# Closed-Form Method for Atmospheric Correction (CMAC) of SmallSat Data Using Scene Statistics
## 2 Materials and Methods
### Developing an Atmospheric Index, Atm-I, to Scale the Correction  
The VNIR atmospheric effect in imagery is treated in CMAC as a single lump-sum variable. TOAR band statistics are measured across each image within discrete non-overlapping square grid cells. An atmospheric index, Atm-I, is calculated for the S2 blue band (B02) based on VNIR band statistics. This approach resulted from the choice of vegetation as a reference against which atmospheric image effects could be measured. Vegetation is also used as a reference for MODIS, S2 and Landsat as \"dense dark vegetation\" (DDV) to assess atmospheric aerosol content pursuant to AC application [23]. B02 was selected for Atm-I rather than the shorter-wavelength coastal aerosol band, B01, which saturates at much lower levels of visible haze, thus limiting the potential range for AC. Further reference to the S2 blue band is made specifically to B02. Development of a statistical model to assess Atm-I as a scalar for CMAC AC began with spectral measurements of continuous DDV plant canopies using an ASD field spectrometer. These data were normalized to S2 responses using the published relative spectral responses for each band [19]. Test applications of this surface reflectance reference measured the lowest non-water blue band values discriminated by NIR threshold in grid cells arrayed across images dominated by DDV from the Amazon Basin and the intensive mechanized farming of the American Midwest. This testing confirmed that a workflow employing vegetation as a surface reflectance reference can produce highly sensitive grayscale maps that emulate visible haze. The remarkable stability of blue reflectance across many plant species is a product of physiologic mechanisms that optimize photosynthesis. Plant carotenoid pigments permit the absorbance of blue light for photosynthesis safely across a range of insolation from shade or cloudy days while avoiding damage during cloudless summer days by dissipating the excess energy as heat [24; 25; 26]. Against this known surface reflectance, the atmospheric effect can be readily estimated as the increased reflectance due to backscatter. Though proving to be an excellent reference for measuring atmospheric effect, a method based solely on vegetation would restrict application only to areas where such plant cover is present [27]. However, DDV can also provide the means to train a predictive statistical model to assess atmospheric effects based solely on scene statistics, regardless of the surface conditions or presence of DDV. The following workflow was used to establish a model to measure the atmospheric effect of images spatially in the form of a single index, Atm-I, from the spectral responses of the four VNIR bands included on virtually all optical smallsats. Translating the vegetation reference would require an enormous amount of ground truth data that did not exist; however, by assuming the surface reflectance of a calibrated vegetation type, Atm-I model development could proceed. Model development was also enabled through the quality, cadence, and resolution of the S2 data. Standardization of the surface reflectance of cultivated crops to serve as DDV provided the means to assume the surface reflectance of target DDV identified on S2 images for model calibration. This workflow proceeded through the following steps:  
1. ASD spectrometer measurements of cultivated crops demonstrated consistent surface reflectance usable as a surrogate blue surface reflectance for the crop when identified in imagery. 2. A DDV target crop, alfalfa, was adopted as a surrogate estimator of surface reflectance when found in healthy closed canopies. Alfalfa was chosen specifically because it is commonly grown under both irrigated and rainfed conditions. This offered the opportunity to measure spectral responses from DDV index plots and adjacent subplots of variable cover ranging from sparse desert through full DDV expression in humid climates. 3.