Photoacclimation by phytoplankton determines the distribution of global subsurface chlorophyll maxima in the ocean

Physical model

The physical part of the model is a global Oceanic General Circulation Model, Meteorological Research Institute Community Ocean Model version 3 (MRI.COM3)⁴⁰. The model has horizontal resolutions of 1° in longitude and 0.5° in latitude south of 64° N, and tripolar coordinates are applied north of 64° N. The model is discretized in 51 vertical layers. In the upper 160 m, tracers are calculated at depths of 2.0, 6.5, 12.25, 19.25, 27.5, 37.75, 50.5, 65.5, 82.25, 100.0, 118.2, 137.5, and 157.75 m, and therefore vertical variation in chlorophyll concentration below the grid-scale is not represented in our model. The model was forced with realistic wind stress, surface heat and freshwater fluxes⁴⁰.

Marine ecosystem model

We developed a marine ecosystem model composed of phytoplankton, zooplankton, nitrate, ammonia, particulate organic nitrogen, dissolved organic nitrogen, dissolved iron (Fe_d), and particulate iron. Our model is a 3D version of the FlexPFT model²⁷ and is called the FlexPFT-3D model. The main changes of the FlexPFT-3D from original FlexPFT model are the introduction of iron limitation and substitution of the carbon-based phytoplankton biomass in the original with nitrogen-based biomass herein. The iron cycle is based on the nitrogen-, silicon- and iron-regulated Marine Ecosystem Model⁴¹ including the process of scavenging and iron input from dust and sediment. Dissolved iron starts from the distribution calculated by the Biological Elemental Cycling model in Misumi et al.⁴². Nitrate starts from the distribution of World Ocean Database 1998⁴³. After the connection of the physical model, a 20 years of historical simulation (1985–2004) is performed. In addition to the standard case with the chlorophyll-specific initial slope of growth versus irradiance, a_I, of 0.35 m² E⁻¹ mol C (g chl)⁻¹, the case studies with a_I of 0.5 and 1.0 m² E⁻¹ mol C (g chl)⁻¹ were implemented. The case studies are calculated from 2003 to 2004, starting from the distributions of biological variables at the end of 2002 in the standard case.

Phytoplankton growth

The procedures of numerical integration of phytoplankton concentration are described here. Readers can construct a numerical model using the following equations. The derivations of the following equations from theories are presented by Smith et al.²⁷ (hereafter Smith2016). Values of biological parameters are described in Supplementary Table 1.

In accordance with Pahlow’s resource allocation theory²⁸, the FlexPFT model assumes that resources are allocated among structural material, nutrient uptake and, light harvesting (Supplementary Fig. 1a). The fraction of structural material is assumed to be Q_s/Q, where Q is the nitrogen cell quota, which is the intracellular nitrogen to carbon ratio (mol N mol C⁻¹), and Q_s is the structural cell quota (mol N mol C⁻¹) given as a fixed parameter. The fraction of nutrient uptake is defined as f_V (non-dimensional), so that the residual fraction available for light-harvesting is equal to ((1-frac{{Q}_{{rm{s}}}}{Q}-{f}_{{rm{v}}})). Optimal uptake kinetics further sub-divides the resources allocated to nutrient uptake between surface uptake sites (affinity) and enzymes for assimilation (maximum uptake rate), the fraction of which is given by f_A and (1 − f_A), respectively. Under nutrient-deficient conditions, the number of surface uptake sites (and hence affinity) increases, while enzyme concentration (hence, maximum uptake rate) decreases. The FlexPFT model assumes instantaneous resource allocation, which means that resource allocation tracks temporal environmental change with no lag time. It has elsewhere been demonstrated that an instantaneous acclimation model provides an accurate approximation of a fully dynamic acclimation model⁴⁴.

We assume that acclimation responds to daily-averaged environmental conditions, which are used to calculate the optimal values of f_V, f_A, and Q as ({f}_{V}^{o}), ({f}_{A}^{o}), and ({Q}^{o}). The optimal values are estimated at the beginning of a day and are retained for the following 24 h. The daily-averaged environmental variables of the seawater temperature, T (°C), intensity of photosynthetically active radiation, I, nitrogen concentration, [N], which is the sum of nitrate and ammonia concentrations, and dissolved iron concentration, [Fe_d] are defined as (bar{T}), (bar{I}), ([bar{{rm{N}}}]), and ([{overline{{rm{Fe}}}}_{{rm{d}}}]), respectively. Based on the assumption that diurnal variation of temperature and nutrient are very small, T, [N] and [Fe_d] at the beginning of a day are used as (bar{T}), ([bar{{rm{N}}}]), and ([{overline{{rm{Fe}}}}_{{rm{d}}}]), respectively. For (bar{I}), we use the average in sunshine duration in a day, which is slightly modified from the daily average in Smith2016.

Phytoplankton growth rate per unit carbon biomass (day⁻¹), μ, is given by

where ({hat{mu }}^{I}) is the potential carbon fixation rate per unit carbon biomass (day⁻¹), ({zeta }^{N}) is the energetic respiratory cost of assimilating inorganic nitrogen (0.6 mol C mol N⁻¹), and ({hat{V}}^{N}) is the potential nitrogen uptake rate per unit carbon biomass (mol N mol C⁻¹ day⁻¹). Equation (1) represents the balance of net carbon fixation and respiration costs of nitrogen uptake, which are proportional to the fraction of resource allocation. ({hat{V}}^{N}([bar{{rm{N}}}],,bar{T})) is

where ({hat{A}}_{0}) and ({hat{V}}_{0}) are the maximum value of affinity and maximum nitrogen uptake rate.

From here, we will explain how the optimized values such as ({f}_{V}^{o}), ({f}_{A}^{o}), and ({Q}^{o}) are calculated. The optimal fraction of resource allocation to affinity, ({f}_{A}^{o}), is given by

which is derived by substituting Eqs. (18) and (19) in Smith2016 into Eq. (17). (F(bar{T})) is temperature dependence, defined as

where E_a is the parameter of the activation energy of 4.8 × 10⁴ J mol⁻¹, R is the gas constant of 8.3145 J (mol K)⁻¹, and T_ref is the reference temperature of 20 °C.

Optimization for light-harvesting is described below. The potential carbon fixation rate per unit carbon biomass (day⁻¹), ({hat{mu }}^{I},)(day⁻¹), in Eq. (1) is

where ({hat{mu }}_{0}) and k_Fe are the maximum carbon fixation rate and half saturation constant for iron, respectively. S specifies the dependence of light. Defining ({hat{mu }}_{0}^{{rm{limFe}}}={hat{mu }}_{0}frac{[{overline{{rm{Fe}}}}_{{rm{d}}}]}{[{overline{{rm{Fe}}}}_{{rm{d}}}]+{k}_{{rm{Fe}}}}),

Iron limitation is imposed by substituting ({hat{mu }}_{0}) to ({hat{mu }}_{0}^{{rm{limFe}}}) in all equations in Smith2016. S is defined as

where ({a}_{I}) is the chlorophyll-specific initial slope of growth versus irradiance. ({hat{Theta }}^{o}), optimal chloroplast chl:phyC (g chl (mol C)⁻¹), is

where constant parameters ({{rm{zeta }}}^{{rm{chl}}}) and ({R}_{M}^{{rm{chl}}}) are the respiratory cost of photosynthesis (mol C (g chl)⁻¹) and the loss rate of chlorophyll (day⁻¹), respectively. L_d is the fractional day length in 24 h. W₀ is the zero-branch of Lambert’s W function. I₀ is the threshold irradiance below which the respiratory costs overweight the benefits of producing chlorophyll:

The optimal fraction of resource allocation to nutrient uptake, ({f}_{V}^{o}), is

The optimal nitrogen cell quota, ({Q}^{o}) is

Optimal cellular chl:phyC (g chl (mol C)⁻¹), ({Theta }^{o}), is

which is the multiplication of the fraction of resource allocation to light-harvesting and optimal chloroplast chl:phyC. The cellular chl:phyC and chloroplast chl:phyC in Figs. 1 and 2 are optimal cellular chl:phyC, ({Theta }^{o}), and optimal chloroplast chl:phyC, ({hat{Theta }}^{o}), respectively. The relation in Eq. (12) is displayed in Fig. 1i-n. If we artificially turn off the optimization of resource allocation by applying the constant ({Q}^{o}) and ({f}_{V}^{o}) to the all grid points, optimal cellular chl:phyC (Fig. 1i,j) only depends on optimal chloroplast chl:phyC (Fig. 1k, l), and therefore significant variation of SCM depth across the equatorial, subtropical, and subpolar regions is not reproduced.

In the above equations, Eqs. (3), (8), (10), (11), and (12), optimized values related to acclimation processes are obtained and then used in calculating the phytoplankton growth rate. Phytoplankton growth rate per unit carbon biomass (day⁻¹), (mu), in Eq. (1) is calculated at each time step:

where ({hat{mu }}^{I}(I,,T,,[{{rm{Fe}}}_{{rm{d}}}])) is obtained by substituting I, T, and [Fe_d] for (bar{I}), (bar{{rm{T}}}), and ([{overline{{rm{Fe}}}}_{{rm{d}}}]) in Eq. (5), respectively. Note that the model calculates circadian variation in solar irradiance, I, and therefore the phytoplankton growth rate, μ, reaches its maximum at noon local time and is zero during night. On the other hand, phytoplankton optimization is assumed to respond to daily-averaged conditions. The FlexPFT model introduces phytoplankton respiration proportional to chlorophyll content, which is another important originality of Pahlow’s resource allocation theory^30,33.

The carbon biomass-specific respiratory costs of maintaining chlorophyll, R^chl, is

The growth rate per unit nitrogen biomass, ({mu }_{{rm{N}}}), is equal to that per unit carbon biomass, μ. Instantaneous acclimation assumes that the quota of nitrogen to carbon biomass obtained by phytoplankton growth is equal to the nitrogen quota in a cell: (frac{{mu }_{{rm{N}}}[{{rm{p}}}^{{rm{N}}}]}{mu [{{rm{p}}}^{{rm{C}}}]}={Q}^{o}), where [p^C] and [p^N] are phytoplankton carbon and nitrogen concentration in a cell, respectively. Since (frac{[{{rm{p}}}^{{rm{N}}}]}{[{{rm{p}}}^{C}]}={Q}^{o}), ({mu }_{{rm{N}}}=mu). When temporal ({Q}^{o}) change occurs, to satisfy the mass conservation, carbon or nitrogen biomass is adjusted with the other fixed. The FlexPFT fixes carbon biomass, while the FlexPFT-3D fixes nitrogen biomass to the temporal ({Q}^{o}) change.

The rate of change in the phytoplankton nitrogen concentration, [p^N], except for the advection and diffusion terms is given by the following equation:

where R^cnst and M_p are the coefficient of respiration not related to chlorophyll concentration and mortality rate coefficient, respectively. The extracellular excretion is

where ({gamma }_{{rm{ex}}}) is the coefficient of extracellular excretion. The grazing term is represented by

where G_20deg is the maximum grazing rate at 20 °C, and [z^N] is zooplankton concentration. Temperature dependency, F(T), is obtained by substituting T for (bar{T}) in Eq. (4). ({a}_{{rm{H}}}) is the parameter controlling Holling-type grazing, which takes a value from 1 to 2. k_H is the grazing coefficient in Holling-type grazing.

Once [p^N] is calculated, phytoplankton carbon concentration (mol C L⁻¹), and chlorophyll concentration (g chl L⁻¹) are uniquely determined in an environmental condition, without prognostic calculation. Therefore, an instantaneous acclimation model can represent stoichiometric flexibility with lower computational costs compared with a dynamic acclimation model⁴⁴.

Model validation

The spatial pattern of simulated annually mean chlorophyll at the ocean surface agrees with that of satellite observation⁴⁵ (Supplementary Fig. 3). The model reproduced the contrast of the surface chlorophyll concentration between subtropical and subpolar regions, although simulated surface chlorophyll concentration in subtropical regions is lower than that of the observation partly due to the lack of nitrogen fixers. Nitrogen fixation is estimated to support about 30–50% of carbon export in subtropical regions^46,47. Simulated surface chlorophyll distribution in the Pacific equatorial region is close to the observed.

Our model properly simulates the meridional distribution of nitrate compared with that of observations⁴⁸ (Supplementary Fig. 4). The simulated horizontal distribution of primary production is consistent with that estimated by satellite data^9,49 (Supplementary Fig. 5), although simulated primary production is underestimated in subtropical regions, associated with the underestimation of surface chlorophyll in these regions (Supplementary Fig. 3).

Source: Ecology - nature.com