## 2 Materials and Methods
### Data Analysis Workflow
Tests 1 and 2 provided a robust sample for analysis of atmospheric correction for three treatments, TOAR, CMAC and LaSRC, across the 31 images in each of the five QIAs evaluated in 21 percentile-steps of the reflectance distributions. This sampling provided 9765 separate statistics for each band. **Test 3. Quantitative performance in moderate-to-extreme Atm-I:** Atm-I is increasing due to climate change-driven wildfires in many regions around the globe. For example, smoke from pervasive West Coast, Intermountain Region and Canadian wildfires dominates the skies across the American Midwest and much of North America during each summer growing season at levels that impact imagery-based applications for precision agriculture and carbon farming. Similarly, extreme anthropogenic emissions in Southern Asia produce high levels of visible haze that may impact remote sensing applications through much of the year [18]. Tests 1 and 2 were performed using QIA targets known to express consistent reflectance through the summer period. However, the images used captured only low-to-moderate levels of Atm-I. Located in an urbanized region of Southern California within 60 km of the Pacific Ocean to the west and receiving onshore southwesterly winds throughout each summer day, the SoCal QIAs offered no potential to assess AC performance for high levels of Atm-I resulting from wildfire smoke or other causes. Future remote sensing applications are expected to be dominated by automated applications applying various indices, e.g., NDVI. To answer the question of how the increasing levels of smoke will affect such applications, Test 3 was formulated to investigate how such indices, generated from TOAR, CMAC and LaSRC-corrected data, perform under moderate-to-extreme Atm-I conditions. In Test 3, CMAC and LaSRC-corrections were compared across low Atm-I that were assessed first in Tests 1 and 2. Landsat images acquired over British Columbia, Canada, that were expected to form QIAs with consistent surface reflectance conditions across yearly snapshot-in-time images were identified exhibiting low Atm-I and high Atm-I. Sampling was performed for these conditions from clear conditions and from visibly homogeneous haze in three urban locations: Penticton, Kelowna and Vernon. Polygons were mapped to enclose visibly homogeneous areas of haze (Figure 5). Landsat images were selected to support this analysis from three consecutive years within a six day-of-year time span for each year: 3 August 2021 (smoke-affected L8) and 6 August 2022 (clear L8) and 1 August 2023 (clear L9). The third image was selected to test an assumption underlying this experimental design: that the conditions affecting peak vegetation expression were consistent across the annual snapshots during the day-of-year period of image selection. The peak plant expression in these polygons was not expected to be limited by antecedent rainfall because of irrigation. Three circular sample areas were mapped around each of the three city polygons to include and sample irrigation-cultivated crops. For direct comparison between clear versus smoke-affected conditions, the pixel values for blue, green, red and NIR were extracted for the three treatments from the three images for the 20 pixels expressing the highest NDVI values in each sampled circle. The null hypothesis was for no difference among the three years, confirming that the predisposing environmental conditions were consistent and that the treatment was effective for SR retrieval. A fair comparison among the three years was sought through a checklist of conditions to be met to assure that peak NDVI would be present each year: irrigated crops cultivated in a strongly Mediterranean-type climate, sampling at the height of the growing season, nearly exact day-of-year image snapshot times, and relatively large, sampled areas encompassing numerous cultivated fields. These considerations were expected to isolate the effects of the smoke haze on the images and for the treatments.