4.2.1. Atmospheric Correction

Remote-sensing applications require removing the atmospheric effect from the imagery, to retrieve the spectral reflectance of the surface materials. In this study, the data were atmospherically corrected using the quick atmospheric correction (QUAC) algorithm [34,35], since we had no prior knowledge to perform empirical calibration [36,37]. QUAC is an in-scene approach, requiring only an approximate specification of sensor band locations (i.e., central wavelengths) and their radiometric calibration; no additional metadata is required [35]. QUAC does not involve first principles radiative transfer calculations, and therefore it is significantly faster than physics-based methods; however, it is also more approximate [35].

#### 4.2.2. Data Masking, Geocorrection, Reprojection, and Resampling

In this study, we use the Airborne Processing Library (APL) software for processing the data [38]. The first step of the APL processing is to apply the mask of bad channels to atmospherically corrected data, creating a new file with bad channels set to zero (Appendix A on Figure A1). The next step uses the navigation file, the view vector file, and the digital elevation file (DEM) to calculate the ground position for each pixel then change the projection to UTM (Universal Transverse Mercator) Zone 28N [38]. We used satellite-based ASTER sensor for the DEM. In the final step we resampled output pixel size to ~3.5 m according to the height above ground level (AGL) that is given by the theoretical pixel size chart that can be found in Appendix A on Figure A2 (https://nerc-arf-dan.pml.ac.uk/trac/ wiki/Processing/PixelSize) [39].

#### 4.2.3. Endmembers Selection

The conventional image-based endmember selection approach based on scatterplots of the image bands may not be effective in identifying a sufficient number of endmembers. In this paper, we employed the sequential maximum angle convex cone (SMACC) algorithm [34] to identify spectral image endmembers. Endmembers are spectra that represent pure surface materials in a spectral image. The extreme points were used to determine a convex cone, which defined the first endmember. A constrained oblique projection was applied to the existing cone to derive the next endmember. The cone was then increased to include a new endmember [8,40]. This process was repeated until a projection derived an endmember that already existed within the convex cone, or until a specified number of endmembers was satisfied [21]. When implemented with SMACC, the output endmember number was set as 5, 10, 15, 20, and 30 respectively. Better endmembers could be identified easily from the 15 endmembers output (more detail in Section 6.2). Then, we used the selected 15 endmembers for deriving the abundance.

#### 4.2.4. Linear Spectral Mixture Analysis

The linear spectral mixture analysis (LSMA) approach was adopted to calculate the abundance of endmembers for each pixel. LSMA assumes that the spectrum measured by a sensor is a linear combination of the spectra of all components (endmembers) within the pixel, and the spectral proportions of the endmembers (i.e., their abundance) reflect the proportion of area covered by distinct features on the ground [8,21]. The general equation for linear spectral mixing can be expressed as:

$$\mathcal{R}\_{ij,\lambda} = \sum\_{n=1}^{N} p\_{ij,n} \mathcal{R}\_{n,\lambda} + E\_{\lambda} \tag{1}$$

where *Rij,<sup>λ</sup>* is the measured reflectance at wavelength *<sup>λ</sup>* for pixel *ij*, where *<sup>i</sup>* is the column pixel number, and *<sup>j</sup>* is the line pixel number; *pij,n* is the fraction of endmembers *<sup>n</sup>* contributing to the image spectrum of pixel *ij*; *<sup>N</sup>* is the total number of endmembers; *Rn,<sup>λ</sup>* is the reflectance of endmember *<sup>n</sup>* at wavelength *<sup>λ</sup>*; and *<sup>E</sup><sup>λ</sup>* is the error at wavelength *<sup>λ</sup>* of the fit of *<sup>N</sup>* spectral endmembers. The fraction *pij,n* can be solved using a least-square method with fully constrained unmixing. Fully constrained unmixing means that the sum of the endmember fractional (abundance) values for each pixel must equal unity, which requires a complete set of endmembers. Therefore, it should meet the following two conditions:

$$0 \le p\_{ij,\mu} \le 1 \tag{2}$$

$$\sum\_{n=1}^{N} p\_{ij,n} = 1\tag{3}$$

In the majority of cases, the unmixing is only partially constrained because the extracted endmember set is incomplete for the image and only term (2) (i.e., Equation (2)) is satisfied. In this study, fully constrained LSMA were applied to the FENIX image to obtain the abundance result and both SMACC and LSMA were executed by ENVI 5.3 and IDL 8.5 language programming.

**Figure 4.** The workflow processing to derive an abundance map from the FENIX hyperspectral data
