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Timestamp:
2019-05-23T15:51:08+02:00 (2 years ago)
Author:
nicolasmartin
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Several fixes for the LaTeX compilation of the manuals

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  • NEMO/trunk/doc/latex/TOP/subfiles/model_description.tex

    r11032 r11043  
    2626\end{equation} 
    2727 
    28 where expressions of $D^{lC}$ and $D^{vC}$ depend on the choice for the lateral and vertical subgrid scale parameterizations, see equations 5.10 and 5.11 in \citep{Madec_Bk2008}  
     28where expressions of $D^{lC}$ and $D^{vC}$ depend on the choice for the lateral and vertical subgrid scale parameterizations, see equations 5.10 and 5.11 in \citep{nemo_manual}  
    2929 
    3030{S(C)} , the first term on the right hand side of \ref{Eq_tracer}; is the SMS - Source Minus Sink - inherent to the tracer.  In the case of biological tracer such as phytoplankton, {S(C)} is the balance between phytoplankton growth and its decay through mortality and grazing. In the case of a tracer comprising carbon,  {S(C)} accounts for gas exchange, river discharge, flux to the sediments, gravitational sinking and other biological processes. In the case of a radioactive tracer, {S(C)} is simply loss due to radioactive decay. 
     
    6161        \item \textbf{AGE}     :    Water age tracking 
    6262        \item \textbf{MY\_TRC}  :   Template for creation of new modules and external BGC models coupling 
    63         \item \textbf{PISCES}    :   Built in BGC model. See \citep{Aumont_al_2015} for a throughout description. 
     63        \item \textbf{PISCES}    :   Built in BGC model. See \citep{aumont_2015} for a throughout description. 
    6464\end{itemize} 
    6565%  ---------------------------------------------------------- 
     
    7373\nlst{namtrc_adv} 
    7474%------------------------------------------------------------------------------------------------------------- 
    75 The advection schemes used for the passive tracers are the same than the ones for $T$ and $S$ and described in section 5.1 of \citep{Madec_Bk2008}. The choice of an advection scheme  can be selected independently and  can differ from the ones used for active tracers. This choice is made in the \textit{namtrc\_adv} namelist, by  setting to \textit{true} one and only one of the logicals \textit{ln\_trcadv\_xxx}, the same way of what is done for dynamics. 
     75The advection schemes used for the passive tracers are the same than the ones for $T$ and $S$ and described in section 5.1 of \citep{nemo_manual}. The choice of an advection scheme  can be selected independently and  can differ from the ones used for active tracers. This choice is made in the \textit{namtrc\_adv} namelist, by  setting to \textit{true} one and only one of the logicals \textit{ln\_trcadv\_xxx}, the same way of what is done for dynamics. 
    7676cen2, MUSCL2, and UBS are not \textit{positive} schemes meaning that negative values can appear in an initially strictly positive tracer field which is advected, implying that false extrema are permitted. Their use is not recommended on passive tracers 
    7777 
     
    8080\nlst{namtrc_ldf} 
    8181%------------------------------------------------------------------------------------------------------------- 
    82 In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set  in the \ngn{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{Madec_Bk2008}.  
     82In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set  in the \ngn{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{nemo_manual}.  
    8383 
    8484 
     
    145145 
    146146 
    147  This implementation was first used in the CORE-II intercomparison runs described e.g.\ in \citet{Danabasoglu_al_2014}. 
     147 This implementation was first used in the CORE-II intercomparison runs described e.g.\ in \citet{danabasoglu_2014}. 
    148148 
    149149\subsection{Inert carbons tracer} 
     
    178178Measuring the dissolved concentrations of the gases -- as well as the mixing ratios between them -- shows circulation pathways within the ocean as well as water mass ages (i.e. the time since last contact with the 
    179179atmosphere). This feature of the gases has made them valuable across a wide range of oceanographic problems. One use lies in ocean modelling, where they can be used to evaluate the realism of the circulation and  
    180 ventilation of models, key for understanding the behaviour of wider modelled marine biogeochemistry (e.g. \citep{Dutay_al_2002,Palmieri_2015}). \\ 
     180ventilation of models, key for understanding the behaviour of wider modelled marine biogeochemistry (e.g. \citep{dutay_2002,palmieri_2015}). \\ 
    181181 
    182182Modelling these gases (henceforth CFCs) in NEMO is done within the passive tracer transport module, TOP, using the conservation state equation \ref{Eq_tracer} 
     
    187187stable within the ocean, we assume that there are no sinks (i.e. no loss processes) within the ocean interior.  
    188188Consequently, the sinks-minus-sources term for CFCs consists only of their air-sea fluxes, $F_{cfc}$, as 
    189 described in the Ocean Model Inter-comparison Project (OMIP) protocol \citep{Orr_al_2017}: 
     189described in the Ocean Model Inter-comparison Project (OMIP) protocol \citep{orr_2017}: 
    190190 
    191191% Because CFCs being stable in the ocean, we consider that there is no CFCs sink. 
     
    213213Where $Sol$ is the gas solubility in mol~m$^{-3}$~pptv$^{-1}$, as defined in Equation \ref{equ_Sol_CFC};  
    214214and $P_{cfc}$ is the atmosphere concentration of the CFC (in parts per trillion by volume, pptv). 
    215 This latter concentration is provided to the model by the historical time-series of \citet{Bullister_2015}. 
     215This latter concentration is provided to the model by the historical time-series of \citet{bullister_2017}. 
    216216This includes bulk atmospheric concentrations of the CFCs for both hemispheres -- this is necessary because of  
    217217the geographical asymmetry in the production and release of CFCs to the atmosphere.  
     
    220220 
    221221The piston velocity $K_{w}$ is a function of 10~m wind speed (in m~s$^{-1}$) and sea surface temperature,  
    222 $T$ (in $^{\circ}$C), and is calculated here following \citet{Wanninkhof_1992}: 
     222$T$ (in $^{\circ}$C), and is calculated here following \citet{wanninkhof_1992}: 
    223223 
    224224\begin{eqnarray} 
     
    229229Where $X_{conv}$ = $\frac{0.01}{3600}$, a conversion factor that changes the piston velocity  
    230230from cm~h$^{-1}$ to m~s$^{-1}$;  
    231 $a$ is a constant re-estimated by \citet{Wanninkhof_2014} to 0.251 (in $\frac{cm~h^{-1}}{(m~s^{-1})^{2}}$); 
     231$a$ is a constant re-estimated by \citet{wanninkhof_2014} to 0.251 (in $\frac{cm~h^{-1}}{(m~s^{-1})^{2}}$); 
    232232and $u$ is the 10~m wind speed in m~s$^{-1}$ from either an atmosphere model or reanalysis atmospheric forcing. 
    233 $Sc$ is the Schmidt number, and is calculated as follow, using coefficients from \citet{Wanninkhof_2014} (see Table \ref{tab_Sc}). 
     233$Sc$ is the Schmidt number, and is calculated as follow, using coefficients from \citet{wanninkhof_2014} (see Table \ref{tab_Sc}). 
    234234 
    235235\begin{eqnarray} 
     
    240240The solubility, $Sol$, used in Equation \ref{equ_C_sat} is calculated in mol~l$^{-1}$~atm$^{-1}$,  
    241241and is specific for each gas.  
    242 It has been experimentally estimated by \citet{Warner_Weiss_1985} as a function of temperature  
     242It has been experimentally estimated by \citet{warner_1985} as a function of temperature  
    243243and salinity: 
    244244 
     
    363363where $\Rq_{\textrm{ref}}$ is a reference ratio. For the purpose of ocean ventilation studies $\Rq_{\textrm{ref}}$ is set to one. 
    364364 
    365 Here we adopt the approach of \cite{Fiadeiro_1982} and \cite{Toggweiler_al_1989a,Toggweiler_al_1989b} in which  the ratio $\Rq$ is transported rather than the individual concentrations C and $\cq$. 
    366 This approach calls for a strong assumption, i.e., that of a homogeneous and constant dissolved inorganic carbon (DIC) field \citep{Toggweiler_al_1989a,Mouchet_2013}. While in terms of 
    367 oceanic $\Dcq$, it yields similar results to approaches involving carbonate chemistry, it underestimates the bomb radiocarbon inventory because it assumes a constant air-sea $\cd$ disequilibrium (Mouchet, 2013). Yet, field reconstructions of the ocean bomb $\cq$ inventory are also biased low \citep{Naegler_2009} since they assume that the anthropogenic perturbation did not affect ocean DIC since the pre-bomb epoch. For these reasons, bomb $\cq$ inventories obtained with the present method are directly comparable to reconstructions based on field measurements. 
    368  
    369 This simplified approach also neglects the effects of fractionation (e.g.,  air-sea exchange) and of biological processes. Previous studies by \cite{Bacastow_MaierReimer_1990} and \cite{Joos_al_1997} resulted in nearly identical $\Dcq$ distributions among experiments considering biology or not. 
    370 Since observed $\Rq$ ratios are corrected for the isotopic fractionation when converted to the standard $\Dcq$ notation \citep{Stuiver_Polach_1977} the model results are directly comparable to observations.  
     365Here we adopt the approach of \cite{fiadeiro_1982} and \cite{toggweiler_1989a,toggweiler_1989b} in which  the ratio $\Rq$ is transported rather than the individual concentrations C and $\cq$. 
     366This approach calls for a strong assumption, i.e., that of a homogeneous and constant dissolved inorganic carbon (DIC) field \citep{toggweiler_1989a,mouchet_2013}. While in terms of 
     367oceanic $\Dcq$, it yields similar results to approaches involving carbonate chemistry, it underestimates the bomb radiocarbon inventory because it assumes a constant air-sea $\cd$ disequilibrium (Mouchet, 2013). Yet, field reconstructions of the ocean bomb $\cq$ inventory are also biased low \citep{naegler_2009} since they assume that the anthropogenic perturbation did not affect ocean DIC since the pre-bomb epoch. For these reasons, bomb $\cq$ inventories obtained with the present method are directly comparable to reconstructions based on field measurements. 
     368 
     369This simplified approach also neglects the effects of fractionation (e.g.,  air-sea exchange) and of biological processes. Previous studies by \cite{bacastow_1990} and \cite{joos_1997} resulted in nearly identical $\Dcq$ distributions among experiments considering biology or not. 
     370Since observed $\Rq$ ratios are corrected for the isotopic fractionation when converted to the standard $\Dcq$ notation \citep{stuiver_1977} the model results are directly comparable to observations.  
    371371 
    372372Therefore the simplified approach is justified for the purpose of assessing the circulation and ventilation of OGCMs. 
     
    378378where $\lambda$ is the radiocarbon decay rate, ${\mathbf{u}}$ the 3-D velocity field, and $\mathbf{K}$ the diffusivity tensor. 
    379379 
    380 At the air-sea interface a Robin boundary condition \citep{Haine_2006} is applied to \eqref{eq:quick}, i.e., the flux 
     380At the air-sea interface a Robin boundary condition \citep{haine_2006} is applied to \eqref{eq:quick}, i.e., the flux 
    381381through the interface is proportional to the difference in the ratios between 
    382382the ocean and the atmosphere 
     
    391391 
    392392 
    393 The $\cd$ transfer velocity is based on the empirical formulation of \cite{Wanninkhof_1992} with chemical enhancement \citep{Wanninkhof_Knox_1996,Wanninkhof_2014}. The original formulation is modified to account for the reduction of the  air-sea exchange rate in the presence of sea ice. Hence 
     393The $\cd$ transfer velocity is based on the empirical formulation of \cite{wanninkhof_1992} with chemical enhancement \citep{wanninkhof_1996,wanninkhof_2014}. The original formulation is modified to account for the reduction of the  air-sea exchange rate in the presence of sea ice. Hence 
    394394\begin{equation} 
    395395\kappa_\cd=\left( K_W\,\mathrm{w}^2 + b  \right)\, (1-f_\mathrm{ice})\,\sqrt{660/Sc}, \label{eq:wanc14} 
     
    397397with $\mathrm{w}$ the wind magnitude, $f_\mathrm{ice}$ the fractional ice cover, and $Sc$ the Schmidt number. 
    398398$K_W$ in \eqref{eq:wanc14} is an empirical coefficient with dimension of an inverse velocity. 
    399 The chemical enhancement term $b$ is represented as a function of temperature $T$ \citep{Wanninkhof_1992} 
     399The chemical enhancement term $b$ is represented as a function of temperature $T$ \citep{wanninkhof_1992} 
    400400\begin{equation} 
    401401b=2.5 ( 0.5246 + 0.016256 T+ 0.00049946  * T^2 ). \label{eq:wanchem} 
     
    413413\label{sec:param} 
    414414 % 
    415 The radiocarbon decay rate (\CODE{rlam14}; in \texttt{trcnam\_c14} module) is set to $\lambda=(1/8267)$ yr$^{-1}$ \citep{Stuiver_Polach_1977}, which corresponds to a half-life of 5730 yr.\\[1pt] 
    416 % 
    417 The Schmidt number $Sc$, Eq. \eqref{eq:wanc14}, is calculated with the help of the formulation of \cite{Wanninkhof_2014}. The $\cd$ solubility $K_0$ in \eqref{eq:Rspeed} is taken from \cite{Weiss_1974}. $K_0$ and $Sc$ are computed with the OGCM temperature and salinity fields (\texttt{trcsms\_c14} module).\\[1pt] 
     415The radiocarbon decay rate (\CODE{rlam14}; in \texttt{trcnam\_c14} module) is set to $\lambda=(1/8267)$ yr$^{-1}$ \citep{stuiver_1977}, which corresponds to a half-life of 5730 yr.\\[1pt] 
     416% 
     417The Schmidt number $Sc$, Eq. \eqref{eq:wanc14}, is calculated with the help of the formulation of \cite{wanninkhof_2014}. The $\cd$ solubility $K_0$ in \eqref{eq:Rspeed} is taken from \cite{weiss_1974}. $K_0$ and $Sc$ are computed with the OGCM temperature and salinity fields (\texttt{trcsms\_c14} module).\\[1pt] 
    418418% 
    419419The following parameters intervening in the air-sea exchange rate are set in \texttt{namelist\_c14}: 
    420420\begin{itemize} 
    421 \item The reference DIC concentration $\overline{\Ct}$ (\CODE{xdicsur}) intervening in \eqref{eq:Rspeed} is classically set to 2 mol m$^{-3}$ \citep{Toggweiler_al_1989a,Orr_al_2001,Butzin_al_2005}. 
    422 % 
    423 \item The value of the empirical coefficient $K_W$ (\CODE{xkwind}) in \eqref{eq:wanc14} depends on the wind field and on the model upper ocean mixing rate \citep{Toggweiler_al_1989a,Wanninkhof_1992,Naegler_2009,Wanninkhof_2014}. 
    424 It should be adjusted so that the globally averaged $\cd$ piston velocity is $\kappa_\cd = 16.5\pm 3.2$ cm/h \citep{Naegler_2009}. 
     421\item The reference DIC concentration $\overline{\Ct}$ (\CODE{xdicsur}) intervening in \eqref{eq:Rspeed} is classically set to 2 mol m$^{-3}$ \citep{toggweiler_1989a,orr_2001,butzin_2005}. 
     422% 
     423\item The value of the empirical coefficient $K_W$ (\CODE{xkwind}) in \eqref{eq:wanc14} depends on the wind field and on the model upper ocean mixing rate \citep{toggweiler_1989a,wanninkhof_1992,naegler_2009,wanninkhof_2014}. 
     424It should be adjusted so that the globally averaged $\cd$ piston velocity is $\kappa_\cd = 16.5\pm 3.2$ cm/h \citep{naegler_2009}. 
    425425%The sensitivity to this parametrization is discussed in section \ref{sec:result}. 
    426426% 
     
    440440\CODE{kc14typ}=0 
    441441 
    442 Unless otherwise specified in \texttt{namelist\_c14}, the atmospheric $\Rq_a$ (\CODE{rc14at}) is set to one, the atmospheric $\cd$ (\CODE{pco2at}) to 280 ppm, and the ocean $\Rq$ is initialized with \CODE{rc14init=0.85}, i.e., $\Dcq=$-150\textperthousand  \cite[typical for deep-ocean, Fig 6 in][]{Key_al_2004}. 
    443  
    444 Equilibrium experiment should last until 98\% of the ocean volume exhibit a drift of less than 0.001\textperthousand/year \citep{Orr_al_2000}; this is usually achieved after few kyr (Fig. \ref{fig:drift}). 
     442Unless otherwise specified in \texttt{namelist\_c14}, the atmospheric $\Rq_a$ (\CODE{rc14at}) is set to one, the atmospheric $\cd$ (\CODE{pco2at}) to 280 ppm, and the ocean $\Rq$ is initialized with \CODE{rc14init=0.85}, i.e., $\Dcq=$-150\textperthousand  \cite[typical for deep-ocean, Fig 6 in][]{key_2004}. 
     443 
     444Equilibrium experiment should last until 98\% of the ocean volume exhibit a drift of less than 0.001\textperthousand/year \citep{orr_2000}; this is usually achieved after few kyr (Fig. \ref{fig:drift}). 
    445445% 
    446446\begin{figure}[!h] 
     
    469469 
    470470The model  is integrated from a given initial date following the observed records provided from 1765 AD on ( Fig. \ref{fig:bomb}). 
    471 The file \texttt{atmc14.dat}  \cite[][\& I. Levin, personal comm.]{Enting_al_1994} provides atmospheric $\Dcq$ for three latitudinal bands: 90S-20S,    20S-20N \&    20N-90N. 
    472 Atmospheric $\cd$ in the file \texttt{splco2.dat} is obtained from a spline fit through ice core data and direct atmospheric measurements \cite[][\& J. Orr, personal comm.]{Orr_al_2000}. 
     471The file \texttt{atmc14.dat}  \cite[][\& I. Levin, personal comm.]{enting_1994} provides atmospheric $\Dcq$ for three latitudinal bands: 90S-20S,    20S-20N \&    20N-90N. 
     472Atmospheric $\cd$ in the file \texttt{splco2.dat} is obtained from a spline fit through ice core data and direct atmospheric measurements \cite[][\& J. Orr, personal comm.]{orr_2000}. 
    473473Dates in these forcing files are expressed as yr AD. 
    474474 
     
    496496Atmospheric $\Rq_a$ and $\cd$ are prescribed from forcing files. The ocean $\Rq$ is initialized with the value attributed to \CODE{rc14init} in \texttt{namelist\_c14}. 
    497497 
    498 The file \texttt{intcal13.14c} \citep{Reimer_al_2013} contains atmospheric $\Dcq$ from 0 to 50 kyr cal BP\footnote{cal BP: number of years before 1950 AD}. 
    499 The $\cd$ forcing is provided in file \texttt{ByrdEdcCO2.txt}. The content of this file is based on  the high resolution record from EPICA Dome C \citep{Monnin_al_2004} for the Holocene and the Transition, and on Byrd Ice Core CO2 Data for 20--90 kyr BP  \citep{Ahn_Brook_2008}. These atmospheric values are reproduced in Fig. \ref{fig:paleo}. Dates in these files are expressed as yr BP.  
     498The file \texttt{intcal13.14c} \citep{reimer_2013} contains atmospheric $\Dcq$ from 0 to 50 kyr cal BP\footnote{cal BP: number of years before 1950 AD}. 
     499The $\cd$ forcing is provided in file \texttt{ByrdEdcCO2.txt}. The content of this file is based on  the high resolution record from EPICA Dome C \citep{monnin_2004} for the Holocene and the Transition, and on Byrd Ice Core CO2 Data for 20--90 kyr BP  \citep{ahn_2008}. These atmospheric values are reproduced in Fig. \ref{fig:paleo}. Dates in these files are expressed as yr BP.  
    500500 
    501501To ensure that the atmospheric forcing is applied properly as well as that output files contain consistent dates and inventories the experiment should be set up carefully. 
     
    539539The radiocarbon age is computed as  $(-1/\lambda) \ln{ \left( \Rq \right)}$, with zero age corresponding to $\Rq=1$.  
    540540 
    541 The reservoir age is the age difference between the ocean uppermost layer and the atmosphere. It is usually reported as conventional radiocarbon age; i.e., computed by means of the Libby radiocarbon mean life \cite[8033 yr;][]{Stuiver_Polach_1977} 
     541The reservoir age is the age difference between the ocean uppermost layer and the atmosphere. It is usually reported as conventional radiocarbon age; i.e., computed by means of the Libby radiocarbon mean life \cite[8033 yr;][]{stuiver_1977} 
    542542\begin{align} 
    543543{^{14}\tau_\mathrm{c}}= -8033 \; \ln \left(1 + \frac{\Dcq}{10^3}\right), \label{eq:convage} 
     
    549549N_A \Rq_\mathrm{oxa} \overline{\Ct} \left( \int_\Omega \Rq d\Omega \right) /10^{26}, \label{eq:inv} 
    550550\end{equation} 
    551 where $N_A$ is the Avogadro's number ($N_A=6.022\times10^{23}$ at/mol), $\Rq_\mathrm{oxa}$ is the oxalic acid radiocarbon standard \cite[$\Rq_\mathrm{oxa}=1.176\times10^{-12}$;][]{Stuiver_Polach_1977}, and $\Omega$ is the ocean volume.  Bomb $\cq$ inventories are traditionally reported in units of $10^{26}$ atoms, hence the denominator in \eqref{eq:inv}. 
     551where $N_A$ is the Avogadro's number ($N_A=6.022\times10^{23}$ at/mol), $\Rq_\mathrm{oxa}$ is the oxalic acid radiocarbon standard \cite[$\Rq_\mathrm{oxa}=1.176\times10^{-12}$;][]{stuiver_1977}, and $\Omega$ is the ocean volume.  Bomb $\cq$ inventories are traditionally reported in units of $10^{26}$ atoms, hence the denominator in \eqref{eq:inv}. 
    552552 
    553553All transformations from second to year, and inversely, are performed with the help of the physical constant \CODE{rsiyea} the sideral year length expressed in seconds\footnote{The variable (\CODE{nyear\_len}) which reports the length in days of the previous/current/future year (see \textrm{oce\_trc.F90}) is not a constant. }. 
     
    564564Two versions of PISCES are available in NEMO v4.0 : 
    565565 
    566 PISCES-v2, by setting in namelist\_pisces\_ref  \np{ln\_p4z} to true,  can be seen as one of the many Monod models \citep{Monod_1942}. It assumes a constant Redfield ratio and phytoplankton growth depends on the external concentration in nutrients. There are twenty-four prognostic variables (tracers) including two phytoplankton compartments  (diatoms and nanophytoplankton), two zooplankton size-classes (microzooplankton and  mesozooplankton) and a description of the carbonate chemistry. Formulations in PISCES-v2 are based on a mixed Monod/Quota formalism: On one hand, stoichiometry of C/N/P is fixed and growth rate of phytoplankton is limited by the external availability in N, P and Si. On the other hand, the iron and silicium quotas are variable and growth rate of phytoplankton is limited by the internal availability in Fe. Various parameterizations can be activated in PISCES-v2, setting for instance the complexity of iron chemistry or the description of particulate organic materials.  
    567  
    568 PISCES-QUOTA has been built on the PISCES-v2 model described in \citet{Aumont_al_2015}. PISCES-QUOTA has thirty-nine prognostic compartments. Phytoplankton growth can be controlled by five modeled limiting nutrients: Nitrate and Ammonium, Phosphate, Silicate and Iron. Five living compartments are represented: Three phytoplankton size classes/groups corresponding to picophytoplankton, nanophytoplankton and diatoms, and two zooplankton size classes which are microzooplankton and mesozooplankton. For phytoplankton, the prognostic variables are the carbon, nitrogen, phosphorus,  iron, chlorophyll and silicon biomasses (the latter only for diatoms). This means that the N/C, P/C, Fe/C and Chl/C ratios of both phytoplankton groups as well as the Si/C ratio of diatoms are prognostically predicted  by the model. Zooplankton are assumed to be strictly homeostatic \citep[e.g.,][]{Sterner_2002,Woods_Wilson_2013,Meunier_al_2014}. As a consequence, the C/N/P/Fe ratios of these groups are maintained constant and are not allowed to vary. In PISCES, the Redfield ratios C/N/P are set to 122/16/1 \citep{Takahashi_al_1985} and the -O/C ratio is set to 1.34 \citep{Kortzinger_al_2001}. No silicified zooplankton is assumed. The bacterial pool is not yet explicitly modeled. 
    569  
    570 There are three non-living compartments: Semi-labile dissolved organic matter, small sinking particles, and large sinking particles. As a consequence of the variable stoichiometric ratios of phytoplankton and of the stoichiometric regulation of zooplankton, elemental ratios in organic matter cannot be supposed constant anymore as that was the case in PISCES-v2. Indeed, the nitrogen, phosphorus, iron, silicon and calcite pools of the particles are now all explicitly modeled. The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (''The ballast effect'', \citep{Honjo_1996,Armstrong_al_2002}). The latter particles are assumed to sink at the same speed as the large organic matter particles. All the non-living compartments experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM. 
     566PISCES-v2, by setting in namelist\_pisces\_ref  \np{ln\_p4z} to true,  can be seen as one of the many Monod models \citep{monod_1958}. It assumes a constant Redfield ratio and phytoplankton growth depends on the external concentration in nutrients. There are twenty-four prognostic variables (tracers) including two phytoplankton compartments  (diatoms and nanophytoplankton), two zooplankton size-classes (microzooplankton and  mesozooplankton) and a description of the carbonate chemistry. Formulations in PISCES-v2 are based on a mixed Monod/Quota formalism: On one hand, stoichiometry of C/N/P is fixed and growth rate of phytoplankton is limited by the external availability in N, P and Si. On the other hand, the iron and silicium quotas are variable and growth rate of phytoplankton is limited by the internal availability in Fe. Various parameterizations can be activated in PISCES-v2, setting for instance the complexity of iron chemistry or the description of particulate organic materials.  
     567 
     568PISCES-QUOTA has been built on the PISCES-v2 model described in \citet{aumont_2015}. PISCES-QUOTA has thirty-nine prognostic compartments. Phytoplankton growth can be controlled by five modeled limiting nutrients: Nitrate and Ammonium, Phosphate, Silicate and Iron. Five living compartments are represented: Three phytoplankton size classes/groups corresponding to picophytoplankton, nanophytoplankton and diatoms, and two zooplankton size classes which are microzooplankton and mesozooplankton. For phytoplankton, the prognostic variables are the carbon, nitrogen, phosphorus,  iron, chlorophyll and silicon biomasses (the latter only for diatoms). This means that the N/C, P/C, Fe/C and Chl/C ratios of both phytoplankton groups as well as the Si/C ratio of diatoms are prognostically predicted  by the model. Zooplankton are assumed to be strictly homeostatic \citep[e.g.,][]{sterner_2003,woods_2013,meunier_2014}. As a consequence, the C/N/P/Fe ratios of these groups are maintained constant and are not allowed to vary. In PISCES, the Redfield ratios C/N/P are set to 122/16/1 \citep{takahashi_1985} and the -O/C ratio is set to 1.34 \citep{kortzinger_2001}. No silicified zooplankton is assumed. The bacterial pool is not yet explicitly modeled. 
     569 
     570There are three non-living compartments: Semi-labile dissolved organic matter, small sinking particles, and large sinking particles. As a consequence of the variable stoichiometric ratios of phytoplankton and of the stoichiometric regulation of zooplankton, elemental ratios in organic matter cannot be supposed constant anymore as that was the case in PISCES-v2. Indeed, the nitrogen, phosphorus, iron, silicon and calcite pools of the particles are now all explicitly modeled. The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (''The ballast effect'', \citep{honjo_1996,armstrong_2001}). The latter particles are assumed to sink at the same speed as the large organic matter particles. All the non-living compartments experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM. 
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