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The growing intensity of impervious surface area (ISA) is one of the most striking effects of urban growth. The expansion of ISA gives rise to a set of changes on the physical environment, impacting the quality of life of the human population as well as the dynamics of fauna and flora. Hence, due to its importance, the present study aimed to examine the ISA distribution in the Metropolitan Region of São Paulo (MRSP), Brazil, using satellite imagery from the Landsat-8 Operational Land Imager (OLI) instrument. In contrast to other investigations that primarily focus on the accuracy of the estimate, the proposal of this study is—besides generating a robust estimate—to perform an integrated analysis of the impervious-surface distribution at pixel scale with the variability present in different territorial units, namely municipalities, sub-prefecture and districts. The importance of this study is that it strengthens the use of information related to impervious cover in the territorial planning, providing elements for a better understanding and connection with other spatial attributes. Reducing the dimensionality of the dataset (visible, near-infrared and short-wave infrared bands) by Karhune–Loeve analysis, the first three principal components (PCs) contained more than 99% of the information present in the original bands. Projecting PC1, PC2 and PC3 onto a series of two-dimensional (2D) scatterplots, four endmembers—Low Albedo (Dark), High Albedo (Substrate), Green Vegetation (GV) and Non-Photosynthetic Vegetation (NPV)—were visually selected to produce the unmixing estimates. The selected endmembers fitted the model well, as the propagated error was consistently low (root-mean-square error = 0.005) and the fraction estimates at pixel scale were found to be in accordance with the physical structures of the landscape. The impervious surface fraction (ISF) was calculated by adding the Dark and Substrate fraction imagery. Reconciling the ISF with reference samples revealed the estimates to be reliable (R2 = 0.97), regardless of an underestimation error (~8% on average) having been found, mostly over areas with higher imperviousness rates. Intra-pixel variability was combined with the territorial units of analysis through a modification of the Lorenz curve, which permitted a straightforward comparison of ISF values at different reference scales. Good adherence was observed when the original 30-m ISF was compared to a resampled 300-m ISF, but with some differences, suggesting a systematic behavior with the degradation of pixel resolution tending to underestimate lower fractions and overestimate higher ones; furthermore, discrepancies were bridged with the increase of scale analysis. The analysis of the IFS model also revealed that, in the context of the MRSP, gross domestic product (GDP) has little potential for explaining the distribution of impervious areas on the municipality scale. Finally, the ISF model was found to be more sensitive in describing impervious surface response than other well-known indices, such as Normalized Difference Vegetation Index (NDVI) and Normalized Difference Built-up Index (NDBI). Remote Sens. 2019, 11, 944; doi:10.3390/rs11080944 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 944 2 of 18

Quantification and Analysis of Impervious Surface Area in the Metropolitan Region of São Paulo, Brazil