## 2 Materials and Methods
### Master Satellite (S2) Calibration and Translating the Calibration to the Proxy L8/9 Satellites  
CMAC calibration enables SR retrieval applications for new, proxy satellites through two possible pathways. Precise calibration can be performed using a purpose-built calibration target. However, no such target yet exists; hence, vicarious (image-to-image) methods were employed. Multiple overpasses were averaged to control the uncertainty inherent in vicarious calibration.  
Assessing how each band's TOAR deviation line slopes and offsets change according to the driving variable, Atm-I, constitutes CMAC calibration. Though simple in concept, Atm-I is variable across a wide range of image states from clear conditions to extreme haze. While calibration could include iterative fitting and testing as different ranges of Atm-I are recorded, such processing is prohibitively time-consuming for application to the many calibrations required annually for an expected vast field of imaging smallsats. As an example of this potentially protracted process, the CMAC S2 calibration alone required several years of testing and analysis. Fortunately, through observation, the calibrated points of slope and offset on the driving parameter of Atm-I form families of curves that stack in Cartesian space according to wavelength. This fact enables master calibration curves to guide extrapolation of single precise proxy calibration points for the slope and offset of each band. The existence of this family-of-curves structure demonstrates that atmospheric reflectance responses are highly structured. Calibration simply encodes bandwise reflectance responses to enable reversing the reflectance changes due to atmospheric transmission.  
The data to run vicarious calibration was extracted from multiple images of the Ontario-1 QIA. The first step for the proxy L8/9 calibration was to run the S2 Atm-I model on the L8/9 images and perform cross-calibration to calculate a relationship that emulates S2 Atm-I results. This was a necessary step because the relative spectral responses (RSRs) of the S2 bands are different than those of L8/9; hence, the input and output statistics from the Atm-I model are different. However, the RSRs of the four VNIR bands of  
Figure 3: A figure from [PERSON] and [PERSON], 1985 [14].  
these two satellites are sufficiently close that the model derived for S2 also functions for L8/9 though imperfectly. A linear function resulting from the cross-calibration of same-day overpasses was added to adjust the S2 Atm-I model output for L8/9 to emulate S2 and included as a step in the CMAC L8/9 software v1.1L. During these and other analyses, no overt differences were noted between Landsat 8 and 9 responses, consistent with the findings from comparison analyses by [PERSON] et al. [15]. Consequently, L8 and L9 were not considered separately.  
A second calibration step for L8/9 was applied to the Ontario-1 data to determine the slopes and offsets for multiple L8/9 low Atm-I TOAR images. The reflectance distributions of these images were adjusted through the iterative fitting of slopes and offsets to match the distributions of a best-available SR estimation from multiple low Atm-I, AC-corrected images of the Ontario-1 QIA. The Atm-I of each image and resulting proxy slopes and offsets for each band were averaged to generate single values that were then projected into the families of S2 slope and offset curves and extrapolated to enable the new L8/9 CMAC version to function across the entire range of Atm-I. This vicarious CMAC calibration workflow applied to L8/9, resulted in calibration \"v1.1L\", requiring about 6 h to select the images, extract the data, and perform the calculations.