Using two field cruise observations collected during September and December 2016 in the Bohai Sea (BS), Yellow Sea (YS), and East China Sea (ECS), our study explores the variability of the particulate backscattering ratio (i.e., a ratio of particulate backscattering, bbp in m−1, to particulate scattering, bp in m−1, denoted as bp, dimensionless). A large variation of bp (using 550 nm as a delegate) in magnitude is observed in the study regions, ranging from 0.0004 to 0.043 (with an average of 0.015 ± 0.0082), which implies optically complex water conditions. Spectral variation in bp is analyzed quantitatively by our proposed so-called “spectral dependence index,” K, recommended as a standard way to determine quantitatively the spectral dependence of bp in water bodies worldwide. The driving mechanism on the bp variability in the study regions is researched for the first time, based on those synchronous data on particle intrinsic attributes, herein mainly referring to particle concentration (TSM, for the content of total suspended matter), composition (using a ratio of Chla/TSM as a surrogate, where Chla refers to the content of chlorophyll a), mean particle size (DA), and mean apparent density (ρa). The TSM, Chla/TSM, and DA cumulatively contribute most (97.8%) of the bp variability, while other factors, such as the ρa, show a weak influence (0.04%). Meanwhile, we model bp with direct linkages to TSM, Chla/TSM, and DA by using a linear regression method, with low estimation errors (such as mean absolute percentage error, MAPE, of about 14%). In short, our findings promote an understanding on the essence of the bp in the BS, YS, and ECS, and are significantly beneficial to the comprehensive grasp of those complex features on suspended particles and those related to biogeochemical processes in marine waters.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The particulate backscattering ratio (bp, see symbols in Table 1), conventionally defined as a ratio of particulate backscattering coefficient (bbp) to scattering coefficient (bp), is an important optical quantity for characterizing the suspended particles in marine waters [1–7]. This parameter can provide significant information on suspended particles, such as their material composition and size distribution [2,8–10]. It has also been used in radiative transfer simulation of water columns, and semianalytical remote sensing algorithms, to detect those inherent optical properties [2,3,11–13]. Thus, a detailed understanding and documentation of bp variability is of fundamental importance to the overall comprehensive cognition of the complex features of the suspended particles and many marine ecological and biogeochemical processes.
The bp, along with the bp, is commonly used to model the bbp, which is a more direct inherent optical quantity used to simulate the remote sensing signals of water bodies in bio-optical models [11,14,15]. Therein, this parameter is initially assumed to be constant, or to change inversely with pigment concentrations [11,15]. However, the subsequent investigations demonstrate that the bp may be not constant and will vary among different particulate features in different water conditions [1,2,4,8–10]. Qualitative analysis on the influence of the particulate feature factors on the bp changes can be found in previous studies. Those related factors can be summarized as the composition of the particulate assemblage [1,2,4,5,10,16], the particulate sizes, structures, and shapes [2,7–10], the small particles [2,8–10], and the bulk refractive index .
Indeed, the association of the bp with the particulate feature factors can be verified by Mie scattering theory, where the bp for a collection of particles can be expressed as follows :
where x is the size parameter given by x = (πDnw)/λ, where D is the particle diameter, nw is the seawater refractive index, and λ is the wavelength; f(x) is the probability density function that can derive the particle size distribution, i.e., Kf(x), where K is the total number of particles per unit volume; Qbbe and Qbe are the effective backscattering and scattering efficiency factors, respectively; Note that the optical efficiency factors are essentially influenced by the composition, size distribution, density, and refractive index of the suspended particles [9,17–21]. In theory, the bp is closely related to those feature factors of the suspended particles.
Nevertheless, we do not know or adequately understand the bp variability, in spite of the abovementioned theoretical relationship and limited qualitative analysis shown in the previous studies. Questions remain as to how the bp changes and whether these changes are in spectrum or in value magnitude. Factors that play important roles in the variability of the bp remain unknown. Providing clear answers to these questions is of great significance to the true understanding of bp changes, particulate backscattering/scattering properties, the underwater radiative transfer of light, and even water color remote sensing.
The current study selects the Bohai Sea (BS), Yellow Sea (YS), and East China Sea (ECS) as the investigated water areas, which are typically large shallow and turbid coastal waters, and represent those so-called optically complex Case II water conditions. By means of an in situ observed data set from two cruise surveys, conducted for the study areas in Sep. and Dec. 2016, the purpose of this study is to explore the variability of the bp, such as its spectral dependence features and value changes. More importantly, this study focuses on the influence of various particulate feature factors to the bp, which are analyzed quantitatively for the first time. Corresponding discussion is attached subsequently.
2. Data and methods
2.1 Study areas and cruise surveys
The investigated water regions of this study are the BS, YS, and ECS [Fig. 1], which are typically large and shallow marginal seas of the western North Pacific. The BS shows a mean depth of 18 m, with most water areas less than 30 m , whereas the average depth of the YS is approximately 44 m , and the ECS shows an average depth of approximately 370 m, with most areas (~70%) below 200 m [24,25]. These marginal seas (BS, YS and ECS) are significantly influenced by a large quantity of sediment loads from river discharge, together with productive waters induced from industrial and agricultural pollutions, as well as domestic sewage [26,27]. Our study areas are thus typically turbid coastal water bodies with complex optical conditions.
Two cruise surveys were carried out during Sep. and Dec. 2016 in the BS, YS and ECS (Table 2). A total of 118 sampling stations were collected for this study. For each station, a series of measurements were implemented by means of optical instruments including a WET Labs AC-S, a HOBI Labs Hydroscat-6 (HS-6), a Sequoia LISST-100X, and a Seabird SBE49 CTD. They were formed to an optical profiling package. This optical package was first fastened to a hydrological winch that could control the raising and lowering of the package. Before the official observation, the optical package would be descended into the water column at a depth of several meters for environment adaptation about 4 min. Then, this package was lifted up to just beneath the surface of water bodies, and then dropped down slowly to the bed.
2.2 Determination of optical parameters
The optical parameters used in this study covered bbp, bp, and bp. The bbp could be observed by using the HS-6 meter, whereas the bp was measured by means of the AC-S instrument. Before the cruise surveys, the HS-6 meter was first calibrated to assure its accurate and stable performance within factory specifications. The HS-6 used in the current study has six spectral bands, i.e., 442, 488, 550, 620, 700, and 852 nm bands. This instrument measures a single-angle (about 140°) volume scattering function at the backward direction , which can be further transformed into backscattering by using corresponding calibration coefficients. The effects by path length attenuation were corrected by carrying out the sigma correction (see details in Hydroscat-6 User’s Manual from www.hobiservices.com). The AC-S meter had been calibrated by using Milli-Q water before and after the cruise surveys, with repeatable readings in all spectral bands below 0.005 m−1. The effects of temperature and salinity were corrected by using the method described by WET Laboratories User’s Guide from www.wetlabs.com, and absorption measurements were calibrated for the effects of reflective tube scattering following Sullivan et al. (2006) . Detailed descriptions on HS-6 and AC-S measurements to obtain the bbp and bp can be found in Sun et al. (2017) . After obtaining the bbp and bp, the bp can be thus derived by dividing bbp by bp. However, it should be noted that particulate backscattering ratios at five bands, namely, 442, 488, 550, 620, and 700 nm bands, were finally used in our study, since the AC-S measurements do not cover the 852 nm band of the HS-6.
2.3 Determination of physical and biogeochemical parameters
Those physical and biogeochemical parameters, analyzed in the present study, include Chla (in mg m−3), TSM (in mg l−1), ISM (in mg l−1), OSM (in mg l−1), DA (in μm), and ρa (in kg l−1). The Chla measurement required a first filtering of 1-2 L water samples by means of 47-mm Whatman GF/F filters. Then, the filters were frozen and stored in liquid nitrogen, and transferred to the laboratory on land. A reverse-phase HPLC technique was used to analyze the pigments; furthermore, the method of Van Heukelem and Thomas (2001)  was utilized to separate and quantitatively extract the Chla. For the measurements of suspended matter concentrations, the collected 0.5-2 L water samples were first percolated onto preweighed 47-mm Whatman GF/F filters. After rinsing the filters with distilled water at least three times, they were stored in a freezer at 20 °C and transferred to the laboratory on land. Then, these filters were dried under 105 °C for approximately four hours, which were reweighed for achieving the TSM. Subsequently, they were transferred into a muffle furnace for one hour under 500 °C and reweighed to derive the ISM. The OSM could thus be calculated by subtracting the ISM from the TSM.
This study used a LISST-100X (Type-C) instrument to observe the size distribution of suspended particles in waters. This instrument could directly measure the near- forward-angles light, which could be used to derive the V(Di) (particle volume concentration, in μl l−1, where Di refers to the i-th diameter, in μm) based on Mie theory. The details on the LISST measurements can be seen in our previous publication . According to the following equation, the N(Di) (particle number concentration, in counts m−3), can be calculated:
The [AC]i (particulate cross-sectional area concentration at size bin i, in m−1) can be deduced as follows:
By summing all size bins, we can obtain the [AC]t (the total of particulate cross-sectional area concentrations at all size bins, in m−1). Accordingly, the DA (in μm) can be obtained as follows:
The ρa (in kg l−1) can be calculated as below (Bowers et al., 2009):
2.4 Mathematical statistic methods
This study implemented a statistical description analysis on the optical, physical, and biogeochemical parameters collected in the study areas. When descriptive statistics for these parameters were calculated, mathematical analyses (such as correlation and regression methods) were performed to find the potential links between different quantities. Several error indicators, used to assess the model’s performance in the present study, include the MAPE, RMSE (root mean square error), NRMS (normalized root mean square error), and mean ratio, which can be obtained as below:
3.1 Variability of water bio-optical conditions
The investigated water bodies of the current study show relatively large variations in bio-optical conditions. The observed Chla ranges from 0.20 to 6.55 mg m−3, with a mean of 1.37 mg m−3 (S.D. = 0.97 mg m−3, CV = 71%), whereas TSM shows a large span of magnitude, i.e., from 0.41 to 223.87 mg l−1, with a CV of 190% (Table 3). There generally exists more ISM (mean = 15.57 mg l−1) in the total suspended particles than OSM, with a mean of 1.81 mg l−1, which indicates a potentially important influence from terrigenous discharge and sediment resuspension. Correspondingly, the bp and bbp (using 550 nm as a reference) also show large variation of magnitude (Table 3). In this study, we observe a variation of bp(550) ranging from 0.0004 to 0.043, and a mean of 0.015 (S.D. = 0.0082, CV = 55%). Meanwhile, the parameters that characterize the intrinsic characteristics of the suspended particles, including DA, ρa, and Chla/TSM, are also measured with their variations, as shown in Table 3 in this study.
3.2 Spectral dependence of particulate backscattering ratio
The bp(λ) observed in this study generally shows few large spectral variations [Fig. 2(A)], though there still exist several individual stations with somewhat great changes between different wave bands. As shown in Fig. 2, the averaged bp(λ) spectrum presents a roughly gentle trend from the short to long wave bands. Even so, in order to accurately characterize the spectral dependence of thebp(λ), this study used bp(550) as a reference and then analyzed the relationships between bp(λ) with bp(550), using a linear regression function such as y = K * x. Here, the parameter K can be defined as “spectral dependence index” to quantitatively indicate the spectral dependence of the bp(λ). It can be conveniently calculated without a unit, and importantly easy-to-use to reflect a general spectral variability normalized to a reference baseline. It would show a potentially important application in future. Very close relationships between bp(λ) with bp(550) can be obtained with corresponding determination coefficients (R2) above 0.917 (p<0.0001) [Figs. 3(A)-3(D)]. The obtained parameter K for the 442, 488, 620, and 700 nm bands are 0.954, 0.940, 0.943, and 0.965, respectively, with K = 1 for the reference 550 nm band [Fig. 3(E)].
3.3 Influence of various factors on the particulate backscattering ratio
Correlation coefficients (R) between the bp(550) and factors including Chla, TSM, ISM, OSM, DA, ρa, and Chla/TSM, are calculated in this study. As shown in Table 4, the TSM shows a relatively high R value (0.516), with a level of significance (p < 0.001). As the inorganic part of the TSM, the ISM also exhibits a close correlation (R = 0.508, p < 0.001) with the bp(550), since the TSM is mainly dominated by the ISM (the R between them can reach 0.984 with p < 0.001). The DA and Chla/TSM all show a significantly negative correlation with the bp(550), and their corresponding R are −0.349 and −0.432 (p < 0.001), respectively. Note that the Chla and ρa all show very low correlations with the bp(550), indicative of their potentially weak influence on the variability of the bp(550) in this study area.
To further quantitatively determine the influence of these factors on the particulate backscattering ratio, this study implemented the regression analysis. The obtained equations for bp(550) vs. Chla, TSM, ISM, OSM, DA, ρa, and Chla/TSM are shown in Fig. 4. Many mathematical functions, such as linear, exponential, cubic quadratic, power, logarithmic, compound, inverse, and logistic functions, have been tested for these pairs of relationships in the present study. Note that the fitting performances by using the equations, shown in Fig. 4, outperform that of other forms.
The formed relationships between bp(550) vs. Chla and bp(550) vs. ρa do not pass the significance test [Figs. 4(A) and 4(F)], and accordingly are excluded in the subsequent analysis on the influence of bp(550) variability. Meanwhile, the fitted equations between bp(550) with ISM and OSM are also removed, despite their close relationships, since the ISM and OSM represent parts of the TSM and their influences can be reflected in the formed relationship between bp(550) with TSM. Therefore, the final determined influencing factors in this study are the TSM, Chla/TSM, and DA.
The largest degree (47.0%) for the bp(550) variability can be ascribed to the TSM (particulate concentration), when 38.5% and 12.3 of the variability in bp(550) can be accounted for by the Chla/TSM (particulate composition) and the DA (particulate size), respectively. Note that these three factors, i.e., TSM, Chla/TSM, and DA, cumulatively contribute to the overwhelming percentage (a total of ~98%) of the bp(550) variability, while the remaining variability, with a much smaller proportion (approximately <4%), may be controlled by other features such as particulate density, structure, shapes, etc.
3.4 Modeling bp(550) from TSM, Chla/TSM, and DA
According to the above findings, the particulate concentration (TSM), composition (Chla/TSM), and size (DA) are regarded as the main factors influencing the bp(550) variability. By means of these factors, this study used a linear regression method with multivariate to model the bp(550). Seventy-five in situ samples were selected randomly from 118 samples to calibrate the bp(550) model, while the remaining 43 samples were used for model validation. Relatively high precision of fitting by the model calibration can be obtained [Fig. 5(A)], with a determination coefficient (R2) of 0.955 at a very high significance level (p<0.001). Meanwhile, the established bp(550) model [Eq. (10)] also shows acceptable performances by using independent validation samples, with relatively low predictive errors, such as a MAPE of 14.0% [Fig. 5].
4.1 Essence of thebp spectral dependence
The spectral dependence of the bp essentially reflects the spectral variation in the capability of percentages of particulate scattering in the backward direction to the total particulate scattering. According to Mie scattering theory, the bp should show a spectral consistency between different wavelengths for the ideal homogeneous and spherical particles, which have a constant refractive index and abide by a Junge law in particle size distribution . Nevertheless, the suspended particles in natural waters do not usually show very ideal conditions in most cases. This induces the presence of two different views on the bp spectral dependence based on those in situ observations, namely, wavelength-independent [7,8,32,33] and wavelength-dependent [34–37]. In our opinion, the two views are not ambivalent to each other, since the bp spectral variability in nature depends on the intrinsic characteristics of the particulates (such as their size and composition ,). The occurrence of the wavelength-independent bp indicates a closer approach to the ideal assumption for the features of the suspended particles, whereas the wavelength-dependent cases possibly imply large deviations in the particulate features from ideal conditions that are assumed in Mie scattering theory.
Strictly speaking, the spectral dependence in the bp exists in any natural waters, and simply exhibits different degrees in the spectral dependence between various water columns. For instance, Macdonald et al. (2000)  reported an ~10% variability of the bp between wave bands that was roughly regarded as wavelength-independent. Similar variation scales were also reported in Whitmire et al. (2007) , which revealed no spectral dependence of the bp. A maximum relative error of the bp between five bands (i.e., 442, 488, 532, 589, and 676 nm) was reported to be approximately 14% in Zhang et al. (2010) . Interestingly, Chami et al. (2005)  reported two existing cases in their observations, i.e., both low (within 4% for the average backscattering ratio) and high (~30%) spectral variability of the bp, indicative of the potential inaccuracy by using a flat spectral shape of bp in the investigated coastal zones. Meanwhile, a relatively significant spectral variability of the bp has also been reported, especially in turbid inland and coastal waters [35,37,40].
In this study, the averaged bp were observed to vary below 6%, between different wavelengths (550 nm as the reference here) [Fig. 2(B)], and the maximum variability reached up to 40% for several individual measurements. To quantitatively analyze the spectral variability of the bp in waters, the current study proposes a new method of definition, i.e., the so-called “spectral dependence index (K)”. This index essentially reflects a general spectral variability normalized to a reference baseline, based on a suite of in situ observations. For the investigated water regions, the K values have been calculated, varying in a range from 0.94 - 0.97. In short, this dependence index provides an effective method to document the spectral variability of the bp, which should be calculated in the future for a consistent comparison and record in various water areas.
4.2 Implications for the physical mechanism of the bp changes
This study shows a relatively large variability in the observed bp (using 550 nm as a delegate) in the BS, YS, and ECS, ranging from 0.0004 to 0.043, with a mean value of 0.015 ± 0.0082. This scope of change is comparable to those reported in the previous studies on open ocean and coastal waters all over the world [Fig. 6] [1,2,7,10,33,35,36]. The question remains as to what factors affect the bp changes. This may still be difficult to answer, since many suspended particles’ physical and biogeochemical characteristics in natural waters are not yet accessible in synchronism.
In this study, we utilized a ratio of Chla to TSM to denote the particulate composition, and found a significantly high inverse correlation (R = −0.432, p<0.001) with the bp. This fact implies that low bp values generally correspond to those particulate populations dominated by phytoplankton, whereas high values tend to appear in the waters with high inorganic particle content. This is consistent with those results presented in Loisel et al. (2007) , Neukermans et al. (2012) , Slade and Boss, (2015) , and Xi et al., (2015)  and indeed indicates an important contribution of the particulate composition to the bp change. We found a distinct inverse correlation (R = −0.349, p<0.001) between DA and bp, indicating that small size particles would lead to a higher bp than large size particles. A similar rule was also elaborated in Loisel et al. (2007)  and Xi et al. (2015) . Meanwhile, there existed a very weak relationship between Chla and bp in our data (Fig. 4), which is in good agreement with those reported in previous studies [3,5,9,10,41,42]. These similar findings adequately indicate a weak contribution of the Chla absolute content to the bp.
The bulk refractive index of particles is closely related to particulate composition, and typically, a high refractive index refers to a higher proportion of inorganic minerals in the composition of the particulate assemblage; whereas a low refractive index indicates the presence of more phytoplankton and organic materials [2,9,16]. As expected, this law of variation also appears in our investigated water areas (Fig. 7); that is, low Chla/TSM represents high inorganic particle content in the particulate assemblage and corresponds to high refraction, and then leads to a high backscattering ratio and vice versa. Therefore, the influence of the particulate refraction on the bp is actually hidden in that of the particulate composition, which is not necessary for the redundant reanalysis in this study. Additionally, data on the particulate structure and shapes are not available to us, and their accurate impact on the bp is beyond the scope of the current study.
In summary, this study exhibits similar findings to those in the previous studies, such as the similar effects from the particulate composition and sizes, and the weak contribution of Chla. However, it should be noted that the present study simultaneously finds a significant influence from TSM on the bp. This implies that the increase of TSM shows a larger degree in augmenting the bbp than changing the bp in the water areas of the study. The reason is probably due to the high proportion of inorganic materials in the total particulate populations (R = 0.984 for ISM vs. TSM, p < 0.001, Table 3), which leads to a stronger backscattering capability. As in Loisel et al. (2007) , high bp(λ) values are generally observed for a particle population dominated by inorganic particles.
4.3 Suggestions for bio-optical modeling
The particulate backscattering ratio essentially reflects a proportion of the particulate backscattering, accounting for its scattering; that is, the contribution of backscattering to scattering of particles. This ratio has been used in semianalytical algorithms for inherent the estimation of optical properties from radiometric measurements [3,11,12] and supports the derivation of an approximate scattering phase function of particles, serving for radiative transfer computations of water columns . An accurate input of the backscattering ratio is thus of great importance to the bio-optical modeling of water bodies. This study comprehensively analyzes the influence of those particulate feature factors, including concentrations (Chla, TSM, OSM, and ISM), composition, size, density, and refraction on the backscattering ratio and then determines the potentially significant influencing factors. Unlike the backscattering coefficient that is determined to the first order by the particulate concentrations, the backscattering ratio exhibits more complex influences from multiple factors together. In this study, the particle composition and size are quantitatively analyzed to show important contributions to the change of the backscattering ratio, as well as the concentration. On this basis, we model the change of the backscattering ratio through those determined factors for the first time, with relatively acceptable predictive accuracies. A novel bridge is built to link the physical and biogeochemical characteristics of particles with optical parameters, which enriches the framework of bio-optical modeling. Even so, note that other factors, such as particle shape, internal structure, etc., might also have important influence on the particulate backscattering ratio. More comprehensive data on the particle features is expected in future to participate in the research on the nature of its backscattering ratio. Indeed, potential discrepancies in the driving factors of the backscattering ratio may appear between different water regions and thus, more investigations, together with multiple physical and biogeochemical factors, should be carried out in the future for a much deeper understanding of the change of the backscattering ratio. This is undoubtedly of vital importance to the field of marine optics.
The present study mainly obtains the following findings: 1) the spectral dependence of bp in the investigated water areas, also thought to exist in other natural waters, with more or less degrees of dependence, is quantitatively determined by our proposed spectral dependence index (K, approximately 0.94 - 0.97 for the visible light range), which is recommended as a standard method; 2) TSM accounts for the largest degree (47.0%) of the bp variability, where 38.5% and 12.3 of its variability can be attributed to Chla/TSM and DA, respectively. The above three factors cumulatively contribute most (97.8%) of the bp variability, whereas others, such as the ρa, show weak influence; 3) bp can be effectively modeled with TSM, Chla/TSM, and DA, through a multivariate regression method, which produces a relatively high precision of fitting (R2 = 0.955, p<0.001) and acceptable predictive errors (MAPE = 14%). Our findings here go deep into the nature of particulate backscattering ratios and serve as a template for the understanding and parameterizing of its variations for other water regions, where further investigation is needed.
National Key Research and Development Program of China (2016YFC1400904, 2016YFC1400901); National Natural Science Foundation of China (41876203, 41576172); Jiangsu Six Talent Summit Project (JY-084); Jiangsu Provincial Programs for Marine Science and Technology Innovation (HY2017-5); State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography (QNHX1812); the Qing Lan Project; and NSFC Open Research Cruise (NORC 2018-01), funded by Ship-time Sharing Project of NSFC.
We acknowledge captains, officers, and crews of R/V Dongfanghong 2 and Science 3 for providing excellent assistance during field sampling and measurements.
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