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5\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
12\paragraph{Changes record} ~\\
15  \begin{tabularx}{\textwidth}{l||X|X}
16    Release & Author(s) & Modifications \\
17    \hline
18    {\em   4.0} & {\em ...} & {\em ...} \\
19    {\em   3.6} & {\em ...} & {\em ...} \\
20    {\em   3.4} & {\em ...} & {\em ...} \\
21    {\em <=3.4} & {\em ...} & {\em ...}
22  \end{tabularx}
28  \nlst{namsbc}
29  \caption{\forcode{&namsbc}}
30  \label{lst:namsbc}
33The ocean needs seven fields as surface boundary condition:
36\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
37\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
38\item the surface freshwater budget $\left( {\textit{emp}} \right)$
39\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
40\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
43Four different ways are available to provide the seven fields to the ocean. They are controlled by
44namelist \nam{sbc}{sbc} variables:
47\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms,
48\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
49\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
50(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
51\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
54The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
56When the fields are supplied from data files (bulk, flux and mixed formulations),
57the input fields do not need to be supplied on the model grid.
58Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
59the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
60If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
61should be masked or filled to avoid spurious results in proximity of the coasts, as
62large sea-land gradients characterize most of the atmospheric variables.
64In addition, the resulting fields can be further modified using several namelist options.
65These options control:
68\item the rotation of vector components supplied relative to an east-north coordinate system onto
69  the local grid directions in the model,
70\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
71\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
72\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
73  (\np[=0..3]{nn_ice}{nn\_ice}),
74\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
75\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
76  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
77\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
78  (\np[=0..2]{nn_fwb}{nn\_fwb}),
79\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
80  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
81\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
82\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
83\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
84\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
85\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
86\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
87\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
88\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
89\item the atmospheric surface pressure gradient effect on ocean and ice dynamics (\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn} with namelist \nam{sbc_apr}{sbc\_apr}),
90\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
93In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
94Then we present the three ways of providing the surface boundary conditions,
95followed by the description of the atmospheric pressure and the river runoff.
96Next, the scheme for interpolation on the fly is described.
97Finally, the different options that further modify the fluxes applied to the ocean are discussed.
98One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
99which act as drifting sources of fresh water.
100Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
101which provides additional sources of fresh water.
103%% =================================================================================================
104\section{Surface boundary condition for the ocean}
107The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
108It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
109the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
110As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
111\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
113The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
114$Q_{ns}$ and $Q_{sr}$, respectively.
115The former is the non penetrative part of the heat flux
116(\ie\ the sum of sensible, latent and long wave heat fluxes plus
117the heat content of the mass exchange between the ocean and sea-ice).
118It is applied in \mdl{trasbc} module as a surface boundary condition trend of
119the first level temperature time evolution equation
120(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
121The latter is the penetrative part of the heat flux.
122It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
124The way the light penetrates inside the water column is generally a sum of decreasing exponentials
125(see \autoref{subsec:TRA_qsr}).
127The surface freshwater budget is provided by the \textit{emp} field.
128It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
129possibly with the sea-ice and ice shelves (freezing minus melting of ice).
130It affects the ocean in two different ways:
131$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
132a volume flux, and
133$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
134the mass exchanged with atmosphere, sea-ice and ice shelves.
136%\colorbox{yellow}{Miss: }
137%A extensive description of all namsbc namelist (parameter that have to be
139%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
140%ssv) \ie\ information required by flux computation or sea-ice
141%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
142%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
143%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
144%Fluxes update only each nf\_sbc time step (namsbc) explain relation
145%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
147%Explain here all the namlist namsbc variable{\ldots}.
148% explain : use or not of surface currents
149%\colorbox{yellow}{End Miss }
151The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
152the surface currents, temperature and salinity.
153These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
154these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
157  \centering
158  \begin{tabular}{|l|l|l|l|}
159    \hline
160    Variable description                           & Model variable  & Units  & point                 \\
161    \hline
162    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
163    \hline
164    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
165    \hline
166    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
167    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
168  \end{tabular}
169  \caption[Ocean variables provided to the surface module)]{
170    Ocean variables provided to the surface module (\texttt{SBC}).
171    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
172    \ie\ the frequency of computation of surface fluxes.}
173  \label{tab:SBC_ssm}
176%\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
178%% =================================================================================================
179\section{Input data generic interface}
182A generic interface has been introduced to manage the way input data
183(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
184This task is achieved by \mdl{fldread}.
185The module is designed with four main objectives in mind:
187\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
188  and according to the different calendars available in the model.
189\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
190\item make the run duration independent from the period cover by the input files.
191\item provide a simple user interface and a rather simple developer interface by
192  limiting the number of prerequisite informations.
195As a result, the user has only to fill in for each variable a structure in the namelist file to
196define the input data file and variable names, the frequency of the data (in hours or months),
197whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
198and three additional parameters for the on-the-fly interpolation.
199When adding a new input variable, the developer has to add the associated structure in the namelist,
200read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
201and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
203The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
204(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
205if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
207Note that when an input data is archived on a disc which is accessible directly from the workspace where
208the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
209By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
211%% =================================================================================================
212\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
215The structure associated with an input variable contains the following information:
217!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
218!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
222\item [File name]: the stem name of the NetCDF file to be opened.
223  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
224  by date information and possibly a prefix (when using AGRIF).
225  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
226  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
227  \begin{table}[htbp]
228    \centering
229    \begin{tabular}{|l|c|c|c|}
230      \hline
231                                  &  daily or weekLL     &  monthly           &  yearly        \\
232      \hline
233      \np[=.false.]{clim}{clim} &  fn\  &  fn\   &  fn\  \\
234      \hline
235      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
236      \hline
237    \end{tabular}
238    \caption[Naming nomenclature for climatological or interannual input file]{
239      Naming nomenclature for climatological or interannual input file,
240      as a function of the open/close frequency.
241      The stem name is assumed to be 'fn'.
242      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
243      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
244      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
245      always coded with 4 or 2 digits.
246      Note that (1) in mpp, if the file is split over each subdomain,
247      the suffix '.nc' is replaced by '\',
248      where 'PPPP' is the process number coded with 4 digits;
249      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
250    }
251    \label{tab:SBC_fldread}
252  \end{table}
253\item [Record frequency]: the frequency of the records contained in the input file.
254  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
255  (for example -1 for monthly forcing or -12 for annual forcing).
256  Note that this frequency must REALLY be an integer and not a real.
257  On some computers, setting it to '24.' can be interpreted as 240!
258\item [Variable name]: the name of the variable to be read in the input NetCDF file.
259\item [Time interpolation]: a logical to activate, or not, the time interpolation.
260  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
261  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
262  00h00'00'' to 23h59'59".
263  If set to 'true', the forcing will have a broken line shape.
264  Records are assumed to be dated at the middle of the forcing period.
265  For example, when using a daily forcing with time interpolation,
266  linear interpolation will be performed between mid-day of two consecutive days.
267\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
268  or an interannual forcing which will requires additional files if
269  the period covered by the simulation exceeds the one of the file.
270  See the above file naming strategy which impacts the expected name of the file to be opened.
271\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
272  Four cases are coded:
273  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
274  means the forcing files will contain data for one day, one week, one month or one year.
275  Files are assumed to contain data from the beginning of the open/close period.
276  For example, the first record of a yearly file containing daily data is Jan 1st even if
277  the experiment is not starting at the beginning of the year.
278\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
279  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
282Additional remarks:\\
283(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
284The only tricky point is therefore to specify the date at which we need to do the interpolation and
285the date of the records read in the input files.
286Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
287For example, for an experiment starting at 0h00'00" with a one-hour time-step,
288a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
289However, for forcing data related to the surface module,
290values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
291For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
292The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
293In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
294(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
295The calendar associated with the forcing field is build according to the information provided by
296user in the record frequency, the open/close frequency and the type of temporal interpolation.
297For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
298start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
299(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
300interpolating data with the first (last) record of the open/close period.
301For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
302the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
303Dec 31st 12h00'00" and Jan 1st 12h00'00".
304If the forcing is climatological, Dec and Jan will be keep-up from the same year.
305However, if the forcing is not climatological, at the end of
306the open/close period, the code will automatically close the current file and open the next one.
307Note that, if the experiment is starting (ending) at the beginning (end) of
308an open/close period, we do accept that the previous (next) file is not existing.
309In this case, the time interpolation will be performed between two identical values.
310For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
311we do accept that the file related to year Y-1 is not existing.
312The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
313If the file of year Y-1 exists, the code will read its last record.
314Therefore, this file can contain only one record corresponding to Dec 31st,
315a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
317%% =================================================================================================
318\subsection{Interpolation on-the-fly}
321Interpolation on the Fly allows the user to supply input files required for the surface forcing on
322grids other than the model grid.
323To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
324interpolate from the data grid to the model grid.
325The original development of this code used the SCRIP package
326(freely available \href{}{here} under a copyright agreement).
327In principle, any package such as CDO can be used to generate the weights, but the variables in
328the input weights file must have the same names and meanings as assumed by the model.
329Two methods are currently available: bilinear and bicubic interpolations.
330Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
331the input file and substitute the corresponding values with the average of the 8 neighbouring points in
332the native external grid.
333Only "sea points" are considered for the averaging.
334The land/sea mask file must be provided in the structure associated with the input variable.
335The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
336the associated variables and should be equal to 1 over land and 0 elsewhere.
337The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
338Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
340%% =================================================================================================
341\subsubsection{Bilinear interpolation}
344The input weights file in this case has two sets of variables:
345src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
346The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
347Each src value is an integer corresponding to the index of a point in the input grid when
348written as a one dimensional array.
349For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
350There are four of each variable because bilinear interpolation uses the four points defining
351the grid box containing the point to be interpolated.
352All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
353generate a value for point (i,j) in the model.
355Symbolically, the algorithm used is:
357  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
359where function idx() transforms a one dimensional index src(k) into a two dimensional index,
360and wgt(1) corresponds to variable "wgt01" for example.
362%% =================================================================================================
363\subsubsection{Bicubic interpolation}
366Again, there are two sets of variables: "src" and "wgt".
367But in this case, there are 16 of each.
368The symbolic algorithm used to calculate values on the model grid is now:
371  \begin{split}
372    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
373    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
374    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
375    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
376  \end{split}
378The gradients here are taken with respect to the horizontal indices and not distances since
379the spatial dependency has been included into the weights.
381%% =================================================================================================
385To activate this option, a non-empty string should be supplied in
386the weights filename column of the relevant namelist;
387if this is left as an empty string no action is taken.
388In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
389as and when they are first required.
390This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
391inspecting a global attribute stored in the weights input file.
392This attribute must be called "ew\_wrap" and be of integer type.
393If it is negative, the input non-model grid is assumed to be not cyclic.
394If zero or greater, then the value represents the number of columns that overlap.
395$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
396if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
397If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
398In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
399therefore the grid is assumed to be cyclic with no overlapping columns.
400(In fact, this only matters when bicubic interpolation is required.)
401Note that no testing is done to check the validity in the model,
402since there is no way of knowing the name used for the longitude variable,
403so it is up to the user to make sure his or her data is correctly represented.
405Next the routine reads in the weights.
406Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
407The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
408and when required, for reading in the variable to be interpolated (on the input data grid).
409The size of the input data array is determined by examining the values in the "src" arrays to
410find the minimum and maximum i and j values required.
411Since bicubic interpolation requires the calculation of gradients at each point on the grid,
412the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
413When the array of points from the data file is adjacent to an edge of the data grid,
414the halo is either a copy of the row/column next to it (non-cyclical case),
415or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
417%% =================================================================================================
422\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
423\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
424  a bicubic interpolation method is used.
425\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
426\item The gradients across the ends of a cyclical grid assume that the grid spacing between
427  the two columns involved are consistent with the weights used.
428\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
429  but this has not been implemented.)
432%% =================================================================================================
436% to be completed
437A set of utilities to create a weights file for a rectilinear input grid is available
438(see the directory NEMOGCM/TOOLS/WEIGHTS).
440%% =================================================================================================
441\subsection{Standalone surface boundary condition scheme (SAS)}
445  \nlst{namsbc_sas}
446  \caption{\forcode{&namsbc_sas}}
447  \label{lst:namsbc_sas}
450In some circumstances, it may be useful to avoid calculating the 3D temperature,
451salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
452For example:
455\item Multiple runs of the model are required in code development to
456  see the effect of different algorithms in the bulk formulae.
457\item The effect of different parameter sets in the ice model is to be examined.
458\item Development of sea-ice algorithms or parameterizations.
459\item Spinup of the iceberg floats
460\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
463The Standalone Surface scheme provides this capacity.
464Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
465A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
466However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
467In this configuration, a few routines in the standard model are overriden by new versions.
468Routines replaced are:
471\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
472  Since the ocean state is not calculated all associated initialisations have been removed.
473\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
474\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
475  New surface modules that can function when only the surface level of the ocean state is defined can also be added
476  (\eg\ icebergs).
477\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
478  so calls to restart functions have been removed.
479  This also means that the calendar cannot be controlled by time in a restart file,
480  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
481\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
482\item \mdl{diawri}: All 3D data have been removed from the output.
483  The surface temperature, salinity and velocity components (which have been read in) are written along with
484  relevant forcing and ice data.
487One new routine has been added:
490\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
491  velocity arrays at the surface.
492  These filenames are supplied in namelist namsbc\_sas.
493  Unfortunately, because of limitations with the \mdl{iom} module,
494  the full 3D fields from the mean files have to be read in and interpolated in time,
495  before using just the top level.
496  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
499The user can also choose in the \nam{sbc_sas}{sbc\_sas} namelist to read the mean (nn\_fsbc time-step) fraction of solar net radiation absorbed in the 1st T level using
500 (\np[=.true.]{ln_flx}{ln\_flx}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln_flx}{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in.
502%% =================================================================================================
503\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
506% Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk
507% parameterization'' (i.e NCAR, COARE, ECMWF...)
510  \nlst{namsbc_flx}
511  \caption{\forcode{&namsbc_flx}}
512  \label{lst:namsbc_flx}
515In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
516the surface boundary condition fields are directly read from input files.
517The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
518the name of the variable read in the file, the time frequency at which it is given (in hours),
519and a logical setting whether a time interpolation to the model time step is required for this field.
520See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
522Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
523See \autoref{subsec:SBC_ssr} for its specification.
531%% =================================================================================================
534\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
537% L. Brodeau, December 2019...
540  \nlst{namsbc_blk}
541  \caption{\forcode{&namsbc_blk}}
542  \label{lst:namsbc_blk}
545If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea
546fluxes associated with surface boundary conditions are estimated by means of the
547traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed
548near-surface atmosphere state (typically extracted from a weather reanalysis)
549and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc}
552% Turbulent air-sea fluxes are computed using the sea surface properties and
553% atmospheric SSVs at height $z$ above the sea surface, with the traditional
554% aerodynamic bulk formulae:
556Note: all the NEMO Fortran routines involved in the present section have been
557 initially developed (and are still developed in parallel) in
558 the \href{}{\texttt{AeroBulk}} open-source project
561%%% Bulk formulae are this:
562\subsection{Bulk formulae}\label{subsec:SBC_blkform}
564In NEMO, the set of equations that relate each component of the surface fluxes
565to the near-surface atmosphere and sea surface states writes
568  \label{eq:SBC_bulk_form}
569  \begin{eqnarray}
570    \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
571    Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
572    E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
573    Q_L           &=& -L_v \, E \\
574    %
575    Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\
576    Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4)
577  \end{eqnarray}
581   \[ \theta_z \simeq T_z+\gamma z \]
582   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
584from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
586where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
587$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
590$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
591and longwave radiative fluxes, respectively.
593Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$
594implies a gain of the relevant quantity for the ocean, while a positive $E$
595implies a freshwater loss for the ocean.
597$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
598coefficients for momentum, sensible heat, and moisture, respectively.
600$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
601vaporization of water.
603$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
604and specific humidity of air at height $z$ above the sea surface,
605respectively. $\gamma z$ is a temperature correction term which accounts for the
606adiabatic lapse rate and approximates the potential temperature at height
607$z$ \citep{josey.gulev.ea_2013}.
609$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
610(possibly referenced to the surface current $\mathbf{u_0}$,
611section \ref{s_res1}.\ref{ss_current}).
613The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
614$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution.
616$a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\
618%$p_a$ is the mean sea-level pressure (SLP).
620$T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity
621of air at temperature $T_s$; it includes a 2\% reduction to account for the
622presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}.
623Depending on the bulk parametrization used, $T_s$ can either be the temperature
624at the air-sea interface (skin temperature, hereafter SSST) or at typically a
625few tens of centimeters below the surface (bulk sea surface temperature,
626hereafter SST).
628The SSST differs from the SST due to the contributions of two effects of
629opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL,
630respectively, see section\,\ref{subsec:SBC_skin}).
632Technically, when the ECMWF or COARE* bulk parametrizations are selected
633(\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}),
634$T_s$ is the SSST, as opposed to the NCAR bulk parametrization
635(\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature
636at first T-point level).
638For more details on all these aspects the reader is invited to refer
639to \citet{brodeau.barnier.ea_JPO17}.
643\subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean}
646Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae
647strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and
648$C_E$. They are estimated with what we refer to as a \emph{bulk
649parametrization} algorithm. When relevant, these algorithms also perform the
650height adjustment of humidity and temperature to the wind reference measurement
651height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}).
655For the open ocean, four bulk parametrization algorithms are available in NEMO:
657\item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09}
658\item COARE 3.0 \citep{fairall.bradley.ea_JC03}
659\item COARE 3.6 \citep{edson.jampana.ea_JPO13,fairall.blomquist_rpt18}
660\item ECMWF (IFS documentation, cy45)
664With respect to version 3, the principal advances in version 3.6 of the COARE
665bulk parametrization are built around improvements in the representation of the
666effects of waves on
667fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes
668improved relationships of surface roughness, and whitecap fraction on wave
669parameters. It is therefore recommended to chose version 3.6 over 3.
674\subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin}
675%\subsection[Cool-skin and warm-layer parameterizations
676%(\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})}
679As opposed to the NCAR bulk parametrization, more advanced bulk
680parametrizations such as COARE3.x and ECMWF are meant to be used with the skin
681temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
682the first T-point level, see section\,\ref{subsec:SBC_blkform}).
684As such, the relevant cool-skin and warm-layer parametrization must be
685activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs}
686and \np[=T]{ln_skin_wl}{ln\_skin\_wl} to use COARE3.x or ECMWF in a consistent
691For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same
692basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based
693on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.blomquist_rpt18} for COARE
696For the warm-layer scheme, ECMWF is based on \citet{zeng.beljaars_GRL05} with a
697recent update from \citet{takaya.bidlot.ea_JGR10} (consideration of the
698turbulence input from Langmuir circulation).
700Importantly, COARE warm-layer scheme \citep{fairall.blomquist_rpt18} includes a prognostic
701equation for the thickness of the warm-layer, while it is considered as constant
702in the ECWMF algorithm.
705  \centering
706  \includegraphics[width=0.96\textwidth]{SBC_dT_skin-SST}
707  \caption[Skin temperature]{Hourly difference between skin temperature and
708  bulk SST (1\,m deep) simulated by the NEMO \texttt{STATION\_ASF} test-case,
709  based on in-situ data from PAPA station (50.1\deg N, 144.9\deg W) in 2018; for
710  two different sets of ``bulk algorithm + cool-skin/warm-layer
711  parametrizations'': COARE 3.6 and ECMWF.}
712  \label{fig:SBC_dT_skin-SST}
720\subsection{Appropriate use of each bulk parametrization}
724NCAR bulk parametrizations (formerly known as CORE) is meant to be used with the
725CORE II atmospheric forcing \citep{large.yeager_CD09}. The expected sea surface
726temperature is the bulk SST. Hence the following namelist parameters must be
730  ...
731  ln_NCAR    = .true.
732  ...
733  rn_zqt     = 10.     ! Air temperature & humidity reference height (m)
734  rn_zu      = 10.     ! Wind vector reference height (m)
735  ...
736  ln_skin_cs = .false. ! use the cool-skin parameterization
737  ln_skin_wl = .false. ! use the warm-layer parameterization
738  ...
739  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
745With an atmospheric forcing based on a reanalysis of the ECMWF, such as the
746Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to
747use the ECMWF bulk parametrizations with the cool-skin and warm-layer
748parametrizations activated. In ECMWF reanalyzes, since air temperature and
749humidity are provided at the 2\,m height, and given that the humidity is
750distributed as the dew-point temperature, the namelist must be tuned as follows:
753  ...
754  ln_ECMWF   = .true.
755  ...     
756  rn_zqt     =  2.     ! Air temperature & humidity reference height (m)
757  rn_zu      = 10.     ! Wind vector reference height (m)
758  ...
759  ln_skin_cs = .true. ! use the cool-skin parameterization
760  ln_skin_wl = .true. ! use the warm-layer parameterization
761  ...
762  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
763  ...
766Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
767of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
768triggers the use of the ECMWF cool-skin and warm-layer parametrizations,
769respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
772\subsubsection{COARE 3.x}
774Since the ECMWF parametrization is largely based on the COARE* parametrization,
775the two algorithms are very similar in terms of structure and closure
776approach. As such, the namelist tuning for COARE 3.x is identical to that of
780  ...
781  ln_COARE3p6 = .true.
782  ...     
783  ln_skin_cs = .true. ! use the cool-skin parameterization
784  ln_skin_wl = .true. ! use the warm-layer parameterization
785  ...
788Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection
789of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
790triggers the use of the COARE cool-skin and warm-layer parametrizations,
791respectively (found in \textit{sbcblk\_skin\_coare.F90}).
798% In a typical bulk algorithm, the BTCs under neutral stability conditions are
799% defined using \emph{in-situ} flux measurements while their dependence on the
800% stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and
801% the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are
802% functions of the wind speed and the near-surface stability of the atmospheric
803% surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$
804% and $q_z$.
808\subsection{Prescribed near-surface atmospheric state}
810The atmospheric fields used depend on the bulk formulae used.  In forced mode,
811when a sea-ice model is used, a specific bulk formulation is used.  Therefore,
812different bulk formulae are used for the turbulent fluxes computation over the
813ocean and over sea-ice surface.
816%The choice is made by setting to true one of the following namelist
817%variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6}
818%and \np{ln_ECMWF}{ln\_ECMWF}.
820Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
821The required 9 input fields are:
824  \centering
825  \begin{tabular}{|l|c|c|c|}
826    \hline
827    Variable description                 & Model variable & Units              & point \\
828    \hline
829    i-component of the 10m air velocity  & wndi           & $m.s^{-1}$         & T     \\
830    \hline
831    j-component of the 10m air velocity  & wndj           & $m.s^{-1}$         & T     \\
832    \hline
833    10m air temperature                  & tair           & $K$               & T     \\
834    \hline
835    Specific humidity                    & humi           & $-$               & T     \\
836    Relative humidity                    & ~              & $\%$              & T     \\
837    Dew-point temperature                & ~              & $K$               & T     \\   
838    \hline
839    Downwelling longwave radiation       & qlw            & $W.m^{-2}$         & T     \\
840    \hline
841    Downwelling shortwave radiation      & qsr            & $W.m^{-2}$         & T     \\
842    \hline
843    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
844    \hline
845    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
846    \hline
847    Mean sea-level pressure              & slp            & $hPa$              & T     \\
848    \hline
849    \end{tabular}
850  \label{tab:SBC_BULK}
853Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
854It is simpler and faster (less fields to be read), but it is not the recommended method when
855the ocean grid size is the same or larger than the one of the input atmospheric fields.
857The \np{sn_wndi}{sn\_wndi}, \np{sn_wndj}{sn\_wndj}, \np{sn_qsr}{sn\_qsr}, \np{sn_qlw}{sn\_qlw}, \np{sn_tair}{sn\_tair}, \np{sn_humi}{sn\_humi}, \np{sn_prec}{sn\_prec},
858\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
859(spatial and temporal interpolations).
861\np{cn_dir}{cn\_dir} is the directory of location of bulk files
862%\np{ln_taudif}{ln\_taudif} is the flag to specify if we use High Frequency (HF) tau information (.true.) or not (.false.)
863\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
864\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
866Three multiplicative factors are available:
867\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
868increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
869The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
870the calculation of surface wind stress.
871Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
873As for the flux parametrization, information about the input data required by the model is provided in
874the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
877\subsubsection{Air humidity}
879Air humidity can be provided as three different parameters: specific humidity
880[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
895%% =================================================================================================
896%\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare3p0.F90, sbcblk\_algo\_coare3p6.F90, %sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare3p0}, %\mdl{sbcblk\_algo\_coare3p6}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}
899%Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
900%COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
901%their neutral transfer coefficients relationships with neutral wind.
903%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
904%  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
905%  They use an inertial dissipative method to compute the turbulent transfer coefficients
906%  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
907%  This \citet{large.yeager_rpt04} dataset is available through
908%  the \href{}{GFDL web site}.
909%  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
910%  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
911%\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
912%\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details
913%\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{}{IFS (Cy40r1)} %implementation and documentation.
914%  Surface roughness lengths needed for the Obukhov length are computed
915%  following \citet{beljaars_QJRMS95}.
918%% =================================================================================================
919\subsection{Ice-Atmosphere Bulk formulae}
924 For sea-ice, three possibilities can be selected:
925a constant transfer coefficient (1.4e-3; default
926value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
927and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
933Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
936\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
937  default constant value used for momentum and heat neutral transfer coefficients
938\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
939  This scheme adds a dependency on edges at leads, melt ponds and flows
940  of the constant neutral air-ice drag. After some approximations,
941  this can be resumed to a dependency on ice concentration (A).
942  This drag coefficient has a parabolic shape (as a function of ice concentration)
943  starting at 1.5e-3 for A=0, reaching 1.97e-3 for A=0.5 and going down 1.4e-3 for A=1.
944  It is theoretically applicable to all ice conditions (not only MIZ).
945\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
946  Alternative turbulent transfer coefficients formulation between sea-ice
947  and atmosphere with distinct momentum and heat coefficients depending
948  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
949  The parameterization is adapted from ECHAM6 atmospheric model.
950  Compared to Lupkes2012 scheme, it considers specific skin and form drags
951  to compute neutral transfer coefficients for both heat and momentum fluxes.
952  Atmospheric stability effect on transfer coefficient is also taken into account.
955%% =================================================================================================
956\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
960  \nlst{namsbc_cpl}
961  \caption{\forcode{&namsbc_cpl}}
962  \label{lst:namsbc_cpl}
965In the coupled formulation of the surface boundary condition,
966the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
967while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
968the atmospheric component.
970A generalised coupled interface has been developed.
971It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
972An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
973It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
974(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{}{WRF}
975(Weather Research and Forecasting Model).
977When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
978the whole carbon cycle is computed.
979In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
980(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
982The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
983now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
984When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
985the number used in the sea ice model.
986In some limited cases, it may be possible to specify single category coupling fields even when
987the sea ice model is running with multiple categories -
988in this case, the user should examine the code to be sure the assumptions made are satisfactory.
989In cases where this is definitely not possible, the model should abort with an error message.
991%% =================================================================================================
992\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
996  \nlst{namsbc_apr}
997  \caption{\forcode{&namsbc_apr}}
998  \label{lst:namsbc_apr}
1001The optional atmospheric pressure can be used to force ocean and ice dynamics
1002(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
1003The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
1004can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
1005When used to force the dynamics, the atmospheric pressure is further transformed into
1006an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
1008  % \label{eq:SBC_ssh_ib}
1009  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
1011where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
1012A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
1013In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
1014\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
1016The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
1017For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
1018(see \mdl{sbcssr} module).
1019$\eta_{ib}$ can be written in the output.
1020This can simplify altimetry data and model comparison as
1021inverse barometer sea surface height is usually removed from these date prior to their distribution.
1023When using time-splitting and BDY package for open boundaries conditions,
1024the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
1025\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
1027%% =================================================================================================
1028\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
1032  \nlst{nam_tide}
1033  \caption{\forcode{&nam_tide}}
1034  \label{lst:nam_tide}
1037The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
1038is activated if \np{ln_tide}{ln\_tide} and \np{ln_tide_pot}{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{_tide}{\_tide}.
1039This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
1041  % \label{eq:SBC_PE_dyn_tides}
1042  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
1043  +g\nabla (\Pi_{eq} + \Pi_{sal})
1045where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
1046$\Pi_{sal}$ is a self-attraction and loading term (SAL).
1048The equilibrium tidal forcing is expressed as a sum over a subset of
1049constituents chosen from the set of available tidal constituents
1050defined in file \hf{SBC/tide} (this comprises the tidal
1051constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
1052  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
1053constituents are selected by including their names in the array
1054\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
1055\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
1056and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
1057\forcode{.true.}, the equilibrium tidal forcing can be ramped up
1058linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
1059model run.
1061The SAL term should in principle be computed online as it depends on
1062the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
1063discussion about the practical implementation of this term).
1064Nevertheless, the complex calculations involved would make this
1065computationally too expensive. Here, two options are available:
1066$\Pi_{sal}$ generated by an external model can be read in
1067(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
1068used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
1070  \Pi_{sal} = \beta \eta,
1072where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
1073spatially constant scalar, often chosen to minimize tidal prediction
1074errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
1075\forcode{.false.} removes the SAL contribution.
1077%% =================================================================================================
1078\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
1082  \nlst{namsbc_rnf}
1083  \caption{\forcode{&namsbc_rnf}}
1084  \label{lst:namsbc_rnf}
1087%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1088%Many models, however, have traditionally inserted river runoff to the top model cell.
1089%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
1090%throughout a nonzero depth has been motivated by the numerical and physical problems
1091%that arise when the top grid cells are of the order of one meter. This situation is common in
1092%coastal modelling and becomes more and more often open ocean and climate modelling
1093%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
1094%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
1096%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
1097%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
1098%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
1099%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
1100%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
1101%emp or emps and the changes made are below:
1104River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1105Many models, however, have traditionally inserted river runoff to the top model cell.
1106This was the case in \NEMO\ prior to the version 3.3,
1107and was combined with an option to increase vertical mixing near the river mouth.
1109However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
1110This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
1112  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
1113  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
1114  see also \autoref{fig:SBC_dcy}.}.
1116As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
1117and for the temperature and salinity of the river to effect the surrounding ocean.
1118The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
1119along with the depth (in metres) which the river should be added to.
1121Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
1122\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
1123If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
1124and/or taken as surface temperature respectively.
1126The runoff value and attributes are read in in sbcrnf.
1127For temperature -999 is taken as missing data and the river temperature is taken to
1128be the surface temperatue at the river point.
1129For the depth parameter a value of -1 means the river is added to the surface box only,
1130and a value of -999 means the river is added through the entire water column.
1131After being read in the temperature and salinity variables are multiplied by the amount of runoff
1132(converted into m/s) to give the heat and salt content of the river runoff.
1133After the user specified depth is read ini,
1134the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
1135The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
1136the bottom of the lowest box the river water is being added to
1137(\ie\ the total depth that river water is being added to in the model).
1139The mass/volume addition due to the river runoff is, at each relevant depth level, added to
1140the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
1141This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
1142The sea surface height is calculated using the sum of the horizontal divergence terms,
1143and so the river runoff indirectly forces an increase in sea surface height.
1145The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
1146This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
1147The heat and salt content of the river runoff is not included in this step,
1148and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
1149the box and replaced by the same volume of river water with no corresponding heat and salt addition.
1151For the linear free surface case, at the surface box the tracer advection causes a flux of water
1152(of equal volume to the runoff) through the sea surface out of the domain,
1153which causes a salt and heat flux out of the model.
1154As such the volume of water does not change, but the water is diluted.
1156For the non-linear free surface case, no flux is allowed through the surface.
1157Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
1158no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
1159(The runoff addition to the top box along with the water being moved up through
1160boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
1162In trasbc the addition of heat and salt due to the river runoff is added.
1163This is done in the same way for both vvl and non-vvl.
1164The temperature and salinity are increased through the specified depth according to
1165the heat and salt content of the river.
1167In the non-linear free surface case (vvl),
1168near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
1169so that the original ratios of grid box heights are restored.
1170In doing this water is moved into boxes below, throughout the water column,
1171so the large volume addition to the surface box is spread between all the grid boxes.
1173It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
1174\ie\ modelling the Baltic flow in and out of the North Sea.
1175When the flow is out of the domain there is no change in temperature and salinity,
1176regardless of the namelist options used,
1177as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
1179%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1181%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1183%\colorbox{yellow}{river mouths{\ldots}}
1185%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1186%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1189\cmtgm{  word doc of runoffs:
1190In the current \NEMO\ setup river runoff is added to emp fluxes,
1191these are then applied at just the sea surface as a volume change (in the variable volume case
1192this is a literal volume change, and in the linear free surface case the free surface is moved)
1193and a salt flux due to the concentration/dilution effect.
1194There is also an option to increase vertical mixing near river mouths;
1195this gives the effect of having a 3d river.
1196All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
1197at the same temperature as the sea surface.
1198Our aim was to code the option to specify the temperature and salinity of river runoff,
1199(as well as the amount), along with the depth that the river water will affect.
1200This would make it possible to model low salinity outflow, such as the Baltic,
1201and would allow the ocean temperature to be affected by river runoff.
1203The depth option makes it possible to have the river water affecting just the surface layer,
1204throughout depth, or some specified point in between.
1206To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
1207the \mdl{tra_sbc} module.
1208We decided to separate them throughout the code,
1209so that the variable emp represented solely evaporation minus precipitation fluxes,
1210and a new 2d variable rnf was added which represents the volume flux of river runoff
1211(in $kg/m^2s$ to remain consistent with $emp$).
1212This meant many uses of emp and emps needed to be changed,
1213a list of all modules which use $emp$ or $emps$ and the changes made are below:}
1215%% =================================================================================================
1216\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
1220  \nlst{namsbc_isf}
1221  \caption{\forcode{&namsbc_isf}}
1222  \label{lst:namsbc_isf}
1225The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
1226Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1227The different options are illustrated in \autoref{fig:SBC_isf}.
1230  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1231  The fwf and heat flux are depending of the local water properties.
1233  Two different bulk formulae are available:
1235  \begin{description}
1236  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
1237    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
1238  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
1239    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1240    A complete description is available in \citet{jenkins_JGR91}.
1241  \end{description}
1243  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1244  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
1245  The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m.
1246  Then, the fluxes are spread over the same thickness (ie over one or several cells).
1247  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature.
1248  This can lead to super-cool temperature in the top cell under melting condition.
1249  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
1251  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1252  There are 3 different ways to compute the exchange coeficient:
1253  \begin{description}
1254  \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}.
1255    \begin{gather*}
1256       % \label{eq:SBC_isf_gamma_iso}
1257      \gamma^{T} = rn\_gammat0 \\
1258      \gamma^{S} = rn\_gammas0
1259    \end{gather*}
1260    This is the recommended formulation for ISOMIP.
1261  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
1262    \begin{gather*}
1263      \gamma^{T} = rn\_gammat0 \times u_{*} \\
1264      \gamma^{S} = rn\_gammas0 \times u_{*}
1265    \end{gather*}
1266    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
1267    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1268  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1269    \[
1270      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1271    \]
1272    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
1273    $\Gamma_{Turb}$ the contribution of the ocean stability and
1274    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1275    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1276    This formulation has not been extensively tested in \NEMO\ (not recommended).
1277  \end{description}
1278\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1279  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1280  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1281  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1282  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
1283  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
1284\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1285  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1286  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
1287  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
1288  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1289\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1290  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
1291  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1292  As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl})
1295$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
1296the water mass properties, ocean velocities and depth.
1297This flux is thus highly dependent of the model resolution (horizontal and vertical),
1298realism of the water masses onto the shelf ...\\
1300$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
1301You have total control of the fwf forcing.
1302This can be useful if the water masses on the shelf are not realistic or
1303the resolution (horizontal/vertical) are too coarse to have realistic melting or
1304for studies where you need to control your heat and fw input.\\
1306The ice shelf melt is implemented as a volume flux as for the runoff.
1307The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1308the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1309See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1312  \centering
1313  \includegraphics[width=0.66\textwidth]{SBC_isf}
1314  \caption[Ice shelf location and fresh water flux definition]{
1315    Illustration of the location where the fwf is injected and
1316    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1317  \label{fig:SBC_isf}
1320%% =================================================================================================
1321\section{Ice sheet coupling}
1325  \nlst{namsbc_iscpl}
1326  \caption{\forcode{&namsbc_iscpl}}
1327  \label{lst:namsbc_iscpl}
1330Ice sheet/ocean coupling is done through file exchange at the restart step.
1331At each restart step:
1334\item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1335\item a new file is built using the DOMAINcfg tools.
1336\item \NEMO\ run for a specific period and output the average melt rate over the period.
1337\item the ice sheet model run using the melt rate outputed in step 4.
1338\item go back to 1.
1341If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1342potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1343The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1346\item [Thin a cell down]: T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1347  ($bt_b=bt_n$).
1348\item [Enlarge  a cell]: See case "Thin a cell down"
1349\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
1350  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1351\item [Wet a cell]: mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1352  If no neighbours, T/S is extrapolated from old top cell value.
1353  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1354\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1355\item [Wet a column]: set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1356  If no neighbour, T/S/U/V and mask set to 0.
1359Furthermore, as the before and now fields are not compatible (modification of the geometry),
1360the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1362The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1363It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1364the code will be unable to fill all the new wet cells properly.
1365The default number is set up for the MISOMIP idealised experiments.
1366This coupling procedure is able to take into account grounding line and calving front migration.
1367However, it is a non-conservative processe.
1368This could lead to a trend in heat/salt content and volume.\\
1370In order to remove the trend and keep the conservation level as close to 0 as possible,
1371a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1372The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1373A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1374For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1375The corrective increment is apply into the cell itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry).
1377%% =================================================================================================
1378\section{Handling of icebergs (ICB)}
1382  \nlst{namberg}
1383  \caption{\forcode{&namberg}}
1384  \label{lst:namberg}
1387Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1388Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1389(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1390Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1391described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1392Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1393which is an integer representing how many icebergs of this class are being described as one lagrangian point
1394(this reduces the numerical problem of tracking every single iceberg).
1395They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1397Two initialisation schemes are possible.
1399\item [{\np{nn_test_icebergs}{nn\_test\_icebergs}~$>$~0}] In this scheme, the value of \np{nn_test_icebergs}{nn\_test\_icebergs} represents the class of iceberg to generate
1400  (so between 1 and 10), and \np{nn_test_icebergs}{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1401  which an iceberg is generated at the beginning of the run.
1402  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1403  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1404  the geographical box: lonmin,lonmax,latmin,latmax
1405\item [{\np[=-1]{nn_test_icebergs}{nn\_test\_icebergs}}] In this scheme, the model reads a calving file supplied in the \np{sn_icb}{sn\_icb} parameter.
1406  This should be a file with a field on the configuration grid (typically ORCA)
1407  representing ice accumulation rate at each model point.
1408  These should be ocean points adjacent to land where icebergs are known to calve.
1409  Most points in this input grid are going to have value zero.
1410  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1411  At each time step, a test is performed to see if there is enough ice mass to
1412  calve an iceberg of each class in order (1 to 10).
1413  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1414  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1417Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1418The latter act to disintegrate the iceberg.
1419This is either all melted freshwater,
1420or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1421which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1422Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1424Extensive diagnostics can be produced.
1425Separate output files are maintained for human-readable iceberg information.
1426A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1427The amount of information is controlled by two integer parameters:
1429\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1430  represents an increasing number of points in the code at which variables are written,
1431  and an increasing level of obscurity.
1432\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1435Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1436A non-zero value represents how many timesteps between writes of information into the output file.
1437These output files are in NETCDF format.
1438When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1439Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1440So care is needed to recreate data for individual icebergs,
1441since its trajectory data may be spread across multiple files.
1443%% =================================================================================================
1444\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1448  \nlst{namsbc_wave}
1449  \caption{\forcode{&namsbc_wave}}
1450  \label{lst:namsbc_wave}
1453Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1454physical processes related to ocean surface waves, namely the surface stress modified by growth and
1455dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1456tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1457the wind stress.
1459Physical processes related to ocean surface waves can be accounted by setting the logical variable
1460\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1461different processes should be activated as explained in the following sections.
1463Wave fields can be provided either in forced or coupled mode:
1465\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1466for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1467Input Data generic Interface (see \autoref{sec:SBC_input}).
1468\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1469in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1472%% =================================================================================================
1473\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1476The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1477can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1478Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1479the drag coefficient is computed according to the stable/unstable conditions of the
1480air-sea interface following \citet{large.yeager_rpt04}.
1482%% =================================================================================================
1483\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1486The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1487It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1488and the current measured at a fixed point (Eulerian velocity).
1489As waves travel, the water particles that make up the waves travel in orbital motions but
1490without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1491at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1492An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1493representation of surface physics in ocean general circulation models. %GS: reference needed
1494The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1497  % \label{eq:SBC_wave_sdw}
1498  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1499  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1500  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1503where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1504$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1505$k$ is the mean wavenumber defined as:
1506$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1508In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1509and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1510To simplify, it is customary to use approximations to the full Stokes profile.
1511Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1512are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1513$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1514and makes possible the estimation of the surface Stokes drift for random directional waves in
1515realistic wave conditions:
1518\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1522  % \label{eq:SBC_wave_sdw_0a}
1523  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1526where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1529  % \label{eq:SBC_wave_sdw_0b}
1530  k_e = \frac{|\mathbf{U}_{\\right|_{z=0}}|} {|T_{st}|}
1531  \quad \text{and }\
1532  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1535where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1537\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1538reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1542  % \label{eq:SBC_wave_sdw_1}
1543  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1544  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1547where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1549\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1550but using the wave frequency from a wave model.
1554The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1555and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1558  % \label{eq:SBC_wave_eta_sdw}
1559  \frac{\partial{\eta}}{\partial{t}} =
1560  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1563The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1564for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1565that is induced by the three-dimensional Stokes velocity.
1566The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1567can be formulated as follows:
1570  % \label{eq:SBC_wave_tra_sdw}
1571  \frac{\partial{c}}{\partial{t}} =
1572  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1575%% =================================================================================================
1576\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1579In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1580in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1581This additional force may have impact on the Ekman turning of the surface current.
1582In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1583approximations described in \autoref{subsec:SBC_wave_sdw}),
1584\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1586%% =================================================================================================
1587\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1590The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1591into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1592available for forcing the mean circulation, while in the opposite case of a decaying sea
1593state, more momentum is available for forcing the ocean.
1594Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1595but in practice, an equilibrium sea state is a fairly rare event.
1596So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1599  % \label{eq:SBC_wave_tauoc}
1600  \tau_{oc,a} = \tau_a - \tau_w
1603where $\tau_a$ is the atmospheric surface stress;
1604$\tau_w$ is the atmospheric stress going into the waves defined as:
1607  % \label{eq:SBC_wave_tauw}
1608  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1611where: $c_p$ is the phase speed of the gravity waves,
1612$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1613the physics of ocean waves. The first one, $S_{in}$, describes the generation
1614of ocean waves by wind and therefore represents the momentum and energy transfer
1615from air to ocean waves; the second term $S_{nl}$ denotes
1616the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1617describes the dissipation of waves by processes such as white-capping, large scale breaking
1618eddy-induced damping.
1620The wave stress derived from an external wave model can be provided either through the normalized
1621wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1622meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1624%% =================================================================================================
1625\section{Miscellaneous options}
1628%% =================================================================================================
1629\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1633  \centering
1634  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
1635  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1636    Example of reconstruction of the diurnal cycle variation of short wave flux from
1637    daily mean values.
1638    The reconstructed diurnal cycle (black line) is chosen as
1639    the mean value of the analytical cycle (blue line) over a time step,
1640    not as the mid time step value of the analytically cycle (red square).
1641    From \citet{bernie.guilyardi.ea_CD07}.}
1642  \label{fig:SBC_diurnal}
1645\cite{bernie.woolnough.ea_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less.
1646%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1647Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at high frequency \citep{bernie.guilyardi.ea_CD07}.
1648Furthermore, only the knowledge of daily mean value of SWF is needed,
1649as higher frequency variations can be reconstructed from them,
1650assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1651The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1652setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1653using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1654the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1655The reconstruction is performed in the \mdl{sbcdcy} module.
1656The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1657The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1658a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1659The use of diurnal cycle reconstruction requires the input SWF to be daily
1660(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1661Furthermore, it is recommended to have a least 8 surface module time steps per day,
1662that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1663An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1664one every 2~hours (from 1am to 11pm).
1667  \centering
1668  \includegraphics[width=0.66\textwidth]{SBC_dcy}
1669  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1670    Example of reconstruction of the diurnal cycle variation of short wave flux from
1671    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1672    The display is on (i,j) plane.}
1673  \label{fig:SBC_dcy}
1676Note also that the setting a diurnal cycle in SWF is highly recommended when
1677the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1678an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1680%% =================================================================================================
1681\subsection{Rotation of vector pairs onto the model grid directions}
1684When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1685pairs of vector components can be rotated from east-north directions onto the local grid directions.
1686This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1687be defined relative to a rectilinear grid.
1688To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1689The eastward component must start with "U" and the northward component with "V".
1690The remaining characters in the strings are used to identify which pair of components go together.
1691So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1692rotate them on to the model grid directions;
1693"U2" and "V2" could be used against a second pair of components, and so on.
1694The extra characters used in the strings are arbitrary.
1695The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1697%% =================================================================================================
1698\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1702  \nlst{namsbc_ssr}
1703  \caption{\forcode{&namsbc_ssr}}
1704  \label{lst:namsbc_ssr}
1707Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1708On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1709a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1711  % \label{eq:SBC_dmp_q}
1712  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1714where SST is a sea surface temperature field (observed or climatological),
1715$T$ is the model surface layer temperature and
1716$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1717For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1718This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1720In the fresh water budget, a feedback term can also be added.
1721Converted into an equivalent freshwater flux, it takes the following expression :
1724  \label{eq:SBC_dmp_emp}
1725  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1726  {\left.S\right|_{k=1}}
1729where $\textit{emp}_{o }$ is a net surface fresh water flux
1730(observed, climatological or an atmospheric model product),
1731\textit{SSS}$_{Obs}$ is a sea surface salinity
1732(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1733$\left.S\right|_{k=1}$ is the model surface layer salinity and
1734$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1735Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1736the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1737The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1738reduce the uncertainties we have on the observed freshwater budget.
1740%% =================================================================================================
1741\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1744The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1745There are several way to handle sea-ice in the system depending on
1746the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1748\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1749  This is a typical namelist value used for tropical ocean domain.
1750  The surface fluxes are simply specified for an ice-free ocean.
1751  No specific things is done for sea-ice.
1752\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1753  An observed ice covered area is read in a file.
1754  Below this area, the SST is restored to the freezing point and
1755  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1756  The associated modification of the freshwater fluxes are done in such a way that
1757  the change in buoyancy fluxes remains zero.
1758  This prevents deep convection to occur when trying to reach the freezing point
1759  (and so ice covered area condition) while the SSS is too large.
1760  This manner of managing sea-ice area, just by using a IF case,
1761  is usually referred as the \textit{ice-if} model.
1762  It can be found in the \mdl{sbcice\_if} module.
1763\item [nn\_ice = 2 or more] A full sea ice model is used.
1764  This model computes the ice-ocean fluxes,
1765  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1766  provide the surface averaged ocean fluxes.
1767  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1768  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1769  (\ie\ $2$ for SI3 or $3$ for CICE).
1772% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1773%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1775%% =================================================================================================
1776\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1779It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1780to the CICE sea-ice model by using \key{cice}.
1781The CICE code can be obtained from \href{}{LANL} and
1782the additional 'hadgem3' drivers will be required, even with the latest code release.
1783Input grid files consistent with those used in \NEMO\ will also be needed,
1784and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1785(seek advice from UKMO if necessary).
1786Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1787(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1788or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1789(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1790The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1791(although coupling ocean and ice less frequently should work,
1792it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1793the user should check that results are not significantly different to the standard case).
1795There are two options for the technical coupling between \NEMO\ and CICE.
1796The standard version allows complete flexibility for the domain decompositions in the individual models,
1797but this is at the expense of global gather and scatter operations in the coupling which
1798become very expensive on larger numbers of processors.
1799The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1800the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1801and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1802allows much more efficient direct coupling on individual processors.
1803This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1804there is no sea ice.
1806%% =================================================================================================
1807\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1810For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1811prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1812In \NEMO, two way of controlling the freshwater budget are proposed:
1815\item [{\np[=0]{nn_fwb}{nn\_fwb}}] no control at all.
1816  The mean sea level is free to drift, and will certainly do so.
1817\item [{\np[=1]{nn_fwb}{nn\_fwb}}] global mean \textit{emp} set to zero at each model time step.
1818  %GS: comment below still relevant ?
1819  %Note that with a sea-ice model, this technique only controls the mean sea level with linear free surface and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling).
1820\item [{\np[=2]{nn_fwb}{nn\_fwb}}] freshwater budget is adjusted from the previous year annual mean budget which
1821  is read in the \textit{EMPave\_old.dat} file.
1822  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1823  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1826% Griffies doc:
1827% When running ocean-ice simulations, we are not explicitly representing land processes,
1828% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1829% it is important to balance the hydrological cycle in ocean-ice models.
1830% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1831% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1832% a chosen time scale.
1833% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1834% so that there is always a zero net input of water to the ocean-ice system.
1835% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1836% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1837% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1838% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1839% and ice models when aiming to balance the hydrological cycle.
1840% 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,
1841% not the water in any one sub-component. As an extreme example to illustrate the issue,
1842% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1843% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1844% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1845% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1846% in ocean-ice models.
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