**1. Introduction**

Fire behavior, size, and severity are changing in the western United States [1–3]. To fully comprehend these changes, techniques to reliably map fire effects over large areas are required. The most common means of assessing fire severity with remote sensing is using the Normalized Burn Ratio (NBR) and its derivatives [4,5]. NBR based techniques are popular because of their simplicity, ease of use, and relatively good performance when compared to field measurements [6,7]. The NBR, however, is sensitive to variations in soil brightness [8], vegetation type [9], and vegetation density [10]. These limitations constrain the use of NBR-based indices for consistent fire severity assessments over large areas within heterogeneous ecosystems [10]. Variation in fire severity can effectively be broken down into detectable differences in the relative abundance of char, green vegetation, dead vegetation, and bare soil; remotely sensed fire severity assessments are therefore essentially based on mixtures composed of these four constituents. Under this paradigm, Spectral Mixture Analysis (SMA), in which reflectance is assumed to a be a linear combination of components or endmembers at a subpixel level [11,12], represents a viable alternative to NBR-based analysis, potentially overcoming NBR's sensitivity to different cover type and soil brightness variation [13,14]. SMA has been used previously to characterize tree mortality and soil char cover [10,15–18].

Lentile et al. [19] defines fire severity as the immediate ecosystem impacts of fire; burn severity, in contrast, is defined as the combined shorter and longer term ecosystem impacts and response to fire. Key and Benson [4] also separates first-order effects, which are related to the fire only, and second-order effects, which are related to other environmental (e.g., wind and rain) and vegetative processes. Veraverbeke et al. [20] followed these conventions and used the term fire severity when images were acquired soon after the fire (e.g., within the first month) and second-order effects can safely be neglected.

In SMA, an endmember class is one of the categories the image will be divided into, and an endmember is the individual training spectra that are constituents of each endmember class. In simple SMA, only one endmember represents each endmember class across the image. Multiple Endmember SMA (MESMA), in contrast, allows the endmember representing each endmember class to vary on a per-pixel basis [21]. This approach accounts for the variability that may exist within each endmember class and further allows for consistency and accuracy across ecosystems where there could be considerable spectral variability within an endmember class [21,22].

SMA is particularly well suited for imaging spectrometry data, as the large number of bands provide additional information for cover type discrimination in critical, but spectrally narrow regions; for example, the red edge for green vegetation discrimination [23]. The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), samples spectra from 350 nm to 2500 nm at a nominal sampling interval of 10 nm [24]. There is currently no spaceborne imaging spectrometer with a similar signal-to-noise ratio to AVIRIS and global coverage with frequent return intervals, which currently impedes the use of imaging spectroscopy for fire severity comparisons at regional scales and over longer time periods. However, there are several proposed spaceborne imaging spectrometers, including the Environmental Mapping and Analysis Program (EnMAP, [25]), the PRecursore IperSpettrale della Missione Applicativa (PRISMA, [26]), and the Hyperspectral Infrared Imager (HyspIRI, [27]), that would make using imaging spectroscopy to monitor fire severity possible at regional to global scales within the decade.

A drawback of MESMA, particularly if three or more endmember classes are allowed to be modeled within a single pixel, is that the number of endmember combinations tested can be large. A variety of approaches have been developed that attempt to select the minimum number of spectra in a library needed to represent within endmember class variation and therefore eliminate redundant spectra. Many techniques focus on automated or semi-automated endmember selection, which identifies pure pixels through the extremes of image data [28] or the construction of synthetic endmembers based on image data [29]. Other techniques first create a large spectral library from various sources and then reduce its size to achieve a library that is both parsimonious and captures each endmember class's variability [30–32]. Several means exist to evaluate which endmembers to keep. Generally, criteria evaluated focus on either which endmembers best represent their endmember class [33–35], or which endmembers best model the library as a whole [31]. All techniques have slightly difference balances between capturing spectral variability and creating efficient libraries. While there

are several studies reviewing endmember extraction techniques [36–38], the comparison of endmember selection techniques for MESMA is rare [32], and to our knowledge, there has been no evaluation of various endmember selections techniques for cover fraction identification (MESMA with multiple non-shade endmembers allowed per pixel).

Individual bands in imaging spectroscopy tend to be highly correlated, and the inclusion of all bands in image analysis techniques increases computational times and can decrease accuracy [36,39]. Data reduction techniques are therefore often applied imaging spectroscopy data sets prior to SMA [36]; two of the more common are Principal Component Analysis (PCA; [40]) and maximum noise fraction (MNF; [41]). PCA, MNF, and similar techniques reduce data dimensionality based on the spectral properties of the image; however, they do not necessarily do so in a manner that improves separability between endmember classes [42]. Asner and Lobell [43] proposed a data reduction technique designed specifically to improve the accuracy of SMA when applied to plant cover with AutoSWIR. AutoSWIR uses a priori optical properties of leaf, litter, and soil material to select critical spectral regions to use for spectral unmixing. Somers et al. [44] proposed a technique similar to AutoSWIR in stable zone unmixing (SZU), which uses variability within and between endmember classes to select spectral regions to use in SMA. Since SZU is based solely on the input spectral library, it has the built-in assumption that the endmembers in a spectral library are representative of the variability of the spectra in the image to be analyzed; however, it has the advantage of selecting spectral regions specific to the problem. SZU has been demonstrated to be effective in invasive species monitoring, soil type classification, and oil spill detection and tracking [44–46]. Neither autoSWIR nor SZU specifically addresses the highly correlated nature of adjacent bands. Somers and Asner [47] proposed a further refinement on SZU, uncorrelated SZU (uSZU), which selects bands that capture the maximum variability within and between endmember classes while eliminating highly correlated bands. uSZU was shown to have improved cover abundance estimate accuracy and performance times compared to SZU [47].

In this study, we test the ability of imaging spectroscopy based MESMA to derive cover fractions that correspond with field measurements. Additionally, we test the specific effects of four different endmember selection techniques and one band reduction technique on MESMA's accuracy and processing time in the context of deriving indicators of fire severity of a large wildfire using imaging spectroscopy.
