A Four-Step Method for Estimating Suspended Particle Size Based on In Situ Comprehensive Observations in the Pearl River Estuary in China

Abstract

The suspended particle size has great impacts on marine biology environments and biogeochemical processes, such as the settling rates of particles and sunlight transmission in marine water. However, the spatial–temporal variations in particle sizes in coastal waters are rarely reported due to the paucity of appropriate observations and the limitations of particle size retrieval methods, especially in areas with complex optical properties. This study proposed a remote sensing-based method for estimating the median particle size D_v⁵⁰ (calculated with a size range of 2.05–297 μm) that correlates D_v⁵⁰ with the inherent optical properties (IOPs) retrieved from in situ remote sensing reflectance above the water’s surface (R_rs(λ)) in the Pearl River estuary (PRE) in China. R_rs(λ) was resampled to simulate the Multispectral Instrument (MSI) onboard Sentinel-2A/B, and the wavebands in 490, 560, and 705 nm were utilized for the retrieval of the IOPs. The results of this method had a statistical performance of 0.86, 18.52, 21.28%, and −1.85 for the R², RMSE, MAPE, and bias values, respectively, in validation, which indicated that D_v⁵⁰ could be estimated by R_rs(λ) with the proposed four-step method. Then, the proposed method was applied to Sentinel-2 MSI imagery, and a clear difference in D_v⁵⁰ distribution which was retrieved from a different time could be seen. The proposed method holds great potential for monitoring the suspended particle size of coastal waters.

1. Introduction

The suspended particle size in marine water has great impacts on marine biology environments and biogeochemistry processes (e.g., the settling velocity, resuspension, aggregates, and carbon cycle of particles [1]), and it has been proven to have a significant effect on the inherent optical properties (IOPs) of water so as to change the signals of ocean color remote sensing [2]. Hence, it is of great significance to obtain the characteristics of particle size. The median particle size (D_v⁵⁰) [3,4,5], which is the diameter corresponding to the 50th percentile of the accumulated volume concentration, is frequently used to describe the particle size distribution (PSD) of marine systems [6]. The parameter D_v⁵⁰ represents the proportional relationship between small particles and large particles in the particle size range; that is to say, a larger value of D_v⁵⁰ indicates that larger particles are more dominant, and vice versa [2,5]. Therefore, the spatiotemporal dynamics of D_v⁵⁰ can describe the characteristics of the particle size in marine water.

To determine the particle size, various particle sizing instruments, including particle imaging systems (FlowCAM) [7], electrical impedance particle sizers (Coulter Counter) [8], and laser diffractometers (LISST) [9], have been applied in both oceanic and inland water observation. Although many valuable observations have been carried out using these instruments worldwide, the spatial–temporal variations in D_v⁵⁰ have seldom been investigated due to the limitation of traditional observation methods [10]. Ocean color remote sensing provides the possibility of monitoring the state of the ocean routinely and in a cost-effective manner at a large scale [11], which makes it possible to observe D_v⁵⁰ more appropriately.

According to Mie theory [12], the particle size and particle composition make significant contributions to the scattering properties of particle assemblages that are suspended in marine water, and thus, some studies have suggested a relationship between scattering or backscattering and the particle size. Bowers et al. (2007) [3] developed an algorithm for particle size estimation by building a relationship with light scattering per unit concentration, and van der Lee et al. (2009) [4] applied this method to a much larger set of MODIS imagery to obtain the monthly average particle size in the southern Irish Sea. Qing et al. (2014) [13] utilized the ratio of green to red channels to build the empirical model for particle size estimation in the Bohai Sea in China. Sun et al. (2016) [5] evaluated the inadequacies of the above studies and proposed a hybrid method by combining analytical, semi-analytical, and empirical processes to estimate D_v⁵⁰ from remote sensing reflectance (R_rs(λ)). These studies indicate that PSD can be estimated by a remote sensing method.

Ocean color satellite sensors such as SeaWiFS, MODIS, MERIS, and OLCI were designed specifically to observe the water’s bio-optical properties. However, the mixed pixel problems caused by low spatial resolutions of their imagery sometimes limit their application when observing coastal waters or areas close to islands, particularly in areas with high variability of suspended particles [14]. The multi-spectral instrument (MSI) sensor onboard the Sentinel-2 A/B satellite can obtain higher spatial resolution imagery (10 m at visible and near infrared bands), with a relatively short revisit interval (10 days for one satellite and 5 days for double satellites) compared with other sensors with high special resolutions, such as Landsat-8. Despite Sentinel-2 being designed for global land monitoring, some studies have demonstrated its potential for assessing coastal and inland water quality [14,15,16].

The Pearl River estuary (PRE) is a tropical estuary, and the hydrodynamic conditions in the PRE are complex due to many factors, such as river discharges, topography, tides, and monsoons [17]. It is heavily influenced by frequent anthropogenic activities, such as industrialization and urbanization. The suspended sediment concentration in the coastal water and its variation as impacted by anthropogenic activity have been analyzed by many studies. However, the spatial–temporal variation of the suspended particle size in this area has rarely been reported. This study aimed to develop a method for retrieving the suspended particle size in the water areas with complex optical properties based on ocean color remote sensing and furthermore to apply the proposed method to Sentinel-2 MSI data for obtaining the spatiotemporal variation of the suspended particle size in the PRE. The findings of this study may provide information for understanding the characteristics of the particle size distributions in optically complex coastal waters.

2. Materials and Methods

2.1. Study Area and Fieldwork

The complex hydrodynamics of the study site are determined by many physical factors that were mainly contributed by the Pearl River discharge, coastal current, and oceanic waters from the South China Sea [18]. In this study, a total of three trips were conducted (Figure 1). Two of them were around four islands in the central and western area of the PRE (Neilingding, Dachan, Xiaochan, and Mazhou) in spring (21 May and 22 May) and autumn (20 September) of 2019, and the other trip was to an observation section on 8 January 2020. A total of 39 observations were conducted at 25 sites (N1–N9, S1–S8, and P1–P8), including 39 inherent optical property data (i.e., absorption coefficient, attenuation coefficient and scattering coefficient), 39 PSD datasets, and only 16 apparent optical property data (i.e., R_rs(λ)) due to bad observation conditions (

Table 1. Observation stations with respect to three trips, including IOP, PSD, and AOP data.

Data Type	2019		2020	Count
	21 May, 22 May	20 September	8 January
IOPs	N1–N6, S1–S8	N1–N9, S1–S8	P1–P8	39
PSD	N1–N6, S1–S8	N1–N9, S1–S8	P1–P8	39
AOPs	No data	N1–N8, S1–S8	No data	16

).

2.2. PSD Acquisition

In this study, a LISST-200X Type-C particle size analyzer (Sequoia Scientific, Inc., Bellevue, WA, USA) was used for PSD measurements. It is an upgraded version of the LISST-100X, which is a widely used instrument for in situ PSD measurements in marine waters [19,20,21]. The LISST-200X type-C has 36 size bins that cover a size range from 1 to 500 µm, and the size spectrum is logarithmically spaced [22]. For each bin, the upper size is 1.18 times the lower, and the width varies from 0.26 to 80 µm, with the exception of bin 1. The LISST uses particle diffraction, which is received by an optics receiving system formed by 36 concentric ring-shaped detectors, to perform a nonintrusive measurement of the volume concentration of suspended particles through a collimated laser beam (670 nm) [23,24,25].

Before the trip, the LISST was calibrated with Milli-Q water. The particle volume concentration (V(D) in µL/L) in the 36 size bins could be derived from the manufacturer-provided software LISST-SOP after in situ measurements. In addition, the total volume concentration (V_tot(D)) could be retrieved by a simple summation calculation of V(D) in all the size bins. There were two particle shape models for the V(D) data derived when using the LISST-SOP software, and we selected the irregularly shaped model, as it was more fitting than the spherical model when working with natural waters [22]. As a parameter for characterizing the particle size, the in situ D_v⁵⁰ corresponded to the particle diameter when the cumulated V(D) reached 50% of the V_tot(D), which was calculated by summarizing the V(D) between the 4th and 33rd size bins (i.e., a size range from 2.05 to 297 μm), since the data in the biggest and smallest bins were not stable.

2.3. Optical Property Measurements

In the case of the apparent optical properties (AOPs), the remote sensing reflectance (R_rs(λ)) was measured using an ASD FieldSpec 4 spectroradiometer (Analytical Spectral Devices, Boulder, CO, USA) which covered a spectral range of 350–2500 nm with 1 nm intervals. The measurements were carried out following the NASA marine optical protocol [26]. We adopted the observing geometry of a zenith angle of 40° from the water’s surface and an azimuth angle of 135° from the direction of the sun irradiance to perform the measurements, thus avoiding the shadow of the ship and direct irradiance from the sun [27]. Aside from that, the foam patches and whitecaps were kept away from the field of view to avoid signal interference by them. The measured R_rs(λ) was calculated with Equation (1):

$${\mathrm{R}}_{\mathrm{r}\mathrm{s}}(\lambda )=\frac{{\mathrm{L}}_{\mathrm{w}}(\lambda )-\mathsf{\rho }{\mathrm{L}}_{\mathrm{sky}}(\lambda )}{\mathsf{\pi }{\mathrm{L}}_{\mathrm{p}}(\lambda )/{\mathsf{\rho }}_{\mathrm{p}}}$$

(1)

where L_w, L_sky, and L_p stand for the radiances measured from the water’s surface, sky, and a standard gray reference panel, respectively; ρ_p is the diffuse reflectance of the reference panel; and ρ is the dimensionless air–water reflectance, which is always a constant value (here, we adopted 0.025 as the value due to the wind speed being lower than 5 m/s) [28].

As for the IOPs, the absorption coefficient (a(λ) in m⁻¹) and attenuation coefficient (c(λ) in m⁻¹) were obtained by an AC-S spectral absorption and attenuation meter (WET Labs, USA). As the scattering coefficient of CDOM could be disregarded, the particle scattering (b_p(λ) in m⁻¹) was calculated through the relationship b_p(λ) = c(λ) − a(λ) [29]. The AC-S instrument provides 84 channels within the range of about 400–730 nm with approximately 4-nm steps [30]. The backscattering coefficient of the suspended particles (b_bp(λ) in m⁻¹) was obtained using a BB9 (WET Labs, Philomath, OR, USA) with 9 bands (412, 440, 488, 532, 595, 695, and 715 nm for backscattering and 2 bands for CDOM and Chl-a fluorescence). For the postprocessing and correction of AC-S and BB9, the temperature and salinity data were measured synchronously with an SBE37 CTD (Sea-Bird Electronics, Bellevue, WA, USA). Before the trip, the AC-S, BB9, and CTD instruments would be sent to the manufacturer for periodic factory calibrations, and the instruments were rinsed with pure water immediately after each observation. To obtain accurate absorption and attenuation information, temperature and salinity corrections were performed on the raw data by following the ac Meter Protocol Document [30], and the effects of reflective tube scattering were corrected by following the method proposed by Sullivan et al. (2006) [31]. The raw BB9 data were corrected by following the BB9 User’s Guide [32].

2.4. Sentinel-2 A/B MSI Image

The level-1C (L1C) Sentinel-2 A/B MSI images were obtained from the European Space Agency’s (ESA) Copernicus Open Access Hub. Two cloudless images were selected from both the wet season (22 September 2019) and the dry season (30 January 2020) in this study. Unfortunately, there were no matchups with the sampling sites due to clouds. The L1C images were projected to Universal Transverse Mercator/World Geodetic System 84 (UTM/WGS84) and resampled to a 10-m spatial resolution. To retrieve the R_rs(λ) above the water’s surface, the Case 2 Regional Coast Colour processor (C2RCC) [33], which has been proven to perform well in atmosphere correction over coastal areas [34,35], was applied to carry out atmosphere correction. These processes were completed in the free Sentinel Application Platform (SNAP) version 8.0.0 with the C2RCC plug-in.

2.5. D_v⁵⁰ Retrieval

A four-step method was proposed for D_v⁵⁰ retrieval in this study (Figure 2), and the steps are as follows.

2.5.1. Step 1

The in situ R_rs(λ) was simulated to the Sentinel-2 MSI equivalent R_rs(λ) with the Sentinel-2 corresponding spectral response function (SRF) (Equation (2)), and the b_bp(λ) retrieval algorithm was developed using the simulated R_rs(λ). For b_bp(λ) retrieval, a quasi-analytical algorithm (QAA) based on radiative transfer theory was applied to invert R_rs(λ) to the water IOPs [36]. The updated versions (e.g., QAA-v5 and QAA-v6) were developed both for open oceanic and coastal waters [37]. In the QAA, the relationship between R_rs(λ) and the spectral backscattering and absorption coefficients can be written as the following equations (Equations (3)–(5)):

$${\mathrm{R}}_{\mathrm{r}\mathrm{s}\left(\mathrm{sentinel}-2\right)}(\lambda )=\frac{{{\displaystyle \int }}_{\lambda 1}^{\lambda 2}{\mathrm{R}}_{\mathrm{r}\mathrm{s}}(\lambda )\mathrm{SRF}(\lambda )\mathrm{d}(\lambda )}{{{\displaystyle \int }}_{\lambda 1}^{\lambda 2}\mathrm{SRF}(\lambda )\mathrm{d}(\lambda )}$$

(2)

$${\mathrm{r}}_{\mathrm{r}\mathrm{s}}(\lambda )=\frac{{\mathrm{R}}_{\mathrm{r}\mathrm{s}}(\lambda )}{(0.52+1.7\times {\mathrm{R}}_{\mathrm{r}\mathrm{s}}(\lambda )}$$

(3)

$$\mathrm{u}(\lambda )=\frac{{\mathrm{b}}_{\mathrm{b}}(\lambda )}{\mathrm{a}(\lambda )+{\mathrm{b}}_{\mathrm{b}}(\lambda )}$$

(4)

$${\mathrm{r}}_{\mathrm{r}\mathrm{s}}(\lambda )={\mathrm{g}}_0\times \mathrm{u}(\lambda )+{\mathrm{g}}_1\times \mathrm{u}{(\lambda )}^2$$

(5)

where R_rs(λ) is the spectral remote sensing reflectance just below the water surface; a(λ) and b_b(λ) are the total absorption coefficient and total backscattering coefficient, respectively; and u(λ) is the ratio of the backscattering coefficient to the sum of the absorption coefficient and backscattering coefficient. The coefficients g₀ (0.0895) and g₁ (0.1247) were proposed for relatively turbid coastal waters through radiative transfer theory [36]. Several studies showed that if the NIR band was used, a(λ) could be replaced by the absorption coefficient of pure water a_w(λ) due to the absorption of water being much larger than those for other substances [38,39]. We tested the applicability in this study, and our results show that absorbance above 95% was contributed by pure water. Hence, we took 705 nm of the Sentinel-2 bands as the reference band of b_bp(λ) (Equation (6)):

$${\mathrm{b}}_{\mathrm{b}\mathrm{p}}\left(705\right)=\frac{\mathrm{u}\left(705\right)\times {\mathrm{a}}_{\mathrm{w}}\left(705\right)}{1-\mathrm{u}\left(705\right)}-{\mathrm{b}}_{\mathrm{b}\mathrm{w}}\left(705\right)$$

(6)

where the values of a_w(705) and b_bw(705) (backscattering coefficient of pure water) are known [40]. In this study, wavelengths of 490 and 560 nm were used in our empirical model to estimate the slope of particle backscattering coefficient Y (Equation (7)) rather than 443 nm, as it suffered from larger errors in atmospheric correction due to the high absorption of CDOM and suspended particles in a coastal environment. Finally, b_bp(λ) can be calculated with the estimated b_bp(705) and slope Y (Equation (8)):

$$\mathrm{Y}=2.0\left\{1-1.2\exp \left[-0.9\times \frac{{\mathrm{r}}_{\mathrm{r}\mathrm{s}}\left(490\right)}{{\mathrm{r}}_{\mathrm{r}\mathrm{s}}\left(560\right)}\right]\right\}$$

(7)

$${\mathrm{b}}_{\mathrm{b}\mathrm{p}}(\lambda )={\mathrm{b}}_{\mathrm{b}\mathrm{p}}\left(705\right)\times {\left(\frac{705}{\lambda }\right)}^{\mathrm{Y}}$$

(8)

2.5.2. Step 2

The backscattering ratio (b_bp^~(λ)) was used to obtain b_p(λ) (Equation (9)). It should be noted that b_bp^~(λ) is usually not a constant value due to some physical properties (such as the component, size, and structure) of the suspended particles [41,42,43]. However, for some specific study areas, b_bp^~(λ) is regarded a constant or to be within certain limits [44,45]. In this study, we performed a least square fitting using in situ measured b_bp(λ) and b_p(λ) to obtain b_bp^~(λ) and to evaluate the applicability of b_bp^~(λ) as a constant in the present study area:

$${\mathrm{b}}_{\mathrm{p}}=\frac{{\mathrm{b}}_{\mathrm{b}\mathrm{p}}}{{\mathrm{b}}_{\mathrm{b}\mathrm{p}}{}^{~}}$$

(9)

2.5.3. Step 3

In general, b_p(λ) is affected by the total suspended matter (TSM), the scattering efficiency (Q_be), the apparent density (ρ_a), and the mean diameter weighted by the area (D_A), and it is most affected by the TSM. Hence, the mass-specific scattering or backscattering (i.e., b_p(λ) or b_bp(λ) divided by the TSM) are usually used to estimate the particle size [11]. However, as we can see from Equation (10), the mass-specific scattering is affected not only by D_A but also by the value ρ_a multiplied by D_A. The volume-specific scattering coefficient (b_p*(λ)), which was calculated by the ratio of b_p(λ) to V_tot(D), was introduced in this study because the scattering per unit volume concentration was likely to scale with the particle diameter (Equation (11)). To calculate the value of b_p*(λ), V_tot(D) should first be estimated according to Equation (11). The V_tot(D) prediction model was calibrated by b_p(λ) and b_bp(λ) separately, for b_p(λ) and b_bp(λ) were both considered to be dependent on the suspended particle concentration. The accuracy of the V_tot(D) prediction models calibrated by b_p(λ) and b_bp(λ) were compared, and we adopted the one with better performance:

$${\mathrm{b}}_{\mathrm{p}}=\frac{3}{2}\frac{{\mathrm{Q}}_{\mathrm{b}\mathrm{e}}}{{\mathsf{\rho }}_{\mathrm{a}}{\mathrm{D}}_{\mathrm{A}}}\mathrm{TSM}=\frac{3}{2}\frac{{\mathrm{Q}}_{\mathrm{b}\mathrm{e}}}{{\mathrm{D}}_{\mathrm{A}}}{\mathrm{V}}_{\mathrm{tot}}\left(\mathrm{D}\right)$$

(10)

$${\mathrm{b}}_{\mathrm{p}}{}^{\ast }=\frac{{\mathrm{b}}_{\mathrm{p}}}{{\mathrm{V}}_{\mathrm{tot}}\left(\mathrm{D}\right)}=\frac{3}{2}\frac{{\mathrm{Q}}_{\mathrm{b}\mathrm{e}}}{{\mathrm{D}}_{\mathrm{A}}}$$

(11)

2.5.4. Step 4

D_v⁵⁰ was obtained from the D_v⁵⁰ model developed using in situ calculated b_p*(λ) and D_v⁵⁰. In the past few years, several D_v⁵⁰ models have been proposed for certain areas. For instance, an inverse proportion model and a negative power function model were developed for the Irish Sea and the nearshore waters of Imperial Beach, respectively [3,46]. Then, the negative power function model was optimized and applied in the Bohai Sea and Yellow Sea [5]. All of the above models were developed based on the relationship between D_v⁵⁰ and the mass-specific b_p(λ) or b_bp(λ). We validated the previous models in our study area and proposed a negative exponential function model for D_v⁵⁰ estimation. We compared these models calibrated by b_p*(λ) and b_bp*(λ) separately, and we adopted the one with the best performance.

2.6. Accuracy Assessment

To assess the consistency of the estimated in situ measured values, the root mean squared error (RMSE) (Equation (12)), mean absolute percentage error (MAPE) (Equation (13)), and bias (Equation (14)) were used in this study:

$$\mathrm{RMSE}=\sqrt{\frac{1}{\mathrm{N}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{y}}_{\mathrm{i}}^{\prime }-{\mathrm{y}}_{\mathrm{i}}\right)}^2}$$

(12)

$$\mathrm{MAPE}=\frac{1}{\mathrm{N}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{N}}\left|\frac{{\mathrm{y}}_{\mathrm{i}}^{\prime }-{\mathrm{y}}_{\mathrm{i}}}{{\mathrm{y}}_{\mathrm{i}}}\right|$$

(13)

$$\mathrm{bias}=\frac{1}{\mathrm{N}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{N}}\left({\mathrm{y}}_{\mathrm{i}}^{\prime }-{\mathrm{y}}_{\mathrm{i}}\right)$$

(14)

where y_i′ is the predicted value, y_i is the measured value, and N is the number of samples.

3. Results

3.1. Optical Properties and PSD

A summary of the measured data (including the optical properties and particle size parameters) is shown in

Table 2. Descriptive statistics for particulate backscattering b_bp(λ), scattering b_p(λ), volume-specific scattering b_p*(λ), coefficients at 532 nm, total volume concentration V_tot(D), and median particle size D_v⁵⁰. S.D. = standard deviation; C.V. = coefficient of variation; and N = number of observations.

Variable	Units	Min	Max	Mean	S.D.	C.V. (%)	N
bbp(532)	m−1	0.02	0.22	0.11	0.1	44.3	39 *
bp(532)	m−1	1.26	14.34	5.85	2.8	47.2	39
bp*(532)	m2/mL	0.04	0.34	0.18	0.1	40.7	39
Vtot(D)	μL/L	9.37	144.76	38.77	26.8	69.0	39
Dv50	μm	28.89	263.02	103.10	74.6	72.4	39

* For b_bp(532), 37 measurements were available from 39 measurements due to the saturation of the signal that appeared in 2 observations.

. All of the parameters showed a wide range with a high C.V. value, which indicated the large variation of the optical properties and PSD in the study area. It needs to be mentioned that the wavelength of 532 nm was used both for b_p(λ) and b_bp(λ), because signal saturation appeared in the red and NIR bands for in situ BB9 backscattering measurement (especially at 695 and 715 nm). We also abandoned the blue bands for the reason that large errors would appear when calculating b_bp(λ) at wavelengths far from the reference wavelength in the NIR region.

3.2. D_v⁵⁰ Model Development

The validation of the QAA for b_bp(532) retrieval is shown in Figure 3a. The QAA estimated and in situ measured b_bp(532) values showed a good fit (R² = 0.85, RMSE = 0.02), with MAPE = 17.2% and bias = −0.0021. As we can see, the scattered dots were mostly close to the 1:1 line. This finding indicates that the QAA method held good potential for b_bp(λ) retrieval in our study area. The backscattering ratio b_bp^~(λ) was derived from the least square fitting using the in situ measured b_bp(λ) and b_p(λ), with a high R² value of 0.94 and a low RMSE value of 0.012 (Figure 3b). The slope of the fitted equation was 0.0202, which was the ratio of b_bp(λ) and b_p(λ) and was equivalent to b_bp^~(λ) in this study.

As for V_tot(D) retrieval, we compared the results of the empirical models calibrated by b_p(532) and b_bp(532). The V_tot(D) retrieval model calibrated by b_p(532) held a higher accuracy, with an R² of 0.75 (Figure 4a), and the V_tot(D) retrieval model calibrated by b_bp(532) showed a lower accuracy, with an R² of 0.72 (Figure 4b). Moreover, signal saturation appeared in two sites for the b_bp(532) data, which indicates that b_bp(532) might not be available in high-turbidity water. Hence, b_p(532) was used to calculate V_tot(D) in this study.

For D_v⁵⁰ retrieval, 23 simultaneous b_p*(λ), b_bp*(λ), and D_v⁵⁰ datasets were used in the calibration of the inverse proportion model (Figure 5a for b_p*(λ) and Figure 5b for b_bp*(λ)), negative power function model ((Figure 5c for b_p*(λ) and Figure 5d for b_bp*(λ))), and negative exponential function model (Figure 5e for b_p*(λ) and Figure 5f for b_bp*(λ)). The results for all models are shown in

Table 3. Comparison of Dv50 models reported by previous studies and that proposed in this study in calibration.

Relation	Model	R2	RMSE (μm)	Reference
Dv50 vs. bp*	Inverse proportion	0.65	50.78	Bowers et al. (2007)
	Negative power function	0.71	48.9	Woźniak et al. (2010)
	Negative exponential function	0.85	33.5	This study
Dv50 vs. bbp*	Inverse proportion	0.64	51.6	Bowers et al. (2007)
	Negative power function	0.67	50.7	Woźniak et al. (2010)
	Negative exponential function	0.78	41.3	This study

. Overall, a good fit (R² = 0.85, RMSE = 33.5 μm) was found by the proposed model for the relationship between b_p*(λ) and D_v⁵⁰ (Figure 5e). The proposed model also showed the potential (R² = 0.78, RMSE = 41.3 μm) in the relationship between b_bp*(λ) and D_v⁵⁰ (Figure 5f), while the other two models obtained poorer results for estimating D_v⁵⁰. The findings indicated that the negative exponential model performed best in our study area.

3.3. D_v⁵⁰ Model Validation and Application

In this study, 16 in situ measurements were used to validate the performance of the D_v⁵⁰ retrieval models proposed by previous studies and developed in this study. The model validation results showed that the proposed method performed well, with an R² of 0.86, RMSE of 18.52 μm, MAPE of 21.28%, and bias of −1.85 (

Table 4. Performance comparison of Dv50 models reported by previous studies and that proposed in this study in validation.

Model	R2	RMSE	MAPE	Bias
Inverse proportion	0.78	30.28	31.6%	−6.01
Negative power function	0.79	31.17	32.36%	8.74
This study	0.86	18.52	21.28%	−1.85

). The scattered dots were mostly close to the 1:1 line, except for some dots with large D_v⁵⁰ values (Figure 6) due to a shortage of training data for model calibration, especially in the case of the large D_v⁵⁰ samples. The findings proved that D_v⁵⁰ could be estimated using the remote sensing method.

The proposed D_v⁵⁰ model was further applied to the remote-sensed ocean color data. After applying the proposed method to the Sentinel-2 MSI images, we obtained the D_v⁵⁰ distribution at different times in our study area (Figure 7). The satellite-retrieved D_v⁵⁰ values ranged from approximately 50 to 180 μm. It can be seen that there existed obvious differences in the D_v⁵⁰ distribution in both time and space; D_v⁵⁰ on 30 January 2020 was higher than that on 22 September 2019 in most areas, with the exception of the western area of the PRE, and D_v⁵⁰ in the western area was lower than that in the eastern and southern area of the PRE on both days. The results indicate the potential for monitoring D_v⁵⁰ on a large scale with Sentinel-2 MSI data.

4. Discussion

4.1. Robustness of the D_v⁵⁰ Model

Accurate estimation of b_bp(λ) is of fundamental importance for accurate D_v⁵⁰ retrieval. Some inversion models, such as Generalized IOP (GIOP) [47], the Garver–Seigel–Maritorena (GSM) algorithm [48], and the QAA [36], provide fairly accurate estimations of b_bp(λ) for the open ocean, but they are less accurate in highly turbid or eutrophic coastal water [15]. We adopted 705 nm as the reference band in the QAA method, and thus the contribution of the absorption of CDOM and suspended particles to the total absorption in the reference band could be neglected. Consequently, the total absorption could be represented by pure water. In fact, the total absorption sometimes cannot be represented by pure water in the NIR band, especially for water with a high concentration of TSM [34]. In that case, the band in which water absorption is more obvious should be considered, such as the bands in the mid-infrared region [38].

It is known from previous studies that the backscattering ratio b_bp^~(λ) is impacted by the bulk refractive index and the relative proportion between small- and large-sized particles, and theoretically, a higher proportion of small-sized particles indicates a higher b_bp^~(λ) value [29,42,49]. Thus, the b_bp^~(λ) value is not always constant between different waters. McKee and Cunningham (2006) [50] found that b_bp^~(λ) varied over an order of magnitude from 0.005 to 0.050 in the Irish Sea and its coastal area, and Petzold (2007) [51] found that b_bp^~(λ) was 0.019 for turbid waters in a San Diego harbor and 0.013 for the coastal waters. That aside, Loisel et al. (2007) [52] found that the value of b_bp^~(λ) was highly related to the refractive index of particles and that particle populations dominated by phytoplankton or inorganic particles were the trigger for higher or lower values of b_bp^~(λ), respectively. In the present study, b_bp^~(532) was regarded as a constant value, and the fitted b_bp^~(λ) of 0.0202 was in line with previous studies performed in different coastal and oceanic waters. However, the value of b_bp^~(λ) should be discussed accordingly over the long term and with a large number of observations to ensure the accuracy of the D_v⁵⁰ model.

In general, b_p(λ) and b_bp(λ) are driven by the particle concentration to the first order, whereas the particle size, refractive index, internal structure, and shape are driven to the second order [11,52]. In light of this, the relationships between the particle volume concentration V(D) against b_p(532), b_bp(532), and c_p(670) as measured by the LISST were observed (Figure 8). Consequently, the b_p(532) and V(D) in the particle size range between 3.7 and 85.2 μm showed a great correlation, and similar results were also found for b_bp(532) and c_p(670). However, there turned out to be a poor correlation when focusing on smaller and larger particles. These results might be explained by small particles that were not well-proportioned (Figure 8b) and particles that deviated from the “Junge distribution” model [53] when the particle size was smaller than 3.7 μm, while larger particles contributed less to the scattering because larger particles generally corresponded to phytoplankton that had a low refractive index, and this finding is in agreement with a previous study [52]. On account of these uncertainties, the estimation of V_tot(D) (in a size range of 2.05–297 μm) from b_p(λ) or b_bp(λ) did not perform excellently. In addition, the relatively good correlation between D_v⁵⁰ and b_p*(λ) with a negative exponential model supports the use of remote sensing to describe the PSD in the coastal water of the PRE.

4.2. Applicability to Sentinel-2 MSI Data

Sentinel-2 MSI was designed initially for land feature monitoring, and a higher signal-to-noise ratio is required for information extraction from water. However, some studies found that it performed well in inland and coastal water areas for water components or optical properties research [15,35]. The D_v⁵⁰ distribution obtained from Sentinel-2 MSI showed that the water areas surrounding islands are full of small-sized particles. This finding is in agreement with previous studies that proposed that sediment resuspension occurs under high winds or tides in coastal water with a shallow bathymetry [54] and that small-sized particles are usually dominated by inorganic particles [1,11]. In general, large particles are dominated by phytoplankton or algae [55]. Therefore, D_v⁵⁰ may be used as an indicator for the variation of phytoplankton and inorganic particle distribution.

5. Conclusions

A four-step method was presented for suspended particle size estimation in the coastal water areas in the PRE through establishing the relationship between D_v⁵⁰ and the IOPs, which could be retrieved from the Rrs(λ) of the water surface. As a consequence, the four-step method performed well for D_v⁵⁰ estimation. However, there are still some limitations that should be considered in future work, such as the value of b_bp^~(λ) should be discussed according to long-term observations, and the V_tot(D) calculated by b_p(λ) is size-dependent. Nevertheless, we found that the in situ hyperspectral data resampled by the Sentinel 2 MSI channels had great potential for monitoring D_v⁵⁰ in the coastal area. The above results provide the possibility to monitor the suspended particle size of coastal complex waters using a remote sensing method.