Characterising urban morphology with spectral unmixing and spatial metrics: a case study on Dublin

In today’s urbanising world, effective urban management and planning strategies are needed to temper the impact of urban change processes on the natural and human environment. To develop and monitor such strategies, and to assess their spatial impact, analysing changes in urban structure is essential. Data from earth observation satellites provide regular information on urban development and, as such, may contribute to the mapping and monitoring of cities and the modelling of urban dynamics. Especially images of medium resolution (Landsat, SPOT, .), which are cheap, widely available and often part of extensive historic archives, offer a wealth of information that may be useful for urban monitoring purposes. The lower resolution of this type of imagery, however, hampers the study of urban morphology and change processes at a more detailed, intra-urban level. Spectral unmixing approaches, which allow characterising land-cover distribution at sub-pixel level, may partly compensate for this lack of spatial detail, and may render medium-resolution imagery more useful for urban studies. The main research question addressed in this paper is how medium-resolution imagery could be used to describe urban morphology, by combining spectral unmixing approaches with spatial metrics. Spatial metrics derived from satellite imagery may be useful to quantify structural characteristics of expanding cities, and may provide indications of functional land use. In this study, we develop a set of urban metrics for use on continuous sealed surface data produced by sub-pixel classification of Landsat ETM+ imagery. Two sub-pixel classification approaches are examined for that purpose. In a first approach, we use a linear spectral mixture model with a vegetation and a nonvegetation endmember to deconvolve each pixel’s spectrum into fractional abundances of the two end member spectra, which are determined by visualising mixture space with principal component analysis. In a second approach, we use a linear regression model to estimate the proportion of vegetation cover within each Landsat pixel. In both approaches, an urban mask is used to indicate pixels belonging to urban land cover. Only pixels within the urban mask are subjected to sub-pixel classification. We hereby assume that the urban area does not contain bare soil and that the area of a pixel not covered by vegetation fully consists of sealed surface cover. The resulting sealed surface proportion map is then used to characterise urban morphology and land use by means of the shape of the cumulative frequency distribution of the estimated sealed surface fractions within a building block. A transformed logistic function is fitted to this distribution with a least-squares approach to obtain function parameters that are used as variables in a supervised classification approach, together with spatially explicit metrics (spatial variance and Moran’s I). Our study demonstrates that images from medium resolution sensors can be used to characterise intra-urban morphology, and that the structure of a building block as described by the proposed metrics gives an indication of its membership to certain morphological/functional urban classes. In future research we will incorporate socioeconomic data in the metric analysis to further improve the distinction of urban land-use categories. The spatial metrics approach developed in this study will be used in experiments to improve the calibration of the MOLAND urban growth model, which is currently calibrated with historical land-use maps available for approximately 10-year intervals. Introduction More than half of the world’s population lives in urbanised areas, and in the future cities will house an increasing number of people in both absolute and relative terms (Martine, 2008). While spatial expansion of cities is a natural consequence of demographic and economic trends and changes in lifestyle on which local and regional policy-makers have seemingly little grasp, local policy should be concerned about how population growth is translated into spatial patterns of urban growth. Urban sprawl and increased soil sealing provide symptomatic evidence for the fact that many European and NorthAmerican cities grow faster spatially than demographically. A study of the European Environment Agency confirms this by reporting that European cities have expanded on average by 78% since the mid-1950s, while during the same period the population increased by only 33% (EAA, 2006). This dilution of the urban fabric has both direct and indirect impacts on the environment and the well-being of urban residents. For instance, uncontrolled sprawl increases energy consumption, pollution and greenhouse gas emissions, demands more transport infrastructure, may lead to increased flood risks and encroaches on natural landscapes. Effective urban management and planning strategies at different levels of government are therefore essential to temper the environmental consequences of urban land consumption. To develop and monitor such strategies and to assess their spatial impact, analysing and characterising changes in urban structure is important. Data from earth observation satellites provide regular information on urban development and could in that way contribute to mapping and monitoring structural characteristics of expanding cities. A rather novel approach in this research area is to describe urban form by means of spatial metrics, i.e. quantitative measures of spatial pattern and composition that have recently shown considerable potential for structural analysis of urban environments (Herold, et al., 2005; Torrens, 2008). Spatial metrics derived from satellite imagery may also help to describe the morphological characteristics of urban areas and their changes through time (Ji, et al., 2006). Because previous studies have demonstrated a relationship between the spatial structure of the built-up environment and its functional characteristics (Barr & Barnsley, 1997), quantifications of urban morphology through spatial metrics can also be related to land use. Despite the currently available high resolution satellite images, which provide increasingly detailed information about urban surface materials, most of the historic archive imagery consists of medium resolution (MR) data such as from the Landsat or SPOT programmes. Therefore, to study urban growth patterns over a time-span that exceeds the availability of high resolution imagery, spatial metrics that succeed in capturing structural information from images with a pixel size of 20 meters or more should be used. In this study, we aim to characterise urban structure and land use in the Greater Dublin area by developing spatial metrics for use on continuous sealed surface data produced by sub-pixel classification of Landsat images. The spatial metrics are calculated for building blocks that are homogeneous in terms of land use, and are used as variables that enable us to allocate each block to a particular morphological / functional urban class. The proposed approach makes it possible to tap into the extensive historic archives of MR images to characterise urban growth patterns at a reasonably detailed level, on an intra-urban basis and at low cost. Study area and data The study area for this research is Dublin, the political and economical capital of Ireland and home to over 40% of the country’s population. Dublin experienced rapid urban expansion in the 1980’s and 1990’s, fuelled by the building of new roads that drove residential and commercial development rapidly outward into the urban fringe (Kitchen, 2002). A Landsat TM image (path 206, row 23) acquired on May 24 2001 was used to derive a sealed surface map for the study area. The image was geometrically co-registered to the Irish Grid projection system and the raw digital numbers were converted to exoatmospheric reflectance according to the formulas and calibration parameters presented by The Landsat 7 Users Handbook (Irish, 2009). An existing high resolution land-cover map, derived from a Quickbird image acquired on August 4 2003, was used to obtain reference data for training and validation of the sub-pixel classifiers. Homogeneous blocks for structural analysis were defined by overlaying a TeleAtlas road database for the area with the European MOLAND land-use map of 2000. Deriving continuous sealed surface data The downside of using MR data for urban analysis is the relatively low spatial resolution, which limits the level of structural detail that can be resolved from the imagery, and which may also lead to low mapping accuracies because the sensor’s instantaneous field of view (IFOV) often contains different types of land cover. To overcome this drawback we applied spectral unmixing, a technique that relates a pixel’s spectrum to fractions of its surface constituents. One of the most common methods to approach this problem is linear spectral mixture analysis (LSMA), whereby a pixel’s observed reflectance is modelled as a linear combination of spectrally pure “endmember” reflectances (van der Meer, 1999). LSMA has recently received quite some attention in studies that aim to characterise urban environments (Rashed, et al., 2005). Some of these studies resort to the components of the Vegetation, Impervious surface and Soil (VIS) model proposed by Ridd (1995) to represent the endmembers of the LSMA model. However, not all pure vegetation, man-made impervious surface or soil pixels necessarily occupy well-defined, extreme positions in feature space and can, as such, not directly be used as endmembers for linear unmixing. One reason for this is that pure pixels are spectrally variable because of brightness differences, even though they may represent a similar surface type. This problem can be dealt with by applying brightness normalisation prior to the unmixing (Wu, 2004). Another reason is spectral confusion between VIS components, such as dry bare soils and bright