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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 $\left( {\text{EMP},\;\text{EMP}_S } \right)$
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.
29In addition, the resulting fields can be further modified using
30several namelist options. These options control the addition of a surface restoring
31term to observed SST and/or SSS (\np{ln\_ssr}=true), the modification of fluxes
32below ice-covered areas (using observed ice-cover or a sea-ice model)
33(\np{nn\_ice}=0,1, 2 or 3), the addition of river runoffs as surface freshwater
35order to avoid a mean sea-level drift (\np{nn\_fwb}= 0, 1 or 2), and the
36transformation of the solar radiation (if provided as daily mean) into a diurnal
37cycle (\np{ln\_dm2dc}=true).
38
39In this chapter, we first discuss where the surface boundary condition
40appears in the model equations. Then we present the four ways of providing
41the surface boundary condition. Finally, the different options that further modify
42the fluxes applied to the ocean are discussed.
43
44
45% ================================================================
46% Surface boundary condition for the ocean
47% ================================================================
48\section{Surface boundary condition for the ocean}
49\label{SBC_general}
50
51
52The surface ocean stress is the stress exerted by the wind and the sea-ice
53on the ocean. The two components of stress are assumed to be interpolated
54onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
55at $u$- and $v$-points They are applied as a surface boundary condition of the
56computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
57\begin{equation} \label{Eq_sbc_dynzdf}
58\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
59    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
60\end{equation}
61where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
62stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
63
64The surface heat flux is decomposed into two parts, a non solar and a solar heat
65flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
66of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
67It is applied as a surface boundary condition trend of the first level temperature
68time evolution equation (\mdl{trasbc} module).
69\begin{equation} \label{Eq_sbc_trasbc_q}
70\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho
71_o \;C_p \;e_{3T} }} \right|_{k=1} \quad
72\end{equation}
73$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
74trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
75
76\begin{equation} \label{Eq_sbc_traqsr}
77\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho _o C_p
78\,e_{3T} }\delta _k \left[ {I_w } \right]
79\end{equation}
80where $I_w$ is a non-dimensional function that describes the way the light
81penetrates inside the water column. It is generally a sum of decreasing
82exponentials (see \S\ref{TRA_qsr}).
83
84The surface freshwater budget is provided by fields: EMP and EMP$_S$ which
85may or may not be identical. Indeed, a surface freshwater flux has two effects:
86it changes the volume of the ocean and it changes the surface concentration of
87salt (and other tracers). Therefore it appears in the sea surface height as a volume
88flux, EMP (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
89as a concentration/dilution effect,
90EMP$_{S}$ (\mdl{trasbc} module).
91\begin{equation} \label{Eq_trasbc_emp}
92\begin{aligned}
93&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\text{EMP}\quad  \\
94\\
95 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\text{EMP}_S \;S}{e_{3T} }} \right|_{k=1} \\
96 \end{aligned}
97\end{equation}
98
99In the real ocean, EMP$=$EMP$_S$ and the ocean salt content is conserved,
100but it exist several numerical reasons why this equality should be broken.
101For example:
102
103When rigid-lid assumption is made, the ocean volume becomes constant and
104thus, EMP$=$0, not EMP$_{S }$.
105
106When the ocean is coupled to a sea-ice model, the water exchanged between ice and
107ocean is slightly salty (mean sea-ice salinity is $\sim$\textit{4 psu}). In this case,
108EMP$_{S}$ take into account both concentration/dilution effect associated with
109freezing/melting and the salt flux between ice and ocean, while EMP is
110only the volume flux. In addition, in the current version of \NEMO, the
111sea-ice is assumed to be above the ocean. Freezing/melting does not change
112the ocean volume (not impact on EMP) but it modifies the SSS.
113%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
114
115Note that SST can also be modified by a freshwater flux. Precipitation (in
116particular solid precipitation) may have a temperature significantly different from
117the SST. Due to the lack of information about the temperature of
118precipitation, we assume it is equal to the SST. Therefore, no
119concentration/dilution term appears in the temperature equation. It has to
120be emphasised that this absence does not mean that there is no heat flux
121associated with precipitation! Precipitation can change the ocean volume and thus the
122ocean heat content. It is therefore associated with a heat flux (not yet
123diagnosed in the model) \citep{Roullet2000}).
124
125%\colorbox{yellow}{Miss: }
126%
127%A extensive description of all namsbc namelist (parameter that have to be
128%created!)
129%
130%Especially the \np{nf\_sbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
131%ssv) i.e. information required by flux computation or sea-ice
132%
133%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
134%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
135%
136%Sbcmod manage the providing'' (fourniture) to the ocean the 7 fields
137%
138%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
139%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
140%nf{\_}sbc
141%
142%Explain here all the namlist namsbc variable{\ldots}.
143%
144%\colorbox{yellow}{End Miss }
145
146The ocean model provides the surface currents, temperature and salinity
147averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
148mean is done in \mdl{sbcmod} module.
149
150%-------------------------------------------------TABLE---------------------------------------------------
151\begin{table}[tb]  \label{Tab_ssm}
152\begin{center}
153\begin{tabular}{|l|l|l|l|}
154\hline
155Variable description             & Model variable  & Units  & point \\  \hline
156i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
157j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
158Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
159Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
160\end{tabular}
161\caption{Ocean variables provided by the ocean to the surface module (SBC).
162The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of
163computation of surface fluxes.}
164\end{center}
165\end{table}
166%--------------------------------------------------------------------------------------------------------------
167
168
169
170%\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
171
172
173% ================================================================
174% Analytical formulation (sbcana module)
175% ================================================================
176\section  [Analytical formulation (\textit{sbcana}) ]
177      {Analytical formulation (\mdl{sbcana} module) }
178\label{SBC_ana}
179
180%---------------------------------------namsbc_ana--------------------------------------------------
181\namdisplay{namsbc_ana}
182%--------------------------------------------------------------------------------------------------------------
183
184
185The analytical formulation of the surface boundary condition is the default scheme.
186In this case, all the six fluxes needed by the ocean are assumed to
187be uniform in space. They take constant values given in the namelist
188namsbc{\_}ana by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
189\np{rn\_qsr0}, and \np{rn\_emp0} (EMP$=$EMP$_S$). The runoff is set to zero.
190In addition, the wind is allowed to reach its nominal value within a given number
191of time steps (\np{nn\_tau000}).
192
193If a user wants to apply a different analytical forcing, the \mdl{sbcana}
194module can be modified to use another scheme. As an example,
195the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
196GYRE configuration (see GYRE configuration manual, in preparation).
197
198
199% ================================================================
200% Flux formulation
201% ================================================================
202\section  [Flux formulation (\textit{sbcflx}) ]
203      {Flux formulation (\mdl{sbcflx} module) }
204\label{SBC_flx}
205%------------------------------------------namsbc_flx----------------------------------------------------
206\namdisplay{namsbc_flx}
207%-------------------------------------------------------------------------------------------------------------
208
209In the flux formulation (\np{ln\_flx}=true), the surface boundary
210condition fields are directly read from input files. The user has to define
211in the namelist namsbc{\_}flx the name of the file, the name of the variable
212read in the file, the time frequency at which it is given (in hours), and a logical
213setting whether a time interpolation to the model time step is required
214for this field). (fld\_i namelist structure).
215
216\textbf{Caution}: when the frequency is set to --12, the data are monthly
217values. These are assumed to be climatological values, so time interpolation
218between December the 15$^{th}$ and January the 15$^{th}$ is done using
219records 12 and 1
220
221When higher frequency is set and time interpolation is demanded, the model
222will try to read the last (first) record of previous (next) year in a file
223having the same name but a suffix {\_}prev{\_}year ({\_}next{\_}year) being
224added (e.g. "{\_}1989"). These files must only contain a single record. If they don't exist,
225the model assumes that the last record of the previous year is equal to the first
226record of the current year, and similarly, that the first record of the
227next year is equal to the last record of the current year. This will cause
228the forcing to remain constant over the first and last half fld\_frequ hours.
229
230Note that in general, a flux formulation is used in associated with a
231restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
232specification.
233
234
235% ================================================================
236% Bulk formulation
237% ================================================================
238\section  [Bulk formulation (\textit{sbcblk\_core} or \textit{sbcblk\_clio}) ]
239      {Bulk formulation \small{(\mdl{sbcblk\_core} or \mdl{sbcblk\_clio} module)} }
240\label{SBC_blk}
241
242In the bulk formulation, the surface boundary condition fields are computed
243using bulk formulae and atmospheric fields and ocean (and ice) variables.
244
245The atmospheric fields used depend on the bulk formulae used. Two bulk formulations
246are available : the CORE and CLIO bulk formulea. The choice is made by setting to true
247one of the following namelist variable : \np{ln\_core} and \np{ln\_clio}.
248
249Note : in forced mode, when a sea-ice model is used, a bulk formulation have to be used.
250Therefore the two bulk formulea provided include the computation of the fluxes over both
251an ocean and an ice surface.
252
253% -------------------------------------------------------------------------------------------------------------
254%        CORE Bulk formulea
255% -------------------------------------------------------------------------------------------------------------
256\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
257            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
258\label{SBC_blk_core}
259%------------------------------------------namsbc_core----------------------------------------------------
260\namdisplay{namsbc_core}
261%-------------------------------------------------------------------------------------------------------------
262
263The CORE bulk formulae have been developed by \citet{LargeYeager2004}.
264They have been designed to handle the CORE forcing, a mixture of NCEP
265reanalysis and satellite data. They use an inertial dissipative method to compute
266the turbulent transfer coefficients (momentum, sensible heat and evaporation)
267from the 10 metre wind speed, air temperature and specific humidity.
268
269Note that substituting ERA40 to NCEP reanalysis fields
270does not require changes in the bulk formulea themself.
271
272The required 8 input fields are:
273
274%--------------------------------------------------TABLE--------------------------------------------------
275\begin{table}[htbp]   \label{Tab_CORE}
276\begin{center}
277\begin{tabular}{|l|l|l|l|}
278\hline
279Variable desciption              & Model variable  & Units   & point \\    \hline
280i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
281j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
28210m air temperature              & tair      & \r{}$K$            & T   \\ \hline
283Specific humidity             & humi      & \%              & T \\      \hline
284Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
285Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
286Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
287Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
288\end{tabular}
289\end{center}
290\end{table}
291%--------------------------------------------------------------------------------------------------------------
292
293Note 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
294size is the same or larger than the one of the input atmospheric fields.
295
296% -------------------------------------------------------------------------------------------------------------
297%        CLIO Bulk formulea
298% -------------------------------------------------------------------------------------------------------------
299\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
300            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
301\label{SBC_blk_clio}
302%------------------------------------------namsbc_clio----------------------------------------------------
303\namdisplay{namsbc_clio}
304%-------------------------------------------------------------------------------------------------------------
305
306The CLIO bulk formulae were developed several years ago for the
307Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
308They are simpler bulk formulae. They assume the stress to be known and
309compute the radiative fluxes from a climatological cloud cover.
310
311The required 7 input fields are:
312
313%--------------------------------------------------TABLE--------------------------------------------------
314\begin{table}[htbp]   \label{Tab_CLIO}
315\begin{center}
316\begin{tabular}{|l|l|l|l|}
317\hline
318Variable desciption           & Model variable  & Units           & point \\  \hline
319i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
320j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
321Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
32210m air temperature              & tair         & \r{}$K$            & T \\   \hline
323Specific humidity                & humi         & \%              & T \\   \hline
324Cloud cover                   &           & \%              & T \\   \hline
325Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
326Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
327\end{tabular}
328\end{center}
329\end{table}
330%--------------------------------------------------------------------------------------------------------------
331
332As for the flux formulation, information about the input data required by the
333model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
334namelist (via the structure fld\_i). The first and last record assumption is also made
335(see \S\ref{SBC_flx})
336
337% ================================================================
338% Coupled formulation
339% ================================================================
340\section  [Coupled formulation (\textit{sbccpl}) ]
341      {Coupled formulation (\mdl{sbccpl} module)}
342\label{SBC_cpl}
343%------------------------------------------namsbc_cpl----------------------------------------------------
344\namdisplay{namsbc_cpl}
345%-------------------------------------------------------------------------------------------------------------
346
347In the coupled formulation of the surface boundary condition, the fluxes are
348provided by the OASIS coupler at each \np{nf\_cpl} time-step, while sea and ice
349surface temperature, ocean and ice albedo, and ocean currents are sent to
350the atmospheric component.
351
352The generalised coupled interface is under development. It should be available
353in summer 2008. It will include the ocean interface for most of the European
354atmospheric GCM (ARPEGE, ECHAM, ECMWF, HadAM, LMDz).
355
356
357% ================================================================
358% Miscellanea options
359% ================================================================
360\section{Miscellaneous options}
361\label{SBC_misc}
362
363% -------------------------------------------------------------------------------------------------------------
364%        Surface restoring to observed SST and/or SSS
365% -------------------------------------------------------------------------------------------------------------
366\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
367         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
368\label{SBC_ssr}
369%------------------------------------------namsbc_ssr----------------------------------------------------
370\namdisplay{namsbc_ssr}
371%-------------------------------------------------------------------------------------------------------------
372
373In forced mode using a flux formulation (default option or \key{flx} defined), a
374feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
375\begin{equation} \label{Eq_sbc_dmp_q}
376Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
377\end{equation}
378where SST is a sea surface temperature field (observed or climatological), $T$ is
379the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
380coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$
381mixed-layer depth, this value corresponds to a relaxation time scale of two months.
382This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
383equal to $Q_o$.
384
385In the fresh water budget, a feedback term can also be added. Converted into an
386equivalent freshwater flux, it takes the following expression :
387
388\begin{equation} \label{Eq_sbc_dmp_emp}
389EMP = EMP_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
390                                             {\left.S\right|_{k=1}}
391\end{equation}
392
393where EMP$_{o }$ is a net surface fresh water flux (observed, climatological or an
394atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
395interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
396$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
397feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
398physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
400term should be viewed as a flux correction on freshwater fluxes to reduce the
401uncertainties we have on the observed freshwater budget.
402
403% -------------------------------------------------------------------------------------------------------------
404%        Handling of ice-covered area
405% -------------------------------------------------------------------------------------------------------------
406\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
407\label{SBC_ice-cover}
408
409The presence at the sea surface of an ice covered area modifies all the fluxes
410transmitted to the ocean. There are several way to handle sea-ice in the system
411depending on the value of the \np{nn{\_}ice} namelist parameter.
412\begin{description}
413\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
414This is a typical namelist value used for tropical ocean domain. The surface fluxes
415are simply specified for an ice-free ocean. No specific things is done for sea-ice.
416\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
417is used. An observed ice covered area is read in a file. Below this area, the SST is
418restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
419in the northern (southern) hemisphere. The associated modification of the freshwater
420fluxes are done in such a way that the change in buoyancy fluxes remains zero.
421This prevents deep convection to occur when trying to reach the freezing point
422(and so ice covered area condition) while the SSS is too large. This manner of
423managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if}
424model. It can be found in the \mdl{sbcice{\_}if} module.
425\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
426ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
427each model cell to provide the surface ocean fluxes. Note that the activation of a
428sea-ice model is is done by defining a CPP key (\key{lim2} or \key{lim3}).
429The activation automatically ovewrite the read value of nn{\_}ice to its appropriate
430value ($i.e.$ $2$ for LIM-2 and $3$ for LIM-3).
431\end{description}
432
433% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
434
435% -------------------------------------------------------------------------------------------------------------
437% -------------------------------------------------------------------------------------------------------------
438\subsection   [Addition of river runoffs (\textit{sbcrnf})]
439         {Addition of river runoffs (\mdl{sbcrnf})}
440\label{SBC_rnf}
441%------------------------------------------namsbc_rnf----------------------------------------------------
442\namdisplay{namsbc_rnf}
443%-------------------------------------------------------------------------------------------------------------
444
445The river runoffs
446
447It is convenient to introduce the river runoff in the model as a surface
448fresh water flux.
449
450
451%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.
452
453\colorbox{yellow}{Nevertheless, Pb of vertical resolution and increase of Kz in vicinity of }
454
455\colorbox{yellow}{river mouths{\ldots}}
456
457%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
458%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
459%ENDIF
460
461
462
463% -------------------------------------------------------------------------------------------------------------
464%        Freshwater budget control
465% -------------------------------------------------------------------------------------------------------------
466\subsection   [Freshwater budget control (\textit{sbcfwb})]
467         {Freshwater budget control (\mdl{sbcfwb})}
468\label{SBC_fwb}
469
470For global ocean simulation it can be useful to introduce a control of the mean sea
471level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
472in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
473\begin{description}
474\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
475certainly do so.
476\item[\np{nn\_fwb}=1]  global mean EMP set to zero at each model time step.
477%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).
478\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
479mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
480Boussinesq approximation, the annual mean fresh water budget is simply evaluated
481from the change in the mean sea level at January the first and saved in the
482\textit{EMPav.dat} file.
483\end{description}
484
485% Griffies doc:
486% 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.
487%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.
488%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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