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1% ================================================================
2% Chapter � Surface Boundary Condition (SBC, ICB)
3% ================================================================
4\chapter{Surface Boundary Condition (SBC, ICB) }
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 \ngn{namsbc} 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\_mfs}~=~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}).
41If the Interpolation on the Fly option is used, input data belonging to land points (in the native grid),
42can be masked to avoid spurious results in proximity of the coasts  as large sea-land gradients characterize
43most of the atmospheric variables.
44In addition, the resulting fields can be further modified using several namelist options.
45These options control  the rotation of vector components supplied relative to an east-north
46coordinate system onto the local grid directions in the model; the addition of a surface
47restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes
48below ice-covered areas (using observed ice-cover or a sea-ice model)
49(\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater
50fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of a freshwater flux adjustment
51in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the
52transformation of the solar radiation (if provided as daily mean) into a diurnal
53cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave
54model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or mfs bulk formulas are selected.
55
56In this chapter, we first discuss where the surface boundary condition appears in the
57model equations. Then we present the five ways of providing the surface boundary condition,
58followed by the description of the atmospheric pressure and the river runoff.
59Next the scheme for interpolation on the fly is described.
60Finally, the different options that further modify the fluxes applied to the ocean are discussed.
61One of these is modification by icebergs (see \S\ref{ICB_icebergs}), which act as drifting sources of fresh water.
62
63
64% ================================================================
65% Surface boundary condition for the ocean
66% ================================================================
67\section{Surface boundary condition for the ocean}
68\label{SBC_general}
69
70The surface ocean stress is the stress exerted by the wind and the sea-ice
71on the ocean. The two components of stress are assumed to be interpolated
72onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
73at $u$- and $v$-points They are applied as a surface boundary condition of the
74computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
75\begin{equation} \label{Eq_sbc_dynzdf}
76\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
77    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
78\end{equation}
79where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
80stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
81
82The surface heat flux is decomposed into two parts, a non solar and a solar heat
83flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
84of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
85It is applied as a surface boundary condition trend of the first level temperature
86time evolution equation (\mdl{trasbc} module).
87\begin{equation} \label{Eq_sbc_trasbc_q}
88\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 
89_o \;C_p \;e_{3t} }} \right|_{k=1} \quad
90\end{equation}
91$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
92trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
93
94\begin{equation} \label{Eq_sbc_traqsr}
95\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right]
96\end{equation}
97where $I_w$ is a non-dimensional function that describes the way the light
98penetrates inside the water column. It is generally a sum of decreasing
99exponentials (see \S\ref{TRA_qsr}).
100
101The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which
102may or may not be identical. Indeed, a surface freshwater flux has two effects:
103it changes the volume of the ocean and it changes the surface concentration of
104salt (and other tracers). Therefore it appears in the sea surface height as a volume
105flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
106as a concentration/dilution effect,
107$\textit{emp}_{S}$ (\mdl{trasbc} module).
108\begin{equation} \label{Eq_trasbc_emp}
109\begin{aligned}
110&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\ 
111\\
112 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\ 
113 \end{aligned}
114\end{equation} 
115
116In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,
117but it exist several numerical reasons why this equality should be broken.
118For example, when the ocean is coupled to a sea-ice model, the water exchanged between
119ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,
120$\textit{emp}_{S}$ take into account both concentration/dilution effect associated with
121freezing/melting and the salt flux between ice and ocean, while \textit{emp} is
122only the volume flux. In addition, in the current version of \NEMO, the sea-ice is
123assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does
124not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS.
125%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
126
127Note that SST can also be modified by a freshwater flux. Precipitation (in
128particular solid precipitation) may have a temperature significantly different from
129the SST. Due to the lack of information about the temperature of
130precipitation, 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 no heat flux
133associated with precipitation! Precipitation can change the ocean volume and thus the
134ocean heat content. It is therefore associated with a heat flux (not yet 
135diagnosed in the model) \citep{Roullet_Madec_JGR00}).
136
137%\colorbox{yellow}{Miss: }
138%
139%A extensive description of all namsbc namelist (parameter that have to be
140%created!)
141%
142%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
143%ssv) i.e. information required by flux computation or sea-ice
144%
145%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
146%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
147%
148%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
149%
150%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
151%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
152%nf{\_}sbc
153%
154%Explain here all the namlist namsbc variable{\ldots}.
155%
156%\colorbox{yellow}{End Miss }
157
158The ocean model provides the surface currents, temperature and salinity
159averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
160mean is done in \mdl{sbcmod} module.
161
162%-------------------------------------------------TABLE---------------------------------------------------
163\begin{table}[tb]   \begin{center}   \begin{tabular}{|l|l|l|l|}
164\hline
165Variable description             & Model variable  & Units  & point \\  \hline
166i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
167j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
168Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
169Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
170\end{tabular}
171\caption{  \label{Tab_ssm}   
172Ocean variables provided by the ocean to the surface module (SBC).
173The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of
174computation of surface fluxes.}
175\end{center}   \end{table}
176%--------------------------------------------------------------------------------------------------------------
177
178%\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
179
180
181% ================================================================
182%       Input Data
183% ================================================================
184\section{Input Data generic interface}
185\label{SBC_input}
186
187A generic interface has been introduced to manage the way input data (2D or 3D fields,
188like surface forcing or ocean T and S) are specify in \NEMO. This task is archieved by fldread.F90.
189The module was design with four main objectives in mind:
190\begin{enumerate} 
191\item optionally provide a time interpolation of the input data at model time-step,
192whatever their input frequency is, and according to the different calendars available in the model.
193\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
194\item make the run duration independent from the period cover by the input files.
195\item provide a simple user interface and a rather simple developer interface by limiting the
196 number of prerequisite information.
197\end{enumerate} 
198
199As a results the user have only to fill in for each variable a structure in the namelist file
200to defined the input data file and variable names, the frequency of the data (in hours or months),
201whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
202and three additional parameters for on-the-fly interpolation. When adding a new input variable,
203the developer has to add the associated structure in the namelist, read this information
204by mirroring the namelist read in \rou{sbc\_blk\_init} for example, and simply call \rou{fld\_read} 
205to obtain the desired input field at the model time-step and grid points.
206
207The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
208(see \S\ref{SBC_fldread}), the period it cover is one year, month, week or day, and, if on-the-fly
209interpolation is used, a file of weights must be supplied (see \S\ref{SBC_iof}).
210
211Note that when an input data is archived on a disc which is accessible directly
212from the workspace where the code is executed, then the use can set the \np{cn\_dir} 
213to the pathway leading to the data. By default, the data are assumed to have been
214copied so that cn\_dir='./'.
215
216% -------------------------------------------------------------------------------------------------------------
217% Input Data specification (\mdl{fldread})
218% -------------------------------------------------------------------------------------------------------------
219\subsection{Input Data specification (\mdl{fldread})}
220\label{SBC_fldread}
221
222The structure associated with an input variable contains the following information:
223\begin{alltt}  {{\tiny   
224\begin{verbatim}
225!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
226!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
227\end{verbatim}
228}}\end{alltt} 
229where
230\begin{description} 
231\item[File name]: the stem name of the NetCDF file to be open.
232This stem will be completed automatically by the model, with the addition of a '.nc' at its end
233and by date information and possibly a prefix (when using AGRIF).
234Tab.\ref{Tab_fldread} provides the resulting file name in all possible cases according to whether
235it is a climatological file or not, and to the open/close frequency (see below for definition).
236
237%--------------------------------------------------TABLE--------------------------------------------------
238\begin{table}[htbp]
239\begin{center}
240\begin{tabular}{|l|c|c|c|}
241\hline
242                         & daily or weekLLL          & monthly                   &   yearly          \\   \hline
243clim = false   & fn\_yYYYYmMMdDD  &   fn\_yYYYYmMM   &   fn\_yYYYY  \\   \hline
244clim = true       & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
245\end{tabular}
246\end{center}
247\caption{ \label{Tab_fldread}   naming nomenclature for climatological or interannual input file,
248as a function of the Open/close frequency. The stem name is assumed to be 'fn'.
249For 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
250actual year/month/day, always coded with 4 or 2 digits. Note that (1) in mpp, if the file is split
251over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc', where 'PPPP' is the
252process number coded with 4 digits; (2) when using AGRIF, the prefix
253'\_N' is added to files,
254where 'N'  is the child grid number.}
255\end{table}
256%--------------------------------------------------------------------------------------------------------------
257 
258
259\item[Record frequency]: the frequency of the records contained in the input file.
260Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
261(for example -1 for monthly forcing or -12 for annual forcing).
262Note that this frequency must really be an integer and not a real.
263On some computers, seting it to '24.' can be interpreted as 240!
264
265\item[Variable name]: the name of the variable to be read in the input NetCDF file.
266
267\item[Time interpolation]: a logical to activate, or not, the time interpolation. If set to 'false',
268the forcing will have a steplike shape remaining constant during each forcing period.
269For example, when using a daily forcing without time interpolation, the forcing remaining
270constant from 00h00'00'' to 23h59'59". If set to 'true', the forcing will have a broken line shape.
271Records are assumed to be dated the middle of the forcing period.
272For example, when using a daily forcing with time interpolation, linear interpolation will
273be performed between mid-day of two consecutive days.
274
275\item[Climatological forcing]: a logical to specify if a input file contains climatological forcing
276which can be cycle in time, or an interannual forcing which will requires additional files
277if the period covered by the simulation exceed the one of the file. See the above the file
278naming strategy which impacts the expected name of the file to be opened.
279
280\item[Open/close frequency]: the frequency at which forcing files must be opened/closed.
281Four cases are coded: 'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week),
282'monthly' and 'yearly' which means the forcing files will contain data for one day, one week,
283one month or one year. Files are assumed to contain data from the beginning of the open/close period.
284For example, the first record of a yearly file containing daily data is Jan 1st even if the experiment
285is not starting at the beginning of the year.
286
287\item[Others]: 'weights filename', 'pairing rotation' and 'land/sea mask' are associted with on-the-fly interpolation
288which is described in \S\ref{SBC_iof}.
289
290\end{description}
291
292Additional remarks:\\
293(1) The time interpolation is a simple linear interpolation between two consecutive records of
294the input data. The only tricky point is therefore to specify the date at which we need to do
295the interpolation and the date of the records read in the input files.
296Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the
297time step. For example, for an experiment starting at 0h00'00" with a one hour time-step,
298a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
299However, for forcing data related to the surface module, values are not needed at every
300time-step but at every \np{nn\_fsbc} time-step. For example with \np{nn\_fsbc}~=~3,
301the surface module will be called at time-steps 1, 4, 7, etc. The date used for the time interpolation
302is thus redefined to be at the middle of \np{nn\_fsbc} time-step period. In the previous example,
303this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
304(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file
305calendar. The calendar associated with the forcing field is build according to the information
306provided by user in the record frequency, the open/close frequency and the type of temporal interpolation.
307For example, the first record of a yearly file containing daily data that will be interpolated in time
308is assumed to be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
309(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file
310when interpolating data with the first (last) record of the open/close period.
311For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
312the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values
313between Dec 31st 12h00'00" and Jan 1st 12h00'00". If the forcing is climatological, Dec and Jan will
314be keep-up from the same year. However, if the forcing is not climatological, at the end of the
315open/close period the code will automatically close the current file and open the next one.
316Note that, if the experiment is starting (ending) at the beginning (end) of an open/close period
317we do accept that the previous (next) file is not existing. In this case, the time interpolation
318will be performed between two identical values. For example, when starting an experiment on
319Jan 1st of year Y with yearly files and daily data to be interpolated, we do accept that the file
320related to year Y-1 is not existing. The value of Jan 1st will be used as the missing one for
321Dec 31st of year Y-1. If the file of year Y-1 exists, the code will read its last record.
322Therefore, this file can contain only one record corresponding to Dec 31st, a useful feature for
323user considering that it is too heavy to manipulate the complete file for year Y-1.
324
325
326% -------------------------------------------------------------------------------------------------------------
327% Interpolation on the Fly
328% -------------------------------------------------------------------------------------------------------------
329\subsection [Interpolation on-the-Fly] {Interpolation on-the-Fly}
330\label{SBC_iof}
331
332Interpolation on the Fly allows the user to supply input files required
333for the surface forcing on grids other than the model grid.
334To do this he or she must supply, in addition to the source data file,
335a file of weights to be used to interpolate from the data grid to the model grid.
336The original development of this code used the SCRIP package (freely available
337\href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
338In principle, any package can be used to generate the weights, but the
339variables in the input weights file must have the same names and meanings as
340assumed by the model.
341Two methods are currently available: bilinear and bicubic interpolation.
342Prior to the interpolation, providing a land/sea mask file, the user can decide to
343 remove land points from the input file and substitute the corresponding values
344with the average of the 8 neighbouring points in the native external grid.
345 Only "sea points" are considered for the averaging. The land/sea mask file must
346be provided in the structure associated with the input variable.
347 The netcdf land/sea mask variable name must be 'LSM' it must have the same
348horizontal and vertical dimensions of the associated variable and should
349be equal to 1 over land and 0 elsewhere.
350The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.
351Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied.
352
353\subsubsection{Bilinear Interpolation}
354\label{SBC_iof_bilinear}
355
356The input weights file in this case has two sets of variables: src01, src02,
357src03, src04 and wgt01, wgt02, wgt03, wgt04.
358The "src" variables correspond to the point in the input grid to which the weight
359"wgt" is to be applied. Each src value is an integer corresponding to the index of a
360point in the input grid when written as a one dimensional array.  For example, for an input grid
361of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
362There are four of each variable because bilinear interpolation uses the four points defining
363the grid box containing the point to be interpolated.
364All of these arrays are on the model grid, so that values src01(i,j) and
365wgt01(i,j) are used to generate a value for point (i,j) in the model.
366
367Symbolically, the algorithm used is:
368
369\begin{equation}
370f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
371\end{equation}
372where function idx() transforms a one dimensional index src(k) into a two dimensional index,
373and wgt(1) corresponds to variable "wgt01" for example.
374
375\subsubsection{Bicubic Interpolation}
376\label{SBC_iof_bicubic}
377
378Again there are two sets of variables: "src" and "wgt".
379But in this case there are 16 of each.
380The symbolic algorithm used to calculate values on the model grid is now:
381
382\begin{equation*} \begin{split}
383f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}     
384              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
385              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }   
386              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
387\end{split}
388\end{equation*}
389The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
390
391\subsubsection{Implementation}
392\label{SBC_iof_imp}
393
394To activate this option, a non-empty string should be supplied in the weights filename column
395of the relevant namelist; if this is left as an empty string no action is taken.
396In the model, weights files are read in and stored in a structured type (WGT) in the fldread
397module, as and when they are first required.
398This initialisation procedure determines whether the input data grid should be treated
399as cyclical or not by inspecting a global attribute stored in the weights input file.
400This attribute must be called "ew\_wrap" and be of integer type.
401If it is negative, the input non-model grid is assumed not to be cyclic.
402If zero or greater, then the value represents the number of columns that overlap.
403$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
404if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
405If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
406In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and therefore the grid
407is assumed to be cyclic with no overlapping columns.
408(In fact this only matters when bicubic interpolation is required.)
409Note that no testing is done to check the validity in the model, since there is no way
410of knowing the name used for the longitude variable,
411so it is up to the user to make sure his or her data is correctly represented.
412
413Next the routine reads in the weights.
414Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise
415bilinear interpolation is used. The WGT structure includes dynamic arrays both for
416the storage of the weights (on the model grid), and when required, for reading in
417the variable to be interpolated (on the input data grid).
418The size of the input data array is determined by examining the values in the "src"
419arrays to find the minimum and maximum i and j values required.
420Since bicubic interpolation requires the calculation of gradients at each point on the grid,
421the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
422When the array of points from the data file is adjacent to an edge of the data grid,
423the halo is either a copy of the row/column next to it (non-cyclical case), or is a copy
424of one from the first few columns on the opposite side of the grid (cyclical case).
425
426\subsubsection{Limitations}
427\label{SBC_iof_lim}
428
429\begin{enumerate} 
430\item  The case where input data grids are not logically rectangular has not been tested.
431\item  This code is not guaranteed to produce positive definite answers from positive definite inputs
432          when a bicubic interpolation method is used.
433\item  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
434\item  The gradients across the ends of a cyclical grid assume that the grid spacing between
435          the two columns involved are consistent with the weights used.
436\item  Neither interpolation scheme is conservative. (There is a conservative scheme available
437          in SCRIP, but this has not been implemented.)
438\end{enumerate}
439
440\subsubsection{Utilities}
441\label{SBC_iof_util}
442
443% to be completed
444A set of utilities to create a weights file for a rectilinear input grid is available
445(see the directory NEMOGCM/TOOLS/WEIGHTS).
446
447% -------------------------------------------------------------------------------------------------------------
448% Standalone Surface Boundary Condition Scheme
449% -------------------------------------------------------------------------------------------------------------
450\subsection [Standalone Surface Boundary Condition Scheme] {Standalone Surface Boundary Condition Scheme}
451\label{SAS_iof}
452
453%---------------------------------------namsbc_ana--------------------------------------------------
454\namdisplay{namsbc_sas}
455%--------------------------------------------------------------------------------------------------------------
456
457In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields and simply read them in from  a previous run. 
458Options are defined through the  \ngn{namsbc\_sas} namelist variables.
459For example:
460
461\begin{enumerate}
462\item  Multiple runs of the model are required in code development to see the affect of different algorithms in
463       the bulk formulae.
464\item  The effect of different parameter sets in the ice model is to be examined.
465\end{enumerate}
466
467The StandAlone Surface scheme provides this utility.
468A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
469However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0)
470In this configuration, a few routines in the standard model are overriden by new versions.
471Routines replaced are:
472
473\begin{enumerate}
474\item  \mdl{nemogcm}
475
476       This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90)
477       Since the ocean state is not calculated all associated initialisations have been removed.
478\item  \mdl{step}
479
480       The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
481\item  \mdl{sbcmod}
482
483       This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules
484       that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs).
485\item  \mdl{daymod}
486
487       No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions
488       have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user
489       must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
490\item  \mdl{stpctl}
491
492       Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
493\item  \mdl{diawri}
494
495       All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which
496       have been read in) are written along with relevant forcing and ice data.
497\end{enumerate}
498
499One new routine has been added:
500
501\begin{enumerate}
502\item  \mdl{sbcsas}
503       This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface.
504       These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module,
505       the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level.
506       Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
507\end{enumerate}
508
509% ================================================================
510% Analytical formulation (sbcana module)
511% ================================================================
512\section  [Analytical formulation (\textit{sbcana}) ]
513      {Analytical formulation (\mdl{sbcana} module) }
514\label{SBC_ana}
515
516%---------------------------------------namsbc_ana--------------------------------------------------
517\namdisplay{namsbc_ana}
518%--------------------------------------------------------------------------------------------------------------
519
520The analytical formulation of the surface boundary condition is the default scheme.
521In this case, all the six fluxes needed by the ocean are assumed to
522be uniform in space. They take constant values given in the namelist
523\ngn{namsbc{\_}ana} by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
524\np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero.
525In addition, the wind is allowed to reach its nominal value within a given number
526of time steps (\np{nn\_tau000}).
527
528If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
529module can be modified to use another scheme. As an example,
530the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
531GYRE configuration (see GYRE configuration manual, in preparation).
532
533
534% ================================================================
535% Flux formulation
536% ================================================================
537\section  [Flux formulation (\textit{sbcflx}) ]
538      {Flux formulation (\mdl{sbcflx} module) }
539\label{SBC_flx}
540%------------------------------------------namsbc_flx----------------------------------------------------
541\namdisplay{namsbc_flx} 
542%-------------------------------------------------------------------------------------------------------------
543
544In the flux formulation (\np{ln\_flx}=true), the surface boundary
545condition fields are directly read from input files. The user has to define
546in the namelist \ngn{namsbc{\_}flx} the name of the file, the name of the variable
547read in the file, the time frequency at which it is given (in hours), and a logical
548setting whether a time interpolation to the model time step is required
549for this field. See \S\ref{SBC_fldread} for a more detailed description of the parameters.
550
551Note that in general, a flux formulation is used in associated with a
552restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
553specification.
554
555
556% ================================================================
557% Bulk formulation
558% ================================================================
559\section  [Bulk formulation (\textit{sbcblk\_core}, \textit{sbcblk\_clio} or \textit{sbcblk\_mfs}) ]
560      {Bulk formulation \small{(\mdl{sbcblk\_core} \mdl{sbcblk\_clio} \mdl{sbcblk\_mfs} modules)} }
561\label{SBC_blk}
562
563In the bulk formulation, the surface boundary condition fields are computed
564using bulk formulae and atmospheric fields and ocean (and ice) variables.
565
566The atmospheric fields used depend on the bulk formulae used. Three bulk formulations
567are available : the CORE, the CLIO and the MFS bulk formulea. The choice is made by setting to true
568one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or  \np{ln\_mfs}.
569
570Note : in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
571Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over both
572an ocean and an ice surface.
573
574% -------------------------------------------------------------------------------------------------------------
575%        CORE Bulk formulea
576% -------------------------------------------------------------------------------------------------------------
577\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
578            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
579\label{SBC_blk_core}
580%------------------------------------------namsbc_core----------------------------------------------------
581\namdisplay{namsbc_core} 
582%-------------------------------------------------------------------------------------------------------------
583
584The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
585They have been designed to handle the CORE forcing, a mixture of NCEP
586reanalysis and satellite data. They use an inertial dissipative method to compute
587the turbulent transfer coefficients (momentum, sensible heat and evaporation)
588from the 10 metre wind speed, air temperature and specific humidity.
589This \citet{Large_Yeager_Rep04} dataset is available through the
590\href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.
591
592Note that substituting ERA40 to NCEP reanalysis fields
593does not require changes in the bulk formulea themself.
594This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
595
596Options are defined through the  \ngn{namsbc\_core} namelist variables.
597The required 8 input fields are:
598
599%--------------------------------------------------TABLE--------------------------------------------------
600\begin{table}[htbp]   \label{Tab_CORE}
601\begin{center}
602\begin{tabular}{|l|c|c|c|}
603\hline
604Variable desciption              & Model variable  & Units   & point \\    \hline
605i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
606j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
60710m air temperature              & tair      & \r{}$K$            & T   \\ \hline
608Specific humidity             & humi      & \%              & T \\      \hline
609Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
610Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
611Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
612Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
613\end{tabular}
614\end{center}
615\end{table}
616%--------------------------------------------------------------------------------------------------------------
617
618Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean
619point ($u$- and $v$-points). It is simpler and faster (less fields to be read),
620but it is not the recommended method when the ocean grid size is the same
621or larger than the one of the input atmospheric fields.
622
623% -------------------------------------------------------------------------------------------------------------
624%        CLIO Bulk formulea
625% -------------------------------------------------------------------------------------------------------------
626\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
627            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
628\label{SBC_blk_clio}
629%------------------------------------------namsbc_clio----------------------------------------------------
630\namdisplay{namsbc_clio} 
631%-------------------------------------------------------------------------------------------------------------
632
633The CLIO bulk formulae were developed several years ago for the
634Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
635They are simpler bulk formulae. They assume the stress to be known and
636compute the radiative fluxes from a climatological cloud cover.
637
638Options are defined through the  \ngn{namsbc\_clio} namelist variables.
639The required 7 input fields are:
640
641%--------------------------------------------------TABLE--------------------------------------------------
642\begin{table}[htbp]   \label{Tab_CLIO}
643\begin{center}
644\begin{tabular}{|l|l|l|l|}
645\hline
646Variable desciption           & Model variable  & Units           & point \\  \hline
647i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
648j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
649Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
65010m air temperature              & tair         & \r{}$K$            & T \\   \hline
651Specific humidity                & humi         & \%              & T \\   \hline
652Cloud cover                   &           & \%              & T \\   \hline
653Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
654Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
655\end{tabular}
656\end{center}
657\end{table}
658%--------------------------------------------------------------------------------------------------------------
659
660As for the flux formulation, information about the input data required by the
661model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
662namelist (see \S\ref{SBC_fldread}).
663
664% -------------------------------------------------------------------------------------------------------------
665%        MFS Bulk formulae
666% -------------------------------------------------------------------------------------------------------------
667\subsection    [MFS Bulk formulea (\np{ln\_mfs}=true)]
668            {MFS Bulk formulea (\np{ln\_mfs}=true, \mdl{sbcblk\_mfs})}
669\label{SBC_blk_mfs}
670%------------------------------------------namsbc_mfs----------------------------------------------------
671\namdisplay{namsbc_mfs} 
672%----------------------------------------------------------------------------------------------------------
673
674The MFS (Mediterranean Forecasting System) bulk formulae have been developed by
675 \citet{Castellari_al_JMS1998}.
676They have been designed to handle the ECMWF operational data and are currently
677in use in the MFS operational system \citep{Tonani_al_OS08}, \citep{Oddo_al_OS09}.
678The wind stress computation uses a drag coefficient computed according to \citet{Hellerman_Rosenstein_JPO83}.
679The surface boundary condition for temperature involves the balance between surface solar radiation,
680net long-wave radiation, the latent and sensible heat fluxes.
681Solar radiation is dependent on cloud cover and is computed by means of
682an astronomical formula \citep{Reed_JPO77}. Albedo monthly values are from \citet{Payne_JAS72} 
683as means of the values at $40^{o}N$ and $30^{o}N$ for the Atlantic Ocean (hence the same latitudinal
684band of the Mediterranean Sea). The net long-wave radiation flux
685\citep{Bignami_al_JGR95} is a function of
686air temperature, sea-surface temperature, cloud cover and relative humidity.
687Sensible heat and latent heat fluxes are computed by classical
688bulk formulae parameterized according to \citet{Kondo1975}.
689Details on the bulk formulae used can be found in \citet{Maggiore_al_PCE98} and \citet{Castellari_al_JMS1998}.
690
691Options are defined through the  \ngn{namsbc\_mfs} namelist variables.
692The required 7 input fields must be provided on the model Grid-T and  are:
693\begin{itemize}
694\item          Zonal Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windi})
695\item          Meridional Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windj})
696\item          Total Claud Cover (\%)  (\np{sn\_clc})
697\item          2m Air Temperature ($K$) (\np{sn\_tair})
698\item          2m Dew Point Temperature ($K$)  (\np{sn\_rhm})
699\item          Total Precipitation ${Kg} m^{-2} s^{-1}$ (\np{sn\_prec})
700\item          Mean Sea Level Pressure (${Pa}$) (\np{sn\_msl})
701\end{itemize}
702% -------------------------------------------------------------------------------------------------------------
703% ================================================================
704% Coupled formulation
705% ================================================================
706\section  [Coupled formulation (\textit{sbccpl}) ]
707      {Coupled formulation (\mdl{sbccpl} module)}
708\label{SBC_cpl}
709%------------------------------------------namsbc_cpl----------------------------------------------------
710\namdisplay{namsbc_cpl} 
711%-------------------------------------------------------------------------------------------------------------
712
713In the coupled formulation of the surface boundary condition, the fluxes are
714provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
715while sea and ice surface temperature, ocean and ice albedo, and ocean currents
716are sent to the atmospheric component.
717
718A generalised coupled interface has been developed. It is currently interfaced with OASIS 3
719(\key{oasis3}) and does not support OASIS 4
720\footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}.
721It has been successfully used to interface \NEMO to most of the European atmospheric
722GCM (ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz),
723as well as to \href{http://wrf-model.org/}{WRF} (Weather Research and Forecasting Model).
724
725Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
726The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are
727actually recieved by the ice-ocean system (no calculation of ice sublimation in coupled mode).
728When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
729the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}. In this case,
730CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system (and need to be activated in \ngn{namsbc{\_}cpl} ).
731
732The namelist above allows control of various aspects of the coupling fields (particularly for
733vectors) and now allows for any coupling fields to have multiple sea ice categories (as required by LIM3
734and CICE).  When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be
735determined by the number used in the sea ice model.  In some limited cases it may be possible to specify
736single category coupling fields even when the sea ice model is running with multiple categories - in this
737case the user should examine the code to be sure the assumptions made are satisfactory.  In cases where
738this is definitely not possible the model should abort with an error message.  The new code has been tested using
739ECHAM with LIM2, and HadGAM3 with CICE but although it will compile with \key{lim3} additional minor code changes
740may be required to run using LIM3.
741
742
743% ================================================================
744%        Atmospheric pressure
745% ================================================================
746\section   [Atmospheric pressure (\textit{sbcapr})]
747         {Atmospheric pressure (\mdl{sbcapr})}
748\label{SBC_apr}
749%------------------------------------------namsbc_apr----------------------------------------------------
750\namdisplay{namsbc_apr} 
751%-------------------------------------------------------------------------------------------------------------
752
753The optional atmospheric pressure can be used to force ocean and ice dynamics
754(\np{ln\_apr\_dyn}~=~true, \textit{\ngn{namsbc}} namelist ).
755The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
756can be interpolated in time to the model time step, and even in space when the
757interpolation on-the-fly is used. When used to force the dynamics, the atmospheric
758pressure is further transformed into an equivalent inverse barometer sea surface height,
759$\eta_{ib}$, using:
760\begin{equation} \label{SBC_ssh_ib}
761   \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
762\end{equation}
763where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
764A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. In this case $P_o$ 
765is set to the value of $P_{atm}$ averaged over the ocean domain, $i.e.$ the mean value of
766$\eta_{ib}$ is kept to zero at all time step.
767
768The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation
769(see \mdl{dynspg} for the ocean). For sea-ice, the sea surface height, $\eta_m$,
770which is provided to the sea ice model is set to $\eta - \eta_{ib}$ (see \mdl{sbcssr} module).
771$\eta_{ib}$ can be set in the output. This can simplify altimetry data and model comparison
772as inverse barometer sea surface height is usually removed from these date prior to their distribution.
773
774When using time-splitting and BDY package for open boundaries conditions, the equivalent
775inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
776\np{ln\_apr\_obc}  might be set to true.
777
778% ================================================================
779%        Tidal Potential
780% ================================================================
781\section   [Tidal Potential (\textit{sbctide})]
782                        {Tidal Potential (\mdl{sbctide})}
783\label{SBC_tide}
784
785A module is available to use the tidal potential forcing and is activated with with \key{tide}.
786
787
788%------------------------------------------nam_tide----------------------------------------------------
789\namdisplay{nam_tide}
790%-------------------------------------------------------------------------------------------------------------
791
792Concerning the tidal potential, some parameters are available in namelist \ngn{nam\_tide}:
793
794- \np{ln\_tide\_pot} activate the tidal potential forcing
795
796- \np{nb\_harmo} is the number of constituent used
797
798- \np{clname} is the name of constituent
799
800
801The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem;
802they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\
803
804The potential astronomical expressed, for the three types of tidal frequencies
805following, by : \\
806Tide long period :
807\begin{equation}
808\Pi_{a}=gA_{k}(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{k}t+V_{0k})
809\end{equation}
810diurnal Tide :
811\begin{equation}
812\Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k})
813\end{equation}
814Semi-diurnal tide:
815\begin{equation}
816\Pi_{a}=gA_{k}(cos^{2}\phi)cos(\omega_{k}t+2\lambda+V_{0k})
817\end{equation}
818
819
820$A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave
821$k$ to Greenwich.
822
823We make corrections to the astronomical potential.
824We obtain :
825\begin{equation}
826\Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi)
827\end{equation}
828with $k$ a number of Love estimated to 0.6 which parametrized the astronomical tidal land,
829and $h$ a number of Love to 0.3 which parametrized the parametrization due to the astronomical tidal land.
830
831% ================================================================
832%        River runoffs
833% ================================================================
834\section   [River runoffs (\textit{sbcrnf})]
835         {River runoffs (\mdl{sbcrnf})}
836\label{SBC_rnf}
837%------------------------------------------namsbc_rnf----------------------------------------------------
838\namdisplay{namsbc_rnf} 
839%-------------------------------------------------------------------------------------------------------------
840
841%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
842%Many models, however, have traditionally inserted river runoff to the top model cell.
843%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
844%throughout a nonzero depth has been motivated by the numerical and physical problems
845%that arise when the top grid cells are of the order of one meter. This situation is common in
846%coastal modelling and becomes more and more often open ocean and climate modelling
847%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
848%required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
849
850
851%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
852%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
853%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
854%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
855%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
856%emp or emps and the changes made are below:
857
858
859%Rachel:
860River runoff generally enters the ocean at a nonzero depth rather than through the surface.
861Many models, however, have traditionally inserted river runoff to the top model cell.
862This was the case in \NEMO prior to the version 3.3, and was combined with an option
863to increase vertical mixing near the river mouth.
864
865However, with this method numerical and physical problems arise when the top grid cells are
866of the order of one meter. This situation is common in coastal modelling and is becoming
867more common in open ocean and climate modelling
868\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
869required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
870
871As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth, and for the
872temperature and salinity of the river to effect the surrounding ocean.
873The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, along with the   
874depth (in metres) which the river should be added to.
875
876Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and \np{ln\_rnf\_temp} control whether
877the river attributes (depth, salinity and temperature) are read in and used.  If these are set
878as false the river is added to the surface box only, assumed to be fresh (0~psu), and/or
879taken as surface temperature respectively.
880
881The runoff value and attributes are read in in sbcrnf. 
882For temperature -999 is taken as missing data and the river temperature is taken to be the
883surface temperatue at the river point.
884For the depth parameter a value of -1 means the river is added to the surface box only,
885and a value of -999 means the river is added through the entire water column.
886After being read in the temperature and salinity variables are multiplied by the amount of runoff (converted into m/s)
887to give the heat and salt content of the river runoff.
888After the user specified depth is read ini, the number of grid boxes this corresponds to is
889calculated and stored in the variable \np{nz\_rnf}.
890The variable \textit{h\_dep} is then calculated to be the depth (in metres) of the bottom of the
891lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model).
892
893The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence
894(\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
895This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
896The sea surface height is calculated using the sum of the horizontal divergence terms, and so the
897river runoff indirectly forces an increase in sea surface height.
898
899The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
900This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
901The heat and salt content of the river runoff is not included in this step, and so the tracer
902concentrations are diluted as water of ocean temperature and salinity is moved upward out of the box
903and replaced by the same volume of river water with no corresponding heat and salt addition.
904
905For the linear free surface case, at the surface box the tracer advection causes a flux of water
906(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.
907As such the volume of water does not change, but the water is diluted.
908
909For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
910Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water
911is added with no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
912(The runoff addition to the top box along with the water being moved up through boxes below means the surface box has a large
913increase in volume, whilst all other boxes remain the same size)
914
915In trasbc the addition of heat and salt due to the river runoff is added.
916This is done in the same way for both vvl and non-vvl.
917The temperature and salinity are increased through the specified depth according to the heat and salt content of the river.
918
919In the non-linear free surface case (vvl), near the end of the time step the change in sea surface height is redistrubuted
920through the grid boxes, so that the original ratios of grid box heights are restored.
921In 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.
922
923It 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.
924When 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.
925
926
927%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
928
929%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
930
931%\colorbox{yellow}{river mouths{\ldots}}
932
933%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
934%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
935%ENDIF
936
937%\gmcomment{  word doc of runoffs:
938%
939%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.
940%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. 
941
942%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
943
944%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:
945
946%}
947
948
949% ================================================================
950%        Handling of icebergs
951% ================================================================
952\section{ Handling of icebergs (ICB) }
953\label{ICB_icebergs}
954%------------------------------------------namberg----------------------------------------------------
955\namdisplay{namberg}
956%-------------------------------------------------------------------------------------------------------------
957
958Icebergs are modelled as lagrangian particles in NEMO.
959Their physical behaviour is controlled by equations as described in  \citet{Martin_Adcroft_OM10} ).
960(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO.)
961Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described in the \ngn{namberg} namelist:
962\np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
963Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs
964of this class are being described as one lagrangian point (this reduces the numerical problem of tracking every single iceberg).
965They are enabled by setting \np{ln\_icebergs}~=~true.
966
967Two initialisation schemes are possible.
968\begin{description}
969\item[\np{nn\_test\_icebergs}~$>$~0]
970In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
971(so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each
972grid point of which an iceberg is generated at the beginning of the run.
973(Note that this happens each time the timestep equals \np{nn\_nit000}.)
974\np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners
975of the geographical box: lonmin,lonmax,latmin,latmax
976\item[\np{nn\_test\_icebergs}~=~-1]
977In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
978This should be a file with a field on the configuration grid (typically ORCA) representing ice accumulation rate at each model point.
979These should be ocean points adjacent to land where icebergs are known to calve.
980Most points in this input grid are going to have value zero.
981When the model runs, ice is accumulated at each grid point which has a non-zero source term.
982At each time step, a test is performed to see if there is enough ice mass to calve an iceberg of each class in order (1 to 10).
983Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling).
984If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
985\end{description}
986
987Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
988The latter act to disintegrate the iceberg. This is either all melted freshwater, or
989(if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
990which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
991Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
992
993Extensive diagnostics can be produced.
994Separate output files are maintained for human-readable iceberg information.
995A separate file is produced for each processor (independent of \np{ln\_ctl}).
996The amount of information is controlled by two integer parameters:
997\begin{description}
998\item[\np{nn\_verbose\_level}]  takes a value between one and four and represents
999an increasing number of points in the code at which variables are written, and an
1000increasing level of obscurity.
1001\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1002\end{description}
1003
1004Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1005A non-zero value represents how many timesteps between writes of information into the output file.
1006These output files are in NETCDF format.
1007When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1008Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1009So care is needed to recreate data for individual icebergs, since its trajectory data may be spread across
1010multiple files.
1011
1012
1013% ================================================================
1014% Miscellanea options
1015% ================================================================
1016\section{Miscellaneous options}
1017\label{SBC_misc}
1018
1019% -------------------------------------------------------------------------------------------------------------
1020%        Diurnal cycle
1021% -------------------------------------------------------------------------------------------------------------
1022\subsection   [Diurnal  cycle (\textit{sbcdcy})]
1023         {Diurnal cycle (\mdl{sbcdcy})}
1024\label{SBC_dcy}
1025%------------------------------------------namsbc_rnf----------------------------------------------------
1026%\namdisplay{namsbc}
1027%-------------------------------------------------------------------------------------------------------------
1028
1029%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1030\begin{figure}[!t]    \begin{center}
1031\includegraphics[width=0.8\textwidth]{./TexFiles/Figures/Fig_SBC_diurnal.pdf}
1032\caption{ \label{Fig_SBC_diurnal}   
1033Example of recontruction of the diurnal cycle variation of short wave flux 
1034from daily mean values. The reconstructed diurnal cycle (black line) is chosen
1035as the mean value of the analytical cycle (blue line) over a time step, not
1036as the mid time step value of the analytically cycle (red square). From \citet{Bernie_al_CD07}.}
1037\end{center}   \end{figure}
1038%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1039
1040\cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of
1041SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution
1042of the surface fluxes of 3~h or less. Unfortunately high frequency forcing fields are rare,
1043not to say inexistent. Nevertheless, it is possible to obtain a reasonable diurnal cycle
1044of the SST knowning only short wave flux (SWF) at high frequency \citep{Bernie_al_CD07}.
1045Furthermore, only the knowledge of daily mean value of SWF is needed,
1046as higher frequency variations can be reconstructed from them, assuming that
1047the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle
1048of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available
1049in \NEMO by setting \np{ln\_dm2dc}~=~true (a \textit{\ngn{namsbc}} namelist variable) when using
1050CORE bulk formulea (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).
1051The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used
1052can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily
1053mean incomming SWF as the reconstructed SWF at a given time step is the mean value
1054of the analytical cycle over this time step (Fig.\ref{Fig_SBC_diurnal}).
1055The use of diurnal cycle reconstruction requires the input SWF to be daily
1056($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1057Furthermore, it is recommended to have a least 8 surface module time step per day,
1058that is  $\rdt \ \np{nn\_fsbc} < 10,800~s = 3~h$. An example of recontructed SWF
1059is given in Fig.\ref{Fig_SBC_dcy} for a 12 reconstructed diurnal cycle, one every 2~hours
1060(from 1am to 11pm).
1061
1062%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1063\begin{figure}[!t]  \begin{center}
1064\includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_SBC_dcy.pdf}
1065\caption{ \label{Fig_SBC_dcy}   
1066Example of recontruction of the diurnal cycle variation of short wave flux 
1067from daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1068The display is on (i,j) plane. }
1069\end{center}   \end{figure}
1070%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1071
1072Note also that the setting a diurnal cycle in SWF is highly recommended  when
1073the top layer thickness approach 1~m or less, otherwise large error in SST can
1074appear due to an inconsistency between the scale of the vertical resolution
1075and the forcing acting on that scale.
1076
1077% -------------------------------------------------------------------------------------------------------------
1078%        Rotation of vector pairs onto the model grid directions
1079% -------------------------------------------------------------------------------------------------------------
1080\subsection{Rotation of vector pairs onto the model grid directions}
1081\label{SBC_rotation}
1082
1083When using a flux (\np{ln\_flx}=true) or bulk (\np{ln\_clio}=true or \np{ln\_core}=true) formulation,
1084pairs of vector components can be rotated from east-north directions onto the local grid directions. 
1085This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
1086relative to a rectilinear grid.
1087To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1088The eastward component must start with "U" and the northward component with "V". 
1089The remaining characters in the strings are used to identify which pair of components go together.
1090So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
1091and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
1092and so on.
1093The extra characters used in the strings are arbitrary.
1094The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1095
1096% -------------------------------------------------------------------------------------------------------------
1097%        Surface restoring to observed SST and/or SSS
1098% -------------------------------------------------------------------------------------------------------------
1099\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
1100         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
1101\label{SBC_ssr}
1102%------------------------------------------namsbc_ssr----------------------------------------------------
1103\namdisplay{namsbc_ssr} 
1104%-------------------------------------------------------------------------------------------------------------
1105
1106IOptions are defined through the  \ngn{namsbc\_ssr} namelist variables.
1107n forced mode using a flux formulation (\np{ln\_flx}~=~true), a
1108feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1109\begin{equation} \label{Eq_sbc_dmp_q}
1110Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1111\end{equation}
1112where SST is a sea surface temperature field (observed or climatological), $T$ is
1113the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
1114coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
1115mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1116This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
1117equal to $Q_o$.
1118
1119In the fresh water budget, a feedback term can also be added. Converted into an
1120equivalent freshwater flux, it takes the following expression :
1121
1122\begin{equation} \label{Eq_sbc_dmp_emp}
1123\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1124                                             {\left.S\right|_{k=1}}
1125\end{equation}
1126
1127where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an
1128atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
1129interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
1130$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
1131feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
1132physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
1133does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring
1134term should be viewed as a flux correction on freshwater fluxes to reduce the
1135uncertainties we have on the observed freshwater budget.
1136
1137% -------------------------------------------------------------------------------------------------------------
1138%        Handling of ice-covered area
1139% -------------------------------------------------------------------------------------------------------------
1140\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1141\label{SBC_ice-cover}
1142
1143The presence at the sea surface of an ice covered area modifies all the fluxes
1144transmitted to the ocean. There are several way to handle sea-ice in the system
1145depending on the value of the \np{nn{\_}ice} namelist parameter. 
1146\begin{description}
1147\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
1148This is a typical namelist value used for tropical ocean domain. The surface fluxes
1149are simply specified for an ice-free ocean. No specific things is done for sea-ice.
1150\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
1151is used. An observed ice covered area is read in a file. Below this area, the SST is
1152restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
1153in the northern (southern) hemisphere. The associated modification of the freshwater
1154fluxes are done in such a way that the change in buoyancy fluxes remains zero.
1155This prevents deep convection to occur when trying to reach the freezing point
1156(and so ice covered area condition) while the SSS is too large. This manner of
1157managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if} 
1158model. It can be found in the \mdl{sbcice{\_}if} module.
1159\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
1160ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
1161each model cell to provide the surface ocean fluxes. Note that the activation of a
1162sea-ice model is is done by defining a CPP key (\key{lim2}, \key{lim3} or \key{cice}).
1163The activation automatically overwrites the read value of nn{\_}ice to its appropriate
1164value ($i.e.$ $2$ for LIM-2, $3$ for LIM-3 or $4$ for CICE).
1165\end{description}
1166
1167% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1168
1169\subsection   [Interface to CICE (\textit{sbcice\_cice})]
1170         {Interface to CICE (\mdl{sbcice\_cice})}
1171\label{SBC_cice}
1172
1173It is now possible to couple a regional or global NEMO configuration (without AGRIF) to the CICE sea-ice
1174model by using \key{cice}.  The CICE code can be obtained from
1175\href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and the additional 'hadgem3' drivers will be required,
1176even with the latest code release.  Input grid files consistent with those used in NEMO will also be needed,
1177and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used (seek advice from UKMO
1178if necessary).  Currently the code is only designed to work when using the CORE forcing option for NEMO (with
1179\textit{calc\_strair~=~true} and \textit{calc\_Tsfc~=~true} in the CICE name-list), or alternatively when NEMO
1180is coupled to the HadGAM3 atmosphere model (with \textit{calc\_strair~=~false} and \textit{calc\_Tsfc~=~false}).
1181The code is intended to be used with \np{nn\_fsbc} set to 1 (although coupling ocean and ice less frequently
1182should work, it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly - the
1183user should check that results are not significantly different to the standard case).
1184
1185There are two options for the technical coupling between NEMO and CICE.  The standard version allows
1186complete flexibility for the domain decompositions in the individual models, but this is at the expense of global
1187gather and scatter operations in the coupling which become very expensive on larger numbers of processors. The
1188alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that the domain decomposition is
1189identical in both models (provided domain parameters are set appropriately, and
1190\textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and allows
1191much more efficient direct coupling on individual processors.  This solution scales much better although it is at
1192the expense of having more idle CICE processors in areas where there is no sea ice.
1193
1194% -------------------------------------------------------------------------------------------------------------
1195%        Freshwater budget control
1196% -------------------------------------------------------------------------------------------------------------
1197\subsection   [Freshwater budget control (\textit{sbcfwb})]
1198         {Freshwater budget control (\mdl{sbcfwb})}
1199\label{SBC_fwb}
1200
1201For global ocean simulation it can be useful to introduce a control of the mean sea
1202level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
1203in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
1204\begin{description}
1205\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
1206certainly do so.
1207\item[\np{nn\_fwb}=1]  global mean \textit{emp} set to zero at each model time step.
1208%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).
1209\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
1210mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
1211Boussinesq approximation, the annual mean fresh water budget is simply evaluated
1212from the change in the mean sea level at January the first and saved in the
1213\textit{EMPav.dat} file.
1214\end{description}
1215
1216% -------------------------------------------------------------------------------------------------------------
1217%        Neutral Drag Coefficient from external wave model
1218% -------------------------------------------------------------------------------------------------------------
1219\subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})]
1220                        {Neutral drag coefficient from external wave model (\mdl{sbcwave})}
1221\label{SBC_wave}
1222%------------------------------------------namwave----------------------------------------------------
1223\namdisplay{namsbc_wave}
1224%-------------------------------------------------------------------------------------------------------------
1225\begin{description}
1226
1227\item [??] In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the
1228logical variable \np{ln\_cdgw}
1229 in $namsbc$ namelist must be defined ${.true.}$.
1230The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the
1231namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all
1232the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input})
1233and a 2D field of neutral drag coefficient. Then using the routine
1234TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according
1235to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
1236
1237\end{description}
1238
1239% Griffies doc:
1240% 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.
1241%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 year�s 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.
1242%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.
1243
1244
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