.. include:: ../defs.hrst Model equations ^^^^^^^^^^^^^^^ The basic model equations are (omitting transport terms handled by the ptracers package, :ref:`para_phys_pkg_darwin_sink`, :ref:`AirSea` and terms correcting conservation with the linear free surface formulation discussed in :numref:`para_phys_pkg_darwin_cons`): .. math:: \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)} \\ The quotas are defined as :math:`Q^{\mathrm{P}}_j=p_j/c_j`, etc. The following abbreviated source terms are described in sections below: - :math:`U`: uptake, see :ref:`Uptake` and :ref:`Bacteria`, also :ref:`Growth`, :ref:`CarbonStore`, :ref:`Light` and :ref:`Spectral` - :math:`M`: :ref:`Mortality` - :math:`R^{\mathrm{C}}`: :ref:`Respiration` - :math:`H`, :math:`R_j`: bacterial hydrolysis and remineralization, see :ref:`Bacteria` - :math:`R`, :math:`P`: parameterized :ref:`Remineralization` - :math:`D_{\mathrm{NO3}}`: denitrification, see :ref:`Denitrification` - :math:`D_{\mathrm{PIC}}`: dissolution of PIC, see :ref:`CarbonChemistry` - :math:`g`, :math:`G`: grazing gains and losses, see :ref:`Grazing` - :math:`S^{\mathrm{Chl}}`: synthesis, see :ref:`Synthesis` - :math:`S_{\mathrm{Fe}}`: iron sources, see :ref:`Iron` - :math:`S_{\mathrm{CDOM}}`: see :ref:`CDOM`. With :varlink:`DARWIN_ALLOW_CDOM`, all particulate remineralization terms (in square brackets [...]) except Si are absent. Without :varlink:`DARWIN_ALLOW_CDOM`, :math:`f_{\mathrm{CDOM}}=0` and there is no CDOM tracer. The Alk and O\ :sub:`2` tracers are only present with :varlink:`DARWIN_ALLOW_CARBON`. .. csv-table:: General parameters :delim: & :widths: 15,17,14,11,18,25 :class: longtable :header: Trait, Param, Symbol, Default, Units, Description :varlink:`R_PICPOC` & :varlink:`a_R_PICPOC` & :math:`R^{\text{PIC:POC}}_j` & 0.8 & mmol PIC / mmol POC & inorganic-organic carbon ratio & :varlink:`R_OP` & :math:`R_{\mathrm{O}_2:\mathrm{P}}` & 170 & mmol O\ :sub:`2` / mmol P & O\ :sub:`2`:P ratio for respiration and consumption For CDOM elemental ratios, see :ref:`CDOM`.