# Closed-Form Method for Atmospheric Correction (CMAC) of SmallSat Data Using Scene Statistics
###### Abstract  
High-cadence Earth observation smallsat images offer potential for near real-time global reconnaissance of all sunlit cloud-free locations. However, these data must be corrected to remove light-transmission effects from variable atmospheric aerosol that degrade image interpretability. Although existing methods may work, they require ancillary data that delays image output, impacting their most valuable applications: intelligence, surveillance, and reconnaissance. Closed-form Method for Atmospheric Correction (CMAC) is based on observed atmospheric effects that brighten dark reflectance while darkening bright reflectance. Using only scene statistics in near real-time, CMAC first maps atmospheric effects across each image, then uses the resulting grayscale to reverse the effects to deliver spatially correct surface reflectance for each pixel. CMAC was developed using the European Space Agency's Sentinel-2 imagery. After a rapid calibration that customizes the method for each imaging optical smallsat, CMAC can be applied to atmospherically correct visible through near-infrared bands. To assess CMAC functionality against user-applied state-of-the-art software, Sen2 Cor, extensive tests were made of atmospheric correction performance across dark to bright reflectance under a wide range of atmospheric aerosol on multiple images in seven locations. CMAC corrected images faster, with greater accuracy and precision over a range of atmospheric effects more than twice that of Sen2 Cor. s _applied_  
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on dense dark vegetation [8; 9; 10]. Other AC methods have used multi-temporal datasets for aerosol and surface reflectance retrievals [11; 12; 13]. However, such datasets are inherently unreliable because conditions may change profoundly between dataset acquisitions, as shown in Figure 1. Few of these algorithms can work in near real-time, and many are not readily automatable. Near real-time corrected image output with accuracy and precision is needed to serve the expected future massive data volume generated by smallsats. Closed-form Method for Atmospheric Correction (CMAC) is a software package that was developed using Sentinel-2 (S2) image data specifically for application to smallsats. CMAC works in near real-time to convert top-of-atmosphere reflectance (TOAR) directly to surface reflectance, uniquely using only the statistics from the image. In contrast, automated AC methods in current use are all based upon radiative transfer (RadTran), which requires knowledge of sensor radiometry. This is problematic for smallsats that omit onboard radiometric calibration equipment to conserve weight and size. To maintain AC accuracy for any method, sensor radiometry must be updated periodically to counter changes in sensor response that are well known to degrade after launch and while in orbit [14]. Hence, for the ideal application of RadTran, sensor radiometry must be tracked for each smallsat. Also required for the RadTran workflow are ancillary data collected by other satellites for  
Figure 1: Inexact synchronicity is a source of error for ancillary image application as shown in the following example: (**a**) 14 August 2021 Sentinel 2 TOAR RGB of southern Minnesota, (**b**) the cirrus band (B10) of the same scene, and (**c**) the cirrus band (B09) of Landsat 8 taken about 18 min before. Cirrus affects visible bands as in (**a**). the evaluation of atmospheric conditions. Such ancillary data delays AC, thus increasing the latency of the corrected output in direct opposition to the principal value of smallsats: near real-time data for intelligence, surveillance, and reconnaissance afforded by the rapid image cadence from flocks of multiple smallsats. Although delayed image processing due to ancillary data is problematic, a potentially greater impact may arise from frequently mismatched conditions between datasets caused by atmospheric changes in the elapsed time between image captures (Figure 1).