Characterizing urban subpixel composition using spectral mixture analysis - Urban Remote Sensing: Monitoring, Synthesis and Modeling in the Urban Environment - page 104

8.1 Introduction

urban landscape is ''unmixed'' to determine the fraction of each
material component present. The number and type of materials
can vary on a per-pixel basis to accommodate the high spectral
and spatial variability of urban land cover. Sub-pixel fractions of
specific materials are grouped into generalized V-I-S classes, and
continuous maps of each component are generated. Accuracy is
assessed in terms of agreement between modeled fractions and
reference fractions measured in the field or from finer spatial
resolution imagery.
The overview of SMA methodology is followed by a summary
of two case studies that demonstrate the flexibility of MESMA in
mapping V-I-S components in very different environments. In
both studies, SMA is applied to map the fundamental spectral
components of the urban environment generalized in terms of
Ridd's V-I-S model. Additionally, each of these studies lever-
ages temporal information relevant to the mapping objectives
to guide model development and implementation. The first case
study analyzes the evolution of urban morphology in settlements
located along the ''Arc of Deforestation'' in the Brazilian Amazon
(Fig. 8.1a). Assumptions about the unidirectional trajectory of
urban land cover as a function of time informs spectral library
construction and model selection. Additionally, this study illus-
trates for the first time that the same spectral library and model
selection rules can be applied across a region and through time.
The second case study quantifies the abundance of the two
dominant urban vegetation types (i.e., trees and lawn) in the
western US city of Denver, Colorado, (Fig. 8.1b) and demon-
strates that phonological information (i.e., differences in the
timing of ''green-up'') can complement spectral information in
order to discriminate broad vegetation types. Together, these
case studies highlight a major strength of the SMA approach: that
model implementation can be customized to optimally capture
the spatial and spectral variations of land cover specific to a par-
ticular region and that temporal information can be integrated
in the analysis to reduce spectral ambiguities.

Derivingmeaningful, quantitativemeasures to characterize urban
land cover remains a challenge in remote sensing applications
because urban areas are complex landscapes of built struc-
tures and human-modified land cover (Forster, 1983; Zipperer,
et al ., 2000). Globally, urban land cover varies in terms of den-
sity of habitation, structure of buildings, type of construction
materials, abundance of vegetation, and size of open spaces,
among other factors. As a result, there is no globally consis-
tent spectral signature for urban land cover, and there is no
straightforward means of comparing urban environments from
different regions (Ridd, 1995; Small, 2005). Even within a single
urban area, image analysis is complicated because of the high
spectral and spatial variability of built-up materials which results
in a large number of ''mixed pixels'' across a range of spatial
scales and limits the utility of traditional classification approaches
(Forster, 1983; Ridd, 1995; Small, 2001; Franke et al ., 2009; Myint
and Okin, 2009; Wu, 2009).
In order to compare urban systems, whether between coun-
tries, between cities within the same country, or between the same
city at different time periods, standardized units of measurement
and descriptive parameters are needed. One strategy is to focus
on characterizing the bio-physical composition of urban land
cover, because measures based on land cover do not depend on
human interpretation, nor on the economic, historic, or cultural
development of the city (Whyte, 1985; Ridd, 1995). Additionally,
the problem of mixed pixels can be addressed by characteriz-
ing the landscape in terms of continuous variables rather than
assigning discrete, mutually exclusive classes (DeFries et al ., 1999;
Ji and Jensen, 1999; Clapham Jr., 2003; Small, 2005; Weng and
Lu, 2009). Modeling each pixel as the percent cover of basic
urban materials preserves the heterogeneity of urban land cover
(Clapham Jr., 2003; Hansen, et al ., 2002) and captures more
detail than the minimum resolution imposed by the pixel.
One conceptual framework that addresses these issues is the
V-I-S model of urban ecosystem analysis (Ridd, 1995), which
decomposes the urban landscape as a combination of three
fundamental components, in addition to water: vegetation (V),
impervious surfaces (I), and bare soil (S). Spectral mixture analy-
sis (SMA) is a technique to derive the sub-pixel abundance of each
land-cover component, thereby characterizing the urban land-
scape as continuous surfaces of V-I-S components. This strategy
has several advantages. First, the V-I-Smodel does not depend on
land-use classes that may be subjective or regionally and tempo-
rally specific (e.g., Anderson et al ., 1976; Ridd, 1995; Small, 2005).
Fractions derived from SMA represent a physical model of the
landscape (Adams and Gillespie, 2006), and such continuous
descriptions of urban land cover are more readily compared
with other datasets, incorporated in environmental models, and
scaled-up in a physically meaningful manner (Jensen, 1983; Carl-
son and Sanchez-Azofeifa, 1999; DeFries et al ., 1999; Hansen
et al ., 2002; Clapham Jr., 2003; Lepers, et al ., 2005). Finally,
urban extent can be arbitrarily specified by assigning a threshold
value for the impervious component without loss of information
(Ridd, 1995).
This chapter presents an overview of the SMA technique
to characterize the urban physical environment in terms of V-
I-S components. The analysis involves compiling a regionally
specific library of the spectra that best represent the diversity
of urban materials. The spectral response of each pixel in the

8.2 Overview of SMA
implementation

8.2.1 SMA background

SMA is a method that explicitly accounts for mixed pixels and
derives information at the subpixel scale (Adams et al ., 1986;
Small, 2001; Powell et al ., 2007; Franke et al ., 2009). SMA
assumes that (a) the landscape can be modeled as mixtures of a
fewbasic spectral components, known as ''endmembers,'' and (b)
the measured spectrum of each pixel can be modeled as a linear
combination of endmember spectra, weighted by the fraction of
each endmember within the pixel's instantaneous field of view
(IFOV) (Adams et al ., 1986; Roberts et al ., 1998a; Song, 2005;
Powell et al ., 2007). The objective of SMA is to model per-pixel
abundance of the ''pure'' components of the scene.
In virtually any urban environment, the signal recorded
by a sensor will include reflectance from multiple land-cover
components. For example, 30-mLandsat pixels overlaid on high-
resolution imagery from an urbanizing landscape in Rondonia,
Brazil, consist of mixtures of green vegetation, a variety of
impervious surface materials, and soil (Fig. 8.2a). The response