Table A1.

State Variable Equations Including All Biogeochemical Source and Sink Terms

Variable (Symbol)	Processes	Time Rate of Change in Each Term
Phytoplankton (P)	Change per unit time =	∂P/∂t =
	+ Primary production (← [NH4] + [NO3])	$+{\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	− Exudation (→ [DON]SL)	$-\gamma {\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	− Exudation (→ [NH4])	$-\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)\omega {\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	− Grazing assimilation (→ Z)	− βgZ
	− Fecal pellets from grazing on P (→ DL)	− (1 − β)(1 − λ)gZ
	− Sloppy feeding (→ [DON]SL)	− (1 − β)λεgZ
	− Sloppy feeding (→ [NH4])	− (1 − β)λ(1 − ε)gZ
	− Mortality (→ DS)	− m P P
	− Aggregation (→ DL)	− τ(D S + P)P
	− Sinking (→ sediment)	− w P∂P/∂z
Chlorophyll ([Chl])	Change per unit time =	∂[Chl]/∂t =
	+ Primary production ([NH4] + [NO3] → P)	$+{\rho }_{\left[\mathrm{C}\mathrm{h}\mathrm{l}\right]}{\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)\left[\mathrm{C}\mathrm{h}\mathrm{l}\right]$
	− Exudation (P → [DON]SL)	$-{\rho }_{\left[\mathrm{C}\mathrm{h}\mathrm{l}\right]}\gamma {\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)\left[\mathrm{C}\mathrm{h}\mathrm{l}\right]$
	− Exudation (P → [NH4])	$-{\rho }_{\left[\mathrm{C}\mathrm{h}\mathrm{l}\right]}\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)\omega {\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)\left[\mathrm{C}\mathrm{h}\mathrm{l}\right]$
	− Grazing (P → Z + DL + [DON]SL + [NH4])	− gZ/P[Chl]
	− Mortality (P → DS)	− m P[Chl]
	− Aggregation (P → DL)	− τ(D S + P)[Chl]
	− Sinking (P → Sediment)	− ω P∂[Chl]/∂z
Zooplankton (Z)	Change per unit time =	∂Z/∂t =
	+ Grazing assimilation (← P)	+ βgZ
	− Excretion (→ [NH4])	$-\left(l_{\mathrm{B}\mathrm{M}}+l_E\beta \frac{P^2}{K_P+P^2}\right)Z$
	− Mortality ((→ DL)	− m Z Z 2
Small Detritus (DS)	Change per unit time =	∂D S/∂t =
	+ Mortality (← P)	+ m P P
	− Aggregation (→ DL)	− τ(D S + P)D S
	− Solubilization (→ [DON]SL)	$-{\delta }_N{r}_{D_S}{D}_S$
	− Remineralization (→ [NH4])	$-\left(1-{\delta }_N\right)r_{D_S}\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)D_S$
	− Sinking (→ sediment)	− w S∂D S/∂z
Large Detritus (DL)	Change per unit time =	∂D L/∂t =
	+ Fecal pellets production (→ DL)	+ (1 − β)(1 − λ)gZ
	+ Mortality (← Z)	+ m z Z 2
	+ Aggregation (← DS + P)	+ τ(D S + P)2
	− Solubilization (→ [DON]SL)	$-{\delta }_N{r}_{D_L}{D}_L$
	− Remineralization (→ [NH4])	$-\left(1-{\delta }_N\right)r_{D_L}\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)D_L$
	− Sinking (→ sediment)	− w L∂D L/∂z
Semilabile Dissolved Organic Nitrogen [DON]SL	Change per unit time =	∂[DON]SL/∂t =
	+ Exudation (← P)	$+\gamma {\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	+ Sloppy feeding (← P)	+ (1 − β)λεgZ
	+ Solubilization (← DS + DL)	$+{\delta }_N\left(r_{D_S}{D}_S+r_{D_L}{D}_L\right)$
	− Remineralization (→ [NH4])	$-\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)r_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}{e}^{{\kappa }_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}T}{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}$
Ammonium [NH4]	Change per unit time =	∂[NH4]/∂t =
	‐ Uptake (→ P)	$-{\mu }_0{L}_I{L}_{{\mathrm{N}\mathrm{H}}_4}P$
	‐ Nitrification (→ [NO3])	− nf NTR[NH4]
	+ Exudation (← P)	$+\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)\omega {\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	+ Sloppy feeding (← P)	+ (1 − β)λ(1 − ε)gZ
	+ Excretion (← Z)	$+\left(l_{\mathrm{B}\mathrm{M}}+l_E\beta \frac{P^2}{K_P+P^2}\right)Z$
	+ Remineralization (← DS + DL)	$+\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)\left(1-{\delta }_N\right)\left(r_{D_S}{D}_S+r_{D_L}{D}_L\right)$
	+ Remineralization (← [DON]SL)	$+\left(f_{\mathrm{N}\mathrm{T}\mathrm{R}}+f_{\mathrm{D}\mathrm{N}\mathrm{F}}\right)r_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}{e}^{{\kappa }_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}T}{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}$
Nitrate [NO3]	Change per unit time =	∂[NO3]/∂t =
	− Uptake (→ P)	$-{\mu }_0{L}_I{L}_{{\text{NO}}_3}P$
	− Water column denitrification (→ N2)	$-{\eta }_{\mathrm{D}\mathrm{N}\mathrm{F}}{\left[f_{\mathrm{D}\mathrm{N}\mathrm{F}},,,f_{\mathrm{W}\mathrm{C}}\right]}_{\text{min}}\left\{\left(1-{\delta }_N\right)\left(r_{D_S}{D}_S+r_{D_L}{D}_L\right)+r_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}{e}^{{\kappa }_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}T}{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}\right\}$
	+ Nitrification (← [NH4])	+ nf NTR[NH4]
Oxygen [O2]	Change per unit time =	∂[O2]/∂t =
	+ Air‐sea flux	$+\frac{v{k}_{{\mathrm{O}}_2}}{\mathrm{\Delta }z}\left({\left[{\mathrm{O}}_2\right]}_{\mathrm{s}\mathrm{a}\mathrm{t}}-\left[{\mathrm{O}}_2\right]\right)$
	+ Primary production ([NH4] + [NO3] → P)	$+{\mu }_0{L}_I\left({\eta }_{{\mathrm{O}}_2:{\text{NO}}_3}{L}_{{\text{NO}}_3}+{\eta }_{{\mathrm{O}}_2:{\mathrm{N}\mathrm{H}}_4}{L}_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	+  excess‐based production ([CO2]→ P)	$+{\gamma }_C{\eta }_{\mathrm{C}:\mathrm{N}}{\mu }_0{L}_I\left(1-L_{{\text{NO}}_3}-L_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	− Nitrification ([NH4] → NO3])	− 2f NTR n[NH4]
	− Exudation (P → [NH4])	$-{\eta }_{{\mathrm{O}}_2:{\mathrm{N}\mathrm{H}}_4}{f}_{\mathrm{N}\mathrm{T}\mathrm{R}}\omega {\mu }_0{L}_I\left(L_{{\text{NO}}_3}+L_{{\mathrm{N}\mathrm{H}}_4}\right)P$
	− Excretion (Z → [NH4])	$-{\eta }_{{\mathrm{O}}_2:{\mathrm{N}\mathrm{H}}_4}\left(l_{\mathrm{B}\mathrm{M}}+l_E\beta \frac{P^2}{K_P+P^2}\right)Z$
	− Sloppy feeding (Z → [NH4])	$-{\eta }_{{\mathrm{O}}_2:{\mathrm{N}\mathrm{H}}_4}\left(1-\beta \right)\lambda \left(1-\epsilon \right)gZ$
	− Remineralization (DS → NH4])	$-{\eta }_{{\mathrm{O}}_2:{\mathrm{N}\mathrm{H}}_4}{f}_{\mathrm{N}\mathrm{T}\mathrm{R}}\left(1-{\delta }_N\right)r_{D_S}{D}_S$
	− Remineralization (DL → [NH4])	$-{\eta }_{{\mathrm{O}}_2:{\mathrm{N}\mathrm{H}}_4}{f}_{\mathrm{N}\mathrm{T}\mathrm{R}}\left(1-{\delta }_N\right)r_{D_L}{D}_L$
	− Remineralization ([DON]SL → [NH4])	$-{\eta }_{{\mathrm{O}}_2:{\mathrm{N}\mathrm{H}}_4}{f}_{\mathrm{N}\mathrm{T}\mathrm{R}}{r}_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}{e}^{{\kappa }_{{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}}T}{\left[\text{DON}\right]}_{\mathrm{S}\mathrm{L}}$
Inorganic suspended solid [ISS]	Change per unit time	∂[ISS]/∂t =
	− Sinking (→ sediment)	− w ISS∂[ISS]/∂z