Seasonal Variability in the Relationship between the Volume-Scattering Function at 180° and the Backscattering Coefficient Observed from Spaceborne Lidar and Biogeochemical Argo (BGC-Argo) Floats

Abstract

The derivation of the particulate-backscattering coefficient (b_bp) from Lidar signals is highly influenced by the parameter χ_p(π), which is defined by χ_p(π) = b_bp/(2πβ_p(π)). This parameter facilitates the correlation of the particulate-volume-scattering function at 180°, denoted β_p(π), with b_bp. However, studies exploring the global and seasonal fluctuations of χ_p(π) remain sparse, largely due to measurement difficulties of β_p(π) in the field conditions. This study pioneers the global data collection for χ_p(π), integrating b_bp observations from Biogeochemical Argo (BGC-Argo) floats and β_p(π) data from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) spaceborne lidar. Our findings indicate that χ_p(π) experiences significant seasonal differences globally, peaking during summer and nadiring in winter. The global average χ_p(π) was calculated as 0.40, 0.48, 0.43, and 0.35 during spring, summer, autumn, and winter, respectively. The daytime values of χ_p(π) slightly exceeded those registered at night. To illuminate the seasonal variations in χ_p(π) in 26 sea regions worldwide, we deployed passive ocean color data MODIS b_bp and active remote sensing data CALIOP β_p(π), distinguishing three primary seasonal change patterns—the “summer peak”, the “decline”, and the “autumn pole”—with the “summer peak” typology being the most common. Post recalibration of the CALIOP b_bp product considering seasonal χ_p(π) variations, we observed substantial statistical improvements. Specifically, the coefficient of determination (R²) markedly improved from 0.84 to 0.89, while the root mean square error (RMSE) declined from 4.0 × 10⁻⁴ m⁻¹ to 3.0 × 10⁻⁴ m⁻¹. Concurrently, the mean absolute percentage error (MAPE) also dropped significantly, from 31.48% to 25.27%.

1. Introduction

When incident light interacts with a particle, it experiences omnidirectional scattering. The precise characterization of light intensity scattered across diverse scattering angles is encapsulated within the volume-scattering function (VSF), denoted as β(θ) with units of m⁻¹ sr⁻¹ [1,2,3]. The VSF’s relative magnitude, spectral attributes, and angular distribution fundamentally hinge upon the particle’s parameters, including concentration, size, composition, and morphology. Scattering sensors exploit these VSF properties by monitoring precise spectral and angular domains, thereby inferring information about particles [4,5,6,7]. Typically, for the backward portion of VSF with scattering angles (θ) ranging from 90° to 180°, quantification is performed using two variables: the total backscattering coefficient (b_b; m⁻¹) and the χ_p(θ) factor: ${\chi }_{\mathrm{p}}(\mathsf{\theta })={\displaystyle \frac{b_{\mathrm{bp}}}{2\mathsf{\pi }{\beta }_{\mathrm{p}}(\mathsf{\theta })}}$. Particulate backscattering coefficients (b_bp(θ)), a core parameter in ocean optics that are applied in marine ecology and biogeochemistry studies [8,9,10], can be determined through estimation from the measurement of β_p(θ) using an χ_p(θ) factor [11].

Particulate backscattering coefficients (b_bp) are typically determined through in situ methodologies or passive satellite remote sensing of ocean color. The former approach mandates the installation of measurement instruments on vessels or buoys, necessitating substantial expenditures of human labor, resources, and financial resources for on-site data acquisition. Furthermore, it is unsuitable for expeditious large-scale evaluations, thereby imposing constraints on comprehensive global marine investigations [12,13]. Passive satellite remote sensing of ocean color has offered a continuous record of global surface water properties for over two decades. Nevertheless, this approach, reliant on natural light, inherently harbors certain limitations. It is unsuitable for nighttime observations, periods characterized by dense cloud cover, and high-latitude polar regions [14]. In contrast, spaceborne lidar technology possesses the potential to overcome these constraints. By utilizing emitted pulsed laser systems for aquatic data acquisition, it operates independently of solar illumination, thus enabling the study of variations between day and night in the characteristics of planktonic organisms and facilitating continuous observations during polar night periods [15,16].

Lidar echoes encompass two fundamental properties of seawater: the volume-scattering function at a scattering angle of 180° (β(π); m⁻¹ sr⁻¹) and the lidar attenuation coefficient (α) [17,18]. The particulate backscattering coefficient (b_bp) can be obtained through inversion by converting the measured β(π) from spaceborne lidar, but there is some uncertainty in the conversion factor χ_p(π) within the inversion model. Previous investigations scrutinizing the precision of Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) b_bp products have disclosed that modifications to the conversion factor exert a substantial influence on the data quality. For instance, Bisson et al. achieved distinct evaluation outcomes, compared to Lacour, by dividing the conversion factor by 2 [19,20,21,22]. Furthermore, it should be noted that the magnitude of χ_p(π) is profoundly governed by the morphology and internal constitution of particles. Adopting a uniform value of χ_p(π) for the interpretation of lidar signals obtained from varied aquatic environments may engender considerable inaccuracies [23]. Hair et al. conducted measurements of β_p(π) in open waters proximate to the Gulf of Maine, Bermuda, and the coastal regions spanning from Virginia to Rhode Island, employing High Spectral Resolution Lidar (HSRL). Concurrently, they ascertained b_bp in these aqueous domains utilizing the ECO-BB3 sensor, with the resultant mean value of χ_p(π) approximating 0.5 [24]. In other studies [2,25], χ_p(π) values were reported as 1.43, while in some studies [26,27,28], χ_p(π) values were reported as 1.06. Zhang et al. identified notable variations in χ_p data procured in proximity to Ocean Station Papa (50°N 145°W) in contrast to data gathered from multiple global oceanic regions [29]. Consequently, the exploration of seasonal disparities in χ_p(π) and the establishment of optimal reference values for the conversion factor during distinct seasons assume paramount importance in the pursuit of enhanced accuracy in the inversion of CALIOP b_bp products.

Nevertheless, due to the contamination of stray light from reflections, measurements of VSF at angles greater than 173° are not reliable, as they can lead to spurious increases in the scattering of the reflection angle [30,31,32]. Field measurements of the particle volume-scattering function (VSF) at 180° pose certain difficulties, resulting in a limited understanding of the natural variations in χ_p(π) [2,33]. Thus, we employ in situ b_bp measurements collected by Biogeochemical Argo (BGC-Argo) floats to rectify CALIOP’s inverted b_bp products, obtaining calibrated values for the corresponding conversion coefficient χ_p(π). Additionally, we utilize passive ocean-color-remote-sensing data product MODIS b_bp to address the spatial limitations in the global coverage of BGC-Argo, resulting in the acquisition of calibrated values for the conversion coefficient χ_p(π) across diverse oceanic regions.

In this study, based on BGC-Argo and MODIS b_bp data, we investigated the seasonal variability of the conversion coefficient χ_p(π) between the globally observed volume-scattering function at 180° from spaceborne lidar and the particulate-backscattering coefficient. Initially, we established 12 spatiotemporal windows for matching. Utilizing BGC-Argo b_bp as in situ data, we calibrated CALIOP b_bp, obtaining reference values of χ_p(π) at different spatiotemporal scales. We conducted a comprehensive examination and comparison of the seasonal changes in χ_p(π) (refer to Section 3.1), as well as fluctuations between day and night (consult Section 3.2). Subsequently, using the average calibrated χ_p(π) values from all spatiotemporal windows, we corrected the CALIOP b_bp data. An assessment and comparative analysis of the b_bp products’ efficacy both pre-correction and post-correction is presented in Section 3.3. Furthermore, a discussion on the influence of band conversion coefficients on χ_p(π) can be found in Section 4.1. In addition, the effect of atmospheric turbulence can be found in Section 4.2. Finally, to tackle the limited availability of BGC-Argo float measurements in specific marine regions, exploration and analysis of the seasonal oscillations in χ_p(π) within distinct oceanic domains were performed. This was facilitated through the utilization of the passive ocean-color-remote-sensing product, enabling an investigation into the seasonal trends of χ_p(π) across diverse global regions, as detailed in Section 4.3.

2. Materials and Methods

2.1. BGC-Argo b_bp(700)

The sensors used to measure backscattering at 700 nm on the BGC-Argo float include the ECO Triplet water-color measurement instrument, the Eco-FLBB fluorescence and backscattering meter from WET Labs, and the MCOMS from Seabird, with angles of 124°, 142°, and 149°, respectively [34,35]. After subtracting the contribution of pure seawater, the particulate-backscattering coefficient at 700 nm, b_bp(700), is derived [11,36,37]. The data vertical resolution is 1 m between 10 and 250 m, and 0.20 m between 10 m and the sea surface [38].

In this investigation, we employed BGC-Argo float data made available by IFREMER (ftp://ftp.ifremer.fr/ifremer/argo/ (accessed on 9 June 2022)) (

Table 1. Summary of Datasets Including Parameters, Origin, Period, Web Source, and Resolution.

Parameters	Data Origin	Period	Web Source	Resolution
bbp(700), Depth	BGC-Argo	2010–2017	ftp://ftp.ifremer.fr/ifremer/argo/ (accessed on 9 June 2022)	Variable
bbp(532), time	CALIOP	2010–2017	http://orca.science.oregonstate.edu/lidar_nature_2019.php (accessed on 9 June 2022)	16-day visit time 70 m footprint size
bbp(443), Kd(490)	MODIS-Aqua	2010–2017	https://search.earthdata.nasa.gov/ (accessed on 9 June 2022)	monthly averaged 9 km

). The dataset encompasses 43,073 vertical profiles of b_bp(700 nm; m⁻¹), spanning from January 2010 to April 2017, and boasts comprehensive global coverage, even extending into polar regions. This dataset serves as a valuable resource for the calibration and validation of worldwide satellite-based lidar ocean-profile-remote-sensing products.

To ensure the precision and validity of the collected data, we diligently adhered to the technical guidelines provided by WETLabs (2016) and implemented the real-time quality control methodology introduced by Giorgio Dall’Olmo and colleagues [39]. The vertical profiles of b_bp(700) underwent quality control tests for missing data, high outliers, negative values, noise profiles, and mooring spikes, while negative peaks were also eliminated [40] (Figure 1).

After quality control, we identified a total of 1012 float points that did not pass the tests, representing 2.35% of all floats, as shown in Figure 1b. These points are primarily distributed in coastal waters and the Southern Ocean, as depicted in Figure 1a. Upon further inspection, we determined that 237 of these points were bad data which failed the missing data test, negative values test, and mooring spikes (marked with a quality control factor of 4) accounting for 0.55% of all floats, mainly found in the coastal waters of the Indian Ocean and the Southern Ocean. Additionally, we identified 757 potentially invalid data profiles (marked with a quality control factor of 2), constituting 1.76% of all floats, primarily distributed in the Indian Ocean, the Southern Ocean, and the coastal waters of Australia. The quality control tests also revealed 18 missing data float points (marked with a quality control factor of 3), accounting for 0.04% of all floats, mainly located in the Arabian Sea and the Bay of Bengal.

After removing these non-compliant float points, we applied a three-point moving median method to eliminate outliers (values beyond 1.5 times the interquartile range) from the high-quality float b_bp(700) profiles. Ultimately, we used 42,061 profiles marked as high-quality vertical observation profiles for the calculation of the conversion factor χ_p(π) and the calibration of CALIOP product performance.

2.2. MODIS b_bp(700)

The retrieval of the ocean water backscattering coefficient (b_bp(λ)) is a complex problem that requires the use of spectral remote sensing reflectance (R_rs(λ); sr⁻¹) as input and is subject to a series of assumptions and constraints regarding the absorption and backscattering components in the ocean. Bisson et al. (2019) demonstrated in their study that the performance of the MODIS satellite in global ocean-color-remote-sensing is superior to other contemporary satellites such as the Visible Infrared Imaging Radiometer Suite (VIIRS) and the Ocean and Land Color Instrument (OLCI) [20]. Based on this, we selected b_bp(443) derived from MODIS Aqua as the water-color-remote-sensing data. We conducted a spatial–temporal match with BGC-Argo float b_bp within a 9 km spatial window and a 12 h temporal window to study regional differences in the conversion factor χ_p(π). The MODIS data product b_bp(443) used in this study was obtained from the Ocean Color website (https://search.earthdata.nasa.gov/ (accessed on 9 June 2022)) (Table 1). Its temporal resolution is a day, spatial resolution is 9 km, and it has been radiometrically calibrated and atmospherically corrected.

To compare with the validation and evaluation of CALIOP b_bp(532), we first performed a band conversion on MODIS b_bp(443). The conversion to b_bp(532) was conducted using the following band conversion formula:

$$b_{\mathrm{bp}}(532)=b_{\mathrm{bp}}(443){({\displaystyle \frac{443}{532}})}^{\mathsf{\gamma }}$$

(1)

The power–law slope (γ) used in the conversion is 0.78 [41]. Then, the 3σ principle was used to remove outliers from the MODIS b_bp data, following the formula:

$$\left|x_i-\overline{x}\right|>3\sqrt{{\displaystyle \frac{{(x_1-\overline{x})}^2+{(x_2-\overline{x})}^2+\mathrm{\dots }+{(x_n-\overline{x})}^2}{n-1}}}$$

(2)

where x_i represents the observed b_bp values from MODIS.

The specific elimination process involves the following: firstly, calculating the standard deviation; secondly, computing the absolute difference between each sample point and the mean, comparing it with three times the standard deviation, and if it exceeds three times the standard deviation, it is removed; thirdly, repeating steps 1 until no further removals occur in this iteration. After removing outliers using the 3σ rule, it was found that the overall MODIS b_bp is 1.56 times larger than BGC-Argo b_bp. Therefore, based on this factor, an offset correction is applied, ensuring the accuracy of MODIS b_bp and enabling the study of the global conversion factor χ_p(π).

2.3. CALIOP β(π)

The Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite, launched in 2006, is equipped with the CALIOP lidar system, capable of emitting laser pulses at both 1064 nm and 532 nm wavelengths. Notably, the 532 nm channel incorporates dual-polarization features, comprising cross-polarized and co-polarized channels [15]. The parallel channel signals in CALIOP are influenced by molecular scattering, while the cross-polarized channel is mainly caused by the backscattering of particles. The off-nadir tilt enhances the polarization ratio of particles, and it was compared with the diffuse attenuation coefficient (K_d, 532 nm) obtained from airborne lidar, with an average K_d of 1.76 [10,42]. Using these empirical linear relationships between the polarization ratio and K_d, the particle polarization ratio and K_d cancel each other out in the equation.

Due to the negligible contribution of sea surface reflection, the vertically polarized component of the water column integrated attenuated backscatter, β′_w+, is calculated using the following:

$${\beta }_{\mathrm{w}+}^{\prime }={\delta }_{\mathrm{T}}\left({\beta }_{\mathrm{w}/}^{\prime }+{\beta }_{\mathrm{s}}\right)$$

(3)

where δ_T represents the ratio of the signals in the vertical and parallel channels; β′_w/ represents the parallel polarized component of the water column integrated attenuated backscatter; β_s is the sea surface backscatter, which mainly affects the signal in the parallel channel and includes the parallel polarization characteristics of the laser pulse. δ_W is the water column integrated depolarization ratio, which is calculated by the following formula:

$${\delta }_{\mathrm{w}}={\displaystyle \frac{{\beta }_{\mathrm{w}+}^{\prime }}{{\beta }_{\mathrm{w}/}^{\prime }}}$$

(4)

Substituting Formula (4) into Formula (3), we obtain the following:

$${\beta }_{\mathrm{w}+}^{\prime }={\delta }_{\mathrm{T}}{\displaystyle \frac{{\beta }_{\mathrm{s}}}{1-{\delta }_{\mathrm{T}}/{\delta }_{\mathrm{w}}}}$$

(5)

After organizing this formula, we obtain the following:

$${\beta }_{\mathrm{w}+}^{\prime }={\delta }_{\mathrm{T}}{\displaystyle \frac{{\beta }_{\mathrm{s}}}{1-{\delta }_{\mathrm{T}}/{\delta }_{\mathrm{w}}}}$$

(6)

Behrenfeld, based on previous experimental results [43,44], assumed δ_W to be 0.1. Therefore, the above formula simplifies to the following:

$${\beta }_{\mathrm{w}+}^{\prime }\approx {\delta }_{\mathrm{T}}{\displaystyle \frac{{\beta }_{\mathrm{s}}}{1-10{\delta }_{\mathrm{T}}}}$$

(7)

The calculation formula for sea surface backscatter β_s is as follows [45]:

$${\beta }_{\mathrm{s}}\approx {\displaystyle \frac{\mathsf{\rho }}{4\mathsf{\pi }<{\mathrm{s}}^2>{\cos }^4\mathsf{\theta }}}\exp \left[-{\displaystyle \frac{{\tan }^2\mathsf{\theta }}{2<{\mathrm{s}}^2>}}\right]$$

(8)

where θ is the incident angle of the CALIOP lidar, initially 0.3°, changed to 3° after 28 November 2007; ρ represents the Fresnel reflectance, approximately 0.0209 at the 532 nm channel; the mean square slope of the sea surface, <s²>, needs to be calculated using wind speed.

Since the signal in the vertical channel is mainly caused by the backscatter of particles, β′_w+ can be considered as the vertically polarized component of the particle integrated attenuated backscatter, β′_p+. The depolarization ratio of the particles, δ_p, is defined as follows:

$${\delta }_{\mathrm{p}}={\displaystyle \frac{{\beta }_{\mathrm{p}+}^{\prime }}{{\beta }_{\mathrm{p}/}^{\prime }}}$$

(9)

Thus, the particle integrated attenuated backscatter β′_p can be expressed as follows:

$${\beta }_{\mathrm{p}}^{\prime }={\beta }_{\mathrm{p}/}^{\prime }+{\beta }_{\mathrm{p}+}^{\prime }={\displaystyle \frac{1+{\delta }_{\mathrm{p}}}{{\delta }_{\mathrm{p}}}}{\beta }_{\mathrm{w}+}^{\prime }$$

(10)

where β′_p/ represents the parallel polarized component of the particle integrated attenuated backscatter.

For waters with K_d < 0.15 m⁻¹, δ_p is 0.3; if K_d > 0.15 m⁻¹, δ_p can be calculated according to the following formula [46]:

$${\delta }_{\mathrm{p}}=0.1+2\left(K_{\mathrm{d}}-0.05\right)$$

(11)

Off-orbit tilting enhances the depolarization ratio of the particles, which was compared with the downlink diffuse attenuation coefficient K_d(532) obtained from airborne lidar, with an average K_d of 1.76 [10].

The relationship between the particle integrated attenuated backscatter β′_p and the 180° particle backscatter coefficient β(π) is as follows:

$${\beta }_{\mathrm{p}}^{\prime }=t^2{\displaystyle {\int }_0^{\infty }{\beta }_{\mathrm{p}}}(\mathsf{\pi })\exp \left(-2K_{\mathrm{d}}z\right)\mathrm{d}z=t^2{\beta }_{\mathrm{p}}(\mathsf{\pi })/\left(2K_{\mathrm{d}}\right)$$

(12)

where t represents the transmittance of the ocean surface, approximately 0.98 at 532 nm. Therefore, the above formula can be organized as follows:

Using the above empirical relationship, this formula can be transformed into the following:

$${\beta }_{\mathrm{p}}(\mathsf{\pi })=2K_{\mathrm{d}}{{\beta }^{\prime }}_{\mathrm{p}}/t^2$$

(13)

Therefore, the cross-polarized measurement from CALIOP is directly proportional to the backscattering of particles [16]:

$$b_{\mathrm{bp}}(532)={\displaystyle \frac{4\mathsf{\pi }\chi (\mathsf{\theta })K_{\mathrm{d}}\beta (\mathsf{\pi })}{{0.98}^2}}{\displaystyle \frac{1+{\delta }_{\mathrm{p}}}{{\delta }_{\mathrm{p}}}}\approx {\displaystyle \frac{2K_{\mathrm{d}}\beta (\mathsf{\pi })}{0.16\ast {0.98}^2}}{\displaystyle \frac{1+{\delta }_{\mathrm{p}}}{{\delta }_{\mathrm{p}}}}\approx {\displaystyle \frac{2K_{\mathrm{d}}\beta (\mathsf{\pi })}{0.16\ast {0.98}^2}}{\displaystyle \frac{1}{2K_{\mathrm{d}}}}\approx {\displaystyle \frac{\beta (\mathsf{\pi })}{0.16\ast {0.98}^2}}$$

(14)

In our study, we only used CALIOP b_bp data when the cloud layer is less than 1 optical depth (defined by the detection limit of residual underwater ocean signal). Additionally, microwave scanning radiometer data (from AMSR-E/AMSR-2 at a quarter-degree resolution) was utilized to exclude CALIOP detection under high wind speeds (≥9 m/s⁻¹) to avoid the influence of bubbles on b_bp. Furthermore, pixels showing unusually high polarization ratios in the displayed regions were removed in cases of lower wind speeds, as they were suspected to be contaminated by bubbles or sea ice. The CALIOP b_bp product used in this paper was collected from http://orca.science.oregonstate.edu/lidar_nature_2019.php (accessed on 9 June 2022) (Table 1). Subsequently, we computed β(π) from b_bp(532) according to Equation (3).

2.4. Spatial and Temporal Matching Strategy

In the BGC-Argo data processing steps, to match the estimated b_bp values at 532 nm from CALIOP, we converted the measured b_bp(700) from BGC-Argo to 532 nm using the following criteria:

$$b_{\mathrm{bp}}(532)=b_{\mathrm{bp}}(700){\left({\displaystyle \frac{700}{532}}\right)}^{\mathsf{\gamma }}$$

(15)

Here, the power–law slope (γ) was set to 0.78 [41]. Finally, to compare with the estimated values from CALIOP and MODIS, we performed depth averaging of b_bp(532) using the following vertical weighting function [47]:

$$b_{\mathrm{bp}}^{FLOAT}={\displaystyle \frac{{\displaystyle \sum \exp }\left(-2K_{\mathrm{d}}(532)z\right)b_{\mathrm{bp}}(532,z)}{{\displaystyle \sum \exp }\left(-2K_{\mathrm{d}}(532)z\right)}}$$

(16)

where K_d(532) is the diffuse attenuation coefficient of downward irradiance at 532 nm (m⁻¹).

A fourth-degree polynomial function was fitted to the logarithm of downward irradiance E_d(490) measured by the float (OCR-504, Satlantic, Halifax, NS, Canada) to calculate K_d(490) and obtain the average slope for the first 50 m. Subsequently, following the formula of Lu et al. (2016), K_d(490) was converted to K_d(532) [14]:

$$K_{\mathrm{d}}(532)=0.68\left(K_{\mathrm{d}}(490)-0.022\right)+0.054$$

(17)

After data acquisition, we executed a rigorous process of spatial and temporal alignment between the field measurements and satellite data. In terms of spatial alignment, we adopted three distinct spatial windows: 9 km, 50 km, and 1° × 1°. To ensure temporal alignment, we employed four discrete time windows: ±3 h, ±6 h, ±12 h, and ±24 h. This approach yielded a total of twelve unique spatiotemporal windows, which facilitated the alignment of the BGC-Argo float data with CALIOP products. It is worth noting that, considering the inherent spatial resolution of MODIS b_bp products at 9 km, we designed a dedicated spatiotemporal matching window for MODIS and CALIOP, encompassing a 9 km radius with a temporal span of ±12 h. The spatial distribution of matched data points, as well as the corresponding count for each spatiotemporal window, is graphically represented in Figure 2. After completing the spatiotemporal matching, we compared the fitting results of CALIOP b_bp(532) with BGC-Argo b_bp(532) estimates and MODIS b_bp(532) estimates. The results show that CALIOP b_bp(532) has a higher R² when compared with BGC-Argo b_bp(532) estimates and a smaller RMSE when compared with MODIS b_bp(532) estimates. The scatter plots illustrating these comparisons are shown in Figure 3.

2.5. Calculation of Key Conversion Factors χ_p(π)

In aquatic environments, the volume-scattering function (VSF, β; m⁻¹ sr⁻¹) of seawater is typically divided into contributions from pure seawater (β_w) and suspended particles (β_p). The scattering of pure seawater can be predicted as a function of temperature, salinity, and pressure, with an uncertainty of <2%, and this holds for virtually any natural water body in the global oceans [32,36,48]; therefore, it is considered well-known. The scattering of particles undergoes complex variations with changes in particle concentration, size distribution, composition, shape, and internal structure [49,50]. The backscattering portion of VSF, the scattering angle (θ) ranging from 90° to 180°, is usually quantified using two variables: the total backscattering coefficient (b_b; m⁻¹) and the χ(sr) factor. The relationship for converting β_p(π), measured from lidar, into the particulate-backscattering coefficient (b_bp) is as follows [11]:

$$b_{\mathrm{bp}}=2\mathsf{\pi }{\displaystyle {\int }_{\mathsf{\pi }/2}^{\mathsf{\pi }}{\beta }_{\mathrm{p}}}(\mathsf{\theta })\sin \mathsf{\theta }d\mathsf{\theta }$$

(18)

The transformation of this Equation yields the following expression:

$${\chi }_{\mathrm{p}}(\mathsf{\theta })={\displaystyle \frac{b_{\mathrm{bp}}}{2\mathsf{\pi }{\beta }_{\mathrm{p}}(\mathsf{\theta })}}$$

(19)

The current CALIOP data-processing assumes a fixed value of α (anisotropy factor) and assumes the ratio of the 180° backscatter to the average volume-scattering function value between 90 and 180° as 1 [16], overlooking the variability in the VSF-to-b_bp conversion for different angles. To address this discrepancy, we propose investigating the conversion factor of χ_p(π) at various spatial and temporal scales, providing a means to account for the associated error. Therefore, we first calculate the corresponding β_p (π) for b_bp based on the CALIOP’s b_bp inversion formula (Equation (3)). Subsequently, we use the in situ b_bp measurements from the BGC-Argo floats to correct CALIOP’s inverted b_bp product, thus obtaining calibrated values for the corresponding conversion coefficient χ_p(π). Additionally, we employ passive ocean-color-remote-sensing data from MODIS b_bp products to compensate for spatial gaps in the global distribution of BGC-Argo floats, resulting in calibrated values for the conversion coefficient χ_p(π) in different ocean regions. The calculation process for calibrating χ_p(π) is identical to the process for calibrating χ_p(π) with BGC-Argo data. The detailed process is illustrated in Figure 4.

3. Results

3.1. Seasonal Variations in χ_p(π)

We carried out the calibration of CALIOP b_bp using the BGC-Argo float data, resulting in the determination of conversion coefficients, χ_p(π), across twelve distinct spatiotemporal windows. The calibration outcomes for χ_p(π) under a 9 km spatial window matching are presented in Figure 5a, while those under a 50 km spatial window matching are depicted in Figure 5b. Additionally, the results for a 1° × 1° spatial window matching are showcased in Figure 5c. These results are organized into four distinct time windows: ±3 h (±3 h), ±6h (±6 h), ±12 h (±12 h), and ±24 h (±24 h). The seasons are represented along the rows, with spring, summer, autumn, and winter corresponding to the four respective rows. A comparative analysis of these results reveals significant seasonal variations in the conversion coefficient χ_p(π). Notably, during the summer (0.46–0.48), χ_p(π) values exhibit a relatively high range, followed by autumn (0.41–0.44) and spring (0.38–0.42), which fall within an intermediate range. In contrast, the χ_p(π) values during winter (0.33–0.36) are relatively low.

Across various spatiotemporal matching scales, we observed consistent seasonal variations in χ_p(π) values, with differences in χ_p(π) among the 12 matching windows all within 0.04 (Figure 6). By calculating the mean values, we obtained the climatological average of conversion factors calibrated using the BGC-Argo float data. The results indicated that the highest conversion factor was observed during summer (χ_p^summer(π) = 0.48), while the lowest was recorded during winter (χ_p^winter(π) = 0.35). Spring (χ_p^spring(π) = 0.40) and autumn (χ_p^autumn(π) = 0.43) fall in between these two extremes.

The seasonal variations in χ_p(π) may be attributed to seasonal differences in the morphology of phytoplankton. Silvia Pulina et al. found that phytoplankton cells exhibit distinct morphological characteristics during different seasons. In winter (within the deepest mixing layer), they have higher average volume and lower average surface area ratios. In spring (under the lowest nutrient concentrations), they display various geometric shapes, with simple and compact shapes (spheres and cubes) having lower average volume and higher average surface area ratios. In summer (under thermally stratified conditions), they adopt simple and elongated shapes (cylinders), and in autumn (under moderate environmental conditions), they exhibit a variety of geometric shapes [51]. The seasonal morphological variations in phytoplankton result in seasonal changes in the light-scattering properties at the ocean’s surface, leading to corresponding seasonal variations in the χ_p(π) conversion coefficient.

3.2. Variations of χ_p(π) between Day and Night

We calibrated the daytime and nighttime b_bp products from CALIOP using the BGC-Argo float data. We obtained χ_p(π) results for 1° × 1° spatial windows within two different time windows: 12 h and 24 h. According to observations, across all seasons, daytime χ_p(π) values are slightly higher than nighttime χ_p(π) values (Figure 7). The diurnal difference in χ_p(π) values may be associated with the diurnal fluctuations in upper-ocean phytoplankton abundance. Previous studies have shown that the presence of phytoplankton particles typically reduces χ_p(π) [23], and phytoplankton biomass (Chl-a) is highest during the low-light periods of the day, exhibiting noticeable diurnal differences [52]. Therefore, this diurnal variation in χ_p(π) values may be attributed to diurnal migrations of phytoplankton.

Within each time window, noticeable seasonal differences in χ_p(π) are observed during both daytime and nighttime, with summer consistently exhibiting the highest χ_p(π) values and winter the lowest, aligning with the seasonal patterns of χ_p(π) discussed in Section 3.1. This fact indicates that these seasonal variation patterns are robust and not solely driven by diurnal effects.

Extending the time window to ±24 h tends to reduce the day–night contrast, particularly evident in winter. This suggests that a longer time window may mitigate some of the diurnal variations in χ_p(π) values, possibly due to more integrated measurements over the course of a day.

3.3. Comparison before and after Seasonal χ_p(π) Calibration

We utilized the average χ_p(π) conversion factor across the 12 distinct spatiotemporal matching windows to rectify the CALIOP b_bp product. Subsequently, we evaluated the product’s performance both before and after the correction. Prior research has underscored the significant impact of altering the β(π)/b_bp conversion coefficient on the quality of CALIOP data. For instance, Bission et al. demonstrated varying evaluation results by multiplying β(π)/b_bp by a factor of 0.32 [19,20]. Consequently, we employed two different algorithms for evaluation before calibration. One algorithm employed a fixed β(π)/b_bp value of 0.16 (χ_p(π) = 1.00), while the other used a β(π)/b_bp value of 0.32 (χ_p(π) = 0.50). To assess the performance of the corrected products, we established four evaluation windows, each characterized by a 9 km spatial radius and temporal intervals of ±3 h, ±6 h, ±12 h, and ±24 h. These evaluations allowed us to compare the product’s performance among the χ_p(π) = 1.00 algorithm, the χ_p(π) = 0.50 algorithm, and after correction by average seasonal χ_p(π) under different conditions.

The evaluation results show that, in all matching windows, using the χ_p(π) seasonal average calibration values improved the performance of the products, compared to the algorithms with fixed β(π)/b_bp of 0.16 and 0.32 (Figure 8). This indicates that using the χ_p(π) seasonal average calibration values for correction is effective. Taking the 9 km, ±3 h spatiotemporal matching window as an example, the corrected product exhibited higher R² (R²_{after calibration} = 0.89, R²_χp(π)=1.00 = 0.73, R²_χp(π)=0.50 = 0.84), smaller root mean square error (RMSE) (RMSE_{after calibration} = 3.0 × 10⁻⁴ m⁻¹, RMSE_χp(π)=1.00 = 7.0 × 10⁻⁴ m⁻¹, RMSE_χp(π)=0.50 = 4.0 × 10⁻⁴ m⁻¹), and smaller mean absolute percent error (MAPE) (MAPE_{after calibration} = 25.27%, MAPE_χp(π)=1.00 = 121.97%, MAPE_χp(π)=0.50 = 31.48%). These performance metrics are summarized in

Table 2. Performance comparison of CALIOP b_bp before and after calibration in 9 km spatial windows.

Space Window	Time Window	After Calibration
		N	R-Squared	RMSE/m−1	MAPE/%	SD
9 km	±3 h	43	0.89	3.0 × 10−4	25.27	7.0 × 10−4
	±6 h	50	0.84	3.0 × 10−4	26.36	7.0 × 10−4
	±12 h	87	0.70	5.0 × 10−4	30.72	8.0 × 10−4
	±24 h	147	0.60	5.0 × 10−4	29.89	9.0 × 10−4
Space Window	Time Window	Before Calibration (χp(π) = 1.00)
		N	R-Squared	RMSE/m−1	MAPE/%	SD
9 km	±3 h	43	0.73	7.0 × 10−4	121.97	7.0 × 10−4
	±6 h	50	0.64	8.0 × 10−4	125.74	8.0 × 10−4
	±12 h	86	0.52	9.0 × 10−4	120.59	9.0 × 10−4
	±24 h	147	0.47	9.0 × 10−4	118.50	1.0 × 10−3
Space Window	Time Window	Before Calibration (χp(π) = 0.50)
		N	R-Squared	RMSE/m−1	MAPE/%	SD
9 km	±3 h	44	0.84	4.0 × 10−4	31.48	7.0 × 10−4
	±6 h	51	0.78	4.0 × 10−4	32.78	7.0 × 10−4
	±12 h	88	0.67	5.0 × 10−4	36.41	8.0 × 10−4
	±24 h	149	0.58	5.0 × 10−4	34.13	9.0 × 10−4

.

4. Discussion

4.1. Effect of Band Conversion Factor

In this study, a calibration was performed on CALIOP VSF-retrieved b_bp(532) in global ocean regions using b_bp(700) measured by BGC-Argo and b_bp(443) measured by MODIS. The seasonal variations in χ_p(π) were re-examined. During the matching calibration process, because CALIOP estimates b_bp values at a wavelength of 532 nm, it was necessary to convert the b_bp(700) values from BGC-Argo to b_bp(532) and the b_bp(443) values from MODIS to b_bp(532). To do this, the spectral slope of the b_bp values, known as the particle size index (γ, [11]), was obtained through a nonlinear power–law fit to the particle beam attenuation spectrum (with γ as the negative exponent of the power–law). For particles smaller than approximately 20 µm, this parameter is negatively correlated with the mean particle size; smaller values of this parameter correspond to larger mean particle sizes [41].

Lacour et al. used a fixed value of 0.78 for the spectral slope when performing band conversion of BGC-Argo’s b_bp product to match CALISPO b_bp [19]. In contrast, Bisson et al. derived a variable value from the MODIS-Aqua data [20], and the calculation method for the variable slope is as follows:

$$\gamma =2.2\left(1-1.2e^{-0.9\left({\displaystyle \frac{R_{rs}\left(443\right)}{R_{rs}\left(555\right)}}\right)}\right)$$

(20)

where R_rs represents remote sensing reflectance. Vadakke-Chanat and Jamet compared the differences between estimates of b_bp(532) using a fixed slope and a variable slope and found that most values closely aligned with a 1:1 line [22]. However, they also identified a bias resulting in a 40% relative error. Therefore, the choice of spectral slope can also impact the calibration of b_bp from other bands to CALIOP b_bp, thereby influencing the calculation of χ_p(π) seasonal variations.

4.2. Effect of Atmospheric Turbulence

When a laser propagates through turbulent atmosphere, fluctuations in the atmospheric refractive index field cause distortions in the laser wavefront, which degrade the laser’s coherence. This degradation weakens the quality of the laser, manifesting in random phase fluctuations, random beam drift, energy redistribution across the beam cross-section (distortion, broadening, fragmentation, etc.), and resulting intensity fluctuations [53,54]. Therefore, the impact of atmospheric turbulence on the conversion factor is also an important aspect.

According to the study by Liao et al. (2023), when vortex electromagnetic waves propagate through a turbulent atmosphere, their amplitude and phase are disturbed, leading to a scintillation effect [55]. Their results indicate that vortex wave data can be used for the inversion of turbulent refractive structure parameters and provide new research directions for atmospheric remote sensing. Therefore, incorporating the refractive structure of atmospheric turbulence in future research could enable a more accurate interpretation of the variability of the conversion factor, thereby improving the inversion accuracy of CALIOP. Additionally, the study by He et al. (2024) reveals stratospheric disturbance information through new detection technology, which is crucial for understanding atmospheric turbulence and quantifying its impact on the conversion factor [56].

We plan to further explore the specific impact of atmospheric turbulence on the conversion factor in future research, and to conduct a comprehensive analysis combining the turbulent refractive structure and stratospheric disturbance information, with the aim of enhancing the accuracy and reliability of inversion methods.

4.3. Regional Differences in χ_p(π) Based on MODIS

Due to the limited data availability of BGC-Argo floats in certain marine areas, in order to facilitate the study of the regional variations in seasonal differences of χ_p(π), we employed passive ocean-color-remote-sensing product MODIS b_bp to investigate the seasonal changes of χ_p(π) in 26 global marine regions.

The results of the study revealed three distinct types of patterns in the Global Ocean. The first type, referred to as the “summer peak” type, was identified in 15 regions including 1, 5, 7, 8, 10, 11, 12, 13, 14, 17, 18, 19, 21, 22, and 25 (Figure 9). This type exhibited a distinct seasonal variation with the highest χ_p(π) values occurring during the summer and gradually decreasing during the autumn and winter seasons. Upon further subdivision, it was observed that in nine of these regions (1, 8, 10, 11, 13, 17, 18, 21, and 25), the χ_p(π) values during spring were higher than those in autumn and winter. Additionally, in six regions (5, 7, 12, 14, 19, and 22), the χ_p(π) values during spring were intermediate between those of autumn and winter, while no region displayed lower spring values compared to winter values.

The seasonal variation in χ_p(π) is predominant in “summer peak” type regions globally, and the primary reason for this seasonal difference lies in the seasonal variations in the shape of phytoplankton particles, as described in Section 2.1. Additionally, the thickness (D_c) and relative refractive index (n_c) of phytoplankton shells (membranes) can vary depending on the growth stage. For instance, cell membrane thickness can range from 0.05 to 0.13 µm, and the relative refractive index can vary from 1.06 to 1.22 [57,58]. Hu et al.’s research found that when the shell is very thin (≤0.05 µm), or the refractive index of the shell is low (≤1.06), or both conditions are met, the χ_p(π) derived from the coated sphere model approximates that of a homogeneous sphere (dashed line). As D_c or n_c increases, χ_p(π) decreases [23]. Therefore, the different growth stages of phytoplankton can lead to variations in χ_p(π) in different marine regions where they exist.

The second type, labeled as the “decline” type, was identified in seven regions including 3, 4, 8, 15, 16, 20, and 26 (Figure 9). This type exhibited a consistent decrease in χ_p(π) values from spring to winter. Among these regions, four (4, 8, 15, and 16) displayed a strict decline in values across the seasons. Region 26 also exhibited this strict decline, but data for winter values were unavailable. Region 3 displayed a non-strict decline, with summer values being lower than those in spring and autumn, while maintaining an overall “decline” type trend. Similarly, region 20 lacked winter data, but its general trend aligned with the “decline” type.

The seasonal variation in χ_p(π) in “decline” type regions is primarily concentrated near the equator and the arctic regions. Compared to “summer peak” type regions, the main difference in “decline” type regions is the absence of a peak advantage during the summer season. There is a strong link between the morphology of phytoplankton cells and their physiological and metabolic processes [59,60,61]. To maximize chloroplast exposure to light, adaptive strategies are employed [62]. It appears that the optimal morphological adaptation strategy for phytoplankton is to maintain an optimal surface-to-volume ratio (S/V), which facilitates rapid surface exchange, more efficient use of light and nutrients, and reduces sinking losses [63]. Changes in the surface-to-volume ratio result in corresponding changes in χ_p(π). Because the physicochemical environmental conditions in equatorial and arctic regions during the summer season differ from those in other regions, phytoplankton adopt different morphological adaptation strategies, resulting in distinct seasonal variations in χ_p(π).

The third type, denoted as the “autumn pole” type, emerged in three regions: 6, 23, and 24 (Figure 9). This type was characterized by the autumn χ_p(π) values being either the highest or lowest among the four seasons. Sub-categorically, regions 23 and 24 exhibited the autumn peak pattern, with the highest values observed during that season. In contrast, region 6 displayed the autumn trough pattern, with the lowest values occurring during autumn.

In summary, the study identified three distinct seasonal patterns—summer peak, decline, and autumn pole—in the examined regions based on variations in χ_p(π) values throughout the four seasons. These findings provide valuable insights into the complex seasonal dynamics and variations in the studied regions.

5. Conclusions

Due to the difficulty in obtaining in situ data for the 180° particle volume-scattering function, there is a lack of investigation and understanding of the natural variations in the key conversion coefficient χ_p(π) on a global, large-scale, and long-term basis. The persistent deployment of BGC-Argo floats and the prolonged accumulation of data through its wide array have furnished a substantial repository of in situ data. This has enabled the in-depth scrutiny of the critical conversion factor, χ_p(π), which is fundamental to CALIOP’s inversion of b_bp. Using the in situ b_bp readings from the BGC-Argo floats, we were able to determine calibrated χ_p(π) values. These values serve as a central conversion coefficient in CALIOP’s b_bp inversion procedure across diverse seasons. This study revealed noticeable seasonal deviations in χ_p(π). In addition, the existing b_bp inversion model is still relatively coarse, with many assumptions carrying certain uncertainties. The error caused by using a constant conversion factor in the current inversion algorithm cannot be ignored. Therefore, by focusing on the conversion factor, the CALIOP b_bp inversion model is corrected to further improve the accuracy of the CALIOP b_bp product.

(1)

Consistent seasonal fluctuations in the χ_p(π) values were seen at varying spatiotemporal scales, with the highest values recorded in summer (0.46–0.48) and lowest in winter (0.33–0.36), while fall and spring values remained in the middle range. The average calibrated conversion factor χ_p(π) through the 12 matching windows was computed; 0.40 for spring, 0.48 for summer, 0.43 for fall, and 0.35 for winter.

(2)

An analysis of the diurnal differences in χ_p(π) showed daytime values to be slightly higher than nighttime values in all seasons, with the highest daytime and lowest nighttime values in summer and winter, respectively, matching the overall daily trend in χ_p(π).

(3)

The passive ocean-color-remote-sensing product, MODIS b_bp, was used to observe the seasonal fluctuations in χ_p(π) in 26 global sea areas, revealing three major seasonal variation patterns: “summer peak”, “decline”, and “autumn pole”. The “summer peak” was the most prevalent, aligning with the trend detected through the BGC-Argo floats.

(4)

After factoring in the seasonal variations in χ_p(π), the CALIOP b_bp product was duly calibrated, yielding improved statistical results. The coefficient of determination increased noticeably from 0.84 to 0.89 post-calibration. Additionally, the root mean square error dropped from 4.0 × 10⁻⁴ m⁻¹ to 3.0 × 10⁻⁴ m⁻¹, and the mean absolute percentage error saw a considerable reduction from 31.48% to 25.27%.

The matching points between BGC-Argo floats and CALIOP obtained in this study from 2010 to 2017 are limited in number. However, we believe that with the widespread deployment of BGC-Argo floats and the increase in accumulation time, more comprehensive matching points and finer matching scales will be generated. This will allow for the acquisition of key conversion factors χ_p(π) across different ocean regions globally, thereby further improving the inversion accuracy of CALIPSO b_bp products.