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3% ================================================================
4% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)
5% ================================================================
6\chapter{Surface Boundary Condition (SBC, ISF, ICB) }
11$\ $\newline    % force a new ligne
15$\ $\newline    % force a new ligne
17The ocean needs six fields as surface boundary condition:
19   \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$
20   \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
21   \item the surface freshwater budget $\left( {\textit{emp}} \right)$
22   \item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
24plus an optional field:
26   \item the atmospheric pressure at the ocean surface $\left( p_a \right)$
29Five different ways to provide the first six fields to the ocean are available which
30are controlled by namelist \ngn{namsbc} variables: an analytical formulation (\np{ln\_ana}\forcode{ = .true.}),
31a flux formulation (\np{ln\_flx}\forcode{ = .true.}), a bulk formulae formulation (CORE
32(\np{ln\_blk\_core}\forcode{ = .true.}), CLIO (\np{ln\_blk\_clio}\forcode{ = .true.}) or MFS
33\footnote { Note that MFS bulk formulae compute fluxes only for the ocean component}
34(\np{ln\_blk\_mfs}\forcode{ = .true.}) bulk formulae) and a coupled or mixed forced/coupled formulation
35(exchanges with a atmospheric model via the OASIS coupler) (\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}).
36When used ($i.e.$ \np{ln\_apr\_dyn}\forcode{ = .true.}), the atmospheric pressure forces both ocean and ice dynamics.
38The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.
39When the fields are supplied from data files (flux and bulk formulations), the input fields
40need not be supplied on the model grid. Instead a file of coordinates and weights can
41be supplied which maps the data from the supplied grid to the model points
42(so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
43If the Interpolation on the Fly option is used, input data belonging to land points (in the native grid),
44can be masked to avoid spurious results in proximity of the coasts  as large sea-land gradients characterize
45most of the atmospheric variables.
47In addition, the resulting fields can be further modified using several namelist options.
48These options control
50\item the rotation of vector components supplied relative to an east-north
51coordinate system onto the local grid directions in the model ;
52\item the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}\forcode{ = .true.}) ;
53\item the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model) (\np{nn\_ice}\forcode{ = 0..3}) ;
54\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}\forcode{ = .true.}) ;
55\item the addition of isf melting as lateral inflow (parameterisation) or as fluxes applied at the land-ice ocean interface (\np{ln\_isf}) ;
56\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}\forcode{ = 0..2}) ;
57\item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}\forcode{ = .true.}) ;
58and a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}\forcode{ = .true.}).
60The latter option is possible only in case core or mfs bulk formulas are selected.
62In this chapter, we first discuss where the surface boundary condition appears in the
63model equations. Then we present the five ways of providing the surface boundary condition,
64followed by the description of the atmospheric pressure and the river runoff.
65Next the scheme for interpolation on the fly is described.
66Finally, the different options that further modify the fluxes applied to the ocean are discussed.
67One of these is modification by icebergs (see \autoref{sec:ICB_icebergs}), which act as drifting sources of fresh water.
68Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
69which provides additional sources of fresh water.
72% ================================================================
73% Surface boundary condition for the ocean
74% ================================================================
75\section{Surface boundary condition for the ocean}
78The surface ocean stress is the stress exerted by the wind and the sea-ice
79on the ocean. It is applied in \mdl{dynzdf} module as a surface boundary condition of the
80computation of the momentum vertical mixing trend (see \autoref{eq:dynzdf_sbc} in \autoref{sec:DYN_zdf}).
81As such, it has to be provided as a 2D vector interpolated
82onto the horizontal velocity ocean mesh, $i.e.$ resolved onto the model
83(\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
85The surface heat flux is decomposed into two parts, a non solar and a solar heat
86flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
87of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes
88plus the heat content of the mass exchange with the atmosphere and sea-ice).
89It is applied in \mdl{trasbc} module as a surface boundary condition trend of
90the first level temperature time evolution equation (see \autoref{eq:tra_sbc} 
91and \autoref{eq:tra_sbc_lin} in \autoref{subsec:TRA_sbc}).
92The latter is the penetrative part of the heat flux. It is applied as a 3D
93trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}\forcode{ = .true.}.
94The way the light penetrates inside the water column is generally a sum of decreasing
95exponentials (see \autoref{subsec:TRA_qsr}).
97The surface freshwater budget is provided by the \textit{emp} field.
98It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation)
99and possibly with the sea-ice and ice shelves (freezing minus melting of ice).
100It affects both the ocean in two different ways:
101$(i)$   it changes the volume of the ocean and therefore appears in the sea surface height
102equation as a volume flux, and
103$(ii)$  it changes the surface temperature and salinity through the heat and salt contents
104of the mass exchanged with the atmosphere, the sea-ice and the ice shelves.
107%\colorbox{yellow}{Miss: }
109%A extensive description of all namsbc namelist (parameter that have to be
112%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
113%ssv) i.e. information required by flux computation or sea-ice
115%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
116%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
118%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
120%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
121%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
124%Explain here all the namlist namsbc variable{\ldots}.
126% explain : use or not of surface currents
128%\colorbox{yellow}{End Miss }
130The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
131the surface currents, temperature and salinity. 
132These variables are averaged over \np{nn\_fsbc} time-step (\autoref{tab:ssm}),
133and it is these averaged fields which are used to computes the surface fluxes
134at a frequency of \np{nn\_fsbc} time-step.
138\begin{table}[tb]   \begin{center}   \begin{tabular}{|l|l|l|l|}
140Variable description             & Model variable  & Units  & point \\  \hline
141i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
142j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
143Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
144Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
146\caption{  \protect\label{tab:ssm}   
147Ocean variables provided by the ocean to the surface module (SBC).
148The variable are averaged over nn{\_}fsbc time step,
149$i.e.$ the frequency of computation of surface fluxes.}
150\end{center}   \end{table}
153%\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
156% ================================================================
157%       Input Data
158% ================================================================
159\section{Input data generic interface}
162A generic interface has been introduced to manage the way input data (2D or 3D fields,
163like surface forcing or ocean T and S) are specify in \NEMO. This task is archieved by \mdl{fldread}.
164The module was design with four main objectives in mind:
166\item optionally provide a time interpolation of the input data at model time-step,
167whatever their input frequency is, and according to the different calendars available in the model.
168\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
169\item make the run duration independent from the period cover by the input files.
170\item provide a simple user interface and a rather simple developer interface by limiting the
171 number of prerequisite information.
174As a results the user have only to fill in for each variable a structure in the namelist file
175to defined the input data file and variable names, the frequency of the data (in hours or months),
176whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
177and three additional parameters for on-the-fly interpolation. When adding a new input variable,
178the developer has to add the associated structure in the namelist, read this information
179by mirroring the namelist read in \rou{sbc\_blk\_init} for example, and simply call \rou{fld\_read} 
180to obtain the desired input field at the model time-step and grid points.
182The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
183(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and, if on-the-fly
184interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
186Note that when an input data is archived on a disc which is accessible directly
187from the workspace where the code is executed, then the use can set the \np{cn\_dir} 
188to the pathway leading to the data. By default, the data are assumed to have been
189copied so that cn\_dir='./'.
191% -------------------------------------------------------------------------------------------------------------
192% Input Data specification (\mdl{fldread})
193% -------------------------------------------------------------------------------------------------------------
194\subsection{Input data specification (\protect\mdl{fldread})}
197The structure associated with an input variable contains the following information:
199!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
200!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
204\item[File name]: the stem name of the NetCDF file to be open.
205This stem will be completed automatically by the model, with the addition of a '.nc' at its end
206and by date information and possibly a prefix (when using AGRIF).
207Tab.\autoref{tab:fldread} provides the resulting file name in all possible cases according to whether
208it is a climatological file or not, and to the open/close frequency (see below for definition).
215                         & daily or weekLLL          & monthly                   &   yearly          \\   \hline
216\np{clim}\forcode{ = .false.} & fn\  &   fn\   &   fn\  \\   \hline
217\np{clim}\forcode{ = .true.}        & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
220\caption{ \protect\label{tab:fldread}   naming nomenclature for climatological or interannual input file,
221as a function of the Open/close frequency. The stem name is assumed to be 'fn'.
222For 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
223actual year/month/day, always coded with 4 or 2 digits. Note that (1) in mpp, if the file is split
224over each subdomain, the suffix '.nc' is replaced by '\', where 'PPPP' is the
225process number coded with 4 digits; (2) when using AGRIF, the prefix
226'\_N' is added to files,
227where 'N'  is the child grid number.}
232\item[Record frequency]: the frequency of the records contained in the input file.
233Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
234(for example -1 for monthly forcing or -12 for annual forcing).
235Note that this frequency must really be an integer and not a real.
236On some computers, seting it to '24.' can be interpreted as 240!
238\item[Variable name]: the name of the variable to be read in the input NetCDF file.
240\item[Time interpolation]: a logical to activate, or not, the time interpolation. If set to 'false',
241the forcing will have a steplike shape remaining constant during each forcing period.
242For example, when using a daily forcing without time interpolation, the forcing remaining
243constant from 00h00'00'' to 23h59'59". If set to 'true', the forcing will have a broken line shape.
244Records are assumed to be dated the middle of the forcing period.
245For example, when using a daily forcing with time interpolation, linear interpolation will
246be performed between mid-day of two consecutive days.
248\item[Climatological forcing]: a logical to specify if a input file contains climatological forcing
249which can be cycle in time, or an interannual forcing which will requires additional files
250if the period covered by the simulation exceed the one of the file. See the above the file
251naming strategy which impacts the expected name of the file to be opened.
253\item[Open/close frequency]: the frequency at which forcing files must be opened/closed.
254Four cases are coded: 'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week),
255'monthly' and 'yearly' which means the forcing files will contain data for one day, one week,
256one month or one year. Files are assumed to contain data from the beginning of the open/close period.
257For example, the first record of a yearly file containing daily data is Jan 1st even if the experiment
258is not starting at the beginning of the year.
260\item[Others]: 'weights filename', 'pairing rotation' and 'land/sea mask' are associted with on-the-fly interpolation
261which is described in \autoref{subsec:SBC_iof}.
265Additional remarks:\\
266(1) The time interpolation is a simple linear interpolation between two consecutive records of
267the input data. The only tricky point is therefore to specify the date at which we need to do
268the interpolation and the date of the records read in the input files.
269Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the
270time step. For example, for an experiment starting at 0h00'00" with a one hour time-step,
271a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
272However, for forcing data related to the surface module, values are not needed at every
273time-step but at every \np{nn\_fsbc} time-step. For example with \np{nn\_fsbc}\forcode{ = 3},
274the surface module will be called at time-steps 1, 4, 7, etc. The date used for the time interpolation
275is thus redefined to be at the middle of \np{nn\_fsbc} time-step period. In the previous example,
276this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
277(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file
278calendar. The calendar associated with the forcing field is build according to the information
279provided by user in the record frequency, the open/close frequency and the type of temporal interpolation.
280For example, the first record of a yearly file containing daily data that will be interpolated in time
281is assumed to be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
282(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file
283when interpolating data with the first (last) record of the open/close period.
284For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
285the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values
286between Dec 31st 12h00'00" and Jan 1st 12h00'00". If the forcing is climatological, Dec and Jan will
287be keep-up from the same year. However, if the forcing is not climatological, at the end of the
288open/close period the code will automatically close the current file and open the next one.
289Note that, if the experiment is starting (ending) at the beginning (end) of an open/close period
290we do accept that the previous (next) file is not existing. In this case, the time interpolation
291will be performed between two identical values. For example, when starting an experiment on
292Jan 1st of year Y with yearly files and daily data to be interpolated, we do accept that the file
293related to year Y-1 is not existing. The value of Jan 1st will be used as the missing one for
294Dec 31st of year Y-1. If the file of year Y-1 exists, the code will read its last record.
295Therefore, this file can contain only one record corresponding to Dec 31st, a useful feature for
296user considering that it is too heavy to manipulate the complete file for year Y-1.
299% -------------------------------------------------------------------------------------------------------------
300% Interpolation on the Fly
301% -------------------------------------------------------------------------------------------------------------
302\subsection{Interpolation on-the-fly}
305Interpolation on the Fly allows the user to supply input files required
306for the surface forcing on grids other than the model grid.
307To do this he or she must supply, in addition to the source data file,
308a file of weights to be used to interpolate from the data grid to the model grid.
309The original development of this code used the SCRIP package (freely available
310\href{}{here} under a copyright agreement).
311In principle, any package can be used to generate the weights, but the
312variables in the input weights file must have the same names and meanings as
313assumed by the model.
314Two methods are currently available: bilinear and bicubic interpolation.
315Prior to the interpolation, providing a land/sea mask file, the user can decide to
316 remove land points from the input file and substitute the corresponding values
317with the average of the 8 neighbouring points in the native external grid.
318 Only "sea points" are considered for the averaging. The land/sea mask file must
319be provided in the structure associated with the input variable.
320 The netcdf land/sea mask variable name must be 'LSM' it must have the same
321horizontal and vertical dimensions of the associated variable and should
322be equal to 1 over land and 0 elsewhere.
323The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.
324Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied.
326\subsubsection{Bilinear interpolation}
329The input weights file in this case has two sets of variables: src01, src02,
330src03, src04 and wgt01, wgt02, wgt03, wgt04.
331The "src" variables correspond to the point in the input grid to which the weight
332"wgt" is to be applied. Each src value is an integer corresponding to the index of a
333point in the input grid when written as a one dimensional array.  For example, for an input grid
334of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
335There are four of each variable because bilinear interpolation uses the four points defining
336the grid box containing the point to be interpolated.
337All of these arrays are on the model grid, so that values src01(i,j) and
338wgt01(i,j) are used to generate a value for point (i,j) in the model.
340Symbolically, the algorithm used is:
343f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
345where function idx() transforms a one dimensional index src(k) into a two dimensional index,
346and wgt(1) corresponds to variable "wgt01" for example.
348\subsubsection{Bicubic interpolation}
351Again there are two sets of variables: "src" and "wgt".
352But in this case there are 16 of each.
353The symbolic algorithm used to calculate values on the model grid is now:
355\begin{equation*} \begin{split}
356f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}     
357              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
358              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }   
359              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
362The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
367To activate this option, a non-empty string should be supplied in the weights filename column
368of the relevant namelist; if this is left as an empty string no action is taken.
369In the model, weights files are read in and stored in a structured type (WGT) in the fldread
370module, as and when they are first required.
371This initialisation procedure determines whether the input data grid should be treated
372as cyclical or not by inspecting a global attribute stored in the weights input file.
373This attribute must be called "ew\_wrap" and be of integer type.
374If it is negative, the input non-model grid is assumed not to be cyclic.
375If zero or greater, then the value represents the number of columns that overlap.
376$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
377if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
378If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
379In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and therefore the grid
380is assumed to be cyclic with no overlapping columns.
381(In fact this only matters when bicubic interpolation is required.)
382Note that no testing is done to check the validity in the model, since there is no way
383of knowing the name used for the longitude variable,
384so it is up to the user to make sure his or her data is correctly represented.
386Next the routine reads in the weights.
387Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise
388bilinear interpolation is used. The WGT structure includes dynamic arrays both for
389the storage of the weights (on the model grid), and when required, for reading in
390the variable to be interpolated (on the input data grid).
391The size of the input data array is determined by examining the values in the "src"
392arrays to find the minimum and maximum i and j values required.
393Since bicubic interpolation requires the calculation of gradients at each point on the grid,
394the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
395When the array of points from the data file is adjacent to an edge of the data grid,
396the halo is either a copy of the row/column next to it (non-cyclical case), or is a copy
397of one from the first few columns on the opposite side of the grid (cyclical case).
403\item  The case where input data grids are not logically rectangular has not been tested.
404\item  This code is not guaranteed to produce positive definite answers from positive definite inputs
405          when a bicubic interpolation method is used.
406\item  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
407\item  The gradients across the ends of a cyclical grid assume that the grid spacing between
408          the two columns involved are consistent with the weights used.
409\item  Neither interpolation scheme is conservative. (There is a conservative scheme available
410          in SCRIP, but this has not been implemented.)
416% to be completed
417A set of utilities to create a weights file for a rectilinear input grid is available
418(see the directory NEMOGCM/TOOLS/WEIGHTS).
420% -------------------------------------------------------------------------------------------------------------
421% Standalone Surface Boundary Condition Scheme
422% -------------------------------------------------------------------------------------------------------------
423\subsection{Standalone surface boundary condition scheme}
430In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields
431and simply read them in from a previous run or receive them from OASIS. 
432For example:
435\item  Multiple runs of the model are required in code development to see the effect of different algorithms in
436       the bulk formulae.
437\item  The effect of different parameter sets in the ice model is to be examined.
438\item  Development of sea-ice algorithms or parameterizations.
439\item  spinup of the iceberg floats
440\item  ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}\forcode{ = .true.})
443The StandAlone Surface scheme provides this utility.
444Its options are defined through the \ngn{namsbc\_sas} namelist variables.
445A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
446However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0)
447In this configuration, a few routines in the standard model are overriden by new versions.
448Routines replaced are:
451\item \mdl{nemogcm} : This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step})
452       Since the ocean state is not calculated all associated initialisations have been removed.
453\item  \mdl{step} : The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
454\item  \mdl{sbcmod} : This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules
455       that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs).
456\item  \mdl{daymod} : No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions
457       have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user
458       must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
459\item  \mdl{stpctl} : Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
460\item  \mdl{diawri} : All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which
461       have been read in) are written along with relevant forcing and ice data.
464One new routine has been added:
467\item  \mdl{sbcsas} : This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface.
468       These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module,
469       the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level.
470       Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
474% Missing the description of the 2 following variables:
475%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field
476%   ln_read_frq = .false.    !  specify whether we must read frq or not
480% ================================================================
481% Analytical formulation (sbcana module)
482% ================================================================
483\section{Analytical formulation (\protect\mdl{sbcana})}
490The analytical formulation of the surface boundary condition is the default scheme.
491In this case, all the six fluxes needed by the ocean are assumed to
492be uniform in space. They take constant values given in the namelist
493\ngn{namsbc{\_}ana} by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
494\np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero.
495In addition, the wind is allowed to reach its nominal value within a given number
496of time steps (\np{nn\_tau000}).
498If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
499module can be modified to use another scheme. As an example,
500the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
501GYRE configuration (see GYRE configuration manual, in preparation).
504% ================================================================
505% Flux formulation
506% ================================================================
507\section{Flux formulation (\protect\mdl{sbcflx})}
513In the flux formulation (\np{ln\_flx}\forcode{ = .true.}), the surface boundary
514condition fields are directly read from input files. The user has to define
515in the namelist \ngn{namsbc{\_}flx} the name of the file, the name of the variable
516read in the file, the time frequency at which it is given (in hours), and a logical
517setting whether a time interpolation to the model time step is required
518for this field. See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
520Note that in general, a flux formulation is used in associated with a
521restoring term to observed SST and/or SSS. See \autoref{subsec:SBC_ssr} for its
525% ================================================================
526% Bulk formulation
527% ================================================================
528\section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio,\_mfs\}.F90})}]
529         {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio}, \protect\mdl{sbcblk\_mfs})}}
532In the bulk formulation, the surface boundary condition fields are computed
533using bulk formulae and atmospheric fields and ocean (and ice) variables.
535The atmospheric fields used depend on the bulk formulae used. Three bulk formulations
536are available : the CORE, the CLIO and the MFS bulk formulea. The choice is made by setting to true
537one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or  \np{ln\_mfs}.
539Note : in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
540Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over both
541an ocean and an ice surface.
543% -------------------------------------------------------------------------------------------------------------
544%        CORE Bulk formulea
545% -------------------------------------------------------------------------------------------------------------
546\subsection{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})}
552The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
553They have been designed to handle the CORE forcing, a mixture of NCEP
554reanalysis and satellite data. They use an inertial dissipative method to compute
555the turbulent transfer coefficients (momentum, sensible heat and evaporation)
556from the 10 metre wind speed, air temperature and specific humidity.
557This \citet{Large_Yeager_Rep04} dataset is available through the
558\href{}{GFDL web site}.
560Note that substituting ERA40 to NCEP reanalysis fields
561does not require changes in the bulk formulea themself.
562This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
564Options are defined through the  \ngn{namsbc\_core} namelist variables.
565The required 8 input fields are:
568\begin{table}[htbp]   \label{tab:CORE}
572Variable desciption              & Model variable  & Units   & point \\    \hline
573i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
574j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
57510m air temperature              & tair      & \r{}$K$            & T   \\ \hline
576Specific humidity             & humi      & \%              & T \\      \hline
577Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
578Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
579Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
580Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
586Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean
587point ($u$- and $v$-points). It is simpler and faster (less fields to be read),
588but it is not the recommended method when the ocean grid size is the same
589or larger than the one of the input atmospheric fields.
591The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi},
592\np{sn\_prec}, \np{sn\_snow}, \np{sn\_tdif} parameters describe the fields
593and the way they have to be used (spatial and temporal interpolations).
595\np{cn\_dir} is the directory of location of bulk files
596\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
597\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
598\np{rn\_zu}: is the height of wind measurements (m)
600Three multiplicative factors are availables :
601\np{rn\_pfac} and \np{rn\_efac} allows to adjust (if necessary) the global freshwater budget
602by increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
603The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account
604in the calculation of surface wind stress. Its range should be between zero and one,
605and it is recommended to set it to 0.
607% -------------------------------------------------------------------------------------------------------------
608%        CLIO Bulk formulea
609% -------------------------------------------------------------------------------------------------------------
610\subsection{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})}
616The CLIO bulk formulae were developed several years ago for the
617Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
618They are simpler bulk formulae. They assume the stress to be known and
619compute the radiative fluxes from a climatological cloud cover.
621Options are defined through the  \ngn{namsbc\_clio} namelist variables.
622The required 7 input fields are:
625\begin{table}[htbp]   \label{tab:CLIO}
629Variable desciption           & Model variable  & Units           & point \\  \hline
630i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
631j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
632Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
63310m air temperature              & tair         & \r{}$K$            & T \\   \hline
634Specific humidity                & humi         & \%              & T \\   \hline
635Cloud cover                   &           & \%              & T \\   \hline
636Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
637Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
643As for the flux formulation, information about the input data required by the
644model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
645namelist (see \autoref{subsec:SBC_fldread}).
647% -------------------------------------------------------------------------------------------------------------
648%        MFS Bulk formulae
649% -------------------------------------------------------------------------------------------------------------
650\subsection{MFS formulea (\protect\mdl{sbcblk\_mfs}, \protect\np{ln\_mfs}\forcode{ = .true.})}
656The MFS (Mediterranean Forecasting System) bulk formulae have been developed by
657 \citet{Castellari_al_JMS1998}.
658They have been designed to handle the ECMWF operational data and are currently
659in use in the MFS operational system \citep{Tonani_al_OS08}, \citep{Oddo_al_OS09}.
660The wind stress computation uses a drag coefficient computed according to \citet{Hellerman_Rosenstein_JPO83}.
661The surface boundary condition for temperature involves the balance between surface solar radiation,
662net long-wave radiation, the latent and sensible heat fluxes.
663Solar radiation is dependent on cloud cover and is computed by means of
664an astronomical formula \citep{Reed_JPO77}. Albedo monthly values are from \citet{Payne_JAS72} 
665as means of the values at $40^{o}N$ and $30^{o}N$ for the Atlantic Ocean (hence the same latitudinal
666band of the Mediterranean Sea). The net long-wave radiation flux
667\citep{Bignami_al_JGR95} is a function of
668air temperature, sea-surface temperature, cloud cover and relative humidity.
669Sensible heat and latent heat fluxes are computed by classical
670bulk formulae parameterised according to \citet{Kondo1975}.
671Details on the bulk formulae used can be found in \citet{Maggiore_al_PCE98} and \citet{Castellari_al_JMS1998}.
673Options are defined through the  \ngn{namsbc\_mfs} namelist variables.
674The required 7 input fields must be provided on the model Grid-T and  are:
676\item          Zonal Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windi})
677\item          Meridional Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windj})
678\item          Total Claud Cover (\%)  (\np{sn\_clc})
679\item          2m Air Temperature ($K$) (\np{sn\_tair})
680\item          2m Dew Point Temperature ($K$)  (\np{sn\_rhm})
681\item          Total Precipitation ${Kg} m^{-2} s^{-1}$ (\np{sn\_prec})
682\item          Mean Sea Level Pressure (${Pa}$) (\np{sn\_msl})
684% -------------------------------------------------------------------------------------------------------------
685% ================================================================
686% Coupled formulation
687% ================================================================
688\section{Coupled formulation (\protect\mdl{sbccpl})}
694In the coupled formulation of the surface boundary condition, the fluxes are
695provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
696while sea and ice surface temperature, ocean and ice albedo, and ocean currents
697are sent to the atmospheric component.
699A generalised coupled interface has been developed.
700It is currently interfaced with OASIS-3-MCT (\key{oasis3}).
701It has been successfully used to interface \NEMO to most of the European atmospheric
703as well as to \href{}{WRF} (Weather Research and Forecasting Model).
705Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
706The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are
707actually recieved by the ice-ocean system (no calculation of ice sublimation in coupled mode).
708When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
709the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}. In this case,
710CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system (and need to be activated in \ngn{namsbc{\_}cpl} ).
712The namelist above allows control of various aspects of the coupling fields (particularly for
713vectors) and now allows for any coupling fields to have multiple sea ice categories (as required by LIM3
714and CICE).  When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be
715determined by the number used in the sea ice model.  In some limited cases it may be possible to specify
716single category coupling fields even when the sea ice model is running with multiple categories - in this
717case the user should examine the code to be sure the assumptions made are satisfactory.  In cases where
718this is definitely not possible the model should abort with an error message.  The new code has been tested using
719ECHAM with LIM2, and HadGAM3 with CICE but although it will compile with \key{lim3} additional minor code changes
720may be required to run using LIM3.
723% ================================================================
724%        Atmospheric pressure
725% ================================================================
726\section{Atmospheric pressure (\protect\mdl{sbcapr})}
732The optional atmospheric pressure can be used to force ocean and ice dynamics
733(\np{ln\_apr\_dyn}\forcode{ = .true.}, \textit{\ngn{namsbc}} namelist ).
734The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
735can be interpolated in time to the model time step, and even in space when the
736interpolation on-the-fly is used. When used to force the dynamics, the atmospheric
737pressure is further transformed into an equivalent inverse barometer sea surface height,
738$\eta_{ib}$, using:
739\begin{equation} \label{eq:SBC_ssh_ib}
740   \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
742where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
743A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. In this case $P_o$ 
744is set to the value of $P_{atm}$ averaged over the ocean domain, $i.e.$ the mean value of
745$\eta_{ib}$ is kept to zero at all time step.
747The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation
748(see \mdl{dynspg} for the ocean). For sea-ice, the sea surface height, $\eta_m$,
749which is provided to the sea ice model is set to $\eta - \eta_{ib}$ (see \mdl{sbcssr} module).
750$\eta_{ib}$ can be set in the output. This can simplify altimetry data and model comparison
751as inverse barometer sea surface height is usually removed from these date prior to their distribution.
753When using time-splitting and BDY package for open boundaries conditions, the equivalent
754inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
755\np{ln\_apr\_obc}  might be set to true.
757% ================================================================
758%        Surface Tides Forcing
759% ================================================================
760\section{Surface tides (\protect\mdl{sbctide})}
767The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems, is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \np{.true.} in \ngn{nam\_tide}. This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that:
768\begin{equation}     \label{eq:PE_dyn_tides}
769\frac{\partial {\rm {\bf U}}_h }{\partial t}= ...
770+g\nabla (\Pi_{eq} + \Pi_{sal})
772where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a self-attraction and loading term (SAL).
774The equilibrium tidal forcing is expressed as a sum over the chosen constituents $l$ in \ngn{nam\_tide}. The constituents are defined such that \np{clname(1) = 'M2', clname(2)='S2', etc...}. For the three types of tidal frequencies it reads : \\
775Long period tides :
779diurnal tides :
781\Pi_{eq}(l)=A_{l}(1+k-h)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l})
783Semi-diurnal tides:
787Here $A_{l}$ is the amplitude, $\omega_{l}$ is the frequency, $\phi$ the latitude, $\lambda$ the longitude, $V_{0l}$ a phase shift with respect to Greenwich meridian and $t$ the time. The Love number factor $(1+k-h)$ is here taken as a constant (0.7).
789The SAL term should in principle be computed online as it depends on the model tidal prediction itself (see \citet{Arbic2004} for a discussion about the practical implementation of this term). Nevertheless, the complex calculations involved would make this computationally too expensive. Here, practical solutions are whether to read complex estimates $\Pi_{sal}(l)$ from an external model (\np{ln\_read\_load=.true.}) or use a ``scalar approximation'' (\np{ln\_scal\_load=.true.}). In the latter case, it reads:\\
791\Pi_{sal} = \beta \eta
793where $\beta$ (\np{rn\_scal\_load}, $\approx0.09$) is a spatially constant scalar, often chosen to minimize tidal prediction errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to false removes the SAL contribution.
795% ================================================================
796%        River runoffs
797% ================================================================
798\section{River runoffs (\protect\mdl{sbcrnf})}
804%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
805%Many models, however, have traditionally inserted river runoff to the top model cell.
806%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
807%throughout a nonzero depth has been motivated by the numerical and physical problems
808%that arise when the top grid cells are of the order of one meter. This situation is common in
809%coastal modelling and becomes more and more often open ocean and climate modelling
810%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
811%required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}.
814%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
815%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
816%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
817%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
818%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
819%emp or emps and the changes made are below:
823River runoff generally enters the ocean at a nonzero depth rather than through the surface.
824Many models, however, have traditionally inserted river runoff to the top model cell.
825This was the case in \NEMO prior to the version 3.3, and was combined with an option
826to increase vertical mixing near the river mouth.
828However, with this method numerical and physical problems arise when the top grid cells are
829of the order of one meter. This situation is common in coastal modelling and is becoming
830more common in open ocean and climate modelling
831\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
832required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}.
834As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth, and for the
835temperature and salinity of the river to effect the surrounding ocean.
836The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, along with the   
837depth (in metres) which the river should be added to.
839Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and \np{ln\_rnf\_temp} control whether
840the river attributes (depth, salinity and temperature) are read in and used.  If these are set
841as false the river is added to the surface box only, assumed to be fresh (0~psu), and/or
842taken as surface temperature respectively.
844The runoff value and attributes are read in in sbcrnf. 
845For temperature -999 is taken as missing data and the river temperature is taken to be the
846surface temperatue at the river point.
847For the depth parameter a value of -1 means the river is added to the surface box only,
848and a value of -999 means the river is added through the entire water column.
849After being read in the temperature and salinity variables are multiplied by the amount of runoff (converted into m/s)
850to give the heat and salt content of the river runoff.
851After the user specified depth is read ini, the number of grid boxes this corresponds to is
852calculated and stored in the variable \np{nz\_rnf}.
853The variable \textit{h\_dep} is then calculated to be the depth (in metres) of the bottom of the
854lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model).
856The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence
857(\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
858This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
859The sea surface height is calculated using the sum of the horizontal divergence terms, and so the
860river runoff indirectly forces an increase in sea surface height.
862The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
863This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
864The heat and salt content of the river runoff is not included in this step, and so the tracer
865concentrations are diluted as water of ocean temperature and salinity is moved upward out of the box
866and replaced by the same volume of river water with no corresponding heat and salt addition.
868For the linear free surface case, at the surface box the tracer advection causes a flux of water
869(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.
870As such the volume of water does not change, but the water is diluted.
872For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
873Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water
874is added with no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
875(The runoff addition to the top box along with the water being moved up through boxes below means the surface box has a large
876increase in volume, whilst all other boxes remain the same size)
878In trasbc the addition of heat and salt due to the river runoff is added.
879This is done in the same way for both vvl and non-vvl.
880The temperature and salinity are increased through the specified depth according to the heat and salt content of the river.
882In the non-linear free surface case (vvl), near the end of the time step the change in sea surface height is redistrubuted
883through the grid boxes, so that the original ratios of grid box heights are restored.
884In 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.
886It 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.
887When 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.
890%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
892%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
894%\colorbox{yellow}{river mouths{\ldots}}
896%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
897%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
900%\gmcomment{  word doc of runoffs:
902%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.
903%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. 
905%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
907%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:
910% ================================================================
911%        Ice shelf melting
912% ================================================================
913\section{Ice shelf melting (\protect\mdl{sbcisf})}
918Namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation used.
920\item[\np{nn\_isf}\forcode{ = 1}]
921The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{ = .true.} needed). The fwf and heat flux are computed.
922Two different bulk formula are available:
923   \begin{description}
924   \item[\np{nn\_isfblk}\forcode{ = 1}]
925   The bulk formula used to compute the melt is based the one described in \citet{Hunter2006}.
926        This formulation is based on a balance between the upward ocean heat flux and the latent heat flux at the ice shelf base.
928   \item[\np{nn\_isfblk}\forcode{ = 2}] 
929   The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}.
930        This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget
931         and a linearised freezing point temperature equation).
932   \end{description}
934For this 2 bulk formulations, there are 3 different ways to compute the exchange coeficient:
935   \begin{description}
936        \item[\np{nn\_gammablk}\forcode{ = 0}]
937   The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}
939   \item[\np{nn\_gammablk}\forcode{ = 1}]
940   The salt and heat exchange coefficients are velocity dependent and defined as \np{rn\_gammas0}$ \times u_{*}$ and \np{rn\_gammat0}$ \times u_{*}$
941        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
942        See \citet{Jenkins2010} for all the details on this formulation.
944   \item[\np{nn\_gammablk}\forcode{ = 2}]
945   The salt and heat exchange coefficients are velocity and stability dependent and defined as
946        $\gamma_{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}$
947        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
948        $\Gamma_{Turb}$ the contribution of the ocean stability and
949        $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
950        See \citet{Holland1999} for all the details on this formulation.
951        \end{description}
953\item[\np{nn\_isf}\forcode{ = 2}]
954A parameterisation of isf is used. The ice shelf cavity is not represented.
955The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL)
956(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}).
957Furthermore the fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting.
958The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
960\item[\np{nn\_isf}\forcode{ = 3}]
961A simple parameterisation of isf is used. The ice shelf cavity is not represented.
962The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between the depth of the average grounding line (GL)
963(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
964The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
966\item[\np{nn\_isf}\forcode{ = 4}]
967The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed). However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
968The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\
972$\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on the water mass properties, ocean velocities and depth.
973 This flux is thus highly dependent of the model resolution (horizontal and vertical), realism of the water masses onto the shelf ...\\
976$\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file. You have total control of the fwf forcing.
977This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too
978coarse to have realistic melting or for studies where you need to control your heat and fw input.\\ 
980A namelist parameters control over how many meters the heat and fw fluxes are spread.
981\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}.
982This parameter is only used if \np{nn\_isf}\forcode{ = 1} or \np{nn\_isf}\forcode{ = 4}
984If \np{rn\_hisf\_tbl}\forcode{ = 0}., the fluxes are put in the top level whatever is its tickness.
986If \np{rn\_hisf\_tbl} $>$ 0., the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells).\\
988The ice shelf melt is implemented as a volume flux with in the same way as for the runoff.
989The fw addition due to the ice shelf melting is, at each relevant depth level, added to the horizontal divergence
990(\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}.
991See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.
994\section{Ice sheet coupling}
999Ice sheet/ocean coupling is done through file exchange at the restart step. NEMO, at each restart step,
1000read the bathymetry and ice shelf draft variable in a netcdf file.
1001If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step
1002with potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1003The wetting and drying scheme applied on the restart is very simple and described below for the 6 different cases:
1005\item[Thin a cell down:]
1006   T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant ($bt_b=bt_n$).
1007\item[Enlarge  a cell:]
1008   See case "Thin a cell down"
1009\item[Dry a cell:]
1010   mask, T/S, U/V and ssh are set to 0. Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1011\item[Wet a cell:] 
1012   mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0. If no neighbours along i,j and k, T/S/U/V and mask are set to 0.
1013\item[Dry a column:]
1014   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1015\item[Wet a column:]
1016   set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0. If no neighbour, T/S/U/V and mask set to 0.
1018The extrapolation is call \np{nn\_drown} times. It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,
1019 the code will be unable to fill all the new wet cells properly. The default number is set up for the MISOMIP idealised experiments.\\
1020This coupling procedure is able to take into account grounding line and calving front migration. However, it is a non-conservative processe.
1021This could lead to a trend in heat/salt content and volume. In order to remove the trend and keep the conservation level as close to 0 as possible,
1022 a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}. The heat/salt/vol. gain/loss is diagnose, as well as the location.
1023Based on what is done on sbcrnf to prescribed a source of heat/salt/vol., the heat/salt/vol. gain/loss is removed/added,
1024 over a period of \np{rn\_fiscpl} time step, into the system.
1025So after \np{rn\_fiscpl} time step, all the heat/salt/vol. gain/loss due to extrapolation process is canceled.\\
1027As the before and now fields are not compatible (modification of the geometry), the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.
1029% ================================================================
1030%        Handling of icebergs
1031% ================================================================
1032\section{Handling of icebergs (ICB)}
1038Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}.
1039Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ).
1040(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO).
1041Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described
1042in the \ngn{namberg} namelist:
1043\np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1044Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs
1045of this class are being described as one lagrangian point (this reduces the numerical problem of tracking every single iceberg).
1046They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}.
1048Two initialisation schemes are possible.
1051In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1052(so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each
1053grid point of which an iceberg is generated at the beginning of the run.
1054(Note that this happens each time the timestep equals \np{nn\_nit000}.)
1055\np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners
1056of the geographical box: lonmin,lonmax,latmin,latmax
1057\item[\np{nn\_test\_icebergs}\forcode{ = -1}]
1058In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
1059This should be a file with a field on the configuration grid (typically ORCA) representing ice accumulation rate at each model point.
1060These should be ocean points adjacent to land where icebergs are known to calve.
1061Most points in this input grid are going to have value zero.
1062When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1063At 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).
1064Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling).
1065If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1068Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1069The latter act to disintegrate the iceberg. This is either all melted freshwater, or
1070(if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1071which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1072Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
1074Extensive diagnostics can be produced.
1075Separate output files are maintained for human-readable iceberg information.
1076A separate file is produced for each processor (independent of \np{ln\_ctl}).
1077The amount of information is controlled by two integer parameters:
1079\item[\np{nn\_verbose\_level}]  takes a value between one and four and represents
1080an increasing number of points in the code at which variables are written, and an
1081increasing level of obscurity.
1082\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1085Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1086A non-zero value represents how many timesteps between writes of information into the output file.
1087These output files are in NETCDF format.
1088When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1089Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1090So care is needed to recreate data for individual icebergs, since its trajectory data may be spread across
1091multiple files.
1094% ================================================================
1095% Miscellanea options
1096% ================================================================
1097\section{Miscellaneous options}
1100% -------------------------------------------------------------------------------------------------------------
1101%        Diurnal cycle
1102% -------------------------------------------------------------------------------------------------------------
1103\subsection{Diurnal cycle (\protect\mdl{sbcdcy})}
1110\begin{figure}[!t]    \begin{center}
1112\caption{ \protect\label{fig:SBC_diurnal}   
1113Example of recontruction of the diurnal cycle variation of short wave flux 
1114from daily mean values. The reconstructed diurnal cycle (black line) is chosen
1115as the mean value of the analytical cycle (blue line) over a time step, not
1116as the mid time step value of the analytically cycle (red square). From \citet{Bernie_al_CD07}.}
1117\end{center}   \end{figure}
1120\cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of
1121SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution
1122of the surface fluxes of 3~h or less. Unfortunately high frequency forcing fields are rare,
1123not to say inexistent. Nevertheless, it is possible to obtain a reasonable diurnal cycle
1124of the SST knowning only short wave flux (SWF) at high frequency \citep{Bernie_al_CD07}.
1125Furthermore, only the knowledge of daily mean value of SWF is needed,
1126as higher frequency variations can be reconstructed from them, assuming that
1127the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle
1128of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available
1129in \NEMO by setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when using
1130CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or the flux formulation (\np{ln\_flx}\forcode{ = .true.}).
1131The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used
1132can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily
1133mean incomming SWF as the reconstructed SWF at a given time step is the mean value
1134of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1135The use of diurnal cycle reconstruction requires the input SWF to be daily
1136($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1137Furthermore, it is recommended to have a least 8 surface module time step per day,
1138that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$. An example of recontructed SWF
1139is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle, one every 2~hours
1140(from 1am to 11pm).
1143\begin{figure}[!t]  \begin{center}
1145\caption{ \protect\label{fig:SBC_dcy}   
1146Example of recontruction of the diurnal cycle variation of short wave flux 
1147from daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1148The display is on (i,j) plane. }
1149\end{center}   \end{figure}
1152Note also that the setting a diurnal cycle in SWF is highly recommended  when
1153the top layer thickness approach 1~m or less, otherwise large error in SST can
1154appear due to an inconsistency between the scale of the vertical resolution
1155and the forcing acting on that scale.
1157% -------------------------------------------------------------------------------------------------------------
1158%        Rotation of vector pairs onto the model grid directions
1159% -------------------------------------------------------------------------------------------------------------
1160\subsection{Rotation of vector pairs onto the model grid directions}
1163When using a flux (\np{ln\_flx}\forcode{ = .true.}) or bulk (\np{ln\_clio}\forcode{ = .true.} or \np{ln\_core}\forcode{ = .true.}) formulation,
1164pairs of vector components can be rotated from east-north directions onto the local grid directions. 
1165This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
1166relative to a rectilinear grid.
1167To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1168The eastward component must start with "U" and the northward component with "V". 
1169The remaining characters in the strings are used to identify which pair of components go together.
1170So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
1171and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
1172and so on.
1173The extra characters used in the strings are arbitrary.
1174The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1176% -------------------------------------------------------------------------------------------------------------
1177%        Surface restoring to observed SST and/or SSS
1178% -------------------------------------------------------------------------------------------------------------
1179\subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1185IOptions are defined through the  \ngn{namsbc\_ssr} namelist variables.
1186n forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}), a
1187feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1188\begin{equation} \label{eq:sbc_dmp_q}
1189Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1191where SST is a sea surface temperature field (observed or climatological), $T$ is
1192the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
1193coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
1194mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1195This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
1196equal to $Q_o$.
1198In the fresh water budget, a feedback term can also be added. Converted into an
1199equivalent freshwater flux, it takes the following expression :
1201\begin{equation} \label{eq:sbc_dmp_emp}
1202\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1203                                             {\left.S\right|_{k=1}}
1206where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an
1207atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
1208interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
1209$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
1210feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
1211physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as the atmosphere
1212does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring
1213term should be viewed as a flux correction on freshwater fluxes to reduce the
1214uncertainties we have on the observed freshwater budget.
1216% -------------------------------------------------------------------------------------------------------------
1217%        Handling of ice-covered area
1218% -------------------------------------------------------------------------------------------------------------
1219\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1222The presence at the sea surface of an ice covered area modifies all the fluxes
1223transmitted to the ocean. There are several way to handle sea-ice in the system
1224depending on the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist. 
1226\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
1227This is a typical namelist value used for tropical ocean domain. The surface fluxes
1228are simply specified for an ice-free ocean. No specific things is done for sea-ice.
1229\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
1230is used. An observed ice covered area is read in a file. Below this area, the SST is
1231restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
1232in the northern (southern) hemisphere. The associated modification of the freshwater
1233fluxes are done in such a way that the change in buoyancy fluxes remains zero.
1234This prevents deep convection to occur when trying to reach the freezing point
1235(and so ice covered area condition) while the SSS is too large. This manner of
1236managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if} 
1237model. It can be found in the \mdl{sbcice{\_}if} module.
1238\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
1239ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
1240each model cell to provide the surface ocean fluxes. Note that the activation of a
1241sea-ice model is is done by defining a CPP key (\key{lim3} or \key{cice}).
1242The activation automatically overwrites the read value of nn{\_}ice to its appropriate
1243value ($i.e.$ $2$ for LIM-3 or $3$ for CICE).
1246% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1248\subsection{Interface to CICE (\protect\mdl{sbcice\_cice})}
1251It is now possible to couple a regional or global NEMO configuration (without AGRIF) to the CICE sea-ice
1252model by using \key{cice}.  The CICE code can be obtained from
1253\href{}{LANL} and the additional 'hadgem3' drivers will be required,
1254even with the latest code release.  Input grid files consistent with those used in NEMO will also be needed,
1255and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used (seek advice from UKMO
1256if necessary).  Currently the code is only designed to work when using the CORE forcing option for NEMO (with
1257\textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE name-list), or alternatively when NEMO
1258is coupled to the HadGAM3 atmosphere model (with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}).
1259The code is intended to be used with \np{nn\_fsbc} set to 1 (although coupling ocean and ice less frequently
1260should work, it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly - the
1261user should check that results are not significantly different to the standard case).
1263There are two options for the technical coupling between NEMO and CICE.  The standard version allows
1264complete flexibility for the domain decompositions in the individual models, but this is at the expense of global
1265gather and scatter operations in the coupling which become very expensive on larger numbers of processors. The
1266alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that the domain decomposition is
1267identical in both models (provided domain parameters are set appropriately, and
1268\textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and allows
1269much more efficient direct coupling on individual processors.  This solution scales much better although it is at
1270the expense of having more idle CICE processors in areas where there is no sea ice.
1272% -------------------------------------------------------------------------------------------------------------
1273%        Freshwater budget control
1274% -------------------------------------------------------------------------------------------------------------
1275\subsection{Freshwater budget control (\protect\mdl{sbcfwb})}
1278For global ocean simulation it can be useful to introduce a control of the mean sea
1279level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
1280in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
1282\item[\np{nn\_fwb}\forcode{ = 0}]  no control at all. The mean sea level is free to drift, and will
1283certainly do so.
1284\item[\np{nn\_fwb}\forcode{ = 1}]  global mean \textit{emp} set to zero at each model time step.
1285%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).
1286\item[\np{nn\_fwb}\forcode{ = 2}]  freshwater budget is adjusted from the previous year annual
1287mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
1288Boussinesq approximation, the annual mean fresh water budget is simply evaluated
1289from the change in the mean sea level at January the first and saved in the
1290\textit{EMPav.dat} file.
1293% -------------------------------------------------------------------------------------------------------------
1294%        Neutral Drag Coefficient from external wave model
1295% -------------------------------------------------------------------------------------------------------------
1296\subsection[Neutral drag coeff. from external wave model (\protect\mdl{sbcwave})]
1297            {Neutral drag coefficient from external wave model (\protect\mdl{sbcwave})}
1303In order to read a neutral drag coefficient, from an external data source ($i.e.$ a wave model), the
1304logical variable \np{ln\_cdgw} in \ngn{namsbc} namelist must be set to \forcode{.true.}.
1305The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the
1306namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all
1307the miscellanous options allowed by Input Data generic Interface see \autoref{sec:SBC_input})
1308and a 2D field of neutral drag coefficient.
1309Then using the routine TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided,
1310the drag coefficient is computed according to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
1313% Griffies doc:
1314% When running ocean-ice simulations, we are not explicitly representing land processes,
1315% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1316% it is important to balance the hydrological cycle in ocean-ice models.
1317% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1318% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1319% a chosen time scale.
1320%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1321% so that there is always a zero net input of water to the ocean-ice system.
1322% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1323% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1324% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1325% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1326% and ice models when aiming to balance the hydrological cycle.
1327% 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,
1328% not the water in any one sub-component. As an extreme example to illustrate the issue,
1329% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1330% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1331% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1332% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1333% in ocean-ice models.
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