1. Introduction

Bio-optical measurements from different in-situ and remote platforms provide important information about the biogeochemical characteristics of ocean waters [1]. For example, researchers can now perform optical measurements of discrete samples of surface water and can also examine long-term time series of in-water vertical profiles using research vessels and moorings, profiling floats, autonomous vehicles, and instruments on airborne and space-borne platforms. Thus, studies of the bio-optical properties of ocean waters and the construction of bio-optical algorithms have greatly improved our understanding of the vertical structure of ocean waters [2–7]. The advent of underwater optical sensors has increased our understanding of the spatial and temporal characteristics of phytoplankton photosynthesis in the ocean and its role in carbon cycling [8]. However, the increased knowledge of these temporal and spatial characteristics also led to the identification of complexities in certain variables, such as changes in the chlorophyll index due to the physiological variability of phytoplankton [4,9–12] and null or negative correlations between the concentration of chlorophyll a (Chla) and the particulate backscattering coefficient (b_bp(λ)) due to photoacclimation processes or changes in the relative abundance of non-algal particles (NAPs) in subtropical regimes [5–7,13,14]. These complexities lead to low correlations between b_bp(λ) values and Chla in ultra-oligotrophic oceanic areas and prevent precise estimation of relevant parameters in oligotrophic regions, such as subtropical gyres [13].

For historical and practical reasons, researchers use Chla as an index of phytoplankton abundance [15,16]. The empirical relationships between Chla and the inherent optical properties (IOPs) of ocean water, such as the absorption coefficient, beam attenuation coefficient, scattering coefficient, and b_bp(λ), can be used to develop optical models and algorithms that characterize the biogeochemical properties of these systems and estimate biological pumping and carbon flux [1,17]. For example, earlier research described an empirical relationship between the particle scattering coefficient at 550 nm and the concentration of Chla based on statistical analysis of field data [18,19]. Subsequent research extended this initial expression for particle scattering at 660 nm in the upper homogeneous layer of the ocean [15]. A more recent study described the nonlinear relationship between spectral scattering by particulates and b_bp(λ) values with the level of Chla along an 8000 km transect that crossed Case 1 waters of the eastern South Pacific gyre (which has levels of Chla ranging from about 0.02–2 mg m^-3), and provided statistical methods for determination of the correlation [3]. Nevertheless, there are relatively large variations in the b_bp(λ) and Chla in more eutrophic waters and in clear oligotrophic waters, and the factors responsible for this variability differ among different areas [4]. The biogeochemical-argo (BGC-Argo) bio-optical database identified the sources of variability in the relationship of b_bp(700) and Chla at vertical, regional, and seasonal scales. The results suggested that a decoupling between these two variables was due to photoacclimation processes and changes in the relative abundance of NAPs in subtropical regimes [5]. Furthermore, the decoupling of Chla and b_bp(λ) in the upper layer water of oligotrophic waters affects the estimated levels of NAPs matter. For example, a recent study reported a smooth annual cycle of the b_bp(700) for NAPs in oligotrophic waters using the global BGC-Argo data set [7]. Other recent studies assessed the spatial and temporal variability of photoacclimation processes and phytoplankton biomass in global-scale open ocean waters [20]. The results showed that oligotrophic regions had permanent deep photo-acclimation maximums (DAMs) that were occasionally replaced by deep biomass maximums (DBMs), and that these two processes can cause a deep Chla maximum (DCM). Moreover, the presence of DCMs at low-latitudes (below 15°, where oligotrophic waters account for 60% of the ocean surface) significantly contribute to global primary production [20]. These findings point to a need for further studies of this topic.

Therefore, we examined subtropical gyres at low-latitudes in the tropical Western Pacific Ocean. This is one of the most complex hydrographic regions in the world because equatorial currents and western boundary currents affect surface circulation, and it has typical oligotrophic conditions [21–23]. An investigation of the particle beam attenuation coefficient in July and September of 2004 showed stratification in the vertical attenuation of spectral downwelling irradiance. In particular, at the superficial upper layer (< 55 m), the vertical attenuation of light was primarily due to roughly equivalent effects NAPs and phytoplankton; below this layer, NAPs generally had a greater effect on attenuation than phytoplankton [24]. In addition, measurements of Chla and suspended particles in December of 2014 showed that DCMs occurred due to the vertical distribution of Chla in water depths of 50 to 150 m, and that vertical variation in the size of suspended particles was affected by water temperature. The vertical profile of Chla was unrelated to the mass concentration and size of suspended particles, but it was related to the volume concentration of suspended particles [25]. All of these studies suggest that the vertical variability of Chla may be driven by changes in phytoplankton biomass or a consequence of photoacclimation processes.

Indeed, several factors can affect the relationship between Chla and b_bp(λ) over space and time. These include the ratio of non-algal to phytoplankton biomass, the carbon/Chla ratio of phytoplankton [26], the species composition and diversity of phytoplankton (which vary in size and shape), and the characteristics of non-algal components [4,11,13,27]. Further study of the variability of Chla and b_bp(λ) — especially in ultra-oligotrophic oceanic areas — is needed to improve our understanding of their major determinants and improve our estimates of phytoplankton carbon cycling derived from remote sensing data [26,28]. The present study focused on the variability of b_bp(λ) and Chla in the upper layer (< 200 m) of the water column in oligotrophic areas of subtropical gyres. We used in-situ optical data from the tropical Western Pacific Ocean (20° N to the equatorial regions) to characterize the relationship between b_bp(λ) and Chla and to determine the sources of their variations. We also used the BGC-argo database to characterize the vertical, seasonal, and regional variability in this relationship. Based on measurements of particle size distribution in this region, the b_bp(λ) within the water column has been simulated by a homogenous and coated-sphere model, respectively.

2. Materials and methods

2.1 Field measurements

In September 2020 and April to May 2021, two expeditions in the Philippine Sea and nearby waters (0°–21° N, 126°–163° E) of the tropical Western Pacific Ocean were organized by the Institute of Oceanology of the Chinese Academy of Sciences in the Kexue Research Vessel. Field measurements and discrete sampling consisted of measurements of spectral IOPs, Chla, particle size distribution, and related data at 33 stations (Fig. 1). A bio-optical profiling package that consisted of a variety of instruments was used to measure various optical, biogeochemical, and physical parameters. These instruments were a Sequoia LISST-100X, used to measure the size of particles up to 500 µm; a HOBI Labs Hydroscat-6 (HS-6), used to determine light backscattering; a Sea-bird SBE911 CTD, used to measure the physical structure of the water column; and a Wet Star fluorometer, used to measure Chla fluorescence. This profiling package was slowly lowered into the water column (0.2 m s^-1) to a depth of 200 m. Only downcast measurements were used to minimize interference from the instrument cage.

 

Fig. 1. Geographical location of the BGC-Argo dataset (black stars) and location of stations sampled during the different cruises in Philippine Sea and nearby waters (other symbols). Filled triangles: sampling in September 2020; open circles: sampling between April and May in 2021 at depths greater than 100 m; filled circles: sampling between April and May in 2021 at depths less than 100 m. Area filled with diagonal lines represents the range of Chla distribution with less than 0.05 mg m^-3 in September 2021, The area filled with squares refers to that in January, and yellow dots filled area represents that in December; and the average Chla in 2021 is represented in the background.

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The in-situ vertical profiles of total backscattering coefficients (b_b(λ)) values were measured at six wavelengths (442, 488, 550, 620, 700, and 852 nm) using a HydroScat-6 (Hyd-6, Hobi Labs) according to the manufacturer’s protocol (2003). Before the cruise surveys, the HS-6 meter was calibrated for dark offset and gain ratio. This instrument measures the single-angle (about 140°) volume scattering function in a backward direction [29], and these measurements can be transformed into backscattering using the corresponding calibration coefficients. The effects of path length attenuation were modified using sigma correction, as described in the Hydroscat-6 User’s Manual [30]. Thus, after field sampling, sigma correction was applied to improve the accuracy of backscattering results. The backscattering coefficient of particles b_bp(λ) was then calculated by subtracting the b_b(λ) of pure water from the total b_b(λ). The scattering coefficient of pure seawater has been reassessed by Ref. [31].

Particle size distribution was measured using a LISST-100X (Type C, Sequoia Scientific), and size ranges were plotted on a logarithmic scale ranging from 2.72 to 500 µm for analysis. This instrument records the light scattering of particles at 670 nm at 32 angles, with bins evenly distributed on a logarithmic scale, at the near-forward direction [32]. Particle size and volume concentrations for each bin were processed using the manufacturer’s software (LISST-100X Particle Size Analyzer, 2013). Particle number concentrations were obtained by dividing the volume concentration for each bin by the volume of the sphere diameter of the bin.

Three guidelines proposed by Ref. [33] were used to standardize the measurements and data processing. These guidelines prevent adverse effects from a low signal-to-noise ratio in particle scattering [34]; laser diffraction by sunlight, which could alter the derivation of particle size distribution; scattering due to gradients in seawater density [35,36]; and air bubbles close to the surface [37]. Consequently, the analysis was limited to depths greater than 20 m, and excluded the nine largest bins (122–500 µm). Moreover, the remaining 23 discrete LISST bins were grouped into two size classes: LISST bins 1 to 13 (effective size range: 2.72–19.8 µm; referred to as 2–20 µm particles; and LISST bins 14 to 23 (effective size range: 19.8–103.7 µm; referred to as 20–100 µm particles). The piecewise volume was defined as the sum of the volumetric concentrations of all parts.

The absorption coefficients of phytoplankton (a_ph(λ)) and non-algal particles (a_NAP(λ)) were measured following the standard quantitative filter technique (QFT) procedure [38]. Discrete water samples (2 L) were collected at seven depths (5, 25, 50, 75, 100, 150, and 200 m) using Niskin bottles that were mounted onto a rosette sampler, which was attached to the Sea-bird SBE911 CTD. The sample was passed through a 25 mm Whatman GF/F filter (pore size: 0.7 µm) at low vacuum pressure, and then stored in Petri dishes at –80 °C until analysis for particulate absorption and Chla. The concentration of Chla was computed as the sum of the concentrations of Chla (including allomers and epimers), chlorophyllide a, and divinyl Chla. The absorption spectrum of particles retained on the GF/F filter was determined using the transmittance-reflectance method. In particular, before pigments were extracted, the spectral particulate absorption was measured using a Perkin-Elmer Lambda 35 dual-path spectrometer with an attached integrating sphere. A blank filter wetted with Milli-Q water, was used as a reference. All spectra were shifted to zero in the near infrared by subtracting the average optical density between 750 nm and 800 nm. Pigmented particles were extracted pigments (1-4 h) in methanol for separating the phytoplankton pigments within the particulate matter from NAPs. The sample filter paper thoroughly rinsed with Milli-Q water before being re-scanned to obtain NAPs absorbance. The path length amplification factor which was corrected using the expression given by Ref. [39]. This correction was shown to be dependable when using the T-R technique [40]. Then, for each sample, the spectral values of absorption coefficient of Chla were obtained by subtracting a_NAP(λ) from a_ph(λ). To account for the effect of NAPs on the low correlation between b_bp(λ) and Chla, the b_bp(λ) of NAPs was estimated using the absorption coefficient of Chla and NAPs at seven depths. The calculation is mainly based on the total b_b(λ) are the sum of the backscattering coefficients of pure water (b_bw(λ)), planktonic component (b_bc(λ)), and suspended particles (b_bp(λ)) [41], of which b_bw(λ) can be obtained using the experimental results of Ref. [42] and Ref. [43], and b_bc(λ) can be obtained from the Chla concentration and backscattering wavelength dependence using the method of Ref. [44]. The calculation processes are described in detail in Ref. [45].

2.2 BGC-Argo database

Eight BGC-Argo profiling floats were deployed in oligotrophic waters of the tropical Western Pacific Ocean as part of several national and international programs [46]. Data collected from November 2019 to November 2022 at 1 to 3-day intervals were used for this study. These floats acquired vertical profiles (0–1000 m) of pressure, temperature, and salinity using a Seabird Scientific SBE 41 CTD sensor, measured Chla fluorescence using an ECO_FLBBCD-WetLABS, and measured the angular scattering function at 700 nm using an ECO_FLBBCD-WetLABS. Chla fluorescence was converted to Chla concentration (units of mg m^-3) and angular scattering was converted to b_bp(700) (units of m^-1; see Supplement 1). All the data were downloaded from the Argo database [47] and quality controlled (see Supplement 1). A total of 2167 Chla and b_bp(700) vertical profiles were collected, and the average vertical resolution was greater than 1 m in the upper 300 m. Subsequently, the depth of the euphotic zone (i.e., the depth at which the level of photosynthetically active radiation [PAR] reached 1% of its surface value) was estimated from the Chla profile using an iterative process, as described by Ref. [16]. The productive layer was calculated as the region from the surface to 1.5 times the depth of euphotic zone [48]. The mixed layer, where all measured properties are expected to be homogenous, includes a large fraction of the phytoplankton biomass [40,49] and was determined using a 0.03 kg m^-3 density criterion [50]. The Chla maximum was then determined for depths of 0 to 300 m.

2.3 Estimation of vertical profile backscattering

According to previous studies [24], NAPs generally had a greater effect on attenuation than phytoplankton. In this study, the contributions of phytoplankton and NAPs to bulk backscattering are modeled as coasted spheres and homogeneous spheres using Aden-Kerker and Mie scattering computations, respectively. According to Mie scattering theory, the relationship between the particulate backscattering spectrum and the particle size distribution (PSD) can be quantified using efficiency factors for scattering (Q_bb(λ)). The b_bp(λ) at a given wavelength is then obtained by integration over all particles of a given size, as described by Ref. [51]. The backscattering efficiency can be computed using the methods of Ref. [52], which is based on the Mie scattering theory for homogenous spherical particles. Reference [45] recently provided a detailed description of the procedures used to set these parameters. Special attention should be given to the particle’s complex index of refraction relative to the medium ($m = n + n^{\prime}i$), in which the real part, n, is the ratio of the speed of light in seawater to that of the particle. This value is close to the upper limit of the range of variations for different algal classes [53], and NAPs accounted for half of the b_bp(λ). The imaginary part, $n^{\prime}$, is proportional to the bulk absorption coefficient of the particle. The absorption coefficients of a suspended particle were calculated to assess the best imaginary component of the refractive index equation during the period of two expeditions in study region. The input for Mie scattering calculations of suspended particles requires a particle size distribution from 2.72 to 20 µm, as described in section 3.5. The distribution function describing the number of particles per unit volume within each size class of suspended particulate matter was obtained from LISST, and the backscattering efficiencies estimated by Mie scattering model were then used to estimate the vertical profile of b_bp(λ). Inputs for the coasted-sphere refer to Ref. [54] and Supplement 1.

2.4 Statistical analyses

Correlation and regression analyses were all performed. Some indicators were used to assess the performance of the developed models in this study, including determination coefficient (r²), root mean square error (RMSE), All r coefficients are statistically significant (p < 0.01). The model performance was evaluated by calculating the systematic error, in logarithmic space, as follows:

3. Results

3.1 Variations in the b_bp(λ) -to-Chla ratio in the water column

Based on previous studies, we selected four layers of the water column (euphotic layer, productive layer, mixed layer, and DCM layer) for estimating the average b_bp(λ) /Chla ratio in the entire euphotic layer of the water column. We first examined the dependence of the spectral b_bp(λ) on Chla at all field stations. The results showed a high correlation between b_bp(λ) and Chla in the lower DCM layer (Fig. 2, where the black dashed line is a linear regression of the two variables from random two-thirds, and the remaining third is used to verify the correlation. Take 442 nm and 488 nm wavelength data for example), but a decoupling of this relationship in the other three layers. Below the DCM layer, the linear relationship can be expressed as: b_bp(λ) = a(λ)Chla + b(λ), in which the slope parameter a(λ) decreased linearly with wavelength, and the slope value is also consistent with the results of previous studies [3]. In other words, b_bp(λ) decreased with decreasing Chla at all wavelengths, and the intercept parameter b(λ) had a non-linear relationship with wavelength, in that it could be described as a power function. This means that the minimum b_bp(λ) in the water column below the DCM layer decreased in a non-linear manner with an increase in wavelength. This correlation coefficient was therefore higher in the blue-green spectral bands (Fig. 3).

 

Fig. 2. Correlation between b_bp(λ) and Chla in the water column below the DCM at 442 nm (a) and at 488 nm (b). Black dashed line is a linear regression of the two variables from random two-thirds, and the remaining third is used to verify the correlation. The gradient color is used to distinguish data from different stations.

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Fig. 3. Effect of wavelength on the slope (a) and the intercept (b) in the linear relationship of b_bp(λ) with Chla: b_bp(λ) = a(λ)Chla + b(λ). Error bars (black vertical lines within each point) represent the 95% confidence interval on the parameters.

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Above the DCM layer, there was a weak correlation between b_bp(λ) and Chla. In particular, from the surface layer to the DCM layer, the b_bp(λ) value remain nearly constant as the Chla level increased. According to the seasonal variance in Chla method proposed by Ref. [8], in this study area, the maximum value distribution of Chla subsurface presents two conditions, namely, the high-variance regions (less than 100 m) and the low-variance regions (more than 100 m). The maximum Chla level was in a shallow area (< 100 m), and the b_bp(λ) increased slightly or decreased as the Chla level increased. However, for the maximum value of Chla in deep areas (>100 m), the change in the b_bp(λ) was unrelated to the level of Chla.

3.2 Contribution of non-algal particulate matter to backscattering

Because the nature of NAPs may have contributed to the decoupling of these two variables, we analyzed the relationship of b_bpNAP(λ)/ b_bp(λ) with depth and wavelength. The results suggested an increased contribution of NAPs to backscattering from 442 to 700 nm, and that NAPs accounted for about half of the b_bp(λ) at 700 nm (Fig. 4(a)). Analysis of the effect of depth indicated the effect of NAPs was maximal at about 50 m, and then decreased gradually (Fig. 4(b) and (c)). However, the depth at which NAP made the maximum contribution to backscattering was different from the depth that had the maximum level of Chla.

 

Fig. 4. Effect of depth on b_bpNAP(442)/b_bp(442) (a) and effect of wavelength on the b_bpNAP(λ)/ b_bp(λ) at a depth of 50 m (b) and 200 m (c).

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3.3 Spectral dependence of b_bp(λ)

Because the relationship of b_bp(λ) with wavelength depends on the particle size distribution, we estimated the spectral dependence of slope using a power law model of b_bp(λ) spectral dependency. Field data regarding the effect of depth on the spectral slope had two main characteristics. First, the spectral slope slowly decreased with water depth, reached a minimum of 0.7 at 150 m, and then rapidly increased to 1.6 at 200 m. Second, the spectral slope decreased rapidly with water depth, reached a minimum of 0.6 at 50 m and then rapidly increased to 1.8 at 200 m (Fig. 5). The vertical changes in this first characteristic indicated slight changes in the proportion of small and large particles in the water column; this corresponded with the vertical variations of Chla in the water column, in that the maximum value of Chla was in the deep water (>100 m). The proportions of small and large particles in the latter water column changed greatly, and this corresponded with the vertical variation of Chla in the water column, whose maximum value was in shallow water (< 100 m) (Fig. 5).

 

Fig. 5. Effect of depth on Chla, b_bp(700), and the b_bp(λ) slope in the water column when the DCM is less than 100 m (a, b, c) and greater than 100 m (d, e, f). The gradient color is used to distinguish data from different stations (see Fig. 1).

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3.4 Relationship between b_bp(700) and Chla in the BGC-Argo data

Based on these data, there are two area in the oligotrophic area of the Western Pacific Ocean that differ in their relationships between b_bp(λ) and Chla, and these areas were bounded by the region with maximum Chla in the water column. From the surface layer to region with the Chla maximum, there was no significant correlation relationship between the b_bp(λ) and Chla concentration; there was a linear correlation between b_b(λ) or b_bp(λ) with Chla in the range of the maximum Chla at a depth of 300 m (Fig. 2). To further evaluate the nature of these relationships and their regional and seasonal characteristics, we examined biogeochemical buoy data from eight stations in the study area to assess the relationship between b_bp(700) and Chla. These data covered the field stations from November 2019 to November 2022.

The results from the BGC Argo dataset showed that the vertical profiles of b_bp(700) had two different patterns. The pattern from the middle of November to the following April had a leptokurtic distribution (increased concentration near the mean) in the vertical distribution of b_bp(700) (Fig. 6(a)). In the other months, the pattern had a platykurtic distribution (decreased concentration near the mean). The results showed that the backscattering effect of particles was strong from winter to following spring (Fig. 6(b)). This phenomenon also occurred in our data in September 2020 and from March to May 2021, and BGC-Argo data from November 2019 to November 2022 (Fig. 6, the colored open circles represent the annual average, and the blue solid circle represents the statistical sample number).

 

Fig. 6. Effect of depth on b_bp(700) from mid-April to mid-November (a) and from mid-November to mid-April of the following year (b) from BGC-Argo dataset. Note the platykurtic distribution in (a) and the leptokurtic distribution in (b). Open yellow circles represent the annual average of blue gradient colors circles (Gradient colors are used to distinguish data at different times), the range of that is from mid-November 2020 to mid-November 2021. Open red circles refer to from mid-November 2019 to mid-November 2020, and open green circles represents from mid-November 2021 to mid-November 2022.

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However, there was no significant correlation between the vertical profile of Chla and seasonal variations. In 2021, the peak of Chla level was in the deep-water during January, March, and May, and was in shallow water during February and April. In July, the Chla level began to increase, and the peak value moved to shallow regions. The December peak of Chla was always in shallow water.

Although the b_bp(700) and Chla in the water column are constantly changing with the seasons, the b_bp(700) mostly fluctuated within a certain range. This peak was between 0.0003 and 0.0004 m^-1 in shallow water and was about 0.0002 m^-1 in deep water, and the peak varied with depth in the range of 100 to 130 m. However, the Chla level was very low in shallow water and deep water, with a maximum of 0.5 mg m^-3, and there were fluctuations at depths of 100 to 150 m.

We then analyzed the correlation between the vertical profile of Chla and b_bp(700) at each BGC-Argo station. The results showed that three stations (2902753, 2902756, and 2902822), which were located at about the same latitude, had similar nonlinear relationships between b_bp(700) and Chla from mid-November to mid-April of the following year (Fig. 7(a)) and from mid-April to mid-November (Fig. 7(b)). In addition, the b_bp(700) values of three stations (2902762, 2902823, and 2902824) in the annual oligotrophic area had a good correlation with the concentration of Chla only in the range from the region with maximal Chla level to a depth of 300 m. This relationship was logarithmic between April and December (Fig. 7(c)), and linear between January and April (Fig. 7(d)), and the correlation of these variables from the surface to the maximum Chla layer was not significant.

 

Fig. 7. Relationship between b_bp(700) and Chla in the water column below the DCM from mid-November to mid-April of the following year (a) and from mid-April to mid-November (b) at the same latitude; a good linear correlation between mid-November to mid-April of the following year (c) and a logarithmic correlation from April to November (d) in the annual oligotrophic ocean area.

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3.5 Variations of particle size in the water column

Because the effective size range of the LISST laser diffractometer used in this study was 2.72 to 500 µm, no particles smaller than 2.72 µm were included in our calculations. Statistical analysis of the concentration of particles that were 2.7 to 20 µm and 20 to 100 µm showed that the number of small particles (2.7–20 µm) gradually decreased as water depth increased (Fig. 8(a) and (b)). Moreover, the number of small particles in the region with the maximum Chla level in the deeper area increased, and then dropped sharply as the Chla level decreased. The quantity of large particles (20–100 µm) increased as water depth increased, with a large increase near a depth of 60 m. This depth corresponds to the DCM in regions where the maximum Chla level was at a shallower depth, but not in areas that had a deeper DCM (Fig. 8(c) and (d)). These results showed that small particles had a large influence on the distribution of Chla in areas that had a deep DCM, and the distribution of large particles in areas with shallow DCM was similar to the distribution of Chla, although the quantity and concentration of large particles were very low. Similarly, as water depth increased, the number of particles smaller than 3.2 µm gradually decreased (Fig. 8(e) and (f)), and the concentration of particles larger than 3.2 µm and smaller than 10 µm increased gradually in the upper part of the region as the maximum Chla level increased. Until the bottom of the region with the maximum Chla level, particles smaller than 3.2 µm no longer made major contributions to in water column. Particles larger than 3.2 µm and smaller than 10 µm made the major contribution; there was very little particulate matter in the range of 20 to 100 µm.

 

Fig. 8. Effect of depth on the total volume concentration (VC) of particulate matter in the range of 2.7 to 20 µm (a, b) and 20 to 200 µm (c, d) and the Chla maximum in the water column for DCM less than 100 m (a, c) and greater than 100 m (b, d). Open circles: Chla concentration; filled circles: the total volume concentration, and number concentration of particles (×10⁹) varied with water depth at E163-05 station, from surface to 94 m depth (e) and 94 m to 200 m depth (f) in which two red lines from top to bottom represent 95 m and 125 m, respectively.

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4. Discussion

4.1 Relationship of b_bp and Chla

The field data from the study region in the Western Pacific Ocean showed no consistent correlation between b_bp(λ) and Chla from the surface to a depth of 200 m from March 25 to May 9, 2021. The lower b_bp(λ) shows a linearly decreasing trend with Chla decrease below the maximum value of Chla (Fig. 2), while a rather constant value for the upper b_bp(λ) above the maximum value of Chla. Previous studies indicated that the scattering and b_bp(λ) values of particles in the upper layer of the water column (< 80 m) in the Southeast Pacific Ocean had a non-linear relationship with Chla, in that it could be described by a power function [3]. Yet, the upper layer of the region with the maximum Chla level in our study area was generally at a depth of 50 to 150 m, and the correlation between b_bp(λ) and Chla in this layer was not significant during the sampling period. In subtropical regimes, this phenomenon is often attributed to photoacclimation processes or changes in the relative abundance of NAPs [5]. Based on the method for detection of DCM and classification of DBM and DAM proposed by Ref. [20], we believe the different vertical profiles of b_bp(λ) and Chla in the present study resulted from phytoplankton photoacclimation at low irradiance at greater depths (>100 m). Moreover, the effect of phytoplankton biomass accumulation was significant when the maximum value of Chla was at shallow depths (< 100 m) (Fig. 5). In addition, our analysis of NAPs showed that they accounted for 40% of the backscattering (Fig. 4), and their distribution in the water column was not consistent with the distribution of Chla (Fig. 5). This also contributed to the decoupling of Chla and particulate backscattering [20].

Previous studies of the upper layer of the oceanic water column suggested that the exponent of a power law model of the b_bp(λ) spectral dependency varied as a function of Chla in the upper layer [3]. The present study found that the spectral dependence of b_bp(λ) decreased logarithmically with increasing Chla in the water column for depths below the Chla maximum; at shallower regions of the water column, the correlation between these two variables was not significant. This relationship is also reflected in our finding that the b_bp(λ) of particles in the upper water was affected by particle size, but b_bp(λ) in the lower water was mostly affected by the Chla concentration.

4.2 Temporal and spatial variations in the correlation of b_bp(700) and Chla

Our analysis of the BGC-Argo dataset indicated the nature of the relationship between b_bp(700) and Chla had seasonal and regional variations. More specifically, there was a linear relationship mostly during winter (usually December to February of the following year), but the relationship was non-linear during other seasons, in that b_bp(700) increased more rapidly with an increase of Chla. Nonetheless, these characteristics mainly appeared in regions where the maximum depth of Chla was generally greater (>100 m), namely at stations 2902762, 2902822, 2902823, and 2902824 (Fig. 7). These two variables had a non-linear relationship at stations in the northern regions of the study area (2902753, 2902754, and 2902756) throughout the whole water column and during the whole year. For station at higher latitudes (2902755), the maximum Chla level was at a depth of 30 m, and there was a good correlation of Chla with b_bp(700) in the entire water column. Based on the locations of these stations, the correlation between these two variables gradually increased from the warm pool area to the north and south on both sides. Thus, we processed monthly mean data of surface Chla obtained from the MODIS products of 4 km in 2021 to analyze the spatial distribution of Chla in this region (Fig. 1). The results showed that water with a Chla level below 0.05 mg m^-3 was mainly in the range from 10° to 20° N, and the range gradually expanded from the coast of the Philippines to the east; with the change of seasons, the range of low Chla concentration gradually expanded to the north and south on both sides (Fig. 1). The range of low Chla concentration reached a maximum during September, when it was in the range of 5° to 30° N latitude, but from October onward the range of low Chla concentration gradually decreased.

However, regions in which the relationship between Chla and b_bp(700) were significantly affected by seasons mainly had low annual Chla concentrations. The decoupling of these two variables in the water column was mainly driven by photoacclimation of algae. At the same time, the contribution of NAPs to the b_bp(700) had little variation in the vertical profile (about 40% on average) (Fig. 4). In this region, our measurements showed that the spectral slope of the b_bp(λ) of particles in the upper layer of the region with the Chla maximum had a logarithmic relationship with Chla. This confirmed that the size of particulate matter had great effect on b_bp(λ).

4.3 Effect of particle size on b_bp(λ) and Chla in vertical water

It can be inferred that the amount of particulate matter smaller than 3.2 µm was the main contributor in the upper water layer based on variations of particulate concentrations with depth (Fig. 8(e)). The LISST results showed that particles in the range of 2.7 to 20 µm and 20 to 100 µm made almost equivalent contributions to the volumetric particle concentration at depths of 20 to 120 m, where the maximum Chla level was at depths greater than 100 m (Fig. 8). The peak of the volumetric particle concentration occurred near a depth of 60 m, the main location of the mixed layer, and particles in the range of 2.7 to 20 µm had a low volumetric concentration in this region. This concentration remained constant in the upper layer of the region with the maximum Chla level, and decreased rapidly in the lower layer of the region with the maximum Chla level. These vertical variations in the volume concentration of particulate matter are consistent with variations of b_bp(λ) and photoacclimation processes (Fig. 8). Our results above confirmed the influence of particle size and volume concentration on b_bp(λ) in the water column. However, it is important to note that the two smallest bins in the LISST are typically affected by sub-micron particles as well as larger particles in varying ratios over different regions, so there is still a great deal of uncertainty in the results inferred from instrumental data. In addition, due to the driving effect of phytoplankton community structure on Chla fluorescence signals, its effects on bio-optical properties, reflectance, and the satellite-derived Chla products have recently been received extensive attention [55]. It may also be an important factor in the non-covariant relationship between Chla and b_bp(λ).

4.4 Use of the homogeneous and coated models to estimate b_bp(λ)

In summary, for oligotrophic regions where Chla and b_bp(λ) are not correlated, it is necessary to determine the reasons for this lack of correlation. First, according to the monthly average annual variation of Chla, the vertical variation of Chla can be divided into a period of maximum of Chla, generally in deep areas (>100 m) and in shallow areas (< 100 m). Then, according to the upper and lower parts of the region with the maximum Chla level, the relationship between Chla and the spectral slope of b_bp(λ) and the relationship between Chla concentration and b_bp(λ) were constructed, respectively. During the process of estimating the b_bp(λ) in different regions of the water column, the simulation should consider the volume concentration of particles smaller than 20 µm.

A comparison of the b_bp(λ) estimated by homogeneous (Mie scattering) and coated (Aden-Kerker) sphere with the measured b_bp(λ) in the corresponding region indicated that when the Chla maximum was deeper (generally greater than 100 m) the b_bp(λ) of particulate matter can be obtained according to the particle matter simulation in the range of 2.7 to 20 µm, which had a good correlation with measured data, the correlation coefficient (r) decreases with the increase of wavelength (Fig. 9). However, for shallow DCM waters, mainly in areas where the Chla concentration is greater than 0.1 mg m^-3, a simulated b_bp(λ) that is only based on particles in the range of 2.7 to 20 µm was quite different from the measured results. Increasing the simulated particle range still failed to achieve satisfactory results. This may show that smaller particles had a relatively large contribution to backscattering, and that the simulation needs to increase the volume concentration of particles that are smaller than 2.7 µm.

 

Fig. 9. Relationship of the simulated b_bp(λ) at different wavelengths (442, 488, 550, 620, 700, and 852 nm) and in-situ measurements, where bias, rmse, and r is expressed as a range of values for all wavelengths.

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Furthermore, in regions with low Chla levels, such as QB12, 14, 16, and E142-10, the maximal Chla occurs at deep depths (greater than 100 m), the vertical profile of b_bp(700) were estimated in basis of the coated-spheres and homogeneous spheres model, respectively. We used the estimated of the coated-spheres model to compare with the measured values from the BGC-Argo dataset (2902762 station) from 31 March 2021 to 30 May 2021, the time period of measurement at this site. The estimated and measured b_bp(700) results agreed at the lower layer of the DCM (from 130 m to 200 m, r = 0.63), but the estimated results were larger than the measured results at the upper layer of the DCM (from 20 m to100 m water depth, r = 0.07) (Fig. 10(a)). When homogeneous-spheres model was used, the correlation between simulated and measured results was higher from the surface layer to the DCM layer (from 20 m to100 m water depth, r = 0.55), but the estimated results were smaller than the measured results at the lower layer of the DCM (from 20 m to 200 m, r = 0.13) (Fig. 10(b)). The effect of the structural complexity of particles on backscattering in open-ocean has been proposed [54,55]. In our study, the results simulated by the homogeneous-sphere model are closer to the measured values in the upper water body, which corresponds to the greater contribution of NAPs in this layer. Correspondingly, the simulation results of coated spheres are closer to the measured values in the lower water body, and are related to the distribution of maximum chlorophyll in this area. This result can also confirm that the complex change of particle structure caused by the change of distribution of phytoplankton and NAPs in the vertical water column in this region affects the vertical coupling relationship between chlorophyll and backscattering. In addition, this characteristic is possibly due to the vertical variation of the volume concentration of suspended particulate matter that is 2.7 to 20 µm in size. The PSD is characterized by a slow decrease from the surface to a depth of 100 m, and then a small peak in the region with the maximal level of Chla, and then a rapid decrease with increasing water depth. Moreover, another important reason for this relationship is that the spatial positions of the measured stations and the BGC-Argo are inconsistent. Thus, when measured stations are more distant from the BGC-Argo station, this difference is more obvious in the lower waters where the Chla has a maximum.

 

Fig. 10. Effect of depth on b_bp(700) in data measured at BGC-Argo station 2902762 from 31 March to 30 May in 2021 (Solid circles) and the simulated b_bp(700) at nearby stations (QB-12, QB-16, and E14210) during the same period by the coated-spheres (a, purple open circles) and homogeneous spheres model (b, black open circles).

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5. Conclusion

The aim of this study was to examine the relationship between b_bp(λ) and Chla in the subtropical gyres at low-latitude regions in the tropical Western Pacific Ocean, a region in which previous studies reported null or negative correlations of these variables. Our results demonstrated that there was no significant correlation relationship between b_bp(λ) and Chla in regions of the water column that were above the region with the maximum level of Chla. In regions of the water column below the maximum value of Chla, there was a linear correlation between these two variables. This relationship was also reflected in our finding that the b_bp(λ) of particles in the upper water was significantly affected particle size, but b_bp(λ) in the lower water was significantly affected by Chla concentration. The BGC-Argo dataset for this region showed that the linear relationship between these two variables mostly occurred during winter, and that this relationship was nonlinear during other seasons in the lower layer of the DCM, in that b_bp(700) increased more rapidly with an increase of Chla. The correlation between these two variabilities gradually increased from the warm pool area to the north and south on both sides, and was affected by the spatial distribution of Chla.

There is evidence that the size of particulate matter affects the b_bp(λ) of the vertical profile, that NAPs account for an average of about 40% of this variation, and that there is a good linear correlation between the b_bp(λ) and Chla. Our observations also confirmed that the amount of particulate matter smaller than 3.2 µm was the main contributor to b_bp(λ) in the upper water layer. However, in deeper regions, the number of particles smaller than 3.2 µm gradually decreased, and the number of particles that were 3.2 µm to 10 µm gradually increased in the upper part of the region with the maximum Chla. At the bottom of the layer with the maximum Chla, particles smaller than 3.2 µm no longer made significant contributions to b_bp(λ). Particles between 3.2 µm and 10 µm had the greatest effects in these regions. Based on the volume concentration of particles less than 20 µm, the coated-spheres and homogeneous-spheres were used to estimate b_bp(λ) in water column of DCM >100 m. These estimated values of the lower and upper layers of DCM deviated from the measured data and the BGC-Argo dataset, respectively, which further demonstrated the influence of particle size and complex structure caused by the variation characteristics of the vertical distribution of phytoplankton and NAPs in the water column on the coupling relationship between backscattering and Chla.