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<article article-type="research-article" dtd-version="2.3" xml:lang="EN" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Remote Sens.</journal-id>
<journal-title>Frontiers in Remote Sensing</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Remote Sens.</abbrev-journal-title>
<issn pub-type="epub">2673-6187</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">867570</article-id>
<article-id pub-id-type="doi">10.3389/frsen.2022.867570</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Remote Sensing</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Autonomous Shipborne <italic>In Situ</italic> Reflectance Data in Optically Complex Coastal Waters: A Case Study of the Salish Sea, Canada</article-title>
<alt-title alt-title-type="left-running-head">Wang and Costa</alt-title>
<alt-title alt-title-type="right-running-head">Autonomous Shipborne <italic>In Situ</italic> Reflectance</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wang</surname>
<given-names>Ziwei</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1480266/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Costa</surname>
<given-names>Maycira</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/427695/overview"/>
</contrib>
</contrib-group>
<aff>
<institution>Department of Geography</institution>, <institution>University of Victoria</institution>, <addr-line>Victoria</addr-line>, <addr-line>BC</addr-line>, <country>Canada</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1376846/overview">Lian Feng</ext-link>, Southern University of Science and Technology, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/258134/overview">Peter Gege</ext-link>, German Aerospace Center (DLR), Germany</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/622503/overview">Matteo Ottaviani</ext-link>, National Aeronautics and Space Administration (NASA), United States</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Ziwei Wang, <email>ziweiwang@uvic.ca</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Multi- and Hyper-Spectral Imaging, a section of the journal Frontiers in Remote Sensing</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>30</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>3</volume>
<elocation-id>867570</elocation-id>
<history>
<date date-type="received">
<day>01</day>
<month>02</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>19</day>
<month>04</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Wang and Costa.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Wang and Costa</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Present limitations on using satellite imagery to derive accurate chlorophyll concentrations and phytoplankton functional types arise from insufficient <italic>in situ</italic> measurements to validate the satellite reflectance, R<sub>rs</sub>
<sup>0&#x2b;</sup>. We installed a set of hyperspectral radiometers with autonomous solar tracking capability, collectively named SAS Solar Tracker (Satlantic Inc./Sea-Bird), on top of a commercial ferry, to measure the <italic>in situ</italic> reflectance as the ferry crosses the Salish Sea, Canada. We describe the SAS Solar Tracker installation procedure, which enables a clear view of the sea surface and minimizes the interference caused by the ship superstructure. Corrections for residual ship superstructure perturbations and non-nadir-viewing geometry are applied during data processing to ensure optimal data quality. It is found that the ship superstructure perturbation correction decreased the overall R<sub>rs</sub>
<sup>0&#x2b;</sup> by 0.00055 sr<sup>&#x2212;1</sup>, based on a black-pixel assumption for the infrared band of the lowest acquired turbid water. The BRDF correction using the inherent optical properties approach lowered the spectral signal by &#x223c;5&#x2013;10%, depending on the wavelength. Data quality was evaluated according to a quality assurance method considering spectral shape similarity, and &#x223c;92% of the acquired reflectance data matched well against the global database, indicating high quality.</p>
</abstract>
<kwd-group>
<kwd>SAS Solar Tracker</kwd>
<kwd>ship superstructure perturbation correction</kwd>
<kwd>BRDF correction</kwd>
<kwd>data quality evaluation</kwd>
<kwd>reflectance</kwd>
</kwd-group>
<contract-sponsor id="cn001">Mitacs<named-content content-type="fundref-id">10.13039/501100004489</named-content>
</contract-sponsor>
<contract-sponsor id="cn002">Pacific Salmon Foundation<named-content content-type="fundref-id">10.13039/501100016065</named-content>
</contract-sponsor>
<contract-sponsor id="cn003">Hakai Institute<named-content content-type="fundref-id">10.13039/100016884</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Ocean color satellite sensors are a practical approach for large-scale synoptic monitoring of aquatic environments by providing bio-optical variables such as chlorophyll concentration (a direct proxy for phytoplankton biomass) and inherent optical properties (<xref ref-type="bibr" rid="B59">Sathyendranath et al., 2017</xref>; <xref ref-type="bibr" rid="B75">Werdell et al., 2018</xref>; <xref ref-type="bibr" rid="B21">Groom et al., 2019</xref>). However, proper vicarious calibration (space sensor calibration) and atmospheric correction of top-of-atmosphere measured radiance (L<sup>TOA</sup>) are required to retrieve accurate water-leaving radiance (L<sub>w</sub>) and, consequently, remote sensing reflectance (R<sub>rs</sub>
<sup>0&#x2b;</sup>) and biogeochemical products (<xref ref-type="bibr" rid="B81">Zibordi et al., 2015a</xref>; <xref ref-type="bibr" rid="B82">2015b</xref>). For space sensor calibration, Fiducial Reference Measurements (FRMs), which come with uncertainty budgets including those for sensors calibration and high-quality protocols for data acquisition, are ultimately required (<xref ref-type="bibr" rid="B58">Ruddick et al., 2019</xref>). Long-term international programs providing FRMs are, for example, the Marine Optical Buoy (MOBY), the Buoy for the Acquisition of a Long-Term Optical Time Series (Bou&#xe9;e pour L&#x2019;acquisition de S&#xe9;ries Optiques &#xe0; Long Terme, BOUSSOLE), the NASA bio-Optical Algorithm Data set (NOMAD), the Ocean Reflectance Models (ORM), and the Ocean Color component of the Aerosol Robotic Network (AERONET-OC). Generally, these programs have provided a range of 46&#x2013;241 high-quality matchups over 3&#x2013;7&#xa0;years for vicarious calibration of various ocean color satellites (<xref ref-type="bibr" rid="B82">Zibordi et al., 2015b</xref>). For addressing the atmospheric signal from L<sup>TOA</sup>, high-quality <italic>in situ</italic> radiometric data are also required for the development and validation of optimal atmospheric correction models (<xref ref-type="bibr" rid="B57">Ruddick et al., 2006</xref>; <xref ref-type="bibr" rid="B1">Ahmad et al., 2010</xref>; <xref ref-type="bibr" rid="B86">M&#xfc;ller et al., 2015</xref>; <xref ref-type="bibr" rid="B8">Carswell et al., 2017</xref>; <xref ref-type="bibr" rid="B79">Zibordi et al., 2018</xref>; <xref ref-type="bibr" rid="B19">Giannini et al., 2021</xref>). Atmospherically-corrected L<sub>w</sub> and R<sub>rs</sub>
<sup>0&#x2b;</sup> are generally validated in comparison with <italic>in situ</italic> matchups acquired with radiometers installed on moored buoys (e.g., <xref ref-type="bibr" rid="B4">Antoine et al., 2008</xref>), stationary platforms (e.g., <xref ref-type="bibr" rid="B83">Zibordi et al., 2006</xref>, <xref ref-type="bibr" rid="B80">2009</xref>; <xref ref-type="bibr" rid="B72">Vansteenwegen et al., 2019</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>; <xref ref-type="bibr" rid="B71">Vanhellemont and Ruddick 2021</xref>), and mobile platforms such as research vessels and ship of opportunities (e.g., <xref ref-type="bibr" rid="B62">Simis and Olsson, 2013</xref>; <xref ref-type="bibr" rid="B7">Brando et al., 2016</xref>; <xref ref-type="bibr" rid="B8">Carswell et al., 2017</xref>; <xref ref-type="bibr" rid="B51">Ottaviani et al., 2018</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>; <xref ref-type="bibr" rid="B19">Giannini et al., 2021</xref>). Among mobile platforms, deploying sensors aboard research vessels is the most common approach and requires different levels of human interaction to provide optimal geometry for data acquisition. For instance, <xref ref-type="bibr" rid="B57">Ruddick et al. (2006)</xref>, <xref ref-type="bibr" rid="B8">Carswell et al. (2017)</xref>, <xref ref-type="bibr" rid="B54">Phillips and Costa (2017)</xref>, and <xref ref-type="bibr" rid="B66">Tilstone et al. (2020)</xref> adjusted the geometry as required according to the Sun and vessel position. <xref ref-type="bibr" rid="B26">Hooker et al. (2012)</xref>, <xref ref-type="bibr" rid="B62">Simis and Olsson (2013)</xref>, <xref ref-type="bibr" rid="B7">Brando et al. (2016)</xref>, and <xref ref-type="bibr" rid="B51">Ottaviani et al. (2018)</xref> deployed instead radiometers with the autonomous capability of defining optimal geometry based on real-time Sun position and ship orientation.</p>
<p>Within the scope of autonomous measurements from stationary and mobile platforms, predefined optimal geometry of acquisition, flagging of non-optimal environmental conditions, data correction for the effects of Sun glint and skylight contributions, and structure interferences are the most important to obtain high-quality R<sub>rs</sub>
<sup>0&#x2b;</sup> measurements (<xref ref-type="bibr" rid="B28">Hooker and Morel, 2003</xref>; <xref ref-type="bibr" rid="B83">Zibordi et al., 2006</xref>; <xref ref-type="bibr" rid="B80">Zibordi et al., 2009</xref>; <xref ref-type="bibr" rid="B62">Simis and Olsson, 2013</xref>; <xref ref-type="bibr" rid="B81">Zibordi et al., 2015a</xref>; <xref ref-type="bibr" rid="B51">Ottaviani et al., 2018</xref>). First, maintaining optimal viewing geometry is a considerable challenge in shipborne reflectance measurement as the ship and the Sun are constantly moving. The general ideal geometry of acquisition, as recommended in the literature, is as follows: a viewing zenith angle (&#x3b8;<sub>v</sub>) of the upwelling radiance sensor (L<sub>t</sub>) of 40<sup>o</sup> and a viewing azimuth angle (&#x3c6;<sub>v</sub>) between the sensors and the Sun of 90 <sup>o</sup> &#x3c; &#x3c6;<sub>v</sub> &#x3c; 135 <sup>o</sup> (ideally 135 <sup>o</sup>) to minimize Sun glint (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>; <xref ref-type="bibr" rid="B62">Simis and Olsson, 2013</xref>). At the same time, the sensors should be deployed to avoid the effect of ship shadow, sea spray, and minimize ship superstructure perturbation (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>; <xref ref-type="bibr" rid="B28">Hooker and Morel, 2003</xref>; <xref ref-type="bibr" rid="B51">Ottaviani et al., 2018</xref>). Second, the instantaneous cloud cover conditions affect the spectral (ir)radiance distributions from the Sun and sky, thus resulting in variation in measurements of sky radiance and in the sky glint contribution to the upwelling radiance (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>; <xref ref-type="bibr" rid="B57">Ruddick et al., 2006</xref>). Therefore, clear sky conditions are ideal for high-quality measurements. As such, meteorological flags need to be applied. Finally, the presence of a fixed platform or the research vessel itself modifies the radiance field, since the platform shadow or multiple reflections between the superstructure and the water can fall into the sensor&#x2019;s field of view (<xref ref-type="bibr" rid="B28">Hooker and Morel, 2003</xref>).</p>
<p>Here, we provide a framework for the acquisition, processing, and quality control of above-water remote sensing reflectance acquired with the SAS Solar Tracker (Satlantic Inc./Sea-Bird, denoted as SAS-ST). This autonomous sensor is installed aboard a ship of opportunity, the Queen of Oak Bay (QoOB) ferry, which crosses multiple times each day the Salish Sea off the west coast of Canada. The data processing included screening <italic>via</italic> meteorological flags, reflected sky radiance correction, superstructure signal correction, and BRDF corrections, followed by quality control of R<sub>rs</sub>
<sup>0&#x2b;</sup> based on method by <xref ref-type="bibr" rid="B73">Wei et al. (2016)</xref>. The defined framework was based on published protocols (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>; <xref ref-type="bibr" rid="B28">Hooker and Morel, 2003</xref>; <xref ref-type="bibr" rid="B62">Simis and Olsson, 2013</xref>), and adapted for acquiring high-quality R<sub>rs</sub>
<sup>0&#x2b;</sup> measurements according to the local conditions. The purpose of these measurements is to provide matchups for validation of satellite-derived atmospheric corrected R<sub>rs</sub>
<sup>0&#x2b;</sup>, and the development of regional hyperspectral-based bio-optical models for deriving biogeochemical products (e.g., phytoplankton functional types). Off the west coast of Canada, the number of available matchups is restricted due to the limited research vessel trips, required labor on the ships of opportunity to manually adjust the radiometer&#x2019;s geometry (<xref ref-type="bibr" rid="B32">Komick et al., 2009</xref>; <xref ref-type="bibr" rid="B8">Carswell et al., 2017</xref>) and the frequent cloud coverage (<xref ref-type="bibr" rid="B25">Hilborn and Costa, 2018</xref>). Therefore, the successful operation of the autonomous SAS-ST is very desirable in this area. The methodology presented here is adaptable to other regions of the world lacking <italic>in situ</italic> reflectance data, and provides a step forward to complement a network of fixed platforms above-water sensors such as AERONET-OC (<xref ref-type="bibr" rid="B80">Zibordi et al., 2009</xref>) and WATERHYPERNET (<xref ref-type="bibr" rid="B71">Vanhellemont and Ruddick, 2021</xref>).</p>
</sec>
<sec id="s2">
<title>2 Materials and Methods</title>
<sec id="s2-1">
<title>2.1 Study Area</title>
<p>The Salish Sea is an estuarine system in the southwest of Canada, extending about 200&#xa0;km in length by 30&#xa0;km in width with an average depth of 150&#xa0;m (<xref ref-type="fig" rid="F1">Figure 1A</xref>). It is composed of the Strait of Georgia (SoG), the Puget Sound, and the Juan de Fuca Strait, and it is connected to the Pacific Ocean via the Juan de Fuca Strait in the South and the Johnstone Strait in the North. Since the northern passage is very constricted, most of the water exchange between the Salish Sea and the Pacific waters flows through the southern passage (<xref ref-type="bibr" rid="B40">Masson, 2002</xref>; <xref ref-type="bibr" rid="B53">Pawlowicz et al., 2019</xref>). A vital feature of the SoG is the significant freshwater inputs from the Fraser River (<xref ref-type="bibr" rid="B31">Johannessen et al., 2003</xref>; <xref ref-type="bibr" rid="B77">Yunker and Macdonald, 2003</xref>), which drive southward estuarine circulation, and the corresponding river plume extends into and occasionally entirely across the central and southern SoG (<xref ref-type="bibr" rid="B38">Li et al., 2000</xref>; <xref ref-type="bibr" rid="B23">Halverson and Pawlowicz, 2008</xref>, <xref ref-type="bibr" rid="B24">2011</xref>; <xref ref-type="bibr" rid="B52">Pawlowicz et al., 2017</xref>, <xref ref-type="bibr" rid="B53">2019</xref>). The river plume has a high concentration of total suspended matter (TSM) and colored dissolved organic matter (CDOM) due to its terrestrial origin, which produces optically complex waters with the highest light attenuation, particularly in the spring and summer times (<xref ref-type="bibr" rid="B39">Loos and Costa, 2010</xref>). The discharge of the Fraser River typically peaks with a freshet in mid-June following snowpack melt (<xref ref-type="bibr" rid="B40">Masson, 2002</xref>; <xref ref-type="bibr" rid="B42">Masson, 2006</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>
<bold>(A)</bold> The Salish Sea study area. The red line indicates the track of QoOB. Two yellow dots are Entrance Island (49.21&#xa0;N, 123.81&#xa0;W) and Halibut Bank (49.34&#xa0;N, 123.72&#xa0;W) for local wind measurement. <bold>(B)</bold> The SAS-ST is installed on the deck of QoOB (red circle) at a total height of 19&#xa0;m above the water surface. <bold>(C)</bold> The SAS-ST is mounted on top of a custom-fabricated pedestal, and the base of the pedestal is bolted to a welded stand.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g001.tif"/>
</fig>
<p>Biologically, the Salish Sea typically has maximum diatom-dominated spring blooms followed by weaker fall bloom events (<xref ref-type="bibr" rid="B3">Allen and Wolfe, 2013</xref>). The timing of the spring phytoplankton bloom varies interannually and is mediated by light availability due to cloud cover, wind dynamics, and timing of spring freshwater outflow (<xref ref-type="bibr" rid="B10">Collins et al., 2009</xref>; <xref ref-type="bibr" rid="B41">Masson and Pe&#xf1;a, 2009</xref>; <xref ref-type="bibr" rid="B3">Allen and Wolfe, 2013</xref>; <xref ref-type="bibr" rid="B54">Phillips and Costa, 2017</xref>; <xref ref-type="bibr" rid="B63">Suchy et al., 2019</xref>). The second most abundant phytoplankton group in this region is dinoflagellates, peaking in the summer and early fall (<xref ref-type="bibr" rid="B55">Pospelova et al., 2010</xref>). Calcifying phytoplankton, such as coccolithophore (<italic>Emiliania huxleyi</italic>), uncommon within the SoG (<xref ref-type="bibr" rid="B22">Haigh et al., 2015</xref>), were observed to flourish in July and August of 2016 when SAS-ST acquired data for the research presented here. With the high particulate discharge from the Fraser River, the Salish Sea is thus an optically dynamic coastal system (<xref ref-type="bibr" rid="B39">Loos and Costa, 2010</xref>).</p>
</sec>
<sec id="s2-2">
<title>2.2 Dataset</title>
<p>Here, we describe the installation of the SAS-ST on QoOB and data acquisition and processing. Biogeochemical data from BC FerryBox, which automatically measures a series of environmental oceanographic parameters, aided in the ferry&#x2019;s perturbation correction approach and the characterization of the water spectral types.</p>
<sec id="s2-2-1">
<title>2.2.1 SAS Solar Tracker Installation and Acquisition Geometry</title>
<p>The SAS-ST was installed on a commercial ferry, BC Ferries QoOB, about 139&#xa0;m long and 27&#xa0;m wide. The ferry sails at approximately 20 knots (10.3&#xa0;m/s) from Departure Bay, Nanaimo, to Horseshoe Bay, West Vancouver, BC, totaling a distance of about 55&#xa0;km (<xref ref-type="fig" rid="F1">Figure 1A</xref>). The SAS-ST is mounted 19&#xa0;m above the water surface on top of a custom-fabricated pedestal designed by Ocean Networks Canada (ONC), and the base of the pedestal is bolted to a welded stand (<xref ref-type="fig" rid="F1">Figures 1B,C</xref>). The SAS-ST is equipped with a drive unit as a base and thus has the advantage of solar tracking capability, which permits autonomous operation to maintain optimal viewing geometry (<xref ref-type="bibr" rid="B60">Satlantic, 2016</xref>). The SAS-ST consists of two hyperspectral radiometers to measure sea surface total upwelling radiance, L<sub>t</sub>(<italic>&#x3bb;</italic>) and sky radiance, L<sub>i</sub>(<italic>&#x3bb;</italic>), with a 3&#xb0; half-angle field of view (FOV) and a third sensor to measure the upper hemisphere downwelling irradiance, E<sub>
<italic>s</italic>
</sub>(<italic>&#x3bb;</italic>) (<xref ref-type="fig" rid="F2">Figure 2A</xref>). For an overview of symbols used in this paper see <xref ref-type="table" rid="T1">Table 1</xref>. These sensors perform automated measurements up to a frequency of 3Hz and automatically adjust their integration time to the instantaneously measured light intensity (<xref ref-type="bibr" rid="B60">Satlantic, 2016</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>). In addition to the three radiometers and the drive unit, a GPS receiver and a junction box (including power and communication components) are mounted onto the SAS-ST system. The true ship heading data are acquired by a Hemisphere Vector GPS sensor installed by ONC beside SAS-ST, and process signals from two GPS antennas to determine the true ship heading. These data are fed into the SAS-ST&#x2019;s acquisition module housed in the junction box. The auxiliary GPS was required because the metal structure of the ferry causes the internal SAS-ST GPS&#x2019;s heading measurement to lack the necessary accuracy. The SAS-ST serial data stream and auxiliary GPS heading measurement are sent to a serial-to-Ethernet converter, served on the ONC local area network (LAN) on a transmission control protocol (TCP) port. Mounted in the ONC telemetry box is a small computer that runs a driver developed on a Linux operating system. It has Ethernet connectivity and collects SAS-ST data from the LAN, stores the data, and sends them to ONC&#x2019;s server onshore. This setup allows data to be downloaded in near real-time directly from ONC&#x2019;s Oceans 2.0 portal (<ext-link ext-link-type="uri" xlink:href="https://data.oceannetworks.ca/DataSearch">https://data.oceannetworks.ca/DataSearch</ext-link>).</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>
<bold>(A)</bold> SAS-ST geometry of acquisition. Red bars are the three radiometers with &#x3b8;<sub>v</sub> &#x3d; 50&#xb0;. The solar zenith angle &#x3b8;<sub>s</sub> is about 30&#xb0; at the time of data acquisition in spring and summer. <bold>(B)</bold> Position of SAS-ST regarding the ferry and Sun. The red bar indicates the SAS-ST, blue indicates water, the orange stripe indicates the L<sub>t</sub> footprint, and the gray area indicates ship shadow as far as 14&#xa0;m from the ship wall. &#x3b3; is 90&#xb0;&#x2013;140&#xb0;, and &#x3b1; is -15&#xb0; to -50&#xb0; in this research. Note that the ferry is not at scale.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g002.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Symbols used in this paper.</p>
</caption>
<table>
<tbody valign="top">
<tr>
<td align="left">E<sub>s</sub>
</td>
<td align="left">Upper hemisphere downwelling irradiance</td>
</tr>
<tr>
<td align="left">L<sub>i</sub>
</td>
<td align="left">Sky radiance</td>
</tr>
<tr>
<td align="left">L<sub>t</sub>
</td>
<td align="left">Total upwelling radiance received by the sensor pointing at the water surface</td>
</tr>
<tr>
<td align="left">L<sub>w</sub>
</td>
<td align="left">Water-leaving radiance</td>
</tr>
<tr>
<td align="left">&#x3b8;<sub>v</sub>
</td>
<td align="left">Sensor viewing zenith angle</td>
</tr>
<tr>
<td align="left">&#x3b8;<sub>s</sub>
</td>
<td align="left">Solar zenith angle</td>
</tr>
<tr>
<td align="left">&#x3c6;<sub>v</sub>
</td>
<td align="left">Sensor-Sun azimuth angle</td>
</tr>
<tr>
<td align="left">&#x03B1;</td>
<td align="left">SAS-ST rotator angle with reference to the home position</td>
</tr>
<tr>
<td align="left">&#x03B3;</td>
<td align="left">Sun azimuth angle relative to the ferry heading</td>
</tr>
<tr>
<td align="left">&#x3c1;<sub>s</sub>
</td>
<td align="left">Sea surface reflectance factor</td>
</tr>
<tr>
<td align="left">R<sub>rs</sub>
<sup>0&#x2b;</sup>
</td>
<td align="left">Above-water reflectance</td>
</tr>
<tr>
<td align="left">
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<td align="left">Sky glint corrected R<sub>rs</sub>
<sup>0&#x2b;</sup> (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>)</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf59">
<mml:math id="m68">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mn>99</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Sky glint and ship superstructure perturbation corrected R<sub>rs</sub>
<sup>0&#x2b;</sup>
</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf60">
<mml:math id="m69">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Sky glint, ship superstructure perturbation, and BRDF corrected R<sub>rs</sub>
<sup>0&#x2b;</sup>
</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf61">
<mml:math id="m70">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Ship superstructure perturbation introduced reflectance</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf62">
<mml:math id="m71">
<mml:mi>&#x3b5;</mml:mi>
</mml:math>
</inline-formula>
</td>
<td align="left">Percentage difference for IOP-based BRDF correction</td>
</tr>
<tr>
<td align="left">r</td>
<td align="left">a precipitation flag based on the ratio between Es(&#x03BB; &#x003D; 720 nm) and Es(&#x03BB; &#x003D; 370 nm) adapted from <xref ref-type="bibr" rid="B76">Wernand (2002)</xref>
</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf63">
<mml:math id="m72">
<mml:mrow>
<mml:msup>
<mml:mi>u</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Threshold value between two neighbouring classes of weather conditions</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf64">
<mml:math id="m73">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Total absorption</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf65">
<mml:math id="m74">
<mml:mrow>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mrow>
<mml:mi>b</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Particle backscattering</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf66">
<mml:math id="m75">
<mml:mrow>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mrow>
<mml:mi>b</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Water backscattering</td>
</tr>
<tr>
<td align="left">K</td>
<td align="left">Sum of <inline-formula id="inf67">
<mml:math id="m76">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf68">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mrow>
<mml:mi>b</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf69">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mrow>
<mml:mi>b</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf70">
<mml:math id="m79">
<mml:mrow>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>0</mml:mn>
<mml:mi>w</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf71">
<mml:math id="m80">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>1</mml:mn>
<mml:mi>w</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf72">
<mml:math id="m81">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>0</mml:mn>
<mml:mi>p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf73">
<mml:math id="m82">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>1</mml:mn>
<mml:mi>p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Model coefficients <inline-formula id="inf74">
<mml:math id="m83">
<mml:mrow>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>0</mml:mn>
<mml:mi>w</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf75">
<mml:math id="m84">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>1</mml:mn>
<mml:mi>w</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf76">
<mml:math id="m85">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>0</mml:mn>
<mml:mi>p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf77">
<mml:math id="m86">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>G</mml:mi>
<mml:mn>1</mml:mn>
<mml:mi>p</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> for water and particles in <xref ref-type="bibr" rid="B37">Lee et al. (2011)</xref>
</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf78">
<mml:math id="m87">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Reflectance normalized by the respective root-sum-squares at all wavelengths</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf79">
<mml:math id="m88">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mo>&#x2217;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Normalized reflectance for each water type from <xref ref-type="bibr" rid="B73">Wei et al. (2016)</xref>
</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf80">
<mml:math id="m89">
<mml:mrow>
<mml:mi>cos</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>&#x03B2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">Angle defined between the predefined reference normalized spectrum, <inline-formula id="inf81">
<mml:math id="m90">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mo>&#x2217;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, and the normalized spectrum <inline-formula id="inf82">
<mml:math id="m91">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>To avoid the effects of Sun glint and reduce ship shadow and ship superstructure influence, the L<sub>t</sub>(<italic>&#x3bb;</italic>) and L<sub>i</sub>(<italic>&#x3bb;</italic>) sensors were positioned at a fixed viewing zenith angle, &#x3b8;<sub>v</sub> &#x3d; 50<sup>o</sup>, and programmed to maintain a sensor-Sun azimuth &#x3c6;<sub>v</sub> &#x3d; 120 &#xb1; 5&#xb0;, following <xref ref-type="bibr" rid="B28">Hooker and Morel (2003)</xref> (<xref ref-type="fig" rid="F2">Figure 2A</xref>). The value of &#x3b8;<sub>v</sub> was adapted from the optimal guidelines to keep the FOV of the L<sub>t</sub> sensor further away from the ferry and avoid ship shadow, while &#x3c6;<sub>v</sub> was chosen around 120&#xb0;, roughly the median of 90&#xb0;&#x2013;135&#xb0;, to allow the drive unit to operate within a range of angles. These parameters are programmed as part of the &#x201c;deployment setup&#x201d; (see <xref ref-type="sec" rid="s11">Supplementary Appendix A</xref>, Section 1) before the system starts acquiring data and can be changed as needed. To attain the optimal geometric conditions, the ferry run from 12:50 to 14:30 local time was designated for data acquisition during spring and summer.</p>
<p>The preset &#x3c6;<sub>v</sub> is maintained using the autonomous stepper motor platform that triggers the required positioning according to the ship heading and the Sun azimuth. The geometric setup was planned for the ferry run that approximately coincides with the time of imagery acquisition by several operational ocean color satellites. First, for the optimal time of data acquisition (12:50 to 14:30 LT), the Sun azimuth angle relative to the ferry heading, indicated as &#x3b3; in <xref ref-type="fig" rid="F2">Figure 2B</xref>, changed within the 90&#xb0;&#x2013;140&#xb0; range, with the Sun always at starboard. This is important because the port side, where the SAS-ST was installed, was not directly illuminated by the Sun, so that the ship reflections in the region where the <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> FOV falls (orange area in <xref ref-type="fig" rid="F2">Figure 2B</xref>) are minimized. The defined geometry of acquisition adjusted optimal guidelines (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>) to local conditions, and the data analysis followed the protocol of <xref ref-type="bibr" rid="B28">Hooker and Morel (2003)</xref> to minimize the interference of the white wall of the ship (<xref ref-type="sec" rid="s2-2-2">Section 2.2.2.4</xref>). Moreover, based on the solar geometry at typical times of acquisition (&#x3b8;<sub>s</sub> &#x2248; 30&#xb0;), a ship&#x2019;s shadow measuring 14&#xa0;m in extent (gray area in <xref ref-type="fig" rid="F2">Figure 2B</xref>) was predicted to be cast at the port side, a fact which was confirmed during the field observations. The ship&#x2019;s shadow was within the FOV of the <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> sensor when the rotator angle (denoted as <italic>&#x3b1;</italic>, with reference to the home position) was lower than &#x2212;50&#xb0;. Therefore, any SAS-ST data acquired at &#x3b1; lower than &#x2212;50&#xb0; were filtered out from further analysis.</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 SAS Solar Tracker Data Processing</title>
<p>This section explains the data calibration and the meteorological flags used to preprocess the raw SAS-ST data. After the calibration and the application of the screening flags, data were subjected to sky and Sun glint, ship perturbation, and BRDF corrections.</p>
<sec id="s2-2-2-1">
<title>2.2.2.1 Calibration and Flags</title>
<p>An application with batch-mode capability, PySciDON (Python Scientific Framework for Development of Ocean Network application; <xref ref-type="bibr" rid="B70">Vandenberg et al., 2017</xref>), was developed by our research group to apply the calibration files to the raw data stream for each sensor. The software accounts for the rotator angle and Sun azimuth angle flag, time and wavelength interpolation, longitude or time binning, meteorological flags, Mobley&#x2019;s wind-based &#x3c1;<sub>s</sub> factor correction (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>), and the correction for the ship superstructure perturbation. This application also provides band simulations for Sentinel-3 and MODIS-Aqua (not used in this paper) and general statistical tools, including mean, median, and standard deviation for the specified binning mode. Sensors were freshly calibrated before deployment (and optics were cleaned bi-weekly during deployment), and the calibration files from Satlantic Inc. provide descriptions of the format of the raw data files. More details can be found in <xref ref-type="bibr" rid="B70">Vandenberg et al. (2017)</xref> and Satlantic Inc.&#x2019;s Instrument File Standard document (<xref ref-type="bibr" rid="B61">Satlantic, 2011</xref>).</p>
</sec>
<sec id="s2-2-2-2">
<title>2.2.2.2 Meteorological Flags</title>
<p>The definition of meteorological flags followed the recommendations by <xref ref-type="bibr" rid="B76">Wernand (2002)</xref> to address unfavorable measurement circumstances such as low light, dusk and dawn, and precipitation. The author defined a precipitation flag based on the ratio (denoted as r) between E<sub>s</sub> (<italic>&#x3bb;</italic> &#x3d; 940&#xa0;nm) and E<sub>s</sub> (<italic>&#x3bb;</italic> &#x3d; 370&#xa0;nm) to infer the influence of Mie scattering by raindrops at 370&#xa0;nm and absorption by H<sub>2</sub>O at 940&#xa0;nm (<xref ref-type="bibr" rid="B12">Eismann, 2012</xref>). This part of the spectra is beyond the SAS-ST&#x2019;s spectral range (350&#x2013;798&#xa0;nm); therefore, the precipitation flag uses 720&#xa0;nm, which is also an absorption band of water vapor (<xref ref-type="bibr" rid="B12">Eismann, 2012</xref>), as also suggested by <xref ref-type="bibr" rid="B76">Wernand (2002)</xref>. The low-light and dawn/dusk flags were also adjusted to the wavelength range of the SAS-ST. The meteorological flags were therefore specified as follows:<list list-type="simple">
<list-item>
<p>Flag 1, E<sub>s</sub> (<italic>&#x3bb;</italic> &#x3d; 480&#xa0;nm) &#x3e; 2&#xa0;<inline-formula id="inf3">
<mml:math id="m3">
<mml:mi>u</mml:mi>
</mml:math>
</inline-formula>W&#xa0;cm<sup>&#x2212;2</sup>&#xa0;nm<sup>&#x2212;1</sup>: selecting significant Es (not low light).</p>
</list-item>
<list-item>
<p>Flag 2, E<sub>s</sub> (<italic>&#x3bb;</italic> &#x3d; 470&#xa0;nm)/E<sub>s</sub> (<italic>&#x3bb;</italic> &#x3d; 680&#xa0;nm) &#x3e; 1: masking spectra acquired at dawn/dusk.</p>
</list-item>
<list-item>
<p>Flag 3, r &#x3d; E<sub>s</sub> (<italic>&#x3bb;</italic> &#x3d; 720&#xa0;nm)/E<sub>s</sub> (<italic>&#x3bb;</italic> &#x3d; 370&#xa0;nm): value defined according to predefined threshold masking spectra affected by rainfall and high humidity.</p>
</list-item>
</list>
</p>
<p>The definition of Flag 3 took into consideration approximately 35,000 <italic>in situ</italic> E<sub>s</sub> spectra acquired with the SAS-ST system at different meteorological conditions between 12:50 and 14:30 LT from 18 June to 13 July 2016. All the measured <italic>in situ</italic> spectra were averaged every 1&#xa0;min, resulting in about 1,400 averaged spectra. Humidity data at 1&#xa0;min intervals were acquired with an RM Young Temperature RH probe installed on the ferry. Additionally, a camera was installed horizontally on top of the SAS-ST supporting frame, to acquire sky photos with a similar viewing geometry to the E<sub>s</sub> sensor. Weather conditions were determined based on the visual evaluation of 1,400 sky photos, which were organized into four classes: rainy, overcast, variable clouds (corresponding to 100%, 75%, and 50% cloudy conditions), and clear sky (corresponding to &#x2264;25% cloudy and clear sky conditions).</p>
<p>To address Flag 3, E<sub>s</sub> and humidity data measured simultaneously were associated with the four weather classes. With this dataset, a discriminant analysis (<xref ref-type="bibr" rid="B15">Gao, 2005</xref>) was applied to r (N &#x3d; 1,400) to determine the threshold value between two neighboring classes of weather conditions (denoted as <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:msup>
<mml:mi>u</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>) according to<disp-formula id="e1">
<mml:math id="m5">
<mml:mrow>
<mml:msup>
<mml:mi>u</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>u</mml:mi>
<mml:mi mathvariant="bold">1</mml:mi>
<mml:mo>&#x2217;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c3;</mml:mi>
<mml:mi mathvariant="bold">2</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>u</mml:mi>
<mml:mi mathvariant="bold">2</mml:mi>
<mml:mo>&#x2217;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c3;</mml:mi>
<mml:mi mathvariant="bold">1</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3c3;</mml:mi>
<mml:mi mathvariant="bold">1</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c3;</mml:mi>
<mml:mi mathvariant="bold">2</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf5">
<mml:math id="m6">
<mml:mi>u</mml:mi>
</mml:math>
</inline-formula> and <inline-formula id="inf6">
<mml:math id="m7">
<mml:mi>&#x3c3;</mml:mi>
</mml:math>
</inline-formula> are the mean and the standard deviation of the two neighboring weather classes. The spectra were organized according to <inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:msup>
<mml:mi>u</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> into the weather condition classes. An accuracy assessment was conducted following a standard classification confusion matrix approach, which summarizes agreement and disagreement in the classified and <italic>in situ</italic>, with the matrix&#x2019;s diagonal elements representing the counts correctly classified (<xref ref-type="bibr" rid="B56">Rosenfield and Fitzpatrick-Lins, 1984</xref>).</p>
</sec>
<sec id="s2-2-2-3">
<title>2.2.2.3 Deriving R<sub>rs</sub>
<sup>0&#x2b;</sup>
</title>
<p>Different approaches are available to derive R<sub>rs</sub>
<sup>0&#x2b;</sup>, each with a certain level of complexity. For instance, <xref ref-type="bibr" rid="B57">Ruddick et al. (2006)</xref> suggested considering the spectral shape of the R<sub>rs</sub>
<sup>0&#x2b;</sup> for moderately to highly turbid waters. <xref ref-type="bibr" rid="B62">Simis and Olsson (2013)</xref> developed the &#x201c;fingerprint method&#x201d; to minimize the atmospheric gas absorption features in the reflectance spectrum by optimizing the sky radiance contribution to the water radiance signal. <xref ref-type="bibr" rid="B18">Gege (2014)</xref> and <xref ref-type="bibr" rid="B20">Groetsch et al. (2017)</xref> put forward a three-component reflectance model, which considers a spectrally resolved offset to correct for residual Sun and sky glint. This method generally performs best with local IOPs measurements, which cannot always be applied to the water conditions of our study area. Here, the remote sensing reflectance (denoted as <inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mn>99</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>) was calculated following <xref ref-type="bibr" rid="B43">Mobley (1999)</xref> considering its good performance, simplicity, and the wide use by the community (e.g., <xref ref-type="bibr" rid="B80">Zibordi et al., 2009</xref>; <xref ref-type="bibr" rid="B78">Zibordi, 2016</xref>):<disp-formula id="e2">
<mml:math id="m10">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi mathvariant="bold">99</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where the numerator represents the water-leaving radiance, <inline-formula id="inf9">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, and &#x3c1;<sub>s</sub> is the fraction of sky radiance (<inline-formula id="inf10">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) that is measured by the sea viewing sensor (<inline-formula id="inf11">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>). Variable illumination and surface roughness conditions make the determination of &#x3c1;<sub>s</sub> a challenge (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>). The value of &#x3c1;<sub>s</sub> is usually less than 5% of the acquired L<sub>i</sub> (<xref ref-type="bibr" rid="B48">Morel and Bricaud, 1981</xref>). However, the sky glint (<inline-formula id="inf12">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c1;</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>) can have a similar magnitude of L<sub>w</sub>, and therefore, the choice of &#x3c1;<sub>s</sub> significantly influences the accuracy of <inline-formula id="inf13">
<mml:math id="m15">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mn>99</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> calculations (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>). The value of &#x3c1;<sub>s</sub> was defined considering the local wind speed measured at Entrance Island (49.21&#xa0;N, 123.81&#xa0;W) and Halibut Bank (49.34&#xa0;N, 123.72&#xa0;W) (<xref ref-type="fig" rid="F1">Figure 1A</xref>), available on the website of Environment and Climate Change Canada. Data from the ship anemometer were not used, due to challenges in correcting for the movement of the ferry.</p>
</sec>
<sec id="s2-2-2-4">
<title>2.2.2.4 Ship Superstructure Perturbation Correction</title>
<p>The ship superstructure influences the above-water radiometry by introducing a signal to the radiance field measured by the sea viewing sensor. Here, we considered that the ship wall was always under non-sunlit conditions, which minimizes any superstructure reflection onto the water. Furthermore, any data acquired at rotator angles lower than &#x2212;50&#xb0; (less than 14&#xa0;m from the ship wall) are removed from further analysis due to possible measurements of shadowed waters. <xref ref-type="bibr" rid="B28">Hooker and Morel (2003)</xref> assumed that the reflection of a white ship&#x2019;s superstructure onto the water (denoted <inline-formula id="inf14">
<mml:math id="m16">
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>) has the same spectral composition as <inline-formula id="inf15">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and that the infrared reflectance (e.g., 780 nm) from clear waters was negligible. Thus, the contribution of <inline-formula id="inf16">
<mml:math id="m18">
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
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<mml:mi>p</mml:mi>
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</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> to <inline-formula id="inf17">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mrow>
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<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> can be written as<disp-formula id="e3">
<mml:math id="m20">
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
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<mml:mi>i</mml:mi>
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<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
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<mml:mi>L</mml:mi>
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</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">780</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c1;</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">780</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">780</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi mathvariant="bold">99</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">780</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>At any wavelength, the reflectance corrected for the sky and ship perturbation contributions, denoted <inline-formula id="inf18">
<mml:math id="m21">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
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<mml:mo>&#x2b;</mml:mo>
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</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, was calculated as<disp-formula id="e4">
<mml:math id="m22">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi mathvariant="bold">99</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
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<mml:mo>[</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c1;</mml:mi>
<mml:mi>s</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>L</mml:mi>
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</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi>L</mml:mi>
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<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
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<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>Substituting for <inline-formula id="inf19">
<mml:math id="m23">
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
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</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> in <xref ref-type="disp-formula" rid="e4">Eq. 4</xref>, we have<disp-formula id="e5">
<mml:math id="m24">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
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<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
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<mml:mo>&#x2b;</mml:mo>
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<mml:mi>i</mml:mi>
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</mml:mrow>
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<mml:mrow>
<mml:mo>(</mml:mo>
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</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
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<mml:mo>(</mml:mo>
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<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
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<mml:mi mathvariant="bold-italic">&#x3c1;</mml:mi>
<mml:mi>s</mml:mi>
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<mml:msub>
<mml:mi>L</mml:mi>
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<mml:mrow>
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</mml:mrow>
</mml:mrow>
<mml:mo>]</mml:mo>
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</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
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</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi mathvariant="bold">99</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn mathvariant="bold">780</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>where <inline-formula id="inf20">
<mml:math id="m25">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mn>99</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>780</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is a constant reflectance at 780&#xa0;nm and corresponds to the ship-contributed reflectance, <inline-formula id="inf21">
<mml:math id="m26">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
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<mml:mi>p</mml:mi>
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</mml:mrow>
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</inline-formula>. To define this constant, L<sub>t</sub> and the corresponding L<sub>i</sub> and E<sub>s</sub> measurements were chosen from the day with the lowest water reflectance, acquired under the lowest water turbidity conditions (turbidity data from the FerryBox system). For these conditions, we selected approximately 731 <inline-formula id="inf22">
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</inline-formula> spectra from 06 July 2016 (Level 3A). The measured <inline-formula id="inf23">
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</inline-formula>, and <xref ref-type="disp-formula" rid="e5">Eq. 5</xref> can be re-written as<disp-formula id="e6">
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<label>(6)</label>
</disp-formula>
</p>
</sec>
<sec id="s2-2-2-5">
<title>2.2.2.5 BRDF Correction</title>
<p>To minimize the non-isotropic distribution of the water-leaving radiances in optically complex waters, a BRDF correction was applied following the inherent optical properties approach proposed by <xref ref-type="bibr" rid="B37">Lee et al. (2011)</xref>. We developed a Python version of the code, adapted from the IDL version developed by <xref ref-type="bibr" rid="B64">Talone et al. (2018)</xref>. The approach considers a two-step process: first, the quasi-analytical algorithm (QAA) method (<xref ref-type="bibr" rid="B36">Lee et al., 2002</xref>; <xref ref-type="bibr" rid="B37">Lee et al., 2011</xref>) is applied to <inline-formula id="inf25">
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</mml:mrow>
</mml:math>
</inline-formula> to retrieve the IOPs; second, the derived IOPs and accompanying G coefficients at nadir view are used to calculate <inline-formula id="inf26">
<mml:math id="m32">
<mml:mrow>
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</mml:math>
</inline-formula>. More specifically, with the input of seawater absorption, seawater backscattering (<xref ref-type="bibr" rid="B37">Lee et al., 2011</xref>), and <inline-formula id="inf27">
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<mml:mrow>
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</inline-formula>, total absorption at a reference wavelength (<inline-formula id="inf28">
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</mml:math>
</inline-formula> 555 or 670&#xa0;nm in QAA_V6) <inline-formula id="inf29">
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</mml:mrow>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and particle scattering <inline-formula id="inf30">
<mml:math id="m36">
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<mml:msub>
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<mml:mrow>
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</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
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</inline-formula> are calculated first. Particle scattering, <inline-formula id="inf31">
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</inline-formula>, is then calculated by applying the power-law model on <inline-formula id="inf32">
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</inline-formula> (<inline-formula id="inf33">
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</inline-formula> 555 or 670&#xa0;nm). Total absorption at all wavelengths, <inline-formula id="inf34">
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</inline-formula>, is derived based on <inline-formula id="inf35">
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</inline-formula> and <inline-formula id="inf36">
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</inline-formula>. The bidirectional effect corrected reflectance <inline-formula id="inf37">
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</mml:mrow>
</mml:math>
</inline-formula> is then calculated using the following equation:<disp-formula id="e7">
<mml:math id="m44">
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</inline-formula>, <inline-formula id="inf41">
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<mml:mrow>
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</inline-formula> are model coefficients for water and particles and are dependent on angular geometry and phase function but independent of water IOPs (<xref ref-type="bibr" rid="B37">Lee et al., 2011</xref>).</p>
</sec>
<sec id="s2-2-2-6">
<title>2.2.2.6 Water Type Clustering and Data Quality Evaluation</title>
<p>Optical water type clustering methods can generally be grouped into two categories. The first category focuses on the spectral magnitude of R<sub>rs</sub>, such as in <xref ref-type="bibr" rid="B34">Le et al. (2011)</xref>, <xref ref-type="bibr" rid="B44">Moore et al. (2009</xref>, <xref ref-type="bibr" rid="B45">2014)</xref>, and <xref ref-type="bibr" rid="B30">Jackson et al. (2017)</xref>. The second category considers the spectral shape of R<sub>rs</sub> for optical water type clustering. For example, <xref ref-type="bibr" rid="B73">Wei et al. (2016)</xref> (hereafter referred to as W16) compared the target spectral shape to a database composed of various global waters, divided into 23 water types including clear blue oceanic waters (type 1) and yellowish sediment-laden waters (higher types). W16 has been proven effective in categorizing various water types and can also be used to evaluate the quality of independent above-water spectra (<xref ref-type="bibr" rid="B5">Barnes et al., 2019</xref>; <xref ref-type="bibr" rid="B11">Cui et al., 2020</xref>), and it is therefore also used in this research. As it focuses on the spectral shape of R<sub>rs</sub> rather than its magnitude, this shape-based classification method minimizes the effect of R<sub>rs</sub> magnitude on water type clustering. The subsequent quality assurance also follows the method developed by W16:</p>
<p>
<statement content-type="step" id="Step_1">
<label>Step 1</label>
<p>After applying the corrections for sky glint, ship perturbation and BRDF effects on R<sub>rs</sub>
<sup>0&#x2b;</sup>, the final reflectance is denoted <inline-formula id="inf43">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
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<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which was convoluted to the corresponding Sentinel-3A OLCI 11 bands from 400 to 709&#xa0;nm using the Sentinel-3A OLCI Spectral Response Functions (SRFs) available from the <xref ref-type="bibr" rid="B14">European Space Agency, 2021</xref>. Sentinel-3A OLCI bands are considered in this study, since the products generated from this satellite are the main focus of a broader program on the coast of British Columbia (<xref ref-type="bibr" rid="B19">Giannini et al., 2021</xref>). However, the adopted approach can easily be extended to any satellite-derived R<sub>rs</sub>
<sup>0&#x2b;</sup>. The seven selected OLCI spectral bands (412, 443, 490, 510, 560, 665, and 681&#xa0;nm) are the closest to those adopted by W16.</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_2">
<label>Step 2</label>
<p>Each OLCI <inline-formula id="inf45">
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<mml:mi>s</mml:mi>
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</inline-formula> spectrum was normalized to the root-sum-squares of <inline-formula id="inf46">
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</inline-formula> corresponding to all wavelengths of the spectrum:<disp-formula id="e8">
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<label>(8)</label>
</disp-formula>where <italic>i</italic> &#x3d; 1, &#x2026; ,7 indicates each specific band. Each spectrum was assigned to one of W16&#x2019;s water types by calculating the &#x201c;spectral angle,&#x201d; cos &#x03B2;, between the predefined reference spectrum, <inline-formula id="inf47">
<mml:math id="m55">
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</mml:msubsup>
</mml:mrow>
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</inline-formula>, and <inline-formula id="inf48">
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<mml:mrow>
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<mml:msub>
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</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="bibr" rid="B33">Kruse et al., 1993</xref>):<disp-formula id="e9">
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<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
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<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
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</mml:msub>
</mml:mrow>
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</mml:mrow>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mi mathvariant="bold">2</mml:mi>
</mml:msup>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
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</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_3">
<label>Step 3</label>
<p>A quality score is computed as the ratio of the number of wavelengths in <inline-formula id="inf49">
<mml:math id="m58">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> falling within the upper and lower bounds of <inline-formula id="inf50">
<mml:math id="m59">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mo>&#x2217;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> given by the corresponding W16 water type. Five quality assurance (QA) scores are possible in this analysis (1.00, 0.86, 0.71, 0.57, or 0.43), corresponding to 7, 6, 5, 4, or 3 wavelengths of <inline-formula id="inf51">
<mml:math id="m60">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> falling within the range of one of the W16 water types. Spectra with QA &#x2265; 0.71 were deemed to be of high quality and used for further analysis.</p>
</statement>
</p>
</sec>
</sec>
<sec id="s2-2-3">
<title>2.2.3 FerryBox Ancillary Data</title>
<p>Ancillary data were collected with a FerryBox system measuring salinity (PSU) with a SeaBird SBE45 thermosalinograph, Chl-a concentration (ug l<sup>&#x2212;1</sup>) with a WET Labs ECO Triplet fluorometer, and CDOM fluorescence (ppb) and turbidity (NTU) with a WET Labs ECO Triplet BBFL2 scattering fluorescence sensor. Data processing details, including biofouling correction of the sensors and quenching correction for Chl-a measurements, are reported in <xref ref-type="bibr" rid="B67">Travers-Smith et al. (2021)</xref>.</p>
</sec>
</sec>
</sec>
<sec id="s3">
<title>3 Results</title>
<sec id="s3-1">
<title>3.1 Meteorological Flags</title>
<p>Flags 1 and 2 are defined in <xref ref-type="sec" rid="s2-2-2">Section 2.2.2.2</xref>. The mean (<inline-formula id="inf52">
<mml:math id="m61">
<mml:mi>u</mml:mi>
</mml:math>
</inline-formula>), standard deviation (<inline-formula id="inf53">
<mml:math id="m62">
<mml:mi>&#x3c3;</mml:mi>
</mml:math>
</inline-formula>), and calculated threshold (<inline-formula id="inf54">
<mml:math id="m63">
<mml:mrow>
<mml:msup>
<mml:mi>u</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>) for r used to define meteorological Flag 3 (<xref ref-type="disp-formula" rid="e1">Eq. 1</xref>) for the four weather conditions are displayed in <xref ref-type="table" rid="T2">Table 2</xref>. Generally, rainy conditions are associated with the lowest mean value of r (0.86, &#x2b;/- 0.05), and the defined range for this weather condition is r &#x3c; 0.92. The value of <inline-formula id="inf56">
<mml:math id="m65">
<mml:mrow>
<mml:msup>
<mml:mi>u</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>discriminating between overcast and variable cloudy conditions is 1.1, while clear sky conditions exhibited the highest average of r (1.29, &#x2b;/- 0.04) and <inline-formula id="inf57">
<mml:math id="m66">
<mml:mrow>
<mml:msup>
<mml:mi>u</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msup>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>&#x003D; 1.26 is obtained between clear sky and variable clouds. <xref ref-type="fig" rid="F3">Figure 3</xref> illustrates the variability of r and the associated humidity measurements and photographs of the sky for 27 June 2016, which experienced different cloudy conditions. Note that, for cloudy conditions, r is mostly lower than 1.26, thus allowing for successful isolation of such measurements, as confirmed by the confusion matrix (<xref ref-type="table" rid="T3">Table 3</xref>). The matrix shows that clear sky conditions are correctly classified in about 98.5% of the measurements, which allows us to easily flag all other sky conditions (cloudy, overcast, rainy) unsuitable for analysis. However, it is important to note that the defined thresholds were ineffective in resolving variable cloud conditions, as about 32% were erroneously classified as clear sky conditions. Still, the r defined for clear sky conditions was implemented in PySciDON (<xref ref-type="bibr" rid="B70">Vandenberg et al., 2017</xref>) as part of our operational analysis of valid spectra, and all approved (not flagged) E<sub>s</sub> spectra were further inspected for possible cloudy conditions.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Mean, standard deviation, and the r &#x3d; Es (<italic>&#x3bb;</italic> &#x3d; 720&#xa0;nm)/Es (<italic>&#x3bb;</italic> &#x3d; 370&#xa0;nm) range between the four weather condition groups.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Group</th>
<th align="center">Mean</th>
<th align="center">Std. deviation</th>
<th align="center">r range</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Rainy</td>
<td align="char" char=".">0.86</td>
<td align="char" char=".">0.05</td>
<td align="center">&#x3c;0.92</td>
</tr>
<tr>
<td align="left">Overcast</td>
<td align="char" char=".">1.02</td>
<td align="char" char=".">0.08</td>
<td align="center">&#x3e;0.92 and &#x3c;1.1</td>
</tr>
<tr>
<td align="left">Variable clouds</td>
<td align="char" char=".">1.19</td>
<td align="char" char=".">0.1</td>
<td align="center">&#x3e;1.1 and &#x3c;1.26</td>
</tr>
<tr>
<td align="left">Clear sky</td>
<td align="char" char=".">1.29</td>
<td align="char" char=".">0.04</td>
<td align="center">&#x3e;1.26</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Plot of humidity and r &#x3d; E<sub>s</sub> (&#x3bb; &#x3d; 720&#xa0;nm)/E<sub>s</sub> (&#x3bb; &#x3d; 370&#xa0;nm) for 27 June 2016 which experienced different cloudy conditions. The sky images above correspond to sky conditions at a specific time. The duration of the specific sky condition is indicated by the black arrow lines.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g003.tif"/>
</fig>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Classification confusion matrix of four groups of weather conditions.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">
<italic>In situ</italic> groups</th>
<th colspan="4" align="center">Predicted group membership (%)</th>
</tr>
<tr>
<th align="center">Rainy</th>
<th align="center">Overcast</th>
<th align="center">Variable cloudy</th>
<th align="center">Sunny</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Rainy (N &#x3d; 164)</td>
<td align="center">97.6</td>
<td align="center">2.4</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
<tr>
<td align="left">Overcast (N &#x3d; 212)</td>
<td align="center">12.7</td>
<td align="center">76.4</td>
<td align="center">9.9</td>
<td align="center">0.9</td>
</tr>
<tr>
<td align="left">Variable cloudy (N &#x3d; 401)</td>
<td align="center">2.2</td>
<td align="center">14.0</td>
<td align="center">51.9</td>
<td align="center">31.9</td>
</tr>
<tr>
<td align="left">Sunny (N &#x3d; 582)</td>
<td align="center">0.3</td>
<td align="center">0.2</td>
<td align="center">1.0</td>
<td align="center">98.5</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3-2">
<title>3.2 R<sub>rs</sub>
<sup>0&#x2b;</sup> Calculation</title>
<p>SAS-ST data collected in the longitude range (123.936&#xb0;W, 123.348&#xb0;W) were divided into 49 bins (0.012&#xb0; longitude step), each corresponding to &#x223c;900&#xa0;m on the ground, which approximates a 3 Sentinel-3A OLCI pixel window as used in <xref ref-type="bibr" rid="B19">Giannini et al. (2021)</xref>. For the sky glint correction (<inline-formula id="inf83">
<mml:math id="m92">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
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</mml:mrow>
<mml:mrow>
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</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>), these sites were split into groups corresponding to their proximity to two meteorological stations maintained by the Canadian government. Wind speed measurements were taken from Entrance Island (<xref ref-type="bibr" rid="B13">Environment and Climate Change Canada, 2021a</xref>) for longitudes between 123.936&#xb0;W and 123.636&#xb0;W (sites 1&#x2013;25) and from Halibut Bank (<xref ref-type="bibr" rid="B84">Environment and Climate Change Canada, 2021b</xref>) for longitudes between 123.636&#xb0;W and 123.348&#xb0;W (sites 26&#x2013;49). The measured wind speed ranged from 0.7 to 10.7&#xa0;m/s with the corresponding &#x3c1;<sub>s</sub> ranging from 0.0355 to 0.0480 (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>). The &#x3c1;<sub>s</sub> correction typically resulted in a decrease in reflectance for clear waters with the lowest R<sub>rs</sub> of 48% (blue bands) and 14% (green bands), while typical turbid waters decreased by 27% (blue bands) and 8% (green bands).</p>
<p>Sites 8 to 32 on 6 July 2016 provided data over the waters with the lowest turbidity (turbidity &#x3c;2.0 NTU, i.e., &#x3c;0.5&#xa0;mg/L), and the <inline-formula id="inf84">
<mml:math id="m93">
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</mml:math>
</inline-formula> from these cases was therefore used to evaluate the correction for the ship superstructure. The <inline-formula id="inf85">
<mml:math id="m94">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
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</inline-formula> values of 0.00196 &#xb1; 10<sup>&#x2013;4</sup>, 0.00202 &#xb1; 8.1&#x2a;10<sup>&#x2013;5</sup>, 0.00109 &#xb1; 5.7&#x2a;10<sup>&#x2013;5</sup>, and 0.00062 &#xb1; 4.2&#x2a;10<sup>&#x2013;5</sup> sr<sup>&#x2212;1</sup> were found for 450, 550, 650, and 750&#xa0;nm, respectively. As seen in <xref ref-type="fig" rid="F4">Figure 4A</xref>, there was no indication of an increase in reflectance as the rotator angle approaches from its maximum to minimum values (from &#x2212;22.5&#xb0; to &#x2212;46.7&#xb0;, corresponding to a distance from the ship wall of 20.9 and 15.5&#xa0;m, respectively). At distances below 14&#xa0;m (<italic>&#x3b1;</italic> &#x3d; &#x2212;51.2&#xb0;), a decrease in <inline-formula id="inf86">
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</inline-formula> was deemed indicative of interference from the ship shadow. Data corresponding to a rotator angle lower than &#x2212;50&#xb0; were therefore removed from further analysis. The measured <inline-formula id="inf87">
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</inline-formula> corresponds to <inline-formula id="inf88">
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</inline-formula>, and the histogram in <xref ref-type="fig" rid="F4">Figure 4B</xref> shows a mean value of u <inline-formula id="inf89">
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</inline-formula> 0.000612 sr<sup>&#x2212;1</sup> and a corresponding standard deviation of <inline-formula id="inf90">
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</inline-formula> &#x3d; 0.000030 sr<sup>&#x2212;1</sup>. Considering the mean value and a confidence level of 2<inline-formula id="inf91">
<mml:math id="m100">
<mml:mi>&#x3c3;</mml:mi>
</mml:math>
</inline-formula>, corresponding to 95% of the Level 3A <inline-formula id="inf92">
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</mml:math>
</inline-formula>, the retrieved <inline-formula id="inf93">
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</inline-formula> was 0.00055 sr<sup>&#x2212;1</sup>. This <inline-formula id="inf94">
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</inline-formula> value ensures longitude-binned Level 4 <inline-formula id="inf95">
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</inline-formula> in the infrared bands from clearest water close to zero and non-negative, and it may vary for a different ship superstructure environment (<xref ref-type="bibr" rid="B28">Hooker and Morel, 2003</xref>). The <inline-formula id="inf96">
<mml:math id="m105">
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</inline-formula> value for the clearest water was on average decreased to 0.00141, 0.00147, 0.00054, and 0.00007 sr<sup>&#x2212;1</sup> for the 450, 550, 650, and 750&#xa0;nm bands, respectively. The <inline-formula id="inf97">
<mml:math id="m106">
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</inline-formula> correction factor consisted of about 13%, 7%, and 22% of the <inline-formula id="inf98">
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</mml:math>
</inline-formula> for the waters with higher turbidity from the Fraser River plume in the blue, green, and red regions of the spectrum, respectively, while it was negligible for spectra collected in coccolithophore bloom conditions.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>
<bold>(A)</bold> Violin plot of L3a resolution <inline-formula id="inf99">
<mml:math id="m108">
<mml:mrow>
<mml:msubsup>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> (sr<sup>&#x2212;1</sup>) (N &#x003D; 725) and water surface footprint in relation to the ship wall distance for 06 July 2016. It is noted that, at a distance lower than 14.2&#xa0;m (&#x3b1; &#x3d; -51.2&#xb0;), there is a decrease in <inline-formula id="inf100">
<mml:math id="m109">
<mml:mrow>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> which indicates the ship shadow influence observed when &#x3b1; &#x3c; -50&#xb0;. <bold>(B)</bold> Histogram of <inline-formula id="inf101">
<mml:math id="m110">
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</mml:msubsup>
<mml:mrow>
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</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> (sr-1)(N &#x003D; 561) for the dataset after deleting 164 spectra influenced by ship shadow. The red dashed line indicates the value determined to represent superstructure-contributed reflectance (<inline-formula id="inf102">
<mml:math id="m111">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
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</mml:math>
</inline-formula> &#x3d; 0.00055 sr<sup>&#x2212;1</sup> for this research).</p>
</caption>
<graphic xlink:href="frsen-03-867570-g004.tif"/>
</fig>
<p>The IOPs-based BRDF correction was applied to generate the final reflectance, <inline-formula id="inf103">
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</mml:mrow>
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</inline-formula>. The <inline-formula id="inf104">
<mml:math id="m113">
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<mml:mi>R</mml:mi>
<mml:mrow>
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</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>dataset was divided into two groups, since the optical properties vary considerably in the presence of a bloom: Group 1 (high and low turbidity waters with no coccolithophore bloom) corresponding to 11&#xa0;days from 26 June to 14 August 2016 (N &#x3d; 513 spectra) and Group 2 (coccolithophore bloom) corresponding to 5&#xa0;days from 15 August to 25 August 2016 (N &#x3d; 213 spectra). <xref ref-type="fig" rid="F5">Figure 5</xref> shows representative <inline-formula id="inf105">
<mml:math id="m114">
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> spectra for Group 1 and Group 2, and Section 2 in <xref ref-type="sec" rid="s11">Supplementary Appendix A</xref> shows the summary plot of <inline-formula id="inf106">
<mml:math id="m115">
<mml:mrow>
<mml:msub>
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<mml:mrow>
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, together with the accompanying E<sub>s</sub>, L<sub>i</sub>, L<sub>t</sub> for the sampled days. The results of the BRDF correction (<xref ref-type="fig" rid="F6">Figure 6</xref>) show wavelength-dependent differences defined by the percentage difference <inline-formula id="inf107">
<mml:math id="m116">
<mml:mrow>
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</inline-formula>:<disp-formula id="e12">
<mml:math id="m117">
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3b5;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi mathvariant="bold">99</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="bold">1</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x2217;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi mathvariant="bold">100</mml:mi>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Representative <inline-formula id="inf108">
<mml:math id="m118">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (sr<sup>&#x2212;1</sup>) with their median (solid lines) and first and third interquartile ranges (shaded areas) based on a &#x223c;900&#xa0;m range, showing typical lowest turbidity, typical plume, and coccolithophore bloom from 06 July 2016 to 22 August 2016.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Joyplot for Groups 1 (non-coccolithophore bloom conditions) and 2 (coccolithophore bloom conditions) of BRDF correction percentage difference <inline-formula id="inf109">
<mml:math id="m119">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> for Sentinel-3A bands from 400 to 709&#xa0;nm.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g006.tif"/>
</fig>
<p>Noticeably, <inline-formula id="inf110">
<mml:math id="m120">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is lower than <inline-formula id="inf111">
<mml:math id="m121">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mn>99</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#xa0;</mml:mo>
<mml:mi mathvariant="normal">by&#xa0;5&#xa0;to</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mn>10</mml:mn>
<mml:mo>%</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, with more significant differences found at green wavelengths (<xref ref-type="fig" rid="F6">Figure 6</xref>).</p>
</sec>
<sec id="s3-3">
<title>3.3 Quality Check and Optical Water Type Clustering</title>
<p>For Group 1 (N &#x3d; 513), 92% of the <inline-formula id="inf112">
<mml:math id="m122">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> presented a QA score equal to or higher than 0.71 (<xref ref-type="fig" rid="F7">Figures 7A,B</xref>), meaning that at least five out of seven specific wavelengths (412, 443, 490, 510, 560, 665, and 681&#xa0;nm) of the individual <inline-formula id="inf113">
<mml:math id="m123">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> spectrum are within the <inline-formula id="inf114">
<mml:math id="m124">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mo>&#x2217;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> range for each water type cluster defined by W16. Also, 60% of the spectra have a score of 1.0; the majority of these spectra belong to water type 11, i.e., medium- and high-reflectance waters, as indicated in <xref ref-type="fig" rid="F7">Figures 7C,D</xref>. About 8% (N &#x3d; 41) of the spectra showed the lowest QA score of 0.57, and among these, 78% were found in water type 9. These waters exhibit the lowest reflectance in the dataset, corresponding to the clearest water types. We further investigated the possible source of the low QA scores and found that, for these 41 spectra, the <inline-formula id="inf115">
<mml:math id="m125">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> corresponding to bands centered at 490 and 510&#xa0;nm fell out of the boundary defining the W16 water types (<xref ref-type="fig" rid="F7">Figure 7E</xref>). For Group 2 (N &#x3d; 231), 94% of the <inline-formula id="inf116">
<mml:math id="m126">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> showed a QA score equal to or higher than 0.71 (<xref ref-type="fig" rid="F8">Figures 8A,B</xref>). <xref ref-type="fig" rid="F8">Figures 8A,B</xref> also show that 78% of the spectra are scored as 1.0. The majority belong to water type 11, with reflectance evenly distributed across the whole range, as indicated in <xref ref-type="fig" rid="F8">Figures 8C,D</xref>. However, the method reported by W16 does not consider algal bloom conditions, and as such, it is not appropriate for evaluating all the spectra in Group 2. Nevertheless, the QA evaluation showed a higher percentage of high-quality scores than that for Group 1, likely due to the high reflectance signal measured during the coccolithophore bloom conditions. In these conditions, only about 7% (N &#x3d; 15) of <inline-formula id="inf117">
<mml:math id="m127">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> showed a QA score lower than 0.71, mainly from water type 11 (<xref ref-type="fig" rid="F8">Figures 8A,B</xref>). Further analysis of these low QA score spectra showed that bands centered at 490&#xa0;nm, 510&#xa0;nm, and 560&#xa0;nm were not included in any W16 water type (<xref ref-type="fig" rid="F8">Figure 8E</xref>).</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Quality assurance results for Group 1. <bold>(A)</bold> Bar plot of the number of points at each water type and each quality score. <bold>(B)</bold> Frequency plot of each quality score. PDF represents the probability density function, and CDF represents the cumulative distribution function. <bold>(C)</bold> Histogram of <inline-formula id="inf118">
<mml:math id="m128">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (560) color-coded by quality scores. <bold>(D)</bold> Histogram of <inline-formula id="inf119">
<mml:math id="m129">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (560) color-coded by water types. <bold>(E)</bold> Number of points falling out of the range of each QA cluster in that wavelength for 41 points from Group 1 which has a score &#x3c;0.71.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g007.tif"/>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Quality assurance results for Group 2. <bold>(A)</bold> Bar plot of the number of points at each water type and each quality score. <bold>(B)</bold> Frequency plot of each quality score. <bold>(C)</bold> Histogram of <inline-formula id="inf120">
<mml:math id="m130">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (560) color-coded by quality scores. <bold>(D)</bold> Histogram of <inline-formula id="inf121">
<mml:math id="m131">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (560) color-coded by water types. <bold>(E)</bold> Number of points falling out of the range of each QA cluster in that wavelength for 15 points from Group 2 which has a score &#x3c;0.71.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g008.tif"/>
</fig>
<p>For each group and water type, the <italic>R</italic>
<sub>
<italic>rs</italic>
</sub> varied in magnitude but presented a similar shape (<xref ref-type="fig" rid="F9">Figures 9</xref>, <xref ref-type="fig" rid="F10">10</xref>). The <inline-formula id="inf123">
<mml:math id="m133">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from Group 1 is clustered into optical water types 8 to 15, excluding 13 (<xref ref-type="fig" rid="F9">Figure 9B</xref>). The <inline-formula id="inf124">
<mml:math id="m134">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in Group 1 ranged from 0.001 to 0.006 sr<sup>&#x2212;1</sup>, 0.001 to 0.01 sr<sup>&#x2212;1</sup>, and 0.0005 to 0.0035 sr<sup>&#x2212;1</sup> in the blue, green, and red bands, respectively (<xref ref-type="fig" rid="F9">Figure 9A</xref>). Specifically, the highest <inline-formula id="inf125">
<mml:math id="m135">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (&#x223c;0.01 sr<sup>&#x2212;1</sup> at 560&#xa0;nm) are observed within water types 10 and 11, which are generally associated with slightly higher turbid waters (<xref ref-type="fig" rid="F11">Figure 11C</xref>); the lowest <inline-formula id="inf126">
<mml:math id="m136">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (&#x3c;0.002 sr<sup>&#x2212;1</sup>) are observed in many of the water types and are associated with low turbidity (&#x3c;2.0 NTU; <xref ref-type="fig" rid="F11">Figure 11C</xref>). For Group 2, dominated by coccolithophore bloom conditions, the <inline-formula id="inf127">
<mml:math id="m137">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are clustered into optical water types 8&#x2013;14 (<xref ref-type="fig" rid="F10">Figure 10B</xref>). For these waters, the lowest <inline-formula id="inf128">
<mml:math id="m138">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at 560&#xa0;nm (&#x3c;0.01 sr<sup>&#x2212;1</sup>) are associated with oceanic waters (salinity &#x3e;26 PSU; <xref ref-type="fig" rid="F12">Figure 12A</xref>), which in turn are characterized by lower turbidity (&#x3c;3.0 NTU), higher Chl-a (&#x3e;14.0 ug l<sup>&#x2212;1</sup>), and lower CDOM (&#x3c;2.0&#xa0;ppb) (<xref ref-type="fig" rid="F12">Figures 12B-D</xref>). The highest <inline-formula id="inf129">
<mml:math id="m139">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at 560&#xa0;nm (0.03&#x2013;0.04 sr<sup>&#x2212;1</sup>) are for water types 11 and 12 (<xref ref-type="fig" rid="F10">Figure 10A</xref>) and correspond to the highest turbidity (&#x3e;5.0 NTU) and CDOM (&#x3e;2.2&#xa0;ppb) and lowest Chl-a (&#x3c;3.0 ug l<sup>&#x2212;1</sup>).</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Plots of SAS-ST reflectance <inline-formula id="inf130">
<mml:math id="m140">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (sr<sup>&#x2212;1</sup>) <bold>(A)</bold> and normalized reflectance <inline-formula id="inf131">
<mml:math id="m141">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(B)</bold> for 513 points from Group 1. Radiometry measurements are clustered into optical water types 8 to 15, excluding 13. A colored line in each water type indicates the median of the cluster.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g009.tif"/>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Plots of SAS-ST reflectance <inline-formula id="inf132">
<mml:math id="m142">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (sr<sup>&#x2212;1</sup>) <bold>(A)</bold> and normalized reflectance <inline-formula id="inf133">
<mml:math id="m143">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <bold>(B)</bold> for 231 points from Group 2. Radiometry measurements are clustered into optical water types 8 to 14. A colored line in each water type indicates the median of the cluster.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g010.tif"/>
</fig>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Reflectance <inline-formula id="inf134">
<mml:math id="m144">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (sr<sup>&#x2212;1</sup>) from Group 1, which is color-coded in the corresponding <bold>(A)</bold> salinity (PSU), <bold>(B)</bold> CDOM fluorescence (ppb), <bold>(C)</bold> turbidity (NTU), and <bold>(D)</bold> chlorophyll (ug/l) values.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g011.tif"/>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Reflectance <inline-formula id="inf135">
<mml:math id="m145">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (sr<sup>&#x2212;1</sup>) from Group 2, which is color-coded in the corresponding <bold>(A)</bold> salinity (PSU), <bold>(B)</bold> CDOM fluorescence (ppb), <bold>(C)</bold> turbidity (NTU), and <bold>(D)</bold> chlorophyll (ug/l) values.</p>
</caption>
<graphic xlink:href="frsen-03-867570-g012.tif"/>
</fig>
</sec>
</sec>
<sec id="s4">
<title>4 Discussion</title>
<p>Our results show that optimizing the geometry of data acquisition, filtering data acquired under unstable illumination conditions (e.g., dawn/dusk, cloudy, and rainy), and correcting for skylight radiance, ship superstructure, and BRDF effects, allowed for R<sub>rs</sub>
<sup>0&#x2b;</sup> data retrieval with high quality when compared with the W16 quality assurance dataset.</p>
<p>The first consideration for optimal data quality is the geometry of data acquisition (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>; <xref ref-type="bibr" rid="B28">Hooker and Morel, 2003</xref>; <xref ref-type="bibr" rid="B83">Zibordi et al., 2006</xref>; <xref ref-type="bibr" rid="B62">Simis and Olsson, 2013</xref>; <xref ref-type="bibr" rid="B16">Garaba et al., 2015</xref>; <xref ref-type="bibr" rid="B7">Brando et al., 2016</xref>; <xref ref-type="bibr" rid="B72">Vansteenwegen et al., 2019</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>). Here, with optimal configuration, the spectral measurements were acquired on the non-sunlit side of the ferry to minimize the reflected ferry signal on the above-water radiance measurements (<xref ref-type="bibr" rid="B28">Hooker and Morel, 2003</xref>), and at an adapted sensor viewing zenith angle to avoid ship superstructure shadows and an optimal sensor-Sun azimuth angle to minimize the skylight radiance signal on the above-water radiance measurements (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>). Various skylight radiance correction approaches are available (e.g., <xref ref-type="bibr" rid="B43">Mobley, 1999</xref>; <xref ref-type="bibr" rid="B57">Ruddick et al., 2006</xref>; <xref ref-type="bibr" rid="B35">Lee et al., 2010</xref>; <xref ref-type="bibr" rid="B20">Groetsch et al., 2017</xref>) requiring different complexity of input data to successfully correct for skylight radiance. For instance, the method suggested by <xref ref-type="bibr" rid="B18">Gege (2014)</xref> and <xref ref-type="bibr" rid="B20">Groetsch et al. (2017)</xref> applies a three-component model, in which using optimized local IOPs, to correct for the residual Sun and sky glint signal on the above-water measurement. We tested (analysis not shown here) this approach with a small set of IOPs measurements collected concomitant to some of the SAS-ST data, and the results were similar to those obtained with the method by <xref ref-type="bibr" rid="B43">Mobley (1999)</xref>. Although Mobley&#x2019;s method is commonly used, the &#x3c1;<sub>s</sub> factor is not wavelength-dependent, resulting in higher uncertainties for longer wavelengths (<xref ref-type="bibr" rid="B35">Lee et al., 2010</xref>). Still, for similar geometry and environmental conditions (wind speed &#x3c;13.0&#xa0;m/s and clear skies), <xref ref-type="bibr" rid="B17">Garaba and Zielinski (2013)</xref> showed that Mobley&#x2019;s method performed similarly to three other approaches, with the advantage of ensuring non-negative R<sub>rs</sub>
<sup>0&#x2b;</sup> retrievals in the near-infrared. Also, uncertainties in the wind speed impact the &#x3c1;<sub>s</sub> factor, especially in the blue bands (<xref ref-type="bibr" rid="B43">Mobley, 1999</xref>).</p>
<p>The ship-specific superstructure correction factor <inline-formula id="inf136">
<mml:math id="m146">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
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</inline-formula> was determined as 0.00055 sr<sup>&#x2212;1</sup>. Although this factor is not commonly addressed in above-water radiometry measurements (e.g., <xref ref-type="bibr" rid="B62">Simis and Olsson, 2013</xref>; <xref ref-type="bibr" rid="B7">Brando et al., 2016</xref>), it can cause significant uncertainties in the final R<sub>rs</sub>
<sup>0&#x2b;</sup>. <xref ref-type="bibr" rid="B65">Talone and Zibordi (2019)</xref> have shown that the structure signal (in this case, a fixed tower covered with a white sheet) was relatively more pronounced in the near-infrared than at visible wavelengths and decreased with the inverse square of the distance between the platform and the sensor footprint. For a similar distance as in our study (15&#x2013;21&#xa0;m), <xref ref-type="bibr" rid="B65">Talone and Zibordi (2019)</xref> estimated a tower perturbation factor of about 10&#x2013;3% for the 750&#x2013;800&#xa0;nm range, resulting in <inline-formula id="inf137">
<mml:math id="m147">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
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</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
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</inline-formula> &#x3d; 0.00002 sr<sup>&#x2212;1</sup>&#xa0;at 780&#xa0;nm. This value is one order of magnitude lower than the value determined for the QoOB, likely because of the larger structure of the QoOB (19&#xa0;m in height and 139&#xa0;m in length) compared with the experimental tower used by the authors (15&#xa0;m in height and &#x223c;10&#xa0;m in length). For a smaller ferry, the Queen of Alberni, using the same SAS-ST and ship perturbation approach adopted here, <xref ref-type="bibr" rid="B19">Giannini et al. (2021)</xref> defined <inline-formula id="inf138">
<mml:math id="m148">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
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<mml:mi>p</mml:mi>
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</inline-formula> &#x3d; 0.00005 sr<sup>&#x2212;1</sup>, a value similar to the one in <xref ref-type="bibr" rid="B65">Talone and Zibordi (2019)</xref>.</p>
<p>A correct evaluation of the dependence of the measured signal on the viewing geometry and the bidirectional effects (<xref ref-type="bibr" rid="B49">Morel and Gentili, 1996</xref>; <xref ref-type="bibr" rid="B47">Morel et al., 2002</xref>; <xref ref-type="bibr" rid="B80">Zibordi et al., 2009</xref>; <xref ref-type="bibr" rid="B37">Lee et al., 2011</xref>) is important for validating satellite-based retrieved reflectance or water radiance (<xref ref-type="bibr" rid="B80">Zibordi et al., 2009</xref>; <xref ref-type="bibr" rid="B64">Talone et al., 2018</xref>) and comparing above-water radiometric data acquired under different geometric conditions (<xref ref-type="bibr" rid="B73">Wei et al., 2016</xref>). Here, a BRDF correction was required because the data quality was evaluated against the W16 global R<sub>rs</sub>
<sup>0&#x2b;</sup> database, composed of reflectance measurements acquired with a nadir viewing geometry. The BRDF correction was found to decrease R<sub>rs</sub>
<sup>0&#x2b;</sup> in this research by &#x223c;5&#x2013;10%, as also found by <xref ref-type="bibr" rid="B64">Talone et al. (2018)</xref>.</p>
<p>The final evaluation of R<sub>rs</sub>
<sup>0&#x2b;</sup> is preferentially performed against <italic>in situ</italic> measurements of below-water R<sub>rs</sub> and/or measurements collected with various instruments at the same location (e.g., <xref ref-type="bibr" rid="B27">Hooker et al., 2002</xref>; <xref ref-type="bibr" rid="B35">Lee et al., 2010</xref>; <xref ref-type="bibr" rid="B78">Zibordi, 2016</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>). However, collecting below-water R<sub>rs</sub> is not possible with our measurement setup. Instead, our <inline-formula id="inf139">
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<mml:mo>&#xa0;</mml:mo>
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</inline-formula> dataset was evaluated against a global water dataset. This evaluation was conducted considering two different clusters of data: Group 1 representing clear and turbid waters and Group 2 representing coccolithophore bloom conditions (<xref ref-type="bibr" rid="B29">Ianson et al., 2018</xref>). Group 1 exhibited values of <inline-formula id="inf140">
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<mml:mi>s</mml:mi>
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</inline-formula> well within the ranges of those measured by <xref ref-type="bibr" rid="B32">Komick et al. (2009)</xref>, <xref ref-type="bibr" rid="B54">Phillips and Costa (2017)</xref>, <xref ref-type="bibr" rid="B8">Carswell et al. (2017)</xref>, and <xref ref-type="bibr" rid="B19">Giannini et al. (2021)</xref> in the same region. Group 1 consisted of a diverse group of waters, as indicated by the large salinity range (12&#x2013;27 PSU; <xref ref-type="fig" rid="F11">Figure 11A</xref>) corresponding to Fraser River plume to oceanic waters (<xref ref-type="bibr" rid="B39">Loos and Costa, 2010</xref>; <xref ref-type="bibr" rid="B67">Travers-Smith et al., 2021</xref>). In these waters, the bio-optical constitutes were generally characterized by a large range of CDOM fluorescence (0.05&#x2013;6&#xa0;ppb) and turbidity (1&#x2013;5 NTU) (<xref ref-type="fig" rid="F11">Figures 11B-D</xref>). Higher <inline-formula id="inf141">
<mml:math id="m151">
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<mml:mrow>
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<mml:mo>&#xa0;</mml:mo>
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</inline-formula> values are associated with the lower salinity of the Fraser River plume and estuarine waters (<xref ref-type="bibr" rid="B39">Loos and Costa, 2010</xref>; <xref ref-type="bibr" rid="B54">Phillips and Costa, 2017</xref>; <xref ref-type="bibr" rid="B67">Travers-Smith et al., 2021</xref>). For Group 2, the <inline-formula id="inf142">
<mml:math id="m152">
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<mml:mi>s</mml:mi>
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</inline-formula> spectra were well within the ranges observed by <xref ref-type="bibr" rid="B46">Moore et al. (2012)</xref>, <xref ref-type="bibr" rid="B50">Neukermans and Fournier (2018)</xref>, and <xref ref-type="bibr" rid="B9">Cazzaniga et al. (2021)</xref> for waters under coccolithophore bloom conditions. Specifically, <xref ref-type="bibr" rid="B9">Cazzaniga et al. (2021)</xref> have shown high values (<inline-formula id="inf143">
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</inline-formula> 0.03 sr<sup>&#x2212;1</sup>) for the peak of a coccolithophore bloom, intermediate values (<inline-formula id="inf144">
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<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
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<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
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</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2248;</mml:mo>
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</inline-formula> 0.02 sr<sup>&#x2212;1</sup>) for receding bloom conditions, and low values (<inline-formula id="inf145">
<mml:math id="m155">
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<mml:mrow>
<mml:mo>(</mml:mo>
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<mml:mn>550</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
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</inline-formula> &#x3c;0.01 sr<sup>&#x2212;1</sup>) for the start and the end of bloom. Similarly, our spectra showed <inline-formula id="inf146">
<mml:math id="m156">
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</mml:mrow>
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<mml:mrow>
<mml:mo>(</mml:mo>
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</inline-formula> &#x3e;<inline-formula id="inf147">
<mml:math id="m157">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
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</mml:mrow>
<mml:mo>)</mml:mo>
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</mml:mrow>
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</inline-formula> likely representing the start of the bloom (water types 11 and 12; <xref ref-type="fig" rid="F10">Figure 10</xref>). Other spectra showed an increase at <inline-formula id="inf148">
<mml:math id="m158">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
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</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
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</inline-formula> (water types 8, 9, and 10), probably associated with a high concentration of detached coccoliths indicative of receding bloom conditions (<xref ref-type="bibr" rid="B50">Neukermans and Fournier, 2018</xref>; <xref ref-type="bibr" rid="B9">Cazzaniga et al., 2021</xref>).</p>
<p>The evaluation of <inline-formula id="inf149">
<mml:math id="m159">
<mml:mrow>
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<mml:mi>R</mml:mi>
<mml:mrow>
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<mml:mi>s</mml:mi>
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</inline-formula> data showed an overall high quality, with about 92% of Group 1 and 94% of Group 2 with a QA score&#x3e;&#x3d;0.71. A QA score &#x3c;0.71 was only observed for 8% (N &#x3d; 41) of Group 1 and corresponded to the lowest <inline-formula id="inf150">
<mml:math id="m160">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
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</inline-formula> for which the out-of-range wavelengths were 490 and 510&#xa0;nm. This was not expected, since uncertainties of <inline-formula id="inf151">
<mml:math id="m161">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> retrievals are mostly associated with shorter wavelengths (<xref ref-type="bibr" rid="B43">Mobley 1999</xref>; <xref ref-type="bibr" rid="B85">Hlaing et al., 2013</xref>; <xref ref-type="bibr" rid="B74">Wei et al., 2020</xref>). However, the W16 method relies on normalizing <inline-formula id="inf152">
<mml:math id="m162">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
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<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> at each wavelength with respect to the integral over all <inline-formula id="inf153">
<mml:math id="m163">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="disp-formula" rid="e8">Eq. 8</xref>). Erroneous values of <inline-formula id="inf154">
<mml:math id="m164">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
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</mml:math>
</inline-formula> at 412 and 443&#xa0;nm can therefore influence the shape of the corresponding <italic>n</italic>R<sub>rs</sub> and, consequently, the water type to which it belongs.</p>
<p>Although our protocols for R<sub>rs</sub>
<sup>0&#x2b;</sup> measurements with the SAS-ST followed rigorous criteria for data acquisition and processing, there is still a level of data variability and uncertainty that it is difficult to account for (<xref ref-type="bibr" rid="B58">Ruddick et al., 2019</xref>; <xref ref-type="bibr" rid="B68">Vabson et al., 2019</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>; <xref ref-type="bibr" rid="B2">Alikas et al., 2020</xref>). These uncertainties may also explain the 8% of acquired spectra with lower quality (QA &#x3c;0.71). Recent evaluations of international field-based radiometers (<xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>), including similar Satlantic HyperOCR radiometers as those used here, indicated that the inaccuracies in downwelling-irradiance measurements resulted in the largest <inline-formula id="inf155">
<mml:math id="m165">
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<mml:mrow>
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</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> variability, especially for the blue (3.5%) and red (3.0%) wavelengths. The E<sub>s</sub> spectra collected for this research at around solar noon (see Section 2 in <xref ref-type="sec" rid="s11">Supplementary Appendix A</xref>) exhibited very low variability in clear sky conditions; thus, we do not expect the same level of uncertainties reported in <xref ref-type="bibr" rid="B66">Tilstone et al. (2020)</xref>. The quantification of specific uncertainties in <inline-formula id="inf156">
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</inline-formula> measurements is challenging, especially considering the lack of simultaneous, below-water reflectance measurements. Our <inline-formula id="inf157">
<mml:math id="m167">
<mml:mrow>
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<mml:mi>R</mml:mi>
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</inline-formula> data showed high quality and have been effectively used for the evaluation of atmospheric correction procedures for Sentinel-3A OLCI (<xref ref-type="bibr" rid="B19">Giannini et al., 2021</xref>). To provide vicarious calibration for satellites, an uncertainty budget of the FRM is a requirement, which should be further investigated by accounting for the environmental conditions during data acquisition, such as in <xref ref-type="bibr" rid="B2">Alikas et al. (2020)</xref>.</p>
</sec>
<sec id="s5">
<title>5 Conclusion</title>
<p>Validation of ocean color satellite R<sub>rs</sub> retrievals requires a large number of high-quality R<sub>rs</sub>
<sup>0&#x2b;</sup> matchups (<xref ref-type="bibr" rid="B86">M&#x00FC;ller et al., 2015</xref>; <xref ref-type="bibr" rid="B75">Werdell et al., 2018</xref>; <xref ref-type="bibr" rid="B69">Valente et al., 2019</xref>). However, the availability of such matchups is often limited due to the difficulty of acquiring high-quality data over large spatial and temporal domains (<xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>). These constraints are reported for many study regions (e.g., <xref ref-type="bibr" rid="B69">Valente et al., 2019</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>, <xref ref-type="bibr" rid="B19">Giannini et al., 2021</xref>), and it is specifically an issue along the west coast of Canada (<xref ref-type="bibr" rid="B32">Komick et al., 2009</xref>; <xref ref-type="bibr" rid="B8">Carswell et al., 2017</xref>; <xref ref-type="bibr" rid="B25">Hilborn and Costa, 2018</xref>; <xref ref-type="bibr" rid="B19">Giannini et al., 2021</xref>). Autonomous radiometers mounted on fixed towers, such as AERONET-OC (<xref ref-type="bibr" rid="B83">Zibordi et al., 2006</xref>, <xref ref-type="bibr" rid="B80">2009</xref>) and the newest WATERHYPERNET hyperspectral network (<xref ref-type="bibr" rid="B72">Vansteenwegen et al., 2019</xref>; <xref ref-type="bibr" rid="B71">Vanhellemont and Ruddick, 2021</xref>), can also provide a large number of high-quality matchups. Another option is to utilize mobile platforms such as ships. We presented the protocols to deploy the SAS-ST instrument on a commercial ferry, together with the evaluation of the large volume of high-quality R<sub>rs</sub> data acquired along the coastal waters of BC, Canada. The summary of our results and recommendations is as follows:<list list-type="simple">
<list-item>
<p>1. The application of meteorological flags in PySciDON successfully identified 98.5% of the spectra as acquired under clear sky conditions. The remaining 1.5% of E<sub>s</sub> spectra were manually inspected.</p>
</list-item>
<list-item>
<p>2. The ship-specific superstructure perturbation signal amounted to <inline-formula id="inf158">
<mml:math id="m168">
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<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 0.00055 sr<sup>&#x2212;1</sup>. This value is about 25% of the R<sub>rs</sub>
<sup>0&#x2b;</sup> signal in blue and green bands for relatively clear waters and about &#x223c;10% in the same bands for waters with higher reflectance (<xref ref-type="sec" rid="s11">Supplementary Appendix A</xref>, Section 2). Therefore, an accurate estimate of <inline-formula id="inf159">
<mml:math id="m169">
<mml:mrow>
<mml:msubsup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>s</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is critical to successfully retrieve the reflectance in blue and green bands, especially for low-reflectance waters.</p>
</list-item>
<list-item>
<p>3. The correction for the BRDF effects lowers R<sub>rs</sub>
<sup>0&#x2b;</sup> by &#x223c;5&#x2013;10%, allowing for proper comparison among R<sub>rs</sub>
<sup>0&#x2b;</sup> measurements from the literature and matchups used to validate satellite retrievals.</p>
</list-item>
<list-item>
<p>4. Quality evaluation showed overall high scores: &#x223c;92% of Group 1 and 94% of Group 2 are associated with a score&#x3e;&#x3d;0.71, implying that the data can be used for validation of atmospheric corrected satellite-retrieved R<sub>rs</sub>.</p>
</list-item>
</list>
</p>
<p>The methodology presented here is adaptable to other ships, to enable surveys of different water types and complement fixed platforms such as AERONET-OC (<xref ref-type="bibr" rid="B80">Zibordi et al., 2009</xref>) and WATERHYPERNET (<xref ref-type="bibr" rid="B71">Vanhellemont and Ruddick 2021</xref>). Further work will focus on providing the error budget based on estimates of the uncertainty contribution from the sensor&#x2019;s calibration, data processing, and environmental variability, essential for FRMs (<xref ref-type="bibr" rid="B82">Zibordi et al., 2015b</xref>; <xref ref-type="bibr" rid="B68">Vabson et al., 2019</xref>; <xref ref-type="bibr" rid="B66">Tilstone et al., 2020</xref>; <xref ref-type="bibr" rid="B2">Alikas et al., 2020</xref>).</p>
</sec>
</body>
<back>
<sec id="s6" sec-type="data-availability">
<title>Data Availability Statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="sec" rid="s11">Supplementary Materials</xref>, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s7">
<title>Author Contributions</title>
<p>The PhD candidate ZW was responsible for data collection and analysis and manuscript writing. MC was responsible for project conceptualization, results, discussions, and significant reviews in the manuscript.</p>
</sec>
<sec id="s8">
<title>Funding</title>
<p>ZW was supported by a Pacific Salmon Foundation/MITACS Fellowship. Fieldwork support through Ocean Networks Canada. MC was supported through funds from the NSERC NCE MEOPAR (Marine Environmental Observation, Prediction and Response Network), the Canadian Space Agency (FAST 18FAVICB09), the Canada Foundation for Innovation (CFI), and the NSERC Discovery Grant, Canada.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ack>
<p>We are thankful to the BC Ferries crew for logistical support during the installation of sensors and Ocean Networks Canada for technical support with the installation and maintenance of sensors.</p>
</ack>
<sec id="s11">
<title>Supplementary Material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/frsen.2022.867570/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/frsen.2022.867570/full&#x23;supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet1.docx" id="SM1" mimetype="application/docx" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
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