Regional Algorithm for Estimating High Coccolithophore Concentration in the Northeastern Part of the Black Sea

Abstract

A modified regional algorithm to quantify the coccolithophore concentration in the northeastern part of the Black Sea under conditions of intense bloom is presented. To modify the algorithm, the data of in situ measurements of coccolithophore Emiliania huxleyi abundance performed in June 2017 and 2022 (when the maximum values were 9 × 10⁶ and 13 × 10⁶ Cells L⁻¹, respectively), as well as the data from hydro-optical and satellite measurements, were used. In addition, the ratio between the number of detached coccoliths and coccolithophore cells was taken into account. Based on the expanded array of in situ data, the optimal values of the regional algorithm parameters were obtained. The modified algorithm makes it possible to obtain more accurate results in areas of high coccolithophore concentrations and takes into account the contribution of coccoliths. To test the sensitivity of the algorithm to variations in bio-optical characteristics, model calculations were performed using Hydrolight software. The updated algorithm is significantly less sensitive to variations in chlorophyll concentration and CDOM absorption coefficient than its previous version.

1. Introduction

Phytoplankton in the world ocean play an important role in the regulation of the planet’s climate. They contain almost half of all carbon assimilated [1,2]. The ocean is the main depositor of absorbed atmospheric carbon; it has 50 times more carbon than the atmosphere [3,4,5]. The flow of carbon dioxide at the ocean–atmosphere boundary, its biological assimilation into the ocean water, and the further transfer of carbon in organic form from the upper layers to the deep ocean and to the ocean floor is carried out through a process called the ‘carbon pump’ [6,7]. Due to this, carbon pump global carbon export occurs, and it is currently estimated at between 5 and 15 × 10¹⁵ g of carbon per year [8,9]. At the ocean–atmosphere interface, the transport of CO₂ molecules takes place. Its speed and direction depend on the difference in the partial pressures of carbon dioxide in the atmosphere and in the ocean surface layer.

In water, phytoplankton convert dissolved carbon into organic form through photosynthetic reactions, and this process is called the ‘organic pump’, while some researchers suggest the term ‘soft tissue pump’ [10]. Diatoms are mainly responsible for the operation of the organic pump in the ocean [11]. The concentration of chlorophyll is an indicator reflecting the functioning of the organic pump [12].

However, in the ocean, evolution has proposed another biological way of fixing dissolved carbon. Calcite is a mineral formed by calcium carbonate (CaCO₃). It is also formed in the ocean in addition to organic carbon. This type of carbon assimilation process is called the ‘carbonate pump’; the main contributors to its work are coccolithophores, which have one important property of forming a calcite cell shell [13,14,15]. This shell consists of separate plates—coccoliths. The release of a CO₂ molecule, as a result of the formation of a single calcite molecule, is important for the functioning of the carbonate pump. In other words, if the organic pump reduces the partial pressure of carbon dioxide in water, the carbonate pump, in contrast, increases it. Therefore, during the coccolithophore bloom (CB), the concentration of carbon dioxide in the water increases and, as a result, there is a significant decrease in its flow into the water or even its release into the atmosphere [16,17,18]. Therefore, the ratio of diatoms and coccolithophores is a fundamental indicator characterizing the state of the carbonate system [19].

Emiliania huxleyi is the main phytoplankton species that determines the functioning of the carbonate pump in the ocean. This species is widespread throughout the Northern and Southern Hemispheres, but its blooms are recorded mainly in high latitudes [20,21,22,23,24]. In the Black Sea, the intensive growth in coccolithophore abundance was noted in the 1950s [25]. In the beginning of this century, their role in the phytoplankton structure increased, as was noted in field observations [26,27,28]. Long-term observations of the phytoplankton structure in the northeastern part of the Black Sea have established that in the end of May and beginning of June, an intensive growth of Emiliania huxleyi is observed almost annually, and the abundance of this species exceeds 10⁶ Cells L⁻¹ [28].

The method of field observations does not allow creation of a unified picture of coccolithophore bloom distributions. Such capabilities are provided by ocean remote sensing, which allows blooms to be studied in a wide range of spatial and temporal scales. Only remote sensing methods give an opportunity to obtain the data necessary for the creation of carbon export global models from the upper layers to the deep ocean [9]. Coccolithophores differ from other phytoplankton species in terms of strong low-selective light scattering, which makes it possible to observe bloom according to satellite ocean color scanner data [15,29,30,31,32,33]. Satellite data are used to observe the CB in the Black Sea, starting with the SeaWiFS ocean color data [34]. The results of observations show that during late spring and early summer, extensive bloom areas are observed, covering most of the sea [29,35,36,37,38,39,40].

Previously, a regional algorithm for the northeastern part of the Black Sea based on bio-optical measurements from 2004–2008 was developed to evaluate the coccolithophore concentration [29]. Using this algorithm, monthly average maps and diagrams for the period 1998–2018 were drawn, and were presented in the Atlas of Bio-optical Characteristics of the Ocean Optics Laboratory at the Shirshov Institute of Oceanology of the Russian Academy of Sciences (SIO RAS) [41]. However, the coccolithophore concentrations obtained in the expeditions, using the results of which this algorithm was created, did not exceed 2.5 × 10⁶ Cells L⁻¹ in most cases. They are significantly lower than the values that can be observed during the period of intense blooms. For example, according to the regional algorithm, the monthly average concentration of coccolithophores in June 2017 exceeded 6 × 10⁶ Cells L⁻¹ [41]. Such a significant difference in the range of values used for the algorithm development with the results of its application requires verification and appropriate modification of the regional algorithm.

Specifically, the purpose of this work is the development of a new algorithm for high coccolithophore and coccolith concentrations using the latest data from in situ and simultaneous satellite measurements.

2. Materials and Methods

For our purpose, the data from in situ and simultaneous satellite measurements in the northeastern part of the Black Sea near Gelendzhik (44.56°N, 38.08°E) in June 2017 and 2022, obtained during the period of intense coccolithophore blooms, were used. In situ measurements included both a complex of hydrooptical works and laboratory measurements of coccolithophore plated cell and detached coccolith abundance. The median coccolithophore concentration in the upper mixed layer according to direct measurements in those years was 7 and 5.4 × 10⁶ Cells L⁻¹. Along with the expansion of the field measurements dataset, model data obtained using Hydrolight 6.0 software [42] were used to modify the algorithm.

2.1. Study Area and Bio-Optical Measurements

The complex optical measurements were performed in June 2017 and 2022 on the small research vessel Ashamba on the transect from the Blue Bay (near Gelendzhik) to the center of the sea (Figure 1a) with simultaneous ocean color satellite observations accompanied by hydrological and biogeochemical studies. Favorable weather conditions provided good-quality remote sensing data.

For a number of stations in 2022, the spectra of the remote sensing reflectance R_rs(λ) were obtained using the floating spectroradiometer PRO-1 [43]. The floating spectroradiometer was developed at SIO RAS and allows the measurement of spectral values of the surface downwelling irradiance E_d(λ,0⁺) and the upwelling radiance below the sea surface L(λ,0⁻). From the obtained values the water, radiance reflectance ρ(λ) is calculated, which then is converted to R_rs(λ), using the following formula [44]:

R_rs(λ) = 0.165 ρ(λ)/[1 − 0.497 ρ(λ)].

(1)

PRO-1 works in the spectral range of 390–700 nm with a spectral resolution of 2.5 nm; its accuracy is about 5%.

Figure 1b shows examples of R_rs(λ) values measured with the help of the floating spectroradiometer PRO-1 in comparison with satellite data for two stations from June 11, 2022. The observed difference in spectra is explained well by the distinction in the intensity of CB at these stations; according to direct measurements, the coccolithophore concentration at station 1_22 was 4.8 × 10⁶ Cells L⁻¹, and at station 4_22 it was 9.3 × 10⁶ Cells L⁻¹.

A submerged transmissometer PUM-200 developed at SIO RAS [45] was used to measure vertical profiles of the beam attenuation coefficient at a 530 nm wavelength c(530). These profiles are quite valuable, as the c(530) profile depicts the vertical distribution of the coccolithophore layer. PUM-200 measurements made it possible to determine the thickness of the coccolithophore layer Z_coc.

2.2. Sampling

At the stations (Figure 1a), water samples were taken from different depths for laboratory determination of the spectral absorption coefficient of colored dissolved organic matter (CDOM) a_g(λ), the concentration of chlorophyll a (Chl), and the species composition of phytoplankton. Water samples were taken using 5-L Niskin bathometers mounted on a Rosette sampler.

An integrated cavity absorption meter (ICAM) was used to measure the absorption spectra of seawater, filtrates, and suspended particles [46,47]. The difference between the values of the filtrate and pure water absorption coefficients allowed the estimation of the CDOM absorption coefficient a_g(λ). The biogeochemical parameters also included the concentrations of chlorophyll a and pheophytin a measured using a fluorometric method [48,49].

Samples for determining the species composition of phytoplankton were fixed using neutralized formaldehyde (final concentration 0.8–1.0%). Sample settling was the main method of cell concentration. The identification of the species and counting of the cells were carried out using a light microscope at 16 × 10 and 16 × 40 magnifications. Identification was based on the described morphology [50,51] (http://www.algaebase.org, accessed on 18 April 2022, and http://www.marinespecies.org, accessed on 18 April 2022). The nano- and microplankton cells were counted using 0.05 mL Nageotte and 1 mL Naumann counting chambers [27]. The small flagellates (2–4, 4–6, and 6–8 μm fractions) and coccoliths were counted using a Finuchs–Rosenthal counting chamber. A method based on the geometric shape of cells was used to calculate biomass [52,53]. The number of coccolithophores equal to 1 × 10⁶ Cells L⁻¹ was taken as the bloom threshold concentration [24].

In our study, we used the results of determining the concentration of coccolithophore cells N_cc and separated coccoliths N_cl. Light scattering occurs both on coccolithophore cells and on detached coccoliths. According to the work presented in [54], the values of the specific backscattering coefficients for a coccolith are, on average, 50 times lower than for a coccolithophore cell, that is, the contribution to the backscattering of 50 coccoliths and one cell is approximately the same. Therefore, according to direct measurements, the value of N_{cc_cl} was calculated as

N_{cc_cl} = N_cc + N_cl/50,

(2)

while the average values for the two upper depths were used (the first one was 0 m, the second was 5–11 m).

2.3. Satellite Data

We used the Level 2 data of the satellite spectroradiometers Moderate-Resolution Imaging Spectroradiometer (MODIS)-Aqua and MODIS-Terra, Visible Infrared Imaging Radiometer Suite (VIIRS)-SNPP and VIIRS-JPSS, available through the NASA website [55]. Satellite data processing was performed using the SMCS 1.9 software package developed at the SIO Ocean Optics Laboratory [56].

The spectra of the remote sensing reflectance R_rs(λ) in the pixel closest to the station were selected for the stations. Two satellite datasets were selected: in the first, shipboard and satellite measurements were performed on the same day, and in the second, satellite data were added on the previous and subsequent days. Thus, in the first dataset, the time difference between shipboard and satellite measurements did not exceed 8 h, and in the second 32 h. Examples of the comparison of satellite (from the first dataset) and in situ R_rs(λ) for two stations in 2022 are shown in Figure 1b. It also shows an example of the MODIS spectrum for station 3_17 in 2017 with laboratory estimates of N_{cc_cl} = 11.6 × 10⁶ Cells L⁻¹.

2.4. Regional Algorithm 2014

Based on field measurements of coccolithophore concentration N_coc performed in 2004–2008, a regional algorithm for estimating N_coc from satellite data in the Black Sea was created [29]. According to this algorithm, the backscattering coefficient is determined by three components:

b_bp = b_{bp_bg} + b_{bp_riv} + b_{bp_coc},

(3)

where b_{bp_bg} is its background value, b_{bp_riv} is the backscattering coefficient due to terrigenous suspended matter brought by river runoff, and b_{bp_coc} is responsible for the presence of coccolithophores and coccoliths in seawater. The value of b_{bp_bg} was selected as the lowest monthly means of b_bp = 0.0025 m⁻¹, derived from satellite data over the period 2003–2010. To account for the contribution of terrigenous suspension, the following formula was used:

b_{bp_riv} = K_riv (a_g − a_{g_bg}),

(4)

where a_g and a_{g_bg} are the absorption coefficients of CDOM at the wavelength 440 nm. The first is determined in the algorithm [29] as a result of solving the inverse problem of obtaining two unknown model parameters (a_g and N_coc) from the R_rs spectra for two wavelengths. The second is determined similarly to b_{bp_bg} based on the minimum values of satellite a_g estimates for 2003–2010, and is equal to 0.047 m⁻¹. We used the following expression for coccolithophore suspension:

b_{bp_coc} = K_coc N_coc.

(5)

The following values of K_coc and K_riv were obtained: K_coc = 2.74 × 10⁻³ and K_riv = 0.157 [29].

To find two parameters of the model, the use of two spectral MODIS bands is proposed: 488 and 555 nm. In the case of VIIRS, we used close bands: 489 and 556 nm for JPSS, and 486 and 551 nm for SNPP. For model R_rs spectra obtained using Hydrolight, we used bands 488 and 551 nm.

The error estimation results for the in situ and satellite R_rs spectra for the obtained algorithm turned out to be close (standard errors 1.15 and 0.99 × 10⁶ Cells L⁻¹). The differences are due to the different dataset used for these estimates. Moreover, in both cases, the average concentration of N_coc according to the results of direct measurements did not exceed 1.5 × 10⁶ Cells L⁻¹ and only a few spectra related to the case of N_coc > 5 × 10⁶ Cells L⁻¹. When deriving the algorithm, differences in N_cl/N_cc for different years were not taken into account. However, it was possible to identify a set of data for which the b_bp correlated well with the a_g coefficient (R² = 0.82). This allowed us to reliably take into account the contribution of terrigenous suspension and not show ‘false’ coccolithophore blooms in the area of strong influence of river runoff.

In our work, we used the approach of the algorithm presented in [29], but tried to use other values for its parameters K_coc, K_riv, and b_{bp_bg} in order to improve its accuracy in conditions of intense coccolithophore bloom, which was observed in 2017 and 2022.

For the 2017 and 2022 dataset, the coefficient of determination R² for the linear correlation between b_bp and a_g is 0.60, which indicates less influence of terrigenous suspended matter in these years. Therefore, reduction by multiple times was considered for the K_riv and b_{bp_bg} parameters.

2.5. Error Assessment

To evaluate the accuracy of the N_coc algorithm and remote sensing reflectance values, the root mean square error (RMSE) and mean absolute percentage error (MAPE) were calculated as

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{N}\sum _{i=1}^N{(y_i-y_i^m)}^2},$$

(6)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{1}{N}{\sum }_{i=1}^{N}100\%·\left|y_i-y_i^m\right|/y_i^m,$$

(7)

where y_i and y_i^m are the calculated and measured values of coccolithophore concentrations or remote sensing reflectance.

The regional N_coc estimation algorithm uses two spectral bands in the range of 486–489 and 551–556 nm. For the 2022 stations, when in situ measurements of R_rs(λ) were carried out, estimates of the correspondence of satellite and in situ R_rs values in spectral bands from the considered spectral ranges were made. For a set with satellite data on the same day (16 pairs in total), the maximum difference for MODIS and VIIRS-JPSS for both bands did not exceed 8%, and MAPE was equal to 4%. With an increase in the permissible time difference between satellite and shipboard measurements to 32 h (37 pairs), the maximum difference reached 60%, and MAPE turned out to be equal to 15% for MODIS and 8–9% for VIIRS-JPSS. Our estimates of the differences between satellite and in situ R_rs values during the CB period are even slightly better than those obtained in earlier work [57], where for the VIIRS-JPSS band 556 nm, MAPE = 9.3%, and for the 555 nm band of two MODIS sensors, MAPE was equal to 10.3 and 12.3%, respectively. It is worth noting that [57] used a dataset with more spectra and a time difference between in situ and satellite measurements less than 2 h, as waters were strongly influenced by river runoff.

The acceptable difference between the satellite and in situ R_rs allowed us to use the combined set of satellite and in situ R_rs spectra to modify the regional N_coc estimation algorithm.

2.6. Tuning of the Hydrolight Model

Hydrolight software was used to calculate the light field parameters. We used the case 2 water model, where inherent optical properties were determined for 4 components [58]. The parameters of pure water absorption and scattering were taken from [59,60].

The optical properties of the component associated with Chl were parameterized through its concentration. The result of field measurements of the concentration of Chl at the depths of 1–10 m shows insignificant (5–10%) changes, so the concentration was set as a constant with depth. Absorption and scattering parameters were introduced using standard models available in Hydrolight [61,62]. The parameters of the scattering phase function represent the Morel model for “large particles” [63].

The CDOM component was considered to be non-scattering. The absorption of CDOM was calculated relatively to the absorption value at wavelength 443 nm a_g(443) [56]. This value and CDOM spectral slope were specified using the results of laboratory ICAM measurements, or through the GIOP R_rs(λ) decomposition algorithm [64].

The mineral suspension component was set, assuming that the suspension is represented only by coccolithophore cells and detached coccoliths, which corresponds to more than 99% of the biomass during intense blooms, according to in situ measurements. The absorption properties of coccolithophores and coccoliths were neglected, as they are several times less than those of Chl and CDOM. We used the typical coccolithophore bloom backscattering ratio value b_b/b = 0.02 [65], and the spectral scattering coefficient b(λ) was assigned as

b(λ) = b₀ (550/λ)^m.

(8)

The parameters b₀ and m were determined to spectrum b_b(λ) and matched the results of the decomposition of the R_rs spectra using GIOP. The depth of a homogeneous surface layer with coccolithophores Z_coc was also specified, below which coccolithophore concentration was set to zero.

Figure 2a shows the comparison of the scattering parameters b₀ and m calculated using GIOP from satellite and in situ R_rs (λ) spectra. In this case, all available satellite spectra were used. The coefficient of determination R² of the linear correlation was 0.49, which made it possible to determine the parameter m based on the value b₀:

m = 1.274 − 0.067·b₀

(9)

Parameter b₀ correlates well with the concentration of N_{cc_cl} according to direct measurements (b₀ = 0.207·N_{cc_cl}, R² = 0.62, Figure 2b). Only satellite spectra with a measurement time difference of less than 8 h were used here. If we expand the array of satellite data by increasing the time interval to 32 h, then R² will decrease to 0.49, and the correlation equation will change slightly: b₀ = 0.212·N_{cc_cl}. However, as can be seen in Figure 2b, there is a significant difference in the location of the data for 2017 and 2022 relative to the regression line for the general dataset, which can be explained by the different phases of blooms recorded according to in situ measurements over these years. If we calculate the regression separately for each year, then for 2017, we will obtain b₀ = 0.245·N_{cc_cl}, and for 2022, it will be b₀ = 0.145·N_{cc_cl}.

3. Results

3.1. Coccolithophore Concentrations in the Northeastern Part of the Black Sea in 2017 and 2022

In 2017, intense coccolithophore bloom represented by one species Emiliania huxleyi was observed at all stations from the shelf to stations above the depth of 1500 m. The maximum number of coccolithophores exceeded 9 × 10⁶ Cells L⁻¹ (Table S1), and their contribution to the total phytoplankton biomass was above 99%. Coccolithophore bloom was observed mainly in the upper mixed layer. The median concentration of coccolithophore cells for all sampling depths was equal to 6 × 10⁶ Cells L⁻¹, and for the two upper ones was 7 × 10⁶ Cells L⁻¹.

In 2022, coccolithophore bloom was generally less intense, although the abnormally high value of 13 × 10⁶ Cells L⁻¹ was obtained at one station (Table S2). Bloom also occurred at all stations of the continental shelf and slope, and it was recorded in the upper mixed layer. The median concentration of coccolithophore cells for all sampling depths was equal to 4 × 10⁶ Cells L⁻¹, and for the two upper ones was 5.4 × 10⁶ Cells L⁻¹.

The median value for the N_cl/N_cc ratio for all sampling depths in 2017 was 11.5, and for the two upper ones was 15.0; in 2022, for all depths it was 1.3, and for the two upper ones was 2.2. Such a strong difference in the value of N_cl/N_cc, apparently, occurs due to the difference in the bloom phase for those two years. In June 2022, the bloom was in an earlier phase, when significantly fewer detached coccoliths were observed; in June 2017, measurements were performed near the end of bloom, so the abundance of detached coccoliths exceeded the abundance of placed coccolithophore cells.

3.2. Sensitivity of the N_coc Algorithm to Variations in Bio-Optical Characteristics

Figure 3 shows a comparison of the measured and model R_rs(λ) spectra using the examples of station 1_22 (11.06.2022, 44.56N, 37.96E) and station 3_17 (08.06.2017, 44.48N, 37.85E). For station 1_22, the model spectra are compared with the field-measured R_rs(λ), and for station 3_17, with the spectrum according to MODIS Terra data. The concentration of N_{cc_cl} according to direct measurements for station 1_22 was 5.2 × 10⁶ Cells L⁻¹, and for station 3_17 was 11.6 × 10⁶ Cells L⁻¹. In this case, for station 1_22, the best agreement of the model spectrum with the measured one was achieved for Z_coc = 10 m, while in the case of more intense bloom at the station 3_17, the spectrum matched for Z_coc = 5 m. For both stations, the value of Z_coc* was calculated, when all model spectra with Z_coc > Z_coc* hardly differed from the one obtained with Z_coc*. This indicates that the R_rs(λ) spectrum is formed by the upper layer of a water column with a thickness of Z_coc*. For the stations shown in Figure 3, the Z_coc* was 15 and 10 m.

To test the stability of the regional coccolithophore concentration algorithm to variations in the Chl concentration and the CDOM content, additional model calculations were carried out (Figure 3 in the center and right column). These variations were set using a multiplier X to the initial values of Chl and a_g(443), for which the best agreement was obtained with the measured R_rs spectra. The effect on the R_rs spectrum of the change in CDOM is more noticeable than the change in Chl (Figure 3). The reason for this is that the CDOM-related absorption is usually significantly greater than the phytoplankton absorption in the northeastern part of the Black Sea. When the Chl value changes by 50%, there is only a slight change in the R_rs(λ) spectra, while the same relative decrease in CDOM brings not only a significant increase in R_rs, but also a noticeable change in the shape of the spectrum. This shape is typical for coccolithophore bloom spectra in the Barents Sea [66], where the content of CDOM is significantly lower than in the Black Sea. Only with such a low content of CDOM or with a significant increase in Chl (3–5 times) is the effect of the maximum absorption by phytoplankton near 450 nm noticeable in the shape of a small deflection of the R_rs(λ) spectrum near this wavelength.

Table 1. The values of N_coc (10⁶ Cells L⁻¹) according to the 2014 algorithm [29] and their difference Δ (%) from the values of N_coc* calculated from the measured spectra, depending on the parameters of the Hydrolight model with an example for stations 1_22 and 3_17. Columns highlighted in bold refer to calculations with the set of parameters when the best match between the measured and calculated R_rs spectra was obtained.

	St. 1_22				St. 3_17
Zcoc	5	10	15	20	3	5	7	10
Ncoc	1.4	3.1	3.6	3.8	11.0	14.3	15.7	16.4
Δ	−53%	1%	19%	24%	−16%	10%	21%	26%
X * Chl	0.5	1	1.5	3	0.5	1	1.5	3
Ncoc	3.5	3.1	2.8	2.0	15.2	14.3	13.6	11.8
Δ	14%	1%	−10%	−36%	17%	10%	4%	−9%
X CDOM	0.5	1	1.5	2	0.5	1	1.5	2
Ncoc	3.8	3.1	2.4	1.7	15.0	14.3	13.6	12.9
Δ	25%	1%	−22%	−45%	15%	10%	5%	−1%

* The notation ‘X’ refers to the case of an X-fold increase in the concentration of Chl or a_g(443).

shows the sensitivity of the regional N_coc algorithm [29] to variations in the Z_coc, Chl, and the absorption of CDOM values. In addition to the N_coc values for different model spectra (Figure 3), their difference (Δ, %) from the N_coc* values calculated from the measured spectra (N_coc* = 3.1 and 13.4 × 10⁶ Cells L⁻¹ for station 1_22 and 3_17, respectively) is shown. A decrease in Z_coc by 2 times leads to underestimation of N_coc estimates by almost 2 times for station 1_22, where the bloom is not so intense. For station 3_17, with a decrease in Z_coc, there is also a significant decrease in N_coc (by more than 3 × 10⁶ Cells L⁻¹, ~26%). The increase in Z_coc does not play such a significant role, since the spectrum of upwelling radiation is formed by the surface layer of the water column—Z_coc*. In fact, a greater relative variability of N_coc estimates in response to changes in modeling parameters was observed for station 1_22, with a less intense CB than for station 3_17. The N_coc for station 1_22 changes particularly noticeably when the CDOM absorption changes. For station 3_17, in an intense CB area, the response to changes in CDOM and Chl is approximately the same, as the absorption of Chl becomes comparable to the absorption of CDOM for the 488 nm spectral band used in the N_coc algorithm. The higher concentration of Chl (0.47 in comparison to 0.2 mg L⁻¹) proves it, while the value of CDOM for station 3_17 is only 26% higher than station 1_22.

3.3. New Values of K_coc as a Result of Hydrolight Modeling

Using a customized bio-optical model, R_rs calculations were carried out for five values of N_{cc_cl} 2, 4, 7, 10, and 15 × 10⁶ Cells L⁻¹. For each value of the concentration of N_{cc_cl}, the values of Chl (0.3, 0.5, and 0.8 mg L⁻¹) and CDOM (0.03, 0.05, and 0.08 m⁻¹) were varied to cover the most likely range of changes in these optically active components (OAC), typical for the northeastern part of the Black Sea [55,67]. The calculations were carried out under the assumption of a homogeneous distribution of coccolithophores in the layer 15 m deep, which generally corresponds to the results of the performed field measurements of the vertical profiles of the beam attenuation coefficient c(530).

Thus, 45 R_rs spectra were obtained, to which the regional algorithm was applied to estimate the N_coc concentration. The comparison of the N_{cc_cl} input values used in Hydrolight calculations and obtained N_coc estimates is shown in Figure 4. If we use the values of the parameters K_coc, K_riv, and b_{bp_bg} defined in the article [29], then the N_coc estimates (shown in pink circles) vary visibly in response to changes in the content of the OAC. Simultaneously, overestimated N_coc evaluations are obtained for N_{cc_cl} = 15 × 10⁶ Cells L⁻¹, and underestimated ones (in a number of cases even negative) for N_{cc_cl} = 2 × 10⁶ Cells L⁻¹. This result arises from the fact that in our Hydrolight model, the contribution of terrigenous suspended matter is not taken into account. The origin of this matter is associated with river runoff, as well as with the b_bp background amount, which is parametrized through the b_{bp_bg} value. Therefore, N_coc estimates were calculated for the case of K_riv = 0 and b_{bp_bg} = 0 (blue circles in Figure 4). In this case, the influence of the OAC practically disappears, but for all N_{cc_cl} data, overestimated N_coc values are obtained, and this overestimation increases in direct proportion to N_{cc_cl}, which indicates an incorrect K_coc value. For the best correspondence of the initial values N_{cc_cl} with the results of N_coc estimates, the value 4.36 × 10⁻³ is used (red circles in Figure 4).

Figure 4 also shows N_coc estimates for the cases of K_riv = 0 (in blue) and b_{bp_bg} = 0 (in green). The results obtained in these cases are close to the variants of K_riv = 0 and b_{bp_bg} = 0 and the original algorithm [29], respectively, showing that the influence of the value of b_{bp_bg} on the algorithm results is significantly less than the influence of K_riv.

As was previously noted (Section 2.4), there are noticeable differences for the data we use depending on the year. Therefore, similar calculations of R_rs spectra arrays were performed, but using the coupling equations between b₀ and N_{cc_cl} obtained separately for 2017 and 2022 data. These arrays allowed us to obtain two more variants of the K_coc value: 5.13 × 10⁻³ for 2017 and 3.10 × 10⁻³ for 2022. Additionally, if the first K_coc value is almost two times higher than the previous K_coc estimate [29], then the second one is very close to it. The use of these K_coc values is discussed in Section 3.4 and Section 4.5.

3.4. Configuring Other Model Parameters

As long as the results of the Hydrolight calculations were obtained without taking into account the terrigenous suspended matter, the presence of which is quite possible when using real data, the data of in situ and satellite measurements of R_rs were used to adjust two parameters of the N_coc algorithm related to the terrigenous suspended matter (K_riv and b_{bp_bg}) for stations where the in situ measurements of N_{cc_cl} were completed. The difference in measurement time between satellite and shipboard data did not exceed 8 h. In total, 41 corresponding spectra were selected for 2017 and 2022.

We set the value of K_riv and b_{bp_bg} as a fraction of their values defined in the previous work [29], leaving values from the original algorithm or decreasing them. For example, the notation ‘0.25_0.5’ means that K_riv = 0.25 × 0.157 = 0.03926 and b_{bp_bg} = 0.5 × 0.0025 = 0.00125.

For the K_coc parameter, both previous values 2.74 × 10⁻³ and three new variants, 3.10, 4.36, and 5.13 × 10⁻³, obtained in Section 3.3 were used. As there is a rather large difference between the variants of the K_coc 3.10 and 4.36 × 10⁻³, two more intermediate ones were used: 3.52 and 3.94 × 10⁻³.

Table 2. The RMSE (10⁶ Cells L⁻¹) and MAPE values of N_coc estimates relative to the measured N_{cc_cl} for the selected dataset and depending on the value of the parameters of the algorithm K_coc, K_riv, and b_{bp_bg}.

Kriv and bbp_bg *	1.0_1.0	1.0_0.5	0.5_1.0	0.5_0.5	0.25_1.0	0.25_0.5	0.1_0.1
Kcoc 103	RMSE
2.74	2.68 **	2.57	2.70	2.77	2.90	3.05	3.47
3.1	2.75	2.54	2.40	2.32	2.37	2.37	2.56
3.52	3.08	2.82	2.52	2.32	2.31	2.16	2.06
3.94	3.46	3.21	2.85	2.61	2.57	2.35	2.08
4.36	3.83	3.59	3.23	2.99	2.93	2.69	2.35
5.13	4.41	4.19	3.86	3.64	3.57	3.35	3.01
Kcoc 103	MAPE
2.74	35%	32%	31%	29%	30%	29%	32%
3.1	36%	33%	31%	29%	29%	27%	25%
3.52	39%	36%	32%	30%	30%	28%	25%
3.94	43%	40%	36%	33%	33%	30%	26%
4.36	48%	45%	40%	37%	37%	34%	29%
5.13	55%	52%	48%	45%	44%	41%	37%

* The values of K_riv and b_{bp_bg} are given as fractions of their values determined in the previous work [29]. ** The underlined values of RMSE and MAPE correspond to the algorithm parameters that were used in Figure 5.

shows the RMSE and MAPE values of the N_coc estimates obtained relative to the measured N_{cc_cl} for the selected dataset and depending on the three parameters values of the algorithm: K_coc, K_riv, and b_{bp_bg}.

If we focus on the RMSE and MAPE values, the best correspondence between the calculated N_coc and the measured N_{cc_cl} is obtained in the case of 0.1_0.1 and K_coc = 3.52 × 10⁻³. In fact, it is the option of reducing the contribution of terrigenous suspended matter to 10% of the initial one, almost regardless of the K_coc value, that leads to a decrease in RMSE and MAPE and, therefore, to an improvement in compliance. Comparison graphs of N_coc vs. N_{cc_cl} show that the discrepancy in the variants with different values of the algorithm parameters are no longer so noticeable (Figure 5). The best option, “10%” (Figure 5b), does not differ much from the original “algorithm 2014” (Figure 5a); it even has less difference from the intermediate “50%” option (Figure 5c), although the values of RMSE and MAPE are noticeably different for all given versions.

Figure 5d shows the variant 0.1_0.1 and K_coc = 5.13 × 10⁻³, as it was the value of K_coc obtained in the Hydrolight calculations with the focus on 2017 data and the corresponding best option for terrigenous suspended matter was selected from Table 2. However, even if we only pay attention to the data for 2017, the “50%” option suits them much better (Figure 5c). Thus, model calculations do not always allow us to find the best variant of the algorithm parameters that works with real satellite data, because atmospheric correction errors begin to contribute to the accuracy of the latter [57,68], as well as errors associated with the time difference between in situ and satellite measurements. In addition, the error is caused by the discrepancy between the spatial resolution of shipboard and satellite data and the interannual dynamics of phytoplankton communities.

Furthermore, we will consider the “10%” option (0.1_0.1 and K_coc = 3.52 × 10⁻³) to be the best one for the conditions of intensive CB in the northeastern part of the Black Sea. We will denote it as ‘algorithm 2023’. The algorithm code (MATLAB script) for both algorithms (2014 and 2023) is available in the Supplementary Materials.

4. Discussion

4.1. Coccolithophore Blooms in the Black Sea

Coccolithophore blooms are an almost annual phenomena in the Black Sea, but in 2017 and 2022, these blooms reached their maximum intensity in comparison to previous years [28]. The maximum concentration of Emiliania huxleyi was registered in 2022, and it has been the maximum for all the years of research since the beginning of this century. Coccolithophore blooms grow in the upper mixed layer with high stability of the water column [22]. In the northeastern part of the Black Sea, weak SE winds dominate in late and early spring, and wind forcing during this period is minimal [28,69]. This contributes to the development of a sharp seasonal thermocline, the presence of which is a necessary condition for the bloom [22,24,28,70].

Typical features of the blooms of 2017 and 2022 are the presence of a large number of detached coccoliths (Tables S1 and S2). In 2017, the number of detached coccoliths per Emiliania huxleyi plated cell reached 600. In 2022, this number was lower, but still high. This suggests that the bloom was in late phase and the number of destroyed cells accumulated. One of the possible mechanisms for the appearance of a large number of detached coccoliths during the bloom is the intensive consumption of living cells by species of a higher trophic level [71].

Due to a large number of plated cells and detached coccoliths in the upper mixed layer, a kind of optical medium is created to generate optimal conditions for the growth of coccolithophore cells, and does not allow other species in competition to win [65]. However, it is not yet clear why intense coccolithophore blooms grow. There is a hypothesis that the intensity of blooms is related to the nature of winters, as after cold winters, there are usually more intense blooms [70,72]. However, the details of this connection remain unclear.

4.2. Sensitivity of the New N_coc Algorithm

Table 3. The values of N_coc (10⁶ Cells L⁻¹) according to the algorithm “10%” and their difference Δ (%) from the value of N_coc* calculated from the measured spectra, depending on the parameters of the HydroLight model for the stations 1_22 and 3_17. Columns highlighted in bold refer to calculations with a set of the parameters when the best match between the measured and calculated R_rs spectra was obtained.

	St. 1_22				St. 3_17
Zcoc	5	10	15	20	3	5	7	10
Ncoc	3.3	4.2	4.5	4.5	11.7	14.1	15.1	15.6
Δ	−30%	−10%	−5%	−4%	−5%	15%	23%	27%
X * Chl	0.5	1	1.5	3	0.5	1	1.5	3
Ncoc	4.23	4.23	4.24	4.24	14.2	14.1	14.0	13.8
Δ	−10%	−10%	−10%	−10%	16%	15%	14%	12%
X CDOM	0.5	1	1.5	2	0.5	1	1.5	2
Ncoc	4.27	4.23	4.20	4.16	14.0	14.1	14.3	14.4
Δ	−10%	−10%	−11%	−12%	−5%	15%	15%	23%

* The notation ‘X’ refers to the case of an X-fold increase in the concentration of Chl or a_g(443).

shows the sensitivity test results of the 2023 regional algorithm to determine N_coc with the example of the 1_22 and 3_17 stations (just as in Table 1). Firstly, the new algorithm has allowed us to obtain N_coc* estimates from the measured spectra that better correspond to the data of direct measurements of N_{cc_cl}. For the station 1_22, N_coc* = 4.7 × 10⁶ Cells L⁻¹, and for 3_17 it is 12.3 × 10⁶ Cells L⁻¹, which is much closer to the estimates of N_{cc_cl}: 5.2 and 11.6 × 10⁶ Cells L⁻¹, respectively. Secondly, the new algorithm has become significantly less sensitive to Chl and CDOM value changes, which is a consequence of a reduction in the contribution of terrigenous suspended matter to the total suspension matter backscattering. With a 50% change in Chl and CDOM, the N_coc estimates for both stations now hardly change. The influence of the Z_coc layer thickness has somewhat decreased, but the mechanism of this influence remains the same.

4.3. Comparison of N_coc Distributions for 2014 and 2023 Algorithms

Figure 6 shows a comparison of the distributions of N_coc concentration estimates calculated with the old [29] and the new 2023 algorithms for the entire Black Sea. For this figure, we used data from two VIIRS overpasses for 12 June 2017 and 17 June 2022, which gives us an opportunity to see almost the entire Black Sea water area and relate to the time of the expeditions in those years. For both images, the comparison of the two algorithms shows that the main difference between their results arises primarily in areas affected by river runoff: for example, near the mouth of the Danube River or in the Sea of Azov. There are also noticeable differences in the area of low N_coc concentrations. This is especially noticeable for 2022 in the central part of the sea, where according to the 2014 algorithm, there was no CB; However, the modified algorithm indicates its presence (N_coc > 10⁶ Cells L⁻¹).

In addition, Figure 6 shows the differences in CB in the studied years. In 2017, intensive CB with N_coc > 4 × 10⁶ Cells L⁻¹ covers almost the entire Black Sea area (with the exception of the northwestern shelf area). In 2022, extremely high values of N_coc > 15 × 10⁶ Cells L⁻¹ were observed near the northeastern coast, but for the rest of the Black Sea, the CB was less intensive or absent.

Since the modification of the N_coc algorithm in conditions of intense CB has been carried out on the basis of field measurement data in a fairly small area in the northeastern part of the Black Sea, the new algorithm may not be suitable for the entire sea. The informative MODIS Terra data from 8 June 2017 were selected to see the differences between the two algorithms’ performance in the eastern part of the sea (Figure 7). Note that a different scale was chosen. As there are no rivers as large as the Danube or Dnieper in the eastern part of the sea, the differences between the two algorithms appear only in the area of relatively small N_coc values. In addition, it is worth noting that despite a very intense CB near the northeast coast in 2022, satellite N_coc values were clearly lower in the sampling area near Gelendzhik than those from 2017. Thus, the differences for satellite estimates of the CB near Gelendzhik are consistent with the field measurement data.

Thus, the new algorithm gives more accurate estimates in conditions of intense CB and the absence of strong influence of terrigenous suspended matter. However, for areas affected by significant river runoff and in areas of weak CB (N_coc < 3 × 10⁶ Cells L⁻¹), it seems that the previous version of the algorithm should be used. To set up a regional algorithm in such waters, it is necessary to conduct complex expedition studies, including in situ determination of the coccolithophore concentration. Note that spectral variations of the remote sensing reflectance during coccolithophore blooms in the western part of the Black Sea, affected by river runoff, were carried out in [57] according to AERONET-OC. Nevertheless, the authors did not have in situ data on the coccolithophore concentration, although it is typical for a number of other works [73,74,75,76,77], due to the complexity of such measurements.

4.4. The Comparison with PIC Product

The standard satellite data processing product particle inorganic carbon (PIC) is widely used for CB intensity and calcite (CaCO₃) concentration assessments [78,79]. In the work [29], an equation of the relationship between N_coc and PIC with a correlation coefficient of 0.61 was obtained. The comparison of the distributions of N_coc and PIC for two satellite overpasses with intensive CB in June 2017 and 2022 is shown in Figure 6. It can be seen that, in fact, the N_coc and PIC distributions are visually similar. Note that for PIC values in areas affected by river runoff (for example, near the mouth of the Danube River) the data are masked, while the 2014 algorithm yields low N_coc estimates in these areas. Moreover, sometimes, areas where the algorithm for N_coc shows an intense CB are hidden in PIC distribution map, as was the case near the Kerch Strait (45N, 37E) for the 2017 image, for example.

According to the 8 June 2017 MODIS Terra data in the eastern part of the Black Sea (Figure 7 upper image), the pixel-by-pixel comparison of PIC and N_coc values was performed for both N_coc algorithms. The proportionality coefficients between N_coc and PIC transpired to be 252 and 250, which is quite consistent with the previous value of 223 [29]. It is of interest to make comparisons under non-typical Saharan dust transfer conditions, for which additional data correction is recommended [80].

4.5. The Effect of the Bloom Phase (The Difference for Two Years)

To select the best algorithm for estimating N_coc in conditions of intensive CB in the north-eastern part of the Black Sea, we focused on the correspondence of the measured and calculated N_coc values for the total dataset for two years. Moreover, it was seen that, on the whole, the data in these years have their own peculiarities (see Figure 5). In addition, according to direct measurements, a different ratio was recorded for them between the concentrations of placed coccolithophore cells N_cc and detached coccoliths N_cl, which may be the result of a different bloom phase during field measurements. In order to select the best algorithm for each year separately, the statistical parameters (RMSE and MAPE) of the calculated N_coc and measured N_{cc_cl} are presented separately for each year (

Table 4. The RMSE (10⁶ Cells L⁻¹) and MAPE values of the N_coc estimates relative to the measured N_{cc_cl} for the 2017 and 2022 data separately and depending on the value of the parameters of the algorithm K_coc, K_riv, and b_{bp_bg}.

	2017			2022
Kriv and bbp_bg	1.0_1.0	0.5_0.5	0.1_0.1	1.0_1.0	0.5_0.5	0.1_0.1
Kcoc 103	RMSE
2.74	2.53	3.92	5.31	2.76	1.68	1.31 *
3.1	1.94	2.60	3.68	3.17	2.11	1.43
3.52	2.16	1.86	2.39	3.54	2.58	1.83
3.94	2.76	1.95	1.79	3.85	2.96	2.24
4.36	3.38	2.45	1.88	4.09	3.29	2.61
5.13	4.35	3.46	2.76	4.44	3.75	3.16
Kcoc 103	MAPE
2.74	23%	35%	50%	42%	26%	21%
3.1	16%	23%	33%	48%	33%	21%
3.52	17%	16%	21%	53%	39%	27%
3.94	22%	16%	15%	57%	44%	33%
4.36	28%	19%	15%	61%	49%	38%
5.13	38%	29%	22%	67%	55%	46%

* The underlined values of RMSE and MAPE correspond to the algorithm parameters for which the best correspondence between the calculated N_coc and the measured N_{cc_cl} was obtained (see text).

).

As in the case of a general data array, the smallest difference between the measured and calculated values was obtained with the smallest fraction of terrigenous suspension (option 0.1_0.1). Although the K_coc = 3.94 × 10⁻³ value suits 2017 better, for 2022, it should be changed to 2.74 × 10⁻³. However, this choice is rather arbitrary as for other parameters of the algorithm almost the same compliance estimates were obtained. For example, for the 2017 data, RMSE = 1.79 and MAPE = 15% in the case of the 0.1_0.1 option and K_coc = 3.94 × 10⁻³, while for the 0.5_0.5 option and K_coc = 3.52 × 10⁻³, we obtain almost the same difference parameters: RMSE = 1.86 and MAPE = 16%. This means that although the regional algorithm can be customized for specific bloom phases, the algorithm without taking into account the bloom phase will give almost the same N_coc estimations equally well, which should certainly be attributed as one of its advantages. A number of previously developed optical methods can be used to detect different bloom phases [81,82].

4.6. Influence of the Spectral Index m Values for the Suspended Matter on the R_rs Spectra

To determine the parameter m of the spectral dependence of backscattering by suspended matter in HydroLight calculations, we used Equation (9) with a low coefficient of determination value (R² = 0.49). The value of m could vary in the range 1.0–1.3 (Figure 2). To check what effect the m value has on the model R_rs(λ) spectrum, HydroLight calculations for station 3_17 with different values of m (Figure 8) were performed. It can be seen that even for extreme values of 1.0 and 1.3, the model spectra differ only very slightly. For the 551 nm band, they coincide and for 488 nm, the difference is 3%. That is, in the HydroLight calculation model, in order to improve the N_coc estimation algorithm, it is possible to use Equation (9) or a fixed m value from the range 1.0–1.3 with good accuracy.

5. Conclusions

A modified regional algorithm to quantify the concentration of coccolithophores in the northeastern part of the Black Sea under conditions of intense bloom is presented. Compared to the data underlying the previous version of the algorithm, over recent years, it has been possible to significantly expand the accumulated dataset of in situ coccolithophore and coccolith concentration determinations. In addition, the ratio between the number of detached coccoliths and plated coccolithophore cells was taken into account. The undoubted advantages of the new algorithm include its lower sensitivity to variations in the values of chlorophyll concentration and CDOM absorption, which are not associated with coccolithophorid blooms. In the future, much attention should be paid to the Western part of the Black Sea, where the problem of separating the contribution of the Danube and Dnieper rivers into the remote sensing reflectance signal arises, as well as developing an algorithm for quantifying the concentration of coccolithophorids during winter blooms. This means that it will be necessary to carry out extended expeditionary studies for the mentioned region and season, including direct determinations of the concentration of coccolithophorids. In general, the proposed approach with the separation of particulate matter into two components (terrigenous and coccolithophore) can be used to create regional or seasonal algorithms for estimating the concentration of coccolithophores in any region of the world ocean during any period. It is only necessary to have the data of field measurements of coccolithophore concentration and simultaneous shipboard or satellite measurements of the remote sensing reflectance for the selected region and period.