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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\thispagestyle{plain}
9
10\chaptertoc
11
12\paragraph{Changes record} ~\\
13
14{\footnotesize
15  \begin{tabularx}{\textwidth}{l||X|X}
16    Release & Author(s) & Modifications \\
17    \hline
18    {\em  next} & {\em Simon M{\" u}ller} & {\em Update of \autoref{sec:SBC_TDE}; revision of \autoref{subsec:SBC_fwb}}\\[2mm]
19    {\em   4.0} & {\em ...} & {\em ...} \\
20    {\em   3.6} & {\em ...} & {\em ...} \\
21    {\em   3.4} & {\em ...} & {\em ...} \\
22    {\em <=3.4} & {\em ...} & {\em ...}
23  \end{tabularx}
24}
25
26\clearpage
27
28\begin{listing}
29  \nlst{namsbc}
30  \caption{\forcode{&namsbc}}
31  \label{lst:namsbc}
32\end{listing}
33
34The ocean needs seven fields as surface boundary condition:
35
36\begin{itemize}
37\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
38\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
39\item the surface freshwater budget $\left( {\textit{emp}} \right)$
40\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
41\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
42\end{itemize}
43
44Four different ways are available to provide the seven fields to the ocean. They are controlled by
45namelist \nam{sbc}{sbc} variables:
46
47\begin{itemize}
48\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms,
49\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
50\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
51(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
52\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
53\end{itemize}
54
55The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
56
57When the fields are supplied from data files (bulk, flux and mixed formulations),
58the input fields do not need to be supplied on the model grid.
59Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
60the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
61If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
62should be masked or filled to avoid spurious results in proximity of the coasts, as
63large sea-land gradients characterize most of the atmospheric variables.
64
65In addition, the resulting fields can be further modified using several namelist options.
66These options control:
67
68\begin{itemize}
69\item the rotation of vector components supplied relative to an east-north coordinate system onto
70  the local grid directions in the model,
71\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
72\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
73\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
74  (\np[=0..3]{nn_ice}{nn\_ice}),
75\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
76\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
77  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
78\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
79  (\np[=0..2]{nn_fwb}{nn\_fwb}),
80\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
81  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
82\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
83\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
84\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
85\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
86\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
87\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
88\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
89\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
90\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}),
91\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
92\end{itemize}
93
94In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
95Then we present the three ways of providing the surface boundary conditions,
96followed by the description of the atmospheric pressure and the river runoff.
97Next, the scheme for interpolation on the fly is described.
98Finally, the different options that further modify the fluxes applied to the ocean are discussed.
99One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
100which act as drifting sources of fresh water.
101Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
102which provides additional sources of fresh water.
103
104%% =================================================================================================
105\section{Surface boundary condition for the ocean}
106\label{sec:SBC_ocean}
107
108The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
109It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
110the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
111As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
112\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
113
114The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
115$Q_{ns}$ and $Q_{sr}$, respectively.
116The former is the non penetrative part of the heat flux
117(\ie\ the sum of sensible, latent and long wave heat fluxes plus
118the heat content of the mass exchange between the ocean and sea-ice).
119It is applied in \mdl{trasbc} module as a surface boundary condition trend of
120the first level temperature time evolution equation
121(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
122The latter is the penetrative part of the heat flux.
123It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
124\np[=.true.]{ln_traqsr}{ln\_traqsr}.
125The way the light penetrates inside the water column is generally a sum of decreasing exponentials
126(see \autoref{subsec:TRA_qsr}).
127
128The surface freshwater budget is provided by the \textit{emp} field.
129It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
130possibly with the sea-ice and ice shelves (freezing minus melting of ice).
131It affects the ocean in two different ways:
132$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
133a volume flux, and
134$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
135the mass exchanged with atmosphere, sea-ice and ice shelves.
136
137%\colorbox{yellow}{Miss: }
138%A extensive description of all namsbc namelist (parameter that have to be
139%created!)
140%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
141%ssv) \ie\ information required by flux computation or sea-ice
142%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
143%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
144%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
145%Fluxes update only each nf\_sbc time step (namsbc) explain relation
146%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
147%nf\_sbc
148%Explain here all the namlist namsbc variable{\ldots}.
149% explain : use or not of surface currents
150%\colorbox{yellow}{End Miss }
151
152The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
153the surface currents, temperature and salinity.
154These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
155these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
156
157\begin{table}[tb]
158  \centering
159  \begin{tabular}{|l|l|l|l|}
160    \hline
161    Variable description                           & Model variable  & Units  & point                 \\
162    \hline
163    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
164    \hline
165    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
166    \hline
167    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
168    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
169  \end{tabular}
170  \caption[Ocean variables provided to the surface module)]{
171    Ocean variables provided to the surface module (\texttt{SBC}).
172    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
173    \ie\ the frequency of computation of surface fluxes.}
174  \label{tab:SBC_ssm}
175\end{table}
176
177%\colorbox{yellow}{Penser a} mettre dans le restant l'info nn\_fsbc ET nn\_fsbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt
178
179%% =================================================================================================
180\section{Input data generic interface}
181\label{sec:SBC_input}
182
183A generic interface has been introduced to manage the way input data
184(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
185This task is achieved by \mdl{fldread}.
186The module is designed with four main objectives in mind:
187\begin{enumerate}
188\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
189  and according to the different calendars available in the model.
190\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
191\item make the run duration independent from the period cover by the input files.
192\item provide a simple user interface and a rather simple developer interface by
193  limiting the number of prerequisite informations.
194\end{enumerate}
195
196As a result, the user has only to fill in for each variable a structure in the namelist file to
197define the input data file and variable names, the frequency of the data (in hours or months),
198whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
199and three additional parameters for the on-the-fly interpolation.
200When adding a new input variable, the developer has to add the associated structure in the namelist,
201read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
202and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
203
204The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
205(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
206if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
207
208Note that when an input data is archived on a disc which is accessible directly from the workspace where
209the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
210By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
211
212%% =================================================================================================
213\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
214\label{subsec:SBC_fldread}
215
216The structure associated with an input variable contains the following information:
217\begin{forlines}
218!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
219!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
220\end{forlines}
221where
222\begin{description}
223\item [File name]: the stem name of the NetCDF file to be opened.
224  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
225  by date information and possibly a prefix (when using AGRIF).
226  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
227  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
228  \begin{table}[htbp]
229    \centering
230    \begin{tabular}{|l|c|c|c|}
231      \hline
232                                  &  daily or weekLL     &  monthly           &  yearly        \\
233      \hline
234      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
235      \hline
236      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
237      \hline
238    \end{tabular}
239    \caption[Naming nomenclature for climatological or interannual input file]{
240      Naming nomenclature for climatological or interannual input file,
241      as a function of the open/close frequency.
242      The stem name is assumed to be 'fn'.
243      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
244      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
245      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
246      always coded with 4 or 2 digits.
247      Note that (1) in mpp, if the file is split over each subdomain,
248      the suffix '.nc' is replaced by '\_PPPP.nc',
249      where 'PPPP' is the process number coded with 4 digits;
250      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
251    }
252    \label{tab:SBC_fldread}
253  \end{table}
254\item [Record frequency]: the frequency of the records contained in the input file.
255  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
256  (for example -1 for monthly forcing or -12 for annual forcing).
257  Note that this frequency must REALLY be an integer and not a real.
258  On some computers, setting it to '24.' can be interpreted as 240!
259\item [Variable name]: the name of the variable to be read in the input NetCDF file.
260\item [Time interpolation]: a logical to activate, or not, the time interpolation.
261  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
262  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
263  00h00'00'' to 23h59'59".
264  If set to 'true', the forcing will have a broken line shape.
265  Records are assumed to be dated at the middle of the forcing period.
266  For example, when using a daily forcing with time interpolation,
267  linear interpolation will be performed between mid-day of two consecutive days.
268\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
269  or an interannual forcing which will requires additional files if
270  the period covered by the simulation exceeds the one of the file.
271  See the above file naming strategy which impacts the expected name of the file to be opened.
272\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
273  Four cases are coded:
274  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
275  means the forcing files will contain data for one day, one week, one month or one year.
276  Files are assumed to contain data from the beginning of the open/close period.
277  For example, the first record of a yearly file containing daily data is Jan 1st even if
278  the experiment is not starting at the beginning of the year.
279\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
280  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
281\end{description}
282
283Additional remarks:\\
284(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
285The only tricky point is therefore to specify the date at which we need to do the interpolation and
286the date of the records read in the input files.
287Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
288For example, for an experiment starting at 0h00'00" with a one-hour time-step,
289a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
290However, for forcing data related to the surface module,
291values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
292For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
293The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
294In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
295(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
296The calendar associated with the forcing field is build according to the information provided by
297user in the record frequency, the open/close frequency and the type of temporal interpolation.
298For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
299start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
300(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
301interpolating data with the first (last) record of the open/close period.
302For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
303the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
304Dec 31st 12h00'00" and Jan 1st 12h00'00".
305If the forcing is climatological, Dec and Jan will be keep-up from the same year.
306However, if the forcing is not climatological, at the end of
307the open/close period, the code will automatically close the current file and open the next one.
308Note that, if the experiment is starting (ending) at the beginning (end) of
309an open/close period, we do accept that the previous (next) file is not existing.
310In this case, the time interpolation will be performed between two identical values.
311For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
312we do accept that the file related to year Y-1 is not existing.
313The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
314If the file of year Y-1 exists, the code will read its last record.
315Therefore, this file can contain only one record corresponding to Dec 31st,
316a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
317
318%% =================================================================================================
319\subsection{Interpolation on-the-fly}
320\label{subsec:SBC_iof}
321
322Interpolation on the Fly allows the user to supply input files required for the surface forcing on
323grids other than the model grid.
324To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
325interpolate from the data grid to the model grid.
326The original development of this code used the SCRIP package
327(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
328In principle, any package such as CDO can be used to generate the weights, but the variables in
329the input weights file must have the same names and meanings as assumed by the model.
330Two methods are currently available: bilinear and bicubic interpolations.
331Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
332the input file and substitute the corresponding values with the average of the 8 neighbouring points in
333the native external grid.
334Only "sea points" are considered for the averaging.
335The land/sea mask file must be provided in the structure associated with the input variable.
336The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
337the associated variables and should be equal to 1 over land and 0 elsewhere.
338The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
339Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
340
341%% =================================================================================================
342\subsubsection{Bilinear interpolation}
343\label{subsec:SBC_iof_bilinear}
344
345The input weights file in this case has two sets of variables:
346src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
347The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
348Each src value is an integer corresponding to the index of a point in the input grid when
349written as a one dimensional array.
350For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
351There are four of each variable because bilinear interpolation uses the four points defining
352the grid box containing the point to be interpolated.
353All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
354generate a value for point (i,j) in the model.
355
356Symbolically, the algorithm used is:
357\[
358  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
359\]
360where function idx() transforms a one dimensional index src(k) into a two dimensional index,
361and wgt(1) corresponds to variable "wgt01" for example.
362
363%% =================================================================================================
364\subsubsection{Bicubic interpolation}
365\label{subsec:SBC_iof_bicubic}
366
367Again, there are two sets of variables: "src" and "wgt".
368But in this case, there are 16 of each.
369The symbolic algorithm used to calculate values on the model grid is now:
370
371\[
372  \begin{split}
373    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
374    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
375    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
376    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
377  \end{split}
378\]
379The gradients here are taken with respect to the horizontal indices and not distances since
380the spatial dependency has been included into the weights.
381
382%% =================================================================================================
383\subsubsection{Implementation}
384\label{subsec:SBC_iof_imp}
385
386To activate this option, a non-empty string should be supplied in
387the weights filename column of the relevant namelist;
388if this is left as an empty string no action is taken.
389In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
390as and when they are first required.
391This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
392inspecting a global attribute stored in the weights input file.
393This attribute must be called "ew\_wrap" and be of integer type.
394If it is negative, the input non-model grid is assumed to be not cyclic.
395If zero or greater, then the value represents the number of columns that overlap.
396$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
397if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
398If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
399In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
400therefore the grid is assumed to be cyclic with no overlapping columns.
401(In fact, this only matters when bicubic interpolation is required.)
402Note that no testing is done to check the validity in the model,
403since there is no way of knowing the name used for the longitude variable,
404so it is up to the user to make sure his or her data is correctly represented.
405
406Next the routine reads in the weights.
407Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
408The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
409and when required, for reading in the variable to be interpolated (on the input data grid).
410The size of the input data array is determined by examining the values in the "src" arrays to
411find the minimum and maximum i and j values required.
412Since bicubic interpolation requires the calculation of gradients at each point on the grid,
413the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
414When the array of points from the data file is adjacent to an edge of the data grid,
415the halo is either a copy of the row/column next to it (non-cyclical case),
416or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
417
418%% =================================================================================================
419\subsubsection{Limitations}
420\label{subsec:SBC_iof_lim}
421
422\begin{enumerate}
423\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
424\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
425  a bicubic interpolation method is used.
426\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
427\item The gradients across the ends of a cyclical grid assume that the grid spacing between
428  the two columns involved are consistent with the weights used.
429\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
430  but this has not been implemented.)
431\end{enumerate}
432
433%% =================================================================================================
434\subsubsection{Utilities}
435\label{subsec:SBC_iof_util}
436
437% to be completed
438A set of utilities to create a weights file for a rectilinear input grid is available
439(see the directory NEMOGCM/TOOLS/WEIGHTS).
440
441%% =================================================================================================
442\subsection{Standalone surface boundary condition scheme (SAS)}
443\label{subsec:SBC_SAS}
444
445\begin{listing}
446  \nlst{namsbc_sas}
447  \caption{\forcode{&namsbc_sas}}
448  \label{lst:namsbc_sas}
449\end{listing}
450
451In some circumstances, it may be useful to avoid calculating the 3D temperature,
452salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
453For example:
454
455\begin{itemize}
456\item Multiple runs of the model are required in code development to
457  see the effect of different algorithms in the bulk formulae.
458\item The effect of different parameter sets in the ice model is to be examined.
459\item Development of sea-ice algorithms or parameterizations.
460\item Spinup of the iceberg floats
461\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
462\end{itemize}
463
464The Standalone Surface scheme provides this capacity.
465Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
466A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
467However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
468In this configuration, a few routines in the standard model are overriden by new versions.
469Routines replaced are:
470
471\begin{itemize}
472\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
473  Since the ocean state is not calculated all associated initialisations have been removed.
474\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
475\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
476  New surface modules that can function when only the surface level of the ocean state is defined can also be added
477  (\eg\ icebergs).
478\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
479  so calls to restart functions have been removed.
480  This also means that the calendar cannot be controlled by time in a restart file,
481  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
482\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
483\item \mdl{diawri}: All 3D data have been removed from the output.
484  The surface temperature, salinity and velocity components (which have been read in) are written along with
485  relevant forcing and ice data.
486\end{itemize}
487
488One new routine has been added:
489
490\begin{itemize}
491\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
492  velocity arrays at the surface.
493  These filenames are supplied in namelist namsbc\_sas.
494  Unfortunately, because of limitations with the \mdl{iom} module,
495  the full 3D fields from the mean files have to be read in and interpolated in time,
496  before using just the top level.
497  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
498\end{itemize}
499
500The 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
501 (\np[=.true.]{ln_flx}{ln\_flx}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln_flx}{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in.
502
503%% =================================================================================================
504\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
505\label{sec:SBC_flx}
506
507% Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk
508% parameterization'' (i.e NCAR, COARE, ECMWF...)
509
510\begin{listing}
511  \nlst{namsbc_flx}
512  \caption{\forcode{&namsbc_flx}}
513  \label{lst:namsbc_flx}
514\end{listing}
515
516In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
517the surface boundary condition fields are directly read from input files.
518The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
519the name of the variable read in the file, the time frequency at which it is given (in hours),
520and a logical setting whether a time interpolation to the model time step is required for this field.
521See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
522
523Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
524See \autoref{subsec:SBC_ssr} for its specification.
525
526%% =================================================================================================
527\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
528\label{sec:SBC_blk}
529
530% L. Brodeau, December 2019... %
531
532\begin{listing}
533  \nlst{namsbc_blk}
534  \caption{\forcode{&namsbc_blk}}
535  \label{lst:namsbc_blk}
536\end{listing}
537
538If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea
539fluxes associated with surface boundary conditions are estimated by means of the
540traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed
541near-surface atmosphere state (typically extracted from a weather reanalysis)
542and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc}
543time-step(s).
544
545% Turbulent air-sea fluxes are computed using the sea surface properties and
546% atmospheric SSVs at height $z$ above the sea surface, with the traditional
547% aerodynamic bulk formulae:
548
549Note: all the NEMO Fortran routines involved in the present section have been
550initially developed (and are still developed in parallel) in
551the \href{https://brodeau.github.io/aerobulk}{\texttt{AeroBulk}} open-source project
552\citep{brodeau.barnier.ea_JPO16}.
553
554%%% Bulk formulae are this:
555\subsection{Bulk formulae}
556\label{subsec:SBC_blkform}
557
558In NEMO, the set of equations that relate each component of the surface fluxes
559to the near-surface atmosphere and sea surface states writes
560
561\begin{subequations}
562  \label{eq:SBC_bulk}
563  \label{eq:SBC_bulk_form}
564  \begin{align}
565    \mathbf{\tau} &= \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
566    Q_H           &= \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
567    E             &= \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
568    Q_L           &= -L_v \, E \\
569    Q_{sr}        &= (1 - a) Q_{sw\downarrow} \\
570    Q_{ir}        &= \delta (Q_{lw\downarrow} -\sigma T_s^4)
571  \end{align}
572\end{subequations}
573
574with
575   \[ \theta_z \simeq T_z+\gamma z \]
576   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
577from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
578where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
579$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
580flux.
581$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
582and longwave radiative fluxes, respectively.
583Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$
584implies a gain of the relevant quantity for the ocean, while a positive $E$
585implies a freshwater loss for the ocean.
586$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
587coefficients for momentum, sensible heat, and moisture, respectively.
588$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
589vaporization of water.
590$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
591and specific humidity of air at height $z$ above the sea surface,
592respectively. $\gamma z$ is a temperature correction term which accounts for the
593adiabatic lapse rate and approximates the potential temperature at height
594$z$ \citep{josey.gulev.ea_OCC13}.
595$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
596(possibly referenced to the surface current $\mathbf{u_0}$).%,
597%\autoref{s_res1}.\autoref{ss_current}). %% Undefined references
598The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
599$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution.
600$a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\
601%$p_a$ is the mean sea-level pressure (SLP).
602$T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity
603of air at temperature $T_s$; it includes a 2\% reduction to account for the
604presence of salt in seawater \citep{sverdrup.johnson.ea_bk42,kraus.businger_QJRMS96}.
605Depending on the bulk parametrization used, $T_s$ can either be the temperature
606at the air-sea interface (skin temperature, hereafter SSST) or at typically a
607few tens of centimeters below the surface (bulk sea surface temperature,
608hereafter SST).
609The SSST differs from the SST due to the contributions of two effects of
610opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL,
611respectively, see \autoref{subsec:SBC_skin}).
612Technically, when the ECMWF or COARE* bulk parametrizations are selected
613(\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}),
614$T_s$ is the SSST, as opposed to the NCAR bulk parametrization
615(\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature
616at first T-point level).
617
618For more details on all these aspects the reader is invited to refer
619to \citet{brodeau.barnier.ea_JPO16}.
620
621\subsection{Bulk parametrizations}
622\label{subsec:SBC_blk_ocean}
623%%%\label{subsec:SBC_param}
624
625Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae
626strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and
627$C_E$. They are estimated with what we refer to as a \emph{bulk
628parametrization} algorithm. When relevant, these algorithms also perform the
629height adjustment of humidity and temperature to the wind reference measurement
630height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}).
631
632For the open ocean, four bulk parametrization algorithms are available in NEMO:
633
634\begin{itemize}
635\item NCAR, formerly known as CORE, \citep{large.yeager_trpt04,large.yeager_CD09}
636\item COARE 3.0 \citep{fairall.bradley.ea_JC03}
637\item COARE 3.6 \citep{edson.jampana.ea_JPO13}
638\item ECMWF (IFS documentation, cy45)
639\end{itemize}
640
641With respect to version 3, the principal advances in version 3.6 of the COARE
642bulk parametrization are built around improvements in the representation of the
643effects of waves on
644fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO16}. This includes
645improved relationships of surface roughness, and whitecap fraction on wave
646parameters. It is therefore recommended to chose version 3.6 over 3.
647
648\subsection{Cool-skin and warm-layer parametrizations}
649%\subsection[Cool-skin and warm-layer parameterizations (\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})}
650\label{subsec:SBC_skin}
651
652As opposed to the NCAR bulk parametrization, more advanced bulk
653parametrizations such as COARE3.x and ECMWF are meant to be used with the skin
654temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
655the first T-point level, see \autoref{subsec:SBC_blkform}).
656
657As such, the relevant cool-skin and warm-layer parametrization must be
658activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs}
659and \np[=T]{ln_skin_wl}{ln\_skin\_wl} to use COARE3.x or ECMWF in a consistent
660way.
661
662\texttt{\#LB: ADD BLBLA ABOUT THE TWO CS/WL PARAMETRIZATIONS (ECMWF and COARE) !!!}
663
664For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same
665basis: \citet{fairall.bradley.ea_JGRO96}. With some minor updates based
666on \citet{zeng.beljaars_GRL05} for ECMWF \iffalse, and \citet{fairall.ea_19?} for COARE \fi
6673.6.
668
669For the warm-layer scheme, ECMWF is based on \citet{zeng.beljaars_GRL05} with a
670recent update from \citet{takaya.bidlot.ea_JGR10} (consideration of the
671turbulence input from Langmuir circulation).
672
673Importantly, COARE warm-layer scheme \iffalse \citep{fairall.ea_19?} \fi includes a prognostic
674equation for the thickness of the warm-layer, while it is considered as constant
675in the ECWMF algorithm.
676
677\subsection{Appropriate use of each bulk parametrization}
678
679\subsubsection{NCAR}
680
681NCAR bulk parametrizations (formerly known as CORE) is meant to be used with the
682CORE II atmospheric forcing \citep{large.yeager_CD09}. The expected sea surface
683temperature is the bulk SST. Hence the following namelist parameters must be
684set:
685
686\begin{forlines}
687  ...
688  ln_NCAR    = .true.
689  ...
690  rn_zqt     = 10.     ! Air temperature & humidity reference height (m)
691  rn_zu      = 10.     ! Wind vector reference height (m)
692  ...
693  ln_skin_cs = .false. ! use the cool-skin parameterization
694  ln_skin_wl = .false. ! use the warm-layer parameterization
695  ...
696  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
697\end{forlines}
698
699\subsubsection{ECMWF}
700
701With an atmospheric forcing based on a reanalysis of the ECMWF, such as the
702Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to
703use the ECMWF bulk parametrizations with the cool-skin and warm-layer
704parametrizations activated. In ECMWF reanalyzes, since air temperature and
705humidity are provided at the 2\,m height, and given that the humidity is
706distributed as the dew-point temperature, the namelist must be tuned as follows:
707
708\begin{forlines}
709  ...
710  ln_ECMWF   = .true.
711  ...     
712  rn_zqt     =  2.     ! Air temperature & humidity reference height (m)
713  rn_zu      = 10.     ! Wind vector reference height (m)
714  ...
715  ln_skin_cs = .true. ! use the cool-skin parameterization
716  ln_skin_wl = .true. ! use the warm-layer parameterization
717  ...
718  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
719  ...
720\end{forlines}
721
722Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
723of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
724triggers the use of the ECMWF cool-skin and warm-layer parametrizations,
725respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
726
727\subsubsection{COARE 3.x}
728
729Since the ECMWF parametrization is largely based on the COARE* parametrization,
730the two algorithms are very similar in terms of structure and closure
731approach. As such, the namelist tuning for COARE 3.x is identical to that of
732ECMWF:
733
734\begin{forlines}
735  ...
736  ln_COARE3p6 = .true.
737  ...     
738  ln_skin_cs = .true. ! use the cool-skin parameterization
739  ln_skin_wl = .true. ! use the warm-layer parameterization
740  ...
741\end{forlines}
742
743Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection
744of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
745triggers the use of the COARE cool-skin and warm-layer parametrizations,
746respectively (found in \textit{sbcblk\_skin\_coare.F90}).
747
748%lulu
749
750% In a typical bulk algorithm, the BTCs under neutral stability conditions are
751% defined using \emph{in-situ} flux measurements while their dependence on the
752% stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and
753% the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are
754% functions of the wind speed and the near-surface stability of the atmospheric
755% surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$
756% and $q_z$.
757
758\subsection{Prescribed near-surface atmospheric state}
759
760The atmospheric fields used depend on the bulk formulae used.  In forced mode,
761when a sea-ice model is used, a specific bulk formulation is used.  Therefore,
762different bulk formulae are used for the turbulent fluxes computation over the
763ocean and over sea-ice surface.
764
765%The choice is made by setting to true one of the following namelist
766%variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6}
767%and \np{ln_ECMWF}{ln\_ECMWF}.
768
769Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
770The required 9 input fields are:
771
772\begin{table}[htbp]
773  \centering
774  \begin{tabular}{|l|c|c|c|}
775    \hline
776    Variable description                 & Model variable & Units              & point \\
777    \hline
778    i-component of the 10m air velocity  & wndi           & $m.s^{-1}$         & T     \\
779    \hline
780    j-component of the 10m air velocity  & wndj           & $m.s^{-1}$         & T     \\
781    \hline
782    10m air temperature                  & tair           & $K$               & T     \\
783    \hline
784    Specific humidity                    & humi           & $-$               & T     \\
785    Relative humidity                    & ~              & $\%$              & T     \\
786    Dew-point temperature                & ~              & $K$               & T     \\   
787    \hline
788    Downwelling longwave radiation       & qlw            & $W.m^{-2}$         & T     \\
789    \hline
790    Downwelling shortwave radiation      & qsr            & $W.m^{-2}$         & T     \\
791    \hline
792    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
793    \hline
794    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
795    \hline
796    Mean sea-level pressure              & slp            & $Pa$              & T     \\
797    \hline
798    \end{tabular}
799  \label{tab:SBC_BULK}
800\end{table}
801
802Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
803It is simpler and faster (less fields to be read), but it is not the recommended method when
804the ocean grid size is the same or larger than the one of the input atmospheric fields.
805
806The \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},
807\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
808(spatial and temporal interpolations).
809
810\np{cn_dir}{cn\_dir} is the directory of location of bulk files
811%\np{ln_taudif}{ln\_taudif} is the flag to specify if we use High Frequency (HF) tau information (.true.) or not (.false.)
812\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
813\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
814
815Three multiplicative factors are available:
816\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
817increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
818The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
819the calculation of surface wind stress.
820Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
821
822As for the flux parametrization, information about the input data required by the model is provided in
823the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
824
825\subsubsection{Air humidity}
826
827Air humidity can be provided as three different parameters: specific humidity
828[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
829parameters)...
830
831%% =================================================================================================
832%\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})}
833%\label{subsec:SBC_blk_ocean}
834
835%Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
836%COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
837%their neutral transfer coefficients relationships with neutral wind.
838%\begin{itemize}
839%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_trpt04}.
840%  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
841%  They use an inertial dissipative method to compute the turbulent transfer coefficients
842%  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
843%  This \citet{large.yeager_trpt04} dataset is available through
844%  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
845%  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
846%  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
847%\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
848%\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details
849%\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9204}{IFS (Cy40r1)} %implementation and documentation.
850%  Surface roughness lengths needed for the Obukhov length are computed
851%  following \citet{beljaars_QJRMS95}.
852%\end{itemize}
853
854%% =================================================================================================
855\subsection{Ice-Atmosphere Bulk formulae}
856\label{subsec:SBC_blk_ice}
857
858\texttt{\#out\_of\_place:}
859 For sea-ice, three possibilities can be selected:
860a constant transfer coefficient (1.4e-3; default
861value), \citet{lupkes.gryanik.ea_JGRA12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
862and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
863\texttt{\#out\_of\_place.}
864
865Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
866
867\begin{itemize}
868\item Constant value (\forcode{Cd_ice=1.4e-3}):
869  default constant value used for momentum and heat neutral transfer coefficients
870\item \citet{lupkes.gryanik.ea_JGRA12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
871  This scheme adds a dependency on edges at leads, melt ponds and flows
872  of the constant neutral air-ice drag. After some approximations,
873  this can be resumed to a dependency on ice concentration (A).
874  This drag coefficient has a parabolic shape (as a function of ice concentration)
875  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.
876  It is theoretically applicable to all ice conditions (not only MIZ).
877\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
878  Alternative turbulent transfer coefficients formulation between sea-ice
879  and atmosphere with distinct momentum and heat coefficients depending
880  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
881  The parameterization is adapted from ECHAM6 atmospheric model.
882  Compared to Lupkes2012 scheme, it considers specific skin and form drags
883  to compute neutral transfer coefficients for both heat and momentum fluxes.
884  Atmospheric stability effect on transfer coefficient is also taken into account.
885\end{itemize}
886
887%% =================================================================================================
888\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
889\label{sec:SBC_cpl}
890
891\begin{listing}
892  \nlst{namsbc_cpl}
893  \caption{\forcode{&namsbc_cpl}}
894  \label{lst:namsbc_cpl}
895\end{listing}
896
897In the coupled formulation of the surface boundary condition,
898the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
899while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
900the atmospheric component.
901
902A generalised coupled interface has been developed.
903It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
904An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
905It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
906(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
907(Weather Research and Forecasting Model).
908
909When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
910the whole carbon cycle is computed.
911In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
912(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
913
914The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
915now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
916When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
917the number used in the sea ice model.
918In some limited cases, it may be possible to specify single category coupling fields even when
919the sea ice model is running with multiple categories -
920in this case, the user should examine the code to be sure the assumptions made are satisfactory.
921In cases where this is definitely not possible, the model should abort with an error message.
922
923%% =================================================================================================
924\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
925\label{sec:SBC_apr}
926
927\begin{listing}
928  \nlst{namsbc_apr}
929  \caption{\forcode{&namsbc_apr}}
930  \label{lst:namsbc_apr}
931\end{listing}
932
933The optional atmospheric pressure can be used to force ocean and ice dynamics
934(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
935The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
936can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
937When used to force the dynamics, the atmospheric pressure is further transformed into
938an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
939\[
940  % \label{eq:SBC_ssh_ib}
941  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
942\]
943where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
944A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
945In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
946\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
947
948The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
949For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
950(see \mdl{sbcssr} module).
951$\eta_{ib}$ can be written in the output.
952This can simplify altimetry data and model comparison as
953inverse barometer sea surface height is usually removed from these date prior to their distribution.
954
955When using time-splitting and BDY package for open boundaries conditions,
956the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
957\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
958
959%% =================================================================================================
960\section{Surface tides (TDE)}
961\label{sec:SBC_TDE}
962
963\begin{listing}
964  \nlst{nam_tide}
965  \caption{\forcode{&nam_tide}}
966  \label{lst:nam_tide}
967\end{listing}
968
969\subsection{Tidal constituents}
970Ocean model component TDE provides the common functionality for tidal forcing
971and tidal analysis in the model framework. This includes the computation of the gravitational
972surface forcing, as well as support for lateral forcing at open boundaries (see
973\autoref{subsec:LBC_bdy_tides}) and tidal harmonic analysis \iffalse (see
974\autoref{subsec:DIA_diamlr?} and \autoref{subsec:DIA_diadetide?}) \fi . The module is
975activated with \np[=.true.]{ln_tide}{ln\_tide} in namelist
976\nam{_tide}{\_tide}. It provides the same 34 tidal constituents that are
977included in the
978\href{https://www.aviso.altimetry.fr/en/data/products/auxiliary-products/global-tide-fes.html}{FES2014
979  ocean tide model}: Mf, Mm, Ssa, Mtm, Msf, Msqm, Sa, K1, O1, P1, Q1, J1, S1,
980M2, S2, N2, K2, nu2, mu2, 2N2, L2, T2, eps2, lam2, R2, M3, MKS2, MN4, MS4, M4,
981N4, S4, M6, and M8; see file \hf{tide} and \mdl{tide\_mod} for further
982information and references\footnote{As a legacy option \np{ln_tide_var} can be
983  set to \forcode{0}, in which case the 19 tidal constituents (M2, N2, 2N2, S2,
984  K2, K1, O1, Q1, P1, M4, Mf, Mm, Msqm, Mtm, S1, MU2, NU2, L2, and T2; see file
985  \hf{tide}) and associated parameters that have been available in NEMO version
986  4.0 and earlier are available}. Constituents to be included in the tidal forcing
987(surface and lateral boundaries) are selected by enumerating their respective
988names in namelist array \np{sn_tide_cnames}{sn\_tide\_cnames}.\par
989
990\subsection{Surface tidal forcing}
991Surface tidal forcing can be represented in the model through an additional
992barotropic force in the momentum equation (\autoref{eq:MB_PE_dyn}) such that:
993\[
994  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t} = \ldots +g\nabla (\gamma
995  \Pi_{eq} + \Pi_{sal})
996\]
997where $\gamma \Pi_{eq}$ stands for the equilibrium tidal forcing scaled by a spatially
998uniform tilt factor $\gamma$, and $\Pi_{sal}$ is an optional
999self-attraction and loading term (SAL). These additional terms are enabled when,
1000in addition to \np[=.true.]{ln_tide}{ln\_tide}),
1001\np[=.true.]{ln_tide_pot}{ln\_tide\_pot}.\par
1002
1003The equilibrium tidal forcing is expressed as a sum over the subset of
1004constituents listed in \np{sn_tide_cnames}{sn\_tide\_cnames} of
1005\nam{_tide} (e.g.,
1006\begin{forlines}
1007      sn_tide_cnames(1) = 'M2'
1008      sn_tide_cnames(2) = 'K1'
1009      sn_tide_cnames(3) = 'S2'
1010      sn_tide_cnames(4) = 'O1'
1011\end{forlines}
1012to select the four tidal constituents of strongest equilibrium tidal
1013potential). The tidal tilt factor $\gamma = 1 + k - h$ includes the
1014Love numbers $k$ and $h$ \citep{love_PRSL09}; this factor is
1015configurable using \np{rn_tide_gamma} (default value 0.7). Optionally,
1016when \np[=.true.]{ln_tide_ramp}{ln\_tide\_ramp}, the equilibrium tidal
1017forcing can be ramped up linearly from zero during the initial
1018\np{rn_tide_ramp_dt}{rn\_tide\_ramp\_dt} days of the model run.\par
1019
1020The SAL term should in principle be computed online as it depends on
1021the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
1022discussion about the practical implementation of this term). The complex
1023calculations involved in such computations, however, are computationally very
1024expensive. Here, two mutually exclusive simpler variants are available:
1025amplitudes generated by an external model for oscillatory $\Pi_{sal}$
1026contributions from each of the selected tidal constituents can be read in
1027(\np[=.true.]{ln_read_load}{ln\_read\_load}) from the file specified in
1028\np{cn_tide_load}{cn\_tide\_load} (the variable names are comprised of the
1029tidal-constituent name and suffixes \forcode{_z1} and \forcode{_z2} for the two
1030orthogonal components, respectively); alternatively, a ``scalar approximation''
1031can be used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}), where
1032\[
1033  \Pi_{sal} = \beta \eta,
1034\]
1035with a spatially uniform coefficient $\beta$, which can be configured
1036via \np{rn_scal_load}{rn\_scal\_load} (default value 0.094) and is
1037often tuned to minimize tidal prediction errors.\par
1038
1039For diagnostic purposes, the forcing potential of the individual tidal
1040constituents (incl. load ptential, if activated) and the total forcing
1041potential (incl. load potential, if activated) can be made available
1042as diagnostic output by setting
1043\np[=.true.]{ln_tide_dia}{ln\_tide\_dia} (fields
1044\forcode{tide_pot_<constituent>} and \forcode{tide_pot}).\par
1045
1046%% =================================================================================================
1047\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
1048\label{sec:SBC_rnf}
1049
1050\begin{listing}
1051  \nlst{namsbc_rnf}
1052  \caption{\forcode{&namsbc_rnf}}
1053  \label{lst:namsbc_rnf}
1054\end{listing}
1055
1056%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1057%Many models, however, have traditionally inserted river runoff to the top model cell.
1058%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
1059%throughout a nonzero depth has been motivated by the numerical and physical problems
1060%that arise when the top grid cells are of the order of one meter. This situation is common in
1061%coastal modelling and becomes more and more often open ocean and climate modelling
1062%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
1063%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
1064
1065%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
1066%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
1067%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
1068%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
1069%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
1070%emp or emps and the changes made are below:
1071
1072%Rachel:
1073River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1074Many models, however, have traditionally inserted river runoff to the top model cell.
1075This was the case in \NEMO\ prior to the version 3.3,
1076and was combined with an option to increase vertical mixing near the river mouth.
1077
1078However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
1079This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
1080\footnote{
1081  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
1082  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
1083  see also \autoref{fig:SBC_dcy}.}.
1084
1085As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
1086and for the temperature and salinity of the river to effect the surrounding ocean.
1087The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
1088along with the depth (in metres) which the river should be added to.
1089
1090Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
1091\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
1092If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
1093and/or taken as surface temperature respectively.
1094
1095The runoff value and attributes are read in in sbcrnf.
1096For temperature -999 is taken as missing data and the river temperature is taken to
1097be the surface temperatue at the river point.
1098For the depth parameter a value of -1 means the river is added to the surface box only,
1099and a value of -999 means the river is added through the entire water column.
1100After being read in the temperature and salinity variables are multiplied by the amount of runoff
1101(converted into m/s) to give the heat and salt content of the river runoff.
1102After the user specified depth is read ini,
1103the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
1104The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
1105the bottom of the lowest box the river water is being added to
1106(\ie\ the total depth that river water is being added to in the model).
1107
1108The mass/volume addition due to the river runoff is, at each relevant depth level, added to
1109the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
1110This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
1111The sea surface height is calculated using the sum of the horizontal divergence terms,
1112and so the river runoff indirectly forces an increase in sea surface height.
1113
1114The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
1115This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
1116The heat and salt content of the river runoff is not included in this step,
1117and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
1118the box and replaced by the same volume of river water with no corresponding heat and salt addition.
1119
1120For the linear free surface case, at the surface box the tracer advection causes a flux of water
1121(of equal volume to the runoff) through the sea surface out of the domain,
1122which causes a salt and heat flux out of the model.
1123As such the volume of water does not change, but the water is diluted.
1124
1125For the non-linear free surface case, no flux is allowed through the surface.
1126Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
1127no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
1128(The runoff addition to the top box along with the water being moved up through
1129boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
1130
1131In trasbc the addition of heat and salt due to the river runoff is added.
1132This is done in the same way for both vvl and non-vvl.
1133The temperature and salinity are increased through the specified depth according to
1134the heat and salt content of the river.
1135
1136In the non-linear free surface case (vvl),
1137near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
1138so that the original ratios of grid box heights are restored.
1139In doing this water is moved into boxes below, throughout the water column,
1140so the large volume addition to the surface box is spread between all the grid boxes.
1141
1142It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
1143\ie\ modelling the Baltic flow in and out of the North Sea.
1144When the flow is out of the domain there is no change in temperature and salinity,
1145regardless of the namelist options used,
1146as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
1147
1148%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1149
1150%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1151
1152%\colorbox{yellow}{river mouths{\ldots}}
1153
1154%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1155%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1156%ENDIF
1157
1158\cmtgm{  word doc of runoffs:
1159In the current \NEMO\ setup river runoff is added to emp fluxes,
1160these are then applied at just the sea surface as a volume change (in the variable volume case
1161this is a literal volume change, and in the linear free surface case the free surface is moved)
1162and a salt flux due to the concentration/dilution effect.
1163There is also an option to increase vertical mixing near river mouths;
1164this gives the effect of having a 3d river.
1165All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
1166at the same temperature as the sea surface.
1167Our aim was to code the option to specify the temperature and salinity of river runoff,
1168(as well as the amount), along with the depth that the river water will affect.
1169This would make it possible to model low salinity outflow, such as the Baltic,
1170and would allow the ocean temperature to be affected by river runoff.
1171
1172The depth option makes it possible to have the river water affecting just the surface layer,
1173throughout depth, or some specified point in between.
1174
1175To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
1176the \mdl{tra_sbc} module.
1177We decided to separate them throughout the code,
1178so that the variable emp represented solely evaporation minus precipitation fluxes,
1179and a new 2d variable rnf was added which represents the volume flux of river runoff
1180(in $kg/m^2s$ to remain consistent with $emp$).
1181This meant many uses of emp and emps needed to be changed,
1182a list of all modules which use $emp$ or $emps$ and the changes made are below:}
1183
1184%% =================================================================================================
1185\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
1186\label{sec:SBC_isf}
1187
1188\begin{listing}
1189  \nlst{namsbc_isf}
1190  \caption{\forcode{&namsbc_isf}}
1191  \label{lst:namsbc_isf}
1192\end{listing}
1193
1194The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
1195Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1196The different options are illustrated in \autoref{fig:SBC_isf}.
1197
1198\begin{description}
1199  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1200  The fwf and heat flux are depending of the local water properties.
1201
1202  Two different bulk formulae are available:
1203
1204  \begin{description}
1205  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
1206    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_trpt06}.
1207  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
1208    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1209    A complete description is available in \citet{jenkins_JGR91}.
1210  \end{description}
1211
1212  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1213  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
1214  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.
1215  Then, the fluxes are spread over the same thickness (ie over one or several cells).
1216  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.
1217  This can lead to super-cool temperature in the top cell under melting condition.
1218  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.\\
1219
1220  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1221  There are 3 different ways to compute the exchange coeficient:
1222  \begin{description}
1223  \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}.
1224    \begin{gather*}
1225       % \label{eq:SBC_isf_gamma_iso}
1226      \gamma^{T} = rn\_gammat0 \\
1227      \gamma^{S} = rn\_gammas0
1228    \end{gather*}
1229    This is the recommended formulation for ISOMIP.
1230  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
1231    \begin{gather*}
1232      \gamma^{T} = rn\_gammat0 \times u_{*} \\
1233      \gamma^{S} = rn\_gammas0 \times u_{*}
1234    \end{gather*}
1235    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
1236    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1237  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1238    \[
1239      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1240    \]
1241    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
1242    $\Gamma_{Turb}$ the contribution of the ocean stability and
1243    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1244    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1245    This formulation has not been extensively tested in \NEMO\ (not recommended).
1246  \end{description}
1247\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1248  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1249  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1250  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1251  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
1252  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
1253\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1254  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1255  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
1256  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
1257  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1258\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1259  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
1260  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1261  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})
1262\end{description}
1263
1264$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
1265the water mass properties, ocean velocities and depth.
1266This flux is thus highly dependent of the model resolution (horizontal and vertical),
1267realism of the water masses onto the shelf ...\\
1268
1269$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
1270You have total control of the fwf forcing.
1271This can be useful if the water masses on the shelf are not realistic or
1272the resolution (horizontal/vertical) are too coarse to have realistic melting or
1273for studies where you need to control your heat and fw input.\\
1274
1275The ice shelf melt is implemented as a volume flux as for the runoff.
1276The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1277the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1278See \autoref{sec:SBC_rnf} for all the details about the divergence correction.
1279
1280\begin{figure}[!t]
1281  \centering
1282  \includegraphics[width=0.66\textwidth]{SBC_isf}
1283  \caption[Ice shelf location and fresh water flux definition]{
1284    Illustration of the location where the fwf is injected and
1285    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1286  \label{fig:SBC_isf}
1287\end{figure}
1288
1289%% =================================================================================================
1290\section{Ice sheet coupling}
1291\label{sec:SBC_iscpl}
1292
1293\begin{listing}
1294  \nlst{namsbc_iscpl}
1295  \caption{\forcode{&namsbc_iscpl}}
1296  \label{lst:namsbc_iscpl}
1297\end{listing}
1298
1299Ice sheet/ocean coupling is done through file exchange at the restart step.
1300At each restart step:
1301
1302\begin{enumerate}
1303\item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1304\item a new domcfg.nc file is built using the DOMAINcfg tools.
1305\item \NEMO\ run for a specific period and output the average melt rate over the period.
1306\item the ice sheet model run using the melt rate outputed in step 4.
1307\item go back to 1.
1308\end{enumerate}
1309
1310If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1311potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1312The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1313
1314\begin{description}
1315\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
1316  ($bt_b=bt_n$).
1317\item [Enlarge  a cell]: See case "Thin a cell down"
1318\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
1319  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1320\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.
1321  If no neighbours, T/S is extrapolated from old top cell value.
1322  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1323\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1324\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.
1325  If no neighbour, T/S/U/V and mask set to 0.
1326\end{description}
1327
1328Furthermore, as the before and now fields are not compatible (modification of the geometry),
1329the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1330
1331The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1332It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1333the code will be unable to fill all the new wet cells properly.
1334The default number is set up for the MISOMIP idealised experiments.
1335This coupling procedure is able to take into account grounding line and calving front migration.
1336However, it is a non-conservative processe.
1337This could lead to a trend in heat/salt content and volume.\\
1338
1339In order to remove the trend and keep the conservation level as close to 0 as possible,
1340a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1341The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1342A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1343For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1344The 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).
1345
1346%% =================================================================================================
1347\section{Handling of icebergs (ICB)}
1348\label{sec:SBC_ICB_icebergs}
1349
1350\begin{listing}
1351  \nlst{namberg}
1352  \caption{\forcode{&namberg}}
1353  \label{lst:namberg}
1354\end{listing}
1355
1356Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1357Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1358(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1359Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1360described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1361Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1362which is an integer representing how many icebergs of this class are being described as one lagrangian point
1363(this reduces the numerical problem of tracking every single iceberg).
1364They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1365
1366Two initialisation schemes are possible.
1367\begin{description}
1368\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
1369  (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
1370  which an iceberg is generated at the beginning of the run.
1371  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1372  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1373  the geographical box: lonmin,lonmax,latmin,latmax
1374\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.
1375  This should be a file with a field on the configuration grid (typically ORCA)
1376  representing ice accumulation rate at each model point.
1377  These should be ocean points adjacent to land where icebergs are known to calve.
1378  Most points in this input grid are going to have value zero.
1379  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1380  At each time step, a test is performed to see if there is enough ice mass to
1381  calve an iceberg of each class in order (1 to 10).
1382  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1383  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1384\end{description}
1385
1386Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1387The latter act to disintegrate the iceberg.
1388This is either all melted freshwater,
1389or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1390which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1391Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1392
1393Extensive diagnostics can be produced.
1394Separate output files are maintained for human-readable iceberg information.
1395A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1396The amount of information is controlled by two integer parameters:
1397\begin{description}
1398\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1399  represents an increasing number of points in the code at which variables are written,
1400  and an increasing level of obscurity.
1401\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1402\end{description}
1403
1404Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1405A non-zero value represents how many timesteps between writes of information into the output file.
1406These output files are in NETCDF format.
1407When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1408Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1409So care is needed to recreate data for individual icebergs,
1410since its trajectory data may be spread across multiple files.
1411
1412%% =================================================================================================
1413\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1414\label{sec:SBC_wave}
1415
1416\begin{listing}
1417  \nlst{namsbc_wave}
1418  \caption{\forcode{&namsbc_wave}}
1419  \label{lst:namsbc_wave}
1420\end{listing}
1421
1422Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1423physical processes related to ocean surface waves, namely the surface stress modified by growth and
1424dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1425tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1426the wind stress.
1427
1428Physical processes related to ocean surface waves can be accounted by setting the logical variable
1429\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1430different processes should be activated as explained in the following sections.
1431
1432Wave fields can be provided either in forced or coupled mode:
1433\begin{description}
1434\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1435for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1436Input Data generic Interface (see \autoref{sec:SBC_input}).
1437\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1438in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1439\end{description}
1440
1441%% =================================================================================================
1442\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1443\label{subsec:SBC_wave_cdgw}
1444
1445The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1446can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1447Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1448the drag coefficient is computed according to the stable/unstable conditions of the
1449air-sea interface following \citet{large.yeager_trpt04}.
1450
1451%% =================================================================================================
1452\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1453\label{subsec:SBC_wave_sdw}
1454
1455The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1456It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1457and the current measured at a fixed point (Eulerian velocity).
1458As waves travel, the water particles that make up the waves travel in orbital motions but
1459without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1460at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1461An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1462representation of surface physics in ocean general circulation models. %GS: reference needed
1463The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1464
1465\[
1466  % \label{eq:SBC_wave_sdw}
1467  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1468  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1469  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1470\]
1471
1472where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1473$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1474$k$ is the mean wavenumber defined as:
1475$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1476
1477In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1478and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1479To simplify, it is customary to use approximations to the full Stokes profile.
1480Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1481are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1482$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1483and makes possible the estimation of the surface Stokes drift for random directional waves in
1484realistic wave conditions:
1485
1486\begin{description}
1487\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1488\citet{breivik.janssen.ea_JPO14}:
1489
1490\[
1491  % \label{eq:SBC_wave_sdw_0a}
1492  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1493\]
1494
1495where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1496
1497\[
1498  % \label{eq:SBC_wave_sdw_0b}
1499  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1500  \quad \text{and }\
1501  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1502\]
1503
1504where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1505
1506\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1507reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1508\citep{breivik.bidlot.ea_OM16}:
1509
1510\[
1511  % \label{eq:SBC_wave_sdw_1}
1512  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1513  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1514\]
1515
1516where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1517
1518\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1519but using the wave frequency from a wave model.
1520
1521\end{description}
1522
1523The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1524and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1525
1526\[
1527  % \label{eq:SBC_wave_eta_sdw}
1528  \frac{\partial{\eta}}{\partial{t}} =
1529  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1530\]
1531
1532The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1533for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1534that is induced by the three-dimensional Stokes velocity.
1535The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1536can be formulated as follows:
1537
1538\[
1539  % \label{eq:SBC_wave_tra_sdw}
1540  \frac{\partial{c}}{\partial{t}} =
1541  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1542\]
1543
1544%% =================================================================================================
1545\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1546\label{subsec:SBC_wave_stcor}
1547
1548In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1549in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1550This additional force may have impact on the Ekman turning of the surface current.
1551In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1552approximations described in \autoref{subsec:SBC_wave_sdw}),
1553\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1554
1555%% =================================================================================================
1556\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1557\label{subsec:SBC_wave_tauw}
1558
1559The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1560into the waves \citep{janssen.breivik.ea_trpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1561available for forcing the mean circulation, while in the opposite case of a decaying sea
1562state, more momentum is available for forcing the ocean.
1563Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1564but in practice, an equilibrium sea state is a fairly rare event.
1565So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1566
1567\[
1568  % \label{eq:SBC_wave_tauoc}
1569  \tau_{oc,a} = \tau_a - \tau_w
1570\]
1571
1572where $\tau_a$ is the atmospheric surface stress;
1573$\tau_w$ is the atmospheric stress going into the waves defined as:
1574
1575\[
1576  % \label{eq:SBC_wave_tauw}
1577  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1578\]
1579
1580where: $c_p$ is the phase speed of the gravity waves,
1581$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1582the physics of ocean waves. The first one, $S_{in}$, describes the generation
1583of ocean waves by wind and therefore represents the momentum and energy transfer
1584from air to ocean waves; the second term $S_{nl}$ denotes
1585the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1586describes the dissipation of waves by processes such as white-capping, large scale breaking
1587eddy-induced damping.
1588
1589The wave stress derived from an external wave model can be provided either through the normalized
1590wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1591meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1592
1593%% =================================================================================================
1594\section{Miscellaneous options}
1595\label{sec:SBC_misc}
1596
1597%% =================================================================================================
1598\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1599\label{subsec:SBC_dcy}
1600
1601\begin{figure}[!t]
1602  \centering
1603  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
1604  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1605    Example of reconstruction of the diurnal cycle variation of short wave flux from
1606    daily mean values.
1607    The reconstructed diurnal cycle (black line) is chosen as
1608    the mean value of the analytical cycle (blue line) over a time step,
1609    not as the mid time step value of the analytically cycle (red square).
1610    From \citet{bernie.guilyardi.ea_CD07}.}
1611  \label{fig:SBC_diurnal}
1612\end{figure}
1613
1614\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.
1615%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1616Nevertheless, 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}.
1617Furthermore, only the knowledge of daily mean value of SWF is needed,
1618as higher frequency variations can be reconstructed from them,
1619assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1620The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1621setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1622using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1623the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1624The reconstruction is performed in the \mdl{sbcdcy} module.
1625The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1626The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1627a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1628The use of diurnal cycle reconstruction requires the input SWF to be daily
1629(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1630Furthermore, it is recommended to have a least 8 surface module time steps per day,
1631that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1632An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1633one every 2~hours (from 1am to 11pm).
1634
1635\begin{figure}[!t]
1636  \centering
1637  \includegraphics[width=0.66\textwidth]{SBC_dcy}
1638  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1639    Example of reconstruction of the diurnal cycle variation of short wave flux from
1640    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1641    The display is on (i,j) plane.}
1642  \label{fig:SBC_dcy}
1643\end{figure}
1644
1645Note also that the setting a diurnal cycle in SWF is highly recommended when
1646the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1647an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1648
1649%% =================================================================================================
1650\subsection{Rotation of vector pairs onto the model grid directions}
1651\label{subsec:SBC_rotation}
1652
1653When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1654pairs of vector components can be rotated from east-north directions onto the local grid directions.
1655This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1656be defined relative to a rectilinear grid.
1657To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1658The eastward component must start with "U" and the northward component with "V".
1659The remaining characters in the strings are used to identify which pair of components go together.
1660So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1661rotate them on to the model grid directions;
1662"U2" and "V2" could be used against a second pair of components, and so on.
1663The extra characters used in the strings are arbitrary.
1664The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1665
1666%% =================================================================================================
1667\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1668\label{subsec:SBC_ssr}
1669
1670\begin{listing}
1671  \nlst{namsbc_ssr}
1672  \caption{\forcode{&namsbc_ssr}}
1673  \label{lst:namsbc_ssr}
1674\end{listing}
1675
1676Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1677On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1678a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1679\[
1680  % \label{eq:SBC_dmp_q}
1681  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1682\]
1683where SST is a sea surface temperature field (observed or climatological),
1684$T$ is the model surface layer temperature and
1685$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1686For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1687This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1688
1689In the fresh water budget, a feedback term can also be added.
1690Converted into an equivalent freshwater flux, it takes the following expression :
1691
1692\begin{equation}
1693  \label{eq:SBC_dmp_emp}
1694  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1695  {\left.S\right|_{k=1}}
1696\end{equation}
1697
1698where $\textit{emp}_{o }$ is a net surface fresh water flux
1699(observed, climatological or an atmospheric model product),
1700\textit{SSS}$_{Obs}$ is a sea surface salinity
1701(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1702$\left.S\right|_{k=1}$ is the model surface layer salinity and
1703$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1704Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1705the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1706The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1707reduce the uncertainties we have on the observed freshwater budget.
1708
1709%% =================================================================================================
1710\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1711\label{subsec:SBC_ice-cover}
1712
1713The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1714There are several way to handle sea-ice in the system depending on
1715the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1716\begin{description}
1717\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1718  This is a typical namelist value used for tropical ocean domain.
1719  The surface fluxes are simply specified for an ice-free ocean.
1720  No specific things is done for sea-ice.
1721\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1722  An observed ice covered area is read in a file.
1723  Below this area, the SST is restored to the freezing point and
1724  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1725  The associated modification of the freshwater fluxes are done in such a way that
1726  the change in buoyancy fluxes remains zero.
1727  This prevents deep convection to occur when trying to reach the freezing point
1728  (and so ice covered area condition) while the SSS is too large.
1729  This manner of managing sea-ice area, just by using a IF case,
1730  is usually referred as the \textit{ice-if} model.
1731  It can be found in the \mdl{sbcice\_if} module.
1732\item [nn\_ice = 2 or more] A full sea ice model is used.
1733  This model computes the ice-ocean fluxes,
1734  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1735  provide the surface averaged ocean fluxes.
1736  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1737  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1738  (\ie\ $2$ for SI3 or $3$ for CICE).
1739\end{description}
1740
1741% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1742%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1743
1744%% =================================================================================================
1745\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1746\label{subsec:SBC_cice}
1747
1748It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1749to the CICE sea-ice model by using \key{cice}.
1750The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1751the additional 'hadgem3' drivers will be required, even with the latest code release.
1752Input grid files consistent with those used in \NEMO\ will also be needed,
1753and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1754(seek advice from UKMO if necessary).
1755Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1756(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1757or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1758(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1759The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1760(although coupling ocean and ice less frequently should work,
1761it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1762the user should check that results are not significantly different to the standard case).
1763
1764There are two options for the technical coupling between \NEMO\ and CICE.
1765The standard version allows complete flexibility for the domain decompositions in the individual models,
1766but this is at the expense of global gather and scatter operations in the coupling which
1767become very expensive on larger numbers of processors.
1768The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1769the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1770and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1771allows much more efficient direct coupling on individual processors.
1772This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1773there is no sea ice.
1774
1775%% =================================================================================================
1776\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1777\label{subsec:SBC_fwb}
1778
1779\begin{listing}
1780  \nlst{namsbc_fwb}
1781  \caption{\forcode{&namsbc_fwb}}
1782  \label{lst:namsbc_fwb}
1783\end{listing}
1784
1785For global ocean simulations, it can be useful to introduce a control of the
1786mean sea level in order to prevent unrealistic drifting of the sea surface
1787height due to unbalanced freshwater fluxes. In \NEMO, two options for
1788controlling the freshwater budget are proposed.
1789
1790\begin{description}
1791\item [{\np[=0]{nn_fwb}{nn\_fwb}}:] No control at all; the mean sea level is
1792  free to drift, and will certainly do so.
1793\item [{\np[=1]{nn_fwb}{nn\_fwb}}:] The global mean \textit{emp} is set to zero at each model time step.
1794  %GS: comment below still relevant ?
1795  %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).
1796\item [{\np[=2]{nn_fwb}{nn\_fwb}}:] \textit{emp} is adjusted by adding a
1797  spatially uniform, annual-mean freshwater flux that balances the freshwater
1798  budget at the end of the previous year; as the model uses the Boussinesq
1799  approximation, the freshwater budget can be evaluated from the change in the
1800  mean sea level and in the ice and snow mass after the end of each simulation
1801  year; at the start of the model run, an initial adjustment flux can be set
1802  using parameter \np{rn_rwb0}{rn\_fwb0} in namelist \nam{sbc_fwb}{sbc\_fwb}.
1803\end{description}
1804
1805% Griffies doc:
1806% When running ocean-ice simulations, we are not explicitly representing land processes,
1807% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1808% it is important to balance the hydrological cycle in ocean-ice models.
1809% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1810% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1811% a chosen time scale.
1812% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1813% so that there is always a zero net input of water to the ocean-ice system.
1814% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1815% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1816% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1817% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1818% and ice models when aiming to balance the hydrological cycle.
1819% 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,
1820% not the water in any one sub-component. As an extreme example to illustrate the issue,
1821% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1822% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1823% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1824% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1825% in ocean-ice models.
1826
1827\subinc{\input{../../global/epilogue}}
1828
1829\end{document}
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