Information about polarization of light leaving the ocean surface has the potential to improve the quality of bio-optical parameter retrieval from ocean color remote sensing (OCRS). This improvement can be applied in numerous ways, such as limiting of Sun glints and obtaining information about atmospheric aerosol properties for atmospheric correction as well as increasing the accuracy of the algorithms based on the water-leaving signal. Polarization signals at the top of the atmosphere (ToA) that include the water-leaving signal are strongly influenced by atmospheric molecular scattering and by direct Sun and sky reflections from the sea surface. For these reasons, it is necessary to better understand the factors that change the polarization of light in the atmosphere–ocean system, especially in coastal zones affected by dynamic changes. In this paper, the influence of seasonal variability of light absorption and scattering coefficients (inherent optical properties; IOPs) of seawater, wind speed and solar zenith angle (SZA) on the polarization of upwelling radiance over the sea surface in the visible light bands is discussed. The results come from a polarized radiative transfer model based on the Monte Carlo code and applied to the atmosphere–ocean system using averaged IOPs as input data. The results, presented in the form of polar plots of the total upwelling radiance degree of polarization (DoP), indicate that regardless of the wavelength of light and type of water, the highest value of the above-water DoP is strongly correlated with the absorption-to-attenuation ratio. The correlation is a power function that depends on both the SZA and the wind speed. The correlation versatility for different wavelengths of light is very unusual in optics of the sea and is therefore worth emphasizing.
Satellite ocean color radiometry has been developed for decades to study the interaction of a light field within the visible part of the spectrum (i.e., 400–700 nm) with the different optically significant constituents of seawater. The research has been focusing on information coming from the intensity of water-leaving light – its measurement, retrieval, correlations and interpretation (e.g., Volpe et al., 2012; Zibordi et al., 2013; Sammartino et al., 2015). However, in addition to the light intensity, consideration of light polarization has been demonstrated to improve the accuracy of the information from a variety of remote sensing applications, i.e., in remote radar measurements (Hajnsek et al., 2003; Soloviev et al., 2012; Benassai et al., 2013) and in atmospheric correction algorithms (Chowdhary et al., 2002).
Vector radiative transfer simulations have shown that the polarization of the
underwater light field is sensitive to the nature of the suspended marine
particles. Ibrahim et al. (2012) and Ibrahim et al. (2016) demonstrated that
the attenuation-to-absorption ratio influences the polarization of upwelling
radiance below the sea surface. Polarized measurements have also been
performed near and above the sea surface. Reduction of Sun glints to improve
the ocean color retrieval has been studied by He et al. (2014), Zhou et
al. (2017) or Shaw and Vollmer (2017), and limitation of sky reflections by
observation of sea surface at the Brewster angle from the shipboard has been
examined by Wood and Cunningham (2001) and Cunningham et al. (2002).
Polarization distribution of skylight reflected off the rough sea surface has
been recently examined in many independent studies, e.g., by Zhou et
al. (2013), Harmel et al. (2012), Mobley (2015), Hieronymi (2016), Foster and
Gilerson (2016) and D'Alimonte and Kajiyama (2016). Zhou et al. (2013)
simulated the degree of polarization as well as the angle of polarization
(AoP) for reflected parts of upwelling radiance and discussed its variability
with solar zenith angle (SZA) for 0, 30, 60 and 90
The most challenging part in the analysis of the signal registered by passive
radiometric sensors at the top of the atmosphere is to remove the
contribution of the reflected photons at the air–sea interface as well as the
contribution of the atmosphere. To assess the water-leaving radiance,
Polarized signal can be measured from the satellite sensors, e.g., POLarization and Directionality of the Earth's Reflectances sensor (POLDER-2), above water using a polarization imaging camera (Freda et al., 2015) or underwater as by Loisel et al. (2008) and Harmel et al. (2011). The measurements are often supported by numerical modeling. Although there are many ongoing numerical radiative transfer models applied to ocean–atmosphere system, only some of them include light polarization (e.g., Schulz et al., 1999; Ota et al., 2010; Piskozub and Freda, 2013; Chami et al., 2015, Korkin et al., 2017). Kokhanovsky (2010) compared several vector radiative transfer models.
The polarized radiative transfer has been applied for the open ocean–atmospheric
system since the 1970s (see, for example, Kattawar et al., 1973); however, its
significance in coastal zone remote sensing has been highlighted in the last
decade. Chami et al. (2015) applied the polarized radiative transfer to
retrieve the polarizing properties of the marine phytoplankton and minerals
for different water conditions. Their analysis revealed that the application
of the polarization of light in ocean color algorithms might significantly
improve the retrieval of hydrosol properties, especially in coastal waters.
Piskozub and Freda (2013) applied their polarized radiative transfer model to
the Baltic Sea. They examined how scattering properties of seawater
represented by a single scattering albedo affected the polarization of
water-leaving radiance. They demonstrated the impact of air bubble layers of
various concentrations on the degree of polarization of water-leaving light.
They also concluded that polarization remote sensing should be performed on a
plane tilted approximately 90
The difficulty of comparison of upwelling radiance degree of polarization (DoP) over a wind-roughened southern Baltic surface for various seasons is caused by the small number of sunny days in winter and too many variable weather factors that would make it difficult to explain the differences. These undesirable weather factors are different aerosol optical depths, sky overcast and changing speed and direction of wind relative to the position of the Sun. For those reasons, we applied a polarized radiative transfer model based on the Monte Carlo code to describe the effect of seasonal changes on the polarization of upwelling radiance. The simulations involved seasonally averaged measurements of inherent optical properties from the southern Baltic basin and were run for constant weather conditions. For a detailed description of the inputs and conditions under which the simulation is performed, see the following subsections.
Numerical simulations were carried out using the Monte Carlo algorithm created by Jacek Piskozub and applied previously in Piskozub and Freda (2013). The algorithm solves the vector radiative transfer equation for the atmosphere–ocean system using the successive orders of scattering method and the Stokes formalism to track the polarization of photons. The algorithm collects information about virtual photons involved statistically in optical processes: reflection at the rough sea surface, refraction at the air–water interface, scattering and absorption within the water body and reaching the ToA. Moreover, the original Monte Carlo algorithm has been modified to track polarization changes of each photon during these processes. The unmodified version of the algorithm was successfully used, with results published in Piskozub et al. (2001), Stramski and Piskozub (2003), McKee et al. (2008, 2013) or Piskozub and McKee (2011).
Polarization information is described by four elements of the Stokes vector:
Our polarized radiative transfer model involves a virtual light source to send randomly polarized photons and track their pathways in the means of the probability of occurrence of the processes mentioned above. Reflection and refraction processes are described by Fresnel equations, and the slopes of the sea surface are characterized by the wind-dependent distribution of Cox and Munk (1956). The algorithm does not take into account additional depolarization due to enhanced whitecap fraction, described by Hu et al. (2008) – that is likely for high wind speed. The probability of processes within the water body is determined by the corresponding coefficients of absorption and scattering (including multiple scattering). Angular distribution of scattered photons is described by phase functions that, for both atmosphere and sea depth, are characterized separately for molecular scattering and particle scattering. Polarization properties of particle scattering are described by Mueller matrices that for seawater are taken from Voss and Fry (1984) and for atmospheric aerosol particles from Volten et al. (2001). The model outputs the angular distribution of the upwelling radiance and its degree of polarization at any desired level, which are presented in form of polar plots. Some of the results are additionally specified in the principal plane.
This section reports the input parameters used in the computations. The
dataset of the absorption and attenuation coefficients of seawater constituents
come from in situ measurements in the southern Baltic contained in
Sagan (2008). It is the largest dataset of ac-9 (WET Labs, Inc.) measurements
in the southern Baltic that was published in a tabular form of average
values, extreme values and standard deviations. The instrument was calibrated
in ultrapure water and routinely checked for stability with air readings. The
standard recommended data processing was performed (Zaneveld et al., 1994).
Absolute precision of measurement is 0.005 m
Total absorption coefficient taken to the simulation is a sum
Solar zenith angles in the southern Baltic region depend strongly on the
season. In months described by Sagan (2008) as the summer season, the highest
Sun position over the horizon, which means the minimum of SZA during Sun
culmination, varies between 31
Here and in the following figures, the celestial hemisphere and its reflection patterns are represented in a two-dimensional coordinate system. The zenith and the nadir are at the origin and the horizon is represented by the outermost circle. The zenith angle and azimuth angle are measured radially and tangentially, respectively. The solar azimuth angle is always set to 0.
The area of the southern Baltic Sea, on which the positions of
measurement stations are marked, divided into three areas: Pomeranian Gulf
and Gulf of Gdańsk (
Average values of total absorption coefficients, total attenuation
coefficients, their standard deviations and their ratios. All values measured
by Sagan (2008) in southern Baltic in 1999 and 2003 to 2005 are averaged for
depths 0 to 5 m and then averaged for
The full set of simulation results is available in the repository Freda (2019). It contains tables of Stokes vector elements for sectors marked with zenith–azimuth coordinates, which allows one to calculate the DoP. Examples of simulation results are presented in Fig. 2a and b in the form of
polar plots of the degree of polarization of upwelling radiance just above
the sea surface. Figure 2a shows the DoP for the average IOPs measured in the
open waters of the Baltic Sea for a wavelength of 412 nm in the summer
season, while Fig. 2b depicts an analogous case for the winter season. These
two plots are characterized by one of the highest values of the peak of DoP
of 0.88 for summer and 0.84 for winter. The azimuth position of the Sun is
0
Simulation results of above-water upwelling radiance for average
IOPs of open waters of the southern Baltic, wavelength 412 nm, for wind speed
of 5 m s
The small SZA of the summer season (45
Examples of the lowest values of the maximum DoP, referred to as max(DoP), are shown in Fig. 3a and b. They were obtained for the regions of Gulf of Gdańsk and Pomeranian Gulf, simulated for the spectral band of 555 nm, for the summer season (Fig. 3a) and for the winter season (Fig. 3b).
Simulation results of above-water upwelling radiance for average
IOPs of gulf waters of the southern Baltic, wavelength 555 nm, for speed of
wind of 5 m s
The maximum values of DoP presented in Fig. 2a (summer season, open Baltic
waters) are visible for azimuth angles close to 180
The results of Monte Carlo simulations of angular characteristics of DoP of
upwelling radiance are presented in Fig. 4. These results are obtained for
average IOPs of open Baltic waters for wind speed of 5 m s
Simulation results of above-water upwelling radiance for average
IOPs of open Baltic Sea water, for speed of wind of 5 m s
Degree of polarization plotted for the principal plane, e.g., plane
containing both the incident ray of the Sun and zenith direction (cross-section
through polar plots for azimuths 0 and 180
The analysis of individual spectral bands shows that high values of DoP correspond to the high absorption-to-attenuation ratio for the total of visible light domain (see Table 1). High values of absorption coefficient for 650–676 nm wavelengths (in the red spectral region) are caused by pure water (see Pope and Fry, 1997), while high absorption coefficients for wavelengths of the blue–green range are caused mainly by CDOM (Kowalczuk et al., 2005). The lowest values of max(DoP) for each type of water and for each season are observed for the 555 nm spectral band. The lowest values of absorption and weak spectral variability of the scattering coefficient imply that the wavelength of 555 nm is characterized by the lowest absorption-to-attenuation ratios due to the existence of a minimum of absorption for seawater containing phytoplankton. Algae cells, depending on the composition of their pigments, may have a minimum of absorption in a wide range of spectral bands from 550 nm to 660 nm (Bricaud et al., 2004). Considering the absorption of pure water that is increasing with wavelength (Pope and Fry, 1997), the minimum of the absorption in Baltic waters for the spectral band of 555 nm results.
The spectral shape of the DoP cross-sections contains two maxima, and their
angular positions depend on the absorption-to-attenuation ratio, the season
and the wind speed. The angular position of the higher maximum depends mostly
on the season, varying from approximately 60
Computations of DoP were carried out in three optically different regions of the southern Baltic. Such a division is justified in previous studies of optical and hydrological properties of the south Baltic waters (Olszewski et al., 1992). They showed a relationship between the measured values of IOPs and their location in relation to river estuaries, distance from the shore or bathymetry of the bottom.
Comparison of water type influence on the DoP is shown in Fig. 6 for two wavelengths: 440 (Fig. 6a) and 555 nm (Fig. 6b). The type of water has less influence on the DoP than the season and its representative SZA.
Degree of polarization plotted for the principal plane, i.e., plane
containing both incident ray of the Sun and zenith direction (cross-section
through polar plots for azimuths 0 and 180
However, the highest values of DoP for most zenith angles and the highest values of its peak max(DoP) for each season are observed for open Baltic Sea water. Coastal waters and gulfs are characterized by similar values of DoP in each season. For the wavelength of 440 nm, in the summer, the differences of max(DoP) between the open Baltic and other regions reach 0.02–0.04, while in the winter those differences exceed 0.05. For the 555 nm band, in the summer, the differences of max(DoP) between the open Baltic and other regions reach 0.06–0.09 and in the winter these differences reach 0.07–0.09, respectively. We also observed another regional difference in the angular position of the maxima of DoP that is noticeable in the winter season only. Two maxima of the DoP cross-sections are closer for open Baltic waters than for gulfs and coastal waters.
In the following section, we explain that the degree of polarization depends on the absorption-to-attenuation ratio, and all its regional changes are the result of the absorption-to-attenuation ratio variability.
The results of our simulations are in qualitative agreement with the measurements of above-water DoLP of the total upwelling radiance presented by Freda et al. (2015). This agreement is the similarity of the peak of degree of polarization on the polar plots, which are stretched along the azimuth angles. Freda et al. (2015) obtained lower values of measured DoLP with a maximum of 30 %–40 % (see Figs. 1 and 2 in Freda et al., 2015), which is presumably caused by different weather conditions and unknown environmental parameters during measurements, such as a high absorption coefficient in the waters of the river mouth, different aerosol optical depth or other parameters. However, despite the differences in the maximum degree of polarization, the angular distribution patterns are similar, with the peak in the vicinity of the Sun reflection azimuth angle.
This section contains the comparison of the degree of polarization for summer and winter seasons as a function of the absorption-to-attenuation ratio.
The total
All the values of maximum DoP of above-water upwelling radiance obtained for
each absorption-to-attenuation ratio are collected in Fig. 7. The summer
season case is depicted in Fig. 7a, while the winter case is depicted in
Fig. 7b. The water types are marked with different symbols, and two wind
speeds are marked with different colors. The correlations of the max(DoP) to
the ratio of
Values of maximum of degree of polarization against
absorption-to-attenuation ratios
Parameters of Eq. (3), which describes the power trend lines in Fig. 4a and b.
An analysis of all collected data shows that higher values of maximum DoP are
observed for lower wind speed. Moreover, max(DoP) has a higher range of
variability in the summer season than in the winter. Figure 7a (summer
season) shows that values of max(DoP) are between 0.64 and 0.91 for the wind
speed of 5 m s
The reason for the correlation of the maximum DoP with the absorption-to-attenuation ratio is the occurrence of multiple scattering in water depth. The degree of polarization tends to decrease after multiple scattering events. A high absorption-to-attenuation ratio means simply low scattering-to-attenuation impact and hence shallow penetration of light in the water column and low participation in multiple scattering that decreases the DoP. Such conclusion is in accordance with Piskozub and Freda (2013), who examined the influence of single scattering albedo on the polarization of water-leaving radiance. Their results show that in the Sun reflection plane, the highest value of DoP is observed when the total scattering coefficient is the lowest (see Fig. 3 in Piskozub and Freda, 2013).
The influence of wind speed on the DoP values shown in Fig. 7a and b is very clear: sea-surface roughness depolarizes the reflected light. Zhou et al. (2013) demonstrated that wind speed and wind direction can change the polarization patterns of reflected skylight from a rough sea surface to a certain extent. Our study shows, in particular, that high wind speed results in lower values of max(DoP) of the total upwelling radiance. Such regularity is filled for all types of water and all spectral bands.
Our algorithm does not consider possible additional depolarization, which is
likely especially for high wind speeds (15 m s
The results of the correlation of the maximum DoP with the absorption-to-attenuation ratio seem to be coincident with the results of Ibrahim et al. (2012), who studied the degree of linear polarization just below the air–water interface. Their correlation of attenuation-to-absorption ratio with DoLP displays a hyperbolic shape (see Figs. 5 to 8 in Ibrahim et al., 2012). Therefore, for an inverted absorption-to-attenuation ratio, it would be near linear. The modeling results of Ibrahim et al. cannot be compared directly to the results presented in this paper because they received DoLP just below the sea surface, and we focused on DoP just above the surface. However, our choice of seawater absorption-to-attenuation ratio, which can be called the relative absorption value (to total attenuation), as a parameter correlated to degree of polarization seems to be more suitable.
In this paper, we have investigated the relationship between the seawater
absorption-to-attenuation ratio and the degree of radiance polarization above
the rough sea surface. Using a Monte Carlo polarized radiative transfer
model, we compared simulated polarization patterns in three optically
different regions in the southern Baltic (i.e., open Baltic, gulfs, coastal
waters), two seasons (defined by their typical solar zenith angles:
45
We found that the variability of the maximum of DoP depends more on seasonal
than regional changes and can be explained to a large degree by the
absorption-to-attenuation ratio. A thorough analysis has shown that there is
a strong correlation between max(DoP) and the ratio mentioned previously. The
correlation is well described (
For the ocean color remote sensing application, only the water-leaving part of the upwelling radiance carries useful information about bio-optical parameters of seawater, although it is a small fraction of the total upwelling radiance. Polarized radiative transfer modeling makes it possible to separate the water-leaving part and, in this case, the noise-inducing reflected part and therefore to enhance the quality of information on the seawater optically active components retrieved by above-water sensors – airborne or satellites. Our study is a step toward inclusion of polarization properties in the bio-optical models in the Baltic Sea. However, the conclusions from the research, in our opinion, should be universal and apply also to other water bodies.
All data and modeling results are available online at the following repository:
SS provided the results of absorption and attenuation coefficient measurements, and a contribution to the article on IOPs. KH took part in the preparation of the manuscript and data analysis. WF performed the modeling, developed its results and wrote a large part of the manuscript.
The authors declare that they have no conflict of interest.
The authors are grateful to Jacek Piskozub for his valuable comments and suggestions.
This research has been supported by the National Science Centre Poland (grant no. UMO-2012/07/D/ST10/02865) and by Gdynia Maritime University (grant no. WM/2019/PZ/05).
This paper was edited by Oliver Zielinski and reviewed by two anonymous referees.