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1% ================================================================
2% Chapter Ñ Surface Boundary Condition (SBC)
3% ================================================================
4\chapter{Surface Boundary Condition (SBC) }
5\label{SBC}
6\minitoc
7
8\newpage
9$\ $\newline    % force a new ligne
10%---------------------------------------namsbc--------------------------------------------------
11\namdisplay{namsbc}
12%--------------------------------------------------------------------------------------------------------------
13$\ $\newline    % force a new ligne
14
15The ocean needs six fields as surface boundary condition:
16\begin{itemize}
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 $\left( {\textit{emp},\;\textit{emp}_S } \right)$
20\end{itemize}
21
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
31be supplied which maps the data from the supplied grid to the model points
32(so called "Interpolation on the Fly").
33In addition, the resulting fields can be further modified using several namelist options.
34These options control  the rotation of vector components supplied relative to an east-north
35coordinate system onto the local grid directions in the model; the addition of a surface
36restoring term 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).
43
44In this chapter, we first discuss where the surface boundary condition appears in the
45model equations. Then we present the four ways of providing the surface boundary condition.
46Next the scheme for interpolation on the fly is described.
47Finally, the different options that further modify the fluxes applied to the ocean are discussed.
48
49
50% ================================================================
51% Surface boundary condition for the ocean
52% ================================================================
53\section{Surface boundary condition for the ocean}
54\label{SBC_general}
55
56
57The surface ocean stress is the stress exerted by the wind and the sea-ice
58on the ocean. The two components of stress are assumed to be interpolated
59onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
60at $u$- and $v$-points They are applied as a surface boundary condition of the
61computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
62\begin{equation} \label{Eq_sbc_dynzdf}
63\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
64    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
65\end{equation}
66where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
67stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
68
69The surface heat flux is decomposed into two parts, a non solar and a solar heat
70flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
71of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
72It is applied as a surface boundary condition trend of the first level temperature
73time evolution equation (\mdl{trasbc} module).
74\begin{equation} \label{Eq_sbc_trasbc_q}
75\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 
76_o \;C_p \;e_{3t} }} \right|_{k=1} \quad
77\end{equation}
78$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
79trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
80
81\begin{equation} \label{Eq_sbc_traqsr}
82\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right]
83\end{equation}
84where $I_w$ is a non-dimensional function that describes the way the light
85penetrates inside the water column. It is generally a sum of decreasing
86exponentials (see \S\ref{TRA_qsr}).
87
88The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which
89may or may not be identical. Indeed, a surface freshwater flux has two effects:
90it changes the volume of the ocean and it changes the surface concentration of
91salt (and other tracers). Therefore it appears in the sea surface height as a volume
92flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
93as a concentration/dilution effect,
94$\textit{emp}_{S}$ (\mdl{trasbc} module).
95\begin{equation} \label{Eq_trasbc_emp}
96\begin{aligned}
97&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\ 
98\\
99 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\ 
100 \end{aligned}
101\end{equation} 
102
103In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,
104but it exist several numerical reasons why this equality should be broken.
105For example:
106
107When the rigid-lid assumption is made, the ocean volume becomes constant and
108thus, $\textit{emp}=0$, not $\textit{emp}_S$.
109
110When the ocean is coupled to a sea-ice model, the water exchanged between ice and
111ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,
112$\textit{emp}_{S}$ take into account both concentration/dilution effect associated with
113freezing/melting and the salt flux between ice and ocean, while \textit{emp} is
114only the volume flux. In addition, in the current version of \NEMO, the sea-ice is
115assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does
116not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS.
117%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
118
119Note that SST can also be modified by a freshwater flux. Precipitation (in
120particular solid precipitation) may have a temperature significantly different from
121the SST. Due to the lack of information about the temperature of
122precipitation, we assume it is equal to the SST. Therefore, no
123concentration/dilution term appears in the temperature equation. It has to
124be emphasised that this absence does not mean that there is no heat flux
125associated with precipitation! Precipitation can change the ocean volume and thus the
126ocean heat content. It is therefore associated with a heat flux (not yet 
127diagnosed in the model) \citep{Roullet_Madec_JGR00}).
128
129%\colorbox{yellow}{Miss: }
130%
131%A extensive description of all namsbc namelist (parameter that have to be
132%created!)
133%
134%Especially the \np{nf\_sbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
135%ssv) i.e. information required by flux computation or sea-ice
136%
137%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
138%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
139%
140%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
141%
142%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
143%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
144%nf{\_}sbc
145%
146%Explain here all the namlist namsbc variable{\ldots}.
147%
148%\colorbox{yellow}{End Miss }
149
150The ocean model provides the surface currents, temperature and salinity
151averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
152mean is done in \mdl{sbcmod} module.
153
154%-------------------------------------------------TABLE---------------------------------------------------
155\begin{table}[tb]  \label{Tab_ssm}
156\begin{center}
157\begin{tabular}{|l|l|l|l|}
158\hline
159Variable description             & Model variable  & Units  & point \\  \hline
160i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
161j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
162Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
163Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
164\end{tabular}
165\caption{Ocean variables provided by the ocean to the surface module (SBC).
166The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of
167computation of surface fluxes.}
168\end{center}
169\end{table}
170%--------------------------------------------------------------------------------------------------------------
171
172
173
174%\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
175
176
177% ================================================================
178% Analytical formulation (sbcana module)
179% ================================================================
180\section  [Analytical formulation (\textit{sbcana}) ]
181      {Analytical formulation (\mdl{sbcana} module) }
182\label{SBC_ana}
183
184%---------------------------------------namsbc_ana--------------------------------------------------
185\namdisplay{namsbc_ana}
186%--------------------------------------------------------------------------------------------------------------
187
188
189The analytical formulation of the surface boundary condition is the default scheme.
190In this case, all the six fluxes needed by the ocean are assumed to
191be uniform in space. They take constant values given in the namelist
192namsbc{\_}ana by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
193\np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero.
194In addition, the wind is allowed to reach its nominal value within a given number
195of time steps (\np{nn\_tau000}).
196
197If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
198module can be modified to use another scheme. As an example,
199the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
200GYRE configuration (see GYRE configuration manual, in preparation).
201
202
203% ================================================================
204% Flux formulation
205% ================================================================
206\section  [Flux formulation (\textit{sbcflx}) ]
207      {Flux formulation (\mdl{sbcflx} module) }
208\label{SBC_flx}
209%------------------------------------------namsbc_flx----------------------------------------------------
210\namdisplay{namsbc_flx} 
211%-------------------------------------------------------------------------------------------------------------
212
213In the flux formulation (\np{ln\_flx}=true), the surface boundary
214condition fields are directly read from input files. The user has to define
215in the namelist namsbc{\_}flx the name of the file, the name of the variable
216read in the file, the time frequency at which it is given (in hours), and a logical
217setting whether a time interpolation to the model time step is required
218for this field). (fld\_i namelist structure).
219
220\textbf{Caution}: when the frequency is set to --12, the data are monthly
221values. These are assumed to be climatological values, so time interpolation
222between December the 15$^{th}$ and January the 15$^{th}$ is done using
223records 12 and 1
224
225When higher frequency is set and time interpolation is demanded, the model
226will try to read the last (first) record of previous (next) year in a file
227having the same name but a suffix {\_}prev{\_}year ({\_}next{\_}year) being
228added (e.g. "{\_}1989"). These files must only contain a single record. If they don't exist,
229the model assumes that the last record of the previous year is equal to the first
230record of the current year, and similarly, that the first record of the
231next year is equal to the last record of the current year. This will cause
232the forcing to remain constant over the first and last half fld\_frequ hours.
233
234Note that in general, a flux formulation is used in associated with a
235restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
236specification.
237
238
239% ================================================================
240% Bulk formulation
241% ================================================================
242\section  [Bulk formulation (\textit{sbcblk\_core} or \textit{sbcblk\_clio}) ]
243      {Bulk formulation \small{(\mdl{sbcblk\_core} or \mdl{sbcblk\_clio} module)} }
244\label{SBC_blk}
245
246In the bulk formulation, the surface boundary condition fields are computed
247using bulk formulae and atmospheric fields and ocean (and ice) variables.
248
249The atmospheric fields used depend on the bulk formulae used. Two bulk formulations
250are available : the CORE and CLIO bulk formulea. The choice is made by setting to true
251one of the following namelist variable : \np{ln\_core} and \np{ln\_clio}.
252
253Note : in forced mode, when a sea-ice model is used, a bulk formulation have to be used.
254Therefore the two bulk formulea provided include the computation of the fluxes over both
255an ocean and an ice surface.
256
257% -------------------------------------------------------------------------------------------------------------
258%        CORE Bulk formulea
259% -------------------------------------------------------------------------------------------------------------
260\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
261            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
262\label{SBC_blk_core}
263%------------------------------------------namsbc_core----------------------------------------------------
264\namdisplay{namsbc_core} 
265%-------------------------------------------------------------------------------------------------------------
266
267The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
268They have been designed to handle the CORE forcing, a mixture of NCEP
269reanalysis and satellite data. They use an inertial dissipative method to compute
270the turbulent transfer coefficients (momentum, sensible heat and evaporation)
271from the 10 metre wind speed, air temperature and specific humidity.
272
273Note that substituting ERA40 to NCEP reanalysis fields
274does not require changes in the bulk formulea themself.
275
276The required 8 input fields are:
277
278%--------------------------------------------------TABLE--------------------------------------------------
279\begin{table}[htbp]   \label{Tab_CORE}
280\begin{center}
281\begin{tabular}{|l|l|l|l|}
282\hline
283Variable desciption              & Model variable  & Units   & point \\    \hline
284i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
285j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
28610m air temperature              & tair      & \r{}$K$            & T   \\ \hline
287Specific humidity             & humi      & \%              & T \\      \hline
288Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
289Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
290Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
291Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
292\end{tabular}
293\end{center}
294\end{table}
295%--------------------------------------------------------------------------------------------------------------
296
297Note 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
298size is the same or larger than the one of the input atmospheric fields.
299
300% -------------------------------------------------------------------------------------------------------------
301%        CLIO Bulk formulea
302% -------------------------------------------------------------------------------------------------------------
303\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
304            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
305\label{SBC_blk_clio}
306%------------------------------------------namsbc_clio----------------------------------------------------
307\namdisplay{namsbc_clio} 
308%-------------------------------------------------------------------------------------------------------------
309
310The CLIO bulk formulae were developed several years ago for the
311Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
312They are simpler bulk formulae. They assume the stress to be known and
313compute the radiative fluxes from a climatological cloud cover.
314
315The required 7 input fields are:
316
317%--------------------------------------------------TABLE--------------------------------------------------
318\begin{table}[htbp]   \label{Tab_CLIO}
319\begin{center}
320\begin{tabular}{|l|l|l|l|}
321\hline
322Variable desciption           & Model variable  & Units           & point \\  \hline
323i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
324j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
325Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
32610m air temperature              & tair         & \r{}$K$            & T \\   \hline
327Specific humidity                & humi         & \%              & T \\   \hline
328Cloud cover                   &           & \%              & T \\   \hline
329Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
330Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
331\end{tabular}
332\end{center}
333\end{table}
334%--------------------------------------------------------------------------------------------------------------
335
336As for the flux formulation, information about the input data required by the
337model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
338namelist (via the structure fld\_i). The first and last record assumption is also made
339(see \S\ref{SBC_flx})
340
341% ================================================================
342% Coupled formulation
343% ================================================================
344\section  [Coupled formulation (\textit{sbccpl}) ]
345      {Coupled formulation (\mdl{sbccpl} module)}
346\label{SBC_cpl}
347%------------------------------------------namsbc_cpl----------------------------------------------------
348\namdisplay{namsbc_cpl} 
349%-------------------------------------------------------------------------------------------------------------
350
351In the coupled formulation of the surface boundary condition, the fluxes are
352provided by the OASIS coupler at each \np{nf\_cpl} time-step, while sea and ice
353surface temperature, ocean and ice albedo, and ocean currents are sent to
354the atmospheric component.
355
356The generalised coupled interface is under development. It should be available
357in summer 2008. It will include the ocean interface for most of the European
358atmospheric GCM (ARPEGE, ECHAM, ECMWF, HadAM, LMDz).
359
360% ================================================================
361% Interpolation on the Fly
362% ================================================================
363
364\section [Interpolation on the Fly] {Interpolation on the Fly}
365\label{SBC_iof}
366
367Interpolation on the Fly allows the user to supply input files required
368for the surface forcing on grids other than the model grid.
369To do this he or she must supply, in addition to the source data file,
370a file of weights to be used to interpolate from the data grid to the model
371grid.
372The original development of this code used the SCRIP package (freely available
373under a copyright agreement from http://climate.lanl.gov/Software/SCRIP).
374In principle, any package can be used to generate the weights, but the
375variables in the input weights file must have the same names and meanings as
376assumed by the model.
377Two methods are currently available: bilinear and bicubic interpolation.
378
379\subsection{Bilinear Interpolation}
380\label{SBC_iof_bilinear}
381
382The input weights file in this case has two sets of variables: src01, src02,
383src03, src04 and wgt01, wgt02, wgt03, wgt04.
384The "src" variables correspond to the point in the input grid to which the weight
385"wgt" is to be applied. Each src value is an integer corresponding to the index of a
386point in the input grid when written as a one dimensional array.  For example, for an input grid
387of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
388There are four of each variable because bilinear interpolation uses the four points defining
389the grid box containing the point to be interpolated.
390All of these arrays are on the model grid, so that values src01(i,j) and
391wgt01(i,j) are used to generate a value for point (i,j) in the model.
392
393Symbolically, the algorithm used is:
394
395\begin{equation}
396f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
397\end{equation}
398where function idx() transforms a one dimensional index src(k) into a two dimensional index,
399and wgt(1) corresponds to variable "wgt01" for example.
400
401\subsection{Bicubic Interpolation}
402\label{SBC_iof_bicubic}
403
404Again there are two sets of variables: "src" and "wgt".
405But in this case there are 16 of each.
406The symbolic algorithm used to calculate values on the model grid is now:
407
408\begin{equation*} \begin{split}
409f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}     
410              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
411              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }   
412              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
413\end{split}
414\end{equation*}
415The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
416
417\subsection{Implementation}
418\label{SBC_iof_imp}
419
420To activate this option, a non-empty string should be supplied in the weights filename column of the relevant namelist;
421if this is left as an empty string no action is taken.
422In 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.
423This initialisation procedure tries to determine whether the input data grid should be treated as cyclical or not.
424(In fact this only matters when bicubic interpolation is required.)
425To 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".
426If found, it checks the difference between the first and last values of longitude along a single row.
427If 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.
428If neither "nav\_lon" or "lon" can be found, the model resorts to looking at the first and last columns of data.
429If 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.
430If both of these tests fail, the grid is assumed not to be cyclical.
431
432Next the routine reads in the weights.
433Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
434The 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).
435The 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.
436Since 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.
437When 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).
438
439\subsection{Limitations}
440\label{SBC_iof_lim}
441
442\begin{description}
443\item
444Input data grids must be logically rectangular.
445\item
446This code is not guaranteed to produce positive definite answers from positive definite inputs.
447\item
448The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
449\item
450The gradients across the ends of a cyclical grid assume that the grid spacing between the two columns involved are consistent with the weights used.
451\item
452Neither interpolation scheme is conservative.
453(There is a conservative scheme available in SCRIP, but this has not been implemented.)
454\end{description}
455
456\subsection{Utilities}
457\label{SBC_iof_util}
458
459% to be completed
460A set of utilities to create a weights file for a rectilinear input grid is available.
461
462% ================================================================
463% Miscellanea options
464% ================================================================
465\section{Miscellaneous options}
466\label{SBC_misc}
467
468% -------------------------------------------------------------------------------------------------------------
469%        Rotation of vector pairs onto the model grid directions
470% -------------------------------------------------------------------------------------------------------------
471\subsection{Rotation of vector pairs onto the model grid directions}
472\label{SBC_rotation}
473
474When using a flux (\np{ln\_flx}=true) or bulk (\np{ln\_clio}=true or \np{ln\_core}=true) formulation,
475pairs of vector components can be rotated from east-north directions onto the local grid directions. 
476This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
477relative to a rectilinear grid.
478To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
479The eastward component must start with "U" and the northward component with "V". 
480The remaining characters in the strings are used to identify which pair of components go together.
481So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
482and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
483and so on.
484The extra characters used in the strings are arbitrary.
485The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
486
487% -------------------------------------------------------------------------------------------------------------
488%        Surface restoring to observed SST and/or SSS
489% -------------------------------------------------------------------------------------------------------------
490\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
491         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
492\label{SBC_ssr}
493%------------------------------------------namsbc_ssr----------------------------------------------------
494\namdisplay{namsbc_ssr} 
495%-------------------------------------------------------------------------------------------------------------
496
497In forced mode using a flux formulation (default option or \key{flx} defined), a
498feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
499\begin{equation} \label{Eq_sbc_dmp_q}
500Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
501\end{equation}
502where SST is a sea surface temperature field (observed or climatological), $T$ is
503the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
504coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
505mixed-layer depth, this value corresponds to a relaxation time scale of two months.
506This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
507equal to $Q_o$.
508
509In the fresh water budget, a feedback term can also be added. Converted into an
510equivalent freshwater flux, it takes the following expression :
511
512\begin{equation} \label{Eq_sbc_dmp_emp}
513\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
514                                             {\left.S\right|_{k=1}}
515\end{equation}
516
517where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an
518atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
519interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
520$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
521feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
522physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
523does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring
524term should be viewed as a flux correction on freshwater fluxes to reduce the
525uncertainties we have on the observed freshwater budget.
526
527% -------------------------------------------------------------------------------------------------------------
528%        Handling of ice-covered area
529% -------------------------------------------------------------------------------------------------------------
530\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
531\label{SBC_ice-cover}
532
533The presence at the sea surface of an ice covered area modifies all the fluxes
534transmitted to the ocean. There are several way to handle sea-ice in the system
535depending on the value of the \np{nn{\_}ice} namelist parameter. 
536\begin{description}
537\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
538This is a typical namelist value used for tropical ocean domain. The surface fluxes
539are simply specified for an ice-free ocean. No specific things is done for sea-ice.
540\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
541is used. An observed ice covered area is read in a file. Below this area, the SST is
542restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
543in the northern (southern) hemisphere. The associated modification of the freshwater
544fluxes are done in such a way that the change in buoyancy fluxes remains zero.
545This prevents deep convection to occur when trying to reach the freezing point
546(and so ice covered area condition) while the SSS is too large. This manner of
547managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if} 
548model. It can be found in the \mdl{sbcice{\_}if} module.
549\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
550ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
551each model cell to provide the surface ocean fluxes. Note that the activation of a
552sea-ice model is is done by defining a CPP key (\key{lim2} or \key{lim3}).
553The activation automatically ovewrite the read value of nn{\_}ice to its appropriate
554value ($i.e.$ $2$ for LIM-2 and $3$ for LIM-3).
555\end{description}
556
557% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
558
559% -------------------------------------------------------------------------------------------------------------
560%        Addition of river runoffs
561% -------------------------------------------------------------------------------------------------------------
562\subsection   [Addition of river runoffs (\textit{sbcrnf})]
563         {Addition of river runoffs (\mdl{sbcrnf})}
564\label{SBC_rnf}
565%------------------------------------------namsbc_rnf----------------------------------------------------
566\namdisplay{namsbc_rnf} 
567%-------------------------------------------------------------------------------------------------------------
568
569The river runoffs
570
571It is convenient to introduce the river runoff in the model as a surface
572fresh water flux.
573
574
575%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.
576
577\colorbox{yellow}{Nevertheless, Pb of vertical resolution and increase of Kz in vicinity of }
578
579\colorbox{yellow}{river mouths{\ldots}}
580
581%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
582%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
583%ENDIF
584
585
586
587% -------------------------------------------------------------------------------------------------------------
588%        Freshwater budget control
589% -------------------------------------------------------------------------------------------------------------
590\subsection   [Freshwater budget control (\textit{sbcfwb})]
591         {Freshwater budget control (\mdl{sbcfwb})}
592\label{SBC_fwb}
593
594For global ocean simulation it can be useful to introduce a control of the mean sea
595level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
596in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
597\begin{description}
598\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
599certainly do so.
600\item[\np{nn\_fwb}=1]  global mean \textit{emp} set to zero at each model time step.
601%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).
602\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
603mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
604Boussinesq approximation, the annual mean fresh water budget is simply evaluated
605from the change in the mean sea level at January the first and saved in the
606\textit{EMPav.dat} file.
607\end{description}
608
609% Griffies doc:
610% 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.
611%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.
612%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.
613
614
615
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