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1\documentclass[../main/NEMO_manual]{subfiles}
2\usepackage{fontspec}
3\usepackage{fontawesome}
4
5\begin{document}
6
7\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
8\label{chap:SBC}
9
10\thispagestyle{plain}
11
12\chaptertoc
13
14\paragraph{Changes record} ~\\
15
16{\footnotesize
17  \begin{tabularx}{\textwidth}{l||X|X}
18    Release & Author(s) & Modifications \\
19    \hline
20    {\em   X.X} & {\em Pierre Mathiot} & {\em update of the ice shelf section (2019 development)} \\
21    {\em   4.0} & {\em ...} & {\em ...} \\
22    {\em   3.6} & {\em ...} & {\em ...} \\
23    {\em   3.4} & {\em ...} & {\em ...} \\
24    {\em <=3.4} & {\em ...} & {\em ...}
25  \end{tabularx}
26}
27
28\clearpage
29
30\begin{listing}
31  \nlst{namsbc}
32  \caption{\forcode{&namsbc}}
33  \label{lst:namsbc}
34\end{listing}
35
36The ocean needs seven fields as surface boundary condition:
37
38\begin{itemize}
39\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
40\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
41\item the surface freshwater budget $\left( {\textit{emp}} \right)$
42\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
43\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
44\end{itemize}
45
46Four different ways are available to provide the seven fields to the ocean. They are controlled by
47namelist \nam{sbc}{sbc} variables:
48
49\begin{itemize}
50\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms,
51\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
52\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
53(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
54\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
55\end{itemize}
56
57The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
58
59When the fields are supplied from data files (bulk, flux and mixed formulations),
60the input fields do not need to be supplied on the model grid.
61Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
62the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
63If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
64should be masked or filled to avoid spurious results in proximity of the coasts, as
65large sea-land gradients characterize most of the atmospheric variables.
66
67In addition, the resulting fields can be further modified using several namelist options.
68These options control:
69
70\begin{itemize}
71\item the rotation of vector components supplied relative to an east-north coordinate system onto
72  the local grid directions in the model,
73\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
74\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
75\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
76  (\np[=0..3]{nn_ice}{nn\_ice}),
77\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
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.
101
102%% =================================================================================================
103\section{Surface boundary condition for the ocean}
104\label{sec:SBC_ocean}
105
106The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
107It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
108the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
109As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
110\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
111
112The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
113$Q_{ns}$ and $Q_{sr}$, respectively.
114The former is the non penetrative part of the heat flux
115(\ie\ the sum of sensible, latent and long wave heat fluxes plus
116the heat content of the mass exchange between the ocean and sea-ice).
117It is applied in \mdl{trasbc} module as a surface boundary condition trend of
118the first level temperature time evolution equation
119(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
120The latter is the penetrative part of the heat flux.
121It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
122\np[=.true.]{ln_traqsr}{ln\_traqsr}.
123The way the light penetrates inside the water column is generally a sum of decreasing exponentials
124(see \autoref{subsec:TRA_qsr}).
125
126The surface freshwater budget is provided by the \textit{emp} field.
127It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
128possibly with the sea-ice and ice shelves (freezing minus melting of ice).
129It affects the ocean in two different ways:
130$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
131a volume flux, and
132$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
133the mass exchanged with atmosphere, sea-ice and ice shelves.
134
135%\colorbox{yellow}{Miss: }
136%A extensive description of all namsbc namelist (parameter that have to be
137%created!)
138%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
139%ssv) \ie\ information required by flux computation or sea-ice
140%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
141%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
142%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
143%Fluxes update only each nf\_sbc time step (namsbc) explain relation
144%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
145%nf\_sbc
146%Explain here all the namlist namsbc variable{\ldots}.
147% explain : use or not of surface currents
148%\colorbox{yellow}{End Miss }
149
150The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
151the surface currents, temperature and salinity.
152These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
153these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
154
155\begin{table}[tb]
156  \centering
157  \begin{tabular}{|l|l|l|l|}
158    \hline
159    Variable description                           & Model variable  & Units  & point                 \\
160    \hline
161    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
162    \hline
163    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
164    \hline
165    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
166    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
167  \end{tabular}
168  \caption[Ocean variables provided to the surface module)]{
169    Ocean variables provided to the surface module (\texttt{SBC}).
170    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
171    \ie\ the frequency of computation of surface fluxes.}
172  \label{tab:SBC_ssm}
173\end{table}
174
175%\colorbox{yellow}{Penser a} mettre dans le restant l'info nn\_fsbc ET nn\_fsbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt
176
177%% =================================================================================================
178\section{Input data generic interface}
179\label{sec:SBC_input}
180
181A generic interface has been introduced to manage the way input data
182(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
183This task is achieved by \mdl{fldread}.
184The module is designed with four main objectives in mind:
185\begin{enumerate}
186\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
187  and according to the different calendars available in the model.
188\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
189\item make the run duration independent from the period cover by the input files.
190\item provide a simple user interface and a rather simple developer interface by
191  limiting the number of prerequisite informations.
192\end{enumerate}
193
194As a result, the user has only to fill in for each variable a structure in the namelist file to
195define the input data file and variable names, the frequency of the data (in hours or months),
196whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
197and three additional parameters for the on-the-fly interpolation.
198When adding a new input variable, the developer has to add the associated structure in the namelist,
199read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
200and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
201
202The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
203(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
204if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
205
206Note that when an input data is archived on a disc which is accessible directly from the workspace where
207the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
208By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
209
210%% =================================================================================================
211\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
212\label{subsec:SBC_fldread}
213
214The structure associated with an input variable contains the following information:
215\begin{forlines}
216!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
217!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
218\end{forlines}
219where
220\begin{description}
221\item [File name]: the stem name of the NetCDF file to be opened.
222  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
223  by date information and possibly a prefix (when using AGRIF).
224  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
225  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
226  \begin{table}[htbp]
227    \centering
228    \begin{tabular}{|l|c|c|c|}
229      \hline
230                                  &  daily or weekLL     &  monthly           &  yearly        \\
231      \hline
232      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
233      \hline
234      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
235      \hline
236    \end{tabular}
237    \caption[Naming nomenclature for climatological or interannual input file]{
238      Naming nomenclature for climatological or interannual input file,
239      as a function of the open/close frequency.
240      The stem name is assumed to be 'fn'.
241      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
242      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
243      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
244      always coded with 4 or 2 digits.
245      Note that (1) in mpp, if the file is split over each subdomain,
246      the suffix '.nc' is replaced by '\_PPPP.nc',
247      where 'PPPP' is the process number coded with 4 digits;
248      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
249    }
250    \label{tab:SBC_fldread}
251  \end{table}
252\item [Record frequency]: the frequency of the records contained in the input file.
253  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
254  (for example -1 for monthly forcing or -12 for annual forcing).
255  Note that this frequency must REALLY be an integer and not a real.
256  On some computers, setting it to '24.' can be interpreted as 240!
257\item [Variable name]: the name of the variable to be read in the input NetCDF file.
258\item [Time interpolation]: a logical to activate, or not, the time interpolation.
259  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
260  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
261  00h00'00'' to 23h59'59".
262  If set to 'true', the forcing will have a broken line shape.
263  Records are assumed to be dated at the middle of the forcing period.
264  For example, when using a daily forcing with time interpolation,
265  linear interpolation will be performed between mid-day of two consecutive days.
266\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
267  or an interannual forcing which will requires additional files if
268  the period covered by the simulation exceeds the one of the file.
269  See the above file naming strategy which impacts the expected name of the file to be opened.
270\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
271  Four cases are coded:
272  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
273  means the forcing files will contain data for one day, one week, one month or one year.
274  Files are assumed to contain data from the beginning of the open/close period.
275  For example, the first record of a yearly file containing daily data is Jan 1st even if
276  the experiment is not starting at the beginning of the year.
277\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
278  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
279\end{description}
280
281Additional remarks:\\
282(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
283The only tricky point is therefore to specify the date at which we need to do the interpolation and
284the date of the records read in the input files.
285Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
286For example, for an experiment starting at 0h00'00" with a one-hour time-step,
287a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
288However, for forcing data related to the surface module,
289values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
290For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
291The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
292In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
293(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
294The calendar associated with the forcing field is build according to the information provided by
295user in the record frequency, the open/close frequency and the type of temporal interpolation.
296For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
297start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
298(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
299interpolating data with the first (last) record of the open/close period.
300For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
301the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
302Dec 31st 12h00'00" and Jan 1st 12h00'00".
303If the forcing is climatological, Dec and Jan will be keep-up from the same year.
304However, if the forcing is not climatological, at the end of
305the open/close period, the code will automatically close the current file and open the next one.
306Note that, if the experiment is starting (ending) at the beginning (end) of
307an open/close period, we do accept that the previous (next) file is not existing.
308In this case, the time interpolation will be performed between two identical values.
309For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
310we do accept that the file related to year Y-1 is not existing.
311The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
312If the file of year Y-1 exists, the code will read its last record.
313Therefore, this file can contain only one record corresponding to Dec 31st,
314a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
315
316%% =================================================================================================
317\subsection{Interpolation on-the-fly}
318\label{subsec:SBC_iof}
319
320Interpolation on the Fly allows the user to supply input files required for the surface forcing on
321grids other than the model grid.
322To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
323interpolate from the data grid to the model grid.
324The original development of this code used the SCRIP package
325(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
326In principle, any package such as CDO can be used to generate the weights, but the variables in
327the input weights file must have the same names and meanings as assumed by the model.
328Two methods are currently available: bilinear and bicubic interpolations.
329Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
330the input file and substitute the corresponding values with the average of the 8 neighbouring points in
331the native external grid.
332Only "sea points" are considered for the averaging.
333The land/sea mask file must be provided in the structure associated with the input variable.
334The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
335the associated variables and should be equal to 1 over land and 0 elsewhere.
336The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
337Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
338
339%% =================================================================================================
340\subsubsection{Bilinear interpolation}
341\label{subsec:SBC_iof_bilinear}
342
343The input weights file in this case has two sets of variables:
344src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
345The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
346Each src value is an integer corresponding to the index of a point in the input grid when
347written as a one dimensional array.
348For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
349There are four of each variable because bilinear interpolation uses the four points defining
350the grid box containing the point to be interpolated.
351All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
352generate a value for point (i,j) in the model.
353
354Symbolically, the algorithm used is:
355\[
356  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
357\]
358where function idx() transforms a one dimensional index src(k) into a two dimensional index,
359and wgt(1) corresponds to variable "wgt01" for example.
360
361%% =================================================================================================
362\subsubsection{Bicubic interpolation}
363\label{subsec:SBC_iof_bicubic}
364
365Again, there are two sets of variables: "src" and "wgt".
366But in this case, there are 16 of each.
367The symbolic algorithm used to calculate values on the model grid is now:
368
369\[
370  \begin{split}
371    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
372    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
373    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
374    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
375  \end{split}
376\]
377The gradients here are taken with respect to the horizontal indices and not distances since
378the spatial dependency has been included into the weights.
379
380%% =================================================================================================
381\subsubsection{Implementation}
382\label{subsec:SBC_iof_imp}
383
384To activate this option, a non-empty string should be supplied in
385the weights filename column of the relevant namelist;
386if this is left as an empty string no action is taken.
387In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
388as and when they are first required.
389This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
390inspecting a global attribute stored in the weights input file.
391This attribute must be called "ew\_wrap" and be of integer type.
392If it is negative, the input non-model grid is assumed to be not cyclic.
393If zero or greater, then the value represents the number of columns that overlap.
394$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
395if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
396If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
397In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
398therefore the grid is assumed to be cyclic with no overlapping columns.
399(In fact, this only matters when bicubic interpolation is required.)
400Note that no testing is done to check the validity in the model,
401since there is no way of knowing the name used for the longitude variable,
402so it is up to the user to make sure his or her data is correctly represented.
403
404Next the routine reads in the weights.
405Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
406The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
407and when required, for reading in the variable to be interpolated (on the input data grid).
408The size of the input data array is determined by examining the values in the "src" arrays to
409find the minimum and maximum i and j values required.
410Since bicubic interpolation requires the calculation of gradients at each point on the grid,
411the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
412When the array of points from the data file is adjacent to an edge of the data grid,
413the halo is either a copy of the row/column next to it (non-cyclical case),
414or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
415
416%% =================================================================================================
417\subsubsection{Limitations}
418\label{subsec:SBC_iof_lim}
419
420\begin{enumerate}
421\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
422\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
423  a bicubic interpolation method is used.
424\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
425\item The gradients across the ends of a cyclical grid assume that the grid spacing between
426  the two columns involved are consistent with the weights used.
427\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
428  but this has not been implemented.)
429\end{enumerate}
430
431%% =================================================================================================
432\subsubsection{Utilities}
433\label{subsec:SBC_iof_util}
434
435% to be completed
436A set of utilities to create a weights file for a rectilinear input grid is available
437(see the directory NEMOGCM/TOOLS/WEIGHTS).
438
439%% =================================================================================================
440\subsection{Standalone surface boundary condition scheme (SAS)}
441\label{subsec:SBC_SAS}
442
443\begin{listing}
444  \nlst{namsbc_sas}
445  \caption{\forcode{&namsbc_sas}}
446  \label{lst:namsbc_sas}
447\end{listing}
448
449In some circumstances, it may be useful to avoid calculating the 3D temperature,
450salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
451For example:
452
453\begin{itemize}
454\item Multiple runs of the model are required in code development to
455  see the effect of different algorithms in the bulk formulae.
456\item The effect of different parameter sets in the ice model is to be examined.
457\item Development of sea-ice algorithms or parameterizations.
458\item Spinup of the iceberg floats
459\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
460\end{itemize}
461
462The Standalone Surface scheme provides this capacity.
463Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
464A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
465However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
466In this configuration, a few routines in the standard model are overriden by new versions.
467Routines replaced are:
468
469\begin{itemize}
470\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
471  Since the ocean state is not calculated all associated initialisations have been removed.
472\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
473\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
474  New surface modules that can function when only the surface level of the ocean state is defined can also be added
475  (\eg\ icebergs).
476\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
477  so calls to restart functions have been removed.
478  This also means that the calendar cannot be controlled by time in a restart file,
479  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
480\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
481\item \mdl{diawri}: All 3D data have been removed from the output.
482  The surface temperature, salinity and velocity components (which have been read in) are written along with
483  relevant forcing and ice data.
484\end{itemize}
485
486One new routine has been added:
487
488\begin{itemize}
489\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
490  velocity arrays at the surface.
491  These filenames are supplied in namelist namsbc\_sas.
492  Unfortunately, because of limitations with the \mdl{iom} module,
493  the full 3D fields from the mean files have to be read in and interpolated in time,
494  before using just the top level.
495  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
496\end{itemize}
497
498The user can also choose in the \nam{sbc_sas}{sbc\_sas} namelist to read the mean (nn\_fsbc time-step) fraction of solar net radiation absorbed in the 1st T level using
499 (\np[=.true.]{ln_flx}{ln\_flx}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln_flx}{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in.
500
501%% =================================================================================================
502\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
503\label{sec:SBC_flx}
504
505% Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk
506% parameterization'' (i.e NCAR, COARE, ECMWF...)
507
508\begin{listing}
509  \nlst{namsbc_flx}
510  \caption{\forcode{&namsbc_flx}}
511  \label{lst:namsbc_flx}
512\end{listing}
513
514In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
515the surface boundary condition fields are directly read from input files.
516The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
517the name of the variable read in the file, the time frequency at which it is given (in hours),
518and a logical setting whether a time interpolation to the model time step is required for this field.
519See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
520
521Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
522See \autoref{subsec:SBC_ssr} for its specification.
523
524
525
526
527
528
529
530%% =================================================================================================
531\pagebreak
532\newpage
533\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
534\label{sec:SBC_blk}
535
536% L. Brodeau, December 2019... %
537
538\begin{listing}
539  \nlst{namsbc_blk}
540  \caption{\forcode{&namsbc_blk}}
541  \label{lst:namsbc_blk}
542\end{listing}
543
544If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea
545fluxes associated with surface boundary conditions are estimated by means of the
546traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed
547near-surface atmosphere state (typically extracted from a weather reanalysis)
548and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc}
549time-step(s).
550
551% Turbulent air-sea fluxes are computed using the sea surface properties and
552% atmospheric SSVs at height $z$ above the sea surface, with the traditional
553% aerodynamic bulk formulae:
554
555Note: all the NEMO Fortran routines involved in the present section have been
556 initially developed (and are still developed in parallel) in
557 the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} open-source project
558\citep{brodeau.barnier.ea_JPO17}.
559
560%%% Bulk formulae are this:
561\subsection{Bulk formulae}\label{subsec:SBC_blkform}
562%
563In NEMO, the set of equations that relate each component of the surface fluxes
564to the near-surface atmosphere and sea surface states writes
565%
566\begin{subequations}\label{eq_bulk}
567  \label{eq:SBC_bulk_form}
568  \begin{eqnarray}
569    \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
570    Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
571    E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
572    Q_L           &=& -L_v \, E \\
573    %
574    Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\
575    Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4)
576  \end{eqnarray}
577\end{subequations}
578%
579with
580   \[ \theta_z \simeq T_z+\gamma z \]
581   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
582%
583from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
584%
585where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
586$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
587flux.
588%
589$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
590and longwave radiative fluxes, respectively.
591%
592Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$
593implies a gain of the relevant quantity for the ocean, while a positive $E$
594implies a freshwater loss for the ocean.
595%
596$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
597coefficients for momentum, sensible heat, and moisture, respectively.
598%
599$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
600vaporization of water.
601%
602$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
603and specific humidity of air at height $z$ above the sea surface,
604respectively. $\gamma z$ is a temperature correction term which accounts for the
605adiabatic lapse rate and approximates the potential temperature at height
606$z$ \citep{josey.gulev.ea_2013}.
607%
608$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
609(possibly referenced to the surface current $\mathbf{u_0}$,
610section \ref{s_res1}.\ref{ss_current}).
611%
612The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
613$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution.
614%
615$a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\
616%
617%$p_a$ is the mean sea-level pressure (SLP).
618%
619$T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity
620of air at temperature $T_s$; it includes a 2\% reduction to account for the
621presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}.
622Depending on the bulk parametrization used, $T_s$ can either be the temperature
623at the air-sea interface (skin temperature, hereafter SSST) or at typically a
624few tens of centimeters below the surface (bulk sea surface temperature,
625hereafter SST).
626%
627The SSST differs from the SST due to the contributions of two effects of
628opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL,
629respectively, see section\,\ref{subsec:SBC_skin}).
630%
631Technically, when the ECMWF or COARE* bulk parametrizations are selected
632(\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}),
633$T_s$ is the SSST, as opposed to the NCAR bulk parametrization
634(\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature
635at first T-point level).
636
637For more details on all these aspects the reader is invited to refer
638to \citet{brodeau.barnier.ea_JPO17}.
639
640
641
642\subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean}
643%%%\label{subsec:SBC_param}
644
645Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae
646strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and
647$C_E$. They are estimated with what we refer to as a \emph{bulk
648parametrization} algorithm. When relevant, these algorithms also perform the
649height adjustment of humidity and temperature to the wind reference measurement
650height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}).
651
652
653
654For the open ocean, four bulk parametrization algorithms are available in NEMO:
655\begin{itemize}
656\item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09}
657\item COARE 3.0 \citep{fairall.bradley.ea_JC03}
658\item COARE 3.6 \citep{edson.jampana.ea_JPO13}
659\item ECMWF (IFS documentation, cy45)
660\end{itemize}
661
662
663With respect to version 3, the principal advances in version 3.6 of the COARE
664bulk parametrization are built around improvements in the representation of the
665effects of waves on
666fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes
667improved relationships of surface roughness, and whitecap fraction on wave
668parameters. It is therefore recommended to chose version 3.6 over 3.
669
670
671
672
673\subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin}
674%\subsection[Cool-skin and warm-layer parameterizations
675%(\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})}
676%\label{subsec:SBC_skin}
677%
678As opposed to the NCAR bulk parametrization, more advanced bulk
679parametrizations such as COARE3.x and ECMWF are meant to be used with the skin
680temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
681the first T-point level, see section\,\ref{subsec:SBC_blkform}).
682%
683As such, the relevant cool-skin and warm-layer parametrization must be
684activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs}
685and \np[=T]{ln_skin_wl}{ln\_skin\_wl} to use COARE3.x or ECMWF in a consistent
686way.
687
688\texttt{\#LB: ADD BLBLA ABOUT THE TWO CS/WL PARAMETRIZATIONS (ECMWF and COARE) !!!}
689
690For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same
691basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based
692on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE
6933.6.
694
695For the warm-layer scheme, ECMWF is based on \citet{zeng.beljaars_GRL05} with a
696recent update from \citet{takaya.bidlot.ea_JGR10} (consideration of the
697turbulence input from Langmuir circulation).
698
699Importantly, COARE warm-layer scheme \citep{fairall.ea_19} includes a prognostic
700equation for the thickness of the warm-layer, while it is considered as constant
701in the ECWMF algorithm.
702
703
704\subsection{Appropriate use of each bulk parametrization}
705
706\subsubsection{NCAR}
707
708NCAR bulk parametrizations (formerly known as CORE) is meant to be used with the
709CORE II atmospheric forcing \citep{large.yeager_CD09}. The expected sea surface
710temperature is the bulk SST. Hence the following namelist parameters must be
711set:
712%
713\begin{verbatim}
714  ...
715  ln_NCAR    = .true.
716  ...
717  rn_zqt     = 10.     ! Air temperature & humidity reference height (m)
718  rn_zu      = 10.     ! Wind vector reference height (m)
719  ...
720  ln_skin_cs = .false. ! use the cool-skin parameterization
721  ln_skin_wl = .false. ! use the warm-layer parameterization
722  ...
723  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
724\end{verbatim}
725
726
727\subsubsection{ECMWF}
728%
729With an atmospheric forcing based on a reanalysis of the ECMWF, such as the
730Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to
731use the ECMWF bulk parametrizations with the cool-skin and warm-layer
732parametrizations activated. In ECMWF reanalyzes, since air temperature and
733humidity are provided at the 2\,m height, and given that the humidity is
734distributed as the dew-point temperature, the namelist must be tuned as follows:
735%
736\begin{verbatim}
737  ...
738  ln_ECMWF   = .true.
739  ...     
740  rn_zqt     =  2.     ! Air temperature & humidity reference height (m)
741  rn_zu      = 10.     ! Wind vector reference height (m)
742  ...
743  ln_skin_cs = .true. ! use the cool-skin parameterization
744  ln_skin_wl = .true. ! use the warm-layer parameterization
745  ...
746  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
747  ...
748\end{verbatim}
749%
750Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
751of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
752triggers the use of the ECMWF cool-skin and warm-layer parametrizations,
753respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
754
755
756\subsubsection{COARE 3.x}
757%
758Since the ECMWF parametrization is largely based on the COARE* parametrization,
759the two algorithms are very similar in terms of structure and closure
760approach. As such, the namelist tuning for COARE 3.x is identical to that of
761ECMWF:
762%
763\begin{verbatim}
764  ...
765  ln_COARE3p6 = .true.
766  ...     
767  ln_skin_cs = .true. ! use the cool-skin parameterization
768  ln_skin_wl = .true. ! use the warm-layer parameterization
769  ...
770\end{verbatim}
771
772Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection
773of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
774triggers the use of the COARE cool-skin and warm-layer parametrizations,
775respectively (found in \textit{sbcblk\_skin\_coare.F90}).
776
777
778%lulu
779
780
781
782% In a typical bulk algorithm, the BTCs under neutral stability conditions are
783% defined using \emph{in-situ} flux measurements while their dependence on the
784% stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and
785% the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are
786% functions of the wind speed and the near-surface stability of the atmospheric
787% surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$
788% and $q_z$.
789
790
791
792\subsection{Prescribed near-surface atmospheric state}
793
794The atmospheric fields used depend on the bulk formulae used.  In forced mode,
795when a sea-ice model is used, a specific bulk formulation is used.  Therefore,
796different bulk formulae are used for the turbulent fluxes computation over the
797ocean and over sea-ice surface.
798%
799
800%The choice is made by setting to true one of the following namelist
801%variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6}
802%and \np{ln_ECMWF}{ln\_ECMWF}.
803
804Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
805The required 9 input fields are:
806
807\begin{table}[htbp]
808  \centering
809  \begin{tabular}{|l|c|c|c|}
810    \hline
811    Variable description                 & Model variable & Units              & point \\
812    \hline
813    i-component of the 10m air velocity  & wndi           & $m.s^{-1}$         & T     \\
814    \hline
815    j-component of the 10m air velocity  & wndj           & $m.s^{-1}$         & T     \\
816    \hline
817    10m air temperature                  & tair           & $K$               & T     \\
818    \hline
819    Specific humidity                    & humi           & $-$               & T     \\
820    Relative humidity                    & ~              & $\%$              & T     \\
821    Dew-point temperature                & ~              & $K$               & T     \\   
822    \hline
823    Downwelling longwave radiation       & qlw            & $W.m^{-2}$         & T     \\
824    \hline
825    Downwelling shortwave radiation      & qsr            & $W.m^{-2}$         & T     \\
826    \hline
827    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
828    \hline
829    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
830    \hline
831    Mean sea-level pressure              & slp            & $hPa$              & T     \\
832    \hline
833    \end{tabular}
834  \label{tab:SBC_BULK}
835\end{table}
836
837Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
838It is simpler and faster (less fields to be read), but it is not the recommended method when
839the ocean grid size is the same or larger than the one of the input atmospheric fields.
840
841The \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},
842\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
843(spatial and temporal interpolations).
844
845\np{cn_dir}{cn\_dir} is the directory of location of bulk files
846%\np{ln_taudif}{ln\_taudif} is the flag to specify if we use High Frequency (HF) tau information (.true.) or not (.false.)
847\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
848\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
849
850Three multiplicative factors are available:
851\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
852increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
853The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
854the calculation of surface wind stress.
855Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
856
857As for the flux parametrization, information about the input data required by the model is provided in
858the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
859
860
861\subsubsection{Air humidity}
862
863Air humidity can be provided as three different parameters: specific humidity
864[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
865parameters)...
866
867
868~\\
869
870
871
872
873
874
875
876
877
878
879%% =================================================================================================
880%\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})}
881%\label{subsec:SBC_blk_ocean}
882
883%Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
884%COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
885%their neutral transfer coefficients relationships with neutral wind.
886%\begin{itemize}
887%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
888%  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
889%  They use an inertial dissipative method to compute the turbulent transfer coefficients
890%  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
891%  This \citet{large.yeager_rpt04} dataset is available through
892%  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
893%  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
894%  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
895%\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
896%\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details
897%\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9204}{IFS (Cy40r1)} %implementation and documentation.
898%  Surface roughness lengths needed for the Obukhov length are computed
899%  following \citet{beljaars_QJRMS95}.
900%\end{itemize}
901
902%% =================================================================================================
903\subsection{Ice-Atmosphere Bulk formulae}
904\label{subsec:SBC_blk_ice}
905
906
907\texttt{\#out\_of\_place:}
908 For sea-ice, three possibilities can be selected:
909a constant transfer coefficient (1.4e-3; default
910value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
911and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
912\texttt{\#out\_of\_place.}
913
914
915
916
917Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
918
919\begin{itemize}
920\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
921  default constant value used for momentum and heat neutral transfer coefficients
922\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
923  This scheme adds a dependency on edges at leads, melt ponds and flows
924  of the constant neutral air-ice drag. After some approximations,
925  this can be resumed to a dependency on ice concentration (A).
926  This drag coefficient has a parabolic shape (as a function of ice concentration)
927  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.
928  It is theoretically applicable to all ice conditions (not only MIZ).
929\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
930  Alternative turbulent transfer coefficients formulation between sea-ice
931  and atmosphere with distinct momentum and heat coefficients depending
932  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
933  The parameterization is adapted from ECHAM6 atmospheric model.
934  Compared to Lupkes2012 scheme, it considers specific skin and form drags
935  to compute neutral transfer coefficients for both heat and momentum fluxes.
936  Atmospheric stability effect on transfer coefficient is also taken into account.
937\end{itemize}
938
939%% =================================================================================================
940\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
941\label{sec:SBC_cpl}
942
943\begin{listing}
944  \nlst{namsbc_cpl}
945  \caption{\forcode{&namsbc_cpl}}
946  \label{lst:namsbc_cpl}
947\end{listing}
948
949In the coupled formulation of the surface boundary condition,
950the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
951while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
952the atmospheric component.
953
954A generalised coupled interface has been developed.
955It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
956An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
957It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
958(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
959(Weather Research and Forecasting Model).
960
961When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
962the whole carbon cycle is computed.
963In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
964(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
965
966The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
967now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
968When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
969the number used in the sea ice model.
970In some limited cases, it may be possible to specify single category coupling fields even when
971the sea ice model is running with multiple categories -
972in this case, the user should examine the code to be sure the assumptions made are satisfactory.
973In cases where this is definitely not possible, the model should abort with an error message.
974
975%% =================================================================================================
976\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
977\label{sec:SBC_apr}
978
979\begin{listing}
980  \nlst{namsbc_apr}
981  \caption{\forcode{&namsbc_apr}}
982  \label{lst:namsbc_apr}
983\end{listing}
984
985The optional atmospheric pressure can be used to force ocean and ice dynamics
986(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
987The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
988can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
989When used to force the dynamics, the atmospheric pressure is further transformed into
990an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
991\[
992  % \label{eq:SBC_ssh_ib}
993  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
994\]
995where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
996A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
997In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
998\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
999
1000The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
1001For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
1002(see \mdl{sbcssr} module).
1003$\eta_{ib}$ can be written in the output.
1004This can simplify altimetry data and model comparison as
1005inverse barometer sea surface height is usually removed from these date prior to their distribution.
1006
1007When using time-splitting and BDY package for open boundaries conditions,
1008the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
1009\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
1010
1011%% =================================================================================================
1012\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
1013\label{sec:SBC_tide}
1014
1015\begin{listing}
1016  \nlst{nam_tide}
1017  \caption{\forcode{&nam_tide}}
1018  \label{lst:nam_tide}
1019\end{listing}
1020
1021The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
1022is activated if \np{ln_tide}{ln\_tide} and \np{ln_tide_pot}{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{_tide}{\_tide}.
1023This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
1024\[
1025  % \label{eq:SBC_PE_dyn_tides}
1026  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
1027  +g\nabla (\Pi_{eq} + \Pi_{sal})
1028\]
1029where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
1030$\Pi_{sal}$ is a self-attraction and loading term (SAL).
1031
1032The equilibrium tidal forcing is expressed as a sum over a subset of
1033constituents chosen from the set of available tidal constituents
1034defined in file \hf{SBC/tide} (this comprises the tidal
1035constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
1036  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
1037constituents are selected by including their names in the array
1038\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
1039\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
1040and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
1041\forcode{.true.}, the equilibrium tidal forcing can be ramped up
1042linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
1043model run.
1044
1045The SAL term should in principle be computed online as it depends on
1046the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
1047discussion about the practical implementation of this term).
1048Nevertheless, the complex calculations involved would make this
1049computationally too expensive. Here, two options are available:
1050$\Pi_{sal}$ generated by an external model can be read in
1051(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
1052used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
1053\[
1054  \Pi_{sal} = \beta \eta,
1055\]
1056where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
1057spatially constant scalar, often chosen to minimize tidal prediction
1058errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
1059\forcode{.false.} removes the SAL contribution.
1060
1061%% =================================================================================================
1062\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
1063\label{sec:SBC_rnf}
1064
1065\begin{listing}
1066  \nlst{namsbc_rnf}
1067  \caption{\forcode{&namsbc_rnf}}
1068  \label{lst:namsbc_rnf}
1069\end{listing}
1070
1071%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1072%Many models, however, have traditionally inserted river runoff to the top model cell.
1073%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
1074%throughout a nonzero depth has been motivated by the numerical and physical problems
1075%that arise when the top grid cells are of the order of one meter. This situation is common in
1076%coastal modelling and becomes more and more often open ocean and climate modelling
1077%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
1078%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
1079
1080%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
1081%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
1082%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
1083%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
1084%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
1085%emp or emps and the changes made are below:
1086
1087%Rachel:
1088River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1089Many models, however, have traditionally inserted river runoff to the top model cell.
1090This was the case in \NEMO\ prior to the version 3.3,
1091and was combined with an option to increase vertical mixing near the river mouth.
1092
1093However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
1094This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
1095\footnote{
1096  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
1097  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
1098  see also \autoref{fig:SBC_dcy}.}.
1099
1100As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
1101and for the temperature and salinity of the river to effect the surrounding ocean.
1102The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
1103along with the depth (in metres) which the river should be added to.
1104
1105Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
1106\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
1107If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
1108and/or taken as surface temperature respectively.
1109
1110The runoff value and attributes are read in in sbcrnf.
1111For temperature -999 is taken as missing data and the river temperature is taken to
1112be the surface temperatue at the river point.
1113For the depth parameter a value of -1 means the river is added to the surface box only,
1114and a value of -999 means the river is added through the entire water column.
1115After being read in the temperature and salinity variables are multiplied by the amount of runoff
1116(converted into m/s) to give the heat and salt content of the river runoff.
1117After the user specified depth is read ini,
1118the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
1119The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
1120the bottom of the lowest box the river water is being added to
1121(\ie\ the total depth that river water is being added to in the model).
1122
1123The mass/volume addition due to the river runoff is, at each relevant depth level, added to
1124the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
1125This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
1126The sea surface height is calculated using the sum of the horizontal divergence terms,
1127and so the river runoff indirectly forces an increase in sea surface height.
1128
1129The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
1130This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
1131The heat and salt content of the river runoff is not included in this step,
1132and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
1133the box and replaced by the same volume of river water with no corresponding heat and salt addition.
1134
1135For the linear free surface case, at the surface box the tracer advection causes a flux of water
1136(of equal volume to the runoff) through the sea surface out of the domain,
1137which causes a salt and heat flux out of the model.
1138As such the volume of water does not change, but the water is diluted.
1139
1140For the non-linear free surface case, no flux is allowed through the surface.
1141Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
1142no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
1143(The runoff addition to the top box along with the water being moved up through
1144boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
1145
1146In trasbc the addition of heat and salt due to the river runoff is added.
1147This is done in the same way for both vvl and non-vvl.
1148The temperature and salinity are increased through the specified depth according to
1149the heat and salt content of the river.
1150
1151In the non-linear free surface case (vvl),
1152near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
1153so that the original ratios of grid box heights are restored.
1154In doing this water is moved into boxes below, throughout the water column,
1155so the large volume addition to the surface box is spread between all the grid boxes.
1156
1157It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
1158\ie\ modelling the Baltic flow in and out of the North Sea.
1159When the flow is out of the domain there is no change in temperature and salinity,
1160regardless of the namelist options used,
1161as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
1162
1163%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1164
1165%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1166
1167%\colorbox{yellow}{river mouths{\ldots}}
1168
1169%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1170%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1171%ENDIF
1172
1173\cmtgm{  word doc of runoffs:
1174In the current \NEMO\ setup river runoff is added to emp fluxes,
1175these are then applied at just the sea surface as a volume change (in the variable volume case
1176this is a literal volume change, and in the linear free surface case the free surface is moved)
1177and a salt flux due to the concentration/dilution effect.
1178There is also an option to increase vertical mixing near river mouths;
1179this gives the effect of having a 3d river.
1180All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
1181at the same temperature as the sea surface.
1182Our aim was to code the option to specify the temperature and salinity of river runoff,
1183(as well as the amount), along with the depth that the river water will affect.
1184This would make it possible to model low salinity outflow, such as the Baltic,
1185and would allow the ocean temperature to be affected by river runoff.
1186
1187The depth option makes it possible to have the river water affecting just the surface layer,
1188throughout depth, or some specified point in between.
1189
1190To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
1191the \mdl{tra_sbc} module.
1192We decided to separate them throughout the code,
1193so that the variable emp represented solely evaporation minus precipitation fluxes,
1194and a new 2d variable rnf was added which represents the volume flux of river runoff
1195(in $kg/m^2s$ to remain consistent with $emp$).
1196This meant many uses of emp and emps needed to be changed,
1197a list of all modules which use $emp$ or $emps$ and the changes made are below:}
1198
1199%% =================================================================================================
1200\section[Ice Shelf (ISF)]{Interaction with ice shelves (ISF)}
1201\label{sec:isf}
1202
1203\begin{listing}
1204  \nlst{namisf}
1205  \caption{\forcode{&namisf}}
1206  \label{lst:namisf}
1207\end{listing}
1208
1209The namelist variable in \ngn{namisf}, \np{ln_isf}{ln\_isf}, controls the ice shelf interactions:
1210\begin{description}
1211   \item $\bullet$ representation of the ice shelf/ocean melting/freezing for opened cavity (cav, \np{ln_isfcav_mlt}{ln\_isfcav\_mlt}).
1212   \item $\bullet$ parametrisation of the ice shelf/ocean melting/freezing for closed cavities (par, \np{ln_isfpar_mlt}{ln\_isfpar\_mlt}).
1213   \item $\bullet$ coupling with an ice sheet model (\np{ln_isfcpl}{ln\_isfcpl}).
1214\end{description}
1215
1216  \subsection{Ocean/Ice shelf fluxes in opened cavities}
1217
1218     \np{ln_isfcav_mlt}{ln\_isfcav\_mlt}\forcode{ = .true.} activates the ocean/ice shelf thermodynamics interactions at the ice shelf/ocean interface.
1219     If \np{ln_isfcav_mlt}\forcode{ = .false.}, thermodynamics interactions are desctivated but the ocean dynamics inside the cavity is still active.
1220     The logical flag \np{ln_isfcav}{ln\_isfcav} control wether or not the ice shelf cavities are closed. \np{ln_isfcav}{ln\_isfcav} is not defined in the namelist but in the domcfg.nc input file.\\
1221
1222     3 options are available to represent to ice-shelf/ocean fluxes at the interface:
1223     \begin{description}
1224        \item[\np{cn_isfcav_mlt}\forcode{ = 'spe'}]:
1225        The fresh water flux is specified by a forcing fields \np{sn_isfcav_fwf}{sn\_isfcav\_fwf}. Convention of the input file is: positive toward the ocean (i.e. positive for melting and negative for freezing).
1226        The latent heat fluxes is derived from the fresh water flux.
1227        The heat content flux is derived from the fwf flux assuming a temperature set to the freezing point in the top boundary layer (\np{rn_htbl}{rn\_htbl})
1228
1229        \item[\np{cn_isfcav_mlt}\forcode{ = 'oasis'}]:
1230        The \forcode{'oasis'} is a prototype of what could be a method to spread precipitation on Antarctic ice sheet as ice shelf melt inside the cavity when a coupled model Atmosphere/Ocean is used.
1231        It has not been tested and therefore the model will stop if you try to use it.
1232        Actions will be undertake in 2020 to build a comprehensive interface to do so for Greenland, Antarctic and ice shelf (cav), ice shelf (par), icebergs, subglacial runoff and runoff.
1233
1234        \item[\np{cn_isfcav_mlt}\forcode{ = '2eq'}]:
1235        The heat flux and the fresh water flux (negative for melting) resulting from ice shelf melting/freezing are parameterized following \citet{Grosfeld1997}.
1236        This formulation is based on a balance between the vertical diffusive heat flux across the ocean top boundary layer (\autoref{eq:ISOMIP1})
1237        and the latent heat due to melting/freezing (\autoref{eq:ISOMIP2}):
1238
1239        \begin{equation}
1240        \label{eq:ISOMIP1}
1241        \mathcal{Q}_h = \rho c_p \gamma (T_w - T_f)
1242        \end{equation}
1243        \begin{equation}
1244        \label{eq:ISOMIP2}
1245        q = \frac{-\mathcal{Q}_h}{L_f}
1246        \end{equation}
1247       
1248        where $\mathcal{Q}_h$($W.m^{-2}$) is the heat flux,q($kg.s^{-1}m^{-2}$) the fresh-water flux,
1249        $L_f$ the specific latent heat, $T_w$ the temperature averaged over a boundary layer below the ice shelf (explained below),
1250        $T_f$ the freezing point using  the  pressure  at  the  ice  shelf  base  and  the  salinity  of the water in the boundary layer,
1251        and $\gamma$ the thermal exchange coefficient.
1252
1253        \item[\np{cn_isfcav_mlt}\forcode{ = '3eq'}]:
1254        For realistic studies, the heat and freshwater fluxes are parameterized following \citep{Jenkins2001}. This formulation is based on three equations:
1255        a balance between the vertical diffusive heat flux across the boundary layer
1256        , the latent heat due to melting/freezing of ice and the vertical diffusive heat flux into the ice shelf (\autoref{eq:3eq1});
1257        a balance between the vertical diffusive salt flux across the boundary layer and the salt source or sink represented by the melting/freezing (\autoref{eq:3eq2});
1258        and a linear equation for the freezing temperature of sea water (\autoref{eq:3eq3}, detailed of the linearisation coefficient in \citet{AsayDavis2016}):
1259
1260        \begin{equation}
1261        \label{eq:3eq1}
1262        c_p \rho \gamma_T (T_w-T_b) = -L_f q - \rho_i c_{p,i} \kappa \frac{T_s - T_b}{h_{isf}}
1263        \end{equation}
1264        \begin{equation}
1265        \label{eq:3eq2}
1266        \rho \gamma_S (S_w - S_b) = (S_i - S_b)q
1267        \end{equation}
1268        \begin{equation}
1269        \label{eq:3eq3}
1270        T_b = \lambda_1 S_b + \lambda_2 +\lamda_3 zisf
1271        \end{equation}
1272
1273        where $T_b$ is the temperature at the interface, $S_b$ the salinity at the interface, $\gamma_T$ and $\gamma_S$ the exchange coefficients for temperature and salt, respectively,
1274        $S_i$ the salinity of the ice (assumedto be 0), $h_{isf}$ the ice shelf thickness, $\rho_i$ the density of the iceshelf,
1275        $c_{p,i}$ the specific heat capacity of the ice, $\kappa$ the thermal diffusivity of the ice
1276        and $T_s$ the atmospheric surface temperature (at the ice/air interface, assumed to be -20C).
1277        The Liquidus slope ($\lambda_1$), the liquidus intercept ($\lambda_2$) and the Liquidus pressure coefficient ($\lambda_3$)
1278        for TEOS80 and TEOS10 are described in \citep{AsayDavis2016} and in \citep{Jourdain2017}.
1279        The linear system formed by \autoref{eq:3eq1}, \autoref{eq:3eq2} and the linearised equation for the freezing temperature of sea water (\autoref{eq:3eq3}) can be solved for $S_b$ or $T_b$.
1280        Afterward, the freshwater flux ($q$) and the heat flux ($\mathcal{Q}_h$) can be computed.
1281
1282     \end{description}
1283
1284     \begin{table}[h]
1285        \centering
1286        \caption{Description of the parameters hard coded into the ISF module}
1287        \label{tab:isf}
1288        \begin{tabular}{|l|l|l|l|}
1289        \hline
1290        Symbol    & Description               & Value              & Unit               \\
1291        \hline
1292        $C_p$     & Ocean specific heat       & 3992               & $J.kg^{-1}.K^{-1}$ \\
1293        $L_f$     & Ice latent heat of fusion & $3.34 \times 10^5$ & $J.kg^{-1}$        \\
1294        $C_{p,i}$ & Ice specific heat         & 2000               & $J.kg^{-1}.K^{-1}$ \\
1295        $\kappa$  & Heat diffusivity          & $1.54 \times 10^{-6}$& $m^2.s^{-1}$     \\
1296        $\rho_i$  & Ice density               & 920                & $kg.m^3$           \\
1297        \hline
1298        \end{tabular}
1299     \end{table}
1300
1301     Temperature and salinity used to compute the fluxes in \autoref{eq:ISOMIP1}, \autoref{eq:3eq1} and \autoref{eq:3eq2} are the average temperature in the top boundary layer \citep{losch_JGR08}.
1302     Its thickness is defined by \np{rn_htbl}{rn\_htbl}.
1303     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the first \np{rn_htbl}{rn\_htbl} m.
1304     Then, the fluxes are spread over the same thickness (ie over one or several cells).
1305     If \np{rn_htbl}{rn\_htbl} larger than top $e_{3}t$, there is no more direct feedback between the freezing point at the interface and the top cell temperature.
1306     This can lead to super-cool temperature in the top cell under melting condition.
1307     If \np{rn_htbl}{rn\_htbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
1308
1309     Each melt formula (\np{cn_isfcav_mlt}\forcode{ = '3eq'} or \np{cn_isfcav_mlt}\forcode{ = '2eq'}) depends on an exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1310     Below, the exchange coeficient $\Gamma^{T}$ and $\Gamma^{S}$ are respectively defined by \np{rn_gammat0}{rn\_gammat0} and \np{rn_gammas0}{rn\_gammas0}.
1311     There are 3 different ways to compute the exchange velocity:
1312
1313     \begin{description}
1314        \item[\np{cn_gammablk}\forcode{='spe'}]:
1315        The salt and heat exchange coefficients are constant and defined by:
1316\[
1317\gamma^{T} = \Gamma^{T}
1318\]
1319\[
1320\gamma^{S} = \Gamma^{S}
1321\] 
1322        This is the recommended formulation for ISOMIP.
1323
1324   \item[\np{cn_gammablk}\forcode{='vel'}]:
1325        The salt and heat exchange coefficients are velocity dependent and defined as
1326\[
1327\gamma^{T} = \Gamma^{T} \times u_{*}
1328\]
1329\[
1330\gamma^{S} = \Gamma^{S} \times u_{*}
1331\]
1332        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_htbl}{rn\_htbl} meters).
1333        See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application and ISOMIP+/MISOMIP configuration.
1334
1335   \item[\np{cn_gammablk}\forcode{'vel\_stab'}]:
1336        The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1337\[
1338\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1339\]
1340        where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_tbl}{rn\_htbl} meters),
1341        $\Gamma_{Turb}$ the contribution of the ocean stability and
1342        $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1343        See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1344        This formulation has not been extensively tested in NEMO (not recommended).
1345     \end{description}
1346
1347\subsection{Ocean/Ice shelf fluxes in parametrised cavities}
1348
1349  \begin{description}
1350
1351     \item[\np{cn_isfpar_mlt}\forcode{ = 'bg03'}]:
1352     The ice shelf cavities are not represented.
1353     The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1354     The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1355     (\np{sn_isfpar_zmax}{sn\_isfpar\_zmax}) and the base of the ice shelf along the calving front
1356     (\np{sn_isfpar_zmin}{sn\_isfpar\_zmin}) as in (\np{cn_isfpar_mlt}\forcode{ = 'spe'}).
1357     The effective melting length (\np{sn_isfpar_Leff}{sn\_isfpar\_Leff}) is read from a file.
1358     This parametrisation has not been tested since a while and based on \citet{Favier2019},
1359     this parametrisation should probably not be used.
1360
1361     \item[\np{cn_isfpar_mlt}\forcode{ = 'spe'}]:
1362     The ice shelf cavity is not represented.
1363     The fwf (\np{sn_isfpar_fwf}{sn\_isfpar\_fwf}) is prescribed and distributed along the ice shelf edge between
1364     the depth of the average grounding line (GL) (\np{sn_isfpar_zmax}{sn\_isfpar\_zmax}) and
1365     the base of the ice shelf along the calving front (\np{sn_isfpar_zmin}{sn\_isfpar\_min}). Convention of the input file is positive toward the ocean (i.e. positive for melting and negative for freezing).
1366     The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1367
1368     \item[\np{cn_isfpar_mlt}\forcode{ = 'oasis'}]:
1369     The \forcode{'oasis'} is a prototype of what could be a method to spread precipitation on Antarctic ice sheet as ice shelf melt inside the cavity when a coupled model Atmosphere/Ocean is used.
1370     It has not been tested and therefore the model will stop if you try to use it.
1371     Action will be undertake in 2020 to build a comprehensive interface to do so for Greenland, Antarctic and ice shelf (cav), ice shelf (par), icebergs, subglacial runoff and runoff.
1372
1373  \end{description}
1374
1375\np{cn_isfcav_mlt}\forcode{ = '2eq'}, \np{cn_isfcav_mlt}\forcode{ = '3eq'} and \np{cn_isfpar_mlt}\forcode{ = 'bg03'} compute a melt rate based on
1376the water mass properties, ocean velocities and depth.
1377The resulting fluxes are thus highly dependent of the model resolution (horizontal and vertical) and
1378realism of the water masses onto the shelf.\\
1379
1380\np{cn_isfcav_mlt}\forcode{ = 'spe'} and \np{cn_isfpar_mlt}\forcode{ = 'spe'} read the melt rate from a file.
1381You have total control of the fwf forcing.
1382This can be useful if the water masses on the shelf are not realistic or
1383the resolution (horizontal/vertical) are too coarse to have realistic melting or
1384for studies where you need to control your heat and fw input.
1385However, if your forcing is not consistent with the dynamics below you can reach unrealistic low water temperature.\\
1386
1387The ice shelf fwf is implemented as a volume flux as for the runoff.
1388The fwf addition due to the ice shelf melting is, at each relevant depth level, added to
1389the horizontal divergence (\textit{hdivn}) in the subroutine \rou{isf\_hdiv}, called from \mdl{divhor}.
1390See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1391
1392Description and result of sensitivity tests to \np{ln_isfcav_mlt}{ln\_isfcav\_mlt} and \np{ln_isfpar_mlt}{ln\_isfpar\_mlt} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1393The different options are illustrated in \autoref{fig:ISF}.
1394
1395\begin{figure}[!t]
1396  \centering
1397  \includegraphics[width=0.66\textwidth]{SBC_isf_v4.2}
1398  \caption[Ice shelf location and fresh water flux definition]{
1399    Illustration of the location where the fwf is injected and
1400    whether or not the fwf is interactif or not.}
1401  \label{fig:ISF}
1402\end{figure}
1403
1404\subsection{Available outputs}
1405The following outputs are availables via XIOS:
1406\begin{description}
1407   \item[for parametrised cavities]:
1408      \begin{xmllines}
1409 <field id="isftfrz_par"     long_name="freezing point temperature in the parametrization boundary layer" unit="degC"     />
1410 <field id="fwfisf_par"      long_name="Ice shelf melt rate"                           unit="kg/m2/s"  />
1411 <field id="qoceisf_par"     long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     />
1412 <field id="qlatisf_par"     long_name="Ice shelf latent heat flux"                    unit="W/m2"     />
1413 <field id="qhcisf_par"      long_name="Ice shelf heat content flux of injected water" unit="W/m2"     />
1414 <field id="fwfisf3d_par"    long_name="Ice shelf melt rate"                           unit="kg/m2/s"  grid_ref="grid_T_3D" />
1415 <field id="qoceisf3d_par"   long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
1416 <field id="qlatisf3d_par"   long_name="Ice shelf latent heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
1417 <field id="qhcisf3d_par"    long_name="Ice shelf heat content flux of injected water" unit="W/m2"     grid_ref="grid_T_3D" />
1418 <field id="ttbl_par"        long_name="temperature in the parametrisation boundary layer" unit="degC" />
1419 <field id="isfthermald_par" long_name="thermal driving of ice shelf melting"          unit="degC"     />
1420      \end{xmllines}
1421   \item[for open cavities]:
1422      \begin{xmllines}
1423 <field id="isftfrz_cav"     long_name="freezing point temperature at ocean/isf interface"                unit="degC"     />
1424 <field id="fwfisf_cav"      long_name="Ice shelf melt rate"                           unit="kg/m2/s"  />
1425 <field id="qoceisf_cav"     long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     />
1426 <field id="qlatisf_cav"     long_name="Ice shelf latent heat flux"                    unit="W/m2"     />
1427 <field id="qhcisf_cav"      long_name="Ice shelf heat content flux of injected water" unit="W/m2"     />
1428 <field id="fwfisf3d_cav"    long_name="Ice shelf melt rate"                           unit="kg/m2/s"  grid_ref="grid_T_3D" />
1429 <field id="qoceisf3d_cav"   long_name="Ice shelf ocean  heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
1430 <field id="qlatisf3d_cav"   long_name="Ice shelf latent heat flux"                    unit="W/m2"     grid_ref="grid_T_3D" />
1431 <field id="qhcisf3d_cav"    long_name="Ice shelf heat content flux of injected water" unit="W/m2"     grid_ref="grid_T_3D" />
1432 <field id="ttbl_cav"        long_name="temperature in Losch tbl"                      unit="degC"     />
1433 <field id="isfthermald_cav" long_name="thermal driving of ice shelf melting"          unit="degC"     />
1434 <field id="isfgammat"       long_name="Ice shelf heat-transfert velocity"             unit="m/s"      />
1435 <field id="isfgammas"       long_name="Ice shelf salt-transfert velocity"             unit="m/s"      />
1436 <field id="stbl"            long_name="salinity in the Losh tbl"                      unit="1e-3"     />
1437 <field id="utbl"            long_name="zonal current in the Losh tbl at T point"      unit="m/s"      />
1438 <field id="vtbl"            long_name="merid current in the Losh tbl at T point"      unit="m/s"      />
1439 <field id="isfustar"        long_name="ustar at T point used in ice shelf melting"    unit="m/s"      />
1440 <field id="qconisf"         long_name="Conductive heat flux through the ice shelf"    unit="W/m2"     />
1441      \end{xmllines}
1442\end{description}
1443
1444%% =================================================================================================
1445\subsection{Ice sheet coupling}
1446\label{subsec:ISF_iscpl}
1447
1448Ice sheet/ocean coupling is done through file exchange at the restart step.
1449At each restart step, the procedure is this one:
1450
1451\begin{description}
1452\item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1453\item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools.
1454\item[Step 3]: NEMO run for a specific period and output the average melt rate over the period.
1455\item[Step 4]: the ice sheet model run using the melt rate outputed in step 4.
1456\item[Step 5]: go back to 1.
1457\end{description}
1458
1459If \np{ln_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with
1460potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1461The wetting and drying scheme, applied on the restart, is very simple. The 6 different possible cases for the tracer and ssh are:
1462
1463\begin{description}
1464   \item[Thin a cell]:
1465   T/S/ssh are unchanged.
1466
1467   \item[Enlarge  a cell]:
1468   See case "Thin a cell down"
1469
1470   \item[Dry a cell]:
1471   Mask, T/S, U/V and ssh are set to 0.
1472
1473   \item[Wet a cell]:
1474   Mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$.
1475   If no neighbours, T/S is extrapolated from old top cell value.
1476   If no neighbours along i,j and k (both previous tests failed), T/S/ssh and mask are set to 0.
1477
1478   \item[Dry a column]:
1479   mask, T/S and ssh are set to 0.
1480
1481   \item[Wet a column]:
1482   set mask to 1, T/S/ssh are extrapolated from neighbours.
1483   If no neighbour, T/S/ssh and mask set to 0.
1484\end{description}
1485
1486The method described above will strongly affect the barotropic transport under an ice shelf when the geometry change.
1487In order to keep the model stable, an adjustment of the dynamics at the initialisation after the coupling step is needed.
1488The idea behind this is to keep $\pd[\eta]{t}$ as it should be without change in geometry at the initialisation.
1489This will prevent any strong velocity due to large pressure gradient.
1490To do so, we correct the horizontal divergence before $\pd[\eta]{t}$ is computed in the first time step.\\
1491
1492Furthermore, as the before and now fields are not compatible (modification of the geometry),
1493the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1494
1495The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1496It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1497the code will be unable to fill all the new wet cells properly and the model is likely to blow up at the initialisation.
1498The default number is set up for the MISOMIP idealised experiments.
1499This coupling procedure is able to take into account grounding line and calving front migration.
1500However, it is a non-conservative proccess.
1501This could lead to a trend in heat/salt content and volume.\\
1502
1503In order to remove the trend and keep the conservation level as close to 0 as possible,
1504a simple conservation scheme is available with \np{ln_isfcpl_cons}\forcode{ = .true.}.
1505The heat/salt/vol. gain/loss are diagnosed, as well as the location.
1506A correction increment is computed and applied each time step during the model run.
1507The corrective increment are applied into the cells itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry).
1508
1509%% =================================================================================================
1510\section{Handling of icebergs (ICB)}
1511\label{sec:SBC_ICB_icebergs}
1512
1513\begin{listing}
1514  \nlst{namberg}
1515  \caption{\forcode{&namberg}}
1516  \label{lst:namberg}
1517\end{listing}
1518
1519Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1520Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1521(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1522Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1523described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1524Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1525which is an integer representing how many icebergs of this class are being described as one lagrangian point
1526(this reduces the numerical problem of tracking every single iceberg).
1527They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1528
1529Two initialisation schemes are possible.
1530\begin{description}
1531\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
1532  (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
1533  which an iceberg is generated at the beginning of the run.
1534  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1535  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1536  the geographical box: lonmin,lonmax,latmin,latmax
1537\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.
1538  This should be a file with a field on the configuration grid (typically ORCA)
1539  representing ice accumulation rate at each model point.
1540  These should be ocean points adjacent to land where icebergs are known to calve.
1541  Most points in this input grid are going to have value zero.
1542  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1543  At each time step, a test is performed to see if there is enough ice mass to
1544  calve an iceberg of each class in order (1 to 10).
1545  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1546  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1547\end{description}
1548
1549Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1550The latter act to disintegrate the iceberg.
1551This is either all melted freshwater,
1552or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1553which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1554Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1555
1556Extensive diagnostics can be produced.
1557Separate output files are maintained for human-readable iceberg information.
1558A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1559The amount of information is controlled by two integer parameters:
1560\begin{description}
1561\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1562  represents an increasing number of points in the code at which variables are written,
1563  and an increasing level of obscurity.
1564\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1565\end{description}
1566
1567Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1568A non-zero value represents how many timesteps between writes of information into the output file.
1569These output files are in NETCDF format.
1570When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1571Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1572So care is needed to recreate data for individual icebergs,
1573since its trajectory data may be spread across multiple files.
1574
1575%% =================================================================================================
1576\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1577\label{sec:SBC_wave}
1578
1579\begin{listing}
1580  \nlst{namsbc_wave}
1581  \caption{\forcode{&namsbc_wave}}
1582  \label{lst:namsbc_wave}
1583\end{listing}
1584
1585Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1586physical processes related to ocean surface waves, namely the surface stress modified by growth and
1587dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1588tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1589the wind stress.
1590
1591Physical processes related to ocean surface waves can be accounted by setting the logical variable
1592\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1593different processes should be activated as explained in the following sections.
1594
1595Wave fields can be provided either in forced or coupled mode:
1596\begin{description}
1597\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1598for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1599Input Data generic Interface (see \autoref{sec:SBC_input}).
1600\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1601in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1602\end{description}
1603
1604%% =================================================================================================
1605\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1606\label{subsec:SBC_wave_cdgw}
1607
1608The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1609can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1610Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1611the drag coefficient is computed according to the stable/unstable conditions of the
1612air-sea interface following \citet{large.yeager_rpt04}.
1613
1614%% =================================================================================================
1615\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1616\label{subsec:SBC_wave_sdw}
1617
1618The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1619It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1620and the current measured at a fixed point (Eulerian velocity).
1621As waves travel, the water particles that make up the waves travel in orbital motions but
1622without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1623at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1624An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1625representation of surface physics in ocean general circulation models. %GS: reference needed
1626The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1627
1628\[
1629  % \label{eq:SBC_wave_sdw}
1630  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1631  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1632  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1633\]
1634
1635where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1636$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1637$k$ is the mean wavenumber defined as:
1638$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1639
1640In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1641and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1642To simplify, it is customary to use approximations to the full Stokes profile.
1643Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1644are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1645$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1646and makes possible the estimation of the surface Stokes drift for random directional waves in
1647realistic wave conditions:
1648
1649\begin{description}
1650\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1651\citet{breivik.janssen.ea_JPO14}:
1652
1653\[
1654  % \label{eq:SBC_wave_sdw_0a}
1655  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1656\]
1657
1658where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1659
1660\[
1661  % \label{eq:SBC_wave_sdw_0b}
1662  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1663  \quad \text{and }\
1664  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1665\]
1666
1667where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1668
1669\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1670reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1671\citep{breivik.bidlot.ea_OM16}:
1672
1673\[
1674  % \label{eq:SBC_wave_sdw_1}
1675  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1676  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1677\]
1678
1679where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1680
1681\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1682but using the wave frequency from a wave model.
1683
1684\end{description}
1685
1686The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1687and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1688
1689\[
1690  % \label{eq:SBC_wave_eta_sdw}
1691  \frac{\partial{\eta}}{\partial{t}} =
1692  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1693\]
1694
1695The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1696for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1697that is induced by the three-dimensional Stokes velocity.
1698The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1699can be formulated as follows:
1700
1701\[
1702  % \label{eq:SBC_wave_tra_sdw}
1703  \frac{\partial{c}}{\partial{t}} =
1704  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1705\]
1706
1707%% =================================================================================================
1708\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1709\label{subsec:SBC_wave_stcor}
1710
1711In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1712in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1713This additional force may have impact on the Ekman turning of the surface current.
1714In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1715approximations described in \autoref{subsec:SBC_wave_sdw}),
1716\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1717
1718%% =================================================================================================
1719\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1720\label{subsec:SBC_wave_tauw}
1721
1722The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1723into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1724available for forcing the mean circulation, while in the opposite case of a decaying sea
1725state, more momentum is available for forcing the ocean.
1726Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1727but in practice, an equilibrium sea state is a fairly rare event.
1728So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1729
1730\[
1731  % \label{eq:SBC_wave_tauoc}
1732  \tau_{oc,a} = \tau_a - \tau_w
1733\]
1734
1735where $\tau_a$ is the atmospheric surface stress;
1736$\tau_w$ is the atmospheric stress going into the waves defined as:
1737
1738\[
1739  % \label{eq:SBC_wave_tauw}
1740  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1741\]
1742
1743where: $c_p$ is the phase speed of the gravity waves,
1744$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1745the physics of ocean waves. The first one, $S_{in}$, describes the generation
1746of ocean waves by wind and therefore represents the momentum and energy transfer
1747from air to ocean waves; the second term $S_{nl}$ denotes
1748the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1749describes the dissipation of waves by processes such as white-capping, large scale breaking
1750eddy-induced damping.
1751
1752The wave stress derived from an external wave model can be provided either through the normalized
1753wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1754meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1755
1756%% =================================================================================================
1757\section{Miscellaneous options}
1758\label{sec:SBC_misc}
1759
1760%% =================================================================================================
1761\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1762\label{subsec:SBC_dcy}
1763
1764\begin{figure}[!t]
1765  \centering
1766  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
1767  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1768    Example of reconstruction of the diurnal cycle variation of short wave flux from
1769    daily mean values.
1770    The reconstructed diurnal cycle (black line) is chosen as
1771    the mean value of the analytical cycle (blue line) over a time step,
1772    not as the mid time step value of the analytically cycle (red square).
1773    From \citet{bernie.guilyardi.ea_CD07}.}
1774  \label{fig:SBC_diurnal}
1775\end{figure}
1776
1777\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.
1778%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1779Nevertheless, 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}.
1780Furthermore, only the knowledge of daily mean value of SWF is needed,
1781as higher frequency variations can be reconstructed from them,
1782assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1783The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1784setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1785using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1786the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1787The reconstruction is performed in the \mdl{sbcdcy} module.
1788The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1789The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1790a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1791The use of diurnal cycle reconstruction requires the input SWF to be daily
1792(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1793Furthermore, it is recommended to have a least 8 surface module time steps per day,
1794that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1795An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1796one every 2~hours (from 1am to 11pm).
1797
1798\begin{figure}[!t]
1799  \centering
1800  \includegraphics[width=0.66\textwidth]{SBC_dcy}
1801  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1802    Example of reconstruction of the diurnal cycle variation of short wave flux from
1803    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1804    The display is on (i,j) plane.}
1805  \label{fig:SBC_dcy}
1806\end{figure}
1807
1808Note also that the setting a diurnal cycle in SWF is highly recommended when
1809the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1810an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1811
1812%% =================================================================================================
1813\subsection{Rotation of vector pairs onto the model grid directions}
1814\label{subsec:SBC_rotation}
1815
1816When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1817pairs of vector components can be rotated from east-north directions onto the local grid directions.
1818This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1819be defined relative to a rectilinear grid.
1820To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1821The eastward component must start with "U" and the northward component with "V".
1822The remaining characters in the strings are used to identify which pair of components go together.
1823So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1824rotate them on to the model grid directions;
1825"U2" and "V2" could be used against a second pair of components, and so on.
1826The extra characters used in the strings are arbitrary.
1827The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1828
1829%% =================================================================================================
1830\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1831\label{subsec:SBC_ssr}
1832
1833\begin{listing}
1834  \nlst{namsbc_ssr}
1835  \caption{\forcode{&namsbc_ssr}}
1836  \label{lst:namsbc_ssr}
1837\end{listing}
1838
1839Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1840On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1841a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1842\[
1843  % \label{eq:SBC_dmp_q}
1844  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1845\]
1846where SST is a sea surface temperature field (observed or climatological),
1847$T$ is the model surface layer temperature and
1848$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1849For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1850This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1851
1852In the fresh water budget, a feedback term can also be added.
1853Converted into an equivalent freshwater flux, it takes the following expression :
1854
1855\begin{equation}
1856  \label{eq:SBC_dmp_emp}
1857  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1858  {\left.S\right|_{k=1}}
1859\end{equation}
1860
1861where $\textit{emp}_{o }$ is a net surface fresh water flux
1862(observed, climatological or an atmospheric model product),
1863\textit{SSS}$_{Obs}$ is a sea surface salinity
1864(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1865$\left.S\right|_{k=1}$ is the model surface layer salinity and
1866$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1867Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1868the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1869The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1870reduce the uncertainties we have on the observed freshwater budget.
1871
1872%% =================================================================================================
1873\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1874\label{subsec:SBC_ice-cover}
1875
1876The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1877There are several way to handle sea-ice in the system depending on
1878the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1879\begin{description}
1880\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1881  This is a typical namelist value used for tropical ocean domain.
1882  The surface fluxes are simply specified for an ice-free ocean.
1883  No specific things is done for sea-ice.
1884\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1885  An observed ice covered area is read in a file.
1886  Below this area, the SST is restored to the freezing point and
1887  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1888  The associated modification of the freshwater fluxes are done in such a way that
1889  the change in buoyancy fluxes remains zero.
1890  This prevents deep convection to occur when trying to reach the freezing point
1891  (and so ice covered area condition) while the SSS is too large.
1892  This manner of managing sea-ice area, just by using a IF case,
1893  is usually referred as the \textit{ice-if} model.
1894  It can be found in the \mdl{sbcice\_if} module.
1895\item [nn\_ice = 2 or more] A full sea ice model is used.
1896  This model computes the ice-ocean fluxes,
1897  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1898  provide the surface averaged ocean fluxes.
1899  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1900  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1901  (\ie\ $2$ for SI3 or $3$ for CICE).
1902\end{description}
1903
1904% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1905%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1906
1907%% =================================================================================================
1908\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1909\label{subsec:SBC_cice}
1910
1911It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1912to the CICE sea-ice model by using \key{cice}.
1913The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1914the additional 'hadgem3' drivers will be required, even with the latest code release.
1915Input grid files consistent with those used in \NEMO\ will also be needed,
1916and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1917(seek advice from UKMO if necessary).
1918Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1919(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1920or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1921(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1922The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1923(although coupling ocean and ice less frequently should work,
1924it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1925the user should check that results are not significantly different to the standard case).
1926
1927There are two options for the technical coupling between \NEMO\ and CICE.
1928The standard version allows complete flexibility for the domain decompositions in the individual models,
1929but this is at the expense of global gather and scatter operations in the coupling which
1930become very expensive on larger numbers of processors.
1931The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1932the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1933and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1934allows much more efficient direct coupling on individual processors.
1935This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1936there is no sea ice.
1937
1938%% =================================================================================================
1939\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1940\label{subsec:SBC_fwb}
1941
1942For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1943prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1944In \NEMO, two way of controlling the freshwater budget are proposed:
1945
1946\begin{description}
1947\item [{\np[=0]{nn_fwb}{nn\_fwb}}] no control at all.
1948  The mean sea level is free to drift, and will certainly do so.
1949\item [{\np[=1]{nn_fwb}{nn\_fwb}}] global mean \textit{emp} set to zero at each model time step.
1950  %GS: comment below still relevant ?
1951  %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).
1952\item [{\np[=2]{nn_fwb}{nn\_fwb}}] freshwater budget is adjusted from the previous year annual mean budget which
1953  is read in the \textit{EMPave\_old.dat} file.
1954  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1955  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1956\end{description}
1957
1958\subsection[Closed sea freshwater budget control (\textit{sbcclo.F90})]{Closed sea freswater budget control (\protect\mdl{sbcclo})}
1959\label{subsec:SBC_clo}
1960
1961Some configurations include inland seas and lakes as ocean
1962points. This is particularly the case for configurations that are
1963coupled to an atmosphere model where one might want to include inland
1964seas and lakes as ocean model points in order to provide a better
1965bottom boundary condition for the atmosphere. However there is no
1966route for freshwater to run off from the lakes to the ocean and this
1967can lead to large drifts in the sea surface height over the lakes. The
1968closea module provides options to either fill in closed seas and lakes
1969at run time, or to set the net surface freshwater flux for each lake
1970to zero and put the residual flux into the ocean.
1971Full details on the usage on the closed sea module are available in \autoref{sec:MISC_closea} 
1972
1973The following outputs are availables via XIOS:
1974\begin{xmllines}
1975   <field id="wclosea"  long_name="closed sea empmr correction"   standard_name="closea_empmr"                          unit="kg/m2/s"   />
1976   <field id="qclosea"  long_name="closed sea heat content flux"  standard_name="closea_heat_content_downward_flux"     unit="W/m2"      />
1977\end{xmllines}
1978
1979
1980% Griffies doc:
1981% When running ocean-ice simulations, we are not explicitly representing land processes,
1982% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1983% it is important to balance the hydrological cycle in ocean-ice models.
1984% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1985% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1986% a chosen time scale.
1987% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1988% so that there is always a zero net input of water to the ocean-ice system.
1989% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1990% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1991% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1992% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1993% and ice models when aiming to balance the hydrological cycle.
1994% 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,
1995% not the water in any one sub-component. As an extreme example to illustrate the issue,
1996% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1997% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1998% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1999% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
2000% in ocean-ice models.
2001
2002\subinc{\input{../../global/epilogue}}
2003
2004\end{document}
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