## 3 Methodology
### Accuracy Assessment  
Smoke detection performance of the SSDA was evaluated both qualitatively and quantitatively. First, smoke detection results were evaluated qualitatively using VIIRS true-color images over two recent big fire events in Australia and California. Australia's 2019-2020 bushfire event lasted several months, from October 2019 to February 2020. It resulted in more than six million hectares of land burned, several people died, and billions of animals exterminated [57]. The 2020 fire season in the western United States of America (USA), mainly California, was the most active of the last few years. From mid-August to October, intense fires in the western USA produced large amounts of smoke aerosols that drifted north and east. At present (mid-October 2020), the fires are still burning. In addition, the SSDA smoke detections were also visually compared with other smoke-related datasets, including aerosol detection product (ADP), TROPOMI smoke, and two published smoke results [15; 58] for several other small fire events.  
Second, the SSDA smoke detection was quantitatively evaluated over the selected 109 image subsets from August 2018, as described in Section 2.6.3. The evaluations included: (1) AOD values of smoke and non-smoke pixels from the SSDA were compared with those from VIIRS ADP and TROPOMI smoke; (2) the SSDA smoke detection was statistically assessed using the manually delineated smoke reference data, VIIRS ADP, and TROPOMI smoke based on several indexes including smoke percentage, overall accuracy, commission error, and omission error. The smoke percentage is the ratio of smoke pixels to the total pixels within each subset image Equations (1) and (2). The overall accuracy is the probability that a smoke or non-smoke pixel is correctly classified Equation (3). The commission error of smoke refers to the fraction of non-smoke pixels that are classified as the smoke class Equation (4). In contrast, the omission error of smoke represents the fraction of smoke pixels that are misclassified as the non-smoke class Equation (5). The commission error and omission error are the complements of the producer's accuracy and the user's accuracy, respectively. These indexes were calculated as follows:  
\[Ref_{sp}\ =T1/(T1+T2) \tag{1}\]  
\[Class_{sp}\ =\ (S1+S2)/(T1+T2) \tag{2}\]  
\[OA=(T1+S2)/(T1+T2) \tag{3}\]  
\[CE=S2/(S1+S2) \tag{4}\]  
\[OE=N1/(S1+N1) \tag{5}\]  
where \(Ref_{sp}\) is the smoke percentage reference; \(Class_{sp}\) is the smoke percentage of smoke detection from different products; \(OA\) is overall accuracy; \(CE\) is commission error; \(OE\) is omission error; \(T1\) and \(T2\) are the total number of pixels inside and outside of the delineated smoke polygons, separately; \(S1\) and \(S2\) are the number of smoke pixels inside and outside of the referenced smoke plume, respectively; and \(N1\) is the number of non-smoke pixels inside the referenced smoke plume.  
Finally, we tested the global application of the SSDA algorithm by calculating one-month smoke occurrence frequency based on daily smoke detection during August 2018 and analyzed its spatial distribution pattern by comparing it with a fire density map derived from VIIRS 750 m active fire observations collected in August 2018.