# Closed-Form Method for Atmospheric Correction (CMAC) of SmallSat Data Using Scene Statistics
## 4 Discussion  
Smallsats are unequivocally the future for remote sensing intelligence, surveillance and reconnaissance (ISR) applications. CMAC was developed to support this mission by enabling smallsat AC to be independent of ancillary data and operate in near real-time. Because CMAC correction is generated exclusively from scene statistics, TOAR can be converted to surface reflectance directly upon image download without waiting for ancillary data. Application of scene statistics, therefore, enables AC of smallsat data to support the most time-critical applications for ISR. Statistical analyses show that CMAC suffers no performance loss through the use of scene statistics and instead provided much greater precision and accuracy over a much wider range of atmospheric effects in comparison to Sen2 Cor. This can be attributed to the CMAC conceptual model that captures the effect upon light from atmospheric transmittance. In comparison, Sen2 Cor, like all competing automated methods, is based upon RadTran calculations. For existing smallsat AC applications, similar RadTran workflows must apply radiance calibration from a harmonized set of S2 and L8/9 data. Therefore, such secondary application to smallsats can perform no better than that recorded here for Sentinel 2. CMAC performs within the dark-to-bright reflectance distribution of most concern: lower reflectance in the visible spectrum of less than 2000 DN. This low reflectance carries the signals of greatest interest for remotely sensed ISR, whether for national security, precision agriculture or any other machine analysis. In these tests, Sen2 Cor performed relatively poorly at the low end of visible reflectance and did not reliably estimate surface reflectance unless the image was already virtually clear of atmospheric effects (Figure 15). Smallsats employing RadTran-based correction calibrated with harmonized data can be expected to face these same issues at least. While CMAC can provide enhanced precision and accuracy, its application to smallsats also offers significant convenience through the adoption of a simple two-step procedure for calibration. In the first step, by assuming pre-launch sensor radiance, the digital sensor output can be converted to an assumed TOAR following well-established procedures. Any change of sensor response from benchtop calibration after orbital launch can then be accommodated in a second step through a rapid calibration procedure that customizes the conversion of the assumed TOAR to surface reflectance for the smallsat. In this way, the uncertainty induced by assuming pre-launch calibration is removed through a post-launch calibration step. Once calibrated, CMAC software produces estimates of surface reflectance from that smallsat's assumed TOAR from then on but is subject to periodic recalibration to compensate for sensor response drift. Recalibration can be performed two to three times per year to maintain the highest quality output. CMAC calibration methods and the associated science for their application are undergoing further development and promise to be automatable, rapid, highly precise and applicable to any VNIR spectral band. While CMAC proved accurate and precise for the lowermost limb of reflectance in all four VNIR bands below a surface reflectance of about 2000 DN. CMAC underpredicts surface reflectance values above 2000 DN, which is a behavior also exhibited by Sen2 Cor. This intrinsic divergence is hypothesized to result from the alteration of TOAR reflectance through diffuse shading by aerosol particles. As seen in the CMAC data from all seven QIAs, even for extreme levels of Atm-I, CMAC estimates of true surface reflectance remain relatively stable in the critical reflectance region below 2000 DN. With the exception of beach sand, dry lake plays, ice and snow, most targets exceeding a surface reflectance of 2000 DN are manmade.