Table A3.

Definitions of Functions Used in State Variable Equations

Symbol	Description	Equation	Units
F TON	Flux of total organic matter reaching to the bottom	${\left.w_{P}P\right|}_{z=H}+{\left.w_{D_S}{D}_S\right|}_{z=H}+{\left.w_{D_L}{D}_L\right|}_{z=H}$	mmol N m−2 d−1
F BC	Flux of total organic carbon in the sediment	$\frac{\left[{\left.{\eta }_{\mathrm{C}:\mathrm{N}}{w}_{P}P\right|}_{z=H}+{\eta }_{{\mathrm{C}}_{\mathrm{B}}:{\mathrm{N}}_{\mathrm{B}}}\left({\left.w_{D_S}{D}_S\right|}_{z=H}+{\left.w_{D_L}{D}_L\right|}_{z=H}\right)\right]\times 12\times 365}{1000}$	g C m−2 yr−1
I	Photosynthesis available radiation	$I_0\cdot \text{PARfrac}\cdot e^{z{K}_D}$	W m−2
KD	Light attenuation	1.4 + 0.063[TSS] − 0.057S	m−1
		If 1.4 + .063[TSS] – 0.057S < 0, then
		0.04 + 0.02486[Chl] + 0.003786{0, 6.625 ([DON]SL + [DON]RF) − 70.819}max
$L_{{\text{BO}}_2}$	Bottom oxygen limitation factor	$\frac{{\left.K_{{\text{BO}}_2}(O_{2_{\mathrm{s}\mathrm{a}\mathrm{t}}}\right|}_{z=H}-{\left.O_2\right|}_{z=H})}{{\left.\left(K_{{\text{BO}}_2}+{\left.O_2\right|}_{z=H}\right)O_{2_{\mathrm{s}\mathrm{a}\mathrm{t}}}\right|}_{z=H}}$	dimensionless
L I	Photosynthesis‐light (P‐I) relationship	$\frac{\alpha I}{\sqrt{{\mu }_0^2+{\alpha }^2{I}^2}}$	dimensionless
$L_{{\text{NO}}_3}$	Nitrate uptake limitation with ammonium inhibitor	$\frac{{\text{NO}}_3}{K_{{\text{NO}}_3}+{\text{NO}}_3}\frac{1}{1+{\mathrm{N}\mathrm{H}}_4/K_{{\mathrm{N}\mathrm{H}}_4}}$	dimensionless
$L_{{\mathrm{N}\mathrm{H}}_4}$	Ammonium uptake limitation	$\frac{{\mathrm{N}\mathrm{H}}_4}{K_{{\mathrm{N}\mathrm{H}}_4}+{\mathrm{N}\mathrm{H}}_4}$	dimensionless
TSS	Total suspended solid	$\mathrm{T}\mathrm{S}\mathrm{S}=\mathrm{I}\mathrm{S}\mathrm{S}+{\eta }_{\mathrm{C}:\mathrm{N}}\frac{P+Z+D_S+D_L}{1000}\times 12$	g m−3
f NTF	Oxygen limitation for nitrification	$\frac{O_2}{O_2+K_{\mathrm{N}\mathrm{T}\mathrm{R}}}$	dimensionless
f DNF	Oxygen limitation for denitrification	$\frac{K_{\mathrm{D}\mathrm{N}\mathrm{F}}}{O_2+K_{\mathrm{D}\mathrm{N}\mathrm{F}}}$	dimensionless
f WC	Nitrate limitation for nitrification	$\frac{\left[{\text{NO}}_3\right]}{\left[{\text{NO}}_3\right]+K_{\mathrm{W}\mathrm{N}\mathrm{O}3}}$	dimensionless
g	Zooplankton grazing rate	$g_{\text{max}}\frac{P^2}{K_P+P^2}$	day−1
n	Nitrification rate	$n_{\text{max}}\left(1-{\left[0,,,\frac{I-I_{\mathrm{N}\mathrm{T}\mathrm{R}}}{K_I+I-I_{\mathrm{N}\mathrm{T}\mathrm{R}}}\right]}_{\text{max}}\right)$	day−1
$v{k}_{{\mathrm{O}}_2}$	Gas exchange coefficient	$v{k}_{{\mathrm{O}}_2}=0.31u_{10}^2\sqrt{660/S{c}_{o_2}}$	m/s
		$S{c}_{{\mathrm{O}}_2}$ is the Schmidt number [Wanninkhof, 1992]
		u 10 is the wind speed 10 m above the sea surface
Γ	Bottom shear stress	$\sqrt{{\tau }_{b_x}^2+{\tau }_{b_y}^2}$	Pa
ρ [Chl]	Fraction of phytoplankton growth devoted to chlorophyll synthesis	$\frac{{\theta }_{\text{max}}{\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)P}{\alpha I\left[\mathrm{C}\mathrm{h}\mathrm{l}\right]}$	dimensionless
ϕ 1	Resuspension fraction	$\frac{\mathrm{\Gamma }}{{\mathrm{\Gamma }}_c}$	dimensionless
ϕ 2	Burial efficiency	${\left\{0.092F_{\mathrm{B}\mathrm{C}}^{0.5797};0.75\right\}}_{\text{min}}$	dimensionless