The reflectance were measured for each sample filter to

The remote sensing reflectance of the MS dataset was
acquired in the range of 400–900 nm with a sampling interval of 0.3 nm by
deploying a dual sensor system with two inter-calibrated ocean optics
spectroradiometers (Ocean Optics Inc., Dunedin, FL, USA). The in situ Rrs(?) from LT and LE were measured with a hand-held ASD
spectroradiometer (Analytical Spectral Device, Inc.
Boulder, Colorado, U.S.A.), from 350 to 1050 nm at 1.4 nm intervals.

2.1.3. Absorption Coefficients

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Surface water samples were collected and filtered immediately
after the Rrs(?) measurements and analyzed on the same
day in the laboratory. The particulate absorption coefficient was quantified
utilizing the transmittance or transmittance/reflectance method of Tassan and
Ferrari 22 along with the NASA Ocean Optics Protocols, Revision 4, Volume IV
protocol 23. Percent transmittance and reflectance were measured for each
sample filter to calculate the particulate absorption spectrum. Filters were
then bleached, and the transmittance and reflectance measured to calculate the
absorption coefficients of non-algal particles. The phytoplankton absorption
coefficients (aph(?)) at each station were calculated by
subtraction of non-algal particle absorption coefficients from total particle
absorption coefficients. The Gaussian peak heights (aGau(?)) were obtained from aph(?) using the Gaussian decomposition scheme described in Wang et
al. 9, which used a least-square curve fitting technique in Matlab to obtain
the aGau(?). These aGau(?) were
used as ground truth to validate the outputs from Rrs(?)
inversions.

For the MS dataset, a Perkin Elmer Lambda 850
Spectrophotometer (Perkin Elmer Inc., Waltham, MA, USA) was used to measure the
absorption coefficient of phytoplankton, detrital matter, and gelbstoff in the
380–750 nm range at 1 nm spectral resolution. Detailed information regarding
the environmental characteristics and measurement methods can be found in Mishra
et al. 18. A Shimadzu UV-2401 Spectrophotometer was used for LT. More
information about LT and details about water sample collection, measurement
protocols, and processing methods can be found in Duan et al. 24 and Ma et
al. 25. Samples from LE were measured with a Perkin-Elmer Lambda 35 UV/Vis
Dual-beam Spectrophotometer from 300–800 nm at 1 nm resolution as described in Mouw
et al. 26.

2.1.4. Pigment Concentrations and Group Composition

Water samples for Chl-a and PC concentration
from Lake Erie were filtered through 0.7 and 0.2 ?m glass fiber filters
(Whatman GF/F, 25-mm and 47-mm diameter), respectively. The Chl-a was estimated
using a Turner Designs 10-AU Fluorometer in the laboratory following the NASA
Ocean Optics Protocols, Revision 5, Volume V 23. Following NASA protocols 27,
filters for phycocyanin concentration determination were extracted in phosphate
buffer (Ricca Chemical, Arlington, Texas, U.S.A. pH 6.8) using
two freeze-thaw cycles, followed by sonication. Then the PC concentration was
estimated from the relative fluorescence measured using a Turner Aquafluor fluorometer
21. Phytoplankton populations for the Lake Erie stations in 2013 were also
used in this study which were identified and counted using standard light
microscopy 21.

2.2. Satellite Imagery

The Hyperspectral Imager for the Coastal Ocean (HICO) was
the first space-borne hyperspectral imaging spectrometer designed to sample the
coastal ocean. HICO covered selected coastal regions at 90 m spatial resolution
with full spectral coverage (380 to 960 nm sampled at 5.73 nm intervals). HICO
imagery of the same time frame as in situ measurements in Lake Erie in 2014 was
downloaded from the Oregon State University website (http://hico.coas.oregonstate.edu/), and
following the steps provided on the website the level 1B (L1B) imagery was
atmospherically corrected to level 2 (L2) data using the online version of
Tafkaa_6s model, followed by georectification. The HICO Rrs(?) data have
about the same spectral resolution as the in situ measured reflectance (5.73 nm
for HICO and 5 nm for original Rrs(?)). These data were used as an example
for MuPI application in hyperspectral satellite imagery.

The
Moderate Resolution Imaging Spectroradiometer onboard the Aqua satellite
(MODIS-Aqua) launched in 2002 is one of the
contemporary satellite ocean color missions. The L1B imagery with 1 km spatial
resolution was downloaded from the National Aeronautics and Space
Administration (NASA) website (https://ladsweb.nascom.nasa.gov/).
The L2 imagery (with 748 nm included in Rrs(?)) from the same time frame as in situ
measurements in Lake Erie in 2014 was obtained using the data processing L2gen
from the SeaWiFS Data Analysis System (SeaDAS) software using the standard near
infrared (NIR) scheme 28–30 for atmospheric correction. MODIS imagery was
used as an example of MuPI application to multi-spectral satellite remote
sensing data.

MEdium Resolution Imaging Spectrometer (MERIS) on board the
European Space Agency’s Envisat platform, was launched in 2002 and ended its
mission in May 2012. The L3 seasonal composed imagery and L2 reduced resolution
imagery (1 km spatial resolution) was obtained from NASA ocean color website (https://oceancolor.gsfc.nasa.gov/).
Lacking coincidence with in situ measurements, the same day imagery of MODIS
and MERIS on 3 September 2011 was used for the comparison of the retrieving
results. The MERIS seasonal composed imagery in Lake Erie was used to obtain a
general seasonal variation of Gaussian absorption coefficients.

 

2.3. The aGau(?)
Estimation

2.3.1. MuPI Model

To obtain aGau(?) from remote sensing reflectance, a
multi-pigment inversion method 9 was used. The corresponding functions used
in this method are included in Table 1. In this method, the Gaussian scheme,
which uses 13 Gaussian curves to reconstruct the spectrum of phytoplankton
absorption coefficient, was incorporated into the relationship in which Rrs(?) is a function of total spectral absorption (a(?)) and backscattering
(bb(?)) coefficients 31,32. With an Rrs(?) spectrum
as the only input, the function was solved with a spectral optimization method
which returns the values of unknowns (aGau(?), absorption of non-algal particles
and gelbstoff: adg(?), and backscattering coefficient of
particles, bbp(?)), that minimizes the difference
between the estimated and input Rrs(?) spectra. A summarized flowchart of
the method is shown in Figure 2. The parameters used for the 13 Gaussian curves
in this study are shown in Table 2, which includes the peak locations, widths
and empirical relationships between the peak heights.