8.7.3.1. Model equations
The basic model equations are (omitting transport terms handled by the ptracers
package, sinking and swimming terms discussed in
Section 8.7.3.19, terms correcting conservation with the
linear free surface formulation discussed in
Section 8.7.3.20) and surface fluxes related to
Carbon chemistry:
\[\begin{split}\partial_t\op{DIC} &= \sum_j \bigl( (-U^{\op{DIC}}_j + R^{\mathrm{C}}_j)
\cdot (1 + R^{\text{PIC:POC}}_j)
+ R^{\op{DIC}}_j
\bigr)
+ R_{\op{DOC}} + [R_{\op{POC}}]
+ \kappa^{{\text{diss}}}_{\mathrm{C}}\op{PIC} \\
\partial_t\op{PO}_4 &= \sum_j \bigl( -U^{\op{PO4}}_j + R^{\mathrm{P}}_j + R^{\op{PO4}}_j \bigr)
+ R_{\op{DOP}} + [R_{\op{POP}}] \\
\partial_t\op{NH}_4 &= \sum_j \bigl( -U^{\op{NH4}}_j + R^{\mathrm{N,NH4}}_j + R^{\op{NH4}}_j \bigr)
+ R_{\op{DON}} + [R_{\op{PON}}] - P_{\op{NO2}} - D_{\op{NH4}} \\
\partial_t\op{NO}_2 &= \sum_j \bigl( -U^{\op{NO2}}_j + R^{\mathrm{N,NO2}}_j + R^{\op{NO2}}_j \bigr)
+ P_{\op{NO2}} - P_{\op{NO3}} \\
\partial_t\op{NO}_3 &= \sum_j \bigl( -U^{\op{NO3}}_j + R^{\mathrm{N,NO3}}_j + R^{\op{NO3}}_j \bigr)
+ P_{\op{NO3}} - D_{\op{NO3}} \\
\partial_t\op{FeT} &= \sum_j \bigl( -U^{\op{Fe}}_j + R^{\mathrm{Fe}}_j + R^{\op{FeT}}_j \bigr)
+ R_{\op{DOFe}} + [R_{\op{POFe}}] + S_{\op{Fe}} \\
\partial_t\op{SiO}_2 &= \sum_j \bigl( -U^{\op{SiO2}}_j + R^{\mathrm{Si}}_j \bigr)
+ R_{\op{POSi}} \\
\partial_t c_j &= U^{\op{DIC}}_j - M_j - R^{\mathrm{C}}_j - G_j + g_j^{\mathrm{C}} \\
\partial_t p_j &= U^{\op{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^{{\op{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^{\op{Fe}}_j \;\; - M_j Q^{\op{Fe}}_j - G_j Q^{\op{Fe}}_j + g_j^{\op{Fe}} \qquad\text{(with Fe quota)} \\
\partial_t\op{si}_j &= U^{\op{SiO2}}_j - M_j Q^{\op{Si}}_j - G_j Q^{\op{Si}}_j \qquad\text{(with Si quota)} \\
\partial_t\op{Chl}_j &= S^{\op{Chl}}_j \; - M_j \cdot \op{Chl\text{:}C}_j - G_j \cdot \op{Chl\text{:}C}_j \qquad\text{(with Chl quota)} \\
\partial_t\op{DOC} &= \sum_j M_j^{\op{DOM}} \;\;\;\;\; + g^{\op{DOC}} + \sum_j \left( H^{\op{POC}}_j - U^{\op{DOC}}_j \right) - R_{\op{DOC}} - S_{\op{CDOM}} R^{{\mathrm{C}}:{\mathrm{P}}}_{\op{CDOM}} \\
\partial_t\op{DOP} &= \sum_j M_j^{\op{DOM}} Q_j^{{\mathrm{P}}} + g^{\op{DOP}} + \sum_j \left( H^{\op{POP}}_j - U^{\op{DOP}}_j \right) - R_{\op{DOP}} - S_{\op{CDOM}} \\
\partial_t\op{DON} &= \sum_j M_j^{\op{DOM}} Q_j^{{\mathrm{N}}} + g^{\op{DON}} + \sum_j \left( H^{\op{PON}}_j - U^{\op{DON}}_j \right) - R_{\op{DON}} - S_{\op{CDOM}} R^{{\mathrm{N}}:{\mathrm{P}}}_{\op{CDOM}} \\
\partial_t\op{DOFe} &= \sum_j M_j^{\op{DOM}} Q_j^{\op{Fe}} + g^{\op{DOFe}} + \sum_j \left( H^{\op{POFe}}_j- U^{\op{DOFe}}_j\right) - R_{\op{DOFe}}- S_{\op{CDOM}} R^{{\mathrm{Fe}}:{\mathrm{P}}}_{\op{CDOM}} \\
\partial_t\op{PIC} &= \sum_j M_j R_j^{\text{PIC:POC}} + g^{\op{PIC}} - \kappa^{{\text{diss}}}_{\mathrm{C}}\op{PIC} \\
\partial_t\op{POC} &= \sum_j M_j^{\op{POM}} \;\;\;\;\; + g^{\op{POC}} - \sum_j U^{\op{POC}}_j - R_{\op{POC}} \\
\partial_t\op{POP} &= \sum_j M_j^{\op{POM}} Q_j^{{\mathrm{P}}} + g^{\op{POP}} - \sum_j U^{\op{POP}}_j - R_{\op{POP}} \\
\partial_t\op{PON} &= \sum_j M_j^{\op{POM}} Q_j^{{\mathrm{N}}} + g^{\op{PON}} - \sum_j U^{\op{PON}}_j - R_{\op{PON}} \\
\partial_t\op{POFe} &= \sum_j M_j^{\op{POM}} Q_j^{\op{Fe}} + g^{\op{POFe}} - \sum_j U^{\op{POFe}}_j - R_{\op{POFe}} \\
\partial_t\op{POSi} &= \sum_j M_j Q_j^{\op{Si}} \;\;\;\;\; + g^{\op{POSi}} - R_{\op{POSi}} \\
\partial_t\op{ALK} &= -\biggl( P_{\op{NO3}} - \sum_j U^{\op{NO3}}_j \biggr)
- 2\biggl( \sum_j U^{\op{DIC}}_j R^{{\text{PIC:POC}}}_j - \kappa^{{\text{diss}}}_{\mathrm{C}}\op{PIC}\biggr)
+ D_{\op{NO3}} \\
\partial_t{\mathrm{O}}_2 &= R_{\mathrm{O}_2:\mathrm{P}} \biggl(
\sum_j U^{\op{PO4}}_j
- R_{\op{DOP}} - [R_{\op{POP}}]
\biggr)
\\
\partial_t\op{CDOM} &= S_{\op{CDOM}} \qquad\text{(with CDOM tracer)} \\\end{split}\]
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
\(D\): denitrification, see Denitrification
\(g\), \(G\): grazing gains and losses, see Grazing
\(S^{\op{Chl}}\): synthesis, see Chlorophyll synthesis
\(S_{\op{Fe}}\): iron sources, see Iron chemistry
\(S_{\op{CDOM}}\): see Dynamic CDOM.
With DARWIN_ALLOW_CDOM, all particulate remineralization terms
(in square brackets […]) except Si are absent.
Without DARWIN_ALLOW_CDOM, \(f_{\op{CDOM}}=0\) and there is no CDOM tracer.
Table 8.28 General parameters
Trait |
Param |
Symbol |
Default |
Units |
Description |
|---|
|
Kdissc |
\(\kappa^{\op{diss}}_{\mathrm{C}}\) |
1/(300 days) |
1/s |
dissolution rate for PIC |
R_PICPOC |
a_R_PICPOC |
\(R^{\op{PIC:POC}}_j\) |
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 |