ABSTRACT Ocean colour remote sensing has supported research on subjects ranging from marine ecosystems to climate change for almost 35 years. However, as the framework for ocean colour

remote sensing is based on the radiation intensity at the top-of-atmosphere (TOA), the polarisation of the radiation, which contains additional information on atmospheric and water optical

properties, has largely been neglected. In this study, we propose a new simple concept to ocean colour remote sensing that uses parallel polarisation radiance (PPR) instead of the

traditional radiation intensity. We use vector radiative transfer simulation and polarimetric satellite sensing data to demonstrate that using PPR has two significant advantages in that it

ECOLOGY Article Open access 12 July 2023 ANOMALOUS TRENDS IN GLOBAL OCEAN CARBON CONCENTRATIONS FOLLOWING THE 2022 ERUPTIONS OF HUNGA TONGA-HUNGA HA’APAI Article Open access 10 May 2024 A

GLOBAL LONG-TERM OCEAN SURFACE DAILY/0.05° NET RADIATION PRODUCT FROM 1983–2020 Article Open access 14 June 2022 INTRODUCTION The successful launch of the Coastal Zone Colour Scanner (CZCS)

in 1978 was a milestone in the history of satellite ocean colour remote sensing1. Since then, more than twenty ocean colour satellite sensors have been launched

(www.ioccg.org/sensors_ioccg.html). These sensors capture continuous global ocean colour data (e.g. chlorophyll concentration, primary production), which provide significant benefits for

research in areas such as biological oceanography2,3 and climate change studies4,5,6. According to the current framework for ocean colour remote sensing, the satellite sensor first measures

the intensity of the upward spectral radiation at the top-of-atmosphere (TOA). The varying intensities are then used to retrieve the water-leaving radiance after atmospheric correction,

leading to the further retrieval of the optically active marine components (e.g. phytoplankton, minerals and coloured dissolved organic matter)7. However, the current framework does not

consider the polarisation of light, which could be helpful in the retrieval of water properties8. Previous studies based on radiative transfer simulations have revealed that polarisation

information on the upwelling radiation at the sea surface can improve the retrieval of the suspended particulate matter9,10 and water inherent optical properties (e.g., absorption,

scattering and backscattering coefficients) in coastal waters11,12 and help in the separation of organic and inorganic particles13,14,15. In addition, the polarisation information at the TOA

measured by satellite and airborne sensors is consistent with radiative transfer simulations and field measurements16,17 and can be used to classify aerosol types, thus improving the

water-leaving radiance retrieval18,19,20. However, despite the many advantages of using polarisation information, none of the planned future ocean colour missions include polarimetric ocean

colour sensors (www.ioccg.org/sensors/scheduled.html), which limits the capacity to advance polarisation ocean colour remote sensing. Moreover, the past and current polarimetric satellite

optical sensors, such as the POLDER (Polarisation and Directionality of the Earth's Reflectance) sensors on the ADEOS-I (Nov 1996 – Jun 1997), ADEOS-II (Apr 2003 – Oct 2003) and PARASOL

(Dec 2004 – present) satellites, were mainly designed to measure the radiative and microphysical properties of clouds and aerosols21. In this study, we propose a new simple concept for

ocean colour satellite remote sensing using the parallel polarisation radiance (PPR) instead of the traditional radiation intensity. Although the horizontal and vertical polarisation

radiances have been widely used in microwave satellite remote sensing, they have never been used in ocean colour remote sensing. The reason for the choice of the PPR instead of the vertical

polarisation radiance (VPR) is that the sea surface reflectance of PPR is general less than that of the VPR. In addition, unlike the Stokes vector and its polarisation components, PPR is a

scalar parameter which is similar to the traditional radiation intensity and it could be easily understood and exploited by the ocean colour community. RESULTS THE CONCEPT OF PARALLEL

POLARISATION RADIANCE (PPR) The upward radiation at the TOA can be fully described by the Stokes vector as follows22: where _E__l_ and _E__r_ are components of the electric vector in the

meridian plane (determined by the viewing direction of the satellite and the local zenith) and in the plane perpendicular to the meridian plane, respectively. and are the respective

conjugate values of _E__l_ and . It should be noted that we neglect a common multiplier in Eq. (1). _I_ is the total radiance (i.e., the intensity measured by the ocean colour sensor), _Q_

is the radiance linearly polarised in the meridian plane or perpendicular to the meridian plane, _U_ is the radiance linearly polarised in the direction 45° to the meridian plane and _V_ is

the radiance circularly polarised. _I_, _Q_ and _U_ can be analytically deduced if a satellite sensor measures the upward radiation intensities at three angles. Generally, _V_ is negligible

for the upward radiation at the TOA above oceans. The Stokes vector describes electromagnetic radiation in terms of measurable quantities, including the polarisation state of the

electromagnetic field. For satellite applications, we define PPR as: Then: For unpolarised light, such as the incident solar radiance at the TOA, then _I__p_ = _I_. Although PPR is a basic

parameter in classical electromagnetic radiation theory, it has never been applied in ocean colour remote sensing. In the following sections, we demonstrate two advantages of ocean colour

remote sensing using PPR. DIMINISHING SUN GLINT Sun glint is a major issue for radiation intensity based ocean colour remote sensing23. In most cases, sun glint contaminated pixels are

directly masked and excluded from the data analysis24. To demonstrate the effectiveness of PPR in diminishing sun glint, we simulated the upward Stokes vector at the TOA using the vector

radiative transfer model named PCOART25 (see section Methods). The radiative transfer simulations with flat sea surface reveal that the total radiance at the TOA contains strong sun glint at

the specular reflectance geometries for all solar zenith angles (Figs. 1(a) and 1(c)). However, for the PPR at the TOA, the sun glint decreases with the solar zenith angle and disappears

for solar zenith angles larger than 35° (Figs. 1(b) and 1(d)). For rough surface, we can see that the total radiance at the TOA still contains sun glint at the specular reflectance

geometries for all solar zenith angles (see the supplement Fig. S1). Yet, for the PPR at the TOA under rough surface, the sun glint decreases with solar zenith angle and disappears for solar

zenith angles larger than 35°, which is similar with the results under flat surface. Comparing to the strong sun glints along the principal plane under flat surface, sun glints are weaker

and wider range of azimuth (off principal plane) under rough surface. We used polarimetric remote sensing data from the POLDER sensor on the ADEOS-II satellite to further validate the

ability of diminishing sun glint by PPR under real world conditions. The POLDER on ADEOS-II could measure _I_, _Q_ and _U_ at three bands (443 nm, 670 nm and 865 nm) at 14 observing angles.

Fig. 2 shows the reflectance of total radiance and PPR at 670 nm on 10 July 2003 at the 12th observing angle. It should be noted that the data for the 13th and 14th observing angles on this

day are unusable. At the 12th observing angle, strong sun glint clearly exists in the southern hemisphere in the total radiance map (Fig. 2(a)). However, the glint disappears in the map of

the PPR (Fig. 2(b)) because sun glint is generally located in regions where the solar zenith angle is larger than 35° (Fig. 2(c)). It needs to note that real polarimetric remote sensing data

cover different atmosphere and ocean conditions including the variations of aerosol type, aerosol optical thickness and rough sea surface. Therefore, the POLDER polarimetric observations

fully support the results of the radiative transfer simulation. In summary, the radiative transfer simulation and satellite observations demonstrate that PPR is capable of diminishing the

sun glint at solar zenith angles larger than 35°. This reduced sun glint can improve the data availability of ocean colour remote sensing, especially for early morning and late afternoon

observations by geostationary ocean colour satellite26 and for middle to high latitude observations by polar-orbit ocean colour satellite. ENHANCING THE OCEAN COLOUR SIGNAL The ocean colour

signal for the total radiance at the TOA can be expressed as27: where _I__b_ is the background upward radiance at the TOA with atmosphere and pure seawater, while _I__t_ is the upward

radiance at the TOA with atmosphere and seawater including the ocean colour components (e.g. chlorophyll, suspended particle matter). The first requirement of ocean colour remote sensing is

that the ocean colour signal should be sensitive to the variation in the ocean colour components and that the capacity to discern the changes in the ocean colour components increases with

the sensitivity of the signal. We normalise Eq. (4) according to _I__b_ and then get the normalised ocean colour signal for the total radiance as: Similarly, the normalised ocean colour

signal for PPR can be expressed as: where _I__pb_ is the background PPR at the TOA with atmosphere and pure seawater, while _I__pt_ is the PPR at the TOA with atmosphere and seawater

including the ocean colour components. Generally, the greater the absolute value of the normalised ocean colour signal, the more the ocean colour signal can contribute to the total signal at

the TOA. We simulated the total radiance and the PPR at the TOA for different concentrations of chlorophyll a (_Chla_) and suspended particulate matter (_Tsm_) using the PCOART radiative

transfer model (see section 4 Methods) and obtained the normalised ocean colour signals for total radiance and PPR. Here, we only show the results for the solar-viewing relative azimuth

angles of 0°, 45°, 90°, 135° and 180° (corresponding to the specular plane) in Fig. 3 for _Chla_ and Fig. 4 for _Tsm_. For low solar zenith angles as represented by 0°, the PPR significantly

enhances the ocean colour signal for viewing zenith angles larger than 20° as compared with the total radiance and this enhancement increases rapidly with the viewing zenith angle (Figs.

3(a) and 4(a)). For moderate solar zenith angles as represented by 30°, the PPR continues to enhance the ocean colour signal for both _Chla_ and _Tsm_, especially at the relative azimuth

angles of 135° and 180° (Figs. 3(b) and 4(b)). For large solar zenith angles as represented by 60°, the PPR enhances the ocean colour signal at relative azimuth angles of 0°, 135° and 180°

under a low viewing zenith angle, while it slightly reduces the ocean colour signal at relative azimuth angles of 45° and 90° (Figs. 3(c) and 4(c)). In summary, PPR can enhance the ocean

colour signal relative to the total radiance at the TOA, especially for large satellite viewing zenith angles under a low to moderate solar zenith angle, which can improve the ocean colour

component retrieval at the edge of the view of the ocean colour satellite. APPLICATION TO OCEAN COLOUR REMOTE SENSING The greatest challenge for polarimetric ocean colour remote sensing

relates to the retrieval of the water-leaving radiation from the satellite measured _I_, _Q_ and _U_, or the corresponding atmospheric correction. The total radiance measured by the

satellite sensor can be written as28: where _I__r_ is the Rayleigh-scattering radiance in the absence of aerosols, _I__a_ is the aerosol scattering radiance including the interactive

scattering between molecules and aerosols, _I__w_ is the desired water-leaving radiance and _t__v_ is the diffuse transmittance from sea surface to satellite. It should be noted that we

ignore the reflectance from whitecaps and sun glint. Similarly, _Q_ at the TOA can be expressed as the sum of the contributions from Rayleigh scattering (_Q__r_), aerosol scattering (_Q__a_)

and water-leaving radiation transmitted to the TOA (_Q__w_)29, as follows: We obtain the PPR at the TOA by Eq. (7) plus Eq. (8) as: The Rayleigh-scattering components _I__r_ and _Q__r_ can

be accurately calculated using a vector radiative transfer model (e.g., PCOART) with the knowledge of the atmospheric pressure and wind speed28. However, the aerosol scattering is highly

variable and the components _I__a_ and _Q__a_ cannot be predicted a priori28. In the first stage, we use the method proposed by Gordon and Wang (1994)28 to estimate the aerosol scattering

PPR over open ocean. This method uses two near-infrared bands to select the appropriate aerosol models from a set of predefined candidate models and extrapolates the aerosol scattering

radiation at the near infrared wavelength to a visible light spectral regime. In addition, _t__v_ can be estimated by the determined aerosol model and the optical thickness. Therefore, the

only unknown for the retrieval of the water-leaving radiance is _Q__w_. Based on the simulations in section 2.3 (see section 4 Methods), we get the _Q__w_ at the TOA as: where _Q__bg_ is the

background value from the atmospheric scattering in the absence of seawater and _Q__t_ is the value from both the atmospheric and seawater scatterings. Fig. 5 shows the percentage of the

contribution of _Q__w_ to _I__p_ at the TOA for different wavelengths (443 nm for _Chla_ and 670 nm for _Tsm_), solar zenith angles, relative azimuth angles and _Chla_ and _Tsm_

concentrations. The percentage is relative larger at short wavelength (443 nm) than it at long wavelength (670 nm), but generally less than 1%, indicating that it is reasonable to neglect

_Q__w_ as compared to _I__p_ at the TOA. Actually, both the radiative transfer simulations and polarimetric remote sensing data showed that the polarized reflectance at the TOA was virtually

insensitive to biomass content over open ocean17,30. Two factors are expected to be responsible for this result, one is that the water-leaving radiation is mostly induced by underwater

multi-scattering processing, which results in low polarisation; the other is that the atmospheric scattering further reduces the polarisation of the water-leaving radiation when it transmits

from the sea surface to the TOA. It should be noted that for some specific observing geometries (mainly in the specular plane) _Q__w_ cannot be neglected, as the percentages in these cases

can be up to 3%. Previous studies have also revealed that the polarisation information of the water-leaving radiation at the sea surface at the specular plane can be helpful for the

retrieval of suspended particulate matter9,14. Here, we only focus on the retrieval of the water-leaving radiance by neglecting _Q__w_. Therefore, the retrieval of _Q__w_ is beyond the scope

of this study and needs to be investigated in future studies. In addition to the simulation, we used the polarimetric remote sensing data from POLDER on 10 July 2003 to validate the

feasibility of using the PPR from real satellite data. Because the POLDER sensor only has three polarisation bands, 443 nm, 670 nm and 865 nm, we were unable to apply the method proposed by

Gordon and Wang (1994)28 to estimate the aerosol scattering PPR based on the aerosol model selection and extrapolation. Similar to the traditional atmospheric correction processes, we

obtained the total radiance and PPR of the aerosol scattering at 865 nm using the assumption that water-leaving radiation can be neglected at the near-infrared wavelength over open ocean. We

further assumed that the aerosol scattering is “white”, which means that the aerosol scattering reflectance is equal for all bands31 and obtained the total radiance and PPR of the aerosol

scattering at 443 nm and 670 nm. In the future, if satellites have two or more NIR bands with polarisation observation, we can determine the aerosol models from the satellite data directly.

As in the radiative transfer simulations, we neglected the _Q__w_ and finally obtained the desired water-leaving radiances at 443 nm and 670 nm from both the total radiance and the PPR (Fig.

6 for an example at the 12th observing angle; Supplement Figs. S4–S15 for all the 12 observing angles). The normalised water-leaving radiances retrieved by the total radiance and the PPR

are reasonably consistent for both 443 nm and 670 nm. In addition, the PPR enabled the water-leaving radiance to be retrieved in the sun glint areas of the total radiance with solar zenith

angles larger than 35°, which provides further evidence of the capacity of PPR to diminish sun glint contamination. Quantitative comparison of the normalised water-leaving radiance retrieved

by the total radiance and the PPR at all 12 observing angles combined revealed correlation coefficients of 0.92 and 0.97 with standard deviations of 0.32 and 0.09 for 443 nm and 670 nm,

respectively, indicating the feasibility of using PPR for ocean colour remote sensing (Fig. 7; Supplement Figs. S16–S17 for the results for each observing angle). DISCUSSION Our results from

both the radiative transfer simulation and the polarimetric satellite data reveal that the use of PPR can significantly reduce the sun glint at moderate to high solar zenith angles.

Although the total radiance in sun glint regions is generally one order greater than in non-glint regions, the linear polarisation component _Q_ is also one order larger than in the

non-glint regions but in negative value32. Therefore, the compensating effect between the total radiance and _Q_ reduces the sun glint in the PPR. Furthermore, the results from the radiative

transfer simulations show that PPR can increase the overall ocean colour signal relative to the total radiance at moderate to high viewing zenith angles. The reason for this result is

similar to that for the reduced sun glint using PPR. The total radiance at the TOA increases with the viewing zenith angle due to the increase in the atmospheric path length, while the

water-leaving radiance transmitted to the TOA decreases due to the reduced atmosphere diffuse transmittance. Thus, the ocean colour signal generally decreases as the viewing zenith angle

increases, as revealed in Figs. 3 and 4. Yet, for the PPR at the TOA, although the total radiance increases with the viewing zenith angle, _Q_ also increases correspondingly but generally in

negative value. As the negative value of _Q_ slows the increase in the PPR as the viewing zenith angle increases, the PPR thus enhances the ocean colour signal in relation to the total

radiance. Of course, the advantages demonstrated in this study are only part of the merits of polarimetric observations, as it is well known that polarimetric radiances are useful for the

retrieval of aerosol optical properties18,19,33,34 and can further improve the atmospheric correction of the ocean colour remote sensing20. In conclusion, we propose a new simple concept for

ocean colour satellite remote sensing that uses parallel polarisation radiance (PPR) instead of the traditional radiation intensity. Since PPR is a scalar parameter which is the form used

by the current ocean colour remote sensing based on the radiation intensity, it could be easily understood and exploited by the ocean colour community. Thus, our concept may open new doors

for satellite ocean colour remote sensing and is potentially applicable to forthcoming satellite missions dedicated to measuring the polarimetric properties of radiation, such as the NASA

“Preparatory Aerosols, Clouds and Ecosystems” (PACE) mission and the European Space Agency (ESA) “Multi-directional, Multi-polarisation and Multispectral” (3 MI) mission, which are scheduled

for launch around 2018. However, the polarisation observations of these satellite missions are not designed for ocean colour remote sensing. Although PACE was driven by the ocean colour

community, its polarimeter instrument was designed for the observation of the aerosols and clouds. The low signal-to-noise ratio and small number of the polarimetric bands of these sensors

limit their application to polarimetric ocean colour remote sensing. Thus, we suggest that the next generation of ocean colour sensors should measure PPR to enhance their observational

capability. METHODS We used the PCOART vector radiative transfer model to simulate the upward radiation Stokes vector at the TOA. PCOART uses the matrix-operator method to solve the vector

radiative transfer in a coupled ocean-atmosphere system and has been validated by standard radiative transfer problems in the atmosphere and ocean and by real polarimetric remote sensing

data from POLDER25. RADIATIVE TRANSFER SIMULATION FOR SUN GLINT Using PCOART, we simulated the upward radiation Stokes vector at the TOA in the specular plane using the following conditions:

* 1 The atmosphere-ocean system is divided into three layers. The upper layer comprises atmospheric molecules with optical thicknesses of 0.2361 (443 nm) and 0.0872 (670 nm). The middle

layer is the maritime aerosol with 90% relative humidity and an optical thickness of 0.2 for both 443 nm and 670 nm. The bottom layer is full absorption seawater with a flat surface. The

refractive index of the seawater is 1.34 for both 443 nm and 670 nm25. * 2 The incident solar irradiances at the TOA are 196.98 mW/(cm2·μm) (433 nm) and 159.31 mW/(cm2·μm) (670 nm). * 3 The

solar zenith angle varies from 0° to 70° with a step of 1°. By summing the simulated total radiance and the linear polarisation component _Q_, we get the PPR at the TOA in the specular plane

for different solar and viewing zenith angles. It needs to note that we use a two-layer atmosphere with all molecules placed on top of the aerosols in the simulation. Based on scalar Monte

Carlo simulations, Antoine and Morel (1998)35 found that the differences of total radiances at the TOA between 50-layer and two-layer atmospheres were below 0.5% on average and they

concluded that the total radiances at the TOA were safely computed by using a two-layer atmosphere for viewing zenith angle as great as 70° if the aerosols were not absorbing. Here, we

further validated the rational of the two-layer atmosphere for the simulation of the polarisation radiances by simulating the Stokes vector at the TOA with two-layer atmosphere and

mixed-layer atmosphere (aerosols mixed together with molecules), respectively (see the supplement Figs. S2–S3). Similar to the results of the total radiances founded by Antoine and Morel

(1998)35, the differences of the polarisation radiances at the TOA between these two atmospheres are quite small for viewing zenith angle less than 70°. RADIATIVE TRANSFER SIMULATION FOR THE

OCEAN COLOUR SIGNAL Using PCOART, we simulated the upward radiation Stokes vector at the TOA at solar zenith angles of 0°, 30° and 60° for pure atmosphere, pure seawater and seawater with

different concentrations of _Chla_ and _Tsm_, using the following steps: * 1 Simulate the upward radiation Stokes vectors at 443 nm and 670 nm for pure atmosphere. The atmosphere-ocean

system has the same setup as that in the simulation of the sun glint. * 2 Simulate the upward radiation Stokes vectors at 443 nm and 670 nm for pure seawater. Similar to the simulation of

the sun glint, the atmosphere-ocean system is divided into three layers, with the bottom layer consisting of pure seawater with absorption and scattering coefficients taken from Smith and

Baker (1981)36. * 3 Simulate the upward radiation Stokes vectors at 443 nm for different _Chla_ concentrations. The atmosphere-ocean system has the same setup as the simulation of pure

seawater, except the bottom layer is a mix of pure seawater and phytoplankton (character by _Chla_). The _Chla_ concentrations are taken as 0.01, 0.05, 0.1, 0.5, 1, 2.5, 5.0, 7.5, 10.0 and

30 μg/l with homogeneous vertical distribution. The absorption and scattering coefficients of the phytoplankton are determined by the _Chla_ concentrations according to the bio-optical

models in Morel (1991)37 and Gordon and Morel (1983)38, respectively. The scattering phase matrix of the phytoplankton (refractive index 1.05) is calculated by Mie theory with a Junge power

law size distribution ranging from 0.1 to 50 μm with a slope of −3.09. The optical thickness of the water layer is taken as 1000 to eliminate the reflective effect of the seawater bottom. *

4 Simulate the upward radiation Stokes vectors at 670 nm for different _Tsm_ concentrations. The setup of the atmosphere-ocean system is the same as for step (3), except the _Chla_ is

replaced by _Tsm_. The _Tsm_ concentrations are taken as 0.1, 0.5, 1, 5, 10, 25, 50, 75, 100 and 200 mg/l with homogeneous vertical distribution. The absorption and scattering coefficients

of the particles are determined by the _Tsm_ concentration according to the bio-optical model adopted from Bowers et al. (1998)39. The scattering phase matrix of the _Tsm_ (refractive index

1.2) is calculated by Mie theory with a Junge power law size distribution ranging from 0.1 to 50 μm with a slope of −3.09. We selected the 443 nm and 670 nm bands because 443 nm is highly

sensitive to _Chla_ and 670 nm is highly sensitive to _Tsm_9. Based on the simulated upward radiation Stokes vector, we finally get the PPR at the TOA for different concentrations of _Chla_

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ACKNOWLEDGEMENTS This study was supported by the National Basic Research Programme (“973” Programme) of China (grant #2009CB421202), the Public Science and Technology Research Funds Projects

for Ocean Research (grant #200905012), the National Natural Science Foundation of China (grants #41322039, #41271378 and #40976110), the National Key Technology Support Program of China

(grant #2013BAD13B01 and #2012BAH32B01) and the “Global Change and Air-Sea Interaction” project of China. We thank the French space agency Centre National d'Etudes Spatiales (CNES) for

providing the POLDER data. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic

Administration, Hangzhou, China Xianqiang He, Delu Pan, Yan Bai, Difeng Wang & Zengzhou Hao * Institute of Remote Sensing and Earth Sciences, Hangzhou Normal University, Hangzhou, China

Delu Pan & Yan Bai * Department of Ocean Science and Engineering, Zhejiang University, Hangzhou, China Xianqiang He & Delu Pan Authors * Xianqiang He View author publications You can

also search for this author inPubMed Google Scholar * Delu Pan View author publications You can also search for this author inPubMed Google Scholar * Yan Bai View author publications You

can also search for this author inPubMed Google Scholar * Difeng Wang View author publications You can also search for this author inPubMed Google Scholar * Zengzhou Hao View author

publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS X.H. performed the radiative transfer simulations, designed the algorithm and wrote the manuscript.

D.P. designed the algorithm. Y.B. analyzed the data and wrote the manuscript. D.W. processed the satellite data. Z.H. analyzed the data. ETHICS DECLARATIONS COMPETING INTERESTS The authors

declare no competing financial interests. ELECTRONIC SUPPLEMENTARY MATERIAL SUPPLEMENTARY INFORMATION Supplement Figures RIGHTS AND PERMISSIONS This work is licensed under a Creative Commons

Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ Reprints and permissions ABOUT THIS ARTICLE

CITE THIS ARTICLE He, X., Pan, D., Bai, Y. _et al._ A new simple concept for ocean colour remote sensing using parallel polarisation radiance. _Sci Rep_ 4, 3748 (2014).

https://doi.org/10.1038/srep03748 Download citation * Received: 27 June 2013 * Accepted: 23 December 2013 * Published: 17 January 2014 * DOI: https://doi.org/10.1038/srep03748 SHARE THIS

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