## Abstract

Volume scattering functions were measured using two instruments in waters near the Ocean Station Papa (50°N 145°W) and show consistency in estimating the $\chi$ factor attributable to particles (${\chi _p}$). While ${\chi _p}$ in the study area exhibits a limited variability, it could vary significantly when compared with data obtained in various parts of the global oceans. The global comparison also confirms that the minimal variation of ${\chi _p}$ is at scattering angles near 120°. With an uncertainty of ${\lt}{10}\%$, ${\chi _p}$ can be assumed as spectrally independent. For backscatter sensors with wide field of view (FOV), the averaging of scattering within the FOV reduces the values of ${\chi _p}$ needed to compute the backscattering coefficient by up to 20% at angles ${\lt}{130}^\circ$.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. INTRODUCTION

Upon encountering particles, photons are either absorbed or scattered [1]. The volume scattering function (VSF, $\beta ;\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$) describes angular distribution of the scattered light and is solely determined by the characteristics of the particles. As an inherent optical property of particles in the aquatic environment, the VSF, and in particular its backward portion, plays a vital role in ocean color remote sensing, determining the distribution and magnitude of solar radiation that is scattered out of the water and hence is amenable to remote observation [2]. The backward portion of a VSF, i.e., at scattering angles ($\theta$) from 90° to 180°, is often quantified using two variables: total backscattering coefficient (${b_b};\;{{\rm m}^{- 1}}$) and the $\chi$ (sr) factor, where

andFrom their respective definitions, ${b_b}$ represents the overall magnitude of the backscattering and $\chi$ factor, or, more precisely, its inverse (${1/}\chi$) describes the overall shape of the backscattering. Both quantities are important in ocean color remote sensing, even though ${b_b}$ has been accounted for explicitly in modeling the remote sensing reflectance [3,4], whereas the effect of the $\chi$ factor is implicitly embedded in the bidirectional reflectance distribution function (BRDF) correction [5,6]. Recent theoretical development [7] based on Zaneveld’s remote sensing reflectance formula [2,8] has allowed BRDF to be modeled using the $\chi$ factor explicitly, opening the possibility for estimating the $\chi$ factor and better correcting the BRDF effect from multi-angle observation of ocean color. Scattering by pure seawater can be predicted as a function of temperature, salinity, and pressure with an uncertainty ${\lt}{2}\%$ in almost any natural water body in the global oceans [9–12]; it is, therefore, assumed to be known. Removing the contribution by water from Eqs. (1) and (2), one has ${\chi _p}$, representing the $\chi$ factor attributable to particles. ${\chi _p}$ is the focus of this study.

In the field, the VSF is often measured only at one backward angle and then scaled by the corresponding ${\chi _p}$ factor at this angle to derive ${b_{\textit{bp}}}$ in Eq. (2). The value of ${\chi _p}$ at a particular scattering angle used in scaling has been assumed to be relatively invariant throughout the global oceans. For example, the current biogeochemical Argo (BGC-Argo) backscattering data processing assumes ${\chi _p} = {1.076}$, 1.097, and 1.142 for scattering angles of 124°, 142°, and 150°, respectively [13], with assigned uncertainty for each assumed value being ${\lt}{5}\%$ [14]. In other words, the angular shape of ${\chi _p}$ is assumed to be more or less fixed. This assumption for practical applications is in stark contrast with the theoretical expectation. Because the angular shape of backscattering is very sensitive to the size [15], composition [15], shape [16], and internal structure [17] of particles, all of which are expected to vary significantly in the natural aquatic environment, one expects that the $\chi$ factor for natural particle assemblages should vary significantly as well. Observations of ${\chi _p}$ for natural particles can help to reconcile this disconnect between the practical assumption and the theoretical expectation. As shown in Eqs. (1) and (2), estimation of ${\chi _p}$ requires fine angular resolution of the VSF at scattering angles from 90º to near 180°, which unfortunately few instruments had been capable of measuring in the field until recently [14,18–20]. Because of this, our knowledge of natural variability of ${\chi _p}$ is very limited.

${\chi _p}$ has been estimated from the VSFs measured
using several prototype instruments: volume scattering meter (VSM) [18] and its three improved versions, all
named multispectral VSM (MVSM), multi-angle scattering optical tool
(MASCOT) [14], polarized VSM
(POLVSM) [21] and an imaging VSF
meter (I-VSF) [22]. Results based
on VSM/MVSM, which have mainly operated in various coastal waters around
the world, including the LEO-15 site off of New Jersey [23], Mobile Bay (ZMob14) and Monterey Bay
(ZMon14) [24], the coastal area of
the Black Sea [25], and the coastal
water of the North Adriatic Sea [26], showed a rather variable ${\chi _p}$ [24,27]. Harmel *et al.* [27]
also found ${\chi _p}$ varied among different phytoplankton
cultures that were measured using POLVSM and I-VSF. On the other hand,
results based on MASCOT, which has operated in diverse environments
including both coastal and open oceanic waters, showed a very limited
variability in ${\chi _p}$ [14]. All of these instruments are prototypes, each with different
design. While some of these instruments have been subjected to laboratory
inter-comparison [27], none of them
have been compared directly in the field setting. It is not inconceivable
that the performance of each of these instruments and their differences
could have played a part in skewing the observed variability of ${\chi _p}$ in the natural environment.

The objective of this study is to investigate the natural variability of ${\chi _p}$ in a clear oceanic environment. Specifically, the study was designed to overcome the challenges mentioned above in measuring ${\chi _p}$ and interpreting the results. First, two scattering meters were used: MVSM and a laser in situ scattering and transmissiometry (LISST) VSF. LISST-VSF is the first commercially available scattering instrument that measures the VSF in the field. The use of two different instruments allows us to quantify and/or eliminate the potential observational difference. Second, we focused on a clear oceanic environment, for which relatively fewer data on ${\chi _p}$ exist. We also investigate two issues pertinent to the application of ${\chi _p}$ in scaling the VSF measured at one angle, for example, by a commercial SeaBird backscatter sensor, to derive the total backscattering coefficient. Because different types of SeaBird backscatter sensors measure the VSF at different wavelengths and all with a wide field of view (FOV), it is important to examine the spectral variation of ${\chi _p}$ and the effect of FOV on ${\chi _p}$.

## 2. DATA AND METHOD

The VSFs were measured during the NASA export processes in the ocean from
remote sensing (EXPORTS) first field campaign conducted in the North
Pacific Ocean near Ocean Station Papa (OSP; 50°N 145°W) from 14 August to
10 September 2018 onboard the R/V *Sally Ride*
(Fig. 1). A total of 315 water
samples (10 L each) were collected by a conductivity-temperature-depth
(CTD) rosette at various depths (down to 3000 m). For each water sample,
approximately 1.8 L and 1.5 L were slowly pumped peristaltically to the
sampling enclosure of the LISST-VSF and MVSM (version 3), respectively. A
LISST-VSF consists of two optical components, forward ring detectors
measuring the scattering from 0.08° to 14.4° at 32 angles (similar to
LISST-100X) and an eyeball component measuring the scattering 15° to 155°
with 1° increment. The FOV of the eyeball is 0.9°, achieved using a
spatial filter made up of a 300 µm pin hole and a pair of 15 mm focal
length lenses. This LISST-VSF operates at 517 nm. The LISST-VSF takes
about four seconds to scan the full angular range, where, during the
experiment, 30 full angular measurements were taken for each sample, and
their median values were used for further analysis following Hu *et al.* [20].
The MVSM operates at eight wavelengths (443, 490, 510, 532, 555, 565, 590,
and 620 nm) and measures scattering from 0.5° to 179° with 0.05°
increments, binned to a 0.25° interval [28]. The FOV is 1.5° at scattering angles from 10 to 170° and 0.2°
at near forward and backward directions. The MVSM uses a prism that
rotates 360° and produces two measurements of the VSF (0°–180° in
ascending angular order, and 180°–360° in descending angular order) in
approximately 1 min at each wavelength. Due to time constraint during the
experiment, we generally operated MVSM in full spectral mode only for the
near surface samples, occasionally for the deeper water samples, and at
one wavelength of 532 nm for the others. Also, because of this time
constraint, only one measurement for each water sample was taken in full
spectral mode, and six repeated measurements were taken for each water
sample when using only 532 nm. Because each measurement represents a 360°
scan and hence consists of two VSFs, when operating in the multispectral
mode, the final VSF data from MVSM were an average of two measurements for
each wavelength, and, when operating in the single-wavelength mode, the
final VSF data at 532 nm were an average of 12 measurements.

The VSF due to particles (${\beta _p}$) was calculated by subtracting the pure
seawater VSF (${\beta _w}$) from the bulk VSF ($\beta$). ${\beta _w}$ was computed using the Zhang *et al.* [10]
model using the water temperature and salinity that was measured
concurrently with water sampling. The estimated ${\beta _p}$ was then applied to Eqs. (1) and (2) to compute ${\chi _p}$, which is straightforward for the MVSM
data. For the LISST-VSF data, which are only available up to 155°, of
which data from 145° to 155° were further discarded due to
internal-reflection contamination, ${\beta _p}$ at angles from 145° to 180° is needed to
estimate the backscattering coefficient. To do that, each LISST-VSF data
at angles from 90° to 145° were partitioned into a linear combination of
two end members following Zhang *et al.*
[29]. The two end members, for
which the shapes of backscattering are known analytically, were then used
to reconstruct the VSF at angles from 145° to 180°. An example of VSF
extrapolated using this approach is shown in Fig. 2(a). The backscattering coefficients were then
calculated using the measured VSFs from 90° to 145° and the reconstructed
VSFs from 145° to 180°. This approach of extending the VSF data towards a
180° scattering angle has also been tested in several recent studies
involving the use of LISST-VSF [19,20,30].

Relatively clear water near OSP poses a challenge in using MVSM because the intensity of the scattering, particularly at the backward angles, is low, approaching the detection limit of the instrument. As a result, some of the MVSM data had negative values in the backward angles when the scattering by pure seawater was subtracted. These data were discarded, reducing the number of MVSM data that we used for this study from 315 to 151. On the other hand, the LISST-VSF is sensitive enough to provide valid estimates of particle scattering on all water samples [20].

## 3. RESULTS AND DISCUSSION

#### A. Comparison of the VSFs between the LISST-VSF and MVSM

The MVSM operates at eight wavelengths, but 517 nm, at which the LISST-VSF operates, is not one of them. Therefore, we chose only those MVSM data that were measured at the full spectrum and applied interpolation to estimate values at 517 nm for comparison with the LISST-VSF data. This restricted the comparison to near surface waters and resulted in 32 pairs of matching data (Fig. 2).

In the backward scattering angles, ${\beta _p}$ derived from the MVSM appeared noisy [Fig. 2(a)], mainly because (1) the signal level approached the sensitivity level of the instrument and (2) only two repeated measurements were conducted, and hence greater random noise interference, when running for multiple wavelengths. While the sensitivity of the LISST-VSF is sufficiently fine to resolve the particle scattering in the study area, the scattering at angles ${\gt}{145}^\circ$ is affected by the internal reflection [see upward tail of the red line in Fig. 2(a)]. Again, the LISST-VSF data at angles ${\gt}{145}^\circ$ were not used. Also shown is the LISST-VSF data extrapolated for angles from 145 to 180° using the two-component model [29]. As explained earlier, the extrapolated values were only used for calculating ${b_{\textit{bp}}}$ in Eq. (1) from the LISST-VSF data. For this study, the contribution of extrapolated VSFs from 145° to 180° to the total backscattering ranged from 14% to 19%, averaging about 15%.

Overall, the VSFs of particles measured by the two instruments correspond very well with each other, with a Pearson correlation coefficient ${\gt}{0.98}$. To further compare the two instruments, we examine ratios of ${\beta _p}$ between the LISST-VSF and the MVSM [Fig. 2(b)]. The variability of the ratios (blue box and dashed vertical lines) appears to increase with scattering angles, which is mainly caused by degrading signal-to-noise ratio of the MVSM as the scattering angle increases in this particular clear water environment. However, the median values of the ratios [red dots in Fig. 2(b)] do not show a clear dependence on the scattering angle and have a mean value of 1.36 across the scattering angles from 15° to 145°. As a result, we do not expect that this difference observed in Fig. 2(b) will affect the estimates of the $\chi$ factor very much, which represents a ratio between ${\beta _p}$ and ${b_{\textit{bp}}}$, and, hence, the difference is canceled out. For the following analysis, we further smoothed the MVSM data by a median moving average with a window size of 11 (corresponding to averaging over 2.5° in scattering angle). No smoothing was applied to the LISST-VSF data, which already represented the median values of 30 repeated measurements for every sample.

#### B. Variability of ${\chi _p}$

The variation of ${\chi _p}$ estimated from the LISST-VSF data ($N = {315}$) and from the MVSM 532 nm data ($N = {151}$) is shown in Fig. 3. Within the angular range from 90º to 145°, where both instruments have measurements, ${\chi _p}$ values agree well in both the mean value and the range of variation between the two instruments. This also confirms that the inter-instrument difference shown in Fig. 2(b) has not affected the estimate of ${\chi _p}$, which is expected. It also indicates that the two-component model [29] we used to extend the LISST-VSF data towards the 180° scattering angle for calculating the total backscattering coefficient works well. In waters near OSP, ${\chi _p}$ has mean values increasing from 0.67 at 90° to approximately 1.16 at 170°. The minimal variability of ${\chi _p}$ occurs at ${\sim}{117}^\circ$, where ${\chi _p}\; \approx \;{1.06}$. Even though the mean value of ${\chi _p}$ in this study area does not change very much at scattering angles ${\gt}{130}^\circ$, the corresponding variability is relatively greater.

The variation of ${\chi _p}$ estimated in this study area was compared with data obtained in various waters in the global oceans, including those that have been reported [14,23–26] and those that are reported for the first time, to the best of our knowledge, in this study [Table 1 and Fig. 3(b)]. Clearly, ${\chi _p}$ varies for different waters. It is interesting to notice that the mean value of ${\chi _p}$ estimated in this study [OSP-1 and OSP-2 in Table 1 and Fig. 3(b)] seems to represent a boundary of the ${\chi _p}$ values shown in Fig. 3(b). This is probably because the water around OSP is the clearest among those listed in Table 1. Our result agrees well with the Sullivan and Twardowski [14] data (ST09) for scattering angles up to 140° and deviates slightly at larger angles. Sullivan and Twardowski [14] measured the VSFs in some of clear oligotrophic waters, such as those off the coast of Oahu, Hawaii, in the Ligurian Sea and the Southern Ocean near South Georgia Island. But, their data shown here represents an average of those clear waters as well as several relatively turbid coastal waters. Significant difference in ${\chi _p}$ can be observed for different waters, including river and lake waters in Germany (T15), coastal waters off New Jersey (BP01), the Black Sea (C06), the Adriatic Sea (B07), Chesapeake Bay (ZCh14), ZMob14, and ZMon14 as well as for different coastal and open ocean waters in the North Atlantic Ocean (SABOR) and the Gulf of Mexico (GoM).

All of the data except C06 and to a lesser extent T15 in Fig. 3(b) intercept at angles near 120°.
Zhang *et al.* [29] found that ${\chi _p}$ observed in the oceans can be
decomposed into a linear combination of two end members, one
represents the shape of ${\chi _p}$ of particles of a size much less than
the wavelength of light and the other much greater than the
wavelength. Because ${\chi _p}$ of these two end members intersect at
approximately 120°, their linear combinations also intersect at the
same angle. This also explains why ${\chi _p}$, either simulated or measured for
natural particle populations, were found to exhibit minimal
variability at angles near 120° [14,23,24,32]. Chami *et al.* [25] used an early version of the
MVSM, but we do not know if this is the reason why C06 is an outlier
in terms of its general shape. The data obtained by Tan *et al.* [31] was from very turbid shore waters of the River Elbe and
Lake Schaalsee in Germany. But, we do not know if this could be the
reason for their slightly higher ${\chi _p}$ value at 120°.

#### C. Spectral Variation of ${\chi _p}$

The VSFs were measured with the LISST-VSF at 517 nm and with the MVSM at 443, 490, 510, 532, 555, 565, 590, and 620 nm (mostly for surface samples). We combined these two sets of measurements to examine the spectral variation of ${\chi _p}$. For viewing clarity, only the results at two selected scattering angles of 100° and 140° are shown in Fig. 4(a). The one-way analysis of variance (ANOVA) test showed that there is no statistically significant difference among spectral ${\chi _p}$ values at the scattering angle of 100°. For the scattering angle of 140°, there was no significant difference in spectral ${\chi _p}$ values if ${\chi _p}$ (140°) at 443 nm is excluded, which was found to differ slightly, but statistically significantly, from ${\chi _p}$ (140°) at 517 nm, 532 nm, and 590 nm ($p \lt {0.03}$). At other scattering angles, ${\chi _p}$ behaves similarly, showing insignificant spectral variability (results not shown). We also examined the spectral variation of ${\chi _p}$ using the MVSM data collected at other sites listed in Table 1, including ZCh14, ZMob14, ZMon14, and GoM, by forming ratios of ${\chi _p}(\lambda)$, where $\lambda$ represents the wavelength, to ${\chi _p}(\lambda = {532}\;{\rm nm})$ for scattering angles from 90° to 170° [Fig. 4(b)]. The median values of the ratio are close to unity with negligible difference at all of the backward scattering angles.

That ${\chi _p}$ is more or less spectrally invariant
as shown by our results is consistent with Maffione and Dana [33] who simulated ${\chi _p}$, with Berthon *et al.* [26] who
measured ${\chi _p}$ using the second version of the MVSM,
and with Tan *et al.* [31] who measured ${\chi _p}$ using I-VSF from 400 to 700 nm with
20 nm intervals. Vaillancourt *et al.*
[34] and Whitmire *et al.* [35] also observed no spectral dependence in ${\chi _p}$ for phytoplankton cultures. Chami
*et al.* [25], using the first version of the MVSM, observed no spectral
variation of ${\chi _p}$ in non-blooming coastal water, but up
to 20% variation in algal cultures. From our results and the results
of other studies mentioned above, we conclude that the spectral
variation of ${\chi _p}$ is limited within an uncertainty of
10% [Fig. 4(b)] for oceanic
particles in a natural environment.

#### D. Effects of the Field-of-View

The FOV of sensors is expected to affect the estimation of ${\chi _p}$. Assuming the angular response function of a scattering sensor is $W(\theta)$ with a nominal scattering angle of ${\theta _0}$, the measured VSF, ${\beta _{\rm{FOV}}}({\theta _0})$, is

ECO single-angle backscatter sensors typically operate at one of three
scattering angles, 124°, 142°, and 150°, and the ECO-VSF sensor
operates at three angles of 104°, 130°, and 151°. All ECO backscatter
sensors have an FOV with a full width at half-maximum (FWHM) of
approximately 40°. Sullivan *et al.*
[36] derived the theoretical
angular response functions for different ECO sensors, accounting for
the changes in both illuminating and viewing geometry within the FOVs.
With a 40° FWHM, the FOV of an ECO sensor generally reduces the value
of the $\chi$ factor, with increasing reduction
towards smaller scattering angles [Fig. 5(a)]. At a scattering angle of 104°, the reduction
varies from 10% to 20% depending on the types of waters, and, at 124°,
the reduction averages about 5%. At greater scattering angles (130° to
150°), the change is ${\lt}{5}\%$, and occasionally the FOV would even
cause the $\chi$ factor to increase slightly. During
the EXPORTS 2018 experiment, the median (25th–75th quantiles) values
of ${\chi _{{\rm
FOV},P}}$ for various ECO backscatter sensors
were 0.75 (0.74–0.77), 1.04 (1.03–1.04), 1.08 (1.08–1.09), 1.14
(1.13–1.15), and 1.16 (1.14–1.17) for scattering angles of 104°, 124°,
130°, 142°, and 150°, respectively [Fig. 5(b)]. For comparison, the median values of ${\chi _P}$ estimated directly from MVSM without
considering the FOV effect were 0.91, 1.11, 1.15, 1.18, and 1.19,
respectively.

## 4. CONCLUSIONS

We measured the VSFs and estimated ${\chi _p}$ in clear waters near OSP using two scattering instruments, the LISST-VSF and the MVSM (version 3). Comparison between the two instruments indicates that the measurements are consistent with each other but with an average difference, where the LISST-VSF data measured at 517 nm is on average 36% greater than the MVSM data interpolated to the same wavelength (Fig. 2). This difference, which we believe is caused by the low signal-to-noise ratio for the MVSM in this relatively clear environment, does not affect the estimates of ${\chi _p}$ because of cancellation in forming the ratio of the VSF at a particular angle and the backscattering coefficient calculated over all of the backward angles. As a result, ${\chi _p}$ estimated from the LISST-VSF and MVSM agreed very well at angles from 90° to 145° [Fig. 3(a)].

The comparison among ${\chi _p}$ values estimated in this study and in the other studies listed in Table 1 indicates (1) ${\chi _p}$ exhibits minimal variability at scattering angles near 120° (117° for this study); and (2) the variability of ${\chi _p}$ increases as the scattering angles deviate away from 120°. This implies that the commercial backscatter instruments should be designed by measuring the VSFs at angles close to 120° to minimize the uncertainty in estimating ${b_{\textit{bp}}}$. Also, ${b_{\textit{bp}}}$ estimated using ${\chi _p}$ at other scattering angles should account for the natural variation of ${\chi _p}$. Also, ${\chi _p}$ obtained in this study near OSP seemed to represent a boundary when compared with data obtained in the global coastal and oceanic waters [Fig. 3(b)]. Whether this is because the water near OSP is relatively clear needs to be further tested with additional measurements in other clear oceanic waters.

The SeaBird backscatter sensors employ a wide FOV with an FWHM of approximately 40°. Accounting for the FOV lowers the actual ${\chi _p}$ value [Fig. 5(a)], particularly for scattering angles ${\lt}{130}^\circ$. As a result, for the EXPORTS 2018 campaign, we recommend using ${\chi _p}$ values of 0.75, 1.04, 1.08, 1.14, and 1.16 for SeaBird backscatter sensors with scattering angles at 104°, 124°, 130°, 142°, and 150° respectively.

No significant spectral variation in ${\chi _p}$ can be discerned beyond the natural variability of ${\chi _p}$. From measurements presented here and elsewhere, we conclude that ${\chi _p}$ can be assumed as spectrally independent with an uncertainty ${\lt}{10}\%$.

## Funding

National Aeronautics and Space Administration (80NSSC18M0024, 80NSSC19K0723, 80NSSC20K0350); Directorate for Geosciences (1917337); National Science Foundation.

## Acknowledgment

We thank the captain and crew of the R/V *Sally
Ride* for their help and support during the EXPORTS cruise and
NASA EXPORTS Office for logistic support. We thank Dr. Emmanuel Boss and
an anonymous reviewer for their constructive and insightful comments,
which have helped us to improve the manuscript. We also thank Dr. James
Sullivan and Dr. Michael Twardowski for providing data and helpful
discussion on the angular weighting functions associated with the SeaBird
ECO scattering sensors. The data used for this study have been submitted
to and are available for public access in NASA SeaBASS (at
https://seabass.gsfc.nasa.gov/archive/UND/Zhang/EXPORTS/exportsnp/archive/.).

## Disclosures

The authors declare no conflicts of interest.

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