# Closed-Form Method for Atmospheric Correction (CMAC) of SmallSat Data Using Scene Statistics
## 2 Materials and Methods
### Experimental Design: Testing CMAC against State-of-the-Art Sen2 Cor  
This investigation consists of two analyses to evaluate the accuracy, stability and limits for AC applications by CMAC and Sen2 Cor. Analysis 1 focused on the performance of these two methods for the correction of 18 images that encompass a range of Atm-I from clear to extremely hazy of a QIA northeast of the Reno, Nevada Airport. Analysis 2 developed AC statistics for 28 visibly clear images of a Southern California (SoCal) metropolitan area within an Atm-I range expected to be more commonly encountered in operations. Vegetation and surface wetting are two significant influences on the temporal variability of the true surface reflectance. To minimize these effects, warehouse districts dominated by flat roofs and paved interspaces were chosen as targets. Such AOIs have remarkably stable reflectance and hence form desirable QIAs because (1) the AOI boundaries can be mapped to either exclude vegetation or include minor areas of irrigated cover, and (2) the exposed flat roofs and paved surfaces assure rapid drainage and surface drying. All seven QIAs, located in regions with Mediterranean-type climates, were evaluated during June and through early August when vegetation expression was expected to be relatively static. Weather records indicate that both QIAs received no significant rainfall during multiple days before each image acquisition date. The area of each QIA was variable but sufficiently large such that the influence upon reflectance from variations in numbers of parked cars, semi-trailers, roof repair, etc., constitute a minor stochastic variation. The smallest QIA, Highway in southern California with an area of about 1.5 km\({}^{2}\), contains -15,000 10 m pixels, and the largest, Chino, contains about 6.4 km\({}^{2}\). _Analysis 1_: The Reno QIA shown in Figure 7 is located in a sidelap region between adjacent S2 tiles, thus potentially doubling the number of overpasses otherwise available. Eighteen images were selected for analysis from June through to 22 August 2021, a period that initially captured extremely clear conditions followed by periods of intermittent,occasionally severe smoke haze from regional forest fires. The selected images were confirmed to lack cirrus cover through visual inspection of S2 B10, and the Atm-I mapped across the QIA boundaries was confirmed to be homogeneous with only minor variation, generally between two to three percent. _Analysis 2_: Six warehouse districts were chosen in a metropolitan region of southern California east of Los Angeles covered by a single S2 tile (Figures 8 and 9). Twenty-eight S2 images were selected that met two criteria: (1) collection in June through early August in 2020, 2021 and 2022; and (2) lacking cloud cover, including cirrus determined through visual inspection of S2 band B10. The images exhibited no visibly discernible haze. Figure 8: Map showing locations of six QIAs located east of Los Angeles, CA. (Source: Maxar, Earthstar Geographics and the GIS User Community). QIA locations are designated as follows: Chino (a); Ontario (b); Highgrove (c); Fontana (d); Redlands (e); and Rochester (f). Figure 7: The Reno QIA outlined in red on this S2 image from 6 March 2021 is located just north-east of the Reno, NV airport. The polygon was drawn to exclude vacant lots that might harbor unmanaged vegetation. The restriction for the collection period to about three months controlled for reflectance changes of senescing unirrigated weedy plants and restricted the solar zenith angle (SZA) to remain within five degrees of the minimal angle around the summer solstice. These AOIs were accepted as QIAs, and polygons were drawn around each to exclude vacant land and non-irrigated plant cover. Among the 28 images selected, eleven were from 2020, eight were from 2021 and nine were from 2022. This provided 168 separate Atm-I levels for comparison when viewed across the six AOIs (6 QIAs \(\times\) 28 images).