\(\newcommand{\p}[1]{\frac{\partial }{\partial #1}}\) \(\newcommand{\pp}[2]{\frac{\partial #1}{\partial #2}}\) \(\newcommand{\dd}[2]{\frac{d #1}{d #2}}\) \(\newcommand{\h}{\frac{1}{2}}\) \(\newcommand{\op}[1]{\operatorname{#1}}\)

8.7.3.1. Model equations¶

The basic model equations are (omitting transport terms handled by the ptracers package, Sinking and Swimming, Air-sea exchanges and terms correcting conservation with the linear free surface formulation discussed in Section 8.7.3.21):

\[\begin{split}\partial_t\op{DIC} &= \sum_j \bigl( (-U^{\mathrm{DIC}}_j + R^{\mathrm{C}}_j) \cdot (1 + R^{\text{PIC:POC}}_j) + R^{\mathrm{DIC}}_j \bigr) + R_{\mathrm{DOC}} + [R_{\mathrm{POC}}] + D_{\mathrm{PIC}} \\ \partial_t\op{PO}_4 &= \sum_j \bigl( -U^{\mathrm{PO4}}_j + R^{\mathrm{P}}_j + R^{\mathrm{PO4}}_j \bigr) + R_{\mathrm{DOP}} + [R_{\mathrm{POP}}] \\ \partial_t\op{NH}_4 &= \sum_j \bigl( -U^{\mathrm{NH4}}_j + R^{\mathrm{N,NH4}}_j + R^{\mathrm{NH4}}_j \bigr) + R_{\mathrm{DON}} + [R_{\mathrm{PON}}] - P_{\mathrm{NO2}} - D_{\mathrm{NH4}} \\ \partial_t\op{NO}_2 &= \sum_j \bigl( -U^{\mathrm{NO2}}_j + R^{\mathrm{N,NO2}}_j + R^{\mathrm{NO2}}_j \bigr) + P_{\mathrm{NO2}} - P_{\mathrm{NO3}} \\ \partial_t\op{NO}_3 &= \sum_j \bigl( -U^{\mathrm{NO3}}_j + R^{\mathrm{N,NO3}}_j + R^{\mathrm{NO3}}_j \bigr) + P_{\mathrm{NO3}} - D_{\mathrm{NO3}} \\ \partial_t\op{FeT} &= \sum_j \bigl( -U^{\mathrm{Fe}}_j + R^{\mathrm{Fe}}_j + R^{\mathrm{FeT}}_j \bigr) + R_{\mathrm{DOFe}} + [R_{\mathrm{POFe}}] + S_{\mathrm{Fe}} \\ \partial_t\op{SiO}_2 &= \sum_j \bigl( -U^{\mathrm{SiO2}}_j + R^{\mathrm{Si}}_j \bigr) + R_{\mathrm{POSi}} \\ \partial_t c_j &= U^{\mathrm{DIC}}_j - M_j - R^{\mathrm{C}}_j - G_j + g_j^{\mathrm{C}} \\ \partial_t p_j &= U^{\mathrm{PO4}}_j - M_j Q^{\mathrm{P}}_j - G_j Q^{\mathrm{P}}_j + g_j^{\mathrm{P}} \qquad\text{(with P quota)} \\ \partial_t n_j &= U^{{\mathrm{N}}}_j \;\;\; - M_j Q^{\mathrm{N}}_j - G_j Q^{\mathrm{N}}_j + g_j^{\mathrm{N}} \qquad\text{(with N quota)} \\ \partial_t\op{fe}_j &= U^{\mathrm{Fe}}_j \;\; - M_j Q^{\mathrm{Fe}}_j - G_j Q^{\mathrm{Fe}}_j + g_j^{\mathrm{Fe}} \qquad\text{(with Fe quota)} \\ \partial_t\op{si}_j &= U^{\mathrm{SiO2}}_j - M_j Q^{\mathrm{Si}}_j - G_j Q^{\mathrm{Si}}_j \qquad\text{(with Si quota)} \\ \partial_t\op{Chl}_j &= S^{\mathrm{Chl}}_j \; - M_j Q^{\mathrm{Chl}}_j - G_j Q^{\mathrm{Chl}}_j \qquad\text{(with Chl quota)} \\ \partial_t\op{DOC} &= \sum_j M_j^{\mathrm{DOM}} \;\;\;\;\; + g^{\mathrm{DOC}} + \sum_j \left( H^{\mathrm{POC}}_j - U^{\mathrm{DOC}}_j \right) - R_{\mathrm{DOC}} - S_{\mathrm{CDOM}} R^{{\mathrm{C}}:{\mathrm{P}}}_{\mathrm{CDOM}} \\ \partial_t\op{DOP} &= \sum_j M_j^{\mathrm{DOM}} Q_j^{{\mathrm{P}}} + g^{\mathrm{DOP}} + \sum_j \left( H^{\mathrm{POP}}_j - U^{\mathrm{DOP}}_j \right) - R_{\mathrm{DOP}} - S_{\mathrm{CDOM}} \\ \partial_t\op{DON} &= \sum_j M_j^{\mathrm{DOM}} Q_j^{{\mathrm{N}}} + g^{\mathrm{DON}} + \sum_j \left( H^{\mathrm{PON}}_j - U^{\mathrm{DON}}_j \right) - R_{\mathrm{DON}} - S_{\mathrm{CDOM}} R^{{\mathrm{N}}:{\mathrm{P}}}_{\mathrm{CDOM}} \\ \partial_t\op{DOFe} &= \sum_j M_j^{\mathrm{DOM}} Q_j^{\mathrm{Fe}} + g^{\mathrm{DOFe}} + \sum_j \left( H^{\mathrm{POFe}}_j- U^{\mathrm{DOFe}}_j\right) - R_{\mathrm{DOFe}}- S_{\mathrm{CDOM}} R^{{\mathrm{Fe}}:{\mathrm{P}}}_{\mathrm{CDOM}} \\ \partial_t\op{PIC} &= \sum_j M_j R_j^{\text{PIC:POC}} + g^{\mathrm{PIC}} - D_{\mathrm{PIC}} \\ \partial_t\op{POC} &= \sum_j M_j^{\mathrm{POM}} \;\;\;\;\; + g^{\mathrm{POC}} - \sum_j U^{\mathrm{POC}}_j - R_{\mathrm{POC}} \\ \partial_t\op{POP} &= \sum_j M_j^{\mathrm{POM}} Q_j^{{\mathrm{P}}} + g^{\mathrm{POP}} - \sum_j U^{\mathrm{POP}}_j - R_{\mathrm{POP}} \\ \partial_t\op{PON} &= \sum_j M_j^{\mathrm{POM}} Q_j^{{\mathrm{N}}} + g^{\mathrm{PON}} - \sum_j U^{\mathrm{PON}}_j - R_{\mathrm{PON}} \\ \partial_t\op{POFe} &= \sum_j M_j^{\mathrm{POM}} Q_j^{\mathrm{Fe}} + g^{\mathrm{POFe}} - \sum_j U^{\mathrm{POFe}}_j - R_{\mathrm{POFe}} \\ \partial_t\op{POSi} &= \sum_j M_j Q_j^{\mathrm{Si}} \;\;\;\;\; + g^{\mathrm{POSi}} - R_{\mathrm{POSi}} \\ \partial_t\op{ALK} &= -\biggl( P_{\mathrm{NO3}} - \sum_j U^{\mathrm{NO3}}_j \biggr) - 2\biggl( \sum_j U^{\mathrm{DIC}}_j R^{{\text{PIC:POC}}}_j - D_{\mathrm{PIC}} \biggr) + D_{\mathrm{NO3}} \\ \partial_t{\mathrm{O}}_2 &= R_{\mathrm{O}_2:\mathrm{P}} \biggl( \sum_j U^{\mathrm{PO4}}_j - R_{\mathrm{DOP}} - [R_{\mathrm{POP}}] \biggr) \\ \partial_t\op{CDOM} &= S_{\mathrm{CDOM}} \qquad\text{(with CDOM tracer)} \\\end{split}\]

The quotas are defined as \(Q^{\mathrm{P}}_j=p_j/c_j\), etc. The following abbreviated source terms are described in sections below:

\(U\): uptake, see Nutrient uptake and limitation and Bacteria, also Growth, Internal carbon store and exudation, Non-spectral Light and Spectral Light
\(M\): Mortality
\(R^{\mathrm{C}}\): Respiration
\(H\), \(R_j\): bacterial hydrolysis and remineralization, see Bacteria
\(R\), \(P\): parameterized Remineralization and Nitrification
\(D_{\mathrm{NO3}}\): denitrification, see Denitrification
\(D_{\mathrm{PIC}}\): dissolution of PIC, see Carbon chemistry
\(g\), \(G\): grazing gains and losses, see Grazing
\(S^{\mathrm{Chl}}\): synthesis, see Chlorophyll synthesis
\(S_{\mathrm{Fe}}\): iron sources, see Iron chemistry
\(S_{\mathrm{CDOM}}\): see Dynamic CDOM.

With DARWIN_ALLOW_CDOM, all particulate remineralization terms (in square brackets […]) except Si are absent. Without DARWIN_ALLOW_CDOM, \(f_{\mathrm{CDOM}}=0\) and there is no CDOM tracer. The Alk and O₂ tracers are only present with DARWIN_ALLOW_CARBON.

Table 8.28 General parameters¶
Trait	Param	Symbol	Default	Units	Description
R_PICPOC	a_R_PICPOC	\(R^{\text{PIC:POC}}_j\)	0.8	mmol PIC / mmol POC	inorganic-organic carbon ratio
	R_OP	\(R_{\mathrm{O}_2:\mathrm{P}}\)	170	mmol O₂ / mmol P	O₂:P ratio for respiration and consumption

For CDOM elemental ratios, see Dynamic CDOM.