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1\documentclass[../main/TOP_manual]{subfiles}
2
3\begin{document}
4
5\newcommand{\cd}{\mathrm{CO_2}}
6\newcommand{\Ct}{\mathrm{C_T}}
7\newcommand{\pacd}{\mathrm{p^a_{CO_2}}}
8\newcommand{\cq}{\mathrm{^{14}C}}
9\newcommand{\Dcq}{\Delta ^{14}\mathrm{C}}
10\newcommand{\Rq}{\mathrm{^{14}{R}}}
11
12\chapter{Model Description}
13\label{chap:ModDes}
14\chaptertoc
15
16\section{Basics}
17\label{sec:Bas}
18
19The time evolution of any passive tracer $C$ follows the transport equation, which is similar to that of active tracer - temperature or salinity :
20
21\begin{equation}
22\frac{\partial C}{\partial t} = {S(C)} -  \frac{1}{b_t} \left[   \frac{\partial e_{2u}\,e_{3u} \;  u\, C}{\partial i} +   \frac{\partial e_{1v}\,e_{3v} \;  uv, C}{\partial i}  \right] + \frac{1}{e_{3t}} \frac{\partial w\, C}{\partial k} + D^{lC} + D^{vC}
23\label{Eq_tracer}
24\end{equation}
25
26where 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}
27
28{S(C)} , the first term on the right hand side of \autoref{Eq_tracer}; is the SMS - Source Minus Sink - inherent to the tracer.
29In the case of biological tracer such as phytoplankton, {S(C)} is the balance between phytoplankton growth and its decay through mortality and grazing.
30In 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.
31In the case of a radioactive tracer, {S(C)} is simply loss due to radioactive decay.
32
33The second term (within brackets) represents the advection of the tracer in the three directions.
34It can be interpreted as the budget between the incoming and outgoing tracer fluxes in a volume $T$-cells $b_t= e_{1t}\,e_{2t}\,e_{3t}$
35
36The third term  represents the change due to lateral diffusion.
37
38The fourth term is change due to vertical diffusion, parameterized as eddy diffusion to represent vertical turbulent fluxes :
39
40\begin{equation}
41D^{vC} =  \frac{1}{e_{3t}} \frac{\partial}{\partial k} \left[  A^{vT} \frac{\partial C}{\partial k} \right]
42\label{Eq_trczdf}
43\end{equation}
44
45where $A^{vT}$ is the vertical eddy diffusivity coefficient of active tracers
46
47\section{The NEMO-TOP interface}
48\label{sec:TopInt}
49
50TOP is the NEMO hardwired interface toward biogeochemical models and provide the physical constraints/boundaries for oceanic tracers.
51It consists of a modular framework to handle multiple ocean tracers, including also a variety of built-in modules.
52
53This component of the NEMO framework allows one to exploit available modules  and further develop a range of applications, spanning from the implementation of a dye passive tracer to evaluate dispersion processes (by means of MY\_TRC), track water masses age (AGE module), assess the ocean interior penetration of persistent chemical compounds (e.g., gases like CFC or even PCBs), up to the full set of equations involving marine biogeochemical cycles.
54
55TOP interface has the following location in the code repository : \path{<repository>/src/TOP/}
56
57and the following modules are available:
58
59% -----------  tableau  ------------------------------------
60\begin{itemize}
61        \item \textbf{TRP}           :    Interface to NEMO physical core for computing tracers transport
62        \item \textbf{CFC}     :    Inert carbon tracers (CFC11,CFC12, SF6)
63        \item \textbf{C14}     :    Radiocarbon passive tracer
64        \item \textbf{AGE}     :    Water age tracking
65        \item \textbf{MY\_TRC}  :   Template for creation of new modules and external BGC models coupling
66        \item \textbf{PISCES}    :   Built in BGC model.
67See \citep{aumont_2015} for a throughout description.
68\end{itemize}
69%  ----------------------------------------------------------
70
71\section{The transport component : TRP}
72
73The passive tracer transport component  shares the same advection/diffusion routines with the dynamics, with specific treatment of some features like the surface boundary conditions, or the positivity of passive tracers concentrations.
74
78%-------------------------------------------------------------------------------------------------------------
79The 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}.
80The choice of an advection scheme  can be selected independently and  can differ from the ones used for active tracers.
81This 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.
82cen2, 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.
83Their use is not recommended on passive tracers
84
85\subsection{Lateral diffusion}
86%------------------------------------------namtrc_ldf----------------------------------------------------
87\nlst{namtrc_ldf}
88%-------------------------------------------------------------------------------------------------------------
89In 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.
90However 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}.
91The choice of numerical scheme is then set in the \forcode{&namtra_ldf} namelist for the dynamic described in section 5.2 of \citep{nemo_manual}.
92
93%-----------------We also offers the possibility to increase zonal equatorial diffusion for passive tracers by introducing an enhanced zonal diffusivity coefficent in the equatorial domain which can be defined by the equation below :
95%-----------------Aht  = Aht *  rn_fact_lap * \exp( - \max( 0., z -1000  ) / 1000}  \quad \text{for $L=1$ to $N$}
96%-----------------
97
98\subsection{Tracer damping}
99
100%------------------------------------------namtrc_dmp----------------------------------------------------
101\nlst{namtrc_dmp}
102%-------------------------------------------------------------------------------------------------------------
103
104The use of newtonian damping  to climatological fields or observations is also coded, sharing the same routine dans active tracers.
105Boolean variables are defined in the namelist\_top\_ref to select the tracers on which restoring is applied
106Options are defined through the \nam{trc_dmp}{trc\_dmp} namelist variables.
107The restoring term is added when the namelist parameter \np{ln\_trcdmp} is set to true.
108The restoring coefficient is a three-dimensional array read in a file, which name is specified by the namelist variable \np{cn\_resto\_tr}.
109This netcdf file can be generated using the DMP\_TOOLS tool.
110
111\subsection{Tracer positivity}
112
115%-------------------------------------------------------------------------------------------------------------
116
117Sometimes, numerical scheme can generates negative values of passive tracers concentration that must be positive.
118For exemple,  isopycnal diffusion can created extrema.
119The trcrad routine artificially corrects negative concentrations with a very crude solution that either sets negative concentration to zero without adjusting the tracer budget, or by removing negative concentration and keeping mass conservation.
120The treatment of negative concentrations is an option and can be selected in the namelist \nam{trc_rad}{trc\_rad} by setting the parameter \np{ln\_trcrad}  to true.
121
122\section{The SMS modules}
123
124\label{SMS_models}
125%------------------------------------------namtrc_sms----------------------------------------------------
126%\nlst{namtrc}
127%-------------------------------------------------------------------------------------------------------------
128
129\subsection{Ideal Age}
130%------------------------------------------namage----------------------------------------------------
131%
132\nlst{namage}
133%----------------------------------------------------------------------------------------------------------
134
135An `ideal age' tracer is integrated online in TOP when \textit{ln\_age} = \texttt{.true.} in namelist \textit{namtrc}.
136This tracer marks the length of time in units of years that fluid has spent in the interior of the ocean, insulated from exposure to the atmosphere.
137Thus, away from the surface for $z<-H_{\mathrm{Age}}$ where $H_{\mathrm{Age}}$ is specified by the \textit{namage} namelist variable \textit{rn\_age\_depth}, whose default value is 10~m, there is a source $\mathrm{SMS_{\mathrm{Age}}}$ of the age tracer $A$:
138
139\begin{equation}
140  \label{eq:TOP-age-interior}
141  \mathrm{SMS_{\mathrm{Age}}} = 1 \mathrm{yr}\;^{-1} = 1/T_{\mathrm{year}},
142\end{equation}
143
144where the length of the current year $T_{\mathrm{year}} = 86400*N_{\mathrm{days\;in\;current\; year}}\;\mathrm{s}$, where $N_{\mathrm{days\;in\;current\; year}}$ may be 366 or 365 depending on whether the current year is a leap year or not.
145Near the surface, for $z>-H_{\mathrm{Age}}$, ideal age is relaxed back to zero:
146
147\begin{equation}
148  \label{eq:TOP-age-surface}
149   \mathrm{SMS_{\mathrm{Age}}} = -\lambda_{\mathrm{Age}}A,
150\end{equation}
151
152where the relaxation rate $\lambda_{\mathrm{Age}}$  (units $\mathrm{s}\;^{-1}$) is specified by the \textit{namage} namelist variable \textit{rn\_age\_kill\_rate} and has a default value of 1/7200~s.
153Since this relaxation is applied explicitly, this relaxation rate in principle should not exceed $1/\Delta t$, where $\Delta t$ is the time step used to step forward passive tracers (2 * \textit{nn\_dttrc * rn\_rdt} when the default  leapfrog time-stepping scheme is employed).
154
155Currently the 1-dimensional reference depth of the grid boxes is used rather than the dynamically evolving depth to determine whether the age tracer is incremented or relaxed to zero.
156This means that the tracer only works correctly in z-coordinates.
157To ensure that the forcing is independent of the level thicknesses, where the tracer cell at level $k$ has its upper face $z=-depw(k)$ above the depth $-H_{\mathrm{Age}}$, but its lower face $z=-depw(k+1)$ below that depth, then the age source
158
159\begin{equation}
160  \label{eq:TOP-age-mixed}
161   \mathrm{SMS_{\mathrm{Age}}} = -f_{\mathrm{kill}}\lambda_{\mathrm{Age}}A +f_{\mathrm{add}}/T_{\mathrm{year}} ,
162\end{equation}
163
164where
165
166\begin{align}
167    f_{\mathrm{kill}} &= e3t_k^{-1}(H_{\mathrm{Age}} - depw(k)) , \\
168    f_{\mathrm{add}} &= 1 - f_{\mathrm{kill}}.
169\end{align}
170
171
172This implementation was first used in the CORE-II intercomparison runs described e.g.\ in \citet{danabasoglu_2014}.
173
174\subsection{Inert carbons tracer}
175
176%------------------------------------------namage----------------------------------------------------
177%
178\nlst{namcfc}
179%----------------------------------------------------------------------------------------------------------
180
181Chlorofluorocarbons 11 and 12 (CFC-11 and CFC-12), and sulfur hexafluoride (SF6), are synthetic chemicals manufactured for industrial and domestic applications from the early 20th century onwards.
182CFC-11 (CCl$_{3}$F) is a volatile liquid at room temperature, and was widely used in refrigeration.
183CFC-12 (CCl$_{2}$F$_{2}$) is a gas at room temperature, and, like CFC-11, was widely used as a refrigerant,
184and additionally as an aerosol propellant.
185SF6 (SF$_{6}$) is also a gas at room temperature, with a range of applications based around its property as an excellent electrical insulator (often replacing more toxic alternatives).
186All three are relatively inert chemicals that are both non-toxic and non-flammable, and their wide use has led to their accumulation within the Earth's atmosphere.
187Large-scale production of CFC-11 and CFC-12 began in the 1930s, while production of SF6 began in the 1950s, and their atmospheric concentration time-histories are shown in Figure \autoref{img_cfcatm}.
188As can be seen in the figure, while the concentration of SF6 continues to rise to the present  day, the concentrations of both CFC-11 and CFC-12 have levelled off and declined since around the 1990s.
189These declines have been driven by the Montreal Protocol (effective since August 1989), which has banned the production of CFC-11 and CFC-12 (as well as other CFCs) because of their role in the depletion of
190stratospheric ozone (O$_{3}$), critical in decreasing the flux of ultraviolet radiation to the Earth's surface.
191Separate to this role in ozone-depletion, all three chemicals are significantly more potent greenhouse gases
192than CO$_{2}$ (especially SF6), although their relatively low atmospheric concentrations limit their role in climate change. \\
193
194% Chlorofluorocarbons 11 and 12 (CFC-11 and CFC-12), and sulfur hexafluoride (SF6),
195% are greenhouse gases that have been released into the atmosphere by human activities.
196% In the case of CFC-11 and CFC-12, this release began in the 1930s, and atmospheric
197% concentrations increased until around the late 1990s afterwhich they began to decline in
198% response to the Montreal Protocol.
199% In the case of SF6, release began in the 1950s
200% This release began in the 1930s for CFC-11 and CFC-12, and the 1950s for SF6, and
201% regularly increasing their atmospheric concentration until the 1090s, 2000s for respectively CFC11, CFC12,
202% and is still increasing, and SF6 (see Figure \autoref{img_cfcatm}).  \\
203
204The ocean is a notable sink for all three gases, and their relatively recent occurrence in the atmosphere, coupled to the ease of making high precision measurements of their dissolved concentrations, has made them
205valuable in oceanography. % for tracking interior ventilation and mixing.
206Because they only enter the ocean via surface air-sea exchange, and are almost completely chemically and biologically inert, their distribution within the ocean interior reveals its ventilation via transport and mixing.
207Measuring 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
208atmosphere).
209This feature of the gases has made them valuable across a wide range of oceanographic problems.
210One use lies in ocean modelling, where they can be used to evaluate the realism of the circulation and
211ventilation of models, key for understanding the behaviour of wider modelled marine biogeochemistry (e.g. \citep{dutay_2002,palmieri_2015}). \\
212
213Modelling these gases (henceforth CFCs) in NEMO is done within the passive tracer transport module, TOP, using the conservation state equation \autoref{Eq_tracer}
214
215Advection and diffusion of the CFCs in NEMO are calculated by the physical module, OPA,
216whereas sources and sinks are done by the CFC module within TOP.
217The only source for CFCs in the ocean is via air-sea gas exchange at its surface, and since CFCs are generally
218stable within the ocean, we assume that there are no sinks (i.e. no loss processes) within the ocean interior.
219Consequently, the sinks-minus-sources term for CFCs consists only of their air-sea fluxes, $F_{cfc}$, as
220described in the Ocean Model Inter-comparison Project (OMIP) protocol \citep{orr_2017}:
221
222% Because CFCs being stable in the ocean, we consider that there is no CFCs sink.
223% The only CFC source in the ocean is through the Air-Sea gas exchange at the surface.
224% These are calculated as air-sea fluxes (F$_{cfc}$), as described in the OMIP6 protocol \citep{artOMIP6}:
225
226\begin{eqnarray}
227F_{cfc} = K_{w} \, \cdot \, (C_{sat} - C_{surf}) \, \cdot  \, (1 - f_{i})
228\label{equ_CFC_flux}
229\end{eqnarray}
230
231Where $K_{w}$ is the piston velocity (in m~s$^{-1}$), as defined in Equation \autoref{equ_Kw};
232$C_{sat}$ is the saturation concentration of the CFC tracer, as defined in Equation \autoref{equ_C_sat};
233$C_{surf}$ is the local surface concentration of the CFC tracer within the model (in mol~m$^{-3}$);
234and $f_{i}$ is the fractional sea-ice cover of the local ocean (ranging between 0.0 for ice-free ocean,
235through to 1.0 for completely ice-covered ocean with no air-sea exchange).
236
237The saturation concentration of the CFC, $C_{sat}$, is calculated as follows:
238
239\begin{eqnarray}
240C_{sat} = Sol \, \cdot \, P_{cfc}
241\label{equ_C_sat}
242\end{eqnarray}
243
244Where $Sol$ is the gas solubility in mol~m$^{-3}$~pptv$^{-1}$, as defined in Equation \autoref{equ_Sol_CFC};
245and $P_{cfc}$ is the atmosphere concentration of the CFC (in parts per trillion by volume, pptv).
246This latter concentration is provided to the model by the historical time-series of \citet{bullister_2017}.
247This includes bulk atmospheric concentrations of the CFCs for both hemispheres -- this is necessary because of
248the geographical asymmetry in the production and release of CFCs to the atmosphere.
249Within the model, hemispheric concentrations are uniform, with the exception of the region between
25010$^{\circ}$N and 10$^{\circ}$ in which they are linearly interpolated.
251
252The piston velocity $K_{w}$ is a function of 10~m wind speed (in m~s$^{-1}$) and sea surface temperature,
253$T$ (in $^{\circ}$C), and is calculated here following \citet{wanninkhof_1992}:
254
255\begin{eqnarray}
256K_{w} = X_{conv} \, \cdot \, a \, \cdot \, u^2 \, \cdot \, \sqrt{ \frac{Sc(T)}{660} }
257\label{equ_Kw}
258\end{eqnarray}
259
260Where $X_{conv}$ = $\frac{0.01}{3600}$, a conversion factor that changes the piston velocity
261from cm~h$^{-1}$ to m~s$^{-1}$;
262$a$ is a constant re-estimated by \citet{wanninkhof_2014} to 0.251 (in $\frac{cm~h^{-1}}{(m~s^{-1})^{2}}$);
263and $u$ is the 10~m wind speed in m~s$^{-1}$ from either an atmosphere model or reanalysis atmospheric forcing.
264$Sc$ is the Schmidt number, and is calculated as follow, using coefficients from \citet{wanninkhof_2014} (see Table \autoref{tab_Sc}).
265
266\begin{eqnarray}
267Sc =  a0 + (a1 \, \cdot \, T) + (a2  \, \cdot \, T^2) + (a3 \, \cdot \, T^3) + (a4 \, \cdot \, T^4)
268\label{equ_Sc}
269\end{eqnarray}
270
271The solubility, $Sol$, used in Equation \autoref{equ_C_sat} is calculated in mol~l$^{-1}$~atm$^{-1}$,
272and is specific for each gas.
273It has been experimentally estimated by \citet{warner_1985} as a function of temperature
274and salinity:
275
276% AXY: this equation looks both weird and possibly wrong; it doesn't look like the one in the
277% code version that I have to hand, although this might be out of date; in any case, I'dag
278% strongly suggest avoiding the use of the \frac{}{100}, and instead substitute a term that is
279% "degrees Kelvin divided by 100" (which is weird in itself); and make this term use Celcius
280% so that you're not using T twice in different ways
281
282\begin{eqnarray}
283\ln{(Sol)} = a_1 + \frac{a_2}{ T_{X}} + a_3 \, \cdot \, \ln{ T_{X} } + a_4 \, \cdot \, T_{X}^2 + S \, \cdot \, ( b_1 + b_2 \, \cdot \, T_{X} + b_3 \, \cdot \, T_{X}^2 )
284\label{equ_Sol_CFC}
285\end{eqnarray}
286
287% \begin{eqnarray}
288% \ln{(Sol)} = a1 + a2 \, \frac{100}{T} + a3 \, \ln{ (\frac{T}{100}) } + a4 \, \frac{T}{100}^2 + S \, ( b1 + b2 \, \frac{T}{100} + b3 \, \frac{T}{100}^2 )
289% \label{equ_Sol_CFC}
290% \end{eqnarray}
291
292Where $T_{X}$ is $\frac{T + 273.16}{100}$, a function of temperature;
293and the $a_{x}$ and $b_{x}$ coefficients are specific for each gas (see Table \autoref{tab_ref_CFC}).
294This is then converted to mol~m$^{-3}$~pptv$^{-1}$ assuming a constant atmospheric surface pressure of 1~atm.
295The solubility of CFCs thus decreases with rising $T$ while being relatively insensitive to salinity changes.
296Consequently, this translates to a pattern of solubility where it is greatest in cold, polar regions (see Figure \autoref{img_cfcsol}).
297
298% AXY: not 100% sure about the units below; they might be in nanomol, or in seconds or years
299
300The standard outputs of the CFC module are seawater CFC concentrations (in mol~m$^{-3}$), the net air-sea flux (in mol~m$^{-2}$~d$^{-1}$) and the cumulative net air-sea flux (in mol~m$^{-2}$).
301Using XIOS, it is possible to obtain outputs such as the vertical integral of CFC concentrations (in mol~m$^{-2}$; see Figure \autoref{img_cfcinv}).
302This property, when divided by the surface CFC concentration, estimates the local penetration depth (in m) of the CFC.
303
304% AXY: not sure what's meant by some of the below; I've tried to reword it above
305% The standard outputs of the CFC module are the CFCs concentration in the sea water, and the records of the outputs-frequency-averaged as well as the total air-sea fluxes.
306% Using XIOS, it is also possible to ask for the CFCs vertical inventory in the output file (see Figure cfc inventory example ?).
307
308\subsubsection{Notes}
309
310In comparison to the OMIP protocol, the CFC module in NEMO has several differences:
311
312% AXY: consider an itemized list here if you've got a list of differences
313
314For instance, C$_{sat}$ is calculated for a fixed surface pressure of 1atm, what could be corrected in a further version of the module.
315
316
317\begin{table}[!t]
318\caption{Coefficients for fit of the CFCs solubility (Eq. \autoref{equ_Sol_CFC}).}
319\vskip4mm
320\centering
321\begin{tabular}{l l l l l l l l l}
322\hline
323Gas   & & a1 & a2 & a3 & a4 & b1 & b2 & b3 \\
324\hline
325CFC-11 & & -218.0971 & 298.9702 & 113.8049 & -1.39165 & -0.143566  & 0.091015   & -0.0153924 \\
326CFC-12 & & -229.9261 & 319.6552 & 119.4471 & -1.39165 & -0.142382  & 0.091459   & -0.0157274 \\
327SF6    & & -80.0343  & 117.232  & 29.5817  & 0.0      & 0.0335183  & -0.0373942 & 0.00774862 \\
328\hline
329\end{tabular}
330\label{tab_ref_CFC}
331\end{table}
332
333
334\begin{table}[!t]
335\caption{Coefficients for fit of the CFCs Schmidt number (Eq. \autoref{equ_Sc}). }
336\vskip4mm
337\centering
338\begin{tabular}{l l l l l l l }
339\hline
340Gas  & & a0 & a1 & a2 & a3 & a4 \\
341\hline
342CFC-11 & & 3579.2  & -222.63 & 7.5749 & -0.14595 & 0.0011874   \\
343CFC-12 & & 3828.1  & -249.86 & 8.7603 & -0.1716  & 0.001408    \\
344SF6    & & 3177.5  & -200.57 & 6.8865 & -0.13335 & 0.0010877   \\
345\hline
346\end{tabular}
347\label{tab_Sc}
348\end{table}
349
350%% -----------------------------------
351%% -----------------------------------
352%% Figures %%
353
354
355\begin{figure}[!h]
356\centering
357\includegraphics[width=0.80\textwidth]{CFC-atm-evol}
358  \caption{Atmospheric CFC11, CFC12 and SF6 partial pressure evolution in both hemispheres.}
359\label{img_cfcatm}
360\end{figure}
361
362\begin{figure}[!h]
363\centering
364\includegraphics[width=0.80\textwidth]{CFC_solub}
365  \caption{CFC11 solubility in mol m$^{-3}$ pptv$^{-1}$, calculated from the World Ocean Atlas 2013 temperature and salinity annual climatology.}
366\label{img_cfcsol}
367\end{figure}
368
369\begin{figure}[!h]
370\centering
371\includegraphics[width=0.80\textwidth]{CFC_inventory}
372  \caption{CFC11 vertical inventory in $\mu$mol m$^{-2}$, from one of the UK Earth System Model 1 model (UKESM1 - which uses NEMO as ocean component, with TOP for the passive tracers) historical run at year 2000.}
373\label{img_cfcinv}
374\end{figure}
375
376
378
379%------------------------------------------namage----------------------------------------------------
380%
381\nlst{namc14_fcg}
382\nlst{namc14_typ}
383\nlst{namc14_sbc}
384%----------------------------------------------------------------------------------------------------------
385
386The C14 package implemented in NEMO by Anne Mouchet models ocean $\Dcq$.
387It offers several possibilities: $\Dcq$ as a physical tracer of the ocean ventilation (natural $\cq$), assessment of bomb radiocarbon uptake, as well as transient studies of paleo-historical ocean radiocarbon distributions.
388
389\subsubsection{Method}
390
391Let  $\Rq$ represent the ratio of $\cq$ atoms to the total number of carbon atoms in the sample, i.e. $\cq/\mathrm{C}$.
392Then, radiocarbon anomalies are reported as
393
394\begin{equation}
395\Dcq = \left( \frac{\Rq}{\Rq_\mathrm{ref}} - 1 \right) 10^3, \label{eq:c14dcq}
396\end{equation}
397
398where $\Rq_{\textrm{ref}}$ is a reference ratio.
399For the purpose of ocean ventilation studies $\Rq_{\textrm{ref}}$ is set to one.
400
401Here 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 $\cq$.
402This approach calls for a strong assumption, i.e., that of a homogeneous and constant dissolved inorganic carbon (DIC) field \citep{toggweiler_1989a,mouchet_2013}.
403While in terms of
404oceanic $\Dcq$, 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).
405Yet, 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.
406For these reasons, bomb $\cq$ inventories obtained with the present method are directly comparable to reconstructions based on field measurements.
407
408This simplified approach also neglects the effects of fractionation (e.g.,  air-sea exchange) and of biological processes.
409Previous studies by \cite{bacastow_1990} and \cite{joos_1997} resulted in nearly identical $\Dcq$ distributions among experiments considering biology or not.
410Since 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.
411
412Therefore the simplified approach is justified for the purpose of assessing the circulation and ventilation of OGCMs.
413
414The equation governing the transport of $\Rq$  in the ocean is
415
416\begin{equation}
417\frac{\partial}{\partial t} {\Rq} =  - \bigtriangledown \cdot ( \mathbf{u} \Rq - \mathbf{K} \cdot \bigtriangledown \Rq )  - \lambda \Rq, \label{eq:quick}
418\end{equation}
419
420where $\lambda$ is the radiocarbon decay rate, ${\mathbf{u}}$ the 3-D velocity field, and $\mathbf{K}$ the diffusivity tensor.
421
422At the air-sea interface a Robin boundary condition \citep{haine_2006} is applied to \autoref{eq:quick}, i.e., the flux
423through the interface is proportional to the difference in the ratios between
424the ocean and the atmosphere
425
426\begin{equation}
427\mathcal{\!F} =  \kappa_{R}  (\Rq  - \Rq_{a} ), \label{eq:BCR}
428\end{equation}
429
430where $\mathcal{\!F}$ is the flux out of the ocean, and $\Rq_{a}$ is the atmospheric $\cq/\mathrm{C}$ ratio.
431The transfer velocity $\kappa_{R}$ for the radiocarbon ratio in \autoref{eq:BCR} is computed as
432
433\begin{equation}
434 \kappa_{R} =  \frac{\kappa_{\cd} K_0}{\overline{\Ct}} \, \pacd   \label{eq:Rspeed}
435\end{equation}
436
437with $\kappa_{\cd}$ the carbon dioxide transfer or piston velocity, $K_0$ the $\cd$ solubility in seawater, $\pacd$ the atmospheric $\cd$ pressure at sea level, and $\overline{\Ct}$ the average sea-surface dissolved inorganic carbon concentration.
438
439The $\cd$ transfer velocity is based on the empirical formulation of \cite{wanninkhof_1992} with chemical enhancement \citep{wanninkhof_1996,wanninkhof_2014}.
440The original formulation is modified to account for the reduction of the  air-sea exchange rate in the presence of sea ice.
441Hence
442
443\begin{equation}
444\kappa_\cd=\left( K_W\,\mathrm{w}^2 + b  \right)\, (1-f_\mathrm{ice})\,\sqrt{660/Sc}, \label{eq:wanc14}
445\end{equation}
446with $\mathrm{w}$ the wind magnitude, $f_\mathrm{ice}$ the fractional ice cover, and $Sc$ the Schmidt number.
447$K_W$ in \autoref{eq:wanc14} is an empirical coefficient with dimension of an inverse velocity.
448The chemical enhancement term $b$ is represented as a function of temperature $T$ \citep{wanninkhof_1992}
449\begin{equation}
450b=2.5 ( 0.5246 + 0.016256 T+ 0.00049946  * T^2 ). \label{eq:wanchem}
451\end{equation}
452
453%We compare the results of equilibrium and transient experiments obtained with both methods in section \autoref{sec:UNDEU}.
454
455%
456\subsubsection{Model setup}
457\label{sec:setup}
458
459To activate the \texttt{C14} package, set the parameter \textit{ln\_c14} = \texttt{.true.} in namelist \textit{namtrc}.
460
461\paragraph{Parameters and formulations}
462\label{sec:param}
463 %
464The radiocarbon decay rate (\forcode{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]
465%
466The Schmidt number $Sc$, Eq. \autoref{eq:wanc14}, is calculated with the help of the formulation of \cite{wanninkhof_2014}.
467The $\cd$ solubility $K_0$ in \autoref{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]
468%
469The following parameters intervening in the air-sea exchange rate are set in \texttt{namelist\_c14}:
470
471\begin{itemize}
472\item The reference DIC concentration $\overline{\Ct}$ (\forcode{xdicsur}) intervening in \autoref{eq:Rspeed} is classically set to 2 mol m$^{-3}$ \citep{toggweiler_1989a,orr_2001,butzin_2005}.
473%
474\item The value of the empirical coefficient $K_W$ (\forcode{xkwind}) in \autoref{eq:wanc14} depends on the wind field and on the model upper ocean mixing rate \citep{toggweiler_1989a,wanninkhof_1992,naegler_2009,wanninkhof_2014}.
475It should be adjusted so that the globally averaged $\cd$ piston velocity is $\kappa_\cd = 16.5\pm 3.2$ cm/h \citep{naegler_2009}.
476%The sensitivity to this parametrization is discussed in section \autoref{sec:result}.
477%
478\item Chemical enhancement (term $b$  in Eq. \autoref{eq:wanchem}) may be set on/off by means of the logical variable \forcode{ln\_chemh}.
479\end{itemize}
480
481%
482\paragraph{Experiment type}
483The type of experiment is determined by the value given to \forcode{kc14typ} in \texttt{namelist\_c14}.
484There are three possibilities:
485
486\begin{enumerate}
487\item natural                    $\Dcq$: \forcode{kc14typ}=0
488\item bomb                       $\Dcq$: \forcode{kc14typ}=1
489\item transient paleo-historical $\Dcq$: \forcode{kc14typ}=2
490\end{enumerate}
491
492%
494\forcode{kc14typ}=0
495
496Unless otherwise specified in \texttt{namelist\_c14}, the atmospheric $\Rq_a$ (\forcode{rc14at}) is set to one, the atmospheric $\cd$ (\forcode{pco2at}) to 280 ppm, and the ocean $\Rq$ is initialized with \forcode{rc14init=0.85}, i.e., $\Dcq=$-150\textperthousand \cite[typical for deep-ocean, Fig 6 in][]{key_2004}.
497
498Equilibrium 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. \autoref{fig:drift}).
499%
500
501\begin{figure}[!h]
502\begin{center}
503\includegraphics[width=0.9\hsize]{drift-EXP06}
504\end{center}
505\vspace{-4ex}
506\caption{ Time evolution of $\Rq$ inventory anomaly for equilibrium run with homogeneous ocean initial state.
507The anomaly (or drift) is given in \%  change in total ocean inventory per 50 years.
508Time on x-axis is in simulation year.\label{fig:drift} }
509\end{figure}
510
511\textbf{Transient: Bomb}
512\label{sec:bomb}
513\forcode{kc14typ}=1
514
515\begin{figure}[!h]
516\begin{center}
517\includegraphics[width=0.9\hsize]{C14bombCO2-NB}
518\end{center}
519\vspace{-4ex}
520\caption{Atmospheric $\Dcq$ (solid; left axis) and $\cd$ (dashed; right axis)  forcing for the $\cq$-bomb experiments.
521The $\Dcq$ is illustrated for the three zonal bands (upper, middle, and lower curves correspond to latitudes $> 20$N, $\in [20\mathrm{S},20\mathrm{N}]$, and $< 20$S, respectively.} \label{fig:bomb}
522\end{figure}
523
524Performing this type of experiment requires that a pre-industrial equilibrium run be performed beforehand (\forcode{ln\_rsttr} should be set to \texttt{.TRUE.}).
525
526An exception to this rule is when wishing to perform a perturbation bomb experiment as was possible with the package \texttt{C14b}.
527It is still possible to easily set-up that type of transient experiment for which no previous run is needed.
528In addition to the instructions as given in this section it is however necessary to adapt the \texttt{atmc14.dat} file so that it does no longer contain any negative $\Dcq$ values (Suess effect in the pre-bomb period).
529
530The model  is integrated from a given initial date following the observed records provided from 1765 AD on ( Fig. \autoref{fig:bomb}).
531The file \texttt{atmc14.dat}  \cite[][\& I.
532Levin, personal comm.]{enting_1994} provides atmospheric $\Dcq$ for three latitudinal bands: 90S-20S,    20S-20N \&    20N-90N.
533Atmospheric $\cd$ in the file \texttt{splco2.dat} is obtained from a spline fit through ice core data and direct atmospheric measurements \cite[][\& J.
534Orr, personal comm.]{orr_2000}.
535Dates in these forcing files are expressed as yr AD.
536
537To 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:
538
539\begin{itemize}
540\item Specify the starting date of the experiment: \forcode{nn\_date0} in \texttt{namelist}\forcode{nn\_date0} is written as Year0101 where Year may take any positive value (AD).
541\item Then the parameters \forcode{nn\_rstctl} in  \texttt{namelist} (on-line) and \forcode{nn\_rsttr} in \texttt{namelist\_top} (off-line)  must be \textbf{set to 0} at the start of the experiment (force the date to \forcode{nn\_date0} for the \textbf{first} experiment year).
542\item These two parameters (\forcode{nn\_rstctl} and \forcode{nn\_rsttr}) have then to be \textbf{set to 2} for the following years (the date must be read in the restart file).
543\end{itemize}
544
545If the experiment date is outside the data time span then the first or last atmospheric concentrations are prescribed depending on whether the date is earlier or later.
546Note that \forcode{tyrc14\_beg} (\texttt{namelist\_c14}) is not used in this context.
547
548%
549\textbf{Transient: Past}
550\forcode{kc14typ}=2
551%
552\begin{figure}[!h]
553\begin{center}
554\includegraphics[width=0.9\hsize]{PaleoCO2C14-NB}
555\end{center}
556\vspace{-4ex}
557\caption{Atmospheric $\Dcq$ (solid) and $\cd$ (dashed)  forcing for the Paleo experiments.
558The $\cd$ scale is given on the right axis.} \label{fig:paleo}
559\end{figure}
560
561This experiment type does not need a previous equilibrium run.
562It should start 5--6 kyr earlier than the period to be analyzed.
563Atmospheric $\Rq_a$ and $\cd$ are prescribed from forcing files.
564The ocean $\Rq$ is initialized with the value attributed to \forcode{rc14init} in \texttt{namelist\_c14}.
565
566The 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}.
567The $\cd$ forcing is provided in file \texttt{ByrdEdcCO2.txt}.
568The 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}.
569These atmospheric values are reproduced in Fig. \autoref{fig:paleo}.
570Dates in these files are expressed as yr BP.
571
572To 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.
573The true experiment starting date is given by \forcode{tyrc14\_beg} (in yr BP) in \texttt{namelist\_c14}.
574In consequence, \forcode{nn\_date0} in \texttt{namelist} MUST be set to 00010101.\\
575Then the parameters \forcode{nn\_rstctl} in  \texttt{namelist} (on-line) and \forcode{nn\_rsttr} in \texttt{namelist\_top} (off-line)  must be set to 0 at the start of the experiment (force the date to \forcode{nn\_date0} for the first experiment year).
576These two parameters have then to be set to 2 for the following years (read the date in the restart file). \\
577If the experiment date is outside the data time span then the first or last atmospheric concentrations are prescribed depending on whether the date is earlier or later.
578
579%
580\paragraph{Model output}
581\label{sec:output}
582
583All output fields in Table \autoref{tab:out} are routinely computed.
584It depends on the actual settings in \texttt{iodef.xml} whether they are stored or not.
585%
586\begin{table}[!h]
587\begin{center}
588\caption{Standard output fields for the C14 package \label{tab:out}.}
589%\begin{small}
590\renewcommand{\arraystretch}{1.3}%
591\begin{tabular}[h]{|l*{3}{|c}|l|}
592\hline
593Field     & Type   & Dim & Units              & Description                                               \\ \hline
594RC14      & ptrc   & 3-D & -                  & Radiocarbon ratio                                         \\
595DeltaC14  & diad   & 3-D & \textperthousand   & $\Dcq$                                                    \\
597RAge      & diad   & 2-D & yr                 & Reservoir age                                             \\
598qtr\_c14  & diad   & 2-D & m$^{-2}$ yr$^{-1}$ & Air-to-sea net $\Rq$ flux                                 \\
599qint\_c14 & diad   & 2-D & m$^{-2}$           & Cumulative air-to-sea $\Rq$ flux                          \\
600AtmCO2    & scalar & 0-D & ppm                & Global atmospheric $\cd$                                  \\
601AtmC14    & scalar & 0-D & \textperthousand   & Global atmospheric $\Dcq$                                 \\
602K\_CO2    & scalar & 0-D & cm h$^{-1}$        & Global $\cd$ piston velocity ($\overline{\kappa_{\cd}}$) \\
603K\_C14    & scalar & 0-D & m yr$^{-1}$        & Global $\Rq$ transfer velocity  ($\overline{\kappa_R}$\\
604C14Inv    & scalar & 0-D & $10^{26}$ atoms    & Ocean radiocarbon inventory                               \\ \hline
605\end{tabular}
606%\end{small}
607\end{center}
608\end{table}
609%!   Standard ratio: 1.176E-12 ; Avogadro's nbr = 6.022E+23 at/mol ; bomb C14 traditionally reported as 1.E+26 atoms
610%   REAL(wp), PARAMETER            :: atomc14=1.176*6.022E-15   ! conversion factor
611% atomc14 * xdicsur * zdum
612
613The radiocarbon age is computed as  $(-1/\lambda) \ln{ \left( \Rq \right)}$, with zero age corresponding to $\Rq=1$.
614
615The reservoir age is the age difference between the ocean uppermost layer and the atmosphere.
616It is usually reported as conventional radiocarbon age; i.e., computed by means of the Libby radiocarbon mean life \cite[8033 yr;][]{stuiver_1977}
617
618\begin{align}
619{^{14}\tau_\mathrm{c}}= -8033 \; \ln \left(1 + \frac{\Dcq}{10^3}\right), \label{eq:convage}
620\end{align}
621
622where ${^{14}\tau_\mathrm{c}}$ is expressed in years B.P.
623Here we do not use that convention and compute reservoir ages with the mean lifetime $1/\lambda$.
624Conversion from one scale to the other is readily performed.
625The conventional radiocarbon age is lower than the radiocarbon age by $\simeq3\%$.
626
627The ocean radiocarbon  inventory is computed as
628
629\begin{equation}
630N_A \Rq_\mathrm{oxa} \overline{\Ct} \left( \int_\Omega \Rq d\Omega \right) /10^{26}, \label{eq:inv}
631\end{equation}
632
633where $N_A$ 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.
634Bomb $\cq$ inventories are traditionally reported in units of $10^{26}$ atoms, hence the denominator in \autoref{eq:inv}.
635
636All transformations from second to year, and inversely, are performed with the help of the physical constant \forcode{rsiyea} the sideral year length expressed in seconds\footnote{The variable (\forcode{nyear\_len}) which reports the length in days of the previous/current/future year (see \textrm{oce\_trc.F90}) is not a constant. }.
637
638The global transfer velocities represent time-averaged\footnote{the actual duration is set in \texttt{iodef.xml}} global integrals of the transfer rates:
639
640\begin{equation}
641 \overline{\kappa_{\cd}}= \int_\mathcal{S} \kappa_{\cd} d\mathcal{S}  \text{ and } \overline{\kappa_R}= \int_\mathcal{S} \kappa_R d\mathcal{S}
642\end{equation}
643
644
645\subsection{PISCES biogeochemical model}
646
647PISCES is a biogeochemical model which simulates the lower trophic levels of marine ecosystem (phytoplankton, microzooplankton and mesozooplankton) and the biogeochemical cycles of carbonand of the main nutrients (P, N, Fe, and Si).
648The  model is intended to be used for both regional and global configurations at high or low spatial resolutions as well as for  short-term (seasonal, interannual) and long-term (climate change, paleoceanography) analyses.
649Two versions of PISCES are available in NEMO v4.0 :
650
651PISCES-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}.
652It assumes a constant Redfield ratio and phytoplankton growth depends on the external concentration in nutrients.
653There 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.
654Formulations 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.
655On the other hand, the iron and silicium quotas are variable and growth rate of phytoplankton is limited by the internal availability in Fe.
656Various parameterizations can be activated in PISCES-v2, setting for instance the complexity of iron chemistry or the description of particulate organic materials.
657
658PISCES-QUOTA has been built on the PISCES-v2 model described in \citet{aumont_2015}.
659PISCES-QUOTA has thirty-nine prognostic compartments.
660Phytoplankton growth can be controlled by five modeled limiting nutrients: Nitrate and Ammonium, Phosphate, Silicate and Iron.
661Five 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.
662For phytoplankton, the prognostic variables are the carbon, nitrogen, phosphorus,  iron, chlorophyll and silicon biomasses (the latter only for diatoms).
663This 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.
664Zooplankton are assumed to be strictly homeostatic \citep[e.g.,][]{sterner_2003,woods_2013,meunier_2014}.
665As a consequence, the C/N/P/Fe ratios of these groups are maintained constant and are not allowed to vary.
666In 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}.
667No silicified zooplankton is assumed.
668The bacterial pool is not yet explicitly modeled.
669
670There are three non-living compartments: Semi-labile dissolved organic matter, small sinking particles, and large sinking particles.
671As 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.
672Indeed, the nitrogen, phosphorus, iron, silicon and calcite pools of the particles are now all explicitly modeled.
673The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (''The ballast effect'', \citep{honjo_1996,armstrong_2001}).
674The latter particles are assumed to sink at the same speed as the large organic matter particles.
675All the non-living compartments experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM.
676
677\subsection{MY\_TRC interface for coupling external BGC models}
678\label{Mytrc}
679
680The NEMO-TOP has only one built-in biogeochemical model - PISCES - but there are several BGC models - MEDUSA, ERSEM, BFM or ECO3M - which are meant to be coupled with the NEMO dynamics.
681Therefore it was necessary to provide to the users a framework for easily add their own BGCM model, that can be a single passive tracer.
682The generalized interface is pivoted on MY\_TRC module that contains template files to build the coupling between NEMO and any external BGC model.
683The call to MY\_TRC is activated by setting  \textit{ln\_my\_trc} = \texttt{.true.} in namelist \textit{namtrc}
684
685The following 6 fortran files are available in MY\_TRC with the specific purposes here described.
686
687\begin{itemize}
688   \item \textit{par\_my\_trc.F90} :  This module allows to define additional arrays and public variables to be used within the MY\_TRC interface
689   \item \textit{trcini\_my\_trc.F90} :  Here are initialized user defined namelists and the call to the external BGC model initialization procedures to populate general tracer array (trn and trb).
690Here are also likely to be defined suport arrays related to system metrics that could be needed by the BGC model.
691  \item \textit{trcnam\_my\_trc.F90} :  This routine is called at the beginning of trcini\_my\_trc and should contain the initialization of additional namelists for the BGC model or user-defined code.
692  \item \textit{trcsms\_my\_trc.F90} :  The routine performs the call to Boundary Conditions and its main purpose is to contain the Source-Minus-Sinks terms due to the biogeochemical processes of the external model.
693Be aware that lateral boundary conditions are applied in trcnxt routine.
694IMPORTANT: the routines to compute the light penetration along the water column and the tracer vertical sinking should be defined/called in here, as generalized modules are still missing in the code.
695 \item \textit{trcice\_my\_trc.F90} : Here it is possible to prescribe the tracers concentrations in the seaice that will be used as boundary conditions when ice melting occurs (nn\_ice\_tr =1 in namtrc\_ice).
696See e.g. the correspondent PISCES subroutine.
697 \item \textit{trcwri\_my\_trc.F90} : This routine performs the output of the model tracers using IOM module (see Manual Chapter Output and Diagnostics).
698It is possible to place here the output of additional variables produced by the model, if not done elsewhere in the code, using the call to \textit{iom\_put}.
699\end{itemize}
700
701\section{The Offline Option}
702\label{Offline}
703
704%------------------------------------------namtrc_sms----------------------------------------------------
705\nlst{namdta_dyn}
706%-------------------------------------------------------------------------------------------------------------
707
708Coupling passive tracers offline with NEMO requires precomputed  physical fields from OGCM.
709Those fields are read from files and interpolated on-the-fly at each model time step
710At least the following dynamical parameters should be absolutely passed to the transport : ocean velocities, temperature, salinity, mixed layer depth and for ecosystem models like PISCES, sea ice concentration, short wave radiation at the ocean surface, wind speed (or at least, wind stress).
711The so-called offline mode is useful since it has lower computational costs for example to perform very longer simulations - about 3000 years - to reach equilibrium of CO2 sinks for climate-carbon studies.
712
713The offline interface is located in the code repository : \path{<repository>/src/OFF/}.
714It is activated by adding the CPP key  \textit{key\_offline} to the CPP keys list.
715There are two specifics routines for the Offline code :
716
717\begin{itemize}
718   \item \textit{dtadyn.F90} :  this module allows to read and compute the dynamical fields at each model time-step
719   \item \textit{nemogcm.F90} :  a degraded version of the main nemogcm.F90 code of NEMO to manage the time-stepping
720\end{itemize}
721
722%-
723%-
724%-
725%-  Describes here the specifities of oflline : At least the dynamical variables needed - u/v/w transport T/S for isopycnal MLD for biogeo models etc ...
726%-  the specfities of vvl - ssh + runoffs and how to
727%-
728\end{document}
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