**4. Discussion**

#### *4.1. Potential Bias and Uncertainty in the Cover Types*

Whereas previous studies found the relationship between the char fraction and GeoCBI to be linear [18,58] this was not the case in this study. The GV fraction retrieval by MESMA, was found to be linear, however. GV's high accuracy is likely due to both the spectral separability and the temporal persistence of the class. In contrast to GV, at the spectral resolution of WorldView-2 soil, NPV, and ash were all somewhat difficult to separate. Human interpretation likely reduced inter-class confusion in classifying the WorldView-2 imagery, but this was still a source of error associated with the WorldView-2 image classification. In particular, separation of the soil and ash areas was particularly difficult with the WorldView-2 imagery. This is partially because of insufficient spectral information and partially because even at 2 m pixel resolutions, many pixels were likely a mixture of mostly ash with some soil. This mixture would impact the spectral signal, and therefore be reflected in the MESMA generated cover fractions, but these areas were generally just classified as ash in the manual interpretation of the WorldView-2 image. Another possible factor in diminished char is the amount of time between when the fire burned the area of the GeoCBI plots, which was in late August and early September (evaluated from fire spread map in [59]), and image acquisition, which was 28 September for the WorldView images and 17 November for AVIRIS. During the time period between the fire occurring and AVIRIS image acquisition, there were four rain events totaling 64.8 mm at a weather station in Groveland, CA (data accessed from http://www.ncdc.noaa.gov/cdo-web/datasets#GHCNDMS) within 20 km from where the field plots were collected. Combined with wind, rain likely attenuated the ash portion of the char signal. The impact of weather, combined with other previously mentioned

factors, likely account for why char was more prevalent and soil less prevalent in the WorldView-2 classification than the MESMA cover fraction (Figure 6).

#### *4.2. Evaluation of MESMA Techniques' Performance*

The balance of library complexity with accuracy must be considered if MESMA is to be used on spaceborne imaging spectroscopy at regional to global scales for ecological monitoring [58]. Schaff et al. [31] and Roth et al. [32] have shown IES endmember selection produces high classification accuracy in the two endmember MESMA case. However, IES selected the most endmembers in its final spectral library in our study and when compared to other methods in [32]. In this study, regardless of the technique used to generate cover fractions, the more spectrally unique classes (GV and ash) had approximately similar performances when compared with the WorldView-2 cover fractions. Using uSZU In-CoB to generate MESMA cover fractions produced relatively high r2 values when compared to WorldView-2, even though the number of endmembers used and processing times were significantly less. That a variant of In-CoB would perform as well as IES is not consistent with [32]. One possible explanation for this is that when using endmembers for classification of vegetation types, as was done in [32], some degrees of mixture within endmembers, particularly with soil and NPV, is necessary for accurate classification across a landscape. If endmembers within the endmember classes of the starting library are to some degree mixed, in order maximize kappa IES will tend to select mixed pixels. However, when using MESMA for spectral unmixing to estimate cover fractions, as was done in this study, the purest endmembers will obtain the highest accuracy.

The margin of computational efficiency created by uSZU, a 30–50% reduction in processing times, was similar to Somers and Asner [47]. However, unlike [47], we did not observe a clear trend of increased accuracy (Table 6). In Figure 5 and Table 3, it is clear that the techniques that used uSZU generally mapped less NPV than techniques that did not. Spectral regions that are critical for the separation of soils and NPV due to their association with lignin and cellulose absorption, such as the 2300–2400 nm region [60], did not ge<sup>t</sup> selected by uSZU (Figure 4). Many of the bands which were selected appear associated with atmospheric noise. In Veraverbeke et al. [58] bands were reduced to similar numbers as the uSZU, however they were not selected in a way that was designed to maximize differences between endmember classes, resulting in a much larger decrease in accuracy than was observed here. Future studies should investigate other band selection techniques and the optimal bands for the simultaneous separation of GV, NPV, soils, and ash.

#### *4.3. Endmember Sources and Endmember Selection*

Beyond pre-processing, another challenge to SMA becoming a global means of objective comparison is determining a proper base spectral library. Studies have shown the timing of the acquisition of the base spectra and the image is important [61], as is the spatial scale that the spectra were acquired [35,51]. It is notable that spectra collected in a different spatial location than the images and at different spatial scales than the images, were frequently selected to model cover fractions. This suggests that a common spectral library could be developed to map fire across at least a regional scale. It also suggests that even in environments not composed of as many complex materials as the urban [35,62,63], a diversity of spatial scales may be beneficial to cover fraction mapping.

Although, impurity of endmembers collected in non-laboratory settings is inevitable, it is a particular challenge at the spatial scale of AVIRIS or proposed spaceborne imaging spectrometers. It is notable that the endmember classes which it is most difficult to ge<sup>t</sup> pure pixels from images, NPV and soil (that was not exposed rock), also appeared least accurate. Although spectra collected in the field were included in our spectral library, these may not perfectly scale to the canopy level AVIRIS observations [51]. AVIRIS-Next Generation (AVIRIS-NG; [64]) poses a potential means for overcoming some of these challenges [55]. The superior spatial and spectral resolutions allows for collecting and evaluating endmembers that are closer to being pure while still being collected at the canopy-scale of AVIRIS.

#### *4.4. SMA as a Novel Means for Assessing Fire Severity*

Since properly identified cover fractions have physical meaning, they have the potential to be an objective and global means of assessing fire severity. Cover fractions, if shown to be accurate and comparable to field derived fire severity estimates, have the potential to overcome many of the criticisms of NBR-based indices [10,19,65,66]. With the potential launch of several spaceborne imaging spectrometers, and considering the demonstrated higher correlations of SMA with imaging spectroscopy data compared to broad-band data [58], the use of SMA for fire may increase in the future. Since the variation of soil and GV's spectral profile across space is one of the key reasons for NBR's subjectivity, if SMA is going to become an important means of assessing burn severity, endmember variability must be accounted for, and MESMA is one of the most reliable technique for doing so [22]. In this study, only a single fire is included in the study area; however, if SMA is to become a commonly used tool for fire severity assessment, a global assortment of geographic locations and their spectral variability will need to be tested and compared. As imaging spectroscopy data becomes more common, both through more airborne and spaceborne acquisitions, global assessment will become viable.

One possibility for assessing change using SMA is using a differenced SMA (dSMA) approach. By using dSMA the entirety of the information provided by MESMA classes could be used, potentially providing a robust and more ecologically meaningful method of evaluating fire severity. However, this approach would have an inherent disadvantage of all differenced imagery comparisons, in that relatively analogous pre-fire imagery would be needed. Since all imaging spectroscopy data with signal-to-noise ratios and spectral and spatial resolutions similar to AVIRIS are currently acquired from airborne platforms, pre-fire data is rare; however proposed spaceborne imaging spectrometers such as HyspIRI and ever-increasing computational power would make this analysis possible at regional to global scales. Future studies evaluating dSMA usefulness in fire severity evaluation will require careful planning in field validation plot placement to assure that plots are placed in areas that pre-fire were heterogeneous in terms of type and percentages of vegetation cover. Given the relative accuracy of mapping the GV cover class, using a differenced GV cover fraction (dGV) is likely to have high correlation with the field measures of burn severity. In addition, the high correlation observed for the char cover type, suggests that adding a post-fire char cover to a dGV assessment could further enhance the discrimination of burn severity.
