The uncertainties for aGau(?) at wavelength longer than

The MuPI performance was validated for multi-spectral Rrs(?) at six different band configurations. Table 5 shows the mean
UAPD of 13 aGau(?) for all three in situ datasets with
the spectral bands of different sensors, respectively. Table 6 provides
detailed information for LE 2014 data regarding the variation of the mean UAPD
in the aGau(?) retrieval with Rrs(?) at
different spectral configurations. OLCI and MERIS produced similar mean UAPD,
which is around 35% for all three datasets and 28% for the LE 2014 data.
Compared with MODIS, VIIRS showed slightly higher mean UAPD (All data: VIIRS:
36%, MODIS: 34%; LE 2014: VIIRS: ?40%, MODIS: ?37%), which is potentially
caused by the lack of a spectral band around 665 nm in VIIRS. MSI and OLI
produced the highest uncertainties for aGau(?) at wavelength longer than 550 nm, but,
surprisingly, a ?50% mean UAPD was achieved for the four spectral bands of the
Landsat-8 OLI sensor with the data used here, which demonstrates the potential
of applying MuPI to these high spatial resolution satellite remote sensing data.

By removing and adding specific bands such as 645 and 748
nm for MODIS, and 754 nm in MERIS, differences in the aGau(?)
accuracy were observed. A 10% increase in mean UAPD was observed when the 748
nm band was removed from MODIS, and a 3% decrease in the mean UAPD when adding
the 745 nm band to MERIS. However, with the existence of the 748 nm band, the
adding and removing of the 645 nm band did not show a large influence (<3% mean UAPD variation). In addition, due to the existence of the 746 nm band in VIIRS, reasonable results were obtained in aGau(?) retrievals. Such a result suggests, at least for this dataset of bloom waters, with MuPI there is little impact on the retrieval of aGau(?) when hyperspectral Rrs(?) is degraded to multiple-spectral measurements such as MERIS and MODIS-like sensors. This is consistent with conclusions from previous studies that Rrs(?) data do not need to be as fine as 1 nm in spectral resolution to obtain reliable retrievals of inherent optical properties 41–43. When taking a closer look at the results from the LE 2014 data (Table 6, Figure 6), a mean UAPD of ?35% was achieved for most of aGau(?) from Rrs(?) with MERIS, OLCI, and MODIS bands. The relatively low contributions of phytoplankton absorption coefficients at longer wavelengths was the main reason for the relatively larger uncertainties (e.g., aGau(?) at 653 nm: ~36% for MODIS and MERIS). In addition, the lack of enough bands between 570 and 660 nm (only 620 nm for MERIS and 645 nm for MODIS) made it difficult to obtain more accurate retrievals. As one of the most widely used indices for phytoplankton, concentration and light absorption coefficients of chlorophyll a (Chl-a) have been the focus of many studies 33,44–47. Previous studies 9,10,17 have indicated that some Gaussian peak heights (aGau(?)) obtained from aph(?), such as peaks around 390, 413, 435 and 675 nm, represent the absorption properties of chlorophyll a. Phycocyanin (PC), the bio-marker of the blue-green cyanobacteria, is an important indicator for cyanobacteria biomass 6,7,48. Based on the regression analysis between aGau(?), Chl-a and PC from the LE dataset, the Gaussian peaks at 386.6, 414, 435 and 677 nm showed high correlation coefficients with Chl-a concentration with R2 of 0.95, 0.96, 0.97, and 0.98, respectively; and the Gaussian peaks at 617.6 nm showed a 0.93 correlation coefficient with PC concentration. The empirical relationships for Chl-a and PC estimation from aGau(677) and aGau(617.6) were obtained, as shown in Figure 7. The above results further highlight the values of using aGau(?) as a proxy to obtain pigment absorption or concentration, which may be used to map cyanobacteria bloom waters from ocean color imagery. In analysis of the aGau(?) and cell counts from LE 2013 measurements, we found the spectral shapes formed by aGau(435), aGau(584.4), and aGau(617.6) vary with the composition of cyanobacteria species at different locations in western basin of Lake Erie, as shown in Figure 8. As shown in Table 2, the aGau(435), aGau(584.4), and aGau(617.6) contain absorption properties of pigments Chl-a, PE, and PC, respectively. The variation of pigment compositions, especially the different intracellular Chl-a:PE:PC ratios of the cyanobacteria at the species level is the main reason of the spectral shape variation. This can potentially be used in separating different cyanobacteria species in the bloom waters.Before applying MuPI to satellite imagery for aGau(?) retrieval, the Rrs(?) data from HICO and MODIS imagery for Lake Erie were first assessed with in situ measurements. Three criteria were employed to find matchups: (1) Within ±2 days; (2) median of a 3 × 3 box, with no masks of land or clouds; and (3) coefficients of variance smaller than 0.15. The spectral response function was applied to the in situ Rrs(?) spectrum before comparing it with satellite data. Most of the bands have a mean difference within 35% for Rrs(?) for both sensors. At the shorter wavelengths (?500 nm for HICO, and 412 and 443 nm for MODIS), the mean UAPD was as high as 65% and some satellite Rrs(?) were even negative values because of the poor atmospheric correction for optically complex inland waters 49,50. For MODIS, the mean UAPD of Rrs(?) at 748 nm was 52%, possibly due to low Rrs(?) values at this band and the influence from residual and likely uncorrected oxygen and water vapor absorption in the atmosphere. Since the main focus of this work is the retrieval of aGau(?) from Rrs(?), we took advantage of the aGau(?) information from the Rrs(?) spectrum in the longer wavelengths (>500 nm for HICO and
>480 nm for MODIS) in the model application, to minimize the influence of ineffective
atmospheric correction on the shorter bands of satellite Rrs(?). To
validate this adjustment, MuPI was first applied to in situ measured Rrs(?) with HICO and MODIS bands but without data from the shorter
wavelengths (?500 nm for HICO and 412 and 443 nm for MODIS). The retrieved aGau(?) from such Rrs(?) agreed quite well with aGau(?) from in situ aph(?) decomposition, with the mean UAPD
?38% for HICO, and ?48% for MODIS bands (Table 7). The estimated Chl-a
concentration has a mean UAPD of 28% which is better than the results from the
standard products 45 and those shown in Pan et al. 8, and the mean UAPD for
the estimated PC concentration is 32% which is consistent or even better than
that reported in the literature 6,7,48. Figure 9 presents one match-up of
satellite and in situ Rrs(?) spectra and the estimated Rrs(?) spectra from MuPI for both HICO and MODIS, as well as, the 13
derived aGau(?) from the corresponding spectrum. The aGau(?) from the corresponding satellite and in situ match-up data
showed the same trend.We further explored the aGau(?) distribution obtained from HICO and
MODIS of the western basin of Lake Erie. The MuPI scheme was applied without
using Rrs(?) data at the shorter spectral bands
(those <500 nm for HICO and <480 nm for MODIS). The power-law relationships obtained in Section 3.4 between aGau(677) and Chl-a, and aGau(617.6) and PC concentration were applied to the obtained aGau(?) images to map the spatial distribution of Chl-a and PC concentration (Figure 10). The estimated spatial distributions of Chl-a and PC from MODIS showed a similar pattern with those from HICO. A two-day difference exists between the HICO (15 August 2014) and MODIS (13 August 2014) observations due to the availability of satellite image, which explains the slightly different locations of the high biomass patches as shown in Figure 9. The non-value patches with in HICO image was a result of the poor Rrs(?) quality due to the failing of the atmospheric correction.MERIS imagery did not coincide with the in situ observations used in this study. Thus, to provide an example of MERIS imagery, aGau(?) were retrieved from MERIS imagery on 3 September 2011. MODIS imagery of this day was also considered. As shown in Figure 11, similar patterns for high and low absorption patches were noticed for the two sensors, but the two images showed different magnitudes of aGau(?). In further analysis of the Rrs(?) from these two sensors at the same locations, good agreement was observed, as shown in Figure 12. The existence of 709 nm band in MERIS could be the main reason for the differences in the retrieval results. The patch of high values in the MERIS (marked with solid star: ?) imagery was not included in MODIS because the standard L1B to L2 processing in SeaDAS masked those pixels as clouds. Further validation and evaluation of MERIS and MODIS Rrs(?) with in situ data are necessary to have a better understanding of the differences in the results, which is beyond the scope of the current work.We further explored the seasonal variation of aGau(435) and aGau(617.6) in Lake Erie retrieved from MERIS seasonal composed 4 km Rrs(?) imagery (Figure 13). The differences in the spatial distribution of high pigment absorption patches in Spring, Summer, Autumn and Winter were captured. An obvious summer bloom in western basin of Lake Erie is shown in the figure.In the retrieval of aGau(?) from in situ Rrs(?) data, we found that a band around 695–715 nm is important for accurate aGau(?) estimation in bloom waters. This is consistent with previous studies for the estimation of Chl-a in turbid productive waters 51–54. Fundamentally, for phytoplankton bloom waters, the reflectance at wavelengths 695–715 nm can be augmented in the same way as occurs with terrestrial plants 51–53. Lacking a proper spectral band within this spectral region for MODIS, the near-infrared band at 748 nm was included when inverting MODIS Rrs(?). Although higher uncertainties at 748 nm band were noticed (Section 3.4.1), the inclusion of the band at 748 nm results in much more reasonable aGau(?) retrieval from MODIS-Aqua measured Rrs(?) (Figure 9, Table 7) versus without Rrs(?) at this band. The same results were noticed in Section 3.1 for the aGau(?) retrieval from Rrs(?) at VIIRS and MSI spectral bands.4.2. The seasonal aGau(?) Variation in Lake ErieThe MERIS derived seasonal aGau(435) and aGau(617.6) variation in Lake Erie follows the pattern recorded in the literature 55,56. In the central basin of Lake Erie, the different patterns, as shown in Figure 13, are due to the greater nutrients in the spring and autumn, and lower availability in the summer as a result of water stratification. The nutrient inputs due to agricultural activities as well as an expanding non-native mussel population, along with the light and temperature changes in different seasons form the main drivers for the different algal bloom patterns in Lake Erie during the four seasons 55–59. As discovered in Moon 55, the biomass and taxonomic composition and the dominant taxa of surface assemblages varied in different seasons, which can be explained by the light, temperature and nutrient combinations in different seasons, and the strong spatial variability associated with mesoscale physical processes such as upwelling and basin-scale circulation 59. 4.3. Pigment Retrieval and HABs DetectionIn this study, MuPI as a semi-analytical inversion scheme was applied to retrieve multiple Gaussian curves from satellite remote sensing data. As demonstrated in previous study 10, these Gaussian curves are related to the different phytoplankton pigments. This phytoplankton pigment information has been used in the quantification of phytoplankton community composition, at least to a functional group level (5 and the references therein), because many pigments are particular to specific taxonomic groups or even species 1. However, only limited work has been conducted to obtain these phytoplankton pigments from satellite remote sensing data. Pan et al. 8 and Moisan et al. 60, as two of them, attempted to obtain 12 and 18 different phytoplankton pigments from satellite remote sensing data, respectively, but both of them are empirical approach based. Pan et al. 8 proposed using empirical relationships of 12 different phytoplankton pigments with the same band ratios of satellite Rrs(?) around 490 nm to 550 nm. However, using 490 and 550 nm alone is not a good strategy for multiple pigments, as different pigments have different absorption peaks and troughs at different wavelengths 1. Compared with Pan et al. 8, Moisan et al. 60 directly used the Chl-a product of satellite remote sensing to estimate aph(?), then decompose this aph(?) to 18 pigments based on their specific absorption coefficients. However, this satellite Chl-a product used similar empirical algorithm and spectral bands as in Pan et al. 8. As both works were focused on coastal waters, another large uncertainty comes from non-algal particles and gelbstoff in these waters, which have a big influence on wavelengths shorter than 550 nm, and this influence cannot be eliminated by the band-ratio based algorithm. Compared with these works, MuPI not only considers the contribution of non-algal particles and gelbstoff in the coastal or inland waters, but also the different absorption properties of pigments, as shown in Tables 1 and 2.Another application of the pigment information is in HAB detection. The algorithms for HAB detection are usually based on Chl-a and its anomalies 47, or marker pigments, such as phycocyanin (PC) for cyanobacteria 6,7,18,48,61. With MuPI, a successful discrimination of phycocyanin (PC) and Chl-a was achieved in this study. Limited by the dataset, the estimation of other pigment concentrations (phycoerythrin, chlorophyll b and c, carotenoids) from aGau(?), as demonstrated in Hoepffner and Sathyendranath 10, could not be conducted here. Cyanobacteria dominated HABs are increasing globally and presenting a major environmental and human health issue. Extensive Microsystis blooms with toxin production occur during summer and fall in different regions around the world and Microcystis contamination has been documented at many regions including Pinto Lake (California), Lake Erie (U.S.A.) and Lake Taihu (China) 6,7,21,61. Other common bloom-forming pelagic genera include Aphanizomenon, Anabaena, Rhodomonas and Planktothrix. However, since toxicity is primarily associated with Microcystis, these other cyanobacteria blooms are generally considered nuisance blooms which will not cause acutely dangers to humans and wildlife 62, but they are frequently present in impacted water bodies (Figure 8). However, the ability to discriminate the different bloom-causing species is one of the challenges that existing algorithms are facing. In our analysis with aGau(?) in Section 3.3, the possibility of discriminating different cyanobacteria species was shown. The variation of the spectral shape defined by aGau(435), aGau(584.4), and aGau(617.6) was found vary with different species and their composition in the water body as a result of the variation in pigment ratios 6. This result showed the potential of MuPI in the application of separating species in HAB waters, which will be useful in detecting and monitoring potential toxin producers. However, because of data limitation, this potential is not fully addressed in this study, but it will be further explored with a larger dataset in the future. 5. Conclusions In this study, the MuPI model was validated for obtaining the peak heights of Gaussian curves (aGau(?)) from multi-spectral satellite remote sensing data. The model performance was validated in the retrieval accuracy of aGau(?) with Rrs(?) of six multi-spectral band configurations, and the spectral requirements were discussed. Less than 35% of mean unbiased absolute percentage differences were achieved for aGau(?) from Rrs(?) spectra with OLCI, MERIS and MODIS bands, and less than 45% for VIIRS, MSI and OLI bands. Using data from the western basin of Lake Erie as an example, the Rrs(?) obtained from HICO and MODIS satellites were validated with in situ data over cyanobacterial bloom waters in Lake Erie, and the spatial distributions of aGau(?) and the concentrations of chlorophyll a and phycocyanin were obtained, where the patches of cyanobacteria bloom were clearly presented. A seasonal distribution of pigment absorption coefficients was obtained from MERIS seasonal composed imagery of 2011 for Lake Erie. These results demonstrate that, with MuPI, it is possible to analytically retrieve information of not only Chl-a, but also PC and potentially other pigments, which will significantly enhance our capability to characterize and evaluate the status of phytoplankton blooms and discriminate phytoplankton groups using satellite ocean color remote sensing.