**3. Results**

#### *3.1. uSZU Band Selection*

After uSZU of the 177 original bands, 20 were retained in the analysis. Selected bands ranged across the spectrum with a preference for the red edge (five bands were selected between 670 and 735 nm). uSZU also appears to have selected several bands that are at the edges of wavelengths removed due to atmospheric noise, suggesting the sensitivity of the technique to spectral artifacts. Figure 4 shows the final selection of bands using the uSZU algorithm.

**Figure 4.** Spectral profile of the average spectra in each endmember class (solid line), plus or minus one standard deviation of the spectral average (dotted line). Green vegetation is represented by dark green, non-photosynthetic vegetation is represented by yellow, soil is represented by blue, and char is represented by black. Spectral bands selected by the uncorrelated Stable Zone Unmixing (uSZU) algorithm are represented by red vertical lines.

#### *3.2. Endmember Selection and Processing Times*

The number of endmembers selected by each technique varied considerably (Table 2). EMC has an inherent limit to the number of endmembers that may be selected; in EMC no more than the number of endmember classes multiplied by three endmembers are kept (the maximum possible number of endmembers in an EMC reduced library is therefore 12 in this study). uSZU generally had the effect of increasing the number of endmembers selected for all techniques except EMC. The increase was generally moderate, resulting in a 10–25% increase in the number of endmembers. Despite the larger number of endmembers selected, the processing time for the MESMA algorithm was dramatically reduced for all band reduction techniques, with time reductions ranging between 30% and 55%.

**Table 2.** The number of endmembers and modeling times of various combinations of endmember and band selection techniques. Modeling time was assessed on a 640 × 530 pixel Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) scene within the Rim Fire. Models were run using a computer with an Intel Xeon central processing unit E7-4850v2 at 2.3 GHz with 48 cores and 512 gigabytes of random-access memory. Models were run in a manner to minimize run time with computer resources. Uncorrelated Stable Zone Unmixing (uSZU) represents a feature reduction technique. EMC, In-COB, and IES are all endmember reduction technique for Multiple Endmember Spectral Mixture Analysis (MESMA). Total models represents the number of models need to run four endmember MESMA.


#### *3.3. Unmixed Images and Overall Model Comparison*

The eight endmember libraries produced broadly similar patterns (Figure 5). The EMC method without band selection stands out as modeling more NPV than the others, notably modeling NPV in areas that other approaches modeled as GV. Unmixed images generated from libraries without uSZU band selection appear to have slightly more NPV than their uSZU counterparts, but otherwise give similar results.

While the models were qualitatively similar, there were quantifiable differences between them (Table 3). The number of pixels successfully modeled, defined by the number of pixels where any endmember combination tested by the MESMA algorithm resulted in an RMSE below the threshold of 0.025, ranged from 79.1% of the fire area (uSZU In-CoB) to 93.0% of the fire area (IES). Soil was the most variable endmember class between the models, with one scene containing as few as 7.5% of pixels with any modeled soil cover (uSZU EMC) to 41.8% of pixels (IES). Char and GV were the most commonly modeled endmember classes with between 36.9% and 53.1% of pixels containing char and between 35.3% and 54.1% of pixels containing GV.

**Table 3.** Percent of total pixels within the Rim Fire boundary that were successfully modeled and the percent of pixels containing each endmember class for various endmember selection techniques. In total, approximately 7,850,000 pixels within the Rim Fire boundary were considered. A single pixel was allowed to contain up to three endmember classes (not including shade).


**Figure 5.** MESMA cover fraction images within the Rim Fire burn scar, soil cover is not shown in the image series. The boundary of the Rim Fire is represented by a white line. Black indicates areas that were not classified or only had soil cover. Endmember selection and band selection techniques are as follows: (**i**) EMC; (**ii**) uSZU EMC; (**iii**) In-CoB; (**iv**) uSZU In-CoB; (**v**) IES; (**vi**) uSZU IES; (**vii**) Reduced IES, (**viii**) uSZU Reduced IES.

#### *3.4. Endmember Sources in Model Selection and the Image*

Most spectral libraries selected endmembers from all sources (Table 4). In the initial spectral library, a majority of spectra were derived from AVIRIS imagery, however, a disproportionally small amount of spectra from this source were selected by most endmember reduction techniques. This suggests that, by the metrics used by the endmember reduction techniques, most image derived spectra were redundant and were therefore eliminated. In contrast, spectra created in Wind River [51] were

disproportionally retained by most endmember selection techniques. This indicates spectra from that source were generally distinct from other spectra included in the initial spectral library.


**Table 4.** The source of endmembers for each endmember reduction technique.

When spectral libraries were used to model cover fractions across the Rim Fire, spectra generated from the AVIRIS images were disproportionally selected, given their abundance in the reduced spectral libraries (Table 5). All spectral sources were used to some degree. It should be noted that not all endmember classes modeled in this study were collected for each spectral source and there were large differences in the number of spectra collected for each source.

**Table 5.** Percentage of pixels modeled by source for each endmember reduction technique. A single pixel can be modeled by multiple different sources, resulting in totals that exceed 100%.

