The problem of mixed pixels negatively affects the delineation of accurate surface water in Landsat Imagery. Linear spectral unmixing has been demonstrated to be a powerful technique for extracting surface materials at a sub-pixel scale. Therefore, in this paper, we propose an innovative low albedo fraction (LAF) method based on the idea of unconstrained linear spectral unmixing. The LAF stands on the "High Albedo-Low Albedo-Vegetation" model of spectral unmixing analysis in urban environments,

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... and investigates the urban surface water extraction problem with the low albedo fraction map. Three experiments are carefully designed using Landsat TM/ETM+ images on the three metropolises of Wuhan, Shanghai, and Guangzhou in China, and per-pixel and sub-pixel accuracies are estimated. The results are compared against extraction accuracies from three popular water extraction methods including the normalized difference water index (NDWI), modified normalized difference water index (MNDWI), and automated water extraction index (AWEI). Experimental results show that LAF achieves a better accuracy when extracting urban surface water than both MNDWI and AWEI do, especially in boundary mixed pixels. Moreover, the LAF has the smallest threshold variations among the three methods, and the fraction threshold of 1 is a proper choice for LAF to obtain good extraction results. Therefore, the LAF is a promising approach for extracting urban surface water coverage. Remote Sens. 2017, 9, 428 2 of 15 and is clearly superior to conventional in-situ measurements [6, 7] . Among current remote sensing sensors, Landsat sensors have the greatest reputation in urban monitoring because of its advantages in terms of free availability, and moderate spectral, temporal, and spatial resolutions. Therefore, in our study, we implement Landsat imagery to investigate the urban surface water coverage problem. Many studies have previously reported urban surface water extraction achievements using Landsat images. Regular water extraction methods can be categorized into three main groups [8, 9] : (1) thematic classification methods [10-12]; (2) single-band thresholding methods [13, 14] ; and (3) water index methods [15] [16] [17] . Thematic classification methods formulate urban surface water extraction into a regular binary unsupervised or supervised classification problem on urban land cover types, and select surface water as the exclusive thematic class for mapping [10] . The methods easily bring about low accuracy in areas where the background land cover includes low albedo surfaces, such as asphalt roads and building shadows in urban areas [11] . Moreover, they utilize a Boolean set to classify each pixel as either water or non-water, and fail to achieve the desired accuracy, especially at the water-land (i.e., non-water) interface [12] . Single-band thresholding methods select a single diagnostic spectral band from Landsat images (e.g., band 5 from TM/ETM+) and delineate the urban surface water coverage with a manually-defined threshold [18] . Accordingly, the subjectivity of the threshold selection can lead to an overestimated or underestimated result and, moreover, the extracted surface water is affected by shadow noise [16] . Different from the above two methods, water index methods combine two or more spectral bands using algebraic operations to enlarge the divergence between water and non-water areas. McFeeters proposed the normalized difference water index (NDWI) to delineate urban surface water. The NDWI is implemented with a ratio model using the green band (i.e., band 2) and the near-infrared band (i.e., band 4) from Landsat TM/ETM+ data [15] . An empirical value of 0 is set as the threshold for extracting surface water from the raw Landsat images, and pixels with positive NDWI values are regarded as belonging to surface water. Unfortunately, the obtained NDWI surface water suffers from noise in built-up areas, and the threshold of 0 always results in an over-estimation of the surface water [16] . Subsequently, Xu presented another surface water index called modified normalized difference water index (MNDWI) [16] . MNDWI improves NDWI by replacing the near-infrared band (i.e., band 4) with the middle-infrared band (i.e., band 5) from Landsat TM/ETM+ images. MNDWI reduces the built-up area noise in NDWI, and it performs better than NDWI in extracting urban surface water where built-up areas dominate in the image scene. Nevertheless, the threshold of MNDWI is difficult to estimate because of their scene-driven features, and the problem adversely impacts its realistic performance of MNDWI [8]. To address the instability of MNDWI, the automated water extraction index (AWEI) was presented by combining multi-band Landsat images (i.e., bands 2, 4, 5, and 7 of Landsat TM/ETM+ images) [9] . The AWEI argues that the threshold of 0 is a good initialization for urban surface water extraction in the method. The above three types of methods greatly benefit the studies of urban surface water extraction. However, one big problem of mixed pixels still exists in the urban surface water extraction procedure when using moderate spatial resolution Landsat images. In particular, the problem becomes more pronounced when extracting accurate boundaries of surface water. A simple cause for this problem is that the scale of urban land cover is often smaller than the field of view in the Landsat TM/ETM+ sensor (30 m) [19, 20] . Subsequently, a few sub-pixel classifiers were presented to handle the mixed pixel problem. Sethre proposed a sub-pixel classifier named analysis spectral analytical process (AASAP), which aimed to expand the regular classifier into the sub-pixel field to detect the size and shape of ponds [21] . The classifier focuses on sub-pixel wetlands or ponds and requires careful verifications when implemented in the case of urban water extraction. Sun optimized the training samples with mixed training samples and then combined them with the support vector machine (SVM) classifier to improve the urban surface water extraction results [22] . However, the scheme suffers from slow Remote Sens. 2017, 9, 428 3 of 15