# Closed-Form Method for Atmospheric Correction (CMAC) of SmallSat Data Using Scene Statistics
## 4 Discussion
Depending upon the intent of analysis, highly reflective manmade surfaces subject to such divergence from true surface reflectance may not be of interest, though their brightness certainly could be. Perhaps a better representation for such highly reflective targets is simply to map the targets that exceed some set threshold. This solution could be especially robust for machine analyses and AI while alleviating the need to adjust bright target reflectance to compensate for this systematic divergence. Such compensation can be made, but only at the cost of additional processing time. Future technical upgrades are planned for CMAC. A version that includes additional bands of interest for agriculture (such as S2's red edge bands B05-B07 and 10m NIR B08 is under development. As previously mentioned, this paper examined image data through periods selected to constrain solar zenith angle (SZA) to yield the most robust comparison possible. Otherwise, significant errors in surface reflectance estimation can occur as SZA increases in the presence of high levels of Atm-I. Such conditions force incident sunlight to travel a greater path length through layers of atmospheric aerosol, thus causing more light attenuation (i.e., reduction of signal) than from Atm-I alone. Current efforts for CMAC R&D include measuring the interactive effect of SZA and Atm-I and then formulating a bivariate model accounting for both; this is a required step to prepare AC of smallsat imagery to address all conditions that can be encountered. This advancement will be made applicable to all smallsats as a last step in CMAC processing. Pointable smallsats will open a new world of ISR application for areas of conflict to serially gather data nearly continuously during daylight. An additional application of interest involves the development of systematic adjustment for AC of data gathered from far off-nadir viewing by pointable smallsats. Through edge applications with CMAC software operating on board, pointable smallsats may effectively achieve real-time AC by correcting lines of push brown-scanned image data after a few-second lag. Such AC-corrected data could then be forwarded to AI feature extraction and on to first responders or warfighters within minutes of collection. CMAC confers promotional benefits for solving all of these problems through its simplicity, i.e., nothing is black box, and the correction is made only with scene statistics. Simply stated, this will be a rules-based \"see it, correct it\" approach for smallsat ISR. CMAC is currently applicable for nadir-look four-band smallsats and is ready for test application to other bands in the VNIR spectrum. In principle, CMAC AC should be applicable to hyperspectral image datasets. Perhaps of greater interest and utility are completed algorithms for AC application over oceans, where CMAC can produce excellent results with respect to appearance (Figure 17). AC over large water bodies is inherently more difficult than over land because the air-water interface is highly reflective and can affect AC output due to wave effects and the geometry of image capture relative to the solar angle. AC over water deserves focused R&D effort. While CMAC was developed specifically for smallsats it was enabled by the consistent quality and cadence of free data from the Copernicus S2 program that flies two research-grade satellites. For convenience, this paper applies a statistical comparison of CMAC output to the existing method for the AC of S2 data, Sen2 Cor. CMAC calibration is readily translatable to other satellites. Figure 18 displays Atm-I and CMAC for Landsat 8/9 data for comparison to TOAR and the RadTRAN-based method, LaSRC, that was developed for the correction of L8/9. An example of L8 correction is presented in Figure 18, where problems  
Figure 17: S2 image, 5 March 2021 closeup of the Mexican Gulf Coast north of Veracruz: (**a**) TOAR with smoke effects from fields burned before planting; (**b**) CMAC v1.1 corrected.