantified.
However, at every time step, impervious materials were mod-
eled with the highest density in the vicinity of the urban core, and
in general were not modeled in periurban areas of the landscape,
indicating that errors of commission were relatively low for the
impervious fractions. Additionally, the fact that overall measures
of area covered by impervious materials increased or remained
constant through time for all of the urban areas in the sample
increased confidence in the accuracy of impervious fractions.
Still lacking is extensive data to assess errors of omission for
impervious surface mapping.
Maps of model complexity (i.e., the number of endmem-
bers in each ''winning'' model, assumed to be the number
of endmembers needed to adequately model per-pixel spectral
variability) illustrate the relationship between spectral complexity