## 2 Data and Methods
### Extraction of Impervious Surface Distribution  
#### 2.2.1 Proposed Method  
According to the vegetation-impervious surface-soil (VIS) model [24], land cover consists mainly of vegetation (V), impervious surfaces (I) and bare soil (S), with the exception of water bodies. In remote sensing imagery, the largest difference in land cover is that between water bodies and land, and land can further be divided into impervious surfaces and permeable surfaces (vegetation and bare soil). Hence, the workflow can be divided into two steps, namely, masking water bodies and extracting impervious surfaces from land.  
An impervious surface is an area without vegetation coverage and thus has a lower NDVI value [25]. Studies by [PERSON] et al. and [PERSON] et al. showed that impervious surfaces usually have higher values in the blue band [10; 26]. Besides, [PERSON] pointed out that the coastal band in Landsat 8 imagery can enhance information on impervious surfaces more significantly than the blue band, and the addition of the coastal band in the supervised classification of land use is beneficial for further distinguishing impervious surfaces from other ground objects [27].  
In this study, a RISI was proposed for extracting impervious surface distribution on the basis of the coastal band and NDVI of a digital number (DN) image and is defined by Equation (1):  
\[RISI=\frac{B1}{NDVI1} \tag{1}\]  
where B1 and NDVI1 denote the coastal band and NDVI, respectively, after a 0-1 transformation.  
The workflow comprises the following four steps:  
(a) Water bodies are first masked;  
(b) The coastal band undergoes a 0-1 transformation to obtain B1;  
(c) The NDVI is calculated, and then a 0-1 transformation is performed to obtain NDVI1; and  
(d) The RISI is calculated and then segmented using a threshold determined by the Otsu method [28].  
1. Water Body Masking  
Figure 1: (5, 4, 3) false colour composite images with a linear stretch of 2%: (a) Case 1, 2017/7/21; (b) Case 2, 2014/7/23; (c) Case 3, 2013/12/13.  
The water body index (WI) is calculated using Equation (2) [29]:  
\[WI=\frac{Green}{SWIR1} \tag{2}\]  
where Green denotes the green band and SWIR1 denotes the shortwave-infrared band.  
The value corresponding to the right valley of the WI histogram is manually fine-tuned as the segmentation threshold to mask water bodies.  
2. 0-1 Transformation of the Coastal Band  
The coastal band undergoes a 0-1 transformation to obtain B1 according to Equation (3):  
\[T1=\frac{T0-min}{max-min} \tag{3}\]  
where T0 and T1 denote the band before and after the 0-1 transformation according to Equation (3), respectively, and max and min are the maximum and minimum values of the band, respectively.  
3. Calculation of the NDVI  
The NDVI is calculated using Equation (4) [30]:  
\[NDVI=\frac{NIR-Red}{NIR+Red} \tag{4}\]  
where Red denotes the red band and NIR denotes the near-infrared band. Then, the NDVI undergoes a 0-1 transformation to obtain NDVI1 in an analogous way to Equation (3).  
4. Calculation of the RISI  
The RISI is calculated using Equation (1), and then its threshold is determined by the Otsu method and used to segment the image to obtain the impervious surface region.  
The Otsu method is an adaptive threshold determination method and is widely used in image segmentation, which maximizes the class variance between objects and background [28].