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1% ================================================================
2% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)
3% ================================================================
4\chapter{Surface Boundary Condition (SBC, ISF, ICB) }
9$\ $\newline    % force a new ligne
13$\ $\newline    % force a new ligne
15The ocean needs six fields as surface boundary condition:
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 $\left( {\textit{emp}} \right)$
20   \item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
22plus an optional field:
24   \item the atmospheric pressure at the ocean surface $\left( p_a \right)$
27Five different ways to provide the first six fields to the ocean are available which
28are controlled by namelist \ngn{namsbc} variables: an analytical formulation (\np{ln\_ana}~=~true),
29a flux formulation (\np{ln\_flx}~=~true), a bulk formulae formulation (CORE
30(\np{ln\_blk\_core}~=~true), CLIO (\np{ln\_blk\_clio}~=~true) or MFS
31\footnote { Note that MFS bulk formulae compute fluxes only for the ocean component}
32(\np{ln\_blk\_mfs}~=~true) bulk formulae) and a coupled or mixed forced/coupled formulation
33(exchanges with a atmospheric model via the OASIS coupler) (\np{ln\_cpl} or \np{ln\_mixcpl}~=~true).
34When used ($i.e.$ \np{ln\_apr\_dyn}~=~true), the atmospheric pressure forces both ocean and ice dynamics.
36The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist 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.
45In addition, the resulting fields can be further modified using several namelist options.
46These options control
48\item the rotation of vector components supplied relative to an east-north
49coordinate system onto the local grid directions in the model ;
50\item the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true) ;
51\item the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model) (\np{nn\_ice}~=~0,1, 2 or 3) ;
52\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ;
53\item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false)
54or as fluxes applied at the land-ice ocean interface (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true) ;
55\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ;
56\item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ;
57and a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}~=~true).
59The latter option is possible only in case core or mfs bulk formulas are selected.
61In this chapter, we first discuss where the surface boundary condition appears in the
62model equations. Then we present the five ways of providing the surface boundary condition,
63followed by the description of the atmospheric pressure and the river runoff.
64Next the scheme for interpolation on the fly is described.
65Finally, the different options that further modify the fluxes applied to the ocean are discussed.
66One of these is modification by icebergs (see \S\ref{ICB_icebergs}), which act as drifting sources of fresh water.
67Another example of modification is that due to the ice shelf melting/freezing (see \S\ref{SBC_isf}),
68which provides additional sources of fresh water.
71% ================================================================
72% Surface boundary condition for the ocean
73% ================================================================
74\section{Surface boundary condition for the ocean}
77The surface ocean stress is the stress exerted by the wind and the sea-ice
78on the ocean. It is applied in \mdl{dynzdf} module as a surface boundary condition of the
79computation of the momentum vertical mixing trend (see \eqref{Eq_dynzdf_sbc} in \S\ref{DYN_zdf}).
80As such, it has to be provided as a 2D vector interpolated
81onto the horizontal velocity ocean mesh, $i.e.$ resolved onto the model
82(\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
84The surface heat flux is decomposed into two parts, a non solar and a solar heat
85flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
86of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes
87plus the heat content of the mass exchange with the atmosphere and sea-ice).
88It is applied in \mdl{trasbc} module as a surface boundary condition trend of
89the first level temperature time evolution equation (see \eqref{Eq_tra_sbc} 
90and \eqref{Eq_tra_sbc_lin} in \S\ref{TRA_sbc}).
91The latter 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}=\textit{true}.
93The way the light penetrates inside the water column is generally a sum of decreasing
94exponentials (see \S\ref{TRA_qsr}).
96The surface freshwater budget is provided by the \textit{emp} field.
97It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation)
98and possibly with the sea-ice and ice shelves (freezing minus melting of ice).
99It affects both the ocean in two different ways:
100$(i)$   it changes the volume of the ocean and therefore appears in the sea surface height
101equation as a volume flux, and
102$(ii)$  it changes the surface temperature and salinity through the heat and salt contents
103of the mass exchanged with the atmosphere, the sea-ice and the ice shelves.
106%\colorbox{yellow}{Miss: }
108%A extensive description of all namsbc namelist (parameter that have to be
111%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
112%ssv) i.e. information required by flux computation or sea-ice
114%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
115%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
117%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
119%Fluxes update only each nn{\_}fsbc time step (namsbc) explain relation
120%between nn{\_}fsbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
123%Explain here all the namlist namsbc variable{\ldots}.
125% explain : use or not of surface currents
127%\colorbox{yellow}{End Miss }
129The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
130the surface currents, temperature and salinity. 
131These variables are averaged over \np{nn\_fsbc} time-step (\ref{Tab_ssm}),
132and it is these averaged fields which are used to computes the surface fluxes
133at a frequency of \np{nn\_fsbc} time-step.
137\begin{table}[tb]   \begin{center}   \begin{tabular}{|l|l|l|l|}
139Variable description             & Model variable  & Units  & point \\  \hline
140i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
141j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
142Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
143Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
145\caption{  \label{Tab_ssm}   
146Ocean variables provided by the ocean to the surface module (SBC).
147The variable are averaged over nn{\_}fsbc time step, $i.e.$ the frequency of
148computation of surface fluxes.}
149\end{center}   \end{table}
152%\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
155% ================================================================
156%       Input Data
157% ================================================================
158\section{Input Data generic interface}
161A generic interface has been introduced to manage the way input data (2D or 3D fields,
162like surface forcing or ocean T and S) are specify in \NEMO. This task is archieved by fldread.F90.
163The module was design with four main objectives in mind:
165\item optionally provide a time interpolation of the input data at model time-step,
166whatever their input frequency is, and according to the different calendars available in the model.
167\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
168\item make the run duration independent from the period cover by the input files.
169\item provide a simple user interface and a rather simple developer interface by limiting the
170 number of prerequisite information.
173As a results the user have only to fill in for each variable a structure in the namelist file
174to defined the input data file and variable names, the frequency of the data (in hours or months),
175whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
176and three additional parameters for on-the-fly interpolation. When adding a new input variable,
177the developer has to add the associated structure in the namelist, read this information
178by mirroring the namelist read in \rou{sbc\_blk\_init} for example, and simply call \rou{fld\_read} 
179to obtain the desired input field at the model time-step and grid points.
181The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
182(see \S\ref{SBC_fldread}), the period it cover is one year, month, week or day, and, if on-the-fly
183interpolation is used, a file of weights must be supplied (see \S\ref{SBC_iof}).
185Note that when an input data is archived on a disc which is accessible directly
186from the workspace where the code is executed, then the use can set the \np{cn\_dir} 
187to the pathway leading to the data. By default, the data are assumed to have been
188copied so that cn\_dir='./'.
190% -------------------------------------------------------------------------------------------------------------
191% Input Data specification (\mdl{fldread})
192% -------------------------------------------------------------------------------------------------------------
193\subsection{Input Data specification (\mdl{fldread})}
196The structure associated with an input variable contains the following information:
197\begin{alltt}  {{\tiny   
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      !
205\item[File name]: the stem name of the NetCDF file to be open.
206This stem will be completed automatically by the model, with the addition of a '.nc' at its end
207and by date information and possibly a prefix (when using AGRIF).
208Tab.\ref{Tab_fldread} provides the resulting file name in all possible cases according to whether
209it is a climatological file or not, and to the open/close frequency (see below for definition).
216                         & daily or weekLLL          & monthly                   &   yearly          \\   \hline
217clim = false   & fn\_yYYYYmMMdDD  &   fn\_yYYYYmMM   &   fn\_yYYYY  \\   \hline
218clim = true       & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
221\caption{ \label{Tab_fldread}   naming nomenclature for climatological or interannual input file,
222as a function of the Open/close frequency. The stem name is assumed to be 'fn'.
223For 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
224actual year/month/day, always coded with 4 or 2 digits. Note that (1) in mpp, if the file is split
225over each subdomain, the suffix '.nc' is replaced by '\', where 'PPPP' is the
226process number coded with 4 digits; (2) when using AGRIF, the prefix
227'\_N' is added to files,
228where 'N'  is the child grid number.}
233\item[Record frequency]: the frequency of the records contained in the input file.
234Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
235(for example -1 for monthly forcing or -12 for annual forcing).
236Note that this frequency must really be an integer and not a real.
237On some computers, seting it to '24.' can be interpreted as 240!
239\item[Variable name]: the name of the variable to be read in the input NetCDF file.
241\item[Time interpolation]: a logical to activate, or not, the time interpolation. If set to 'false',
242the forcing will have a steplike shape remaining constant during each forcing period.
243For example, when using a daily forcing without time interpolation, the forcing remaining
244constant from 00h00'00'' to 23h59'59". If set to 'true', the forcing will have a broken line shape.
245Records are assumed to be dated the middle of the forcing period.
246For example, when using a daily forcing with time interpolation, linear interpolation will
247be performed between mid-day of two consecutive days.
249\item[Climatological forcing]: a logical to specify if a input file contains climatological forcing
250which can be cycle in time, or an interannual forcing which will requires additional files
251if the period covered by the simulation exceed the one of the file. See the above the file
252naming strategy which impacts the expected name of the file to be opened.
254\item[Open/close frequency]: the frequency at which forcing files must be opened/closed.
255Four cases are coded: 'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week),
256'monthly' and 'yearly' which means the forcing files will contain data for one day, one week,
257one month or one year. Files are assumed to contain data from the beginning of the open/close period.
258For example, the first record of a yearly file containing daily data is Jan 1st even if the experiment
259is not starting at the beginning of the year.
261\item[Others]: 'weights filename', 'pairing rotation' and 'land/sea mask' are associted with on-the-fly interpolation
262which is described in \S\ref{SBC_iof}.
266Additional remarks:\\
267(1) The time interpolation is a simple linear interpolation between two consecutive records of
268the input data. The only tricky point is therefore to specify the date at which we need to do
269the interpolation and the date of the records read in the input files.
270Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the
271time step. For example, for an experiment starting at 0h00'00" with a one hour time-step,
272a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
273However, for forcing data related to the surface module, values are not needed at every
274time-step but at every \np{nn\_fsbc} time-step. For example with \np{nn\_fsbc}~=~3,
275the surface module will be called at time-steps 1, 4, 7, etc. The date used for the time interpolation
276is thus redefined to be at the middle of \np{nn\_fsbc} time-step period. In the previous example,
277this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
278(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file
279calendar. The calendar associated with the forcing field is build according to the information
280provided by user in the record frequency, the open/close frequency and the type of temporal interpolation.
281For example, the first record of a yearly file containing daily data that will be interpolated in time
282is assumed to be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
283(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file
284when interpolating data with the first (last) record of the open/close period.
285For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
286the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values
287between Dec 31st 12h00'00" and Jan 1st 12h00'00". If the forcing is climatological, Dec and Jan will
288be keep-up from the same year. However, if the forcing is not climatological, at the end of the
289open/close period the code will automatically close the current file and open the next one.
290Note that, if the experiment is starting (ending) at the beginning (end) of an open/close period
291we do accept that the previous (next) file is not existing. In this case, the time interpolation
292will be performed between two identical values. For example, when starting an experiment on
293Jan 1st of year Y with yearly files and daily data to be interpolated, we do accept that the file
294related to year Y-1 is not existing. The value of Jan 1st will be used as the missing one for
295Dec 31st of year Y-1. If the file of year Y-1 exists, the code will read its last record.
296Therefore, this file can contain only one record corresponding to Dec 31st, a useful feature for
297user considering that it is too heavy to manipulate the complete file for year Y-1.
300% -------------------------------------------------------------------------------------------------------------
301% Interpolation on the Fly
302% -------------------------------------------------------------------------------------------------------------
303\subsection [Interpolation on-the-Fly] {Interpolation on-the-Fly}
306Interpolation on the Fly allows the user to supply input files required
307for the surface forcing on grids other than the model grid.
308To do this he or she must supply, in addition to the source data file,
309a file of weights to be used to interpolate from the data grid to the model grid.
310The original development of this code used the SCRIP package (freely available
311\href{}{here} under a copyright agreement).
312In principle, any package can be used to generate the weights, but the
313variables in the input weights file must have the same names and meanings as
314assumed by the model.
315Two methods are currently available: bilinear and bicubic interpolation.
316Prior to the interpolation, providing a land/sea mask file, the user can decide to
317 remove land points from the input file and substitute the corresponding values
318with the average of the 8 neighbouring points in the native external grid.
319 Only "sea points" are considered for the averaging. The land/sea mask file must
320be provided in the structure associated with the input variable.
321 The netcdf land/sea mask variable name must be 'LSM' it must have the same
322horizontal and vertical dimensions of the associated variable and should
323be equal to 1 over land and 0 elsewhere.
324The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.
325Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied.
327\subsubsection{Bilinear Interpolation}
330The input weights file in this case has two sets of variables: src01, src02,
331src03, src04 and wgt01, wgt02, wgt03, wgt04.
332The "src" variables correspond to the point in the input grid to which the weight
333"wgt" is to be applied. Each src value is an integer corresponding to the index of a
334point in the input grid when written as a one dimensional array.  For example, for an input grid
335of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
336There are four of each variable because bilinear interpolation uses the four points defining
337the grid box containing the point to be interpolated.
338All of these arrays are on the model grid, so that values src01(i,j) and
339wgt01(i,j) are used to generate a value for point (i,j) in the model.
341Symbolically, the algorithm used is:
344f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
346where function idx() transforms a one dimensional index src(k) into a two dimensional index,
347and wgt(1) corresponds to variable "wgt01" for example.
349\subsubsection{Bicubic Interpolation}
352Again there are two sets of variables: "src" and "wgt".
353But in this case there are 16 of each.
354The symbolic algorithm used to calculate values on the model grid is now:
356\begin{equation*} \begin{split}
357f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}     
358              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
359              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }   
360              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
363The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
368To activate this option, a non-empty string should be supplied in the weights filename column
369of the relevant namelist; if this is left as an empty string no action is taken.
370In the model, weights files are read in and stored in a structured type (WGT) in the fldread
371module, as and when they are first required.
372This initialisation procedure determines whether the input data grid should be treated
373as cyclical or not by inspecting a global attribute stored in the weights input file.
374This attribute must be called "ew\_wrap" and be of integer type.
375If it is negative, the input non-model grid is assumed not to be cyclic.
376If zero or greater, then the value represents the number of columns that overlap.
377$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
378if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
379If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
380In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and therefore the grid
381is assumed to be cyclic with no overlapping columns.
382(In fact this only matters when bicubic interpolation is required.)
383Note that no testing is done to check the validity in the model, since there is no way
384of knowing the name used for the longitude variable,
385so it is up to the user to make sure his or her data is correctly represented.
387Next the routine reads in the weights.
388Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise
389bilinear interpolation is used. The WGT structure includes dynamic arrays both for
390the storage of the weights (on the model grid), and when required, for reading in
391the variable to be interpolated (on the input data grid).
392The size of the input data array is determined by examining the values in the "src"
393arrays to find the minimum and maximum i and j values required.
394Since bicubic interpolation requires the calculation of gradients at each point on the grid,
395the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
396When the array of points from the data file is adjacent to an edge of the data grid,
397the halo is either a copy of the row/column next to it (non-cyclical case), or is a copy
398of one from the first few columns on the opposite side of the grid (cyclical case).
404\item  The case where input data grids are not logically rectangular has not been tested.
405\item  This code is not guaranteed to produce positive definite answers from positive definite inputs
406          when a bicubic interpolation method is used.
407\item  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
408\item  The gradients across the ends of a cyclical grid assume that the grid spacing between
409          the two columns involved are consistent with the weights used.
410\item  Neither interpolation scheme is conservative. (There is a conservative scheme available
411          in SCRIP, but this has not been implemented.)
417% to be completed
418A set of utilities to create a weights file for a rectilinear input grid is available
419(see the directory NEMOGCM/TOOLS/WEIGHTS).
421% -------------------------------------------------------------------------------------------------------------
422% Standalone Surface Boundary Condition Scheme
423% -------------------------------------------------------------------------------------------------------------
424\subsection [Standalone Surface Boundary Condition Scheme] {Standalone Surface Boundary Condition Scheme}
431In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields
432and simply read them in from a previous run or receive them from OASIS. 
433For example:
436\item  Multiple runs of the model are required in code development to see the effect of different algorithms in
437       the bulk formulae.
438\item  The effect of different parameter sets in the ice model is to be examined.
439\item  Development of sea-ice algorithms or parameterizations.
440\item  spinup of the iceberg floats
441\item  ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}~=~\textit{true})
444The StandAlone Surface scheme provides this utility.
445Its options are defined through the \ngn{namsbc\_sas} namelist variables.
446A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
447However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0)
448In this configuration, a few routines in the standard model are overriden by new versions.
449Routines replaced are:
452\item \mdl{nemogcm} : This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90)
453       Since the ocean state is not calculated all associated initialisations have been removed.
454\item  \mdl{step} : The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
455\item  \mdl{sbcmod} : This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules
456       that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs).
457\item  \mdl{daymod} : No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions
458       have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user
459       must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
460\item  \mdl{stpctl} : Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
461\item  \mdl{diawri} : All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which
462       have been read in) are written along with relevant forcing and ice data.
465One new routine has been added:
468\item  \mdl{sbcsas} : This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface.
469       These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module,
470       the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level.
471       Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
475% Missing the description of the 2 following variables:
476%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field
477%   ln_read_frq = .false.    !  specify whether we must read frq or not
481% ================================================================
482% Analytical formulation (sbcana module)
483% ================================================================
484\section  [Analytical formulation (\textit{sbcana}) ]
485      {Analytical formulation (\mdl{sbcana} module) }
492The analytical formulation of the surface boundary condition is the default scheme.
493In this case, all the six fluxes needed by the ocean are assumed to
494be uniform in space. They take constant values given in the namelist
495\ngn{namsbc{\_}ana} by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
496\np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero.
497In addition, the wind is allowed to reach its nominal value within a given number
498of time steps (\np{nn\_tau000}).
500If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
501module can be modified to use another scheme. As an example,
502the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
503GYRE configuration (see GYRE configuration manual, in preparation).
506% ================================================================
507% Flux formulation
508% ================================================================
509\section  [Flux formulation (\textit{sbcflx}) ]
510      {Flux formulation (\mdl{sbcflx} module) }
516In the flux formulation (\np{ln\_flx}=true), the surface boundary
517condition fields are directly read from input files. The user has to define
518in the namelist \ngn{namsbc{\_}flx} the name of the file, the name of the variable
519read in the file, the time frequency at which it is given (in hours), and a logical
520setting whether a time interpolation to the model time step is required
521for this field. See \S\ref{SBC_fldread} for a more detailed description of the parameters.
523Note that in general, a flux formulation is used in associated with a
524restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
528% ================================================================
529% Bulk formulation
530% ================================================================
531\section  [Bulk formulation (\textit{sbcblk\_core}, \textit{sbcblk\_clio} or \textit{sbcblk\_mfs}) ]
532      {Bulk formulation \small{(\mdl{sbcblk\_core} \mdl{sbcblk\_clio} \mdl{sbcblk\_mfs} modules)} }
535In the bulk formulation, the surface boundary condition fields are computed
536using bulk formulae and atmospheric fields and ocean (and ice) variables.
538The atmospheric fields used depend on the bulk formulae used. Three bulk formulations
539are available : the CORE, the CLIO and the MFS bulk formulea. The choice is made by setting to true
540one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or  \np{ln\_mfs}.
542Note : in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
543Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over both
544an ocean and an ice surface.
546% -------------------------------------------------------------------------------------------------------------
547%        CORE Bulk formulea
548% -------------------------------------------------------------------------------------------------------------
549\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
550            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
556The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
557They have been designed to handle the CORE forcing, a mixture of NCEP
558reanalysis and satellite data. They use an inertial dissipative method to compute
559the turbulent transfer coefficients (momentum, sensible heat and evaporation)
560from the 10 meters wind speed, air temperature and specific humidity.
561This \citet{Large_Yeager_Rep04} dataset is available through the
562\href{}{GFDL web site}.
564Note that substituting ERA40 to NCEP reanalysis fields
565does not require changes in the bulk formulea themself.
566This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
568Options are defined through the  \ngn{namsbc\_core} namelist variables.
569The required 8 input fields are:
572\begin{table}[htbp]   \label{Tab_CORE}
576Variable desciption              & Model variable  & Units   & point \\    \hline
577i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
578j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
57910m air temperature              & tair      & \r{}$K$            & T   \\ \hline
580Specific humidity             & humi      & \%              & T \\      \hline
581Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
582Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
583Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
584Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
590Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean
591point ($u$- and $v$-points). It is simpler and faster (less fields to be read),
592but it is not the recommended method when the ocean grid size is the same
593or larger than the one of the input atmospheric fields.
595The  \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair},\np{sn\_humi},\np{sn\_prec}, \np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used (spatial and temporal interpolations).
597\np{cn\_dir} is the directory of location of bulk files
598\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
599\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
600\np{rn\_zu}: is the height of wind measurements (m)
601The multiplicative factors to activate (value is 1) or deactivate (value is 0) :
602\np{rn\_pfac} for precipitations (total and snow)
603\np{rn\_efac} for evaporation
604\np{rn\_vfac} for for ice/ocean velocities in the calculation of wind stress 
606% -------------------------------------------------------------------------------------------------------------
607%        CLIO Bulk formulea
608% -------------------------------------------------------------------------------------------------------------
609\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
610            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
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 \S\ref{SBC_fldread}).
647% -------------------------------------------------------------------------------------------------------------
648%        MFS Bulk formulae
649% -------------------------------------------------------------------------------------------------------------
650\subsection    [MFS Bulk formulea (\np{ln\_mfs}=true)]
651            {MFS Bulk formulea (\np{ln\_mfs}=true, \mdl{sbcblk\_mfs})}
657The MFS (Mediterranean Forecasting System) bulk formulae have been developed by
658 \citet{Castellari_al_JMS1998}.
659They have been designed to handle the ECMWF operational data and are currently
660in use in the MFS operational system \citep{Tonani_al_OS08}, \citep{Oddo_al_OS09}.
661The wind stress computation uses a drag coefficient computed according to \citet{Hellerman_Rosenstein_JPO83}.
662The surface boundary condition for temperature involves the balance between surface solar radiation,
663net long-wave radiation, the latent and sensible heat fluxes.
664Solar radiation is dependent on cloud cover and is computed by means of
665an astronomical formula \citep{Reed_JPO77}. Albedo monthly values are from \citet{Payne_JAS72} 
666as means of the values at $40^{o}N$ and $30^{o}N$ for the Atlantic Ocean (hence the same latitudinal
667band of the Mediterranean Sea). The net long-wave radiation flux
668\citep{Bignami_al_JGR95} is a function of
669air temperature, sea-surface temperature, cloud cover and relative humidity.
670Sensible heat and latent heat fluxes are computed by classical
671bulk formulae parameterised according to \citet{Kondo1975}.
672Details on the bulk formulae used can be found in \citet{Maggiore_al_PCE98} and \citet{Castellari_al_JMS1998}.
674Options are defined through the  \ngn{namsbc\_mfs} namelist variables.
675The required 7 input fields must be provided on the model Grid-T and  are:
677\item          Zonal Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windi})
678\item          Meridional Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windj})
679\item          Total Claud Cover (\%)  (\np{sn\_clc})
680\item          2m Air Temperature ($K$) (\np{sn\_tair})
681\item          2m Dew Point Temperature ($K$)  (\np{sn\_rhm})
682\item          Total Precipitation ${Kg} m^{-2} s^{-1}$ (\np{sn\_prec})
683\item          Mean Sea Level Pressure (${Pa}$) (\np{sn\_msl})
685% -------------------------------------------------------------------------------------------------------------
686% ================================================================
687% Coupled formulation
688% ================================================================
689\section  [Coupled formulation (\textit{sbccpl}) ]
690      {Coupled formulation (\mdl{sbccpl} module)}
696In the coupled formulation of the surface boundary condition, the fluxes are
697provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
698while sea and ice surface temperature, ocean and ice albedo, and ocean currents
699are sent to the atmospheric component.
701A generalised coupled interface has been developed.
702It is currently interfaced with OASIS-3-MCT (\key{oasis3}).
703It has been successfully used to interface \NEMO to most of the European atmospheric
705as well as to \href{}{WRF} (Weather Research and Forecasting Model).
707Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
708The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are
709actually recieved by the ice-ocean system (no calculation of ice sublimation in coupled mode).
710When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
711the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}. In this case,
712CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system (and need to be activated in \ngn{namsbc{\_}cpl} ).
714The namelist above allows control of various aspects of the coupling fields (particularly for
715vectors) and now allows for any coupling fields to have multiple sea ice categories (as required by LIM3
716and CICE).  When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be
717determined by the number used in the sea ice model.  In some limited cases it may be possible to specify
718single category coupling fields even when the sea ice model is running with multiple categories - in this
719case the user should examine the code to be sure the assumptions made are satisfactory.  In cases where
720this is definitely not possible the model should abort with an error message.  The new code has been tested using
721ECHAM with LIM2, and HadGAM3 with CICE but although it will compile with \key{lim3} additional minor code changes
722may be required to run using LIM3.
725% ================================================================
726%        Atmospheric pressure
727% ================================================================
728\section   [Atmospheric pressure (\textit{sbcapr})]
729         {Atmospheric pressure (\mdl{sbcapr})}
735The optional atmospheric pressure can be used to force ocean and ice dynamics
736(\np{ln\_apr\_dyn}~=~true, \textit{\ngn{namsbc}} namelist ).
737The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
738can be interpolated in time to the model time step, and even in space when the
739interpolation on-the-fly is used. When used to force the dynamics, the atmospheric
740pressure is further transformed into an equivalent inverse barometer sea surface height,
741$\eta_{ib}$, using:
742\begin{equation} \label{SBC_ssh_ib}
743   \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
745where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
746A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. In this case $P_o$ 
747is set to the value of $P_{atm}$ averaged over the ocean domain, $i.e.$ the mean value of
748$\eta_{ib}$ is kept to zero at all time step.
750The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation
751(see \mdl{dynspg} for the ocean). For sea-ice, the sea surface height, $\eta_m$,
752which is provided to the sea ice model is set to $\eta - \eta_{ib}$ (see \mdl{sbcssr} module).
753$\eta_{ib}$ can be set in the output. This can simplify altimetry data and model comparison
754as inverse barometer sea surface height is usually removed from these date prior to their distribution.
756When using time-splitting and BDY package for open boundaries conditions, the equivalent
757inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
758\np{ln\_apr\_obc}  might be set to true.
760% ================================================================
761%        Tidal Potential
762% ================================================================
763\section   [Tidal Potential (\textit{sbctide})]
764                        {Tidal Potential (\mdl{sbctide})}
771A module is available to compute the tidal potential and use it in the momentum equation.
772This option is activated when \key{tide} is defined.
774Some parameters are available in namelist \ngn{nam\_tide}:
776- \np{ln\_tide\_pot} activate the tidal potential forcing
778- \np{nb\_harmo} is the number of constituent used
780- \np{clname} is the name of constituent
782The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem;
783they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\
785The potential astronomical expressed, for the three types of tidal frequencies
786following, by : \\
787Tide long period :
791diurnal Tide :
793\Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k})
795Semi-diurnal tide:
801$A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave
802$k$ to Greenwich.
804We make corrections to the astronomical potential.
805We obtain :
807\Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi)
809with $k$ a number of Love estimated to 0.6 which parameterised the astronomical tidal land,
810and $h$ a number of Love to 0.3 which parameterised the parameterisation due to the astronomical tidal land.
812% ================================================================
813%        River runoffs
814% ================================================================
815\section   [River runoffs (\textit{sbcrnf})]
816         {River runoffs (\mdl{sbcrnf})}
822%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
823%Many models, however, have traditionally inserted river runoff to the top model cell.
824%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
825%throughout a nonzero depth has been motivated by the numerical and physical problems
826%that arise when the top grid cells are of the order of one meter. This situation is common in
827%coastal modelling and becomes more and more often open ocean and climate modelling
828%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
829%required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
832%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
833%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
834%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
835%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
836%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
837%emp or emps and the changes made are below:
841River runoff generally enters the ocean at a nonzero depth rather than through the surface.
842Many models, however, have traditionally inserted river runoff to the top model cell.
843This was the case in \NEMO prior to the version 3.3, and was combined with an option
844to increase vertical mixing near the river mouth.
846However, with this method numerical and physical problems arise when the top grid cells are
847of the order of one meter. This situation is common in coastal modelling and is becoming
848more common in open ocean and climate modelling
849\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
850required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
852As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth, and for the
853temperature and salinity of the river to effect the surrounding ocean.
854The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, along with the   
855depth (in metres) which the river should be added to.
857Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and \np{ln\_rnf\_temp} control whether
858the river attributes (depth, salinity and temperature) are read in and used.  If these are set
859as false the river is added to the surface box only, assumed to be fresh (0~psu), and/or
860taken as surface temperature respectively.
862The runoff value and attributes are read in in sbcrnf. 
863For temperature -999 is taken as missing data and the river temperature is taken to be the
864surface temperatue at the river point.
865For the depth parameter a value of -1 means the river is added to the surface box only,
866and a value of -999 means the river is added through the entire water column.
867After being read in the temperature and salinity variables are multiplied by the amount of runoff (converted into m/s)
868to give the heat and salt content of the river runoff.
869After the user specified depth is read ini, the number of grid boxes this corresponds to is
870calculated and stored in the variable \np{nz\_rnf}.
871The variable \textit{h\_dep} is then calculated to be the depth (in metres) of the bottom of the
872lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model).
875If the depth information is not provide in the NetCDF file, it can be estimate from the runoff input file at the initial time-step, by setting the namelist parameter \np{ln\_rnf\_depth\_ini} to true.
877This estimation is a simple linear relation between the runoff and a given depth :
879h\_dep  = \frac{rn\_dep\_max} {rn\_rnf\_max}  rnf
881where  \np{rn\_dep\_max} is the given maximum depth over which the runoffs is spread,
882 \np{rn\_rnf\_max} is the maximum value of the runoff climatologie over the global domain
883and rnf is the maximum value in time of the runoff climatology at each grid cell (computed online).
885The estimated depth array can be output if needed in a NetCDF file by setting the namelist parameter \np{nn\_rnf\_depth\_file} to 1.
887The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence
888(\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
889This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
890The sea surface height is calculated using the sum of the horizontal divergence terms, and so the
891river runoff indirectly forces an increase in sea surface height.
893The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
894This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
895The heat and salt content of the river runoff is not included in this step, and so the tracer
896concentrations are diluted as water of ocean temperature and salinity is moved upward out of the box
897and replaced by the same volume of river water with no corresponding heat and salt addition.
899For the linear free surface case, at the surface box the tracer advection causes a flux of water
900(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.
901As such the volume of water does not change, but the water is diluted.
903For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
904Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water
905is added with no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
906(The runoff addition to the top box along with the water being moved up through boxes below means the surface box has a large
907increase in volume, whilst all other boxes remain the same size)
909In trasbc the addition of heat and salt due to the river runoff is added.
910This is done in the same way for both vvl and non-vvl.
911The temperature and salinity are increased through the specified depth according to the heat and salt content of the river.
913In the non-linear free surface case (vvl), near the end of the time step the change in sea surface height is redistrubuted
914through the grid boxes, so that the original ratios of grid box heights are restored.
915In 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.
917It 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.
918When 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.
921%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
923%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
925%\colorbox{yellow}{river mouths{\ldots}}
927%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
928%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
931%\gmcomment{  word doc of runoffs:
933%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.
934%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. 
936%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
938%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:
941% ================================================================
942%        Ice shelf melting
943% ================================================================
944\section   [Ice shelf melting (\textit{sbcisf})]
945                        {Ice shelf melting (\mdl{sbcisf})}
950Namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation used.
953The ice shelf cavity is represented. The fwf and heat flux are computed. Two different bulk formula are available:
954   \begin{description}
955   \item[\np{nn\_isfblk}~=~1]
956   The bulk formula used to compute the melt is based the one described in \citet{Hunter2006}.
957        This formulation is based on a balance between the upward ocean heat flux and the latent heat flux at the ice shelf base.
959   \item[\np{nn\_isfblk}~=~2] 
960   The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}.
961        This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation).
962   \end{description}
964For this 2 bulk formulations, there are 3 different ways to compute the exchange coeficient:
965   \begin{description}
966        \item[\np{nn\_gammablk~=~0~}]
967   The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}
969   \item[\np{nn\_gammablk~=~1~}]
970   The salt and heat exchange coefficients are velocity dependent and defined as $\np{rn\_gammas0} \times u_{*}$ and $\np{rn\_gammat0} \times u_{*}$
971        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
972        See \citet{Jenkins2010} for all the details on this formulation.
974   \item[\np{nn\_gammablk~=~2~}]
975   The salt and heat exchange coefficients are velocity and stability dependent and defined as
976        $\gamma_{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}$
977        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
978        $\Gamma_{Turb}$ the contribution of the ocean stability and
979        $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
980        See \citet{Holland1999} for all the details on this formulation.
981        \end{description}
984A parameterisation of isf is used. The ice shelf cavity is not represented.
985The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL)
986(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}~=~3).
987Furthermore the fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting.
988The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
991A simple parameterisation of isf is used. The ice shelf cavity is not represented.
992The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between the depth of the average grounding line (GL)
993(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
994The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
997The ice shelf cavity is opened. However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
998The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\
1002$\bullet$ \np{nn\_isf}~=~1 and \np{nn\_isf}~=~2 compute a melt rate based on the water mass properties, ocean velocities and depth.
1003 This flux is thus highly dependent of the model resolution (horizontal and vertical), realism of the water masses onto the shelf ...\\
1006$\bullet$ \np{nn\_isf}~=~3 and \np{nn\_isf}~=~4 read the melt rate from a file. You have total control of the fwf forcing.
1007This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too
1008coarse to have realistic melting or for studies where you need to control your heat and fw input.\\ 
1010Two namelist parameters control how the heat and fw fluxes are passed to NEMO: \np{rn\_hisf\_tbl} and \np{ln\_divisf}
1012\item[\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}.
1013This parameter is only used if \np{nn\_isf}~=~1 or \np{nn\_isf}~=~4
1014It allows you to control over which depth you want to spread the heat and fw fluxes.
1016If \np{rn\_hisf\_tbl} = 0.0, the fluxes are put in the top level whatever is its tickness.
1018If \np{rn\_hisf\_tbl} $>$ 0.0, the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells).
1020\item[\np{ln\_divisf}] is a flag to apply the fw flux as a volume flux or as a salt flux.
1022\np{ln\_divisf}~=~true applies the fwf as a volume flux. This volume flux is implemented with in the same way as for the runoff.
1023The fw addition due to the ice shelf melting is, at each relevant depth level, added to the horizontal divergence
1024(\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}.
1025See the runoff section \ref{SBC_rnf} for all the details about the divergence correction.
1027\np{ln\_divisf}~=~false applies the fwf and heat flux directly on the salinity and temperature tendancy.
1029\item[\np{ln\_conserve}] is a flag for \np{nn\_isf}~=~1. A conservative boundary layer scheme as described in \citet{Jenkins2001} 
1030is used if \np{ln\_conserve}=true. It takes into account the fact that the melt water is at freezing T and needs to be warm up to ocean temperature.
1031It is only relevant for \np{ln\_divisf}~=~false.
1032If \np{ln\_divisf}~=~true, \np{ln\_conserve} has to be set to false to avoid a double counting of the contribution.
1036% ================================================================
1037%        Handling of icebergs
1038% ================================================================
1039\section{Handling of icebergs (ICB)}
1045Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}.
1046Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ).
1047(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO).
1048Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described
1049in the \ngn{namberg} namelist:
1050\np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1051Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs
1052of this class are being described as one lagrangian point (this reduces the numerical problem of tracking every single iceberg).
1053They are enabled by setting \np{ln\_icebergs}~=~true.
1055Two initialisation schemes are possible.
1058In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1059(so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each
1060grid point of which an iceberg is generated at the beginning of the run.
1061(Note that this happens each time the timestep equals \np{nn\_nit000}.)
1062\np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners
1063of the geographical box: lonmin,lonmax,latmin,latmax
1065In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
1066This should be a file with a field on the configuration grid (typically ORCA) representing ice accumulation rate at each model point.
1067These should be ocean points adjacent to land where icebergs are known to calve.
1068Most points in this input grid are going to have value zero.
1069When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1070At 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).
1071Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling).
1072If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1075Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1076The latter act to disintegrate the iceberg. This is either all melted freshwater, or
1077(if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1078which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1079Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
1081Extensive diagnostics can be produced.
1082Separate output files are maintained for human-readable iceberg information.
1083A separate file is produced for each processor (independent of \np{ln\_ctl}).
1084The amount of information is controlled by two integer parameters:
1086\item[\np{nn\_verbose\_level}]  takes a value between one and four and represents
1087an increasing number of points in the code at which variables are written, and an
1088increasing level of obscurity.
1089\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1092Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1093A non-zero value represents how many timesteps between writes of information into the output file.
1094These output files are in NETCDF format.
1095When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1096Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1097So care is needed to recreate data for individual icebergs, since its trajectory data may be spread across
1098multiple files.
1101% ================================================================
1102% Miscellanea options
1103% ================================================================
1104\section{Miscellaneous options}
1107% -------------------------------------------------------------------------------------------------------------
1108%        Diurnal cycle
1109% -------------------------------------------------------------------------------------------------------------
1110\subsection   [Diurnal  cycle (\textit{sbcdcy})]
1111         {Diurnal cycle (\mdl{sbcdcy})}
1118\begin{figure}[!t]    \begin{center}
1120\caption{ \label{Fig_SBC_diurnal}   
1121Example of recontruction of the diurnal cycle variation of short wave flux 
1122from daily mean values. The reconstructed diurnal cycle (black line) is chosen
1123as the mean value of the analytical cycle (blue line) over a time step, not
1124as the mid time step value of the analytically cycle (red square). From \citet{Bernie_al_CD07}.}
1125\end{center}   \end{figure}
1128\cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of
1129SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution
1130of the surface fluxes of 3~h or less. Unfortunately high frequency forcing fields are rare,
1131not to say inexistent. Nevertheless, it is possible to obtain a reasonable diurnal cycle
1132of the SST knowning only short wave flux (SWF) at high frequency \citep{Bernie_al_CD07}.
1133Furthermore, only the knowledge of daily mean value of SWF is needed,
1134as higher frequency variations can be reconstructed from them, assuming that
1135the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle
1136of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available
1137in \NEMO by setting \np{ln\_dm2dc}~=~true (a \textit{\ngn{namsbc}} namelist variable) when using
1138CORE bulk formulea (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).
1139The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used
1140can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily
1141mean incomming SWF as the reconstructed SWF at a given time step is the mean value
1142of the analytical cycle over this time step (Fig.\ref{Fig_SBC_diurnal}).
1143The use of diurnal cycle reconstruction requires the input SWF to be daily
1144($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1145Furthermore, it is recommended to have a least 8 surface module time step per day,
1146that is  $\rdt \ \np{nn\_fsbc} < 10,800~s = 3~h$. An example of recontructed SWF
1147is given in Fig.\ref{Fig_SBC_dcy} for a 12 reconstructed diurnal cycle, one every 2~hours
1148(from 1am to 11pm).
1151\begin{figure}[!t]  \begin{center}
1153\caption{ \label{Fig_SBC_dcy}   
1154Example of recontruction of the diurnal cycle variation of short wave flux 
1155from daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1156The display is on (i,j) plane. }
1157\end{center}   \end{figure}
1160Note also that the setting a diurnal cycle in SWF is highly recommended  when
1161the top layer thickness approach 1~m or less, otherwise large error in SST can
1162appear due to an inconsistency between the scale of the vertical resolution
1163and the forcing acting on that scale.
1165% -------------------------------------------------------------------------------------------------------------
1166%        Rotation of vector pairs onto the model grid directions
1167% -------------------------------------------------------------------------------------------------------------
1168\subsection{Rotation of vector pairs onto the model grid directions}
1171When using a flux (\np{ln\_flx}=true) or bulk (\np{ln\_clio}=true or \np{ln\_core}=true) formulation,
1172pairs of vector components can be rotated from east-north directions onto the local grid directions. 
1173This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
1174relative to a rectilinear grid.
1175To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1176The eastward component must start with "U" and the northward component with "V". 
1177The remaining characters in the strings are used to identify which pair of components go together.
1178So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
1179and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
1180and so on.
1181The extra characters used in the strings are arbitrary.
1182The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1184% -------------------------------------------------------------------------------------------------------------
1185%        Surface restoring to observed SST and/or SSS
1186% -------------------------------------------------------------------------------------------------------------
1187\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
1188         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
1194IOptions are defined through the  \ngn{namsbc\_ssr} namelist variables.
1195n forced mode using a flux formulation (\np{ln\_flx}~=~true), a
1196feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1197\begin{equation} \label{Eq_sbc_dmp_q}
1198Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1200where SST is a sea surface temperature field (observed or climatological), $T$ is
1201the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
1202coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
1203mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1204This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
1205equal to $Q_o$.
1207In the fresh water budget, a feedback term can also be added. Converted into an
1208equivalent freshwater flux, it takes the following expression :
1210\begin{equation} \label{Eq_sbc_dmp_emp}
1211\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1212                                             {\left.S\right|_{k=1}}
1215where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an
1216atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
1217interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
1218$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
1219feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
1220physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
1221does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring
1222term should be viewed as a flux correction on freshwater fluxes to reduce the
1223uncertainties we have on the observed freshwater budget.
1225% -------------------------------------------------------------------------------------------------------------
1226%        Handling of ice-covered area
1227% -------------------------------------------------------------------------------------------------------------
1228\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1231The presence at the sea surface of an ice covered area modifies all the fluxes
1232transmitted to the ocean. There are several way to handle sea-ice in the system
1233depending on the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist. 
1235\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
1236This is a typical namelist value used for tropical ocean domain. The surface fluxes
1237are simply specified for an ice-free ocean. No specific things is done for sea-ice.
1238\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
1239is used. An observed ice covered area is read in a file. Below this area, the SST is
1240restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
1241in the northern (southern) hemisphere. The associated modification of the freshwater
1242fluxes are done in such a way that the change in buoyancy fluxes remains zero.
1243This prevents deep convection to occur when trying to reach the freezing point
1244(and so ice covered area condition) while the SSS is too large. This manner of
1245managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if} 
1246model. It can be found in the \mdl{sbcice{\_}if} module.
1247\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
1248ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
1249each model cell to provide the surface ocean fluxes. Note that the activation of a
1250sea-ice model is is done by defining a CPP key (\key{lim2}, \key{lim3} or \key{cice}).
1251The activation automatically overwrites the read value of nn{\_}ice to its appropriate
1252value ($i.e.$ $2$ for LIM-2, $3$ for LIM-3 or $4$ for CICE).
1255% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1257\subsection   [Interface to CICE (\textit{sbcice\_cice})]
1258         {Interface to CICE (\mdl{sbcice\_cice})}
1261It is now possible to couple a regional or global NEMO configuration (without AGRIF) to the CICE sea-ice
1262model by using \key{cice}.  The CICE code can be obtained from
1263\href{}{LANL} and the additional 'hadgem3' drivers will be required,
1264even with the latest code release.  Input grid files consistent with those used in NEMO will also be needed,
1265and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used (seek advice from UKMO
1266if necessary).  Currently the code is only designed to work when using the CORE forcing option for NEMO (with
1267\textit{calc\_strair~=~true} and \textit{calc\_Tsfc~=~true} in the CICE name-list), or alternatively when NEMO
1268is coupled to the HadGAM3 atmosphere model (with \textit{calc\_strair~=~false} and \textit{calc\_Tsfc~=~false}).
1269The code is intended to be used with \np{nn\_fsbc} set to 1 (although coupling ocean and ice less frequently
1270should work, it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly - the
1271user should check that results are not significantly different to the standard case).
1273There are two options for the technical coupling between NEMO and CICE.  The standard version allows
1274complete flexibility for the domain decompositions in the individual models, but this is at the expense of global
1275gather and scatter operations in the coupling which become very expensive on larger numbers of processors. The
1276alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that the domain decomposition is
1277identical in both models (provided domain parameters are set appropriately, and
1278\textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and allows
1279much more efficient direct coupling on individual processors.  This solution scales much better although it is at
1280the expense of having more idle CICE processors in areas where there is no sea ice.
1282% -------------------------------------------------------------------------------------------------------------
1283%        Freshwater budget control
1284% -------------------------------------------------------------------------------------------------------------
1285\subsection   [Freshwater budget control (\textit{sbcfwb})]
1286         {Freshwater budget control (\mdl{sbcfwb})}
1289For global ocean simulation it can be useful to introduce a control of the mean sea
1290level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
1291in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
1293\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
1294certainly do so.
1295\item[\np{nn\_fwb}=1]  global mean \textit{emp} set to zero at each model time step.
1296%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).
1297\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
1298mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
1299Boussinesq approximation, the annual mean fresh water budget is simply evaluated
1300from the change in the mean sea level at January the first and saved in the
1301\textit{EMPav.dat} file.
1304% -------------------------------------------------------------------------------------------------------------
1305%        Neutral Drag Coefficient from external wave model
1306% -------------------------------------------------------------------------------------------------------------
1307\subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})]
1308              {Neutral drag coefficient from external wave model (\mdl{sbcwave})}
1314In order to read a neutral drag coeff, from an external data source ($i.e.$ a wave model), the
1315logical variable \np{ln\_cdgw} in \ngn{namsbc} namelist must be set to \textit{true}.
1316The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the
1317namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all
1318the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input})
1319and a 2D field of neutral drag coefficient.
1320Then using the routine TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided,
1321the drag coefficient is computed according to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
1324% Griffies doc:
1325% When running ocean-ice simulations, we are not explicitly representing land processes,
1326% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1327% it is important to balance the hydrological cycle in ocean-ice models.
1328% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1329% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1330% a chosen time scale.
1331%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1332% so that there is always a zero net input of water to the ocean-ice system.
1333% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1334% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1335% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1336% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1337% and ice models when aiming to balance the hydrological cycle.
1338% 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,
1339% not the water in any one sub-component. As an extreme example to illustrate the issue,
1340% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1341% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1342% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1343% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1344% in ocean-ice models.
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