Coupled 1-D physical–biological model study of phytoplankton production at two contrasting time-series stations in the western North Pacific

Abstract

A vertical one-dimensional physical–biological model is applied to clarify the mechanisms controlling the seasonality and interannual variability of primary production in the surface layer at two contrasting time-series stations, K2 (in the subarctic gyre) and S1 (in the subtropical gyre), in the western North Pacific. Using forcing based on realistic atmospheric and oceanic data, the model reproduces seasonal differences in the degree to which different controlling factors affect primary production between these two stations, primarily as a result of differences in the physical environment. At station K2, light intensity is an important factor controlling primary production in summer. After April, the mixed layer depth (MLD) becomes shallow, resulting in higher average light intensity, and the water column remains stratified until September; these sustain high primary production during this period. In contrast, at station S1, the supply of nutrients via entrainment is vital to sustaining production, because light intensity remains sufficient throughout the year. In summer, the relationship between nutricline depth and euphotic layer is a controlling factor. The simulations forced by the different atmospheric conditions for each year, respectively, show different MLD. In the 2012 simulation, the deep winter MLD (200 m) enhances primary production in the surface layer as compared to the other two years (2010 and 2011) simulations.

Appendix: Ecosystem model

The simple nitrogen- and silicon-based plankton ecosystem model, consisting of nine compartments, is coupled with a 1-D physical model of the oceanic mixed layer. The compartments (biological tracers) are nitrate (NO${}_{3}$), ammonium (NH${}_{4}$), silicate (Si), two categories of phytoplankton (small phytoplankton, PS and large phytoplankton, PL), zooplankton (Z), dissolved organic nitrogen (DON), particulate organic nitrogen (PON), and bio-silicate (BSi is opal). The evolution of each biological tracer concentration is determined by vertical diffusive mixing using the diffusivity as calculated by the mixed layer model (Mellor and Yamada 1982), and biogeochemical source-minus-sink (sms) terms. The sms terms resulting from biological activity are shown in Fig. 3. Their equations for each individual biological tracer (NO${}_{3}$, NH${}_{4}$, Si, PS, PL, Z, DON, PON, and BSi) are:

$$\begin{aligned} {\text {sms (PS)}}&= {} {\text {GppPS}} {}^{(1)} - {r}_{\rm PS} {\text {exp}}(\kappa {}_{\rm ResPS}T){\text {PS}} {}^{(3)} \\&\quad-\,\mu {}_{\rm PS} {\text {exp}}(\kappa {}_{\rm MorPS}T){\text {PS}}{}^{2}{}^ {(5)} - \gamma {}_{\rm PS}{\text {GppPS}} {}^ {(7)} - G({\text {PS}}){\text {Z}} {}^ {(9)} \end{aligned}$$

(1)

$$\begin{aligned} {\text {sms (PL)}}&= {} {\text {GppPL}} {}^{(2)} - {r}_{\rm PL} {\text {exp}}(\kappa {}_{\rm ResPL}T){\text {PS}} {}^ {(4)} \\&\quad-\,\mu {}_{\rm PL} {\text {exp}}(\kappa {}_{\rm MorPL}T){\text {PL}}{}^{2} {}^ {(6)} - \gamma {}_{\rm PL}{\text {GppPL}} {}^ {(8)} - G({\text {PL}})Z {}^ {(10)} \end{aligned}$$

(2)

$$\begin{aligned} {\text {sms (Z)}}&= {} \left( G({\text {PS}}){\text {Z}} {}^ {(9)} + G({\text {PL}}){\text {Z}} {}^ {(10)}\right) \\&\quad-\,(\alpha - \beta )(G({\text {PS}}){\text {Z}} + G({\text {PL}}){\text {Z}}) {}^ {(11)} \\&\quad-\,(1 - \alpha )(G({\text {PS}}){\text {Z}} + G({\text {PL}}){\text {Z}}) {}^ {(12)} \\&\quad-\,\mu {}_{\rm Z} {\text {exp}}(\kappa {}_{\rm MorZ}T){\text {Z}}{}^{2} {}^ {(13)} \end{aligned}$$

(3)

$$\begin{aligned} {\text {sms (PON)}}&= {} \mu {}_{\rm PS} {\text {exp}}(\kappa {}_{\rm MorPS}T){\text {PS}}{}^{2} {}^ {(5)} + \mu {}_{\rm PL} {\text {exp}}(\kappa {}_{\rm MorPL}T){\text {PL}}{}^{2} {}^ {(6)} \\&\quad+\, \mu {}_{\rm Z} {\text {exp}}(\kappa {}_{\rm MorZ}T){\text {Z}}{}^{2} {}^ {(13)} + (1 - \alpha )(G({\text {PS}}){\text {Z}} + G({\text {PL}}){\text {Z}}) {}^ {(12)} \\&\quad-\,{\text {VP2N}}{}_{0}{\text {exp}}(\kappa {}_{\rm P2N}T){\text {PON}} \\&\quad\times \,{\rm max}(0,{\text {PON-R}}{}_{\rm pocsi} \times (67.2/12) \times R{}_{\rm nc} \times {\rm Si}) {}^ {(14)} \\&\quad-\,{\text {VP2D}}{}_{0}{\text {exp}}(\kappa {}_{\rm P2D}T){\text {PON}} \\&\quad\times \,{\rm max}(0,{\text {PON-R}}{}_{\rm pocsi} \times (67.2/12) \times {R}_{\rm nc} \times {\rm Si}) {}^ {(15)} \\&\quad-\,\frac{\partial }{\partial z} (W{}_{\rm s} \times {\text {PON}}) {}^ {(18)} \end{aligned}$$

(4)

$$\begin{aligned} {\text {sms (DON)}}&= {} \gamma {}_{\rm PS}{\text {GppPS}} {}^ {(7)} + \gamma {}_{\rm PL}{\text {GppPL}} {}^ {(8)} \\&\quad+\,{\text {VP2D}}{}_{0}{\text {exp}}(\kappa {}_{\rm P2D}T){\text {PON}} \\&\quad\times \,{\rm max}(0,{\text {PON-R}}{}_{\rm pocsi} \times (67.2/12) \times R{}_{\rm nc} \times {\text {Si}}) {}^ {(15)} \\&\quad-\,{\text {VD2N}}{}_{0} {\text {exp}}(\kappa {}_{\rm D2N}T){\text {DON}} {}^ {(16)} \end{aligned}$$

(5)

$$\begin{aligned} {\text {sms}} ({\rm NO}_{3})&= {} -\left( {\text {GppPS}} {}^ {(1)} - r{}_{\rm PS} {\text {exp}}(\kappa {}_{\rm ResPS}T){\text {PS}} {}^ {(3)}\right) {\text {Rnew}}_{\rm PS} \\&\quad-\,\left( {\text {GppPL}} {}^ {(2)} - r{}_{\rm PL} {\text {exp}}(\kappa {}_{\rm ResPL}T){\text {PL}} {}^ {(4)}\right) {\text {Rnew}}_{\rm PL} \\&\quad+\,{\text {Nit}}_{0} {\text {exp}}(\kappa {}_{\rm Nit}T){\text {NH}}_{4} {}^ {(17)} \end{aligned}$$

(6)

$$\begin{aligned} {\text {sms}} ({\rm NH}_{4})&= {} -\left( {\text {GppPS}} {}^ {(1)} - {r}_{\rm PS} {\text {exp}}(\kappa {}_{\rm ResPS}T){\text {PS}} {}^ {(3)}\right) (1 - {\text {Rnew}}_{\rm PS}) \\&\quad-\,\left( {\text {GppPL}} {}^ {(2)} - r{}_{\rm PL} {\text {exp}}(\kappa {}_{\rm ResPL}T){\text {PL}} {}^ {(4)}\right) (1 - {\text {Rnew}}_{\rm PL}) \\&\quad-\,{\text {Nit}}_{0} {\text {exp}}(\kappa {}_{\rm Nit}T){\text {NH}}_{4} {}^ {(17)} \\&\quad+\,{\text {VP2N}}{}_{0}{\text {exp}}(\kappa {}_{\rm P2N}T){\text {PON}} \\&\quad\times \,{\text {max}}(0,{\text {PON-R}}{}_{\rm pocsi} \times (67.2/12) \times R{}_{\rm nc} \times {\text {Si}}) {}^ {(14)} \\&\quad+\,{\text {VD2N}}{}_{0} {\text {exp}}(\kappa {}_{\rm D2N}T){\rm DON} {}^ {(16)} \\&\quad+\,(\alpha - \beta )(G({\rm PS}){\rm Z} + G({\rm PL}){\rm Z}) {}^ {(11)} \end{aligned}$$

(7)

$$\begin{aligned} {\text {sms (Si)}}&= {} -\left( {\text {GppPL}} \times {\rm Rsin} {}^ {(19)}- r{}_{\rm PL} {\text {exp}}(\kappa {}_{\rm ResPL}T){\rm PL} \times {\rm Rsin} {}^ {(20)}\right) \\&\quad+\,\gamma {}_{\rm PL}{\text {GppPL}} \times {\rm Rsin} {}^ {(21)} \\&\quad+\,{\rm VP2Si}_{0} {\text {exp}}(\kappa _{\rm P2Si}T) {\rm BSi} {}^ {(24)} \end{aligned}$$

(8)

$$\begin{aligned} {\text {sms (BSi)}}&= {} \mu _{\rm PL} {\text {exp}}(\kappa _{\rm MorPL}T){\rm PL}^{2} \times {\rm Rsin} {}^ {(22)} \\&\quad+\,(1 - \alpha )(G({\rm PS}){\rm Z} + G({\rm PL}){\rm Z}) \times {\rm Rsin} {}^ {(23)} \\&\quad-\,{\rm VP2Si}_{0} {\text {exp}}(\kappa _{\rm P2Si}T) {\rm BSi} {}^ {(24)} \\&\quad-\,\frac{\partial }{\partial z} ({W}_{\rm s} \times {\rm BSi}) {}^ {(25)} \end{aligned}$$

(9)

where superscript number (1–25) of biological tracer flux term in each equation is corresponding to biological tracer flux number of Fig. 3. GppPS and GppPL are the absolute values of growth rate (gross primary production), as a function of phytoplankton concentration, depth z, time t, nutrient concentration, N and light intensity. Growth rate depends exponentially on temperature, T, via the so-called Q10 relation, and the light limitation follows Steel (1962). Growth rate depends on nutrient concentrations via Optimal Uptake (OU) kinetics (Pahlow 2005; Smith 2009) as applied, assuming fixed composition of phytoplankton (Shigemitsu 2012). By accounting for physiological acclimation to different nutrient concentrations, OU kinetics has been shown to give a different response under changing environmental conditions, compared to the more widely applied Michaelis-Menten/Monod (MM) equation (Smith 2009; Smith et al. 2010). This results in a saturating dependence of growth rate on nutrient concentration, as for the MM equation, but with a slightly different shape expressed by the following equations:

$$\begin{aligned} {\text {GppPS}}&= {} {\text {VmaxS}} \times \left( \frac{{\rm NO}_{3}}{{\rm NO}_{3} + \frac{{\rm VmaxS}}{A_{\rm NO3PS}} + 2 \sqrt{ \frac{{\rm VmaxS} \times {\rm NO}_{3}}{A_{\rm NO3PS}}}} \times {\text {exp}}(- \varphi _{\rm PS}{\rm NH}_{4}) \right. \\&\left. \quad+\,\frac{{\rm NH}_{4}}{{\rm NH}_{4} + \frac{{\rm VmaxS}}{A_{\rm NH4PS}} + 2 \sqrt{\frac{{\rm VmaxS} \times {\rm NH}_{4}}{A_{\rm NH4PS}}}} \right) \\&\quad\times\,{\text {exp}}\left( \kappa _{{\text {GppPS}}}T\right) \\&\quad\times\,\int _{-H}^{0} \frac{I}{I_{\rm opt}} \times {\text {exp}} \left( 1 - \frac{I}{I_{\rm opt}} \right) {\rm d}z \times {\rm PS} \end{aligned}$$

(10)

$$\begin{aligned} {\text {GppPL}}&= {} {\rm VmaxL} \times {\rm Min} \left( \frac{{\rm NO}_{3}}{{\rm NO}_{3} + \frac{{\rm VmaxL}}{A_{\rm NO3PL}} + 2 \sqrt{\frac{{\rm VmaxL} \times {\rm NO}_{3}}{A_{\rm NO3PL}}}} \times {\text {exp}}(- \varphi _{\rm PL}{\rm NH}_{4}) \right. \\&\left. \quad+\,\frac{{\rm NH}_{4}}{{\rm NH}_{4} + \frac{{\rm VmaxL}}{A_{\rm NH4PL}} + 2 \sqrt{\frac{{\rm VmaxL} \times {\rm NH}_{4}}{A_{\rm NH4PL}}}}, \frac{{\rm Si}}{{\rm Si} + \frac{{\rm VmaxL}}{A_{\rm SiPL}} + 2 \sqrt{\frac{{\rm VmaxL} \times {\rm Si}}{A_{\rm SiPL}}}} \right) \\&\quad\times\,{\text {exp}}\left( \kappa _{{\text {GppPL}}}T\right) \\&\quad\times\,\int _{-H}^{0} \frac{I}{I_{\rm opt}} \times {\text {exp}} \left( 1 - \frac{I}{I_{\rm opt}} \right) {\rm d}z \times {\rm PL} \end{aligned}$$

(11)

$$\begin{aligned} I = I_{0} \times {\text {exp}} (-kz) \end{aligned}$$

(12)

$$\begin{aligned} k = 0.04 + 0.054 \times {\text {Rnchla}} \times ({\rm PS}+{\rm PL})^{0.667} + 0.0088 \times {\text {Rnchla}} \times ({\rm PS}+{\rm PL}) \end{aligned}$$

(13)

where ${I}_{0}$ is light intensity at the sea surface, and T is water temperature. Small and large phytoplankton (PS and PL in Eqs. 1, 2) are produced by their own growth, and reduced by respiration, mortality, extracellular excretion), and grazing by zooplankton. Grazing rate of phytoplankton by zooplankton is as follows:

$$\begin{aligned} {G({\rm PS}){\rm Z} =} \\&\quad{\rm Max}\left( 0, {\rm GR}_{\rm max} \times {\text {exp}}(\kappa _{\rm GraPS}T) \times (1 - {\text {exp}}(\lambda _{\rm PS} \times ({\rm P2Z} - {\rm PS}))) \times {\rm Z} \right) \end{aligned}$$

(14)

$$\begin{aligned} {G({\rm PL}){\rm Z} =} \\&\quad{\rm Max}\left( 0, {\rm GR}_{\rm max} \times {\text {exp}}(\kappa _{\rm GraPL}T) \times (1 - {\text {exp}}(\lambda _{\rm PL} \times ({\rm P2Z - PL}))) \times {\rm Z} \right) \end{aligned}$$

(15)

Zooplankton (Z in Eq. 3) depends on the grazing rate of Z, excretion rate of Z, egestion rate of Z, and mortality rate of Z. Particulate organic nitrogen (PON in Eq. 4) is produced by mortality (of PS, PL, and Z), and egestion by Z, and is consumed by its decomposition (to NH${}_{4}$ and DON), and by sinking. Dissolved organic nitrogen (DON in Eq. 5) is produced by extracellular excretion (PS, PL) and decomposition (PON to DON), and is consumed by its remineralization (to NH${}_{4}$). Nitrate (NO${}_{3}$ in Eq. 6) is consumed by the growth rate of phytoplankton (PS, PL), minus their respiration rate, and produced by nitrification (proportional to NH${}_{4}$). The f-ratio of phytoplankton (PS, PL) (no dimension) is defined by the ratio of NO${}_{3}$ uptake to total N (NO${}_{3}$ + NH${}_{4}$) uptake.

$$\begin{aligned} \scriptstyle {\text {Rnew}}_{\rm PS}\,=\,\frac{\frac{{\text {NO}}_{3}}{{\text {NO}}_{3} + \frac{{\text {VmaxS}}}{A_{\rm NO3PS}} + 2 \sqrt{\frac{{\text {VmaxS}} \times {\text {NO}}_{3}}{A_{\rm NO3PS}}}} \times {\text {exp}}(- \varphi _{\rm PS}{\text {NH}}_{4})}{ \frac{{\text {NO}}_{3}}{{\text {NO}}_{3} + \frac{{\rm VmaxS}}{A_{\rm NO3PS}} + 2 \sqrt{ \frac{{\rm VmaxS} \times {\text {NO}}_{3}}{A_{\rm NO3PS}}}} \times {\text {exp}}(- \varphi _{\rm PS}{\text {NH}}_{4}) + \frac{{\text {NH}}_{4}}{{\text {NH}}_{4} + \frac{{\rm VmaxS}}{A_{\rm NH4PS}} + 2 \sqrt{\frac{{\rm VmaxS} \times {\text {NH}}_{4}}{A_{\rm NH4PS}}}}} \end{aligned}$$

(16)

$$\begin{aligned} \scriptstyle {\text {Rnew}}_{\rm PL}\,=\, \frac{\frac{{\text {NO}}_{3}}{{\text {NO}}_{3} + \frac{{\text {VmaxL}}}{A_{\rm NO3PL}} + 2 \sqrt{\frac{{\text {VmaxL}} \times {\text {NO}}_{3}}{A_{\rm NO3PL}}}} \times {\text {exp}}(- \varphi _{\rm PL}{\text {NH}}_{4})}{ \frac{{\text {NO}}_{3}}{{\text {NO}}_{3} + \frac{{\text {VmaxL}}}{A_{\rm NO3PL}} + 2 \sqrt{ \frac{{\text {VmaxL}} \times {\text {NO}}_{3}}{A_{\rm NO3PL}}}} \times {\text {exp}}(- \varphi _{\rm PL}{\text {NH}}_{4}) + \frac{{\text {NH}}_{4}}{{\text {NH}}_{4} + \frac{{\text {VmaxL}}}{A_{\rm NH4PL}} + 2 \sqrt{\frac{{\text {VmaxL}} \times {\text {NH}}_{4}}{A_{\rm NH4PL}}}}} \end{aligned}$$

(17)

The source-sink terms for ammonium (NH${}_{4}$ in Eq. 7) include the growth rate of phytoplankton (PS, PL), respiration rate (PS, PL), nitrification rate, decomposition rate (PON to NH${}_{4}$, DON to NH${}_{4}$), and excretion rate (Z). Silicate Eq. (8) consumed by the growth of PL (diatoms) minus their respiration and excretion, and is consumed by its dissolution (to Si). Opal (BSi in Eq. 9) is produced by mortality of PL, egestion by Z, and is consumed by its decomposition to Si, and by sinking.