Uptake mechanism of anthropogenic CO₂ in the Kuroshio Extension region in an ocean general circulation model

Abstract

The uptake mechanism of anthropogenic CO₂ in the Kuroshio Extension is examined by a Lagrangian approach using a biogeochemical model embedded in an ocean general circulation model. It is found that the uptake of anthropogenic CO₂ is caused mainly by the increase of pCO₂ dependency of seawater on temperature, which is caused by greater dissolved inorganic carbon concentration in the modern state than in the pre-industrial state. In contrast with the view of previous studies, the effect of the vertical entrainment, which brings waters that last contacted the atmosphere with the past lower CO₂ concentration, is comparatively small. Winter uptake of anthropogenic CO₂ increases with the rise of the atmospheric CO₂ level, while summer uptake is relatively stable, resulting in a larger seasonal cycle of the uptake. This increase is significant, especially in the Kuroshio Extension region. It is newly suggested that this increase in the Kuroshio Extension region is largely caused by the combined effects of the increased pCO₂ dependency of the sea water on the temperature and the seasonal difference in cooling.

Appendix: Description of biogeochemical model

The biogeochemical model includes an ecosystem and a carbon-cycle component. The ecosystem component is a so called NPZD model. All the passive tracer concentrations follow advective diffusive equations with source-minus-sink (SMS) terms of exchange between different tracers. The units of the SMS terms are (mol m⁻³ s⁻¹).

SMS terms for the NPZD model are

$$ {\rm SMS}({\rm P}) = J(I,{\rm NO}_3,{\rm PO}_4){\rm P} - \phi_{\rm P} {\rm P} -\phi_{\rm PP} {\rm P}^2 - G({\rm P}){\rm Z}, $$

(18)

$$ {\rm SMS}({\rm Z}) = f_a G({\rm P}){\rm Z} - \phi_{\rm Z} {{\rm P}} - \phi_{{\rm ZZ}} {\rm Z}^2, $$

(19)

$$ {\rm SMS}({\rm D}) = (1-f_a) G({\rm P}){\rm Z} + \phi_{{\rm PP}} {\rm P}^2 + \phi_{{\rm ZZ}}{\rm Z}^2 - \phi_{\rm D} {\rm D} - w_{\rm D} \frac{\partial {\rm D}}{\partial {\rm Z}}, $$

(20)

$$ {\rm SMS}({\rm NO}_3) = \phi_{{\rm P}} {\rm P} + \phi_{\rm z} {\rm Z} + \phi_{\rm D} {\rm D} - J(I,{\rm NO}_3,{\rm PO}_4)P, $$

(21)

$$ {\rm SMS}({\rm PO}_4) = {\rm SMS}({\rm NO}_3) \cdot R_{{\rm pn}}, $$

(22)

$$ {\rm SMS}({\rm O}_2) = - {\rm SMS}({\rm PO}_4) \cdot R_{{\rm on}}\cdot R_{{\rm np}}. $$

(23)

Here Grazing function (G(P)) is $g\epsilon P^2/(g + \epsilon P^2).$ Other notations and values are listed in Table 2.

Table 2 Variables and their values in the biogeochemical model

The growth rate of phytoplankton (J(I, NO₃, PO₄)) is limited by either light or nutrient levels. For the nutrient limitation, we adopt the optimal uptake kinetics, which assumes a physiological trade-off between the efficiency of nutrient encounter at the cell surface and the maximum assimilation rate (Smith et al. 2009).

$$ J(I,{\rm NO}_3,{\rm PO}_4) = {\rm min}\left(J_I,J_{{\rm NO}_3}, J_{{\rm PO}_4} \right) $$

(24)

$$ J_I = \frac{J_{{\rm max}}\alpha I}{\left[J_{{\rm max}}^2 + (\alpha I)^2\right]^{1/2}} $$

(25)

$$ I = I_{z=0} {PAR} \exp{\left(-k_w \tilde{z}-k_{e}\int\limits_0^{\tilde{z}} P\,{\rm d}z\right)} $$

(26)

$$ J_{{\rm max}} = a\cdot b^{cT} $$

(27)

$$ J_{N} = \frac{V_0 N}{N + 2\sqrt{\alpha_{OU} N} + \alpha_{OU}} \quad(N={\rm NO}_3\, {\hbox{or}}\, {\rm PO}_4) $$

(28)

$$ V_{O} = 0.5\left(1+\sqrt{\frac{\alpha_{{\rm OU}}}{K_N}}\right) $$

(29)

Here $\tilde{z} = z/\cos\theta = z/\sqrt{{\rm sin}2\theta /1.33^2}$ is the effective vertical coordinate with 1.33 as the refraction index according to Snell’s law relating the zenith angle of incidence in air (θ) to the angle of incidence in water.

For the carbon-cycle component, formulations for the production of DIC and Alk are based on Schmittner et al. (2008, 2009). Production changes in inorganic nutrients and calcium carbonate (CaCO₃) in molar numbers are

$$ {\rm SMS}({\rm DIC}) = {\rm SMS}(PO_4) \cdot R_{cp} - {\rm SMS}({\rm CaCO}_3), $$

(30)

$$ {\rm SMS}({\rm Alk}) = - {\rm SMS}({\rm NO}_3) - 2 \cdot {\rm SMS}({\rm CaCO}_3), $$

(31)

$$ {\rm SMS}({\rm CaCO}_3) = {\rm Pr}({\rm CaCO}_3) -{\rm Di}({\rm CaCO}_3), $$

(32)

$$ {\rm Pr}({\rm CaCO}_3) = ((1-f_a) G(P)Z + \phi_{PP} P^2 + \phi_{ZZ} Z^2 )R_{{\rm CaCo}_3/{\rm poc}}R_{{\rm cn}}, $$

(33)

$$ {\rm Di}({\rm CaCO}_3) = \int {\rm Pr}({\rm CaCO}_3)\,{\rm d}z \cdot \frac{{\rm d}}{{\rm d}z}({\rm exp}(-z/D_{{\rm CaCO}_3})). $$

(34)

Surface carbon flux is calculated following the OCMIP protocols.