Optimal Assimilation Number of Phytoplankton in the Siberian Seas: Spatiotemporal Variability, Environmental Control and Estimation Using a Region-Specific Model

Abstract

The maximal value of the chlorophyll-specific carbon fixation rate in the water column or the optimal assimilation number (P^b_opt) is an important parameter used to estimate water column integrated primary production (IPP) using models and satellite-derived data. The spatiotemporal variability in the P^b_opt of the total and size-fractionated phytoplankton in the Siberian Seas (SSs) and its links with environmental factors were studied based on long-term (1993–2020) field and satellite-derived (MODIS-Aqua) observations. The average value of P^b_opt in the SSs was equal to 1.38 ± 0.76 mgC (mg Chl a)^–1 h^–1. The monthly average values of P^b_opt decreased during the growing season from 1.95 mgC (mg Chl a)^–1 h^–1 in July to 0.64 mgC (mg Chl a)^–1 h^–1 in October. The average value of P^b_opt for small (<3 μm) phytoplankton 1.6-fold exceeded that for large (>3 μm) phytoplankton. The values of P^b_opt depend mainly on incident photosynthetically available radiation (PAR). Based on the relationship between P^b_opt and PAR, the empirical region-specific algorithm (E_0reg) was developed. The E_0reg algorithm performed better than commonly used temperature-based models. The application of E_0reg for the calculation of P^b_opt will make it possible to more precisely estimate IPP in the SSs.

1. Introduction

The primary production (PP) of oceanic phytoplankton amounts to approximately half of the net autotrophic production of the Earth [1]. PP is an important factor in CO₂ exchange between the atmosphere and ocean, which is one of the factors that determine global climate change [2,3,4,5,6,7]. Therefore, the estimation of the long-term variability in PP under climate trends is one of the main tasks of the biogeochemistry of the World Ocean [8]. Currently, this estimation is carried out using production and biogeochemical models with satellite-derived data as input variables.

Parametrisation is one of the main problems in PP modelling and one of the main factors determining the model performance. Chlorophyll a (Chl a)-normalised PP (chlorophyll-specific carbon fixation rate or assimilation number; P^b = PP/Chl a) is the most important parameter characterising the photoadaptive processes of phytoplankton, used to develop primary production algorithms and estimate the spatiotemporal variations in PP. There are two approaches to P^b determination. One of them is P-I experiments, which establish the relationship between the rate of carbon assimilation and the intensity of artificial light during short (≤4 h) expositions described using the models fitted to the photosynthesis vs. irradiance curves [9,10]. Such experiments are carried out in photosynthetrons where irradiance saturating of photosynthesis is achieved. The value of the chlorophyll-specific carbon fixation rate at saturating light intensity is defined as the maximal assimilation number (P^b_max). With a different approach, P^b is estimated during measurements of integral PP in the water column (IPP) under natural illumination [11,12]. Therein, the maximal P^b is determined at the depth with optimal irradiance for photosynthesis and defined as the optimal assimilation number (P^b_opt). It should be noted that under natural conditions, the maximal values of carbon assimilation can be achieved at a light intensity less than that which saturates photosynthesis. Therefore, the parameters of P^b_max and P^b_opt are not equivalent [13].

The present paper studies the spatiotemporal variations in P^b_opt and its links with environmental variables. This parameter is widely used in so-called chlorophyll-based PP models [13,14]. The comparison of the predictive skill of these algorithms with other models was repeatedly carried out previously [15,16,17,18,19,20,21,22,23,24].

The development and validation of PP models for the assessment of IPP in the Arctic Ocean is a complicated problem. The Arctic Ocean is an under-sampled region in terms of in situ PP measurements, which is one of the components of this problem. Therefore, prominent evaluations of the Arctic Ocean IPP were performed using the models, which were originally developed for other parts of the World Ocean [21]. This approach decreases the accuracy of IPP estimation in the Arctic Ocean. Meanwhile, it is known that using regional-specific algorithms increases the efficiency of IPP assessment [18,21,25,26,27].

The Siberian Seas (SSs), which include the Kara, Laptev, and East Siberian Seas, are the least studied among all areas of the Arctic Ocean in terms of PP processes [28,29,30]. Thus, little is known about the values of P^b_opt in the SSs, its relationships with environmental factors, and the magnitude of P^b_opt of size-fractionated phytoplankton [31,32,33]. Meanwhile, it is known that size composition is an important abiotic factor affecting the P^b_opt value of phytoplankton [34].

Determination of the range in variability and the average value of P^b_opt in the SSs is critically important for the investigation of PP features in this region. These features are linked with the particularity of the phytoplankton biotope that functions on the broad continental shelf under the influence of intense river runoff [35,36,37,38,39]. Freshwater discharge into the Siberian shelf leads to low salinity in the subsurface layer, sharp stratification [40,41,42,43], and high particulate (POM) and coloured dissolved (CDOM) organic matter, as well as the concentration of terrigenous mineral suspension [35,44,45,46]. Consequently, the Kara Sea waters are characterised by high turbidity, low transparency (average Secchi disk depth of 8 m), and a small photosynthetic layer (22 m on average) [47]. Therefore, it seems relevant to develop the region-specific algorithm of P^b_opt for the SSs as one of the main parameters of PP models.

There are two approaches to the application of P^b_opt in PP models. According to one of them, P^b_opt is used as the average value for a particular biogeochemical province [48,49]. The second approach assumes the calculation of P^b_opt by its relationship with a value of an environmental factor that is determined with remote sensing from space. The second one is recommended to be used in areas of the World Ocean with a high spatiotemporal variability in biogeochemical parameters [50]. The intense river runoff is the reason for sharp spatial gradients of hydrophysical, hydrochemical, and biological parameters in the SSs. Therefore, the application of the second approach to P^b_opt modelling can improve the model performance. To implement this method, it is necessary to establish the relationships between P^b_opt and the environmental factors: photosynthetically available radiation (PAR), nutrient concentration, water temperature, salinity, and Chl a concentration.

Thus, for region-specific modelling, it is relevant to develop an empirical algorithm describing the relationships between P^b_opt and environmental factors. The main abiotic variable that determines P^b_opt values and that is easily assessed using remote sensing is sea surface temperature (T₀). Meanwhile, it is known that other environmental factors limiting the rate of photosynthesis such as PAR and nutrients constrain IPP and P^b_opt at high latitudes [51,52,53,54,55]. Here, it is postulated that the PAR-based P^b_opt algorithm is more effective in the SSs than the T-based models. The development of a sufficiently effective region-specific model of P^b_opt will make it possible in the future to obtain new estimates of the annual values of IPP in the SSs using satellite-derived data.

Thus, the aims of the present article were: (1) to establish the ranges in variability and the average values of P^b_opt in the SSs; (2) to evaluate the influence of the environmental factors on P^b_opt; and (3) to develop an empirical region-specific model and apply it to describe the spatial distribution in P^b_opt in the SSs using satellite-derived data.

2. Materials and Methods

2.1. Data Sources and Sampling

The field data were obtained in boreal summer (July, August) and autumn (September, October) during 11 cruises in the Siberian Seas (SSs) in 1993, 2007, 2011, and 2013–2020 (

Table 1. Sources for primary production and chlorophyll a measurements included in the dataset for analysis of the variability in the optimal assimilation number, its links with environmental factors, and model development and verification.

Cruise	Months	Years	Location	Number of Stations	Publications
49th Dmitry Mendeleev	August–September	1993	Kara Sea	29	[56]
54th Akademik Mstislav Keldysh	September	2007	Kara Sea	16	[57]
59th Akademik Mstislav Keldysh	September–October	2011	Kara Sea	36	[58]
125th Professor Shtokman	September	2013	Kara Sea	29	[59]
128th Professor Shtokman	August–September	2014	Kara Sea	48	Unpublished data
63d Akademik Mstislav Keldysh	August–October	2015	Kara and Laptev Seas	56	[60]
66th Akademik Mstislav Keldysh	July–August	2016	Kara Sea	55	[61]
69th Akademik Mstislav Keldysh	August–September	2017	Kara, Laptev, and East Siberian Seas	53	[60,62]
72nd Akademik Mstislav Keldysh	August–September	2018	Kara and Laptev Seas	37	[60]
76th Akademik Mstislav Keldysh	July–August	2019	Kara Sea	32	Unpublished data
81st Akademik Mstislav Keldysh	August–September	2020	Kara Sea	28	Unpublished data

). The sampling sites where the measurements of primary production (PP), chlorophyll a concentration (Chl a) of total and size-fractionated phytoplankton, and environmental parameters were performed are shown in Figure 1. At these sites, the calculations of the optimal assimilation number (P^b_opt) were performed. The values of the measured variables are shown in the Supplementary Materials (Table S1).

The sampling depths were defined after a preliminary sounding of temperature, conductivity, and chlorophyll fluorescence using a CTD probe SBE-19 and SBE-32 (Seabird Electronics Inc., Bellevue, WA, USA). Niskin bottles were deployed at the stations to obtain water samples from discrete depths within the upper 100 m layer. Trace metal cleaning procedures (e.g., Teflon-coated covers and springs for the Niskin bottles) [63] were used during all the cruises.

2.2. The Field Data

The methods for determining PP and Chl a are described in detail in previous studies [47,57]. PP was estimated on board using a radiocarbon technique [64] according to simulated in situ approach. Acid-cleaned 160 mL bottles with water samples after the addition of sodium bicarbonate (NaH₁₄CO₃, 0.05 μCi per 1 mL of sample) were placed under neutral lighting filters and exposed for half of a light day in a deck incubator with the seawater temperature maintained at the in situ conditions. The transparency of neutral lighting filters was chosen based on the light exposure conditions at the sampling depths after the sounding of underwater photosynthetically available radiation (PAR). After exposure, the samples were filtered onto a 0.45 μm nitrocellulose membrane “Vladipore” (Vladipore, Vladimir, Russia). After filtration, the samples were treated with 0.1 N HCl and filtered seawater, dried overnight, and placed in a scintillation vial with 10 mL of the scintillation cocktail “Optiphase HiSafe III” (PerkinElmer, Waltham, MA, USA). The radioactivity in the samples was determined after 24 h using a liquid scintillation counter “Triathler” (Hidex, Turku, Finland).

The Chl a concentration was determined using a spectrophotometric method [65,66] or fluorometrically [67,68]. Previous comparisons have shown good agreement between various methods of Chl a determination [69,70]. The PP and Chl a data that were obtained with these methods were used for P^b_opt calculations. The P^b_opt value was determined as the maximal value of the PP to Chl a ratio in the water column.

The intensity of the incident surface irradiance was measured with an LI-190SA (LI-COR) sensor [58,59,60,61,62]. The daily PAR was obtained from integration in the LI-1400 module for five-minute intervals (mol quanta m⁻²) and saved in the internal memory. Underwater irradiance was measured in the following mode. The LI-192SA underwater light sensor, mounted vertically on a cable and in the sounding mode, was moved down to a depth of ∼60–80 m and, at shallow stations, down to the bottom.

Concentrations of silicates (Si(OH)₄), phosphates (PO₄), nitrites (NO₂), nitrates (NO₃), and ammonium (NH₄) were measured using the methods described previously [71,72]. Colourimetric determinations were performed with HACH Lange DR 2800 and LEKI SS2107UV spectrophotometers. Determination of the total alkalinity (Alk) was carried out using the direct titration technique. Calculations of the dissolved CO₂ and concentrations of various forms of dissolved inorganic carbon were performed with the pH-Alk method using thermodynamic equations for the carbon balance with constants for carbonic acid dissociation [72,73].

The values of environmental variables at the depth with P^b_opt were used for statistical analysis. It should be noted that the P^b_opt values were predominantly observed within the upper 0–2 m layer (Table S1).

To determine Chl a and PP of large phytoplankton (>3 μm), samples were successively filtered through a Nucleopore filter with a 3 μm pore size (Reatrack, Obninsk, Russia). Small (<3 μm) Chl a and PP values were obtained by subtracting the large phytoplankton from the total Chl a and PP values [33].

The spatial variability in PP characteristics in the Siberian Seas (SSs) depends mainly on the distribution of river runoff [58,59,60,61,62]. Therefore, it can be assumed that the values of P^b_opt in the areas under the influence of riverine waters and the areas without such impact can be different. Sea surface salinity (S₀) is the indicator of these types of waters (S₀ < 25 and >25, respectively). Thus, the average values of P^b_opt for the regions with S₀ < 25 and >25 were calculated separately. According to [74], the annual average isohaline 25 separates brackish waters and waters with salinity close to oceanic. Water salinity was measured using the Practical Salinity Scale.

2.3. Statistical Analysis

Before calculations, data were log-transformed to achieve normal distribution and for use in the parametrical statistic methods. Then, data were checked for normality using the Kolmogorov–Smirnov test (Figure S1).

The relationships between parameters were tested using linear regression and principal component analysis (PCA). Correspondences between log-transformed variables were estimated using Pearson’s coefficient of correlation (R). A difference between sample means was assessed using Student’s t-test. The null hypothesis was rejected at p < 0.01. Statistical calculations were performed using the Statistica 6.0 software (StatSoft Inc., Tulsa, OK, USA).

2.4. Development and Verification of P^b_opt Models

The entire dataset was randomly divided into two parts. Two-thirds and one-third were used for model development and validation, respectively. The relationships between the measured and modelled P^b_opt estimates were tested using linear regression. The variance in the dependent values was defined by the coefficient of determination (R²). The slope and intercept of the linear regression determined the fitted line according to a 1:1 agreement.

The root-mean-square difference (RMSD) was used to assess the model performance. The RMSD revealed differences between the log-transformed measured and modelled values and comprised both bias (systematic error) and variability (σ—random error) [75,76]. The log-normalised RMSD was used to assess the overall model performance in Primary Productivity Algorithm Round Robins (PPARR) studies [15,17,18,19,21]. The models with lower RMSD have higher skill and vice versa. An RMSD value close to 0.3 indicates model over- or underestimation by a factor of 2. In addition, the mean bias (B) of each model was calculated to assess over- or underestimated P^b_opt.

2.5. Satellite-Derived Data of Photosynthetically Available Radiation (PAR)

Moderate Resolution Imaging Spectroradiometer (MODIS-Aqua) Level 2 data on PAR with 9 × 9 km resolution were obtained from NASA’s Goddard Space Flight Centre (NASA GSFC) (www.oceancolor.gsfc.nasa.gov/ (accessed on 22 August 2022)). Data on PAR were used as a standard product of the MODIS-Aqua scanner [77]. The time period of the satellite data coincided with in situ observations (2007–2020). In situ and satellite data are considered to be matched up on the same day. All the satellite-derived data products were calculated as average values over acceptable nine pixels around a given point (in situ and satellite match-up sites, N = 373 for P^b_opt and N = 322 for PAR). A pixel was considered acceptable if it was without flags of cloudiness or land. The lists of matched-up in situ and satellite data are represented in Tables S2 and S3.

3. Results

3.1. Values and Spatiotemporal Variability in Optimal Assimilation Number (P^b_opt) in the Siberian Seas (SSs) Using Field Observations

The total values of P^b_opt in the SSs changed from 0.11 to 4.67 mgC (mg Chl a)^–1 h^–1. The average values varied from 1.27 ± 0.58 mgC (mg Chl a)^–1 h^–1 in the Laptev Sea to 1.77 ± 0.70 mgC (mg Chl a)^–1 h^–1 in the East Siberian Sea. The average value of P^b_opt in the SSs was 1.38 ± 0.76 mgC (mg Chl a)^–1 h^–1 (

Table 2. The variability in the optimal assimilation number (mgC (mgChl a))^–1 h^–1 of different phytoplankton size groups in the Siberian Seas. M—mean; σ—standard deviation; N—number of data.

Region	Statistics	>3 μm	<3 μm	Total
Kara Sea	M ± σ	1.15 ± 0.59	1.78 ± 1.29	1.37 ± 0.79
	N	60	59	333
Laptev Sea	M ± σ	1.02 ± 0.55	1.30 ± 0.76	1.27 ± 0.58
	N	33	33	59
East Siberian Sea	M ± σ	1.21 ± 0.68	1.33 ± 0.97	1.77 ± 0.70
	N	12	12	19
Siberian Seas	M ± σ	1.05 ± 0.58	1.65 ± 1.24	1.38 ± 0.76
	N	105	104	411

).

The range of P^b_opt variability in large phytoplankton (>3 μm) (P^b_{opt L}) was 0.23–3.54 mgC (mg Chl a)^–1 h^–1. The average values of P^b_{opt L} varied insignificantly from 1.02 ± 0.55 mgC (mg Chl a)^–1 h^–1 in the Laptev Sea to 1.21 ± 0.68 mgC (mg Chl a)^–1 h^–1 in the East Siberian Sea (Table 2). The total values of P^b_opt for small phytoplankton (<3 μm) (P^b_{opt S}) were more variable than P^b_{opt L} and changed from 0.03 to 6.38 mgC (mg Chl a)^–1 h^–1. The average value of P^b_{opt S} was the highest in the Kara Sea (1.78 ± 1.29 mgC (mg Chl a)^–1 h^–1), and it was the lowest in the Laptev Sea (1.30 ± 0.76 mgC (mg Chl a)^–1 h^–1). The average value of P^b_{opt S} in the SSs was 1.6-fold higher than P^b_{opt L} (Table 2). The difference between the average values of P^b_{opt S} and P^b_{opt L} was statistically significant (Student’s t-test, p < 0.01).

The difference between the average values of P^b_opt, P^b_{opt L}, and P^b_{opt S} in the river runoff regions with surface salinity (S₀) < 25 and in the areas out of the river’s influence (S₀ > 25) was statistically insignificant. In addition, the seasonal average values of P^b_opt, P^b_{opt L}, and P^b_{opt S} in these regions differentiated slightly (

Table 3. The optimal assimilation number (mgC (mgChl a))^–1 h^–1 of different phytoplankton size groups within the different salinity ranges and seasons. S₀—sea surface salinity; M—mean; σ—standard deviation; N—number of data.

Range of S0	Season	Statistics	Phytoplankton Size Fractions
			>3 μm		<3 μm		Total
<25	Summer (July, August)	M ± σ	1.26 ± 0.43	1.10 ± 0.52	2.60 ± 1.96	1.73 ± 1.40	1.72 ± 0.48	1.35 ± 0.64
		N	3		3		41
	Autumn (September, October)	M ± σ	1.07 ± 0.54		1.60 ± 1.32		1.22 ± 0.57
		N	21		21		117
>25	Summer (July, August)	M ± σ	1.13 ± 0.66	1.04 ± 0.60	1.99 ± 1.42	1.63 ± 1.19	1.81 ± 0.88	1.40 ± 0.84
		N	35		35		110
	Autumn (September, October)	M ± σ	0.97 ± 0.54		1.35 ± 0.90		1.08 ± 0.64
		N	46		45		143

).

In the summer, the average values of P^b_opt exceeded those in the autumn over the regions with S₀ < 25 and S₀ > 25 by factors of 1.4 and 1.7, respectively. These differences were statistically significant (Student’s t-test, p < 0.01). In the summer, the average values of P^b_opt for different size fractions of phytoplankton were higher than in the autumn both in the brackish and in the oceanic waters (Table 3). It should be noted that the difference was statistically significant only for P^b_{opt S} at S₀ > 25. The monthly average values of P^b_opt decreased during the growing season from 1.95 mgC (mg Chl a)^–1 h^–1 in July to 0.64 mgC (mg Chl a)^–1 h^–1 in October following the monthly average values of subsurface photosynthetically available radiation (PAR) (E₀) and sea surface temperature (T₀) (Figure 2).

3.2. The Relationships between P^b_opt and Environmental Factors

The relationships between P^b_opt and environmental factors in different seasons are shown in Figure 3. The results of the correlation analysis are represented in

Table 4. The correlation matrix between the log-transformed optimal assimilation numbers for different phytoplankton size groups and environmental variables. P^b_opt—optimal assimilation number of the total phytoplankton; P^b_{opt L}—optimal assimilation number of large phytoplankton (>3 μm); P^b_{opt S}—optimal assimilation number of small phytoplankton (<3 μm); R—coefficient of correlation; p value—statistical significance of R; N—the number of data. T₀—sea surface temperature; S₀—sea surface salinity; PO₄, Si(OH)₄, and DIN–surface concentrations of phosphates, dissolved silicon, and dissolved inorganic nitrogen, respectively; Chl₀—chlorophyll a concentration of the surface total phytoplankton; Chl_S—chlorophyll a concentration of surface small (<3 μm) phytoplankton; E₀—subsurface photosynthetically available radiation. The asterisks indicate significant correlations (p < 0.05).

Parameter	Statistics	T0	S0	Chl0	ChlS/Chl0	E0	PO4	Si(OH)4	DIN
Pbopt	R	0.08	0.08	−0.21 *	0.23 *	0.61 *	−0.02	0.10	−0.20 *
	N	411	408	411	104	395	404	410	387
	p	0.109	0.092	<10−3	0.020	<10−2	0.723	0.12	<10−3
Pbopt L	R	0.20 *	0.07	0.01	0.26*	0.08	0.14	0.16	0.13
	N	105	105	105	104	105	104	104	98
	p	0.04	0.468	0.947	0.008	0.394	0.154	0.106	0.201
Pbopt S	R	0.07	−0.04	0.12	−0.09	0.24 *	−0.11	−0.05	−0.05
	N	104	104	104	103	104	103	103	97
	p	0.457	0.652	0.208	0.379	0.014	0.291	0.594	0.596

. The statistically significant positive link with a high coefficient of correlation (R = 0.61) was established between P^b_opt and E₀. There were weak links between P^b_opt and the other environmental variables (Table 4).

The relationships between different abiotic factors are characterised by multicollinearity (

Table 5. The correlation matrix between the log-transformed values of environmental variables. R—coefficient of correlation; p value—statistical significance of R; N—the number of data. T₀—surface water temperature; S₀—surface salinity; PO₄, Si(OH)₄ and DIN—surface concentrations of phosphates, dissolved silicon, and dissolved inorganic nitrogen, respectively; Chl₀—surface chlorophyll a concentration; E₀—subsurface PAR. The asterisks indicate significant correlations (p < 0.05).

Parameter	Statistics	T0	S0	Chl0	E0	PO4	Si(OH)4	DIN
T	R	1.00
	N	411
	p	<10−3
S0	R	−0.22 *	1.00
	N	408	408
	p	<10−3	<10−3
Chl0	R	0.30 *	−0.61 *	1.00
	N	411	408	411
	p	<10−3	<10−2	<10−3
E0	R	0.11 *	0.07	−0.20 *	1.00
	N	395	392	395	395
	p	0.036	0.163	<10−3	<10−3
PO4	R	−0.14 *	−0.21 *	0.19 *	−0.06	1.00
	N	404	401	404	388	404
	p	0.006	<10−3	<10−3	0.232	<10−3
Si(OH)4	R	0.21 *	−0.52 *	0.67 *	−0.04	0.35 *	1.00
	N	410	407	410	394	404	410
	p	<10−3	<10−2	<10−2	0.473	<10−3	<10−3
DIN	R	−0.11 *	−0.20 *	0.28 *	−0.23 *	0.28 *	0.25 *	1.00
	N	387	384	387	377	385	387	387
	p	0.027	<10−3	<10−3	<10−3	<10−3	<10−3	<10−3

), which leads to uncertainty in the estimations of its influence on P^b_opt. Principal component analysis (PCA) allows a reduction in the multicollinearity effect. PCA also generates an ordination diagram that illustrates links between P^b_opt and environmental factors.

The results of PCA, which are presented in Figure 4, suggest that the main variables that contribute to the first principal component (PC1) are the abiotic factors S₀, Si(OH)₄, and Chl₀. PC1 describes 29.4% of the total variance. The second principal component (PC2) includes the main variables of P^b_opt and E₀ and describes 21.8% of the total variance (Figure 4a).

The PCA analysis illustrates the well-pronounced positive relation between P^b_opt and E₀ that is indicated by the same direction of their vectors on the factorial plane. Similar to the correlation analysis, the results of the PCA show that P^b_opt is weakly linked with salinity and Si(OH)₄ as indicators of riverine waters. This is indicated by their orthogonality on the PCA map. Furthermore, the weak relationships between P^b_opt and surface temperature and nutrients were shown by the PCA results (Figure 4a).

The contribution of PC1 and PC2 to the individual samples is shown on the factorial plane (Figure 4b). For visibility, all samples were divided according to the range in salinity. Figure 4b shows that the individual samples collected at different salinity were strongly divided. Samples at S₀ < 25 and S₀ > 25 were, respectively, positively and negatively influenced by PC1, while the influence of PC2 was rather equal. This finding suggests that there are no differences between the links of P^b_opt with E₀ across the salinity gradient.

3.3. P^b_opt Model Developed with E₀, Its Efficiency, and a Comparison with T-Based Models

It was mentioned above that a strong correlation was obtained between P^b_opt and E₀ (Table 4). There was no other abiotic parameter that was related to P^b_opt so closely. Thus, it is reasonable to use E₀ as the only abiotic factor in the P^b_opt region-specific regression model (E_0reg). To develop this model, we used two-thirds of the dataset as mentioned in [50]. The equation of liner regression relating log-transformed values of P^b_opt and E₀ is

log₁₀ P^b_opt = 0.537 log₁₀ E₀ − 0.399 (R = 0.62, N = 266)

(1)

The results of E_0reg verification using field observations are represented in

Table 6. Regression statistics and performance indices for the log-transformed measured and modelled optimal assimilation number (P^b_opt). Slope and intercept are parameters of the linear regressions; R²—coefficient of determination; N—number of data used for model validation; p-value indicates the significance level of each regression. Indices are the mean model bias (B), the standard deviation of the log-transformed modelled values of P^b_opt (σ), and the root-mean-square difference (RMSD); E_0reg—the region-specific P^b_opt model developed using subsurface photosynthetically available radiation (PAR) and verified with field data. BF-model—the P^b_opt model developed by Behrenfeld and Falkowski [13]. T_reg—the region-specific P^b_opt model developed using the relationship between P^b_opt and sea surface temperature. E_sat—E_0reg verified with satellite-derived data of PAR.

Model	Regression Statistics					Performance Indices
	Slope	Intercept	R2	N	p Value	B	σ	RMSD
E0reg	0.697	0.879	0.35	131	<0.05	0.040	0.176	0.227
BF-model	0.060	0.405	0.02	410	<0.05	0.343	0.409	0.444
Treg	0.036	0.115	0.03	137	<0.05	0.066	0.055	0.279
Esat	0.289	0.226	0.19	373	<0.05	0.183	0.190	0.321

and Figure 5a. The comparison of the measured and modelled values of P^b_opt suggests that E_0reg overestimates the field data on average (the average absolute error (B) is equal to 0.040). The root-mean-square difference (RMSD) value implies that the calculated values of P^b_opt were 1.7-fold higher than the field data on average.

The application of the developed algorithm to study the spatiotemporal variations in P^b_opt and for water column primary production (IPP) estimations assumes the introduction of satellite-derived PAR (E_sat) into Equation (1). Therefore, it is appropriate to validate the E_0reg model using satellite-derived data. The results represented in Table 6 and Figure 5b suggest that the application of E_sat decreases the model performance by a factor of 1.4 according to the RMSD value. The correlation between the measured and modelled values of P^b_opt decreased by a factor of 1.8 in comparison with the data of verification using field observations (R² = 0.19 and 0.35, respectively) (Table 6). Furthermore, the introduction of E_sat into Equation (1) enhanced B by a factor of 4.6.

In the models used for IPP estimation using satellite-derived data, often P^b_opt is retrieved with the polynomial function derived using the worldwide dataset (Equation (11) in [13], the BF model in further) or with the regional-adopted relationships between P^b_opt and T₀ [25,78,79]. In that regard, it is useful to compare the model performances of the BF model and E_0reg for the estimation of their skill in the SSs. Figure 6a presents the distribution of the P^b_opt dataset related to T₀ and the curve of the polynomial function that links P^b_opt and T₀ from [13]. The result presented in Figure 6a implies that the BF model will dramatically overestimate P^b_opt in the SSs. This conclusion is confirmed with the results of the verification of the BF model using the T₀ dataset collected in the SSs (Table 6, Figure 6b). The value of B characterising the error in the BF model is equal to 0.343, which is 9.5-fold higher than that of E_0reg. The coefficient of determination (R²) of the BF model is 17-fold lower than that of E_0reg (0.35 and 0.02, respectively). The value of RMSD of the BF model is 1.9-fold higher than that of E_0reg (Table 6). The index of efficiency of the BF model (RMSD = 0.444) suggests that P^b_opt values calculated using this algorithm can over- or underestimate the measured ones by a factor of 2.8, which is 1.6-fold higher than in the case of E_0reg application.

To illustrate the problems connected with the estimation of P^b_opt in the SSs using T₀ solely, the authors developed the region-specific empirical algorithm based on the relationship between P^b_opt and T₀ established using the SSs dataset (N = 266) (T_reg). In the development of this model, the authors followed the approach described in [13]. The median values of P^b_opt were calculated for each 1 °C temperature span in the range from 0 to 18 °C. The relationship between the median values of P^b_opt and T₀ was described using the exponential function (Figure 6a):

P^b_opt = 1.07 e ^{0.044 T₀}.

(2)

This model was validated with the independent dataset (data that were not used for model development). The results of this verification are presented in Table 6 and Figure 6c. As in the case of applying the BF model, weak links between the measured and modelled values of P^b_opt (R² = 0.03) were observed. The value of RMSD that was equal to 0.279 suggests that the modelled values of P^b_opt can 1.9-fold over- or underestimate the measured ones. The average absolute error of T_reg was equal to 0.066, which was 1.8-fold higher than in the case of E_0reg application. Thus, it can be concluded that the T_reg algorithm is not applicable for P^b_opt estimation in the SSs.

3.4. The Spatial Distribution in P^b_opt Assessed Using Satellite-Derived Data

The introduction of E_sat data into Equation (1) allows retrieving the pattern of the spatial distribution in P^b_opt over the entire area of the SSs. In Figure 7, satellite climatologies (2007–2020) of P^b_opt from July to October are presented. It should be noted that for averaging, the years were chosen that coincided with the field observations (Table 1). As expected, the spatial distribution of P^b_opt was quasi-latitudinal and follows by the spatial distribution in PAR. The values of P^b_opt basically decreased northward (Figure 7).

4. Discussion

4.1. The Average Values and Spatiotemporal Variations in the Optimal Assimilation Number (P^b_opt) in the Siberian Seas (SSs)

The average value of P^b_opt in the SSs (1.38 mgC (mg Chl a^–1 h^–1) was in the range of variability observed in the north of Baffin Bay (0.3–4.1 mgC (mg Chl a^–1 h^–1) [80]. In addition, it was close to the values measured in the Chukchi and Beaufort Seas (from 0.6 to 1 mgC (mg Chl a^–1 h^–1, on average) [81], and it was higher than historical (1956, 1961–1963) values observed in the Canadian Arctic (0.2–0.4 mgC (mg Chl a^–1 h^–1) [82]. It is known that an accurate as possible calculation of the average value of P^b_opt within a particular biogeochemical province [48] is critically important for the estimation of water column primary production (IPP) [21].

The average values of P^b_opt for small (<3 μm) phytoplankton were higher than those for large (>3 μm) phytoplankton in the entire SS (Table 2). This finding is consistent with the investigations that established that the chlorophyll-specific carbon fixation rate declined with a decrease in cell sizes [83,84,85,86,87]. Theoretically, the specific photosynthetic rate of small phytoplankton must be higher than that of the large fraction because of the high size-to-volume ratio that allow it to be more effective at absorbing light and nutrients. As a result, small cells have advantages in conditions of low nutrients and irradiance [34,88,89]. This assumption is confirmed with the analysis of extensive field and laboratory data [90].

The river runoff on the Siberian shelf controversially influences primary production (PP) characteristics. On the one hand, a large amount of dissolved (DOM) and particulate (POM) organic matter of river genesis limits the photosynthetic rate in the water column by decreasing water transparency and euphotic depth as a consequence [47]. On the other hand, large rivers enrich the coastal areas of the SSs with nutrients [37,38], increasing the photosynthetic capacity of phytoplankton. Thus, it can be assumed the differences in the values of P^b_opt between the river runoff regions and those where the influence of rivers is insignificant. Nevertheless, there were no statistically significant differences between the average values of P^b_opt in brackish, with surface salinity (S₀) < 25, and oceanic waters (S₀ > 25). Thus, it can be concluded that P^b_opt in the SSs is influenced by river runoff to a small extent.

To evaluate the relationships between P^b_opt and environmental factors in waters with different salinity, the dataset was differentiated according to the S₀ values (

Table 7. The correlation matrix between the log-transformed optimal assimilation number and environmental variables in the areas with S₀ < 25 and S₀ > 25. P^b_opt—optimal assimilation number of the total phytoplankton; R—coefficient of correlation; p-value—statistical significance of R; N—the number of data; T₀—sea surface temperature; S₀—sea surface salinity; PO₄, Si(OH)₄, and DIN—surface concentrations of phosphates, dissolved silicon, and dissolved inorganic nitrogen, respectively; Chl₀—chlorophyll a concentration of the surface total phytoplankton; E₀—subsurface photosynthetically available radiation. The asterisks indicate significant correlations (p < 0.05).

Parameter	Statistics	T0	S0	Chl0	E0	PO4	Si(OH)4	DIN
Pbopt S0 < 25	R	0.24 *	0.21 *	−0.10	0.59 *	−0.09	0.19 *	−0.24 *
	N	159	156	159	150	154	158	147
	p	0.003	0.009	0.211	<10−3	0.284	0.020	0.003
Pbopt S0 > 25	R	0.02	−0.11	−0.41 *	0.63 *	0.02	0.06	−0.19 *
	N	245	254	254	247	252	254	242
	p	0.713	0.075	<10−3	<10−2	0.696	0.376	0.002

). The results of the correlation analysis suggest that the links between P^b_opt and E₀ were not significantly different in brackish and oceanic waters (R = 0.59 and 0.63, respectively). Thus, these findings suggest that the developed P^b_opt algorithm can be used as universal both in the river runoff regions of the SSs and in the areas out of such influence.

A decrease in P^b_opt from July to October is explained by a decline in the values of the main environmental factors, generally subsurface photosynthetically available radiation (PAR) (Figure 2). Similarly, the tendency toward a decrease in P^b_opt at the end of the growing season was noted in other regions of the Arctic Ocean [80].

4.2. Influence of Environmental Factors on P^b_opt

In theory, the relationships between P^b_opt, as well as the maximal assimilation number (P^b_max), and the main environmental factors must be the same. Therefore, in this section, it is meaningful to discuss the relationships between environmental factors and both P^b_opt and P^b_max due to the most representation of the latter.

4.2.1. Influence of PAR on P^b_opt

The results obtained in this study allow us to characterise the SSs phytoplankton, on the one hand, as highly photoadaptive and, on the other hand, as light-limited. The strong correlation between P^b_opt and PAR is evidence that day-to-day variations in incident radiation have a fast influence on changes in carbon fixation rate. Thus, the SS phytoplankton is capable of fast photoadaptation. In earlier studies, it was shown that in the Arctic Ocean, the assimilation number (P^b) linearly and positively depended on PAR [47,53,91,92]. The absence of a “plateau” on the curves of the relationships between P^b and PAR implies that arctic phytoplankton is light-limited. For that reason, the values of P^b_opt are usually registered under saturated irradiance.

Often, the values of P^b_opt are observed within the upper mixed layer (UML). Therefore, some authors considered the links of P^b_opt with the average values of PAR in the UML (E_UML) [50]. The findings of the present study suggest that in the SSs, P^b_opt was better correlated with subsurface PAR (E₀) (R = 0.61, p < 0.01, N = 397) than with E_UML (R = 0.54, p < 0.01, N = 397). This result can be explained by the fact that in 97% of cases, the highest values of P^b_opt were observed in the subsurface layer of 0–2 m (P^b₀), and a strong positive correlation was established between the log-transformed values of P^b_opt and P^b₀ (Figure 8). Observation of P^b_opt predominantly in the subsurface layer suggests a more pronounced light limitation of the photosynthetic rate in the SSs in comparison with other regions of the Arctic Ocean where P^b_opt can be registered at the depths of the deep maxima of chlorophyll and PP [81]. This phenomenon is linked with the optically complex type of waters in the SSs [93] enriched by DOM and POM of river genesis [37,94,95,96].

4.2.2. Influence of Temperature and Nutrients on P^b_opt

Generally, a weak correlation has been noted in the Arctic Ocean between P^b and temperature [97,98,99,100]. Furthermore, it was established by [101] that the photosynthetic parameters in the Arctic Ocean were not influenced by temperature over the range from −2 to 8 °C. In the dataset used in the presented study, 90% of the values of T₀ fit in this diapason (Table S1). Thus, our findings are consistent with the outcomes of the previous studies.

The absence of a close relationship between P^b_opt and T₀ was explained simultaneously by a negative correlation between T₀ and nutrients and a positive correlation between T₀ and E₀ [83,102]. In accordance with those findings, the authors registered in the SSs significant, but weak, relationships between T₀ and the concentration of dissolved inorganic nitrogen (DIN) and between T₀ and E₀ (Table 5). This result can be explained by a mismatch of seasonal maxima in T₀, DIN, and E₀ in the SSs. High values of T₀ and E₀ are observed in July and August when nutrients are exhausted [103].

The role of nutrients in PP in the Arctic Ocean is well known [51,52,104]. On the other hand, it is difficult to establish close links between PP characteristics and nutrient concentration [32,47,98,105]. There are many reasons for that. A low nutrient concentration very often is not evidence of a low increment in phytoplankton biomass due to grazing by zooplankton, as well as cell death and sedimentation [106]. Moreover, the enrichment in UML by nutrients during the winter convection usually does not coincide with the high values of P^b registered during the phytoplankton bloom in spring. Furthermore, in conditions of high nutrients, the photosynthetic rate can decrease because of energetic competition between the DIN assimilation process and the Calvin cycle [107]. On the other hand, during the limitation of nutrients, phytoplankton can use dissolved organic nitrogen for growth and photosynthesis [108,109] and keep a relatively high photosynthetic rate.

All the reasons listed above can lead to unpredictable, positive or negative, relationships between productivity parameters and nutrients. In the present study, a statistically significant but weak correlation was found only between P^b_opt and DIN (Table 4). The negative relationship between P^b_opt and DIN is determined by the spatial distribution in surface nutrients in the SSs. Thus, the main source of nutrients in the inner shelf of the SSs is the river discharge [37,38]. In these areas, an increase in nutrient concentration is accompanied by a high Chl a content. In turn, the negative correlation between P^b_opt and Chl a (R = –0.21, p < 10^–3, N = 411) (Table 4) to a high extent determines the opposite link between P^b_opt and DIN.

4.2.3. Modelling of P^b_opt and Its Application for Remote Sensing

The results of the correlation analysis and PCA suggest that light is the main environmental factor that constrains the assimilation activity of phytoplankton in the SSs (Figure 4, Table 4). The variability in E₀ explained 37% of P^b_opt variations (R² = 0.37). Therefore, it can be assumed that E₀ can be used as a single input variable to the empirical model of P^b_opt.

A weak correlation between P^b_opt and T₀ does not allow for using the latter parameter as a predictor of the assimilation activity of phytoplankton in the SSs. In the present article, it was revealed that the application of the dependence between P^b_opt and T₀ for the World Ocean [13] led to a significant error in the calculations of P^b_opt in the SSs (Table 6). Using the region-specific relationship between P^b_opt and T₀ did not improve the predictive capacity of the temperature-based model. Thus, according to the authors’ dataset, the empirical formula (1) is the best approximation of P^b_opt, and it can be used for the calculation of this parameter using satellite-derived E₀ (E_sat).

As was mentioned above, using E_sat as an input variable decreased the efficiency of the developed model (1). This result was connected with the errors in E_sat determination [77,110]. To estimate this error, a comparison of the field data of E₀ with matched-up in space and time values of E_sat obtained by a MODIS-Aqua scanner was carried out. The results of this comparison suggest that the values of E_sat overestimate the field observations (Figure 9). As a consequence, the calculations of P^b_opt using E_sat also were overestimated in comparison with the field data as evidenced by the positive bias of linear regression (Table 6).

Another approach to the estimation of P^b_opt is the application of T₀ and Chl₀, also registered using a satellite scanner, as additional input variables in the model [50]. To verify whether model predictive capacity improves after using T₀ and Chl₀ together with E₀, the equation of multiple regression linking the log-transformed values of these variables with P^b_opt was obtained as:

log₁₀ P^b_opt = 0.512 log₁₀ E₀ + 0.015 log₁₀ T₀ − 0.070 log₁₀ Chl₀ − 0.408 (R = 0.64, N = 266).

(3)

The verification of the developed model (3) suggests that the input of T₀ and Chl₀ to the calculations does not improve the model skill in comparison with E_0reg (Table 6). The main parameters of model efficiency were as follows: R² = 0.34, RMSD = 0.228. Thus, according to the authors’ findings, it is sufficient to use only E₀ in the P^b_opt model as the most relevant abiotic parameter.

The tendency of the latitudinal distribution in P^b_opt in the SSs obtained using the Equation (1) with E_sat as an input variable (Figure 7) was consistent with the global distribution in P^b_m according to [50]. In that study, where the spatial distribution in the assimilation number was assessed using PAR, temperature, and chlorophyll a concentration, the values of P^b_m also decreased poleward (Figure 8 in [50]).

5. Conclusions

One objective of the present study was to develop a simple algorithm for P^b_opt estimation that would be useful to evaluate in future IPP in the Siberian Seas (SSs) using chlorophyll-based models and satellite observations. For this purpose, it was needed to choose an environmental parameter that would be most closely linked with P^b_opt and easily detected from space. The analysis of the dataset used in this article suggests that incident PAR is the required variable because its role in the variability in P^b_opt is dominant.

In the present article, it is shown that the commonly used algorithm for the calculation of the optimal assimilation number (P^b_opt) based on sea surface temperature (T₀) registered using a satellite is badly applicable for phytoplankton of high latitudes, in particular, in the SSs. As a consequence, the application of the dependence linking P^b_opt with T₀ must lead to errors in the estimation of the annual value of water column primary production (IPP) using chlorophyll-based models and satellite-derived data. The findings of this study suggest that the application of photosynthetically available radiation can be sufficient for the adequate estimation of P^b_opt in light-limited regions. The main practical result of this study is the developed empirical region-specific algorithm of P^b_opt, which can be used in the future for IPP estimation in the Arctic Ocean.