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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}
21plus an optional field:
22\begin{itemize}
23   \item the atmospheric pressure at the ocean surface $\left( p_a \right)$
24\end{itemize}
25
26Five different ways to provide the first six fields to the ocean are available which
27are controlled by namelist variables: an analytical formulation (\np{ln\_ana}~=~true),
28a flux formulation (\np{ln\_flx}~=~true), a bulk formulae formulation (CORE
29(\np{ln\_core}~=~true), CLIO (\np{ln\_clio}~=~true) or MFS
30\footnote { Note that MFS bulk formulae compute fluxes only for the ocean component}
31(\np{ln\_ecmwf}~=~true) bulk formulae) and a coupled
32formulation (exchanges with a atmospheric model via the OASIS coupler)
33(\np{ln\_cpl}~=~true). When used, the atmospheric pressure forces both
34ocean and ice dynamics (\np{ln\_apr\_dyn}~=~true).
35The frequency at which the six or seven fields have to be updated is the \np{nn\_fsbc} 
36namelist parameter.
37When the fields are supplied from data files (flux and bulk formulations), the input fields
38need not be supplied on the model grid.  Instead a file of coordinates and weights can
39be supplied which maps the data from the supplied grid to the model points
40(so called "Interpolation on the Fly", see \S\ref{SBC_iof}).
41In addition, the resulting fields can be further modified using several namelist options.
42These options control  the rotation of vector components supplied relative to an east-north
43coordinate system onto the local grid directions in the model; the addition of a surface
44restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes
45below ice-covered areas (using observed ice-cover or a sea-ice model)
46(\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater
47fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of a freshwater flux adjustment
48in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the
49transformation of the solar radiation (if provided as daily mean) into a diurnal
50cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave
51model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or ecmwf bulk formulas are selected.
52
53In this chapter, we first discuss where the surface boundary condition appears in the
54model equations. Then we present the five ways of providing the surface boundary condition,
55followed by the description of the atmospheric pressure and the river runoff.
56Next the scheme for interpolation on the fly is described.
57Finally, the different options that further modify the fluxes applied to the ocean are discussed.
58
59
60% ================================================================
61% Surface boundary condition for the ocean
62% ================================================================
63\section{Surface boundary condition for the ocean}
64\label{SBC_general}
65
66The surface ocean stress is the stress exerted by the wind and the sea-ice
67on the ocean. The two components of stress are assumed to be interpolated
68onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
69at $u$- and $v$-points They are applied as a surface boundary condition of the
70computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
71\begin{equation} \label{Eq_sbc_dynzdf}
72\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
73    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
74\end{equation}
75where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
76stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
77
78The surface heat flux is decomposed into two parts, a non solar and a solar heat
79flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
80of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
81It is applied as a surface boundary condition trend of the first level temperature
82time evolution equation (\mdl{trasbc} module).
83\begin{equation} \label{Eq_sbc_trasbc_q}
84\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 
85_o \;C_p \;e_{3t} }} \right|_{k=1} \quad
86\end{equation}
87$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
88trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
89
90\begin{equation} \label{Eq_sbc_traqsr}
91\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right]
92\end{equation}
93where $I_w$ is a non-dimensional function that describes the way the light
94penetrates inside the water column. It is generally a sum of decreasing
95exponentials (see \S\ref{TRA_qsr}).
96
97The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which
98may or may not be identical. Indeed, a surface freshwater flux has two effects:
99it changes the volume of the ocean and it changes the surface concentration of
100salt (and other tracers). Therefore it appears in the sea surface height as a volume
101flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
102as a concentration/dilution effect,
103$\textit{emp}_{S}$ (\mdl{trasbc} module).
104\begin{equation} \label{Eq_trasbc_emp}
105\begin{aligned}
106&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\ 
107\\
108 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\ 
109 \end{aligned}
110\end{equation} 
111
112In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,
113but it exist several numerical reasons why this equality should be broken.
114For example, when the ocean is coupled to a sea-ice model, the water exchanged between
115ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,
116$\textit{emp}_{S}$ take into account both concentration/dilution effect associated with
117freezing/melting and the salt flux between ice and ocean, while \textit{emp} is
118only the volume flux. In addition, in the current version of \NEMO, the sea-ice is
119assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does
120not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS.
121%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
122
123Note that SST can also be modified by a freshwater flux. Precipitation (in
124particular solid precipitation) may have a temperature significantly different from
125the SST. Due to the lack of information about the temperature of
126precipitation, we assume it is equal to the SST. Therefore, no
127concentration/dilution term appears in the temperature equation. It has to
128be emphasised that this absence does not mean that there is no heat flux
129associated with precipitation! Precipitation can change the ocean volume and thus the
130ocean heat content. It is therefore associated with a heat flux (not yet 
131diagnosed in the model) \citep{Roullet_Madec_JGR00}).
132
133%\colorbox{yellow}{Miss: }
134%
135%A extensive description of all namsbc namelist (parameter that have to be
136%created!)
137%
138%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
139%ssv) i.e. information required by flux computation or sea-ice
140%
141%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
142%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
143%
144%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
145%
146%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
147%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
148%nf{\_}sbc
149%
150%Explain here all the namlist namsbc variable{\ldots}.
151%
152%\colorbox{yellow}{End Miss }
153
154The ocean model provides the surface currents, temperature and salinity
155averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
156mean is done in \mdl{sbcmod} module.
157
158%-------------------------------------------------TABLE---------------------------------------------------
159\begin{table}[tb]   \begin{center}   \begin{tabular}{|l|l|l|l|}
160\hline
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
166\end{tabular}
167\caption{  \label{Tab_ssm}   
168Ocean variables provided by the ocean to the surface module (SBC).
169The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of
170computation of surface fluxes.}
171\end{center}   \end{table}
172%--------------------------------------------------------------------------------------------------------------
173
174%\colorbox{yellow}{Penser a} mettre dans le restant l'info nn{\_}fsbc ET nn{\_}fsbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt
175
176
177% ================================================================
178%       Input Data
179% ================================================================
180\section{Input Data generic interface}
181\label{SBC_input}
182
183A generic interface has been introduced to manage the way input data (2D or 3D fields,
184like surface forcing or ocean T and S) are specify in \NEMO. This task is archieved by fldread.F90.
185The module was design with four main objectives in mind:
186\begin{enumerate} 
187\item optionally provide a time interpolation of the input data at model time-step,
188whatever their input frequency is, and according to the different calendars available in the model.
189\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
190\item make the run duration independent from the period cover by the input files.
191\item provide a simple user interface and a rather simple developer interface by limiting the
192 number of prerequisite information.
193\end{enumerate} 
194
195As a results the user have only to fill in for each variable a structure in the namelist file
196to defined the input data file and variable names, the frequency of the data (in hours or months),
197whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
198and two additional parameters for on-the-fly interpolation. When adding a new input variable,
199the developer has to add the associated structure in the namelist, read this information
200by mirroring the namelist read in \rou{sbc\_blk\_init} for example, and simply call \rou{fld\_read} 
201to obtain the desired input field at the model time-step and grid points.
202
203The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
204(see \S\ref{SBC_fldread}), the period it cover is one year, month, week or day, and, if on-the-fly
205interpolation is used, a file of weights must be supplied (see \S\ref{SBC_iof}).
206
207Note that when an input data is archived on a disc which is accessible directly
208from the workspace where the code is executed, then the use can set the \np{cn\_dir} 
209to the pathway leading to the data. By default, the data are assumed to have been
210copied so that cn\_dir='./'.
211
212% -------------------------------------------------------------------------------------------------------------
213% Input Data specification (\mdl{fldread})
214% -------------------------------------------------------------------------------------------------------------
215\subsection{Input Data specification (\mdl{fldread})}
216\label{SBC_fldread}
217
218The structure associated with an input variable contains the following information:
219\begin{alltt}  {{\tiny   
220\begin{verbatim}
221!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation !
222!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  !
223\end{verbatim}
224}}\end{alltt} 
225where
226\begin{description} 
227\item[File name]: the stem name of the NetCDF file to be open.
228This stem will be completed automatically by the model, with the addition of a '.nc' at its end
229and by date information and possibly a prefix (when using AGRIF).
230Tab.\ref{Tab_fldread} provides the resulting file name in all possible cases according to whether
231it is a climatological file or not, and to the open/close frequency (see below for definition).
232
233%--------------------------------------------------TABLE--------------------------------------------------
234\begin{table}[htbp]
235\begin{center}
236\begin{tabular}{|l|c|c|c|}
237\hline
238                         & daily or weekLLL          & monthly                   &   yearly          \\   \hline
239clim = false   & fn\_yYYYYmMMdDD  &   fn\_yYYYYmMM   &   fn\_yYYYY  \\   \hline
240clim = true       & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
241\end{tabular}
242\end{center}
243\caption{ \label{Tab_fldread}   naming nomenclature for climatological or interannual input file,
244as a function of the Open/close frequency. The stem name is assumed to be 'fn'.
245For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week ($i.e.$ 'sun','sat','fri','thu','wed','tue','mon'). The 'YYYY', 'MM' and 'DD' should be replaced by the
246actual year/month/day, always coded with 4 or 2 digits. Note that (1) in mpp, if the file is split
247over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc', where 'PPPP' is the
248process number coded with 4 digits; (2) when using AGRIF, the prefix ÔN\_Õ is added to files,
249where 'N'  is the child grid number.}
250\end{table}
251%--------------------------------------------------------------------------------------------------------------
252 
253
254\item[Record frequency]: the frequency of the records contained in the input file.
255Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
256(for example -1 for monthly forcing or -12 for annual forcing).
257Note that this frequency must really be an integer and not a real.
258On some computers, seting it to '24.' can be interpreted as 240!
259
260\item[Variable name]: the name of the variable to be read in the input NetCDF file.
261
262\item[Time interpolation]: a logical to activate, or not, the time interpolation. If set to 'false',
263the forcing will have a steplike shape remaining constant during each forcing period.
264For example, when using a daily forcing without time interpolation, the forcing remaining
265constant from 00h00'00'' to 23h59'59". If set to 'true', the forcing will have a broken line shape.
266Records are assumed to be dated the middle of the forcing period.
267For example, when using a daily forcing with time interpolation, linear interpolation will
268be performed between mid-day of two consecutive days.
269
270\item[Climatological forcing]: a logical to specify if a input file contains climatological forcing
271which can be cycle in time, or an interannual forcing which will requires additional files
272if the period covered by the simulation exceed the one of the file. See the above the file
273naming strategy which impacts the expected name of the file to be opened.
274
275\item[Open/close frequency]: the frequency at which forcing files must be opened/closed.
276Four cases are coded: 'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week),
277'monthly' and 'yearly' which means the forcing files will contain data for one day, one week,
278one month or one year. Files are assumed to contain data from the beginning of the open/close period.
279For example, the first record of a yearly file containing daily data is Jan 1st even if the experiment
280is not starting at the beginning of the year.
281
282\item[Others]: 'weights filename' and 'pairing rotation' are associted with on-the-fly interpolation
283which is described in \S\ref{SBC_iof}.
284
285\end{description}
286
287Additional remarks:\\
288(1) The time interpolation is a simple linear interpolation between two consecutive records of
289the input data. The only tricky point is therefore to specify the date at which we need to do
290the interpolation and the date of the records read in the input files.
291Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the
292time step. For example, for an experiment starting at 0h00'00" with a one hour time-step,
293a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
294However, for forcing data related to the surface module, values are not needed at every
295time-step but at every \np{nn\_fsbc} time-step. For example with \np{nn\_fsbc}~=~3,
296the surface module will be called at time-steps 1, 4, 7, etc. The date used for the time interpolation
297is thus redefined to be at the middle of \np{nn\_fsbc} time-step period. In the previous example,
298this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
299(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file
300calendar. The calendar associated with the forcing field is build according to the information
301provided by user in the record frequency, the open/close frequency and the type of temporal interpolation.
302For example, the first record of a yearly file containing daily data that will be interpolated in time
303is assumed to be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
304(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file
305when interpolating data with the first (last) record of the open/close period.
306For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
307the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values
308between Dec 31st 12h00'00" and Jan 1st 12h00'00". If the forcing is climatological, Dec and Jan will
309be keep-up from the same year. However, if the forcing is not climatological, at the end of the
310open/close period the code will automatically close the current file and open the next one.
311Note that, if the experiment is starting (ending) at the beginning (end) of an open/close period
312we do accept that the previous (next) file is not existing. In this case, the time interpolation
313will be performed between two identical values. For example, when starting an experiment on
314Jan 1st of year Y with yearly files and daily data to be interpolated, we do accept that the file
315related to year Y-1 is not existing. The value of Jan 1st will be used as the missing one for
316Dec 31st of year Y-1. If the file of year Y-1 exists, the code will read its last record.
317Therefore, this file can contain only one record corresponding to Dec 31st, a useful feature for
318user considering that it is too heavy to manipulate the complete file for year Y-1.
319
320
321% -------------------------------------------------------------------------------------------------------------
322% Interpolation on the Fly
323% -------------------------------------------------------------------------------------------------------------
324\subsection [Interpolation on-the-Fly] {Interpolation on-the-Fly}
325\label{SBC_iof}
326
327Interpolation on the Fly allows the user to supply input files required
328for the surface forcing on grids other than the model grid.
329To do this he or she must supply, in addition to the source data file,
330a file of weights to be used to interpolate from the data grid to the model grid.
331The original development of this code used the SCRIP package (freely available
332\href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
333In principle, any package can be used to generate the weights, but the
334variables in the input weights file must have the same names and meanings as
335assumed by the model.
336Two methods are currently available: bilinear and bicubic interpolation.
337
338\subsubsection{Bilinear Interpolation}
339\label{SBC_iof_bilinear}
340
341The input weights file in this case has two sets of variables: src01, src02,
342src03, src04 and wgt01, wgt02, wgt03, wgt04.
343The "src" variables correspond to the point in the input grid to which the weight
344"wgt" is to be applied. Each src value is an integer corresponding to the index of a
345point in the input grid when written as a one dimensional array.  For example, for an input grid
346of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
347There are four of each variable because bilinear interpolation uses the four points defining
348the grid box containing the point to be interpolated.
349All of these arrays are on the model grid, so that values src01(i,j) and
350wgt01(i,j) are used to generate a value for point (i,j) in the model.
351
352Symbolically, the algorithm used is:
353
354\begin{equation}
355f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
356\end{equation}
357where function idx() transforms a one dimensional index src(k) into a two dimensional index,
358and wgt(1) corresponds to variable "wgt01" for example.
359
360\subsubsection{Bicubic Interpolation}
361\label{SBC_iof_bicubic}
362
363Again there are two sets of variables: "src" and "wgt".
364But in this case there are 16 of each.
365The symbolic algorithm used to calculate values on the model grid is now:
366
367\begin{equation*} \begin{split}
368f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}     
369              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
370              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }   
371              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
372\end{split}
373\end{equation*}
374The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
375
376\subsubsection{Implementation}
377\label{SBC_iof_imp}
378
379To activate this option, a non-empty string should be supplied in the weights filename column
380of the relevant namelist; if this is left as an empty string no action is taken.
381In the model, weights files are read in and stored in a structured type (WGT) in the fldread
382module, as and when they are first required.
383This initialisation procedure determines whether the input data grid should be treated
384as cyclical or not by inspecting a global attribute stored in the weights input file.
385This attribute must be called "ew\_wrap" and be of integer type.
386If it is negative, the input non-model grid is assumed not to be cyclic.
387If zero or greater, then the value represents the number of columns that overlap.
388$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
389if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
390If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
391In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and therefore the grid
392is assumed to be cyclic with no overlapping columns.
393(In fact this only matters when bicubic interpolation is required.)
394Note that no testing is done to check the validity in the model, since there is no way
395of knowing the name used for the longitude variable,
396so it is up to the user to make sure his or her data is correctly represented.
397
398Next the routine reads in the weights.
399Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise
400bilinear interpolation is used. The WGT structure includes dynamic arrays both for
401the storage of the weights (on the model grid), and when required, for reading in
402the variable to be interpolated (on the input data grid).
403The size of the input data array is determined by examining the values in the "src"
404arrays to find the minimum and maximum i and j values required.
405Since bicubic interpolation requires the calculation of gradients at each point on the grid,
406the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
407When the array of points from the data file is adjacent to an edge of the data grid,
408the halo is either a copy of the row/column next to it (non-cyclical case), or is a copy
409of one from the first few columns on the opposite side of the grid (cyclical case).
410
411\subsubsection{Limitations}
412\label{SBC_iof_lim}
413
414\begin{enumerate} 
415\item  The case where input data grids are not logically rectangular has not been tested.
416\item  This code is not guaranteed to produce positive definite answers from positive definite inputs
417          when a bicubic interpolation method is used.
418\item  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
419\item  The gradients across the ends of a cyclical grid assume that the grid spacing between
420          the two columns involved are consistent with the weights used.
421\item  Neither interpolation scheme is conservative. (There is a conservative scheme available
422          in SCRIP, but this has not been implemented.)
423\end{enumerate}
424
425\subsubsection{Utilities}
426\label{SBC_iof_util}
427
428% to be completed
429A set of utilities to create a weights file for a rectilinear input grid is available
430(see the directory NEMOGCM/TOOLS/WEIGHTS).
431
432
433% ================================================================
434% Analytical formulation (sbcana module)
435% ================================================================
436\section  [Analytical formulation (\textit{sbcana}) ]
437      {Analytical formulation (\mdl{sbcana} module) }
438\label{SBC_ana}
439
440%---------------------------------------namsbc_ana--------------------------------------------------
441\namdisplay{namsbc_ana}
442%--------------------------------------------------------------------------------------------------------------
443
444The analytical formulation of the surface boundary condition is the default scheme.
445In this case, all the six fluxes needed by the ocean are assumed to
446be uniform in space. They take constant values given in the namelist
447namsbc{\_}ana by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
448\np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero.
449In addition, the wind is allowed to reach its nominal value within a given number
450of time steps (\np{nn\_tau000}).
451
452If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
453module can be modified to use another scheme. As an example,
454the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
455GYRE configuration (see GYRE configuration manual, in preparation).
456
457
458% ================================================================
459% Flux formulation
460% ================================================================
461\section  [Flux formulation (\textit{sbcflx}) ]
462      {Flux formulation (\mdl{sbcflx} module) }
463\label{SBC_flx}
464%------------------------------------------namsbc_flx----------------------------------------------------
465\namdisplay{namsbc_flx} 
466%-------------------------------------------------------------------------------------------------------------
467
468In the flux formulation (\np{ln\_flx}=true), the surface boundary
469condition fields are directly read from input files. The user has to define
470in the namelist namsbc{\_}flx the name of the file, the name of the variable
471read in the file, the time frequency at which it is given (in hours), and a logical
472setting whether a time interpolation to the model time step is required
473for this field. See \S\ref{SBC_fldread} for a more detailed description of the parameters.
474
475Note that in general, a flux formulation is used in associated with a
476restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
477specification.
478
479
480% ================================================================
481% Bulk formulation
482% ================================================================
483\section  [Bulk formulation (\textit{sbcblk\_core}, \textit{sbcblk\_clio} or \textit{sbcblk\_ecmwf}) ]
484      {Bulk formulation \small{(\mdl{sbcblk\_core} \mdl{sbcblk\_clio} \mdl{sbcblk\_ecmwf} modules)} }
485\label{SBC_blk}
486
487In the bulk formulation, the surface boundary condition fields are computed
488using bulk formulae and atmospheric fields and ocean (and ice) variables.
489
490The atmospheric fields used depend on the bulk formulae used. Three bulk formulations
491are available : the CORE, the CLIO and the MFS bulk formulea. The choice is made by setting to true
492one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or  \np{ln\_ecmwf}.
493
494Note : in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
495Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over both
496an ocean and an ice surface.
497
498% -------------------------------------------------------------------------------------------------------------
499%        CORE Bulk formulea
500% -------------------------------------------------------------------------------------------------------------
501\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
502            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
503\label{SBC_blk_core}
504%------------------------------------------namsbc_core----------------------------------------------------
505\namdisplay{namsbc_core} 
506%-------------------------------------------------------------------------------------------------------------
507
508The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
509They have been designed to handle the CORE forcing, a mixture of NCEP
510reanalysis and satellite data. They use an inertial dissipative method to compute
511the turbulent transfer coefficients (momentum, sensible heat and evaporation)
512from the 10 metre wind speed, air temperature and specific humidity.
513This \citet{Large_Yeager_Rep04} dataset is available through the
514\href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.
515
516Note that substituting ERA40 to NCEP reanalysis fields
517does not require changes in the bulk formulea themself.
518This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
519
520The required 8 input fields are:
521
522%--------------------------------------------------TABLE--------------------------------------------------
523\begin{table}[htbp]   \label{Tab_CORE}
524\begin{center}
525\begin{tabular}{|l|c|c|c|}
526\hline
527Variable desciption              & Model variable  & Units   & point \\    \hline
528i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
529j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
53010m air temperature              & tair      & \r{}$K$            & T   \\ \hline
531Specific humidity             & humi      & \%              & T \\      \hline
532Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
533Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
534Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
535Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
536\end{tabular}
537\end{center}
538\end{table}
539%--------------------------------------------------------------------------------------------------------------
540
541Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean
542point ($u$- and $v$-points). It is simpler and faster (less fields to be read),
543but it is not the recommended method when the ocean grid size is the same
544or larger than the one of the input atmospheric fields.
545
546% -------------------------------------------------------------------------------------------------------------
547%        CLIO Bulk formulea
548% -------------------------------------------------------------------------------------------------------------
549\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
550            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
551\label{SBC_blk_clio}
552%------------------------------------------namsbc_clio----------------------------------------------------
553\namdisplay{namsbc_clio} 
554%-------------------------------------------------------------------------------------------------------------
555
556The CLIO bulk formulae were developed several years ago for the
557Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
558They are simpler bulk formulae. They assume the stress to be known and
559compute the radiative fluxes from a climatological cloud cover.
560
561The required 7 input fields are:
562
563%--------------------------------------------------TABLE--------------------------------------------------
564\begin{table}[htbp]   \label{Tab_CLIO}
565\begin{center}
566\begin{tabular}{|l|l|l|l|}
567\hline
568Variable desciption           & Model variable  & Units           & point \\  \hline
569i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
570j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
571Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
57210m air temperature              & tair         & \r{}$K$            & T \\   \hline
573Specific humidity                & humi         & \%              & T \\   \hline
574Cloud cover                   &           & \%              & T \\   \hline
575Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
576Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
577\end{tabular}
578\end{center}
579\end{table}
580%--------------------------------------------------------------------------------------------------------------
581
582As for the flux formulation, information about the input data required by the
583model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
584namelist (see \S\ref{SBC_fldread}).
585
586% -------------------------------------------------------------------------------------------------------------
587%        ECMWF Bulk formulea
588% -------------------------------------------------------------------------------------------------------------
589\subsection    [MFS Bulk formulea (\np{ln\_ecmwf}=true)]
590            {MFS Bulk formulea (\np{ln\_ecmwf}=true, \mdl{sbcblk\_ecmwf})}
591\label{SBC_blk_ecmwf}
592%------------------------------------------namsbc_ecmwf----------------------------------------------------
593\namdisplay{namsbc_ecmwf} 
594%----------------------------------------------------------------------------------------------------------
595
596The MFS (Mediterranean Forecasting System) bulk formulae have been developed by
597 \citet{Castellari_al_JMS1998}.
598They have been designed to handle the ECMWF operational data and are currently
599in use in the MFS operational system \citep{Tonani_al_OS08}, \citep{Oddo_al_OS09}.
600The wind stress computation uses a drag coefficient computed according to \citet{Hellerman_Rosenstein_JPO83}.
601The surface boundary condition for temperature involves the balance between surface solar radiation,
602net long-wave radiation, the latent and sensible heat fluxes.
603Solar radiation is dependent on cloud cover and is computed by means of
604an astronomical formula \citep{Reed_JPO77}. Albedo monthly values are from \citet{Payne_JAS72} 
605as means of the values at $40^{o}N$ and $30^{o}N$ for the Atlantic Ocean (hence the same latitudinal
606band of the Mediterranean Sea). The net long-wave radiation flux
607\citep{Bignami_al_JGR95} is a function of
608air temperature, sea-surface temperature, cloud cover and relative humidity.
609Sensible heat and latent heat fluxes are computed by classical
610bulk formulae parameterized according to \citet{Kondo1975}.
611Details on the bulk formulae used can be found in \citet{Maggiore_al_PCE98} and \citet{Castellari_al_JMS1998}.
612
613The required 7 input fields must be provided on the model Grid-T and  are:
614\begin{itemize}
615\item          Zonal Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windi})
616\item          Meridional Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windj})
617\item          Total Claud Cover (\%)  (\np{sn\_clc})
618\item          2m Air Temperature ($K$) (\np{sn\_tair})
619\item          2m Dew Point Temperature ($K$)  (\np{sn\_rhm})
620\item          Total Precipitation ${Kg} m^{-2} s^{-1}$ (\np{sn\_prec})
621\item          Mean Sea Level Pressure (${Pa}) (\np{sn\_msl})
622\end{itemize}
623% -------------------------------------------------------------------------------------------------------------
624% ================================================================
625% Coupled formulation
626% ================================================================
627\section  [Coupled formulation (\textit{sbccpl}) ]
628      {Coupled formulation (\mdl{sbccpl} module)}
629\label{SBC_cpl}
630%------------------------------------------namsbc_cpl----------------------------------------------------
631\namdisplay{namsbc_cpl}
632%-------------------------------------------------------------------------------------------------------------
633
634In the coupled formulation of the surface boundary condition, the fluxes are
635provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
636while sea and ice surface temperature, ocean and ice albedo, and ocean currents
637are sent to the atmospheric component.
638
639A generalised coupled interface has been developed. It is currently interfaced with OASIS 3
640(\key{oasis3}) and does not support OASIS 4
641\footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}.
642It has been successfully used to interface \NEMO to most of the European atmospheric
643GCM (ARPEGE, ECHAM, ECMWF, HadAM, LMDz),
644as well as to \href{http://wrf-model.org/}{WRF} (Weather Research and Forecasting Model).
645
646Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
647The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are
648actually recieved by the ice-ocean system (no calculation of ice sublimation in coupled mode).
649When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
650the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}. In this case,
651CO$_2$ fluxes are exchanged between the atmosphere and the ice-ocean system.
652
653
654% ================================================================
655%        Atmospheric pressure
656% ================================================================
657\section   [Atmospheric pressure (\textit{sbcapr})]
658         {Atmospheric pressure (\mdl{sbcapr})}
659\label{SBC_apr}
660%------------------------------------------namsbc_apr----------------------------------------------------
661\namdisplay{namsbc_apr}
662%-------------------------------------------------------------------------------------------------------------
663
664The optional atmospheric pressure can be used to force ocean and ice dynamics
665(\np{ln\_apr\_dyn}~=~true, \textit{namsbc} namelist ).
666The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist) 
667can be interpolated in time to the model time step, and even in space when the
668interpolation on-the-fly is used. When used to force the dynamics, the atmospheric
669pressure is further transformed into an equivalent inverse barometer sea surface height,
670$\eta_{ib}$, using:
671\begin{equation} \label{SBC_ssh_ib}
672   \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right) 
673\end{equation}
674where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
675A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. In this case $P_o$ 
676is set to the value of $P_{atm}$ averaged over the ocean domain, $i.e.$ the mean value of
677$\eta_{ib}$ is kept to zero at all time step.
678
679The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation
680(see \mdl{dynspg} for the ocean). For sea-ice, the sea surface height, $\eta_m$,
681which is provided to the sea ice model is set to $\eta - \eta_{ib}$ (see \mdl{sbcssr} module).
682$\eta_{ib}$ can be set in the output. This can simplify altimetry data and model comparison
683as inverse barometer sea surface height is usually removed from these date prior to their distribution.
684
685% ================================================================
686%        Tidal Potential
687% ================================================================
688\section   [Tidal Potential (\textit{sbctide})]
689                        {Tidal Potential (\mdl{sbctide})}
690\label{SBC_tide}
691
692A module is available to use the tidal potential forcing and is activated with with \key{tide}.
693
694
695%------------------------------------------nam_tide----------------------------------------------------
696\namdisplay{nam_tide}
697%-------------------------------------------------------------------------------------------------------------
698
699Concerning the tidal potential, some parameters are available in namelist:
700
701- \texttt{ln\_tide\_pot} activate the tidal potential forcing
702
703- \texttt{nb\_harmo} is the number of constituent used
704
705- \texttt{clname} is the name of constituent
706
707
708The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem;
709they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\
710
711The potential astronomical expressed, for the three types of tidal frequencies
712following, by : \\
713Tide long period :
714\begin{equation}
715\Pi_{a}=gA_{k}(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{k}t+V_{0k})
716\end{equation}
717diurnal Tide :
718\begin{equation}
719\Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k})
720\end{equation}
721Semi-diurnal tide:
722\begin{equation}
723\Pi_{a}=gA_{k}(cos^{2}\phi)cos(\omega_{k}t+2\lambda+V_{0k})
724\end{equation}
725
726
727$A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave
728$k$ to Greenwich.
729
730We make corrections to the astronomical potential.
731We obtain :
732\begin{equation}
733\Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi)
734\end{equation}
735with $k$ a number of Love estimated to 0.6 which parametrized the astronomical tidal land,
736and $h$ a number of Love to 0.3 which parametrized the parametrization due to the astronomical tidal land.
737
738% ================================================================
739%        River runoffs
740% ================================================================
741\section   [River runoffs (\textit{sbcrnf})]
742         {River runoffs (\mdl{sbcrnf})}
743\label{SBC_rnf}
744%------------------------------------------namsbc_rnf----------------------------------------------------
745\namdisplay{namsbc_rnf}
746%-------------------------------------------------------------------------------------------------------------
747
748%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
749%Many models, however, have traditionally inserted river runoff to the top model cell.
750%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
751%throughout a nonzero depth has been motivated by the numerical and physical problems
752%that arise when the top grid cells are of the order of one meter. This situation is common in
753%coastal modelling and becomes more and more often open ocean and climate modelling
754%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
755%required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
756
757
758%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
759%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
760%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
761%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
762%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
763%emp or emps and the changes made are below:
764
765
766%Rachel:
767River runoff generally enters the ocean at a nonzero depth rather than through the surface.
768Many models, however, have traditionally inserted river runoff to the top model cell.
769This was the case in \NEMO prior to the version 3.3, and was combined with an option
770to increase vertical mixing near the river mouth.
771
772However, with this method numerical and physical problems arise when the top grid cells are
773of the order of one meter. This situation is common in coastal modelling and is becoming
774more common in open ocean and climate modelling
775\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
776required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
777
778As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth, and for the
779temperature and salinity of the river to effect the surrounding ocean.
780The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, along with the   
781depth (in metres) which the river should be added to.
782
783Namelist options, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and \np{ln\_rnf\_temp} control whether
784the river attributes (depth, salinity and temperature) are read in and used.  If these are set
785as false the river is added to the surface box only, assumed to be fresh (0~psu), and/or
786taken as surface temperature respectively.
787
788The runoff value and attributes are read in in sbcrnf. 
789For temperature -999 is taken as missing data and the river temperature is taken to be the
790surface temperatue at the river point.
791For the depth parameter a value of -1 means the river is added to the surface box only,
792and a value of -999 means the river is added through the entire water column.
793After being read in the temperature and salinity variables are multiplied by the amount of runoff (converted into m/s) 
794to give the heat and salt content of the river runoff.
795After the user specified depth is read ini, the number of grid boxes this corresponds to is
796calculated and stored in the variable \np{nz\_rnf}.
797The variable \textit{h\_dep} is then calculated to be the depth (in metres) of the bottom of the
798lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model).
799
800The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence
801(\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
802This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
803The sea surface height is calculated using the sum of the horizontal divergence terms, and so the
804river runoff indirectly forces an increase in sea surface height.
805
806The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
807This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
808The heat and salt content of the river runoff is not included in this step, and so the tracer
809concentrations are diluted as water of ocean temperature and salinity is moved upward out of the box
810and replaced by the same volume of river water with no corresponding heat and salt addition.
811
812For the linear free surface case, at the surface box the tracer advection causes a flux of water
813(of equal volume to the runoff) through the sea surface out of the domain, which causes a salt and heat flux out of the model.
814As such the volume of water does not change, but the water is diluted.
815
816For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
817Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water
818is added with no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
819(The runoff addition to the top box along with the water being moved up through boxes below means the surface box has a large
820increase in volume, whilst all other boxes remain the same size)
821
822In trasbc the addition of heat and salt due to the river runoff is added.
823This is done in the same way for both vvl and non-vvl.
824The temperature and salinity are increased through the specified depth according to the heat and salt content of the river.
825
826In the non-linear free surface case (vvl), near the end of the time step the change in sea surface height is redistrubuted
827through the grid boxes, so that the original ratios of grid box heights are restored.
828In doing this water is moved into boxes below, throughout the water column, so the large volume addition to the surface box is spread between all the grid boxes.
829
830It is also possible for runnoff to be specified as a negative value for modelling flow through straits, i.e. modelling the Baltic flow in and out of the North Sea.
831When the flow is out of the domain there is no change in temperature and salinity, regardless of the namelist options used, as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
832
833
834%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
835
836%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
837
838%\colorbox{yellow}{river mouths{\ldots}}
839
840%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
841%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
842%ENDIF
843
844%\gmcomment{  word doc of runoffs:
845%
846%In the current \NEMO setup river runoff is added to emp fluxes, these are then applied at just the sea surface as a volume change (in the variable volume case this is a literal volume change, and in the linear free surface case the free surface is moved) and a salt flux due to the concentration/dilution effect.  There is also an option to increase vertical mixing near river mouths; this gives the effect of having a 3d river.  All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.
847%Our aim was to code the option to specify the temperature and salinity of river runoff, (as well as the amount), along with the depth that the river water will affect.  This would make it possible to model low salinity outflow, such as the Baltic, and would allow the ocean temperature to be affected by river runoff. 
848
849%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
850
851%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the tra_sbc module.  We decided to separate them throughout the code, so that the variable emp represented solely evaporation minus precipitation fluxes, and a new 2d variable rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use emp or emps and the changes made are below:
852
853}
854
855% ================================================================
856% Miscellanea options
857% ================================================================
858\section{Miscellaneous options}
859\label{SBC_misc}
860
861% -------------------------------------------------------------------------------------------------------------
862%        Diurnal cycle
863% -------------------------------------------------------------------------------------------------------------
864\subsection   [Diurnal  cycle (\textit{sbcdcy})]
865         {Diurnal cycle (\mdl{sbcdcy})}
866\label{SBC_dcy}
867%------------------------------------------namsbc_rnf----------------------------------------------------
868%\namdisplay{namsbc}
869%-------------------------------------------------------------------------------------------------------------
870
871%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
872\begin{figure}[!t]    \begin{center}
873\includegraphics[width=0.8\textwidth]{./TexFiles/Figures/Fig_SBC_diurnal.pdf}
874\caption{ \label{Fig_SBC_diurnal}   
875Example of recontruction of the diurnal cycle variation of short wave flux 
876from daily mean values. The reconstructed diurnal cycle (black line) is chosen
877as the mean value of the analytical cycle (blue line) over a time step, not
878as the mid time step value of the analytically cycle (red square). From \citet{Bernie_al_CD07}.}
879\end{center}   \end{figure}
880%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
881
882\cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of
883SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution
884of the surface fluxes of 3~h or less. Unfortunately high frequency forcing fields are rare,
885not to say inexistent. Nevertheless, it is possible to obtain a reasonable diurnal cycle
886of the SST knowning only short wave flux (SWF) at high frequency \citep{Bernie_al_CD07}.
887Furthermore, only the knowledge of daily mean value of SWF is needed,
888as higher frequency variations can be reconstructed from them, assuming that
889the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle
890of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available
891in \NEMO by setting \np{ln\_dm2dc}~=~true (a \textit{namsbc} namelist parameter) when using
892CORE bulk formulea (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).
893The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used
894can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily
895mean incomming SWF as the reconstructed SWF at a given time step is the mean value
896of the analytical cycle over this time step (Fig.\ref{Fig_SBC_diurnal}).
897The use of diurnal cycle reconstruction requires the input SWF to be daily
898($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
899Furthermore, it is recommended to have a least 8 surface module time step per day,
900that is  $\rdt \ \np{nn\_fsbc} < 10,800~s = 3~h$. An example of recontructed SWF
901is given in Fig.\ref{Fig_SBC_dcy} for a 12 reconstructed diurnal cycle, one every 2~hours
902(from 1am to 11pm).
903
904%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
905\begin{figure}[!t]  \begin{center}
906\includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_SBC_dcy.pdf}
907\caption{ \label{Fig_SBC_dcy}   
908Example of recontruction of the diurnal cycle variation of short wave flux 
909from daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
910The display is on (i,j) plane. }
911\end{center}   \end{figure}
912%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
913
914Note also that the setting a diurnal cycle in SWF is highly recommended  when
915the top layer thickness approach 1~m or less, otherwise large error in SST can
916appear due to an inconsistency between the scale of the vertical resolution
917and the forcing acting on that scale.
918
919% -------------------------------------------------------------------------------------------------------------
920%        Rotation of vector pairs onto the model grid directions
921% -------------------------------------------------------------------------------------------------------------
922\subsection{Rotation of vector pairs onto the model grid directions}
923\label{SBC_rotation}
924
925When using a flux (\np{ln\_flx}=true) or bulk (\np{ln\_clio}=true or \np{ln\_core}=true) formulation,
926pairs of vector components can be rotated from east-north directions onto the local grid directions. 
927This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
928relative to a rectilinear grid.
929To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
930The eastward component must start with "U" and the northward component with "V". 
931The remaining characters in the strings are used to identify which pair of components go together.
932So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
933and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
934and so on.
935The extra characters used in the strings are arbitrary.
936The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
937
938% -------------------------------------------------------------------------------------------------------------
939%        Surface restoring to observed SST and/or SSS
940% -------------------------------------------------------------------------------------------------------------
941\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
942         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
943\label{SBC_ssr}
944%------------------------------------------namsbc_ssr----------------------------------------------------
945\namdisplay{namsbc_ssr}
946%-------------------------------------------------------------------------------------------------------------
947
948In forced mode using a flux formulation (\np{ln\_flx}~=~true), a
949feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
950\begin{equation} \label{Eq_sbc_dmp_q}
951Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
952\end{equation}
953where SST is a sea surface temperature field (observed or climatological), $T$ is
954the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
955coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
956mixed-layer depth, this value corresponds to a relaxation time scale of two months.
957This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
958equal to $Q_o$.
959
960In the fresh water budget, a feedback term can also be added. Converted into an
961equivalent freshwater flux, it takes the following expression :
962
963\begin{equation} \label{Eq_sbc_dmp_emp}
964\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac\left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
965                                             {\left.S\right|_{k=1}}
966\end{equation}
967
968where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an
969atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
970interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
971$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
972feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
973physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
974does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring
975term should be viewed as a flux correction on freshwater fluxes to reduce the
976uncertainties we have on the observed freshwater budget.
977
978% -------------------------------------------------------------------------------------------------------------
979%        Handling of ice-covered area
980% -------------------------------------------------------------------------------------------------------------
981\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
982\label{SBC_ice-cover}
983
984The presence at the sea surface of an ice covered area modifies all the fluxes
985transmitted to the ocean. There are several way to handle sea-ice in the system
986depending on the value of the \np{nn{\_}ice} namelist parameter. 
987\begin{description}
988\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
989This is a typical namelist value used for tropical ocean domain. The surface fluxes
990are simply specified for an ice-free ocean. No specific things is done for sea-ice.
991\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
992is used. An observed ice covered area is read in a file. Below this area, the SST is
993restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) 
994in the northern (southern) hemisphere. The associated modification of the freshwater
995fluxes are done in such a way that the change in buoyancy fluxes remains zero.
996This prevents deep convection to occur when trying to reach the freezing point
997(and so ice covered area condition) while the SSS is too large. This manner of
998managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if}
999model. It can be found in the \mdl{sbcice{\_}if} module.
1000\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
1001ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
1002each model cell to provide the surface ocean fluxes. Note that the activation of a
1003sea-ice model is is done by defining a CPP key (\key{lim2} or \key{lim3}).
1004The activation automatically ovewrite the read value of nn{\_}ice to its appropriate
1005value ($i.e.$ $2$ for LIM-2 and $3$ for LIM-3).
1006\end{description}
1007
1008% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1009
1010% -------------------------------------------------------------------------------------------------------------
1011%        Freshwater budget control
1012% -------------------------------------------------------------------------------------------------------------
1013\subsection   [Freshwater budget control (\textit{sbcfwb})]
1014         {Freshwater budget control (\mdl{sbcfwb})}
1015\label{SBC_fwb}
1016
1017For global ocean simulation it can be useful to introduce a control of the mean sea
1018level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
1019in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
1020\begin{description}
1021\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
1022certainly do so.
1023\item[\np{nn\_fwb}=1]  global mean \textit{emp} set to zero at each model time step.
1024%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).
1025\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
1026mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
1027Boussinesq approximation, the annual mean fresh water budget is simply evaluated
1028from the change in the mean sea level at January the first and saved in the
1029\textit{EMPav.dat} file.
1030\end{description}
1031
1032% -------------------------------------------------------------------------------------------------------------
1033%        Neutral Drag Coefficient from external wave model
1034% -------------------------------------------------------------------------------------------------------------
1035\subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})]
1036                        {Neutral drag coefficient from external wave model (\mdl{sbcwave})}
1037\label{SBC_wave}
1038%------------------------------------------namwave----------------------------------------------------
1039\namdisplay{namsbc_wave}
1040%-------------------------------------------------------------------------------------------------------------
1041\begin{description}
1042
1043In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the
1044logical variable \np{ln\_cdgw}
1045 in $namsbc$ namelist must be defined ${.true.}$.
1046The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the
1047namelist ${namsbc\_wave}$ (for external data names, locations, frequency, interpolation and all
1048the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input}) 
1049and a 2D field of neutral drag coefficient. Then using the routine
1050TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according
1051to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
1052
1053\end{description}
1054
1055% Griffies doc:
1056% 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.
1057%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.
1058%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.
1059
1060
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