## 2 Methods
### Atmospheric Correction of CASI Hyperspectral Aircraft Imagery  
All of the synthetic imagery used for the following performance analysis with regard to the estimation of BGA is derived from VNIR CASI data atmospherically corrected to reflectance [6]. Atmospheric correction is usually incomplete, especially in regions of high humidity, nonetheless, we observed strong visual similarity of our pixel reflectance and Analytical Spectral Devices (ASD) reflectance spectra, very strong visual similarity of spatial pattern between image derived Chl-a indices and our coincident surface observations and strong (r\({}^{2}\) > 0.6; \(p\) < 0.001) to very strong (r\({}^{2}\) > 0.7; \(p\) < 0.001) observed vs. predicted Pearson's r\({}^{2}\) values depending on coincident surface observation type. The visual similarity of our surface and aircraft relative reflectance spectra is also confirmed statistically. For example, we averaged all 16 United States Army Corps of Engineers (USACE) surface ASD and USACE CASI (FLAASH) reflectance spectra from 16 locations from Harsha Lake and then normalized the CASI data to the ASD data in the Spectral Analysis and Management System (SAMS) at 550 nm in Figure 4 for comparison. We then resampled the averaged ASD reflectance spectrum to the averaged CASI reflectance spectrum to obtain relative reflectance values at the same scale at the same wavelengths (Figure 5). Our study used wavelengths from 425 to 865 nm (Table 2) so we created an observed vs. predicted (OP) [PERSON]'s regression (ASD surface vs. CASI aircraft relative reflectance) for all reflectance value pairs between those wavelengths. We verified this atmospheric correction by normalizing CASI to ASD spectroradiometer relative reflectance values at 550 nm at 16 locations and then evaluated their similarity with a linear regression of the relative reflectance value pairs for the 425 to 865 nm wavelengths used in this study with excellent results (Figure 6). Figure 4: Averaged Analytical Spectral Devices (ASD) surface relative reflectance spectra (red) vs. Averaged CASI reflectance spectra (\(n=16\)) (black) for Harsha Lake with CASI data normalized to ASD at 550 nm. Wavelength in nm. They correspond well over the 425 and 865 nm wavelength range used in our study. One can even see a slight depression in the CASI spectra at 620 nm that corresponds to the phyocyanin absorption feature. Figure 5: Averaged ASD surface relative reflectance spectra (red) resampled to the same wavelengths as our CASI data vs. Averaged CASI reflectance spectra (\(n=16\)) (black) for Harsha Lake with CASI data normalized to ASD at 550 nm. Wavelength in nm. Figure 6: [PERSON]’s test of linear correlation for ASD vs. CASI relative reflectance values at 32 wavelengths (\(n=32\)). \(r^{2}=0.89\), \(p<0.001\), degrees of freedom = 30, slope = 1.265, intercept = \(-0.024\). Figures 5 and 6 show some overestimation of reflectance by the atmospherically corrected CASI data, although the spectral shapes are similar. Therefore, the following algorithm/imager vs. coincident surface water observation regression results are for atmospherically corrected imagery for all of the real aircraft and synthetic satellite sensors considered below. The atmospherically corrected (relative reflectance) CASI airborne hyperspectral imagery was upscaled to synthesize moderate resolution satellite data to develop specifications for a prototype multi-satellite monitoring system for HABs in our case study lake, Harsha Lake, in Southwest Ohio [6]. The band characteristics of our synthetic satellite imagers are summarized in Table 1. The original established algorithms, authors and band math with the original wavelength centers for Chl-a (indirect) and BGA/PC (direct) phycocyanin/BGA estimation algorithms are listed in Table 2. The algorithm/imager combinations and our 184 adaptations of the original algorithms to new wavelength centers for several synthetic satellite imagers are listed in Table S1.