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1% ================================================================
2% Chapter Ñ Surface Boundary Condition (SBC)
3% ================================================================
4\chapter{Surface Boundary Condition (SBC) }
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15The ocean needs six fields as surface boundary condition:
17\item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$
18\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
19\item the surface freshwater budget $\left( {\text{EMP},\;\text{EMP}_S } \right)$
22Four different ways to provide those six fields to the ocean are available which
23are controlled by namelist variables: an analytical formulation (\np{ln\_ana}=true),
24a flux formulation (\np{ln\_flx}=true), a bulk formulae formulation (CORE
25(\np{ln\_core}=true) or CLIO (\np{ln\_clio}=true) bulk formulae) and a coupled
26formulation (exchanges with a atmospheric model via the OASIS coupler)
27(\np{ln\_cpl}=true). The frequency at which the six fields have to be updated is
28the  \np{nf\_sbc} namelist parameter.
29When the fields are supplied from data files (flux and bulk formulations), the input fields
30need not be supplied on the model grid.  Instead a file of coordinates and weights can be supplied which
31maps the data from the supplied grid to the model points (so called "Interpolation on the Fly").
32In addition, the resulting fields can be further modified using
33several namelist options. These options control  the rotation of vector components
34supplied relative to an east-north coordinate system onto the local grid directions in the model;
35the addition of a surface restoring
36term to observed SST and/or SSS (\np{ln\_ssr}=true); the modification of fluxes
37below ice-covered areas (using observed ice-cover or a sea-ice model)
38(\np{nn\_ice}=0,1, 2 or 3); the addition of river runoffs as surface freshwater
39fluxes (\np{ln\_rnf}=true); the addition of a freshwater flux adjustment in
40order to avoid a mean sea-level drift (\np{nn\_fwb}= 0, 1 or 2); and the
41transformation of the solar radiation (if provided as daily mean) into a diurnal
42cycle (\np{ln\_dm2dc}=true).
44In this chapter, we first discuss where the surface boundary condition
45appears in the model equations. Then we present the four ways of providing
46the surface boundary condition. Next the scheme for interpolation on the fly is described.
47Finally, the different options that further modify
48the fluxes applied to the ocean are discussed.
51% ================================================================
52% Surface boundary condition for the ocean
53% ================================================================
54\section{Surface boundary condition for the ocean}
58The surface ocean stress is the stress exerted by the wind and the sea-ice
59on the ocean. The two components of stress are assumed to be interpolated
60onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
61at $u$- and $v$-points They are applied as a surface boundary condition of the
62computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
63\begin{equation} \label{Eq_sbc_dynzdf}
64\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
65    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
67where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
68stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
70The surface heat flux is decomposed into two parts, a non solar and a solar heat
71flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
72of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
73It is applied as a surface boundary condition trend of the first level temperature
74time evolution equation (\mdl{trasbc} module).
75\begin{equation} \label{Eq_sbc_trasbc_q}
76\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 
77_o \;C_p \;e_{3T} }} \right|_{k=1} \quad
79$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
80trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
82\begin{equation} \label{Eq_sbc_traqsr}
83\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho _o C_p
84\,e_{3T} }\delta _k \left[ {I_w } \right]
86where $I_w$ is a non-dimensional function that describes the way the light
87penetrates inside the water column. It is generally a sum of decreasing
88exponentials (see \S\ref{TRA_qsr}).
90The surface freshwater budget is provided by fields: EMP and EMP$_S$ which
91may or may not be identical. Indeed, a surface freshwater flux has two effects:
92it changes the volume of the ocean and it changes the surface concentration of
93salt (and other tracers). Therefore it appears in the sea surface height as a volume
94flux, EMP (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
95as a concentration/dilution effect,
96EMP$_{S}$ (\mdl{trasbc} module).
97\begin{equation} \label{Eq_trasbc_emp}
99&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\text{EMP}\quad  \\ 
101 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\text{EMP}_S \;S}{e_{3T} }} \right|_{k=1} \\ 
102 \end{aligned}
105In the real ocean, EMP$=$EMP$_S$ and the ocean salt content is conserved,
106but it exist several numerical reasons why this equality should be broken.
107For example:
109When the rigid-lid assumption is made, the ocean volume becomes constant and
110thus, EMP$=$0, not EMP$_{S }$.
112When the ocean is coupled to a sea-ice model, the water exchanged between ice and
113ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,
114EMP$_{S}$ take into account both concentration/dilution effect associated with
115freezing/melting and the salt flux between ice and ocean, while EMP is
116only the volume flux. In addition, in the current version of \NEMO, the
117sea-ice is assumed to be above the ocean. Freezing/melting does not change
118the ocean volume (no impact on EMP) but it modifies the SSS.
119%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
121Note that SST can also be modified by a freshwater flux. Precipitation (in
122particular solid precipitation) may have a temperature significantly different from
123the SST. Due to the lack of information about the temperature of
124precipitation, we assume it is equal to the SST. Therefore, no
125concentration/dilution term appears in the temperature equation. It has to
126be emphasised that this absence does not mean that there is no heat flux
127associated with precipitation! Precipitation can change the ocean volume and thus the
128ocean heat content. It is therefore associated with a heat flux (not yet 
129diagnosed in the model) \citep{Roullet2000}).
131%\colorbox{yellow}{Miss: }
133%A extensive description of all namsbc namelist (parameter that have to be
136%Especially the \np{nf\_sbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
137%ssv) i.e. information required by flux computation or sea-ice
139%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
140%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
142%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
144%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
145%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
148%Explain here all the namlist namsbc variable{\ldots}.
150%\colorbox{yellow}{End Miss }
152The ocean model provides the surface currents, temperature and salinity
153averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
154mean is done in \mdl{sbcmod} module.
157\begin{table}[tb]  \label{Tab_ssm}
161Variable description             & Model variable  & Units  & point \\  \hline
162i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
163j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
164Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
165Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
167\caption{Ocean variables provided by the ocean to the surface module (SBC).
168The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of
169computation of surface fluxes.}
176%\colorbox{yellow}{Penser a} mettre dans le restant l'info nf{\_}sbc ET nf{\_}sbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt
179% ================================================================
180% Analytical formulation (sbcana module)
181% ================================================================
182\section  [Analytical formulation (\textit{sbcana}) ]
183      {Analytical formulation (\mdl{sbcana} module) }
191The analytical formulation of the surface boundary condition is the default scheme.
192In this case, all the six fluxes needed by the ocean are assumed to
193be uniform in space. They take constant values given in the namelist
194namsbc{\_}ana by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
195\np{rn\_qsr0}, and \np{rn\_emp0} (EMP$=$EMP$_S$). The runoff is set to zero.
196In addition, the wind is allowed to reach its nominal value within a given number
197of time steps (\np{nn\_tau000}).
199If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
200module can be modified to use another scheme. As an example,
201the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
202GYRE configuration (see GYRE configuration manual, in preparation).
205% ================================================================
206% Flux formulation
207% ================================================================
208\section  [Flux formulation (\textit{sbcflx}) ]
209      {Flux formulation (\mdl{sbcflx} module) }
215In the flux formulation (\np{ln\_flx}=true), the surface boundary
216condition fields are directly read from input files. The user has to define
217in the namelist namsbc{\_}flx the name of the file, the name of the variable
218read in the file, the time frequency at which it is given (in hours), and a logical
219setting whether a time interpolation to the model time step is required
220for this field). (fld\_i namelist structure).
222\textbf{Caution}: when the frequency is set to --12, the data are monthly
223values. These are assumed to be climatological values, so time interpolation
224between December the 15$^{th}$ and January the 15$^{th}$ is done using
225records 12 and 1
227When higher frequency is set and time interpolation is demanded, the model
228will try to read the last (first) record of previous (next) year in a file
229having the same name but a suffix {\_}prev{\_}year ({\_}next{\_}year) being
230added (e.g. "{\_}1989"). These files must only contain a single record. If they don't exist,
231the model assumes that the last record of the previous year is equal to the first
232record of the current year, and similarly, that the first record of the
233next year is equal to the last record of the current year. This will cause
234the forcing to remain constant over the first and last half fld\_frequ hours.
236Note that in general, a flux formulation is used in associated with a
237restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
241% ================================================================
242% Bulk formulation
243% ================================================================
244\section  [Bulk formulation (\textit{sbcblk\_core} or \textit{sbcblk\_clio}) ]
245      {Bulk formulation \small{(\mdl{sbcblk\_core} or \mdl{sbcblk\_clio} module)} }
248In the bulk formulation, the surface boundary condition fields are computed
249using bulk formulae and atmospheric fields and ocean (and ice) variables.
251The atmospheric fields used depend on the bulk formulae used. Two bulk formulations
252are available : the CORE and CLIO bulk formulea. The choice is made by setting to true
253one of the following namelist variable : \np{ln\_core} and \np{ln\_clio}.
255Note : in forced mode, when a sea-ice model is used, a bulk formulation have to be used.
256Therefore the two bulk formulea provided include the computation of the fluxes over both
257an ocean and an ice surface.
259% -------------------------------------------------------------------------------------------------------------
260%        CORE Bulk formulea
261% -------------------------------------------------------------------------------------------------------------
262\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
263            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
269The CORE bulk formulae have been developed by \citet{LargeYeager2004}.
270They have been designed to handle the CORE forcing, a mixture of NCEP
271reanalysis and satellite data. They use an inertial dissipative method to compute
272the turbulent transfer coefficients (momentum, sensible heat and evaporation)
273from the 10 metre wind speed, air temperature and specific humidity.
275Note that substituting ERA40 to NCEP reanalysis fields
276does not require changes in the bulk formulea themself.
278The required 8 input fields are:
281\begin{table}[htbp]   \label{Tab_CORE}
285Variable desciption              & Model variable  & Units   & point \\    \hline
286i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
287j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
28810m air temperature              & tair      & \r{}$K$            & T   \\ \hline
289Specific humidity             & humi      & \%              & T \\      \hline
290Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
291Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
292Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
293Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
299Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points). It is simpler and faster (less fields to be read), but it is not the recommended method when the ocean grid
300size is the same or larger than the one of the input atmospheric fields.
302% -------------------------------------------------------------------------------------------------------------
303%        CLIO Bulk formulea
304% -------------------------------------------------------------------------------------------------------------
305\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
306            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
312The CLIO bulk formulae were developed several years ago for the
313Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
314They are simpler bulk formulae. They assume the stress to be known and
315compute the radiative fluxes from a climatological cloud cover.
317The required 7 input fields are:
320\begin{table}[htbp]   \label{Tab_CLIO}
324Variable desciption           & Model variable  & Units           & point \\  \hline
325i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
326j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
327Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
32810m air temperature              & tair         & \r{}$K$            & T \\   \hline
329Specific humidity                & humi         & \%              & T \\   \hline
330Cloud cover                   &           & \%              & T \\   \hline
331Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
332Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
338As for the flux formulation, information about the input data required by the
339model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
340namelist (via the structure fld\_i). The first and last record assumption is also made
341(see \S\ref{SBC_flx})
343% ================================================================
344% Coupled formulation
345% ================================================================
346\section  [Coupled formulation (\textit{sbccpl}) ]
347      {Coupled formulation (\mdl{sbccpl} module)}
353In the coupled formulation of the surface boundary condition, the fluxes are
354provided by the OASIS coupler at each \np{nf\_cpl} time-step, while sea and ice
355surface temperature, ocean and ice albedo, and ocean currents are sent to
356the atmospheric component.
358The generalised coupled interface is under development. It should be available
359in summer 2008. It will include the ocean interface for most of the European
360atmospheric GCM (ARPEGE, ECHAM, ECMWF, HadAM, LMDz).
362% ================================================================
363% Interpolation on the Fly
364% ================================================================
366\section [Interpolation on the Fly] {Interpolation on the Fly}
369Interpolation on the Fly allows the user to supply input files required
370for the surface forcing on grids other than the model grid.
371To do this he or she must supply, in addition to the source data file,
372a file of weights to be used to interpolate from the data grid to the model
374The original development of this code used the SCRIP package (freely available
375under a copyright agreement from
376In principle, any package can be used to generate the weights, but the
377variables in the input weights file must have the same names and meanings as
378assumed by the model.
379Two methods are currently available: bilinear and bicubic interpolation.
381\subsection{Bilinear Interpolation}
384The input weights file in this case has two sets of variables: src01, src02,
385src03, src04 and wgt01, wgt02, wgt03, wgt04.
386The "src" variables correspond to the point in the input grid to which the weight
387"wgt" is to be applied. Each src value is an integer corresponding to the index of a
388point in the input grid when written as a one dimensional array.  For example, for an input grid
389of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
390There are four of each variable because bilinear interpolation uses the four points defining
391the grid box containing the point to be interpolated.
392All of these arrays are on the model grid, so that values src01(i,j) and
393wgt01(i,j) are used to generate a value for point (i,j) in the model.
395Symbolically, the algorithm used is:
398f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
400where function idx() transforms a one dimensional index src(k) into a two dimensional index,
401and wgt(1) corresponds to variable "wgt01" for example.
403\subsection{Bicubic Interpolation}
406Again there are two sets of variables: "src" and "wgt".
407But in this case there are 16 of each.
408The symbolic algorithm used to calculate values on the model grid is now:
411f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
413                        + \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }
415                        + \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
417                        + \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
419The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
424To activate this option, a non-empty string should be supplied in the weights filename column of the relevant namelist;
425if this is left as an empty string no action is taken.
426In the model, weights files are read in and stored in a structured type (WGT) in the fldread module, as and when they are first required.
427This initialisation procedure tries to determine whether the input data grid should be treated as cyclical or not.
428(In fact this only matters when bicubic interpolation is required.)
429To do this the model looks in the input data file (i.e. the data to which the weights are to be applied) for a variable with name "nav\_lon" or "lon".
430If found, it checks the difference between the first and last values of longitude along a single row.
431If the absolute value of this difference is close to 360 degrees or less than twice the maximum spacing from 360 degrees, the grid is assumed to be cyclical, and the difference determines whether the first column is a repeat of the last one or not.
432If neither "nav\_lon" or "lon" can be found, the model resorts to looking at the first and last columns of data.
433If the sum of the absolute values of the differences between the columns is very small, then the grid is assumed to be cyclical with coincident first and last columns.
434If both of these tests fail, the grid is assumed not to be cyclical.
436Next the routine reads in the weights.
437Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
438The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid), and when required, for reading in the variable to be interpolated (on the input data grid).
439The size of the input data array is determined by examining the values in the "src" arrays to find the minimum and maximum i and j values required.
440Since bicubic interpolation requires the calculation of gradients at each point on the grid, the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
441When the array of points from the data file is adjacent to an edge of the data grid, the halo is either a copy of the row/column next to it (non-cyclical case), or is a copy of one from the first two rows/columns on the opposite side of the grid (cyclical case with coincident end rows/columns, or cyclical case with non-coincident end rows/columns).
448Input data grids must be logically rectangular.
450This code is not guaranteed to produce positive definite answers from positive definite inputs.
452The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
454The gradients across the ends of a cyclical grid assume that the grid spacing between the two columns involved are consistent with the weights used.
456Neither interpolation scheme is conservative.
457(There is a conservative scheme available in SCRIP, but this has not been implemented.)
463% to be completed
464A set of utilities to create a weights file for a rectilinear input grid is available.
466% ================================================================
467% Miscellanea options
468% ================================================================
469\section{Miscellaneous options}
472% -------------------------------------------------------------------------------------------------------------
473%        Rotation of vector pairs onto the model grid directions
474% -------------------------------------------------------------------------------------------------------------
475\subsection{Rotation of vector pairs onto the model grid directions}
478When using a flux (\np{ln\_flx}=true) or bulk (\np{ln\_clio}=true or \np{ln\_core}=true) formulation,
479pairs of vector components can be rotated from east-north directions onto the local grid directions. 
480This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
481relative to a rectilinear grid.
482To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
483The eastward component must start with "U" and the northward component with "V". 
484The remaining characters in the strings are used to identify which pair of components go together.
485So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
486and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
487and so on.
488The extra characters used in the strings are arbitrary.
489The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
491% -------------------------------------------------------------------------------------------------------------
492%        Surface restoring to observed SST and/or SSS
493% -------------------------------------------------------------------------------------------------------------
494\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
495         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
501In forced mode using a flux formulation (default option or \key{flx} defined), a
502feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
503\begin{equation} \label{Eq_sbc_dmp_q}
504Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
506where SST is a sea surface temperature field (observed or climatological), $T$ is
507the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
508coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
509mixed-layer depth, this value corresponds to a relaxation time scale of two months.
510This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
511equal to $Q_o$.
513In the fresh water budget, a feedback term can also be added. Converted into an
514equivalent freshwater flux, it takes the following expression :
516\begin{equation} \label{Eq_sbc_dmp_emp}
517EMP = EMP_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
518                                             {\left.S\right|_{k=1}}
521where EMP$_{o }$ is a net surface fresh water flux (observed, climatological or an
522atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
523interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
524$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
525feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
526physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
527does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring
528term should be viewed as a flux correction on freshwater fluxes to reduce the
529uncertainties we have on the observed freshwater budget.
531% -------------------------------------------------------------------------------------------------------------
532%        Handling of ice-covered area
533% -------------------------------------------------------------------------------------------------------------
534\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
537The presence at the sea surface of an ice covered area modifies all the fluxes
538transmitted to the ocean. There are several way to handle sea-ice in the system
539depending on the value of the \np{nn{\_}ice} namelist parameter. 
541\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
542This is a typical namelist value used for tropical ocean domain. The surface fluxes
543are simply specified for an ice-free ocean. No specific things is done for sea-ice.
544\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
545is used. An observed ice covered area is read in a file. Below this area, the SST is
546restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
547in the northern (southern) hemisphere. The associated modification of the freshwater
548fluxes are done in such a way that the change in buoyancy fluxes remains zero.
549This prevents deep convection to occur when trying to reach the freezing point
550(and so ice covered area condition) while the SSS is too large. This manner of
551managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if} 
552model. It can be found in the \mdl{sbcice{\_}if} module.
553\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
554ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
555each model cell to provide the surface ocean fluxes. Note that the activation of a
556sea-ice model is is done by defining a CPP key (\key{lim2} or \key{lim3}).
557The activation automatically ovewrite the read value of nn{\_}ice to its appropriate
558value ($i.e.$ $2$ for LIM-2 and $3$ for LIM-3).
561% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
563% -------------------------------------------------------------------------------------------------------------
564%        Addition of river runoffs
565% -------------------------------------------------------------------------------------------------------------
566\subsection   [Addition of river runoffs (\textit{sbcrnf})]
567         {Addition of river runoffs (\mdl{sbcrnf})}
573The river runoffs
575It is convenient to introduce the river runoff in the model as a surface
576fresh water flux.
579%Griffies:  River runoff generally enters the ocean at a nonzero depth rather than through the surface. Many global models, however, have traditionally inserted river runoff to the top model cell. Such can become problematic numerically and physically when the top grid cells are reÞned to levels common in coastal modelling. Hence, more applications are now considering the input of runoff throughout a nonzero depth. Likewise, sea ice can melt at depth, thus necessitating a mass transport to occur within the ocean between the liquid and solid water masses.
581\colorbox{yellow}{Nevertheless, Pb of vertical resolution and increase of Kz in vicinity of }
583\colorbox{yellow}{river mouths{\ldots}}
585%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
586%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
591% -------------------------------------------------------------------------------------------------------------
592%        Freshwater budget control
593% -------------------------------------------------------------------------------------------------------------
594\subsection   [Freshwater budget control (\textit{sbcfwb})]
595         {Freshwater budget control (\mdl{sbcfwb})}
598For global ocean simulation it can be useful to introduce a control of the mean sea
599level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
600in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
602\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
603certainly do so.
604\item[\np{nn\_fwb}=1]  global mean EMP set to zero at each model time step.
605%Note that with a sea-ice model, this technique only control the mean sea level with linear free surface (\key{vvl} not defined) and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling).
606\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
607mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
608Boussinesq approximation, the annual mean fresh water budget is simply evaluated
609from the change in the mean sea level at January the first and saved in the
610\textit{EMPav.dat} file.
613% Griffies doc:
614% When running ocean-ice simulations, we are not explicitly representing land processes, such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, it is important to balance the hydrological cycle in ocean-ice models. We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. The result of the normalization should be a global integrated zero net water input to the ocean-ice system over a chosen time scale.
615%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, so that there is always a zero net input of water to the ocean-ice system. Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used to alter the subsequent yearÕs water budget in an attempt to damp the annual water imbalance. Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
616%When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean and ice models when aiming to balance the hydrological cycle. The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running ocean-ice models, not the water in any one sub-component. As an extreme example to illustrate the issue, consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up, there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. The total water contained in the ocean plus ice system is constant, but there is an exchange of water between the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle in ocean-ice models.
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