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1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4
5\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB, TDE)}
6\label{chap:SBC}
7
8\chaptertoc
9
10\paragraph{Changes record} ~\\
11
12{\footnotesize
13  \begin{tabularx}{\textwidth}{l||X|X}
14    Release & Author(s) & Modifications \\
15    \hline
16    {\em  next} & {\em Simon M{\" u}ller} & {\em Update of \autoref{sec:SBC_TDE}; revision of \autoref{subsec:SBC_fwb}}\\[2mm]
17    {\em   4.0} & {\em ...} & {\em ...} \\
18    {\em   3.6} & {\em ...} & {\em ...} \\
19    {\em   3.4} & {\em ...} & {\em ...} \\
20    {\em <=3.4} & {\em ...} & {\em ...}
21  \end{tabularx}
22}
23
24\clearpage
25
26\begin{listing}
27  \nlst{namsbc}
28  \caption{\forcode{&namsbc}}
29  \label{lst:namsbc}
30\end{listing}
31
32The ocean needs seven fields as surface boundary condition:
33
34\begin{itemize}
35\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
36\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
37\item the surface freshwater budget $\left( {\textit{emp}} \right)$
38\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
39\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
40\end{itemize}
41
42Four different ways are available to provide the seven fields to the ocean. They are controlled by
43namelist \nam{sbc}{sbc} variables:
44
45\begin{itemize}
46\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms,
47\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
48\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
49(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
50\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
51\end{itemize}
52
53The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
54
55When the fields are supplied from data files (bulk, flux and mixed formulations),
56the input fields do not need to be supplied on the model grid.
57Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
58the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
59If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
60should be masked or filled to avoid spurious results in proximity of the coasts, as
61large sea-land gradients characterize most of the atmospheric variables.
62
63In addition, the resulting fields can be further modified using several namelist options.
64These options control:
65
66\begin{itemize}
67\item the rotation of vector components supplied relative to an east-north coordinate system onto
68  the local grid directions in the model,
69\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
70\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
71\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
72  (\np[=0..3]{nn_ice}{nn\_ice}),
73\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
74\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
75  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
76\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
77  (\np[=0..2]{nn_fwb}{nn\_fwb}),
78\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
79  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
80\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
81\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
82\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
83\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
84\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
85\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
86\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
87\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
88\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}),
89\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
90\end{itemize}
91
92In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
93Then we present the three ways of providing the surface boundary conditions,
94followed by the description of the atmospheric pressure and the river runoff.
95Next, the scheme for interpolation on the fly is described.
96Finally, the different options that further modify the fluxes applied to the ocean are discussed.
97One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
98which act as drifting sources of fresh water.
99Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
100which provides additional sources of fresh water.
101
102%% =================================================================================================
103\section{Surface boundary condition for the ocean}
104\label{sec:SBC_ocean}
105
106The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
107It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
108the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
109As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
110\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
111
112The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
113$Q_{ns}$ and $Q_{sr}$, respectively.
114The former is the non penetrative part of the heat flux
115(\ie\ the sum of sensible, latent and long wave heat fluxes plus
116the heat content of the mass exchange between the ocean and sea-ice).
117It is applied in \mdl{trasbc} module as a surface boundary condition trend of
118the first level temperature time evolution equation
119(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
120The latter is the penetrative part of the heat flux.
121It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
122\np[=.true.]{ln_traqsr}{ln\_traqsr}.
123The way the light penetrates inside the water column is generally a sum of decreasing exponentials
124(see \autoref{subsec:TRA_qsr}).
125
126The surface freshwater budget is provided by the \textit{emp} field.
127It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
128possibly with the sea-ice and ice shelves (freezing minus melting of ice).
129It affects the ocean in two different ways:
130$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
131a volume flux, and
132$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
133the mass exchanged with atmosphere, sea-ice and ice shelves.
134
135%\colorbox{yellow}{Miss: }
136%A extensive description of all namsbc namelist (parameter that have to be
137%created!)
138%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
139%ssv) \ie\ information required by flux computation or sea-ice
140%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
141%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
142%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
143%Fluxes update only each nf\_sbc time step (namsbc) explain relation
144%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
145%nf\_sbc
146%Explain here all the namlist namsbc variable{\ldots}.
147% explain : use or not of surface currents
148%\colorbox{yellow}{End Miss }
149
150The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
151the surface currents, temperature and salinity.
152These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
153these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
154
155\begin{table}[tb]
156  \centering
157  \begin{tabular}{|l|l|l|l|}
158    \hline
159    Variable description                           & Model variable  & Units  & point                 \\
160    \hline
161    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
162    \hline
163    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
164    \hline
165    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
166    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
167  \end{tabular}
168  \caption[Ocean variables provided to the surface module)]{
169    Ocean variables provided to the surface module (\texttt{SBC}).
170    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
171    \ie\ the frequency of computation of surface fluxes.}
172  \label{tab:SBC_ssm}
173\end{table}
174
175%\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
176
177%% =================================================================================================
178\section{Input data generic interface}
179\label{sec:SBC_input}
180
181A generic interface has been introduced to manage the way input data
182(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
183This task is achieved by \mdl{fldread}.
184The module is designed with four main objectives in mind:
185\begin{enumerate}
186\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
187  and according to the different calendars available in the model.
188\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
189\item make the run duration independent from the period cover by the input files.
190\item provide a simple user interface and a rather simple developer interface by
191  limiting the number of prerequisite informations.
192\end{enumerate}
193
194As a result, the user has only to fill in for each variable a structure in the namelist file to
195define the input data file and variable names, the frequency of the data (in hours or months),
196whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
197and three additional parameters for the on-the-fly interpolation.
198When adding a new input variable, the developer has to add the associated structure in the namelist,
199read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
200and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
201
202The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
203(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
204if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
205
206Note that when an input data is archived on a disc which is accessible directly from the workspace where
207the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
208By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
209
210%% =================================================================================================
211\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
212\label{subsec:SBC_fldread}
213
214The structure associated with an input variable contains the following information:
215\begin{forlines}
216!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
217!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
218\end{forlines}
219where
220\begin{description}
221\item [File name]: the stem name of the NetCDF file to be opened.
222  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
223  by date information and possibly a prefix (when using AGRIF).
224  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
225  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
226  \begin{table}[htbp]
227    \centering
228    \begin{tabular}{|l|c|c|c|}
229      \hline
230                                  &  daily or weekLL     &  monthly           &  yearly        \\
231      \hline
232      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
233      \hline
234      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
235      \hline
236    \end{tabular}
237    \caption[Naming nomenclature for climatological or interannual input file]{
238      Naming nomenclature for climatological or interannual input file,
239      as a function of the open/close frequency.
240      The stem name is assumed to be 'fn'.
241      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
242      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
243      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
244      always coded with 4 or 2 digits.
245      Note that (1) in mpp, if the file is split over each subdomain,
246      the suffix '.nc' is replaced by '\_PPPP.nc',
247      where 'PPPP' is the process number coded with 4 digits;
248      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
249    }
250    \label{tab:SBC_fldread}
251  \end{table}
252\item [Record frequency]: the frequency of the records contained in the input file.
253  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
254  (for example -1 for monthly forcing or -12 for annual forcing).
255  Note that this frequency must REALLY be an integer and not a real.
256  On some computers, setting it to '24.' can be interpreted as 240!
257\item [Variable name]: the name of the variable to be read in the input NetCDF file.
258\item [Time interpolation]: a logical to activate, or not, the time interpolation.
259  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
260  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
261  00h00'00'' to 23h59'59".
262  If set to 'true', the forcing will have a broken line shape.
263  Records are assumed to be dated at the middle of the forcing period.
264  For example, when using a daily forcing with time interpolation,
265  linear interpolation will be performed between mid-day of two consecutive days.
266\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
267  or an interannual forcing which will requires additional files if
268  the period covered by the simulation exceeds the one of the file.
269  See the above file naming strategy which impacts the expected name of the file to be opened.
270\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
271  Four cases are coded:
272  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
273  means the forcing files will contain data for one day, one week, one month or one year.
274  Files are assumed to contain data from the beginning of the open/close period.
275  For example, the first record of a yearly file containing daily data is Jan 1st even if
276  the experiment is not starting at the beginning of the year.
277\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
278  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
279\end{description}
280
281Additional remarks:\\
282(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
283The only tricky point is therefore to specify the date at which we need to do the interpolation and
284the date of the records read in the input files.
285Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
286For example, for an experiment starting at 0h00'00" with a one-hour time-step,
287a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
288However, for forcing data related to the surface module,
289values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
290For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
291The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
292In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
293(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
294The calendar associated with the forcing field is build according to the information provided by
295user in the record frequency, the open/close frequency and the type of temporal interpolation.
296For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
297start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
298(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
299interpolating data with the first (last) record of the open/close period.
300For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
301the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
302Dec 31st 12h00'00" and Jan 1st 12h00'00".
303If the forcing is climatological, Dec and Jan will be keep-up from the same year.
304However, if the forcing is not climatological, at the end of
305the open/close period, the code will automatically close the current file and open the next one.
306Note that, if the experiment is starting (ending) at the beginning (end) of
307an open/close period, we do accept that the previous (next) file is not existing.
308In this case, the time interpolation will be performed between two identical values.
309For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
310we do accept that the file related to year Y-1 is not existing.
311The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
312If the file of year Y-1 exists, the code will read its last record.
313Therefore, this file can contain only one record corresponding to Dec 31st,
314a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
315
316%% =================================================================================================
317\subsection{Interpolation on-the-fly}
318\label{subsec:SBC_iof}
319
320Interpolation on the Fly allows the user to supply input files required for the surface forcing on
321grids other than the model grid.
322To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
323interpolate from the data grid to the model grid.
324The original development of this code used the SCRIP package
325(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
326In principle, any package such as CDO can be used to generate the weights, but the variables in
327the input weights file must have the same names and meanings as assumed by the model.
328Two methods are currently available: bilinear and bicubic interpolations.
329Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
330the input file and substitute the corresponding values with the average of the 8 neighbouring points in
331the native external grid.
332Only "sea points" are considered for the averaging.
333The land/sea mask file must be provided in the structure associated with the input variable.
334The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
335the associated variables and should be equal to 1 over land and 0 elsewhere.
336The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
337Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
338
339%% =================================================================================================
340\subsubsection{Bilinear interpolation}
341\label{subsec:SBC_iof_bilinear}
342
343The input weights file in this case has two sets of variables:
344src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
345The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
346Each src value is an integer corresponding to the index of a point in the input grid when
347written as a one dimensional array.
348For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
349There are four of each variable because bilinear interpolation uses the four points defining
350the grid box containing the point to be interpolated.
351All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
352generate a value for point (i,j) in the model.
353
354Symbolically, the algorithm used is:
355\[
356  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
357\]
358where function idx() transforms a one dimensional index src(k) into a two dimensional index,
359and wgt(1) corresponds to variable "wgt01" for example.
360
361%% =================================================================================================
362\subsubsection{Bicubic interpolation}
363\label{subsec:SBC_iof_bicubic}
364
365Again, there are two sets of variables: "src" and "wgt".
366But in this case, there are 16 of each.
367The symbolic algorithm used to calculate values on the model grid is now:
368
369\[
370  \begin{split}
371    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
372    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
373    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
374    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
375  \end{split}
376\]
377The gradients here are taken with respect to the horizontal indices and not distances since
378the spatial dependency has been included into the weights.
379
380%% =================================================================================================
381\subsubsection{Implementation}
382\label{subsec:SBC_iof_imp}
383
384To activate this option, a non-empty string should be supplied in
385the weights filename column of the relevant namelist;
386if this is left as an empty string no action is taken.
387In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
388as and when they are first required.
389This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
390inspecting a global attribute stored in the weights input file.
391This attribute must be called "ew\_wrap" and be of integer type.
392If it is negative, the input non-model grid is assumed to be not cyclic.
393If zero or greater, then the value represents the number of columns that overlap.
394$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
395if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
396If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
397In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
398therefore the grid is assumed to be cyclic with no overlapping columns.
399(In fact, this only matters when bicubic interpolation is required.)
400Note that no testing is done to check the validity in the model,
401since there is no way of knowing the name used for the longitude variable,
402so it is up to the user to make sure his or her data is correctly represented.
403
404Next the routine reads in the weights.
405Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
406The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
407and when required, for reading in the variable to be interpolated (on the input data grid).
408The size of the input data array is determined by examining the values in the "src" arrays to
409find the minimum and maximum i and j values required.
410Since bicubic interpolation requires the calculation of gradients at each point on the grid,
411the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
412When the array of points from the data file is adjacent to an edge of the data grid,
413the halo is either a copy of the row/column next to it (non-cyclical case),
414or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
415
416%% =================================================================================================
417\subsubsection{Limitations}
418\label{subsec:SBC_iof_lim}
419
420\begin{enumerate}
421\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
422\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
423  a bicubic interpolation method is used.
424\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
425\item The gradients across the ends of a cyclical grid assume that the grid spacing between
426  the two columns involved are consistent with the weights used.
427\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
428  but this has not been implemented.)
429\end{enumerate}
430
431%% =================================================================================================
432\subsubsection{Utilities}
433\label{subsec:SBC_iof_util}
434
435% to be completed
436A set of utilities to create a weights file for a rectilinear input grid is available
437(see the directory NEMOGCM/TOOLS/WEIGHTS).
438
439%% =================================================================================================
440\subsection{Standalone surface boundary condition scheme (SAS)}
441\label{subsec:SBC_SAS}
442
443\begin{listing}
444  \nlst{namsbc_sas}
445  \caption{\forcode{&namsbc_sas}}
446  \label{lst:namsbc_sas}
447\end{listing}
448
449In some circumstances, it may be useful to avoid calculating the 3D temperature,
450salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
451For example:
452
453\begin{itemize}
454\item Multiple runs of the model are required in code development to
455  see the effect of different algorithms in the bulk formulae.
456\item The effect of different parameter sets in the ice model is to be examined.
457\item Development of sea-ice algorithms or parameterizations.
458\item Spinup of the iceberg floats
459\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
460\end{itemize}
461
462The Standalone Surface scheme provides this capacity.
463Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
464A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
465However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
466In this configuration, a few routines in the standard model are overriden by new versions.
467Routines replaced are:
468
469\begin{itemize}
470\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
471  Since the ocean state is not calculated all associated initialisations have been removed.
472\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
473\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
474  New surface modules that can function when only the surface level of the ocean state is defined can also be added
475  (\eg\ icebergs).
476\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
477  so calls to restart functions have been removed.
478  This also means that the calendar cannot be controlled by time in a restart file,
479  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
480\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
481\item \mdl{diawri}: All 3D data have been removed from the output.
482  The surface temperature, salinity and velocity components (which have been read in) are written along with
483  relevant forcing and ice data.
484\end{itemize}
485
486One new routine has been added:
487
488\begin{itemize}
489\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
490  velocity arrays at the surface.
491  These filenames are supplied in namelist namsbc\_sas.
492  Unfortunately, because of limitations with the \mdl{iom} module,
493  the full 3D fields from the mean files have to be read in and interpolated in time,
494  before using just the top level.
495  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
496\end{itemize}
497
498The 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
499 (\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.
500
501%% =================================================================================================
502\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
503\label{sec:SBC_flx}
504
505% Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk
506% parameterization'' (i.e NCAR, COARE, ECMWF...)
507
508\begin{listing}
509  \nlst{namsbc_flx}
510  \caption{\forcode{&namsbc_flx}}
511  \label{lst:namsbc_flx}
512\end{listing}
513
514In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
515the surface boundary condition fields are directly read from input files.
516The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
517the name of the variable read in the file, the time frequency at which it is given (in hours),
518and a logical setting whether a time interpolation to the model time step is required for this field.
519See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
520
521Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
522See \autoref{subsec:SBC_ssr} for its specification.
523
524%% =================================================================================================
525\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
526\label{sec:SBC_blk}
527
528% L. Brodeau, December 2019... %
529
530\begin{listing}
531  \nlst{namsbc_blk}
532  \caption{\forcode{&namsbc_blk}}
533  \label{lst:namsbc_blk}
534\end{listing}
535
536If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea
537fluxes associated with surface boundary conditions are estimated by means of the
538traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed
539near-surface atmosphere state (typically extracted from a weather reanalysis)
540and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc}
541time-step(s).
542
543% Turbulent air-sea fluxes are computed using the sea surface properties and
544% atmospheric SSVs at height $z$ above the sea surface, with the traditional
545% aerodynamic bulk formulae:
546
547Note: all the NEMO Fortran routines involved in the present section have been
548initially developed (and are still developed in parallel) in
549the \href{https://brodeau.github.io/aerobulk}{\texttt{AeroBulk}} open-source project
550\citep{brodeau.barnier.ea_JPO16}.
551
552%%% Bulk formulae are this:
553\subsection{Bulk formulae}
554\label{subsec:SBC_blkform}
555
556In NEMO, the set of equations that relate each component of the surface fluxes
557to the near-surface atmosphere and sea surface states writes
558
559\begin{subequations}
560  \label{eq:SBC_bulk}
561  \label{eq:SBC_bulk_form}
562  \begin{align}
563    \mathbf{\tau} &= \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
564    Q_H           &= \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
565    E             &= \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
566    Q_L           &= -L_v \, E \\
567    Q_{sr}        &= (1 - a) Q_{sw\downarrow} \\
568    Q_{ir}        &= \delta (Q_{lw\downarrow} -\sigma T_s^4)
569  \end{align}
570\end{subequations}
571
572with
573   \[ \theta_z \simeq T_z+\gamma z \]
574   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
575from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
576where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
577$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
578flux.
579$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
580and longwave radiative fluxes, respectively.
581Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$
582implies a gain of the relevant quantity for the ocean, while a positive $E$
583implies a freshwater loss for the ocean.
584$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
585coefficients for momentum, sensible heat, and moisture, respectively.
586$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
587vaporization of water.
588$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
589and specific humidity of air at height $z$ above the sea surface,
590respectively. $\gamma z$ is a temperature correction term which accounts for the
591adiabatic lapse rate and approximates the potential temperature at height
592$z$ \citep{josey.gulev.ea_OCC13}.
593$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
594(possibly referenced to the surface current $\mathbf{u_0}$).%,
595%\autoref{s_res1}.\autoref{ss_current}). %% Undefined references
596The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
597$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution.
598$a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\
599%$p_a$ is the mean sea-level pressure (SLP).
600$T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity
601of air at temperature $T_s$; it includes a 2\% reduction to account for the
602presence of salt in seawater \citep{sverdrup.johnson.ea_bk42,kraus.businger_QJRMS96}.
603Depending on the bulk parametrization used, $T_s$ can either be the temperature
604at the air-sea interface (skin temperature, hereafter SSST) or at typically a
605few tens of centimeters below the surface (bulk sea surface temperature,
606hereafter SST).
607The SSST differs from the SST due to the contributions of two effects of
608opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL,
609respectively, see \autoref{subsec:SBC_skin}).
610Technically, when the ECMWF or COARE* bulk parametrizations are selected
611(\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}),
612$T_s$ is the SSST, as opposed to the NCAR bulk parametrization
613(\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature
614at first T-point level).
615
616For more details on all these aspects the reader is invited to refer
617to \citet{brodeau.barnier.ea_JPO16}.
618
619\subsection{Bulk parametrizations}
620\label{subsec:SBC_blk_ocean}
621%%%\label{subsec:SBC_param}
622
623Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae
624strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and
625$C_E$. They are estimated with what we refer to as a \emph{bulk
626parametrization} algorithm. When relevant, these algorithms also perform the
627height adjustment of humidity and temperature to the wind reference measurement
628height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}).
629
630For the open ocean, four bulk parametrization algorithms are available in NEMO:
631
632\begin{itemize}
633\item NCAR, formerly known as CORE, \citep{large.yeager_trpt04,large.yeager_CD09}
634\item COARE 3.0 \citep{fairall.bradley.ea_JC03}
635\item COARE 3.6 \citep{edson.jampana.ea_JPO13}
636\item ECMWF (IFS documentation, cy45)
637\end{itemize}
638
639With respect to version 3, the principal advances in version 3.6 of the COARE
640bulk parametrization are built around improvements in the representation of the
641effects of waves on
642fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO16}. This includes
643improved relationships of surface roughness, and whitecap fraction on wave
644parameters. It is therefore recommended to chose version 3.6 over 3.
645
646\subsection[Cool-skin and warm-layer parameterizations (   \forcode{ln_skin_cs}               \& \forcode{ln_skin_wl}              )]
647           {Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \&      \np{ln_skin_wl}{ln\_skin\_wl})}
648\label{subsec:SBC_skin}
649
650As opposed to the NCAR bulk parametrization, more advanced bulk
651parametrizations such as COARE3.x and ECMWF are meant to be used with the skin
652temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
653the first T-point level, see \autoref{subsec:SBC_blkform}).
654
655As such, the relevant cool-skin and warm-layer parametrization must be
656activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs}
657and \np[=T]{ln_skin_wl}{ln\_skin\_wl} to use COARE3.x or ECMWF in a consistent
658way.
659
660\texttt{\#LB: ADD BLBLA ABOUT THE TWO CS/WL PARAMETRIZATIONS (ECMWF and COARE) !!!}
661
662For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same
663basis: \citet{fairall.bradley.ea_JGRO96}. With some minor updates based
664on \citet{zeng.beljaars_GRL05} for ECMWF \iffalse, and \citet{fairall.ea_19?} for COARE \fi
6653.6.
666
667For the warm-layer scheme, ECMWF is based on \citet{zeng.beljaars_GRL05} with a
668recent update from \citet{takaya.bidlot.ea_JGR10} (consideration of the
669turbulence input from Langmuir circulation).
670
671Importantly, COARE warm-layer scheme \iffalse \citep{fairall.ea_19?} \fi includes a prognostic
672equation for the thickness of the warm-layer, while it is considered as constant
673in the ECWMF algorithm.
674
675\subsection{Appropriate use of each bulk parametrization}
676
677\subsubsection{NCAR}
678
679NCAR bulk parametrizations (formerly known as CORE) is meant to be used with the
680CORE II atmospheric forcing \citep{large.yeager_CD09}. The expected sea surface
681temperature is the bulk SST. Hence the following namelist parameters must be
682set:
683
684\begin{forlines}
685  ...
686  ln_NCAR    = .true.
687  ...
688  rn_zqt     = 10.     ! Air temperature & humidity reference height (m)
689  rn_zu      = 10.     ! Wind vector reference height (m)
690  ...
691  ln_skin_cs = .false. ! use the cool-skin parameterization
692  ln_skin_wl = .false. ! use the warm-layer parameterization
693  ...
694  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
695\end{forlines}
696
697\subsubsection{ECMWF}
698
699With an atmospheric forcing based on a reanalysis of the ECMWF, such as the
700Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to
701use the ECMWF bulk parametrizations with the cool-skin and warm-layer
702parametrizations activated. In ECMWF reanalyzes, since air temperature and
703humidity are provided at the 2\,m height, and given that the humidity is
704distributed as the dew-point temperature, the namelist must be tuned as follows:
705
706\begin{forlines}
707  ...
708  ln_ECMWF   = .true.
709  ...     
710  rn_zqt     =  2.     ! Air temperature & humidity reference height (m)
711  rn_zu      = 10.     ! Wind vector reference height (m)
712  ...
713  ln_skin_cs = .true. ! use the cool-skin parameterization
714  ln_skin_wl = .true. ! use the warm-layer parameterization
715  ...
716  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
717  ...
718\end{forlines}
719
720Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
721of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
722triggers the use of the ECMWF cool-skin and warm-layer parametrizations,
723respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
724
725\subsubsection{COARE 3.x}
726
727Since the ECMWF parametrization is largely based on the COARE* parametrization,
728the two algorithms are very similar in terms of structure and closure
729approach. As such, the namelist tuning for COARE 3.x is identical to that of
730ECMWF:
731
732\begin{forlines}
733  ...
734  ln_COARE3p6 = .true.
735  ...     
736  ln_skin_cs = .true. ! use the cool-skin parameterization
737  ln_skin_wl = .true. ! use the warm-layer parameterization
738  ...
739\end{forlines}
740
741Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection
742of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
743triggers the use of the COARE cool-skin and warm-layer parametrizations,
744respectively (found in \textit{sbcblk\_skin\_coare.F90}).
745
746%lulu
747
748% In a typical bulk algorithm, the BTCs under neutral stability conditions are
749% defined using \emph{in-situ} flux measurements while their dependence on the
750% stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and
751% the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are
752% functions of the wind speed and the near-surface stability of the atmospheric
753% surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$
754% and $q_z$.
755
756\subsection{Prescribed near-surface atmospheric state}
757
758The atmospheric fields used depend on the bulk formulae used.  In forced mode,
759when a sea-ice model is used, a specific bulk formulation is used.  Therefore,
760different bulk formulae are used for the turbulent fluxes computation over the
761ocean and over sea-ice surface.
762
763%The choice is made by setting to true one of the following namelist
764%variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6}
765%and \np{ln_ECMWF}{ln\_ECMWF}.
766
767Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
768The required 9 input fields are:
769
770\begin{table}[htbp]
771  \centering
772  \begin{tabular}{|l|c|c|c|}
773    \hline
774    Variable description                 & Model variable & Units              & point \\
775    \hline
776    i-component of the 10m air velocity  & wndi           & $m.s^{-1}$         & T     \\
777    \hline
778    j-component of the 10m air velocity  & wndj           & $m.s^{-1}$         & T     \\
779    \hline
780    10m air temperature                  & tair           & $K$               & T     \\
781    \hline
782    Specific humidity                    & humi           & $-$               & T     \\
783    Relative humidity                    & ~              & $\%$              & T     \\
784    Dew-point temperature                & ~              & $K$               & T     \\   
785    \hline
786    Downwelling longwave radiation       & qlw            & $W.m^{-2}$         & T     \\
787    \hline
788    Downwelling shortwave radiation      & qsr            & $W.m^{-2}$         & T     \\
789    \hline
790    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
791    \hline
792    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
793    \hline
794    Mean sea-level pressure              & slp            & $Pa$              & T     \\
795    \hline
796    \end{tabular}
797  \label{tab:SBC_BULK}
798\end{table}
799
800Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
801It is simpler and faster (less fields to be read), but it is not the recommended method when
802the ocean grid size is the same or larger than the one of the input atmospheric fields.
803
804The \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},
805\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
806(spatial and temporal interpolations).
807
808\np{cn_dir}{cn\_dir} is the directory of location of bulk files
809%\np{ln_taudif}{ln\_taudif} is the flag to specify if we use High Frequency (HF) tau information (.true.) or not (.false.)
810\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
811\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
812
813Three multiplicative factors are available:
814\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
815increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
816The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
817the calculation of surface wind stress.
818Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
819
820As for the flux parametrization, information about the input data required by the model is provided in
821the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
822
823\subsubsection{Air humidity}
824
825Air humidity can be provided as three different parameters: specific humidity
826[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
827parameters)...
828
829%% =================================================================================================
830%\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})}
831%\label{subsec:SBC_blk_ocean}
832
833%Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
834%COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
835%their neutral transfer coefficients relationships with neutral wind.
836%\begin{itemize}
837%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_trpt04}.
838%  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
839%  They use an inertial dissipative method to compute the turbulent transfer coefficients
840%  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
841%  This \citet{large.yeager_trpt04} dataset is available through
842%  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
843%  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
844%  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
845%\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
846%\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details
847%\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9204}{IFS (Cy40r1)} %implementation and documentation.
848%  Surface roughness lengths needed for the Obukhov length are computed
849%  following \citet{beljaars_QJRMS95}.
850%\end{itemize}
851
852%% =================================================================================================
853\subsection{Ice-Atmosphere Bulk formulae}
854\label{subsec:SBC_blk_ice}
855
856\texttt{\#out\_of\_place:}
857 For sea-ice, three possibilities can be selected:
858a constant transfer coefficient (1.4e-3; default
859value), \citet{lupkes.gryanik.ea_JGRA12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
860and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
861\texttt{\#out\_of\_place.}
862
863Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
864
865\begin{itemize}
866\item Constant value (\forcode{Cd_ice=1.4e-3}):
867  default constant value used for momentum and heat neutral transfer coefficients
868\item \citet{lupkes.gryanik.ea_JGRA12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
869  This scheme adds a dependency on edges at leads, melt ponds and flows
870  of the constant neutral air-ice drag. After some approximations,
871  this can be resumed to a dependency on ice concentration (A).
872  This drag coefficient has a parabolic shape (as a function of ice concentration)
873  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.
874  It is theoretically applicable to all ice conditions (not only MIZ).
875\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
876  Alternative turbulent transfer coefficients formulation between sea-ice
877  and atmosphere with distinct momentum and heat coefficients depending
878  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
879  The parameterization is adapted from ECHAM6 atmospheric model.
880  Compared to Lupkes2012 scheme, it considers specific skin and form drags
881  to compute neutral transfer coefficients for both heat and momentum fluxes.
882  Atmospheric stability effect on transfer coefficient is also taken into account.
883\end{itemize}
884
885%% =================================================================================================
886\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
887\label{sec:SBC_cpl}
888
889\begin{listing}
890  \nlst{namsbc_cpl}
891  \caption{\forcode{&namsbc_cpl}}
892  \label{lst:namsbc_cpl}
893\end{listing}
894
895In the coupled formulation of the surface boundary condition,
896the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
897while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
898the atmospheric component.
899
900A generalised coupled interface has been developed.
901It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
902An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
903It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
904(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
905(Weather Research and Forecasting Model).
906
907When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
908the whole carbon cycle is computed.
909In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
910(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
911
912The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
913now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
914When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
915the number used in the sea ice model.
916In some limited cases, it may be possible to specify single category coupling fields even when
917the sea ice model is running with multiple categories -
918in this case, the user should examine the code to be sure the assumptions made are satisfactory.
919In cases where this is definitely not possible, the model should abort with an error message.
920
921%% =================================================================================================
922\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
923\label{sec:SBC_apr}
924
925\begin{listing}
926  \nlst{namsbc_apr}
927  \caption{\forcode{&namsbc_apr}}
928  \label{lst:namsbc_apr}
929\end{listing}
930
931The optional atmospheric pressure can be used to force ocean and ice dynamics
932(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
933The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
934can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
935When used to force the dynamics, the atmospheric pressure is further transformed into
936an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
937\[
938  % \label{eq:SBC_ssh_ib}
939  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
940\]
941where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
942A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
943In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
944\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
945
946The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
947For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
948(see \mdl{sbcssr} module).
949$\eta_{ib}$ can be written in the output.
950This can simplify altimetry data and model comparison as
951inverse barometer sea surface height is usually removed from these date prior to their distribution.
952
953When using time-splitting and BDY package for open boundaries conditions,
954the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
955\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
956
957%% =================================================================================================
958\section{Surface tides (TDE)}
959\label{sec:SBC_TDE}
960
961\begin{listing}
962  \nlst{nam_tide}
963  \caption{\forcode{&nam_tide}}
964  \label{lst:nam_tide}
965\end{listing}
966
967\subsection{Tidal constituents}
968Ocean model component TDE provides the common functionality for tidal forcing
969and tidal analysis in the model framework. This includes the computation of the gravitational
970surface forcing, as well as support for lateral forcing at open boundaries (see
971\autoref{subsec:LBC_bdy_tides}) and tidal harmonic analysis \iffalse (see
972\autoref{subsec:DIA_diamlr?} and \autoref{subsec:DIA_diadetide?}) \fi . The module is
973activated with \np[=.true.]{ln_tide}{ln\_tide} in namelist
974\nam{_tide}{\_tide}. It provides the same 34 tidal constituents that are
975included in the
976\href{https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/global-tide-fes.html}{FES2014
977  ocean tide model}: Mf, Mm, Ssa, Mtm, Msf, Msqm, Sa, K1, O1, P1, Q1, J1, S1,
978M2, S2, N2, K2, nu2, mu2, 2N2, L2, T2, eps2, lam2, R2, M3, MKS2, MN4, MS4, M4,
979N4, S4, M6, and M8; see file \textit{tide.h90} and \mdl{tide\_mod} for further
980information and references\footnote{As a legacy option \np{ln_tide_var} can be
981  set to \forcode{0}, in which case the 19 tidal constituents (M2, N2, 2N2, S2,
982  K2, K1, O1, Q1, P1, M4, Mf, Mm, Msqm, Mtm, S1, MU2, NU2, L2, and T2; see file
983  \textit{tide.h90}) and associated parameters that have been available in NEMO version
984  4.0 and earlier are available}. Constituents to be included in the tidal forcing
985(surface and lateral boundaries) are selected by enumerating their respective
986names in namelist array \np{sn_tide_cnames}{sn\_tide\_cnames}.\par
987
988\subsection{Surface tidal forcing}
989Surface tidal forcing can be represented in the model through an additional
990barotropic force in the momentum equation (\autoref{eq:MB_PE_dyn}) such that:
991\[
992  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t} = \ldots +g\nabla (\gamma
993  \Pi_{eq} + \Pi_{sal})
994\]
995where $\gamma \Pi_{eq}$ stands for the equilibrium tidal forcing scaled by a spatially
996uniform tilt factor $\gamma$, and $\Pi_{sal}$ is an optional
997self-attraction and loading term (SAL). These additional terms are enabled when,
998in addition to \np[=.true.]{ln_tide}{ln\_tide}),
999\np[=.true.]{ln_tide_pot}{ln\_tide\_pot}.\par
1000
1001The equilibrium tidal forcing is expressed as a sum over the subset of
1002constituents listed in \np{sn_tide_cnames}{sn\_tide\_cnames} of
1003\nam{_tide} (e.g.,
1004\begin{forlines}
1005      sn_tide_cnames(1) = 'M2'
1006      sn_tide_cnames(2) = 'K1'
1007      sn_tide_cnames(3) = 'S2'
1008      sn_tide_cnames(4) = 'O1'
1009\end{forlines}
1010to select the four tidal constituents of strongest equilibrium tidal
1011potential). The tidal tilt factor $\gamma = 1 + k - h$ includes the
1012Love numbers $k$ and $h$ \citep{love_PRSL09}; this factor is
1013configurable using \np{rn_tide_gamma}{rn\_tide\_gamma} (default value 0.7). Optionally,
1014when \np[=.true.]{ln_tide_ramp}{ln\_tide\_ramp}, the equilibrium tidal
1015forcing can be ramped up linearly from zero during the initial
1016\np{rn_tide_ramp_dt}{rn\_tide\_ramp\_dt} days of the model run.\par
1017
1018The SAL term should in principle be computed online as it depends on
1019the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
1020discussion about the practical implementation of this term). The complex
1021calculations involved in such computations, however, are computationally very
1022expensive. Here, two mutually exclusive simpler variants are available:
1023amplitudes generated by an external model for oscillatory $\Pi_{sal}$
1024contributions from each of the selected tidal constituents can be read in
1025(\np[=.true.]{ln_read_load}{ln\_read\_load}) from the file specified in
1026\np{cn_tide_load}{cn\_tide\_load} (the variable names are comprised of the
1027tidal-constituent name and suffixes \forcode{_z1} and \forcode{_z2} for the two
1028orthogonal components, respectively); alternatively, a ``scalar approximation''
1029can be used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}), where
1030\[
1031  \Pi_{sal} = \beta \eta,
1032\]
1033with a spatially uniform coefficient $\beta$, which can be configured
1034via \np{rn_scal_load}{rn\_scal\_load} (default value 0.094) and is
1035often tuned to minimize tidal prediction errors.\par
1036
1037For diagnostic purposes, the forcing potential of the individual tidal
1038constituents (incl. load ptential, if activated) and the total forcing
1039potential (incl. load potential, if activated) can be made available
1040as diagnostic output by setting
1041\np[=.true.]{ln_tide_dia}{ln\_tide\_dia} (fields
1042\forcode{tide_pot_<constituent>} and \forcode{tide_pot}).\par
1043
1044%% =================================================================================================
1045\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
1046\label{sec:SBC_rnf}
1047
1048\begin{listing}
1049  \nlst{namsbc_rnf}
1050  \caption{\forcode{&namsbc_rnf}}
1051  \label{lst:namsbc_rnf}
1052\end{listing}
1053
1054%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1055%Many models, however, have traditionally inserted river runoff to the top model cell.
1056%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
1057%throughout a nonzero depth has been motivated by the numerical and physical problems
1058%that arise when the top grid cells are of the order of one meter. This situation is common in
1059%coastal modelling and becomes more and more often open ocean and climate modelling
1060%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
1061%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
1062
1063%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
1064%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
1065%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
1066%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
1067%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
1068%emp or emps and the changes made are below:
1069
1070%Rachel:
1071River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1072Many models, however, have traditionally inserted river runoff to the top model cell.
1073This was the case in \NEMO\ prior to the version 3.3,
1074and was combined with an option to increase vertical mixing near the river mouth.
1075
1076However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
1077This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
1078\footnote{
1079  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
1080  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
1081  see also \autoref{fig:SBC_dcy}.}.
1082
1083As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
1084and for the temperature and salinity of the river to effect the surrounding ocean.
1085The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
1086along with the depth (in metres) which the river should be added to.
1087
1088Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
1089\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
1090If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
1091and/or taken as surface temperature respectively.
1092
1093The runoff value and attributes are read in in sbcrnf.
1094For temperature -999 is taken as missing data and the river temperature is taken to
1095be the surface temperatue at the river point.
1096For the depth parameter a value of -1 means the river is added to the surface box only,
1097and a value of -999 means the river is added through the entire water column.
1098After being read in the temperature and salinity variables are multiplied by the amount of runoff
1099(converted into m/s) to give the heat and salt content of the river runoff.
1100After the user specified depth is read ini,
1101the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
1102The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
1103the bottom of the lowest box the river water is being added to
1104(\ie\ the total depth that river water is being added to in the model).
1105
1106The mass/volume addition due to the river runoff is, at each relevant depth level, added to
1107the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
1108This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
1109The sea surface height is calculated using the sum of the horizontal divergence terms,
1110and so the river runoff indirectly forces an increase in sea surface height.
1111
1112The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
1113This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
1114The heat and salt content of the river runoff is not included in this step,
1115and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
1116the box and replaced by the same volume of river water with no corresponding heat and salt addition.
1117
1118For the linear free surface case, at the surface box the tracer advection causes a flux of water
1119(of equal volume to the runoff) through the sea surface out of the domain,
1120which causes a salt and heat flux out of the model.
1121As such the volume of water does not change, but the water is diluted.
1122
1123For the non-linear free surface case, no flux is allowed through the surface.
1124Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
1125no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
1126(The runoff addition to the top box along with the water being moved up through
1127boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
1128
1129In trasbc the addition of heat and salt due to the river runoff is added.
1130This is done in the same way for both vvl and non-vvl.
1131The temperature and salinity are increased through the specified depth according to
1132the heat and salt content of the river.
1133
1134In the non-linear free surface case (vvl),
1135near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
1136so that the original ratios of grid box heights are restored.
1137In doing this water is moved into boxes below, throughout the water column,
1138so the large volume addition to the surface box is spread between all the grid boxes.
1139
1140It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
1141\ie\ modelling the Baltic flow in and out of the North Sea.
1142When the flow is out of the domain there is no change in temperature and salinity,
1143regardless of the namelist options used,
1144as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
1145
1146%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1147
1148%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1149
1150%\colorbox{yellow}{river mouths{\ldots}}
1151
1152%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1153%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1154%ENDIF
1155
1156\cmtgm{  word doc of runoffs:
1157In the current \NEMO\ setup river runoff is added to emp fluxes,
1158these are then applied at just the sea surface as a volume change (in the variable volume case
1159this is a literal volume change, and in the linear free surface case the free surface is moved)
1160and a salt flux due to the concentration/dilution effect.
1161There is also an option to increase vertical mixing near river mouths;
1162this gives the effect of having a 3d river.
1163All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
1164at the same temperature as the sea surface.
1165Our aim was to code the option to specify the temperature and salinity of river runoff,
1166(as well as the amount), along with the depth that the river water will affect.
1167This would make it possible to model low salinity outflow, such as the Baltic,
1168and would allow the ocean temperature to be affected by river runoff.
1169
1170The depth option makes it possible to have the river water affecting just the surface layer,
1171throughout depth, or some specified point in between.
1172
1173To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
1174the \mdl{tra_sbc} module.
1175We decided to separate them throughout the code,
1176so that the variable emp represented solely evaporation minus precipitation fluxes,
1177and a new 2d variable rnf was added which represents the volume flux of river runoff
1178(in $kg/m^2s$ to remain consistent with $emp$).
1179This meant many uses of emp and emps needed to be changed,
1180a list of all modules which use $emp$ or $emps$ and the changes made are below:}
1181
1182%% =================================================================================================
1183\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
1184\label{sec:SBC_isf}
1185
1186\begin{listing}
1187%  \nlst{namsbc_isf}
1188  \caption{\forcode{&namsbc_isf}}
1189  \label{lst:namsbc_isf}
1190\end{listing}
1191
1192The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
1193Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1194The different options are illustrated in \autoref{fig:SBC_isf}.
1195
1196\begin{description}
1197  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1198  The fwf and heat flux are depending of the local water properties.
1199
1200  Two different bulk formulae are available:
1201
1202  \begin{description}
1203  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
1204    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_trpt06}.
1205  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
1206    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1207    A complete description is available in \citet{jenkins_JGR91}.
1208  \end{description}
1209
1210  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1211  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
1212  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.
1213  Then, the fluxes are spread over the same thickness (ie over one or several cells).
1214  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.
1215  This can lead to super-cool temperature in the top cell under melting condition.
1216  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.\\
1217
1218  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1219  There are 3 different ways to compute the exchange coeficient:
1220  \begin{description}
1221  \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}.
1222    \begin{gather*}
1223       % \label{eq:SBC_isf_gamma_iso}
1224      \gamma^{T} = rn\_gammat0 \\
1225      \gamma^{S} = rn\_gammas0
1226    \end{gather*}
1227    This is the recommended formulation for ISOMIP.
1228  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
1229    \begin{gather*}
1230      \gamma^{T} = rn\_gammat0 \times u_{*} \\
1231      \gamma^{S} = rn\_gammas0 \times u_{*}
1232    \end{gather*}
1233    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
1234    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1235  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1236    \[
1237      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1238    \]
1239    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
1240    $\Gamma_{Turb}$ the contribution of the ocean stability and
1241    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1242    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1243    This formulation has not been extensively tested in \NEMO\ (not recommended).
1244  \end{description}
1245\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1246  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1247  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1248  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1249  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
1250  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
1251\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1252  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1253  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
1254  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
1255  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1256\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1257  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
1258  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1259  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})
1260\end{description}
1261
1262$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
1263the water mass properties, ocean velocities and depth.
1264This flux is thus highly dependent of the model resolution (horizontal and vertical),
1265realism of the water masses onto the shelf ...\\
1266
1267$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
1268You have total control of the fwf forcing.
1269This can be useful if the water masses on the shelf are not realistic or
1270the resolution (horizontal/vertical) are too coarse to have realistic melting or
1271for studies where you need to control your heat and fw input.\\
1272
1273The ice shelf melt is implemented as a volume flux as for the runoff.
1274The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1275the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1276See \autoref{sec:SBC_rnf} for all the details about the divergence correction.
1277
1278\begin{figure}[!t]
1279  \centering
1280  \includegraphics[width=0.66\textwidth]{SBC_isf}
1281  \caption[Ice shelf location and fresh water flux definition]{
1282    Illustration of the location where the fwf is injected and
1283    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1284  \label{fig:SBC_isf}
1285\end{figure}
1286
1287%% =================================================================================================
1288\section{Ice sheet coupling}
1289\label{sec:SBC_iscpl}
1290
1291\begin{listing}
1292%  \nlst{namsbc_iscpl}
1293  \caption{\forcode{&namsbc_iscpl}}
1294  \label{lst:namsbc_iscpl}
1295\end{listing}
1296
1297Ice sheet/ocean coupling is done through file exchange at the restart step.
1298At each restart step:
1299
1300\begin{enumerate}
1301\item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1302\item a new domcfg.nc file is built using the DOMAINcfg tools.
1303\item \NEMO\ run for a specific period and output the average melt rate over the period.
1304\item the ice sheet model run using the melt rate outputed in step 4.
1305\item go back to 1.
1306\end{enumerate}
1307
1308If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1309potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1310The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1311
1312\begin{description}
1313\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
1314  ($bt_b=bt_n$).
1315\item [Enlarge  a cell]: See case "Thin a cell down"
1316\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
1317  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1318\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.
1319  If no neighbours, T/S is extrapolated from old top cell value.
1320  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1321\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1322\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.
1323  If no neighbour, T/S/U/V and mask set to 0.
1324\end{description}
1325
1326Furthermore, as the before and now fields are not compatible (modification of the geometry),
1327the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1328
1329The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1330It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1331the code will be unable to fill all the new wet cells properly.
1332The default number is set up for the MISOMIP idealised experiments.
1333This coupling procedure is able to take into account grounding line and calving front migration.
1334However, it is a non-conservative processe.
1335This could lead to a trend in heat/salt content and volume.\\
1336
1337In order to remove the trend and keep the conservation level as close to 0 as possible,
1338a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1339The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1340A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1341For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1342The 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).
1343
1344%% =================================================================================================
1345\section{Handling of icebergs (ICB)}
1346\label{sec:SBC_ICB_icebergs}
1347
1348\begin{listing}
1349  \nlst{namberg}
1350  \caption{\forcode{&namberg}}
1351  \label{lst:namberg}
1352\end{listing}
1353
1354Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1355Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1356(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1357Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1358described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1359Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1360which is an integer representing how many icebergs of this class are being described as one lagrangian point
1361(this reduces the numerical problem of tracking every single iceberg).
1362They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1363
1364Two initialisation schemes are possible.
1365\begin{description}
1366\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
1367  (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
1368  which an iceberg is generated at the beginning of the run.
1369  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1370  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1371  the geographical box: lonmin,lonmax,latmin,latmax
1372\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.
1373  This should be a file with a field on the configuration grid (typically ORCA)
1374  representing ice accumulation rate at each model point.
1375  These should be ocean points adjacent to land where icebergs are known to calve.
1376  Most points in this input grid are going to have value zero.
1377  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1378  At each time step, a test is performed to see if there is enough ice mass to
1379  calve an iceberg of each class in order (1 to 10).
1380  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1381  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1382\end{description}
1383
1384Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1385The latter act to disintegrate the iceberg.
1386This is either all melted freshwater,
1387or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1388which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1389Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1390
1391Extensive diagnostics can be produced.
1392Separate output files are maintained for human-readable iceberg information.
1393A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1394The amount of information is controlled by two integer parameters:
1395\begin{description}
1396\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1397  represents an increasing number of points in the code at which variables are written,
1398  and an increasing level of obscurity.
1399\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1400\end{description}
1401
1402Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1403A non-zero value represents how many timesteps between writes of information into the output file.
1404These output files are in NETCDF format.
1405When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1406Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1407So care is needed to recreate data for individual icebergs,
1408since its trajectory data may be spread across multiple files.
1409
1410%% =================================================================================================
1411\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1412\label{sec:SBC_wave}
1413
1414\begin{listing}
1415  \nlst{namsbc_wave}
1416  \caption{\forcode{&namsbc_wave}}
1417  \label{lst:namsbc_wave}
1418\end{listing}
1419
1420Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1421physical processes related to ocean surface waves, namely the surface stress modified by growth and
1422dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1423tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1424the wind stress.
1425
1426Physical processes related to ocean surface waves can be accounted by setting the logical variable
1427\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1428different processes should be activated as explained in the following sections.
1429
1430Wave fields can be provided either in forced or coupled mode:
1431\begin{description}
1432\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1433for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1434Input Data generic Interface (see \autoref{sec:SBC_input}).
1435\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1436in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1437\end{description}
1438
1439%% =================================================================================================
1440\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1441\label{subsec:SBC_wave_cdgw}
1442
1443The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1444can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1445Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1446the drag coefficient is computed according to the stable/unstable conditions of the
1447air-sea interface following \citet{large.yeager_trpt04}.
1448
1449%% =================================================================================================
1450\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1451\label{subsec:SBC_wave_sdw}
1452
1453The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1454It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1455and the current measured at a fixed point (Eulerian velocity).
1456As waves travel, the water particles that make up the waves travel in orbital motions but
1457without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1458at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1459An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1460representation of surface physics in ocean general circulation models. %GS: reference needed
1461The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1462
1463\[
1464  % \label{eq:SBC_wave_sdw}
1465  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1466  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1467  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1468\]
1469
1470where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1471$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1472$k$ is the mean wavenumber defined as:
1473$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1474
1475In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1476and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1477To simplify, it is customary to use approximations to the full Stokes profile.
1478Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1479are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1480$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1481and makes possible the estimation of the surface Stokes drift for random directional waves in
1482realistic wave conditions:
1483
1484\begin{description}
1485\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1486\citet{breivik.janssen.ea_JPO14}:
1487
1488\[
1489  % \label{eq:SBC_wave_sdw_0a}
1490  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1491\]
1492
1493where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1494
1495\[
1496  % \label{eq:SBC_wave_sdw_0b}
1497  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1498  \quad \text{and }\
1499  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1500\]
1501
1502where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1503
1504\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1505reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1506\citep{breivik.bidlot.ea_OM16}:
1507
1508\[
1509  % \label{eq:SBC_wave_sdw_1}
1510  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1511  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1512\]
1513
1514where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1515
1516\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1517but using the wave frequency from a wave model.
1518
1519\end{description}
1520
1521The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1522and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1523
1524\[
1525  % \label{eq:SBC_wave_eta_sdw}
1526  \frac{\partial{\eta}}{\partial{t}} =
1527  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1528\]
1529
1530The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1531for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1532that is induced by the three-dimensional Stokes velocity.
1533The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1534can be formulated as follows:
1535
1536\[
1537  % \label{eq:SBC_wave_tra_sdw}
1538  \frac{\partial{c}}{\partial{t}} =
1539  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1540\]
1541
1542%% =================================================================================================
1543\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1544\label{subsec:SBC_wave_stcor}
1545
1546In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1547in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1548This additional force may have impact on the Ekman turning of the surface current.
1549In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1550approximations described in \autoref{subsec:SBC_wave_sdw}),
1551\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1552
1553%% =================================================================================================
1554\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1555\label{subsec:SBC_wave_tauw}
1556
1557The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1558into the waves \citep{janssen.breivik.ea_trpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1559available for forcing the mean circulation, while in the opposite case of a decaying sea
1560state, more momentum is available for forcing the ocean.
1561Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1562but in practice, an equilibrium sea state is a fairly rare event.
1563So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1564
1565\[
1566  % \label{eq:SBC_wave_tauoc}
1567  \tau_{oc,a} = \tau_a - \tau_w
1568\]
1569
1570where $\tau_a$ is the atmospheric surface stress;
1571$\tau_w$ is the atmospheric stress going into the waves defined as:
1572
1573\[
1574  % \label{eq:SBC_wave_tauw}
1575  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1576\]
1577
1578where: $c_p$ is the phase speed of the gravity waves,
1579$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1580the physics of ocean waves. The first one, $S_{in}$, describes the generation
1581of ocean waves by wind and therefore represents the momentum and energy transfer
1582from air to ocean waves; the second term $S_{nl}$ denotes
1583the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1584describes the dissipation of waves by processes such as white-capping, large scale breaking
1585eddy-induced damping.
1586
1587The wave stress derived from an external wave model can be provided either through the normalized
1588wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1589meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1590
1591%% =================================================================================================
1592\section{Miscellaneous options}
1593\label{sec:SBC_misc}
1594
1595%% =================================================================================================
1596\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1597\label{subsec:SBC_dcy}
1598
1599\begin{figure}[!t]
1600  \centering
1601  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
1602  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1603    Example of reconstruction of the diurnal cycle variation of short wave flux from
1604    daily mean values.
1605    The reconstructed diurnal cycle (black line) is chosen as
1606    the mean value of the analytical cycle (blue line) over a time step,
1607    not as the mid time step value of the analytically cycle (red square).
1608    From \citet{bernie.guilyardi.ea_CD07}.}
1609  \label{fig:SBC_diurnal}
1610\end{figure}
1611
1612\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.
1613%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1614Nevertheless, 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}.
1615Furthermore, only the knowledge of daily mean value of SWF is needed,
1616as higher frequency variations can be reconstructed from them,
1617assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1618The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1619setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1620using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1621the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1622The reconstruction is performed in the \mdl{sbcdcy} module.
1623The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1624The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1625a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1626The use of diurnal cycle reconstruction requires the input SWF to be daily
1627(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1628Furthermore, it is recommended to have a least 8 surface module time steps per day,
1629that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1630An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1631one every 2~hours (from 1am to 11pm).
1632
1633\begin{figure}[!t]
1634  \centering
1635  \includegraphics[width=0.66\textwidth]{SBC_dcy}
1636  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1637    Example of reconstruction of the diurnal cycle variation of short wave flux from
1638    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1639    The display is on (i,j) plane.}
1640  \label{fig:SBC_dcy}
1641\end{figure}
1642
1643Note also that the setting a diurnal cycle in SWF is highly recommended when
1644the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1645an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1646
1647%% =================================================================================================
1648\subsection{Rotation of vector pairs onto the model grid directions}
1649\label{subsec:SBC_rotation}
1650
1651When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1652pairs of vector components can be rotated from east-north directions onto the local grid directions.
1653This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1654be defined relative to a rectilinear grid.
1655To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1656The eastward component must start with "U" and the northward component with "V".
1657The remaining characters in the strings are used to identify which pair of components go together.
1658So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1659rotate them on to the model grid directions;
1660"U2" and "V2" could be used against a second pair of components, and so on.
1661The extra characters used in the strings are arbitrary.
1662The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1663
1664%% =================================================================================================
1665\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1666\label{subsec:SBC_ssr}
1667
1668\begin{listing}
1669  \nlst{namsbc_ssr}
1670  \caption{\forcode{&namsbc_ssr}}
1671  \label{lst:namsbc_ssr}
1672\end{listing}
1673
1674Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1675On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1676a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1677\[
1678  % \label{eq:SBC_dmp_q}
1679  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1680\]
1681where SST is a sea surface temperature field (observed or climatological),
1682$T$ is the model surface layer temperature and
1683$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1684For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1685This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1686
1687In the fresh water budget, a feedback term can also be added.
1688Converted into an equivalent freshwater flux, it takes the following expression :
1689
1690\begin{equation}
1691  \label{eq:SBC_dmp_emp}
1692  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1693  {\left.S\right|_{k=1}}
1694\end{equation}
1695
1696where $\textit{emp}_{o }$ is a net surface fresh water flux
1697(observed, climatological or an atmospheric model product),
1698\textit{SSS}$_{Obs}$ is a sea surface salinity
1699(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1700$\left.S\right|_{k=1}$ is the model surface layer salinity and
1701$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1702Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1703the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1704The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1705reduce the uncertainties we have on the observed freshwater budget.
1706
1707%% =================================================================================================
1708\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1709\label{subsec:SBC_ice-cover}
1710
1711The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1712There are several way to handle sea-ice in the system depending on
1713the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1714\begin{description}
1715\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1716  This is a typical namelist value used for tropical ocean domain.
1717  The surface fluxes are simply specified for an ice-free ocean.
1718  No specific things is done for sea-ice.
1719\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1720  An observed ice covered area is read in a file.
1721  Below this area, the SST is restored to the freezing point and
1722  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1723  The associated modification of the freshwater fluxes are done in such a way that
1724  the change in buoyancy fluxes remains zero.
1725  This prevents deep convection to occur when trying to reach the freezing point
1726  (and so ice covered area condition) while the SSS is too large.
1727  This manner of managing sea-ice area, just by using a IF case,
1728  is usually referred as the \textit{ice-if} model.
1729  It can be found in the \mdl{sbcice\_if} module.
1730\item [nn\_ice = 2 or more] A full sea ice model is used.
1731  This model computes the ice-ocean fluxes,
1732  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1733  provide the surface averaged ocean fluxes.
1734  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1735  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1736  (\ie\ $2$ for SI3 or $3$ for CICE).
1737\end{description}
1738
1739% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1740%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1741
1742%% =================================================================================================
1743\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1744\label{subsec:SBC_cice}
1745
1746It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1747to the CICE sea-ice model by using \key{cice}.
1748The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1749the additional 'hadgem3' drivers will be required, even with the latest code release.
1750Input grid files consistent with those used in \NEMO\ will also be needed,
1751and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1752(seek advice from UKMO if necessary).
1753Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1754(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1755or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1756(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1757The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1758(although coupling ocean and ice less frequently should work,
1759it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1760the user should check that results are not significantly different to the standard case).
1761
1762There are two options for the technical coupling between \NEMO\ and CICE.
1763The standard version allows complete flexibility for the domain decompositions in the individual models,
1764but this is at the expense of global gather and scatter operations in the coupling which
1765become very expensive on larger numbers of processors.
1766The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1767the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1768and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1769allows much more efficient direct coupling on individual processors.
1770This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1771there is no sea ice.
1772
1773%% =================================================================================================
1774\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1775\label{subsec:SBC_fwb}
1776
1777\begin{listing}
1778  \nlst{namsbc_fwb}
1779  \caption{\forcode{&namsbc_fwb}}
1780  \label{lst:namsbc_fwb}
1781\end{listing}
1782
1783For global ocean simulations, it can be useful to introduce a control of the
1784mean sea level in order to prevent unrealistic drifting of the sea surface
1785height due to unbalanced freshwater fluxes. In \NEMO, two options for
1786controlling the freshwater budget are proposed.
1787
1788\begin{description}
1789\item [{\np[=0]{nn_fwb}{nn\_fwb}}:] No control at all; the mean sea level is
1790  free to drift, and will certainly do so.
1791\item [{\np[=1]{nn_fwb}{nn\_fwb}}:] The global mean \textit{emp} is set to zero at each model time step.
1792  %GS: comment below still relevant ?
1793  %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).
1794\item [{\np[=2]{nn_fwb}{nn\_fwb}}:] \textit{emp} is adjusted by adding a
1795  spatially uniform, annual-mean freshwater flux that balances the freshwater
1796  budget at the end of the previous year; as the model uses the Boussinesq
1797  approximation, the freshwater budget can be evaluated from the change in the
1798  mean sea level and in the ice and snow mass after the end of each simulation
1799  year; at the start of the model run, an initial adjustment flux can be set
1800  using parameter \np{rn_rwb0}{rn\_fwb0} in namelist \nam{sbc_fwb}{sbc\_fwb}.
1801\end{description}
1802
1803% Griffies doc:
1804% When running ocean-ice simulations, we are not explicitly representing land processes,
1805% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1806% it is important to balance the hydrological cycle in ocean-ice models.
1807% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1808% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1809% a chosen time scale.
1810% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1811% so that there is always a zero net input of water to the ocean-ice system.
1812% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1813% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1814% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1815% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1816% and ice models when aiming to balance the hydrological cycle.
1817% 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,
1818% not the water in any one sub-component. As an extreme example to illustrate the issue,
1819% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1820% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1821% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1822% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1823% in ocean-ice models.
1824
1825\subinc{\input{../../global/epilogue}}
1826
1827\end{document}
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