## 2 Materials and Methods
### Data Analysis Workflow  
The two overarching goals for this paper were as follows: (1) determining whether CMAC applied to correct L8/9 images provides comparable SR retrievals to LaSRC; (2) evaluating the precision, accuracy and consistency of CMAC SR output derived through MPC in comparison to LaSRC. CMAC performance for v1.1L SR retrieval for L8/9 data is near-real-time, requiring about one minute per image using a compiled C++ implementation executed on a desktop PC with 64 GB system RAM. Thirty-one images were selected and downloaded as standard TOA and LaSRC-corrected products from USGS EarthExplorer [17]. The TOA radiance product was processed to TOAR following the published radiance-to-reflectance conversion workflow [12]. Collection dates for the 31 images were selected to minimize the influence of solar zenith  
Figure 4: The five QIAs selected for analysis, displayed on a Landsat 8 TOAR image. The QIAs are named for their municipalities: Ontario-3 (**a**); Ontario-2 (**b**); Ontario-1 (**c**); Rochester (**d**); and Fontana (**e**). Ontario-1 was also used for MPC calibration. angle (SZA) that would alter building shadows in the QIA and the solar irradiance path-length through the atmosphere. The dates ranged from June 13 to August 11 of 2019, 2020. 2021 and 2022. The scene center SZA ranged between 21.8\({}^{\circ}\) and 28.0\({}^{\circ}\). The same analytics described in paper 1 were applied to the extracted SoCal v1.1L-treated statistical distributions of each image generated from 21 set percentile increments of reflectance: 1%, 3%, 5% and in 5% increments to 95%. This data characterization permitted comparing the distributions for three reflectance \"treatments\": uncorrected TOAR and CMAC and LaSRC SR retrievals. All numerical reflectance values were extracted from the pixels within QIA shapefiles and scaled by 10,000 following the convention adopted by the Sentinel 2 program [8]. In the graphical figures that follow, data are listed as DN (digital number) within the range of 16-bit unsigned integers. Four tests were performed to assess the performance of CMAC versus LaSRC. **Test 1. Performance statistics of corrected images under low-to-moderate Atm-I:** Data were extracted from the 31 images of the Ontario-1, Fontana, Rochester, Ontario-2, and Ontario-3 QIAs. These images were obtained under Atm-I conditions that ranged from relatively clean (Atm-I = 883) to moderate (Atm-I = 1088). Statistical metrics of the CMAC and LaSRC outputs of reflectance averages, standard deviations and coefficients of variation (CV% = StDev/Average \(\times\) 100) were compared across the suite of images for each of the five QIAs. Error estimates were generated based on the logical and measurable assumption that images with the lowest Atm-I values provide best available estimates of true SR. Data distributions from the five lowest Atm-I images were selected and averaged for each QIA to control uncertainty in error estimation. These best-available SR estimates for each QIA were treated as the standard for percent error calculation at each percentile step of each image of each QIA: % error = (value \(-\) standard)/standard \(\times\) 100). For the error calculation of LaSRC, the low Atm-I percentile LaSRC averages were used as the appropriate reference standard. Likewise, the percentile-wise Atm-I averages for CMAC were used as the standard for assessing CMAC. **Test 2. SR distributions derived under low-to-moderate Atm-I:** The CMAC v1.1-L output was compared to LaSRC output in the form of average cumulative distribution functions (CDFs) extracted from the images of each QIA for each band. This test was performed to determine the reproducibility and stability of CMAC and MPC calibration, and to determine whether CMAC v1.1L measures reflectance of L8/9 data within the same numerical ranges as LaSRC. This was tested through displays of the average reflectance distributions of CMAC and LaSRC results compared to TOAR for each band of the 5 QIAs.