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chap_SBC.tex

Timestamp:

2021-05-05T13:18:04+02:00 (3 years ago)

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mcastril

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[2021/HPC-11_mcastril_HPDAonline_DiagGPU] Update externals

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NEMO/branches/2021/dev_r13747_HPC-11_mcastril_HPDAonline_DiagGPU

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NEMO/branches/2021/dev_r13747_HPC-11_mcastril_HPDAonline_DiagGPU

Property svn:externals

-                      old
+                      new
 ^/utils/build/mk@HEAD         mk
 ^/utils/tools@HEAD            tools
 ^/vendors/AGRIF/dev_r12970_AGRIF_CMEMS      ext/AGRIF
+^/vendors/AGRIF/dev@HEAD      ext/AGRIF
 ^/vendors/FCM@HEAD            ext/FCM
 ^/vendors/IOIPSL@HEAD         ext/IOIPSL
+^/vendors/PPR@HEAD            ext/PPR
 # SETTE
 ^/utils/CI/sette@13559        sette
+^/utils/CI/sette@14244        sette

NEMO/branches/2021/dev_r13747_HPC-11_mcastril_HPDAonline_DiagGPU/doc/latex/NEMO/subfiles

Property svn:ignore

-                      old
+                      new
+*.aux
+*.bbl
+*.blg
+*.fdb*
+*.fls
+*.idx
+*.ilg
 *.ind
+*.ilg
+*.lo*
+*.out
+*.pdf
+*.pyg
+*.tdo
+*.toc
+*.xdv
+cache*

NEMO/branches/2021/dev_r13747_HPC-11_mcastril_HPDAonline_DiagGPU/doc/latex/NEMO/subfiles/chap_SBC.tex

-                      r13165
+                      r14789
 \documentclass[../main/NEMO_manual]{subfiles}
-\usepackage{fontspec}
-\usepackage{fontawesome}
 \begin{document}
 \chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
+\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB, TDE)}
 \label{chap:SBC}
-\thispagestyle{plain}
 \chaptertoc
 …
     Release & Author(s) & Modifications \\
     \hline
+    {\em  next} & {\em Simon M{\" u}ller} & {\em Update of \autoref{sec:SBC_TDE}; revision of \autoref{subsec:SBC_fwb}}\\[2mm]
+    {\em  next} & {\em Pierre Mathiot} & {\em update of the ice shelf section (2019 developments)}\\[2mm]
     {\em   4.0} & {\em ...} & {\em ...} \\
     {\em   3.6} & {\em ...} & {\em ...} \\
 …
   (\np[=0..3]{nn_ice}{nn\_ice}),
 \item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
-\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
-  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
 \item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
   (\np[=0..2]{nn_fwb}{nn\_fwb}),
 …
 One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
 which act as drifting sources of fresh water.
-Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
-which provides additional sources of fresh water.
 %% =================================================================================================
 …
 See \autoref{subsec:SBC_ssr} for its specification.
+%% =================================================================================================
+\pagebreak
+\newpage
+%% =================================================================================================
 \section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
 \label{sec:SBC_blk}
 …
 Note: all the NEMO Fortran routines involved in the present section have been
  initially developed (and are still developed in parallel) in
  the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} open-source project
 \citep{brodeau.barnier.ea_JPO17}.
+initially developed (and are still developed in parallel) in
+the \href{https://brodeau.github.io/aerobulk}{\texttt{AeroBulk}} open-source project
+\citep{brodeau.barnier.ea_JPO16}.
 %%% Bulk formulae are this:
+\subsection{Bulk formulae}\label{subsec:SBC_blkform}
+%
+\subsection{Bulk formulae}
+\label{subsec:SBC_blkform}
 In NEMO, the set of equations that relate each component of the surface fluxes
 to the near-surface atmosphere and sea surface states writes
+%
+\begin{subequations}\label{eq_bulk}
+\begin{subequations}
+  \label{eq:SBC_bulk}
   \label{eq:SBC_bulk_form}
+  \begin{eqnarray}
+    \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
+    Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
+    E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
+    Q_L           &=& -L_v \, E \\
+    %
+    Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\
+    Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4)
+  \end{eqnarray}
+  \begin{align}
+    \mathbf{\tau} &= \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
+    Q_H           &= \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
+    E             &= \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
+    Q_L           &= -L_v \, E \\
+    Q_{sr}        &= (1 - a) Q_{sw\downarrow} \\
+    Q_{ir}        &= \delta (Q_{lw\downarrow} -\sigma T_s^4)
+  \end{align}
 \end{subequations}
+%
 with
    \[ \theta_z \simeq T_z+\gamma z \]
    \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
+%
 from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
+%
 where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
 $E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
 flux.
+%
 $Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
 and longwave radiative fluxes, respectively.
+%
 Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$
 implies a gain of the relevant quantity for the ocean, while a positive $E$
 implies a freshwater loss for the ocean.
+%
 $\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
 coefficients for momentum, sensible heat, and moisture, respectively.
+%
 $C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
 vaporization of water.
+%
 $\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
 and specific humidity of air at height $z$ above the sea surface,
 respectively. $\gamma z$ is a temperature correction term which accounts for the
 adiabatic lapse rate and approximates the potential temperature at height
+$z$ \citep{josey.gulev.ea_2013}.
+%
+$z$ \citep{josey.gulev.ea_OCC13}.
 $\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
+(possibly referenced to the surface current $\mathbf{u_0}$,
+section \ref{s_res1}.\ref{ss_current}).
+%
+(possibly referenced to the surface current $\mathbf{u_0}$).%,
+%\autoref{s_res1}.\autoref{ss_current}). %% Undefined references
 The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
 $|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution.
+%
 $a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\
+%
 %$p_a$ is the mean sea-level pressure (SLP).
+%
 $T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity
 of air at temperature $T_s$; it includes a 2\% reduction to account for the
 presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}.
+presence of salt in seawater \citep{sverdrup.johnson.ea_bk42,kraus.businger_QJRMS96}.
 Depending on the bulk parametrization used, $T_s$ can either be the temperature
 at the air-sea interface (skin temperature, hereafter SSST) or at typically a
 few tens of centimeters below the surface (bulk sea surface temperature,
 hereafter SST).
+%
 The SSST differs from the SST due to the contributions of two effects of
 opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL,
+respectively, see section\,\ref{subsec:SBC_skin}).
+%
+respectively, see \autoref{subsec:SBC_skin}).
 Technically, when the ECMWF or COARE* bulk parametrizations are selected
 (\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}),
 …
 For more details on all these aspects the reader is invited to refer
+to \citet{brodeau.barnier.ea_JPO17}.
+\subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean}
+to \citet{brodeau.barnier.ea_JPO16}.
+\subsection{Bulk parametrizations}
+\label{subsec:SBC_blk_ocean}
 %%%\label{subsec:SBC_param}
 …
 height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}).
 For the open ocean, four bulk parametrization algorithms are available in NEMO:
 \begin{itemize}
 \item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09}
+\item NCAR, formerly known as CORE, \citep{large.yeager_trpt04,large.yeager_CD09}
 \item COARE 3.0 \citep{fairall.bradley.ea_JC03}
 \item COARE 3.6 \citep{edson.jampana.ea_JPO13}
 …
 \end{itemize}
 With respect to version 3, the principal advances in version 3.6 of the COARE
 bulk parametrization are built around improvements in the representation of the
 effects of waves on
 fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes
+fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO16}. This includes
 improved relationships of surface roughness, and whitecap fraction on wave
 parameters. It is therefore recommended to chose version 3.6 over 3.
+\subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin}
+%\subsection[Cool-skin and warm-layer parameterizations
+%(\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})}
+%\label{subsec:SBC_skin}
+%
+\subsection[Cool-skin and warm-layer parameterizations (   \forcode{ln_skin_cs}               \& \forcode{ln_skin_wl}              )]
+           {Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \&      \np{ln_skin_wl}{ln\_skin\_wl})}
+\label{subsec:SBC_skin}
 As opposed to the NCAR bulk parametrization, more advanced bulk
 parametrizations such as COARE3.x and ECMWF are meant to be used with the skin
 temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
 the first T-point level, see section\,\ref{subsec:SBC_blkform}).
+%
+the first T-point level, see \autoref{subsec:SBC_blkform}).
 As such, the relevant cool-skin and warm-layer parametrization must be
 activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs}
 …
 For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same
 basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based
 on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE
+basis: \citet{fairall.bradley.ea_JGRO96}. With some minor updates based
+on \citet{zeng.beljaars_GRL05} for ECMWF \iffalse, and \citet{fairall.ea_19?} for COARE \fi
 .6.
 …
 turbulence input from Langmuir circulation).
 Importantly, COARE warm-layer scheme \citep{fairall.ea_19} includes a prognostic
+Importantly, COARE warm-layer scheme \iffalse \citep{fairall.ea_19?} \fi includes a prognostic
 equation for the thickness of the warm-layer, while it is considered as constant
 in the ECWMF algorithm.
 \subsection{Appropriate use of each bulk parametrization}
 …
 temperature is the bulk SST. Hence the following namelist parameters must be
 set:
+%
 \begin{verbatim}
+\begin{forlines}
   ...
   ln_NCAR    = .true.
 …
   ...
   ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
+\end{verbatim}
+\end{forlines}
 \subsubsection{ECMWF}
+%
 With an atmospheric forcing based on a reanalysis of the ECMWF, such as the
 Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to
 …
 humidity are provided at the 2\,m height, and given that the humidity is
 distributed as the dew-point temperature, the namelist must be tuned as follows:
+%
 \begin{verbatim}
+\begin{forlines}
   ...
   ln_ECMWF   = .true.
 …
   ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
   ...
 \end{verbatim}
+%
+\end{forlines}
 Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
 of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
 …
 respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
 \subsubsection{COARE 3.x}
+%
 Since the ECMWF parametrization is largely based on the COARE* parametrization,
 the two algorithms are very similar in terms of structure and closure
 approach. As such, the namelist tuning for COARE 3.x is identical to that of
 ECMWF:
+%
 \begin{verbatim}
+\begin{forlines}
   ...
   ln_COARE3p6 = .true.
 …
   ln_skin_wl = .true. ! use the warm-layer parameterization
   ...
 \end{verbatim}
+\end{forlines}
 Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection
 …
 respectively (found in \textit{sbcblk\_skin\_coare.F90}).
 %lulu
 % In a typical bulk algorithm, the BTCs under neutral stability conditions are
 …
 % and $q_z$.
 \subsection{Prescribed near-surface atmospheric state}
 …
 different bulk formulae are used for the turbulent fluxes computation over the
 ocean and over sea-ice surface.
+%
 %The choice is made by setting to true one of the following namelist
 …
 the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
 \subsubsection{Air humidity}
 …
 [kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
 parameters)...
-~\\
 %% =================================================================================================
 …
 %their neutral transfer coefficients relationships with neutral wind.
 %\begin{itemize}
 %\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
+%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_trpt04}.
 %  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
 %  They use an inertial dissipative method to compute the turbulent transfer coefficients
 %  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
 %  This \citet{large.yeager_rpt04} dataset is available through
+%  This \citet{large.yeager_trpt04} dataset is available through
 %  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
 %  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
 …
 \label{subsec:SBC_blk_ice}
 \texttt{\#out\_of\_place:}
  For sea-ice, three possibilities can be selected:
 a constant transfer coefficient (1.4e-3; default
 value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
+value), \citet{lupkes.gryanik.ea_JGRA12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
 and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
 \texttt{\#out\_of\_place.}
 Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
 \begin{itemize}
 \item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
+\item Constant value (\forcode{Cd_ice=1.4e-3}):
   default constant value used for momentum and heat neutral transfer coefficients
 \item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
+\item \citet{lupkes.gryanik.ea_JGRA12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
   This scheme adds a dependency on edges at leads, melt ponds and flows
   of the constant neutral air-ice drag. After some approximations,
 …
 %% =================================================================================================
 \section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
 \label{sec:SBC_tide}
+\section{Surface tides (TDE)}
+\label{sec:SBC_TDE}
 \begin{listing}
 …
 \end{listing}
+The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
+is activated if \np{ln_tide}{ln\_tide} and \np{ln_tide_pot}{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{_tide}{\_tide}.
+This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
+\subsection{Tidal constituents}
+Ocean model component TDE provides the common functionality for tidal forcing
+and tidal analysis in the model framework. This includes the computation of the gravitational
+surface forcing, as well as support for lateral forcing at open boundaries (see
+\autoref{subsec:LBC_bdy_tides}) and tidal harmonic analysis \iffalse (see
+\autoref{subsec:DIA_diamlr?} and \autoref{subsec:DIA_diadetide?}) \fi . The module is
+activated with \np[=.true.]{ln_tide}{ln\_tide} in namelist
+\nam{_tide}{\_tide}. It provides the same 34 tidal constituents that are
+included in the
+\href{https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/global-tide-fes.html}{FES2014
+  ocean tide model}: Mf, Mm, Ssa, Mtm, Msf, Msqm, Sa, K1, O1, P1, Q1, J1, S1,
+M2, S2, N2, K2, nu2, mu2, 2N2, L2, T2, eps2, lam2, R2, M3, MKS2, MN4, MS4, M4,
+N4, S4, M6, and M8; see file \textit{tide.h90} and \mdl{tide\_mod} for further
+information and references\footnote{As a legacy option \np{ln_tide_var}{ln\_tide\_var} can be
+  set to \forcode{0}, in which case the 19 tidal constituents (M2, N2, 2N2, S2,
+  K2, K1, O1, Q1, P1, M4, Mf, Mm, Msqm, Mtm, S1, MU2, NU2, L2, and T2; see file
+  \textit{tide.h90}) and associated parameters that have been available in NEMO version
+.0 and earlier are available}. Constituents to be included in the tidal forcing
+(surface and lateral boundaries) are selected by enumerating their respective
+names in namelist array \np{sn_tide_cnames}{sn\_tide\_cnames}.\par
+\subsection{Surface tidal forcing}
+Surface tidal forcing can be represented in the model through an additional
+barotropic force in the momentum equation (\autoref{eq:MB_PE_dyn}) such that:
 \[
+  % \label{eq:SBC_PE_dyn_tides}
+  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
+  +g\nabla (\Pi_{eq} + \Pi_{sal})
+  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t} = \ldots +g\nabla (\gamma
+  \Pi_{eq} + \Pi_{sal})
 \]
+where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
+$\Pi_{sal}$ is a self-attraction and loading term (SAL).
+The equilibrium tidal forcing is expressed as a sum over a subset of
+constituents chosen from the set of available tidal constituents
+defined in file \hf{SBC/tide} (this comprises the tidal
+constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
+  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
+constituents are selected by including their names in the array
+\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
+\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
+and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
+\forcode{.true.}, the equilibrium tidal forcing can be ramped up
+linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
+model run.
+where $\gamma \Pi_{eq}$ stands for the equilibrium tidal forcing scaled by a spatially
+uniform tilt factor $\gamma$, and $\Pi_{sal}$ is an optional
+self-attraction and loading term (SAL). These additional terms are enabled when,
+in addition to \np[=.true.]{ln_tide}{ln\_tide}),
+\np[=.true.]{ln_tide_pot}{ln\_tide\_pot}.\par
+The equilibrium tidal forcing is expressed as a sum over the subset of
+constituents listed in \np{sn_tide_cnames}{sn\_tide\_cnames} of
+\nam{_tide} (e.g.,
+\begin{forlines}
+      sn_tide_cnames(1) = 'M2'
+      sn_tide_cnames(2) = 'K1'
+      sn_tide_cnames(3) = 'S2'
+      sn_tide_cnames(4) = 'O1'
+\end{forlines}
+to select the four tidal constituents of strongest equilibrium tidal
+potential). The tidal tilt factor $\gamma = 1 + k - h$ includes the
+Love numbers $k$ and $h$ \citep{love_PRSL09}; this factor is
+configurable using \np{rn_tide_gamma}{rn\_tide\_gamma} (default value 0.7). Optionally,
+when \np[=.true.]{ln_tide_ramp}{ln\_tide\_ramp}, the equilibrium tidal
+forcing can be ramped up linearly from zero during the initial
+\np{rn_tide_ramp_dt}{rn\_tide\_ramp\_dt} days of the model run.\par
 The SAL term should in principle be computed online as it depends on
 the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
+discussion about the practical implementation of this term).
+Nevertheless, the complex calculations involved would make this
+computationally too expensive. Here, two options are available:
+$\Pi_{sal}$ generated by an external model can be read in
+(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
+used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
+discussion about the practical implementation of this term). The complex
+calculations involved in such computations, however, are computationally very
+expensive. Here, two mutually exclusive simpler variants are available:
+amplitudes generated by an external model for oscillatory $\Pi_{sal}$
+contributions from each of the selected tidal constituents can be read in
+(\np[=.true.]{ln_read_load}{ln\_read\_load}) from the file specified in
+\np{cn_tide_load}{cn\_tide\_load} (the variable names are comprised of the
+tidal-constituent name and suffixes \forcode{_z1} and \forcode{_z2} for the two
+orthogonal components, respectively); alternatively, a ``scalar approximation''
+can be used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}), where
 \[
   \Pi_{sal} = \beta \eta,
 \]
+where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
+spatially constant scalar, often chosen to minimize tidal prediction
+errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
+\forcode{.false.} removes the SAL contribution.
+with a spatially uniform coefficient $\beta$, which can be configured
+via \np{rn_scal_load}{rn\_scal\_load} (default value 0.094) and is
+often tuned to minimize tidal prediction errors.\par
+For diagnostic purposes, the forcing potential of the individual tidal
+constituents (incl. load ptential, if activated) and the total forcing
+potential (incl. load potential, if activated) can be made available
+as diagnostic output by setting
+\np[=.true.]{ln_tide_dia}{ln\_tide\_dia} (fields
+\forcode{tide_pot_<constituent>} and \forcode{tide_pot}).\par
 %% =================================================================================================
 …
 %% =================================================================================================
 \section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
+\section[Ice Shelf (ISF)]{Interaction with ice shelves (ISF)}
 \label{sec:SBC_isf}
 \begin{listing}
   \nlst{namsbc_isf}
   \caption{\forcode{&namsbc_isf}}
   \label{lst:namsbc_isf}
+  \nlst{namisf}
+  \caption{\forcode{&namisf}}
+  \label{lst:namisf}
 \end{listing}
+The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
+Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
+The different options are illustrated in \autoref{fig:SBC_isf}.
+The namelist variable in \nam{isf}{isf}, \np{ln_isf}{ln\_isf}, controls the ice shelf interactions:
 \begin{description}
+  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
+  The fwf and heat flux are depending of the local water properties.
+  Two different bulk formulae are available:
+   \item $\bullet$ representation of the ice shelf/ocean melting/freezing for opened cavity (cav, \np{ln_isfcav_mlt}{ln\_isfcav\_mlt}).
+   \item $\bullet$ parametrisation of the ice shelf/ocean melting/freezing for closed cavities (par, \np{ln_isfpar_mlt}{ln\_isfpar\_mlt}).
+   \item $\bullet$ coupling with an ice sheet model (\np{ln_isfcpl}{ln\_isfcpl}).
+\end{description}
+  \subsection{Ocean/Ice shelf fluxes in opened cavities}
+     \np{ln_isfcav_mlt}{ln\_isfcav\_mlt}\forcode{ = .true.} activates the ocean/ice shelf thermodynamics interactions at the ice shelf/ocean interface.
+     If \np{ln_isfcav_mlt}{ln\_isfcav\_mlt}\forcode{ = .false.}, thermodynamics interactions are desctivated but the ocean dynamics inside the cavity is still active.
+     The logical flag \np{ln_isfcav}{ln\_isfcav} control whether or not the ice shelf cavities are closed. \np{ln_isfcav}{ln\_isfcav} is not defined in the namelist but in the domcfg.nc input file.\\
+options are available to represent to ice-shelf/ocean fluxes at the interface:
+     \begin{description}
+        \item[\np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = 'spe'}]:
+        The fresh water flux is specified by a forcing fields \np{sn_isfcav_fwf}{sn\_isfcav\_fwf}. Convention of the input file is: positive toward the ocean (i.e. positive for melting and negative for freezing).
+        The latent heat fluxes is derived from the fresh water flux.
+        The heat content flux is derived from the fwf flux assuming a temperature set to the freezing point in the top boundary layer (\np{rn_htbl}{rn\_htbl})
+        \item[\np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = 'oasis'}]:
+        The \forcode{'oasis'} is a prototype of what could be a method to spread precipitation on Antarctic ice sheet as ice shelf melt inside the cavity when a coupled model Atmosphere/Ocean is used.
+        It has not been tested and therefore the model will stop if you try to use it.
+        Actions will be undertake in 2020 to build a comprehensive interface to do so for Greenland, Antarctic and ice shelf (cav), ice shelf (par), icebergs, subglacial runoff and runoff.
+        \item[\np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = '2eq'}]:
+        The heat flux and the fresh water flux (negative for melting) resulting from ice shelf melting/freezing are parameterized following \citet{Grosfeld1997}.
+        This formulation is based on a balance between the vertical diffusive heat flux across the ocean top boundary layer (\autoref{eq:ISOMIP1})
+        and the latent heat due to melting/freezing (\autoref{eq:ISOMIP2}):
+        \begin{equation}
+        \label{eq:ISOMIP1}
+        \mathcal{Q}_h = \rho c_p \gamma (T_w - T_f)
+        \end{equation}
+        \begin{equation}
+        \label{eq:ISOMIP2}
+        q = \frac{-\mathcal{Q}_h}{L_f}
+        \end{equation}
+        where $\mathcal{Q}_h$($W.m^{-2}$) is the heat flux,q($kg.s^{-1}m^{-2}$) the fresh-water flux,
+        $L_f$ the specific latent heat, $T_w$ the temperature averaged over a boundary layer below the ice shelf (explained below),
+        $T_f$ the freezing point using  the  pressure  at  the  ice  shelf  base  and  the  salinity  of the water in the boundary layer,
+        and $\gamma$ the thermal exchange coefficient.
+        \item[\np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = '3eq'}]:
+        For realistic studies, the heat and freshwater fluxes are parameterized following \citep{Jenkins2001}. This formulation is based on three equations:
+        a balance between the vertical diffusive heat flux across the boundary layer
+        , the latent heat due to melting/freezing of ice and the vertical diffusive heat flux into the ice shelf (\autoref{eq:3eq1});
+        a balance between the vertical diffusive salt flux across the boundary layer and the salt source or sink represented by the melting/freezing (\autoref{eq:3eq2});
+        and a linear equation for the freezing temperature of sea water (\autoref{eq:3eq3}, detailed of the linearisation coefficient in \citet{AsayDavis2016}):
+        \begin{equation}
+        \label{eq:3eq1}
+        c_p \rho \gamma_T (T_w-T_b) = -L_f q - \rho_i c_{p,i} \kappa \frac{T_s - T_b}{h_{isf}}
+        \end{equation}
+        \begin{equation}
+        \label{eq:3eq2}
+        \rho \gamma_S (S_w - S_b) = (S_i - S_b)q
+        \end{equation}
+        \begin{equation}
+        \label{eq:3eq3}
+        T_b = \lambda_1 S_b + \lambda_2 +\lambda_3 z_{isf}
+        \end{equation}
+        where $T_b$ is the temperature at the interface, $S_b$ the salinity at the interface, $\gamma_T$ and $\gamma_S$ the exchange coefficients for temperature and salt, respectively,
+        $S_i$ the salinity of the ice (assumed to be 0), $h_{isf}$ the ice shelf thickness, $z_{isf}$ the ice shelf draft, $\rho_i$ the density of the iceshelf,
+        $c_{p,i}$ the specific heat capacity of the ice, $\kappa$ the thermal diffusivity of the ice
+        and $T_s$ the atmospheric surface temperature (at the ice/air interface, assumed to be -20C).
+        The Liquidus slope ($\lambda_1$), the liquidus intercept ($\lambda_2$) and the Liquidus pressure coefficient ($\lambda_3$)
+        for TEOS80 and TEOS10 are described in \citep{AsayDavis2016} and in \citep{Jourdain2017}.
+        The linear system formed by \autoref{eq:3eq1}, \autoref{eq:3eq2} and the linearised equation for the freezing temperature of sea water (\autoref{eq:3eq3}) can be solved for $S_b$ or $T_b$.
+        Afterward, the freshwater flux ($q$) and the heat flux ($\mathcal{Q}_h$) can be computed.
+     \end{description}
+     \begin{table}[h]
+        \centering
+        \caption{Description of the parameters hard coded into the ISF module}
+        \label{tab:isf}
+        \begin{tabular}{|l|l|l|l|}
+        \hline
+        Symbol    & Description               & Value              & Unit               \\
+        \hline
+        $C_p$     & Ocean specific heat       & 3992               & $J.kg^{-1}.K^{-1}$ \\
+        $L_f$     & Ice latent heat of fusion & $3.34 \times 10^5$ & $J.kg^{-1}$        \\
+        $C_{p,i}$ & Ice specific heat         & 2000               & $J.kg^{-1}.K^{-1}$ \\
+        $\kappa$  & Heat diffusivity          & $1.54 \times 10^{-6}$& $m^2.s^{-1}$     \\
+        $\rho_i$  & Ice density               & 920                & $kg.m^3$           \\
+        \hline
+        \end{tabular}
+     \end{table}
+     Temperature and salinity used to compute the fluxes in \autoref{eq:ISOMIP1}, \autoref{eq:3eq1} and \autoref{eq:3eq2} are the average temperature in the top boundary layer \citep{losch_JGR08}.
+     Its thickness is defined by \np{rn_htbl}{rn\_htbl}.
+     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the first \np{rn_htbl}{rn\_htbl} m.
+     Then, the fluxes are spread over the same thickness (ie over one or several cells).
+     If \np{rn_htbl}{rn\_htbl} is larger than top $e_{3}t$, there is no more direct feedback between the freezing point at the interface and the top cell temperature.
+     This can lead to super-cool temperature in the top cell under melting condition.
+     If \np{rn_htbl}{rn\_htbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
+     Each melt formula (\np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = '3eq'} or \np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = '2eq'}) depends on an exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
+     Below, the exchange coeficient $\Gamma^{T}$ and $\Gamma^{S}$ are respectively defined by \np{rn_gammat0}{rn\_gammat0} and \np{rn_gammas0}{rn\_gammas0}.
+     There are 3 different ways to compute the exchange velocity:
+     \begin{description}
+        \item[\np{cn_gammablk}{cn\_gammablk}\forcode{='spe'}]:
+        The salt and heat exchange coefficients are constant and defined by:
+\[
+\gamma^{T} = \Gamma^{T}
+\]
+\[
+\gamma^{S} = \Gamma^{S}
+\]
+        This is the recommended formulation for ISOMIP.
+   \item[\np{cn_gammablk}{cn\_gammablk}\forcode{='vel'}]:
+        The salt and heat exchange coefficients are velocity dependent and defined as
+\[
+\gamma^{T} = \Gamma^{T} \times u_{*}
+\]
+\[
+\gamma^{S} = \Gamma^{S} \times u_{*}
+\]
+        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_htbl}{rn\_htbl} meters).
+        See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application and ISOMIP+/MISOMIP configuration.
+   \item[\np{cn_gammablk}{cn\_gammablk}\forcode{'vel\_stab'}]:
+        The salt and heat exchange coefficients are velocity and stability dependent and defined as:
+\[
+\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
+\]
+        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_tbl}{rn\_htbl} meters),
+        $\Gamma_{Turb}$ the contribution of the ocean stability and
+        $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
+        See \citet{holland.jenkins_JPO99} for all the details on this formulation.
+        This formulation has not been extensively tested in NEMO (not recommended).
+     \end{description}
+\subsection{Ocean/Ice shelf fluxes in parametrised cavities}
   \begin{description}
+  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
+    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
+  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
+    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
+    A complete description is available in \citet{jenkins_JGR91}.
+     \item[\np{cn_isfpar_mlt}{cn\_isfpar\_mlt}\forcode{ = 'bg03'}]:
+     The ice shelf cavities are not represented.
+     The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
+     The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
+     (\np{sn_isfpar_zmax}{sn\_isfpar\_zmax}) and the base of the ice shelf along the calving front
+     (\np{sn_isfpar_zmin}{sn\_isfpar\_zmin}) as in (\np{cn_isfpar_mlt}{cn\_isfpar\_mlt}\forcode{ = 'spe'}).
+     The effective melting length (\np{sn_isfpar_Leff}{sn\_isfpar\_Leff}) is read from a file.
+     This parametrisation has not been tested since a while and based on \citet{Favier2019},
+     this parametrisation should probably not be used.
+     \item[\np{cn_isfpar_mlt}{cn\_isfpar\_mlt}\forcode{ = 'spe'}]:
+     The ice shelf cavity is not represented.
+     The fwf (\np{sn_isfpar_fwf}{sn\_isfpar\_fwf}) is prescribed and distributed along the ice shelf edge between
+     the depth of the average grounding line (GL) (\np{sn_isfpar_zmax}{sn\_isfpar\_zmax}) and
+     the base of the ice shelf along the calving front (\np{sn_isfpar_zmin}{sn\_isfpar\_min}). Convention of the input file is positive toward the ocean (i.e. positive for melting and negative for freezing).
+     The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
+     \item[\np{cn_isfpar_mlt}{cn\_isfpar\_mlt}\forcode{ = 'oasis'}]:
+     The \forcode{'oasis'} is a prototype of what could be a method to spread precipitation on Antarctic ice sheet as ice shelf melt inside the cavity when a coupled model Atmosphere/Ocean is used.
+     It has not been tested and therefore the model will stop if you try to use it.
+     Action will be undertake in 2020 to build a comprehensive interface to do so for Greenland, Antarctic and ice shelf (cav), ice shelf (par), icebergs, subglacial runoff and runoff.
   \end{description}
+  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
+  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
+  The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m.
+  Then, the fluxes are spread over the same thickness (ie over one or several cells).
+  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature.
+  This can lead to super-cool temperature in the top cell under melting condition.
+  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
+  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
+  There are 3 different ways to compute the exchange coeficient:
+  \begin{description}
+  \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}.
+    \begin{gather*}
+       % \label{eq:SBC_isf_gamma_iso}
+      \gamma^{T} = rn\_gammat0 \\
+      \gamma^{S} = rn\_gammas0
+    \end{gather*}
+    This is the recommended formulation for ISOMIP.
+  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
+    \begin{gather*}
+      \gamma^{T} = rn\_gammat0 \times u_{*} \\
+      \gamma^{S} = rn\_gammas0 \times u_{*}
+    \end{gather*}
+    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
+    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
+  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
+    \[
+      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
+    \]
+    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
+    $\Gamma_{Turb}$ the contribution of the ocean stability and
+    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
+    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
+    This formulation has not been extensively tested in \NEMO\ (not recommended).
+  \end{description}
+\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
+  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
+  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
+  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
+  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
+  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
+\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
+  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
+  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
+  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
+  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
+\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
+  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
+  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
+  As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl})
+\end{description}
+$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
+\np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = '2eq'}, \np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = '3eq'} and \np{cn_isfpar_mlt}{cn\_isfpar\_mlt}\forcode{ = 'bg03'} compute a melt rate based on
 the water mass properties, ocean velocities and depth.
 This flux is thus highly dependent of the model resolution (horizontal and vertical),
 realism of the water masses onto the shelf ...\\
 $\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
+The resulting fluxes are thus highly dependent of the model resolution (horizontal and vertical) and
+realism of the water masses onto the shelf.\\
+\np{cn_isfcav_mlt}{cn\_isfcav\_mlt}\forcode{ = 'spe'} and \np{cn_isfpar_mlt}{cn\_isfpar\_mlt}\forcode{ = 'spe'} read the melt rate from a file.
 You have total control of the fwf forcing.
 This can be useful if the water masses on the shelf are not realistic or
 the resolution (horizontal/vertical) are too coarse to have realistic melting or
+for studies where you need to control your heat and fw input.\\
+The ice shelf melt is implemented as a volume flux as for the runoff.
+The fw addition due to the ice shelf melting is, at each relevant depth level, added to
+the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
+for studies where you need to control your heat and fw input.
+However, if your forcing is not consistent with the dynamics below you can reach unrealistic low water temperature.\\
+The ice shelf fwf is implemented as a volume flux as for the runoff.
+The fwf addition due to the ice shelf melting is, at each relevant depth level, added to
+the horizontal divergence (\textit{hdivn}) in the subroutine \rou{isf\_hdiv}, called from \mdl{divhor}.
 See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
+Description and result of sensitivity tests to \np{ln_isfcav_mlt}{ln\_isfcav\_mlt} and \np{ln_isfpar_mlt}{ln\_isfpar\_mlt} are presented in \citet{mathiot.jenkins.ea_GMD17}.
+The different options are illustrated in \autoref{fig:ISF}.
 \begin{figure}[!t]
   \centering
   \includegraphics[width=0.66\textwidth]{SBC_isf}
+  \includegraphics[width=0.66\textwidth]{SBC_isf_v4.2}
   \caption[Ice shelf location and fresh water flux definition]{
     Illustration of the location where the fwf is injected and
     whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
   \label{fig:SBC_isf}
+    whether or not the fwf is interactive or not.}
+  \label{fig:ISF}
 \end{figure}
+%% =================================================================================================
+\section{Ice sheet coupling}
+\label{sec:SBC_iscpl}
+\begin{listing}
+  \nlst{namsbc_iscpl}
+  \caption{\forcode{&namsbc_iscpl}}
+  \label{lst:namsbc_iscpl}
+\end{listing}
+\subsection{Available outputs}
+The following outputs are availables via XIOS:
+\begin{description}
+   \item[for parametrised cavities]:
+      \begin{xmllines}
+ <field id="isftfrz_par"     long_name="freezing point temperature in the parametrization boundary layer" unit="degC"     />
+ <field id="fwfisf_par"      long_name="Ice shelf melt rate"                           unit="kg/m2/s"  />
+ <field id="qoceisf_par"     long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     />
+ <field id="qlatisf_par"     long_name="Ice shelf latent heat flux"                    unit="W/m2"     />
+ <field id="qhcisf_par"      long_name="Ice shelf heat content flux of injected water" unit="W/m2"     />
+ <field id="fwfisf3d_par"    long_name="Ice shelf melt rate"                           unit="kg/m2/s"  grid_ref="grid_T_3D" />
+ <field id="qoceisf3d_par"   long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
+ <field id="qlatisf3d_par"   long_name="Ice shelf latent heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
+ <field id="qhcisf3d_par"    long_name="Ice shelf heat content flux of injected water" unit="W/m2"     grid_ref="grid_T_3D" />
+ <field id="ttbl_par"        long_name="temperature in the parametrisation boundary layer" unit="degC" />
+ <field id="isfthermald_par" long_name="thermal driving of ice shelf melting"          unit="degC"     />
+      \end{xmllines}
+   \item[for open cavities]:
+      \begin{xmllines}
+ <field id="isftfrz_cav"     long_name="freezing point temperature at ocean/isf interface"                unit="degC"     />
+ <field id="fwfisf_cav"      long_name="Ice shelf melt rate"                           unit="kg/m2/s"  />
+ <field id="qoceisf_cav"     long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     />
+ <field id="qlatisf_cav"     long_name="Ice shelf latent heat flux"                    unit="W/m2"     />
+ <field id="qhcisf_cav"      long_name="Ice shelf heat content flux of injected water" unit="W/m2"     />
+ <field id="fwfisf3d_cav"    long_name="Ice shelf melt rate"                           unit="kg/m2/s"  grid_ref="grid_T_3D" />
+ <field id="qoceisf3d_cav"   long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
+ <field id="qlatisf3d_cav"   long_name="Ice shelf latent heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
+ <field id="qhcisf3d_cav"    long_name="Ice shelf heat content flux of injected water" unit="W/m2"     grid_ref="grid_T_3D" />
+ <field id="ttbl_cav"        long_name="temperature in Losch tbl"                      unit="degC"     />
+ <field id="isfthermald_cav" long_name="thermal driving of ice shelf melting"          unit="degC"     />
+ <field id="isfgammat"       long_name="Ice shelf heat-transfert velocity"             unit="m/s"      />
+ <field id="isfgammas"       long_name="Ice shelf salt-transfert velocity"             unit="m/s"      />
+ <field id="stbl"            long_name="salinity in the Losh tbl"                      unit="1e-3"     />
+ <field id="utbl"            long_name="zonal current in the Losh tbl at T point"      unit="m/s"      />
+ <field id="vtbl"            long_name="merid current in the Losh tbl at T point"      unit="m/s"      />
+ <field id="isfustar"        long_name="ustar at T point used in ice shelf melting"    unit="m/s"      />
+ <field id="qconisf"         long_name="Conductive heat flux through the ice shelf"    unit="W/m2"     />
+      \end{xmllines}
+\end{description}
+%% =================================================================================================
+\subsection{Ice sheet coupling}
+\label{subsec:ISF_iscpl}
 Ice sheet/ocean coupling is done through file exchange at the restart step.
 At each restart step:
 \begin{enumerate}
 \item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
 \item a new domcfg.nc file is built using the DOMAINcfg tools.
 \item \NEMO\ run for a specific period and output the average melt rate over the period.
 \item the ice sheet model run using the melt rate outputed in step 4.
 \item go back to 1.
 \end{enumerate}
 If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
+At each restart step, the procedure is this one:
+\begin{description}
+\item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
+\item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools.
+\item[Step 3]: NEMO run for a specific period and output the average melt rate over the period.
+\item[Step 4]: the ice sheet model run using the melt rate outputed in step 3.
+\item[Step 5]: go back to 1.
+\end{description}
+If \np{ln_iscpl}{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with
 potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
 The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
+The wetting and drying scheme, applied on the restart, is very simple. The 6 different possible cases for the tracer and ssh are:
 \begin{description}
+\item [Thin a cell down]: T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
+  ($bt_b=bt_n$).
+\item [Enlarge  a cell]: See case "Thin a cell down"
+\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
+  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
+\item [Wet a cell]: mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
+  If no neighbours, T/S is extrapolated from old top cell value.
+  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
+\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
+\item [Wet a column]: set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
+  If no neighbour, T/S/U/V and mask set to 0.
+   \item[Thin a cell]:
+   T/S/ssh are unchanged.
+   \item[Enlarge  a cell]:
+   See case "Thin a cell down"
+   \item[Dry a cell]:
+   Mask, T/S, U/V and ssh are set to 0.
+   \item[Wet a cell]:
+   Mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$.
+   If no neighbours, T/S is extrapolated from old top cell value.
+   If no neighbours along i,j and k (both previous tests failed), T/S/ssh and mask are set to 0.
+   \item[Dry a column]:
+   mask, T/S and ssh are set to 0.
+   \item[Wet a column]:
+   set mask to 1, T/S/ssh are extrapolated from neighbours.
+   If no neighbour, T/S/ssh and mask set to 0.
 \end{description}
+The method described above will strongly affect the barotropic transport under an ice shelf when the geometry change.
+In order to keep the model stable, an adjustment of the dynamics at the initialisation after the coupling step is needed.
+The idea behind this is to keep $\pd[\eta]{t}$ as it should be without change in geometry at the initialisation.
+This will prevent any strong velocity due to large pressure gradient.
+To do so, we correct the horizontal divergence before $\pd[\eta]{t}$ is computed in the first time step.\\
 Furthermore, as the before and now fields are not compatible (modification of the geometry),
 …
 The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
 It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
 the code will be unable to fill all the new wet cells properly.
+the code will be unable to fill all the new wet cells properly and the model is likely to blow up at the initialisation.
 The default number is set up for the MISOMIP idealised experiments.
 This coupling procedure is able to take into account grounding line and calving front migration.
 However, it is a non-conservative processe.
+However, it is a non-conservative proccess.
 This could lead to a trend in heat/salt content and volume.\\
 In order to remove the trend and keep the conservation level as close to 0 as possible,
+a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
+The heat/salt/vol. gain/loss is diagnosed, as well as the location.
+A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
+For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
+The corrective increment is apply into the cell itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry).
+a simple conservation scheme is available with \np{ln_isfcpl_cons}{ln\_isfcpl\_cons}\forcode{ = .true.}.
+The heat/salt/vol. gain/loss are diagnosed, as well as the location.
+A correction increment is computed and applied each time step during the model run.
+The corrective increment are applied into the cells itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry).
 %% =================================================================================================
 …
 Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
+By default, iceberg thermodynamic and dynamic are computed using ocean surface variable (sst, ssu, ssv) and the icebergs are not sensible to the bathymetry (only to land) whatever the iceberg draft.
+\citet{Merino_OM2016} developed an option to use vertical profiles of ocean currents and temperature instead (\np{ln_M2016}{ln\_M2016}).
+Full details on the sensitivity to this parameter in done in \citet{Merino_OM2016}.
+If \np{ln_M2016}{ln\_M2016} activated, \np{ln_icb_grd}{ln\_icb\_grd} activate (or not) an option to prevent thick icebergs to move across shallow bank (ie shallower than the iceberg draft).
+This option need to be used with care as it could required to either change the distribution to prevent generation of icebergs with draft larger than the bathymetry
+or to build a variable \forcode{maxclass} to prevent NEMO filling the icebergs classes too thick for the local bathymetry.
 Extensive diagnostics can be produced.
 Separate output files are maintained for human-readable iceberg information.
 …
 Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
 the drag coefficient is computed according to the stable/unstable conditions of the
 air-sea interface following \citet{large.yeager_rpt04}.
+air-sea interface following \citet{large.yeager_trpt04}.
 %% =================================================================================================
 …
 The surface stress felt by the ocean is the atmospheric stress minus the net stress going
 into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
+into the waves \citep{janssen.breivik.ea_trpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
 available for forcing the mean circulation, while in the opposite case of a decaying sea
 state, more momentum is available for forcing the ocean.
 …
 \label{subsec:SBC_fwb}
+For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
+prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
+In \NEMO, two way of controlling the freshwater budget are proposed:
+\begin{listing}
+  \nlst{namsbc_fwb}
+  \caption{\forcode{&namsbc_fwb}}
+  \label{lst:namsbc_fwb}
+\end{listing}
+For global ocean simulations, it can be useful to introduce a control of the
+mean sea level in order to prevent unrealistic drifting of the sea surface
+height due to unbalanced freshwater fluxes. In \NEMO, two options for
+controlling the freshwater budget are proposed.
 \begin{description}
 \item [{\np[=0]{nn_fwb}{nn\_fwb}}] no control at all.
   The mean sea level is free to drift, and will certainly do so.
 \item [{\np[=1]{nn_fwb}{nn\_fwb}}] global mean \textit{emp} set to zero at each model time step.
+\item [{\np[=0]{nn_fwb}{nn\_fwb}}:] No control at all; the mean sea level is
+  free to drift, and will certainly do so.
+\item [{\np[=1]{nn_fwb}{nn\_fwb}}:] The global mean \textit{emp} is set to zero at each model time step.
   %GS: comment below still relevant ?
   %Note that with a sea-ice model, this technique only controls the mean sea level with linear free surface and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling).
+\item [{\np[=2]{nn_fwb}{nn\_fwb}}] freshwater budget is adjusted from the previous year annual mean budget which
+  is read in the \textit{EMPave\_old.dat} file.
+  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
+  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
+\item [{\np[=2]{nn_fwb}{nn\_fwb}}:] \textit{emp} is adjusted by adding a
+  spatially uniform, annual-mean freshwater flux that balances the freshwater
+  budget at the end of the previous year; as the model uses the Boussinesq
+  approximation, the freshwater budget can be evaluated from the change in the
+  mean sea level and in the ice and snow mass after the end of each simulation
+  year; at the start of the model run, an initial adjustment flux can be set
+  using parameter \np{rn_rwb0}{rn\_fwb0} in namelist \nam{sbc_fwb}{sbc\_fwb}.
 \end{description}

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