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Chap_SBC.tex in trunk/NEMO/DOC/BETA/Chapters – NEMO

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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\begin{verbatim}
9At the time of this writing, the new surface module
10that is described in this chapter (SBC) is not yet part
11of the current distribution. The current way to specify
12the surface boundary condition is such a mess that we
13did not attempt to describe it. Nevertheless, apart from
14the way the surface forcing is implemented, the infor-
15mation given here are relevant for a NEMO v2.3 user.
16\end{verbatim}
17
18The ocean needs 7 fields as surface boundary condition:
19
20The two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$
21
22The incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
23
24The surface freshwater budget $\left( {\text{EMP}\;,\;\text{EMP}_S } \right)$
25
26\colorbox {yellow}{ The river runoffs (RUNOFF)}
27
28Four different ways are offered to provide those 7 fields to the ocean: an
29analytical formulation, a flux formulation, a bulk formulae formulation
30(CORE or CLIO bulk formulae) and a coupled formulation (exchanges with a
31atmospheric model via OASIS coupler). In addition, the resulting fields can
32be further modified on used demand via several namelist option. These option
33control the addition of a surface restoring term to observed SST and/or SSS,
34the modification of fluxes below ice-covered area (using observed ice-cover
35or a sea-ice model), the addition of river runoffs as surface freshwater
36fluxes, and the addition of a freshwater flux adjustment on order to avoid a
37mean sea-level drift.
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 modify
42the fluxes inside the ocean are discussed.
43
44
45
46
47
48
49
50
51
52
53
54% ================================================================
55% Surface boundary condition for the ocean
56% ================================================================
57\section{Surface boundary condition for the ocean}
58\label{SBC_general}
59
60
61The surface ocean stress is the stress exerted by the wind and the sea-ice
62on the ocean. Their two components are assumed to be interpolated on the
63ocean mesh, i.e. provided at U- and V-points and projected onto the
64(\textbf{i},\textbf{j}) referential. They are applied as a surface boundary
65condition of the computation of the momentum vertical mixing trend
66(\textbf{dynzdf} module) :
67\begin{equation} \label{Eq_sbc_dynzdf}
68\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
69    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
70\end{equation}
71where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
72stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
73
74The surface heat flux is decomposed in two parts, a non solar and solar heat
75fluxes. The former is the non penetrative part of the heat flux (i.e.
76sensible plus latent plus long wave heat fluxes). It is applied as a surface
77boundary condition trend of the first level temperature time evolution
78equation (\mdl{trasbc} module).
79\begin{equation} \label{Eq_sbc_trasbc_q}
80\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 
81_o \;C_p \;e_{3T} }} \right|_{k=1} \quad
82\end{equation}
83
84The latter is the penetrative part of the heat flux. It is applied as a 3D
85trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=T.
86
87\begin{equation} \label{Eq_sbc_traqsr}
88\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho _o C_p
89\,e_{3T} }\delta _k \left[ {I_w } \right]
90\end{equation}
91
92where $I_w$ is an adimensional function that describes the way the light
93penetrates inside the water column. It is generally a sum of decreasing
94exponential (see \S\ref{TRA_qsr}).
95
96The surface freshwater budget is provided through two non-necessary
97identical fields EMP and EMP$_S $. Indeed, a surface freshwater
98flux has two effects: it changes the volume of the ocean and it changes the
99surface concentration of salt (an others tracers). Therefore it appears in
100the sea surface height and salinity time evolution equations as a volume
101flux, EMP (\textit{dynspg\_xxx} modules), and concentration/dilution effect,
102EMP$_{S}$ (\mdl{trasbc} module), respectively.
103\begin{equation} \label{Eq_trasbc_emp}
104\begin{aligned}
105&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\text{EMP}\quad  \\ 
106\\
107 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\text{EMP}_S \;S}{e_{3T} }} \right|_{k=1} \\ 
108 \end{aligned}
109\end{equation} 
110
111In the real ocean, EMP=EMP$_S$ and the ocean salt content is conserved,
112but it exist several numerical reason why this equality should be broken.
113For example:
114
115When rigid-lid assumption is made, the ocean volume becomes constant and
116thus, EMP=0, not EMP$_{S }$.
117
118When a sea-ice model is considered, the water exchanged between ice and
119ocean is not fresh as mean ice salinity is $\sim $\textit{4 psu}. In this case,
120EMP$_{S}$ take into account both concentration/dilution effect associated with
121freezing/melting together with salt flux between ice and ocean, while EMP is
122only the volume flux. In addition, in the current version of \NEMO, the
123sea-ice is assumed to be above the ocean. Freezing/melting does not change
124the ocean volume (not impact on EMP) while it modifies the SSS
125\colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
126
127Note that SST can also be modified by a freshwater flux. Precipitations (in
128particular solid one) may have a temperature significantly different from
129the SST. Due to the lack of information about the temperature of
130precipitations, we assume it is equal to the SST. Therefore, no
131concentration/dilution term appears in the temperature equation. It has to
132be emphasised that this absence does not mean that there is not heat flux
133associated with precipitation! An excess of precipitation will change the
134ocean heat content and is therefore associated with a heat flux (not
135diagnosed in the model) \citep{Roullet2000}).
136
137\colorbox{yellow}{Miss: }
138
139A extensive description of all namsbc namelist (parameter that have to be
140created!)
141
142Especially the \np{nf\_sbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
143ssv) i.e. information required by flux computation or sea-ice
144
145\colorbox{red}{Add nqsr = 0 / 1 replace key{\_}traqsr}
146
147\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
148a word on runoff: included in surface bc or add as lateral obc{\ldots}.
149
150Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
151
152Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
153between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
154nf{\_}sbc
155
156Explain here all the namlist namsbc variable{\ldots}.
157
158\colorbox{yellow}{End Miss }
159
160The ocean model provides the following variables averaged over nf{\_}sbc
161time-step:
162
163%-------------------------------------------------TABLE---------------------------------------------------
164\begin{table}[htbp]  \label{Tab_ssm}
165\begin{center}
166\begin{tabular}{|l|l|l|l|}
167\hline
168Variable desciption              & Computer name   & Units  & point \\  \hline
169i-component of the surface current  & ssu\_u & $m.s^{-1}$   & U \\   \hline
170j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
171Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
172Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
173\end{tabular}
174\end{center}
175\end{table}
176%--------------------------------------------------------------------------------------------------------------
177
178The mean computation is done in sbcmod (
179
180\colorbox{yellow}{Penser a} mettre dans le restant l'info nf{\_}sbc ET nf{\_}sbc*rdt de sorte de
181reinitialiser la moyenne si on change la frequence ou le pdt
182
183NB: creer cn{\_}sbc{\_}ice (cn{\_} = character in the namelist) with 3
184cases:
185
186= `noice' no specific call
187
188= `iceif ` ``ice-if'' sea ice, i.e. read observed ice-cover and modified sbc
189bellow those area.
190
191= `lim' LIM sea-ice model is called which update the sbc fields in ice
192covered area
193
194? modify the nsbc{\_}ice variable depending of this parameter (from --1, 0
195to 1)
196\colorbox{yellow}{End Penser a}
197
198% ================================================================
199% Analytical formulation (sbcana module)
200% ================================================================
201\section{Analytical formulation (\textit{sbcana} module) }
202\label{SBC_ana}
203
204%---------------------------------------namtau - namflx--------------------------------------------------
205\namdisplay{namtau}
206\namdisplay{namflx}
207%--------------------------------------------------------------------------------------------------------------
208
209
210The analytical formulation of the surface boundary condition is set by
211default. In this case, all the 6 fluxes needed by the ocean are assumed to
212be uniform in space. They take constant values given in the namlist
213namsbc{\_}ana : \textit{utau0}, \textit{vtau0}, \textit{qns0}, \textit{qsr0}, \textit{emp0} and \textit{emps0}. while the runoff is set to zero. In addition,
214the wind is allowed to reach its nominal value within a given number of time
215step (\textit{ntau000}).
216
217If a user wants to applied a different analytical forcing, \mdl{sbcana} 
218module is the very place to do that. As an example, one can have a look to
219the \mdl{sbc\_ana\_gyre} routine which provides the analytical forcing of the
220GYRE configuration (see GYRE configuration manual, in preparation).
221
222
223% ================================================================
224% Flux formulation
225% ================================================================
226\section{Flux formulation (\mdl{sbcflx} module, \key{sbcflx}) }
227\label{SBC_flx}
228
229In the flux formulation (\key{sbcflx} defined), the surface boundary
230condition fields are directly read from input files. The user has to define
231in the namelist namsbc{\_}flx the name of the file, the name of the variable
232read in the file, the time frequency at which it is given, and a logical
233setting whether a time interpolation to the model time step is asked are not
234for this field). (fld\_i namelist structure).
235
236\colorbox{yellow}{ Describe the information given?  }
237
238\colorbox{yellow}{  Add an info about on-line interpolation or not ? at with which scale{\ldots} }
239
240
241\textbf{Caution}: when the frequency is set to --12, the data are monthly
242values. There are assumed to be climatological values, so time interpolation
243between December the 15$^{th}$ and January the 15$^{th}$ is done using
244record 12 and 1
245
246When higher frequency is set and time interpolation is demanded, the model
247will try to read the last (first) record of previous (next) year in a file
248having the same name but a suffix {\_}prev{\_}year (next{\_}year) being
249added. These file must only content a single record. If they don't exist,
250the will assume that the previous year last record is equal to the first
251record of the previous year, and similarly, that the first record of the
252next year is equal to the last record of the current year. This will cause
253the forcing to remain constant over the first and last half fld\_frequ
254hours.
255
256Note that in general, a flux formulation is used in associated with a
257damping term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
258specification.
259
260
261% ================================================================
262% Bulk formulation
263% ================================================================
264\section{Bulk formulation (\mdl{sbcblk\_core} or\mdl{sbcblk\_clio} module) }
265\label{SBC_blk}
266
267In the bulk formulation, the surface boundary condition fields are computed
268using bulk formulae and atmospheric fields and ocean (and ice) variables.
269
270The atmospheric fields used depends on the bulk formulae used. Two of them
271are available : the CORE and CLIO bulk formulea. The choice is made by
272activating the CPP key \key{sbcblk\_core} or
273\key{sbcblk\_clio}, respectively.
274
275\colorbox{yellow}{Note : if a sea-ice model is used then blah blah blah{\ldots}}
276
277CORE bulk formulea
278
279The CORE bulk formulae have been developed by \citet{LargeYeager2004}. They
280have been design to handle the CORE forcing, a mixture of NCEP reanalysis
281and satellite data. They use an inertial dissipative method to compute the
282turbulent transfer coefficients (momentum, sensible heat and evaporation)
283from the 10 meter wind speed, air temperature and specific humidity).
284
285The required 8 input fields are:
286
287%--------------------------------------------------TABLE--------------------------------------------------
288\begin{table}[htbp]   \label{Tab_CORE}
289\begin{center}
290\begin{tabular}{|l|l|l|l|}
291\hline
292Variable desciption              & Computer name   & Units        & point \\     \hline
293i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T or U \\    \hline
294j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T or V \\ \hline
29510m air temperature              & tair      & \r{}$K$            & T   \\ \hline
296Specific humidity             & humi      & \%              & T \\      \hline
297Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
298Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
299Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
300Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
301\end{tabular}
302\end{center}
303\end{table}
304%--------------------------------------------------------------------------------------------------------------
305
306Note that the air velocity can be provided at either tracer ocean point or
307velocity ocean point.
308
309\colorbox{yellow}{Explain low resolution, better to provide it at U-V, high resolution better}
310
311\colorbox{yellow}{at T-point{\ldots} Explain why, scheme?}
312
313\colorbox{yellow}{Add a namelist parameter to provide a switch from U/V or T (or I??) point}
314
315\colorbox{yellow}{ for utau/vtau}
316
317CLIO bulk formulea
318
319The CLIO bulk formulae have been developed several years ago for the
320Louvain-la-neuve coupled ice-ocean model (CLIO, Goosse et al. 1997). It is a
321simpler bulk formulae that assumed the stress to be known and computes the
322radiative fluxes from a climatological cloud cover.
323
324The required 7 input fields are:
325
326%--------------------------------------------------TABLE--------------------------------------------------
327\begin{table}[htbp]   \label{Tab_CLIO}
328\begin{center}
329\begin{tabular}{|l|l|l|l|}
330\hline
331Variable desciption           & Computer name   & Units              & point \\  \hline
332i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
333j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
334Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
33510m air temperature              & tair         & \r{}$K$            & T \\   \hline
336Secific humidity                 & humi         & \%              & T \\   \hline
337Cloud cover                   &           & \%              & T \\   \hline
338Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
339Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
340\end{tabular}
341\end{center}
342\end{table}
343%--------------------------------------------------------------------------------------------------------------
344
345As for the flux formulation, the input data information required by the
346model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
347namelist (via the structure fld\_i). The same assumption is made about the
348value of the first and last record in each file.
349
350
351% ================================================================
352% Coupled formulation
353% ================================================================
354\section{Coupled formulation (\mdl{sbccpl} module)}
355\label{SBC_cpl}
356
357In the coupled formulation of the surface boundary condition, the fluxes are
358provided by the OASIS coupler at each \np{nf\_cpl} time-step, while sea and ice
359surface temperature, ocean and ice albedo, and ocean currents are sent to
360the atmospheric component.
361
362
363% ================================================================
364% Miscellanea options
365% ================================================================
366\section{Miscellanea options}
367\label{SBC_misc}
368
369% -------------------------------------------------------------------------------------------------------------
370%        Surface restoring to observed SST and/or SSS
371% -------------------------------------------------------------------------------------------------------------
372\subsection{Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
373\label{SBC_ssr}
374
375In forced mode using flux formulation (default option or \key{flx} defined), a
376feedback term \emph{must} be added to the specified surface heat flux $Q_{ns}^o$:
377\begin{equation} \label{Eq_sbc_dmp_q}
378Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
379\end{equation}
380where SST is a sea surface temperature field (observed or climatological), $T$ is
381the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
382coefficient usually taken equal to $-40~W.m^{-2}.$\r{}K$^{-1}$. For a $50~m$ mixed-layer depth,
383this value corresponds to a relaxation time scale of two months. This term
384ensures that if $T$ perfectly fits SST then $Q$ is equal to $Q_o$.
385
386In the fresh water budget, a feedback term can also be added:
387
388\begin{equation} \label{Eq_sbc_dmp_emp}
389EMP = EMP_o +\gamma_s^{-1} \left(S-SSS_{Obs}\right)\left|S\right.
390\end{equation}
391
392where EMP$_{o }$ is a net surface fresh water flux (observed, climatological or
393atmospheric model product), \textit{SSS}$_{Obs}$is a sea surface salinity (usually a time
394interpolation of the monthly mean PHC climatology \citep{Steele2001}, $S$ is the model
395surface layer salinity and $\gamma_s$ is a negative feedback coefficient
396which is provided as a namelist parameter. Unlike heat flux, there is no
397physical justification for the feedback term in (III.4.4) as the atmosphere
398does not care about ocean surface salinity \citep{Madec1997}. The
399SSS restoring term can only be view as a flux correction on freshwater
400fluxes to reduce the uncertainties we have on the observed freshwater
401budget.
402
403% -------------------------------------------------------------------------------------------------------------
404%        Handling of ice-covered area
405% -------------------------------------------------------------------------------------------------------------
406\subsection{Handling of ice-covered area}
407\label{SBC_ice-cover}
408The presence of sea-ice at the top of the ocean
409strongly modify the surface fluxes
410
411The presence at the sea surface of an ice cover area modified all the fluxes
412transmitted to the ocean. There is two cases whereas a sea-ice model is used
413or not.
414
415Without sea ice model, the information of ice-cover / open ocean is read in
416a file (either the directly the ice-cover or the observed SST from which
417ice-cover is deduced using a criteria on freezing point temperature).
418
419% -------------------------------------------------------------------------------------------------------------
420%        Addition of river runoffs
421% -------------------------------------------------------------------------------------------------------------
422\subsection{Addition of river runoffs (\mdl{sbcrnf})}
423\label{SBC_rnf}
424
425It is convenient to introduce the river runoff in the model as a surface
426fresh water fluxes. \colorbox{yellow}{{\ldots} blah blah{\ldots}.}
427
428\colorbox{yellow}{Nevertheless, Pb of vertical resolution and increase of Kz in vicinity of }
429
430\colorbox{yellow}{river mouths{\ldots}}
431
432Control of the mean sea level
433
434% -------------------------------------------------------------------------------------------------------------
435%        Addition of river runoffs
436% -------------------------------------------------------------------------------------------------------------
437\subsection{Freshwater budget control (\mdl{sbcfwb})}
438\label{SBC_fwb}
439%--------------------------------------------namfwb--------------------------------------------------------
440\namdisplay{namfwb}
441%--------------------------------------------------------------------------------------------------------------
442
443\colorbox{yellow}{freshwater budget correction{\ldots}}
444
445
446
447
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