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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   4.0} & {\em ...} & {\em ...} \\
21    {\em   3.6} & {\em ...} & {\em ...} \\
22    {\em   3.4} & {\em ...} & {\em ...} \\
23    {\em <=3.4} & {\em ...} & {\em ...}
24  \end{tabularx}
25}
26
27\clearpage
28
29\begin{listing}
30  \nlst{namsbc}
31  \caption{\forcode{&namsbc}}
32  \label{lst:namsbc}
33\end{listing}
34
35The ocean needs seven fields as surface boundary condition:
36
37\begin{itemize}
38\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
39\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
40\item the surface freshwater budget $\left( {\textit{emp}} \right)$
41\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
42\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
43\end{itemize}
44
45Four different ways are available to provide the seven fields to the ocean. They are controlled by
46namelist \nam{sbc}{sbc} variables:
47
48\begin{itemize}
49\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms,
50\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
51\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
52(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
53\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
54\end{itemize}
55
56The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
57
58When the fields are supplied from data files (bulk, flux and mixed formulations),
59the input fields do not need to be supplied on the model grid.
60Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
61the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
62If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
63should be masked or filled to avoid spurious results in proximity of the coasts, as
64large sea-land gradients characterize most of the atmospheric variables.
65
66In addition, the resulting fields can be further modified using several namelist options.
67These options control:
68
69\begin{itemize}
70\item the rotation of vector components supplied relative to an east-north coordinate system onto
71  the local grid directions in the model,
72\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
73\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
74\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
75  (\np[=0..3]{nn_ice}{nn\_ice}),
76\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
77\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
78  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
79\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
80  (\np[=0..2]{nn_fwb}{nn\_fwb}),
81\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
82  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
83\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
84\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
85\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
86\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
87\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
88\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
89\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
90\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
91\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}),
92\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
93\end{itemize}
94
95In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
96Then we present the three ways of providing the surface boundary conditions,
97followed by the description of the atmospheric pressure and the river runoff.
98Next, the scheme for interpolation on the fly is described.
99Finally, the different options that further modify the fluxes applied to the ocean are discussed.
100One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
101which act as drifting sources of fresh water.
102Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
103which provides additional sources of fresh water.
104
105%% =================================================================================================
106\section{Surface boundary condition for the ocean}
107\label{sec:SBC_ocean}
108
109The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
110It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
111the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
112As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
113\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
114
115The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
116$Q_{ns}$ and $Q_{sr}$, respectively.
117The former is the non penetrative part of the heat flux
118(\ie\ the sum of sensible, latent and long wave heat fluxes plus
119the heat content of the mass exchange between the ocean and sea-ice).
120It is applied in \mdl{trasbc} module as a surface boundary condition trend of
121the first level temperature time evolution equation
122(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
123The latter is the penetrative part of the heat flux.
124It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
125\np[=.true.]{ln_traqsr}{ln\_traqsr}.
126The way the light penetrates inside the water column is generally a sum of decreasing exponentials
127(see \autoref{subsec:TRA_qsr}).
128
129The surface freshwater budget is provided by the \textit{emp} field.
130It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
131possibly with the sea-ice and ice shelves (freezing minus melting of ice).
132It affects the ocean in two different ways:
133$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
134a volume flux, and
135$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
136the mass exchanged with atmosphere, sea-ice and ice shelves.
137
138%\colorbox{yellow}{Miss: }
139%A extensive description of all namsbc namelist (parameter that have to be
140%created!)
141%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
142%ssv) \ie\ information required by flux computation or sea-ice
143%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
144%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
145%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
146%Fluxes update only each nf\_sbc time step (namsbc) explain relation
147%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
148%nf\_sbc
149%Explain here all the namlist namsbc variable{\ldots}.
150% explain : use or not of surface currents
151%\colorbox{yellow}{End Miss }
152
153The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
154the surface currents, temperature and salinity.
155These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
156these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
157
158\begin{table}[tb]
159  \centering
160  \begin{tabular}{|l|l|l|l|}
161    \hline
162    Variable description                           & Model variable  & Units  & point                 \\
163    \hline
164    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
165    \hline
166    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
167    \hline
168    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
169    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
170  \end{tabular}
171  \caption[Ocean variables provided to the surface module)]{
172    Ocean variables provided to the surface module (\texttt{SBC}).
173    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
174    \ie\ the frequency of computation of surface fluxes.}
175  \label{tab:SBC_ssm}
176\end{table}
177
178%\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
179
180%% =================================================================================================
181\section{Input data generic interface}
182\label{sec:SBC_input}
183
184A generic interface has been introduced to manage the way input data
185(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
186This task is achieved by \mdl{fldread}.
187The module is designed with four main objectives in mind:
188\begin{enumerate}
189\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
190  and according to the different calendars available in the model.
191\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
192\item make the run duration independent from the period cover by the input files.
193\item provide a simple user interface and a rather simple developer interface by
194  limiting the number of prerequisite informations.
195\end{enumerate}
196
197As a result, the user has only to fill in for each variable a structure in the namelist file to
198define the input data file and variable names, the frequency of the data (in hours or months),
199whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
200and three additional parameters for the on-the-fly interpolation.
201When adding a new input variable, the developer has to add the associated structure in the namelist,
202read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
203and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
204
205The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
206(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
207if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
208
209Note that when an input data is archived on a disc which is accessible directly from the workspace where
210the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
211By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
212
213%% =================================================================================================
214\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
215\label{subsec:SBC_fldread}
216
217The structure associated with an input variable contains the following information:
218\begin{forlines}
219!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
220!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
221\end{forlines}
222where
223\begin{description}
224\item [File name]: the stem name of the NetCDF file to be opened.
225  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
226  by date information and possibly a prefix (when using AGRIF).
227  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
228  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
229  \begin{table}[htbp]
230    \centering
231    \begin{tabular}{|l|c|c|c|}
232      \hline
233                                  &  daily or weekLL     &  monthly           &  yearly        \\
234      \hline
235      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
236      \hline
237      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
238      \hline
239    \end{tabular}
240    \caption[Naming nomenclature for climatological or interannual input file]{
241      Naming nomenclature for climatological or interannual input file,
242      as a function of the open/close frequency.
243      The stem name is assumed to be 'fn'.
244      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
245      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
246      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
247      always coded with 4 or 2 digits.
248      Note that (1) in mpp, if the file is split over each subdomain,
249      the suffix '.nc' is replaced by '\_PPPP.nc',
250      where 'PPPP' is the process number coded with 4 digits;
251      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
252    }
253    \label{tab:SBC_fldread}
254  \end{table}
255\item [Record frequency]: the frequency of the records contained in the input file.
256  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
257  (for example -1 for monthly forcing or -12 for annual forcing).
258  Note that this frequency must REALLY be an integer and not a real.
259  On some computers, setting it to '24.' can be interpreted as 240!
260\item [Variable name]: the name of the variable to be read in the input NetCDF file.
261\item [Time interpolation]: a logical to activate, or not, the time interpolation.
262  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
263  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
264  00h00'00'' to 23h59'59".
265  If set to 'true', the forcing will have a broken line shape.
266  Records are assumed to be dated at the middle of the forcing period.
267  For example, when using a daily forcing with time interpolation,
268  linear interpolation will be performed between mid-day of two consecutive days.
269\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
270  or an interannual forcing which will requires additional files if
271  the period covered by the simulation exceeds the one of the file.
272  See the above file naming strategy which impacts the expected name of the file to be opened.
273\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
274  Four cases are coded:
275  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
276  means the forcing files will contain data for one day, one week, one month or one year.
277  Files are assumed to contain data from the beginning of the open/close period.
278  For example, the first record of a yearly file containing daily data is Jan 1st even if
279  the experiment is not starting at the beginning of the year.
280\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
281  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
282\end{description}
283
284Additional remarks:\\
285(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
286The only tricky point is therefore to specify the date at which we need to do the interpolation and
287the date of the records read in the input files.
288Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
289For example, for an experiment starting at 0h00'00" with a one-hour time-step,
290a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
291However, for forcing data related to the surface module,
292values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
293For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
294The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
295In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
296(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
297The calendar associated with the forcing field is build according to the information provided by
298user in the record frequency, the open/close frequency and the type of temporal interpolation.
299For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
300start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
301(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
302interpolating data with the first (last) record of the open/close period.
303For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
304the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
305Dec 31st 12h00'00" and Jan 1st 12h00'00".
306If the forcing is climatological, Dec and Jan will be keep-up from the same year.
307However, if the forcing is not climatological, at the end of
308the open/close period, the code will automatically close the current file and open the next one.
309Note that, if the experiment is starting (ending) at the beginning (end) of
310an open/close period, we do accept that the previous (next) file is not existing.
311In this case, the time interpolation will be performed between two identical values.
312For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
313we do accept that the file related to year Y-1 is not existing.
314The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
315If the file of year Y-1 exists, the code will read its last record.
316Therefore, this file can contain only one record corresponding to Dec 31st,
317a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
318
319%% =================================================================================================
320\subsection{Interpolation on-the-fly}
321\label{subsec:SBC_iof}
322
323Interpolation on the Fly allows the user to supply input files required for the surface forcing on
324grids other than the model grid.
325To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
326interpolate from the data grid to the model grid.
327The original development of this code used the SCRIP package
328(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
329In principle, any package such as CDO can be used to generate the weights, but the variables in
330the input weights file must have the same names and meanings as assumed by the model.
331Two methods are currently available: bilinear and bicubic interpolations.
332Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
333the input file and substitute the corresponding values with the average of the 8 neighbouring points in
334the native external grid.
335Only "sea points" are considered for the averaging.
336The land/sea mask file must be provided in the structure associated with the input variable.
337The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
338the associated variables and should be equal to 1 over land and 0 elsewhere.
339The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
340Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
341
342%% =================================================================================================
343\subsubsection{Bilinear interpolation}
344\label{subsec:SBC_iof_bilinear}
345
346The input weights file in this case has two sets of variables:
347src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
348The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
349Each src value is an integer corresponding to the index of a point in the input grid when
350written as a one dimensional array.
351For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
352There are four of each variable because bilinear interpolation uses the four points defining
353the grid box containing the point to be interpolated.
354All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
355generate a value for point (i,j) in the model.
356
357Symbolically, the algorithm used is:
358\[
359  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
360\]
361where function idx() transforms a one dimensional index src(k) into a two dimensional index,
362and wgt(1) corresponds to variable "wgt01" for example.
363
364%% =================================================================================================
365\subsubsection{Bicubic interpolation}
366\label{subsec:SBC_iof_bicubic}
367
368Again, there are two sets of variables: "src" and "wgt".
369But in this case, there are 16 of each.
370The symbolic algorithm used to calculate values on the model grid is now:
371
372\[
373  \begin{split}
374    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
375    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
376    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
377    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
378  \end{split}
379\]
380The gradients here are taken with respect to the horizontal indices and not distances since
381the spatial dependency has been included into the weights.
382
383%% =================================================================================================
384\subsubsection{Implementation}
385\label{subsec:SBC_iof_imp}
386
387To activate this option, a non-empty string should be supplied in
388the weights filename column of the relevant namelist;
389if this is left as an empty string no action is taken.
390In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
391as and when they are first required.
392This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
393inspecting a global attribute stored in the weights input file.
394This attribute must be called "ew\_wrap" and be of integer type.
395If it is negative, the input non-model grid is assumed to be not cyclic.
396If zero or greater, then the value represents the number of columns that overlap.
397$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
398if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
399If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
400In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
401therefore the grid is assumed to be cyclic with no overlapping columns.
402(In fact, this only matters when bicubic interpolation is required.)
403Note that no testing is done to check the validity in the model,
404since there is no way of knowing the name used for the longitude variable,
405so it is up to the user to make sure his or her data is correctly represented.
406
407Next the routine reads in the weights.
408Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
409The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
410and when required, for reading in the variable to be interpolated (on the input data grid).
411The size of the input data array is determined by examining the values in the "src" arrays to
412find the minimum and maximum i and j values required.
413Since bicubic interpolation requires the calculation of gradients at each point on the grid,
414the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
415When the array of points from the data file is adjacent to an edge of the data grid,
416the halo is either a copy of the row/column next to it (non-cyclical case),
417or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
418
419%% =================================================================================================
420\subsubsection{Limitations}
421\label{subsec:SBC_iof_lim}
422
423\begin{enumerate}
424\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
425\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
426  a bicubic interpolation method is used.
427\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
428\item The gradients across the ends of a cyclical grid assume that the grid spacing between
429  the two columns involved are consistent with the weights used.
430\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
431  but this has not been implemented.)
432\end{enumerate}
433
434%% =================================================================================================
435\subsubsection{Utilities}
436\label{subsec:SBC_iof_util}
437
438% to be completed
439A set of utilities to create a weights file for a rectilinear input grid is available
440(see the directory NEMOGCM/TOOLS/WEIGHTS).
441
442%% =================================================================================================
443\subsection{Standalone surface boundary condition scheme (SAS)}
444\label{subsec:SBC_SAS}
445
446\begin{listing}
447  \nlst{namsbc_sas}
448  \caption{\forcode{&namsbc_sas}}
449  \label{lst:namsbc_sas}
450\end{listing}
451
452In some circumstances, it may be useful to avoid calculating the 3D temperature,
453salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
454For example:
455
456\begin{itemize}
457\item Multiple runs of the model are required in code development to
458  see the effect of different algorithms in the bulk formulae.
459\item The effect of different parameter sets in the ice model is to be examined.
460\item Development of sea-ice algorithms or parameterizations.
461\item Spinup of the iceberg floats
462\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
463\end{itemize}
464
465The Standalone Surface scheme provides this capacity.
466Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
467A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
468However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
469In this configuration, a few routines in the standard model are overriden by new versions.
470Routines replaced are:
471
472\begin{itemize}
473\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
474  Since the ocean state is not calculated all associated initialisations have been removed.
475\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
476\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
477  New surface modules that can function when only the surface level of the ocean state is defined can also be added
478  (\eg\ icebergs).
479\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
480  so calls to restart functions have been removed.
481  This also means that the calendar cannot be controlled by time in a restart file,
482  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
483\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
484\item \mdl{diawri}: All 3D data have been removed from the output.
485  The surface temperature, salinity and velocity components (which have been read in) are written along with
486  relevant forcing and ice data.
487\end{itemize}
488
489One new routine has been added:
490
491\begin{itemize}
492\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
493  velocity arrays at the surface.
494  These filenames are supplied in namelist namsbc\_sas.
495  Unfortunately, because of limitations with the \mdl{iom} module,
496  the full 3D fields from the mean files have to be read in and interpolated in time,
497  before using just the top level.
498  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
499\end{itemize}
500
501The 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
502 (\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.
503
504%% =================================================================================================
505\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
506\label{sec:SBC_flx}
507
508% Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk
509% parameterization'' (i.e NCAR, COARE, ECMWF...)
510
511\begin{listing}
512  \nlst{namsbc_flx}
513  \caption{\forcode{&namsbc_flx}}
514  \label{lst:namsbc_flx}
515\end{listing}
516
517In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
518the surface boundary condition fields are directly read from input files.
519The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
520the name of the variable read in the file, the time frequency at which it is given (in hours),
521and a logical setting whether a time interpolation to the model time step is required for this field.
522See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
523
524Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
525See \autoref{subsec:SBC_ssr} for its specification.
526
527
528
529
530
531
532
533%% =================================================================================================
534\pagebreak
535\newpage
536\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
537\label{sec:SBC_blk}
538
539% L. Brodeau, December 2019...
540
541\begin{listing}
542  \nlst{namsbc_blk}
543  \caption{\forcode{&namsbc_blk}}
544  \label{lst:namsbc_blk}
545\end{listing}
546
547If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea
548fluxes associated with surface boundary conditions are estimated by means of the
549traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed
550near-surface atmosphere state (typically extracted from a weather reanalysis)
551and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc}
552time-step(s).
553
554% Turbulent air-sea fluxes are computed using the sea surface properties and
555% atmospheric SSVs at height $z$ above the sea surface, with the traditional
556% aerodynamic bulk formulae:
557
558
559%%% Bulk formulae are this:
560\subsection{Bulk formulae}
561%
562In NEMO, the set of equations that relate each component of the surface fluxes
563to the near-surface atmosphere and sea surface states writes
564%
565\begin{subequations}\label{eq_bulk}
566  \begin{eqnarray}
567    \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \label{eq_b_t} \\
568    Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \label{eq_b_qh} \\
569    E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \label{eq_b_e}  \\
570    Q_L           &=& -L_v \, E  \label{eq_b_qe} \\
571    %
572    Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\
573    Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4)
574  \end{eqnarray}
575\end{subequations}
576%
577with
578   \[ \theta_z \simeq T_z+\gamma z \]
579   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
580%
581from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
582%
583where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
584$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
585flux.
586%
587$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
588and longwave radiative fluxes, respectively.
589%
590Note: a positive sign of $\mathbf{\tau}$, the various fluxes of heat implies a
591gain of the relevant quantity for the ocean, while a positive $E$ implies a
592freshwater loss for the ocean.
593%
594$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
595coefficients for momentum, sensible heat, and moisture, respectively (hereafter
596referd to as BTCs).
597%
598$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
599vaporization of water.
600%
601$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
602and specific humidity of air at height $z$ above the sea surface,
603respectively. $\gamma z$ is a temperature correction term which accounts for the
604adiabatic lapse rate and approximates the potential temperature at height
605$z$ \citep{Josey_al_2013}.
606%
607$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
608(possibly referenced to the surface current $\mathbf{u_0}$,
609section \ref{s_res1}.\ref{ss_current}).
610%
611The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
612$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution
613(section \ref{s_res2}.\ref{ss_calm}).
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 $T_s$ and includes a 2\% reduction to account for the
621presence of salt in seawater \citep{Sverdrup_al_1942,Kraus_Businger_1996}.
622Depending on the bulk parameterization 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).
630%
631Technically, when the ECMWF or COARE* bulk parameterizations 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 parameterization
634(\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature
635at first T-point level).
636
637
638For more details on all these aspects the reader is invited to refer
639to \citet{brodeau.barnier.ea_JPO17}.
640
641
642\subsection{Bulk parameterizations}
643
644Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae
645strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and
646$C_E$. They are estimated with what we refer to as a \emph{bulk
647parameterization} algorithm.
648
649... also to adjust humidity and temperature of air to the wind reference measurement
650height (generally 10\,m).
651
652Over the open ocean, four bulk parameterization algorithms are available:
653\begin{itemize}
654\item NCAR, formerly known as CORE, \citep{large.yeager_rpt04}
655\item COARE 3.0 \citep{fairall.bradley.ea_JC03}
656\item COARE 3.6 \citep{edson.jampana.ea_JPO13}
657\item ECMWF (IFS documentation, cy41)
658\end{itemize}
659
660
661\subsubsection{Appropriate use of the  NCAR algorithm}
662
663NCAR bulk parameterizations (formerly know as CORE) is meant to be used with the
664CORE II atmospheric forcing \citep{large.yeager_CD09}. Hence the following
665namelist parameters must be set:
666%
667\begin{verbatim}
668  ...
669  ln_NCAR    = .true.
670  ...
671  rn_zqt     = 10.     ! Air temperature & humidity reference height (m)
672  rn_zu      = 10.     ! Wind vector reference height (m)
673  ...
674  ln_skin_cs = .false. ! use the cool-skin parameterization
675  ln_skin_wl = .false. ! use the warm-layer parameterization
676  ...
677  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
678\end{verbatim}
679
680
681\subsubsection{Appropriate use of the ECMWF algorithm}
682
683With a DFS* or any ECMWF-based type of atmospheric forcing, we strongly
684recommand to use the ECMWF bulk parameterizations with the cool-skin and
685warm-layer parameterizations turned on. In ECMWF reanalyzes, since air temperature and humidity are provided at the 2\,m height, and that the humidity is provided as a dew-point temperature, the namelist must be tuned as follows:
686%
687\begin{verbatim}
688  ...
689  ln_ECMWF   = .true.
690  ...     
691  rn_zqt     =  2.     ! Air temperature & humidity reference height (m)
692  rn_zu      = 10.     ! Wind vector reference height (m)
693  ...
694  ln_skin_cs = .true. ! use the cool-skin parameterization
695  ln_skin_wl = .true. ! use the warm-layer parameterization
696  ...
697  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
698  ...
699\end{verbatim}
700
701Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
702of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitely
703triggers the use of the ECMWF cool-skin and warm-layer parameterizations,
704respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
705
706
707\subsubsection{Appropriate use of the COARE 3.x algorithms}
708
709\begin{verbatim}
710  ...
711  ln_COARE3p6 = .true.
712  ...     
713  ln_skin_cs = .true. ! use the cool-skin parameterization
714  ln_skin_wl = .true. ! use the warm-layer parameterization
715  ...
716\end{verbatim}
717
718Note: when \np{ln_COARE3pX}{ln\_COARE3pX} is selected, the selection
719of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitely
720triggers the use of the COARE cool-skin and warm-layer parameterizations,
721respectively (found in \textit{sbcblk\_skin\_coare.F90}).
722
723
724~
725
726
727
728% In a typical bulk algorithm, the BTCs under neutral stability conditions are
729% defined using \emph{in-situ} flux measurements while their dependence on the
730% stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and
731% the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are
732% functions of the wind speed and the near-surface stability of the atmospheric
733% surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$
734% and $q_z$.
735
736
737\subsection[Cool-skin and warm-layer parameterizations (\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})}
738\label{subsec:SBC_skin}
739
740As oposed to the NCAR bulk parameterization, more advanced bulk
741parameterizations such as COARE3.x and ECMWF are meant to be used with the skin
742temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
743the first T-point level).
744%
745So that, technically, the cool-skin and warm-layer parameterization must be
746activated (XXX) to use COARE3.x and ECMWF in a consistant way.
747
748
749\subsection{Air humidity}
750
751Air humidity can be provided as three different parameters: specific humidity
752[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
753parameters)...
754
755
756~\\
757
758
759
760
761The atmospheric fields used depend on the bulk formulae used.  In forced mode,
762when a sea-ice model is used, a specific bulk formulation is used.  Therefore,
763different bulk formulae are used for the turbulent fluxes computation over the
764ocean and over sea-ice surface.
765%
766
767
768thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package
769(\citet{brodeau.barnier.ea_JPO17}):
770
771The choice is made by setting to true one of the following namelist
772variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6}
773and \np{ln_ECMWF}{ln\_ECMWF}.  For sea-ice, three possibilities can be selected:
774a constant transfer coefficient (1.4e-3; default
775value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
776and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
777
778Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
779The required 9 input fields are:
780
781\begin{table}[htbp]
782  \centering
783  \begin{tabular}{|l|c|c|c|}
784    \hline
785    Variable description                 & Model variable & Units              & point \\
786    \hline
787    i-component of the 10m air velocity  & wndi           & $m.s^{-1}$         & T     \\
788    \hline
789    j-component of the 10m air velocity  & wndj           & $m.s^{-1}$         & T     \\
790    \hline
791    10m air temperature                  & tair           & $K$               & T     \\
792    \hline
793    Specific humidity                    & humi           & $-$               & T     \\
794    Relative humidity                    & ~              & $\%$              & T     \\
795    Dew-point temperature                & ~              & $K$               & T     \\   
796    \hline
797    Downwelling longwave radiation       & qlw            & $W.m^{-2}$         & T     \\
798    \hline
799    Downwelling shortwave radiation      & qsr            & $W.m^{-2}$         & T     \\
800    \hline
801    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
802    \hline
803    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
804    \hline
805    Mean sea-level pressure              & slp            & $hPa$              & T     \\
806    \hline
807    \end{tabular}
808  \label{tab:SBC_BULK}
809\end{table}
810
811Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
812It is simpler and faster (less fields to be read), but it is not the recommended method when
813the ocean grid size is the same or larger than the one of the input atmospheric fields.
814
815The \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},
816\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
817(spatial and temporal interpolations).
818
819\np{cn_dir}{cn\_dir} is the directory of location of bulk files
820\np{ln_taudif}{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
821\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
822\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
823
824Three multiplicative factors are available:
825\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
826increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
827The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
828the calculation of surface wind stress.
829Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
830
831As for the flux parameterization, information about the input data required by the model is provided in
832the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
833
834%% =================================================================================================
835\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})}
836\label{subsec:SBC_blk_ocean}
837
838Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
839COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
840their neutral transfer coefficients relationships with neutral wind.
841\begin{itemize}
842\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
843  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
844  They use an inertial dissipative method to compute the turbulent transfer coefficients
845  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
846  This \citet{large.yeager_rpt04} dataset is available through
847  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
848  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
849  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
850\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
851\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details
852\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9204}{IFS (Cy40r1)} implementation and documentation.
853  Surface roughness lengths needed for the Obukhov length are computed
854  following \citet{beljaars_QJRMS95}.
855\end{itemize}
856
857%% =================================================================================================
858\subsection{Ice-Atmosphere Bulk formulae}
859\label{subsec:SBC_blk_ice}
860
861Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
862
863\begin{itemize}
864\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
865  default constant value used for momentum and heat neutral transfer coefficients
866\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
867  This scheme adds a dependency on edges at leads, melt ponds and flows
868  of the constant neutral air-ice drag. After some approximations,
869  this can be resumed to a dependency on ice concentration (A).
870  This drag coefficient has a parabolic shape (as a function of ice concentration)
871  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.
872  It is theoretically applicable to all ice conditions (not only MIZ).
873\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
874  Alternative turbulent transfer coefficients formulation between sea-ice
875  and atmosphere with distinct momentum and heat coefficients depending
876  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
877  The parameterization is adapted from ECHAM6 atmospheric model.
878  Compared to Lupkes2012 scheme, it considers specific skin and form drags
879  to compute neutral transfer coefficients for both heat and momentum fluxes.
880  Atmospheric stability effect on transfer coefficient is also taken into account.
881\end{itemize}
882
883%% =================================================================================================
884\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
885\label{sec:SBC_cpl}
886
887\begin{listing}
888  \nlst{namsbc_cpl}
889  \caption{\forcode{&namsbc_cpl}}
890  \label{lst:namsbc_cpl}
891\end{listing}
892
893In the coupled formulation of the surface boundary condition,
894the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
895while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
896the atmospheric component.
897
898A generalised coupled interface has been developed.
899It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
900An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
901It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
902(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
903(Weather Research and Forecasting Model).
904
905When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
906the whole carbon cycle is computed.
907In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
908(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
909
910The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
911now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
912When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
913the number used in the sea ice model.
914In some limited cases, it may be possible to specify single category coupling fields even when
915the sea ice model is running with multiple categories -
916in this case, the user should examine the code to be sure the assumptions made are satisfactory.
917In cases where this is definitely not possible, the model should abort with an error message.
918
919%% =================================================================================================
920\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
921\label{sec:SBC_apr}
922
923\begin{listing}
924  \nlst{namsbc_apr}
925  \caption{\forcode{&namsbc_apr}}
926  \label{lst:namsbc_apr}
927\end{listing}
928
929The optional atmospheric pressure can be used to force ocean and ice dynamics
930(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
931The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
932can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
933When used to force the dynamics, the atmospheric pressure is further transformed into
934an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
935\[
936  % \label{eq:SBC_ssh_ib}
937  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
938\]
939where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
940A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
941In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
942\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
943
944The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
945For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
946(see \mdl{sbcssr} module).
947$\eta_{ib}$ can be written in the output.
948This can simplify altimetry data and model comparison as
949inverse barometer sea surface height is usually removed from these date prior to their distribution.
950
951When using time-splitting and BDY package for open boundaries conditions,
952the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
953\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
954
955%% =================================================================================================
956\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
957\label{sec:SBC_tide}
958
959\begin{listing}
960  \nlst{nam_tide}
961  \caption{\forcode{&nam_tide}}
962  \label{lst:nam_tide}
963\end{listing}
964
965The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
966is 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}.
967This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
968\[
969  % \label{eq:SBC_PE_dyn_tides}
970  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
971  +g\nabla (\Pi_{eq} + \Pi_{sal})
972\]
973where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
974$\Pi_{sal}$ is a self-attraction and loading term (SAL).
975
976The equilibrium tidal forcing is expressed as a sum over a subset of
977constituents chosen from the set of available tidal constituents
978defined in file \hf{SBC/tide} (this comprises the tidal
979constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
980  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
981constituents are selected by including their names in the array
982\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
983\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
984and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
985\forcode{.true.}, the equilibrium tidal forcing can be ramped up
986linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
987model run.
988
989The SAL term should in principle be computed online as it depends on
990the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
991discussion about the practical implementation of this term).
992Nevertheless, the complex calculations involved would make this
993computationally too expensive. Here, two options are available:
994$\Pi_{sal}$ generated by an external model can be read in
995(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
996used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
997\[
998  \Pi_{sal} = \beta \eta,
999\]
1000where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
1001spatially constant scalar, often chosen to minimize tidal prediction
1002errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
1003\forcode{.false.} removes the SAL contribution.
1004
1005%% =================================================================================================
1006\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
1007\label{sec:SBC_rnf}
1008
1009\begin{listing}
1010  \nlst{namsbc_rnf}
1011  \caption{\forcode{&namsbc_rnf}}
1012  \label{lst:namsbc_rnf}
1013\end{listing}
1014
1015%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1016%Many models, however, have traditionally inserted river runoff to the top model cell.
1017%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
1018%throughout a nonzero depth has been motivated by the numerical and physical problems
1019%that arise when the top grid cells are of the order of one meter. This situation is common in
1020%coastal modelling and becomes more and more often open ocean and climate modelling
1021%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
1022%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
1023
1024%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
1025%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
1026%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
1027%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
1028%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
1029%emp or emps and the changes made are below:
1030
1031%Rachel:
1032River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1033Many models, however, have traditionally inserted river runoff to the top model cell.
1034This was the case in \NEMO\ prior to the version 3.3,
1035and was combined with an option to increase vertical mixing near the river mouth.
1036
1037However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
1038This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
1039\footnote{
1040  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
1041  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
1042  see also \autoref{fig:SBC_dcy}.}.
1043
1044As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
1045and for the temperature and salinity of the river to effect the surrounding ocean.
1046The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
1047along with the depth (in metres) which the river should be added to.
1048
1049Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
1050\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
1051If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
1052and/or taken as surface temperature respectively.
1053
1054The runoff value and attributes are read in in sbcrnf.
1055For temperature -999 is taken as missing data and the river temperature is taken to
1056be the surface temperatue at the river point.
1057For the depth parameter a value of -1 means the river is added to the surface box only,
1058and a value of -999 means the river is added through the entire water column.
1059After being read in the temperature and salinity variables are multiplied by the amount of runoff
1060(converted into m/s) to give the heat and salt content of the river runoff.
1061After the user specified depth is read ini,
1062the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
1063The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
1064the bottom of the lowest box the river water is being added to
1065(\ie\ the total depth that river water is being added to in the model).
1066
1067The mass/volume addition due to the river runoff is, at each relevant depth level, added to
1068the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
1069This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
1070The sea surface height is calculated using the sum of the horizontal divergence terms,
1071and so the river runoff indirectly forces an increase in sea surface height.
1072
1073The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
1074This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
1075The heat and salt content of the river runoff is not included in this step,
1076and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
1077the box and replaced by the same volume of river water with no corresponding heat and salt addition.
1078
1079For the linear free surface case, at the surface box the tracer advection causes a flux of water
1080(of equal volume to the runoff) through the sea surface out of the domain,
1081which causes a salt and heat flux out of the model.
1082As such the volume of water does not change, but the water is diluted.
1083
1084For the non-linear free surface case, no flux is allowed through the surface.
1085Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
1086no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
1087(The runoff addition to the top box along with the water being moved up through
1088boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
1089
1090In trasbc the addition of heat and salt due to the river runoff is added.
1091This is done in the same way for both vvl and non-vvl.
1092The temperature and salinity are increased through the specified depth according to
1093the heat and salt content of the river.
1094
1095In the non-linear free surface case (vvl),
1096near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
1097so that the original ratios of grid box heights are restored.
1098In doing this water is moved into boxes below, throughout the water column,
1099so the large volume addition to the surface box is spread between all the grid boxes.
1100
1101It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
1102\ie\ modelling the Baltic flow in and out of the North Sea.
1103When the flow is out of the domain there is no change in temperature and salinity,
1104regardless of the namelist options used,
1105as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
1106
1107%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1108
1109%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1110
1111%\colorbox{yellow}{river mouths{\ldots}}
1112
1113%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1114%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1115%ENDIF
1116
1117\cmtgm{  word doc of runoffs:
1118In the current \NEMO\ setup river runoff is added to emp fluxes,
1119these are then applied at just the sea surface as a volume change (in the variable volume case
1120this is a literal volume change, and in the linear free surface case the free surface is moved)
1121and a salt flux due to the concentration/dilution effect.
1122There is also an option to increase vertical mixing near river mouths;
1123this gives the effect of having a 3d river.
1124All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
1125at the same temperature as the sea surface.
1126Our aim was to code the option to specify the temperature and salinity of river runoff,
1127(as well as the amount), along with the depth that the river water will affect.
1128This would make it possible to model low salinity outflow, such as the Baltic,
1129and would allow the ocean temperature to be affected by river runoff.
1130
1131The depth option makes it possible to have the river water affecting just the surface layer,
1132throughout depth, or some specified point in between.
1133
1134To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
1135the \mdl{tra_sbc} module.
1136We decided to separate them throughout the code,
1137so that the variable emp represented solely evaporation minus precipitation fluxes,
1138and a new 2d variable rnf was added which represents the volume flux of river runoff
1139(in $kg/m^2s$ to remain consistent with $emp$).
1140This meant many uses of emp and emps needed to be changed,
1141a list of all modules which use $emp$ or $emps$ and the changes made are below:}
1142
1143%% =================================================================================================
1144\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
1145\label{sec:SBC_isf}
1146
1147\begin{listing}
1148  \nlst{namsbc_isf}
1149  \caption{\forcode{&namsbc_isf}}
1150  \label{lst:namsbc_isf}
1151\end{listing}
1152
1153The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
1154Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1155The different options are illustrated in \autoref{fig:SBC_isf}.
1156
1157\begin{description}
1158  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1159  The fwf and heat flux are depending of the local water properties.
1160
1161  Two different bulk formulae are available:
1162
1163  \begin{description}
1164  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
1165    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
1166  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
1167    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1168    A complete description is available in \citet{jenkins_JGR91}.
1169  \end{description}
1170
1171  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1172  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
1173  The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m.
1174  Then, the fluxes are spread over the same thickness (ie over one or several cells).
1175  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature.
1176  This can lead to super-cool temperature in the top cell under melting condition.
1177  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
1178
1179  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1180  There are 3 different ways to compute the exchange coeficient:
1181  \begin{description}
1182  \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}.
1183    \begin{gather*}
1184       % \label{eq:SBC_isf_gamma_iso}
1185      \gamma^{T} = rn\_gammat0 \\
1186      \gamma^{S} = rn\_gammas0
1187    \end{gather*}
1188    This is the recommended formulation for ISOMIP.
1189  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
1190    \begin{gather*}
1191      \gamma^{T} = rn\_gammat0 \times u_{*} \\
1192      \gamma^{S} = rn\_gammas0 \times u_{*}
1193    \end{gather*}
1194    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
1195    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1196  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1197    \[
1198      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1199    \]
1200    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
1201    $\Gamma_{Turb}$ the contribution of the ocean stability and
1202    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1203    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1204    This formulation has not been extensively tested in \NEMO\ (not recommended).
1205  \end{description}
1206\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1207  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1208  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1209  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1210  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
1211  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
1212\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1213  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1214  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
1215  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
1216  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1217\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1218  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
1219  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1220  As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl})
1221\end{description}
1222
1223$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
1224the water mass properties, ocean velocities and depth.
1225This flux is thus highly dependent of the model resolution (horizontal and vertical),
1226realism of the water masses onto the shelf ...\\
1227
1228$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
1229You have total control of the fwf forcing.
1230This can be useful if the water masses on the shelf are not realistic or
1231the resolution (horizontal/vertical) are too coarse to have realistic melting or
1232for studies where you need to control your heat and fw input.\\
1233
1234The ice shelf melt is implemented as a volume flux as for the runoff.
1235The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1236the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1237See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1238
1239\begin{figure}[!t]
1240  \centering
1241  \includegraphics[width=0.66\textwidth]{SBC_isf}
1242  \caption[Ice shelf location and fresh water flux definition]{
1243    Illustration of the location where the fwf is injected and
1244    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1245  \label{fig:SBC_isf}
1246\end{figure}
1247
1248%% =================================================================================================
1249\section{Ice sheet coupling}
1250\label{sec:SBC_iscpl}
1251
1252\begin{listing}
1253  \nlst{namsbc_iscpl}
1254  \caption{\forcode{&namsbc_iscpl}}
1255  \label{lst:namsbc_iscpl}
1256\end{listing}
1257
1258Ice sheet/ocean coupling is done through file exchange at the restart step.
1259At each restart step:
1260
1261\begin{enumerate}
1262\item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1263\item a new domcfg.nc file is built using the DOMAINcfg tools.
1264\item \NEMO\ run for a specific period and output the average melt rate over the period.
1265\item the ice sheet model run using the melt rate outputed in step 4.
1266\item go back to 1.
1267\end{enumerate}
1268
1269If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1270potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1271The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1272
1273\begin{description}
1274\item [Thin a cell down]: T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1275  ($bt_b=bt_n$).
1276\item [Enlarge  a cell]: See case "Thin a cell down"
1277\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
1278  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1279\item [Wet a cell]: mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1280  If no neighbours, T/S is extrapolated from old top cell value.
1281  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1282\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1283\item [Wet a column]: set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1284  If no neighbour, T/S/U/V and mask set to 0.
1285\end{description}
1286
1287Furthermore, as the before and now fields are not compatible (modification of the geometry),
1288the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1289
1290The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1291It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1292the code will be unable to fill all the new wet cells properly.
1293The default number is set up for the MISOMIP idealised experiments.
1294This coupling procedure is able to take into account grounding line and calving front migration.
1295However, it is a non-conservative processe.
1296This could lead to a trend in heat/salt content and volume.\\
1297
1298In order to remove the trend and keep the conservation level as close to 0 as possible,
1299a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1300The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1301A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1302For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1303The corrective increment is apply into the cell itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry).
1304
1305%% =================================================================================================
1306\section{Handling of icebergs (ICB)}
1307\label{sec:SBC_ICB_icebergs}
1308
1309\begin{listing}
1310  \nlst{namberg}
1311  \caption{\forcode{&namberg}}
1312  \label{lst:namberg}
1313\end{listing}
1314
1315Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1316Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1317(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1318Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1319described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1320Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1321which is an integer representing how many icebergs of this class are being described as one lagrangian point
1322(this reduces the numerical problem of tracking every single iceberg).
1323They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1324
1325Two initialisation schemes are possible.
1326\begin{description}
1327\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
1328  (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
1329  which an iceberg is generated at the beginning of the run.
1330  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1331  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1332  the geographical box: lonmin,lonmax,latmin,latmax
1333\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.
1334  This should be a file with a field on the configuration grid (typically ORCA)
1335  representing ice accumulation rate at each model point.
1336  These should be ocean points adjacent to land where icebergs are known to calve.
1337  Most points in this input grid are going to have value zero.
1338  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1339  At each time step, a test is performed to see if there is enough ice mass to
1340  calve an iceberg of each class in order (1 to 10).
1341  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1342  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1343\end{description}
1344
1345Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1346The latter act to disintegrate the iceberg.
1347This is either all melted freshwater,
1348or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1349which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1350Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1351
1352Extensive diagnostics can be produced.
1353Separate output files are maintained for human-readable iceberg information.
1354A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1355The amount of information is controlled by two integer parameters:
1356\begin{description}
1357\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1358  represents an increasing number of points in the code at which variables are written,
1359  and an increasing level of obscurity.
1360\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1361\end{description}
1362
1363Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1364A non-zero value represents how many timesteps between writes of information into the output file.
1365These output files are in NETCDF format.
1366When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1367Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1368So care is needed to recreate data for individual icebergs,
1369since its trajectory data may be spread across multiple files.
1370
1371%% =================================================================================================
1372\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1373\label{sec:SBC_wave}
1374
1375\begin{listing}
1376  \nlst{namsbc_wave}
1377  \caption{\forcode{&namsbc_wave}}
1378  \label{lst:namsbc_wave}
1379\end{listing}
1380
1381Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1382physical processes related to ocean surface waves, namely the surface stress modified by growth and
1383dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1384tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1385the wind stress.
1386
1387Physical processes related to ocean surface waves can be accounted by setting the logical variable
1388\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1389different processes should be activated as explained in the following sections.
1390
1391Wave fields can be provided either in forced or coupled mode:
1392\begin{description}
1393\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1394for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1395Input Data generic Interface (see \autoref{sec:SBC_input}).
1396\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1397in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1398\end{description}
1399
1400%% =================================================================================================
1401\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1402\label{subsec:SBC_wave_cdgw}
1403
1404The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1405can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1406Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1407the drag coefficient is computed according to the stable/unstable conditions of the
1408air-sea interface following \citet{large.yeager_rpt04}.
1409
1410%% =================================================================================================
1411\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1412\label{subsec:SBC_wave_sdw}
1413
1414The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1415It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1416and the current measured at a fixed point (Eulerian velocity).
1417As waves travel, the water particles that make up the waves travel in orbital motions but
1418without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1419at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1420An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1421representation of surface physics in ocean general circulation models. %GS: reference needed
1422The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1423
1424\[
1425  % \label{eq:SBC_wave_sdw}
1426  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1427  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1428  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1429\]
1430
1431where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1432$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1433$k$ is the mean wavenumber defined as:
1434$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1435
1436In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1437and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1438To simplify, it is customary to use approximations to the full Stokes profile.
1439Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1440are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1441$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1442and makes possible the estimation of the surface Stokes drift for random directional waves in
1443realistic wave conditions:
1444
1445\begin{description}
1446\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1447\citet{breivik.janssen.ea_JPO14}:
1448
1449\[
1450  % \label{eq:SBC_wave_sdw_0a}
1451  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1452\]
1453
1454where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1455
1456\[
1457  % \label{eq:SBC_wave_sdw_0b}
1458  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1459  \quad \text{and }\
1460  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1461\]
1462
1463where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1464
1465\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1466reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1467\citep{breivik.bidlot.ea_OM16}:
1468
1469\[
1470  % \label{eq:SBC_wave_sdw_1}
1471  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1472  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1473\]
1474
1475where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1476
1477\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1478but using the wave frequency from a wave model.
1479
1480\end{description}
1481
1482The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1483and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1484
1485\[
1486  % \label{eq:SBC_wave_eta_sdw}
1487  \frac{\partial{\eta}}{\partial{t}} =
1488  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1489\]
1490
1491The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1492for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1493that is induced by the three-dimensional Stokes velocity.
1494The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1495can be formulated as follows:
1496
1497\[
1498  % \label{eq:SBC_wave_tra_sdw}
1499  \frac{\partial{c}}{\partial{t}} =
1500  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1501\]
1502
1503%% =================================================================================================
1504\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1505\label{subsec:SBC_wave_stcor}
1506
1507In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1508in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1509This additional force may have impact on the Ekman turning of the surface current.
1510In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1511approximations described in \autoref{subsec:SBC_wave_sdw}),
1512\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1513
1514%% =================================================================================================
1515\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1516\label{subsec:SBC_wave_tauw}
1517
1518The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1519into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1520available for forcing the mean circulation, while in the opposite case of a decaying sea
1521state, more momentum is available for forcing the ocean.
1522Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1523but in practice, an equilibrium sea state is a fairly rare event.
1524So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1525
1526\[
1527  % \label{eq:SBC_wave_tauoc}
1528  \tau_{oc,a} = \tau_a - \tau_w
1529\]
1530
1531where $\tau_a$ is the atmospheric surface stress;
1532$\tau_w$ is the atmospheric stress going into the waves defined as:
1533
1534\[
1535  % \label{eq:SBC_wave_tauw}
1536  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1537\]
1538
1539where: $c_p$ is the phase speed of the gravity waves,
1540$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1541the physics of ocean waves. The first one, $S_{in}$, describes the generation
1542of ocean waves by wind and therefore represents the momentum and energy transfer
1543from air to ocean waves; the second term $S_{nl}$ denotes
1544the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1545describes the dissipation of waves by processes such as white-capping, large scale breaking
1546eddy-induced damping.
1547
1548The wave stress derived from an external wave model can be provided either through the normalized
1549wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1550meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1551
1552%% =================================================================================================
1553\section{Miscellaneous options}
1554\label{sec:SBC_misc}
1555
1556%% =================================================================================================
1557\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1558\label{subsec:SBC_dcy}
1559
1560\begin{figure}[!t]
1561  \centering
1562  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
1563  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1564    Example of reconstruction of the diurnal cycle variation of short wave flux from
1565    daily mean values.
1566    The reconstructed diurnal cycle (black line) is chosen as
1567    the mean value of the analytical cycle (blue line) over a time step,
1568    not as the mid time step value of the analytically cycle (red square).
1569    From \citet{bernie.guilyardi.ea_CD07}.}
1570  \label{fig:SBC_diurnal}
1571\end{figure}
1572
1573\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.
1574%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1575Nevertheless, 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}.
1576Furthermore, only the knowledge of daily mean value of SWF is needed,
1577as higher frequency variations can be reconstructed from them,
1578assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1579The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1580setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1581using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1582the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1583The reconstruction is performed in the \mdl{sbcdcy} module.
1584The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1585The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1586a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1587The use of diurnal cycle reconstruction requires the input SWF to be daily
1588(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1589Furthermore, it is recommended to have a least 8 surface module time steps per day,
1590that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1591An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1592one every 2~hours (from 1am to 11pm).
1593
1594\begin{figure}[!t]
1595  \centering
1596  \includegraphics[width=0.66\textwidth]{SBC_dcy}
1597  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1598    Example of reconstruction of the diurnal cycle variation of short wave flux from
1599    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1600    The display is on (i,j) plane.}
1601  \label{fig:SBC_dcy}
1602\end{figure}
1603
1604Note also that the setting a diurnal cycle in SWF is highly recommended when
1605the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1606an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1607
1608%% =================================================================================================
1609\subsection{Rotation of vector pairs onto the model grid directions}
1610\label{subsec:SBC_rotation}
1611
1612When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1613pairs of vector components can be rotated from east-north directions onto the local grid directions.
1614This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1615be defined relative to a rectilinear grid.
1616To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1617The eastward component must start with "U" and the northward component with "V".
1618The remaining characters in the strings are used to identify which pair of components go together.
1619So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1620rotate them on to the model grid directions;
1621"U2" and "V2" could be used against a second pair of components, and so on.
1622The extra characters used in the strings are arbitrary.
1623The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1624
1625%% =================================================================================================
1626\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1627\label{subsec:SBC_ssr}
1628
1629\begin{listing}
1630  \nlst{namsbc_ssr}
1631  \caption{\forcode{&namsbc_ssr}}
1632  \label{lst:namsbc_ssr}
1633\end{listing}
1634
1635Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1636On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1637a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1638\[
1639  % \label{eq:SBC_dmp_q}
1640  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1641\]
1642where SST is a sea surface temperature field (observed or climatological),
1643$T$ is the model surface layer temperature and
1644$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1645For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1646This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1647
1648In the fresh water budget, a feedback term can also be added.
1649Converted into an equivalent freshwater flux, it takes the following expression :
1650
1651\begin{equation}
1652  \label{eq:SBC_dmp_emp}
1653  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1654  {\left.S\right|_{k=1}}
1655\end{equation}
1656
1657where $\textit{emp}_{o }$ is a net surface fresh water flux
1658(observed, climatological or an atmospheric model product),
1659\textit{SSS}$_{Obs}$ is a sea surface salinity
1660(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1661$\left.S\right|_{k=1}$ is the model surface layer salinity and
1662$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1663Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1664the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1665The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1666reduce the uncertainties we have on the observed freshwater budget.
1667
1668%% =================================================================================================
1669\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1670\label{subsec:SBC_ice-cover}
1671
1672The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1673There are several way to handle sea-ice in the system depending on
1674the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1675\begin{description}
1676\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1677  This is a typical namelist value used for tropical ocean domain.
1678  The surface fluxes are simply specified for an ice-free ocean.
1679  No specific things is done for sea-ice.
1680\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1681  An observed ice covered area is read in a file.
1682  Below this area, the SST is restored to the freezing point and
1683  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1684  The associated modification of the freshwater fluxes are done in such a way that
1685  the change in buoyancy fluxes remains zero.
1686  This prevents deep convection to occur when trying to reach the freezing point
1687  (and so ice covered area condition) while the SSS is too large.
1688  This manner of managing sea-ice area, just by using a IF case,
1689  is usually referred as the \textit{ice-if} model.
1690  It can be found in the \mdl{sbcice\_if} module.
1691\item [nn\_ice = 2 or more] A full sea ice model is used.
1692  This model computes the ice-ocean fluxes,
1693  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1694  provide the surface averaged ocean fluxes.
1695  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1696  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1697  (\ie\ $2$ for SI3 or $3$ for CICE).
1698\end{description}
1699
1700% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1701%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1702
1703%% =================================================================================================
1704\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1705\label{subsec:SBC_cice}
1706
1707It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1708to the CICE sea-ice model by using \key{cice}.
1709The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1710the additional 'hadgem3' drivers will be required, even with the latest code release.
1711Input grid files consistent with those used in \NEMO\ will also be needed,
1712and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1713(seek advice from UKMO if necessary).
1714Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1715(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1716or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1717(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1718The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1719(although coupling ocean and ice less frequently should work,
1720it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1721the user should check that results are not significantly different to the standard case).
1722
1723There are two options for the technical coupling between \NEMO\ and CICE.
1724The standard version allows complete flexibility for the domain decompositions in the individual models,
1725but this is at the expense of global gather and scatter operations in the coupling which
1726become very expensive on larger numbers of processors.
1727The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1728the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1729and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1730allows much more efficient direct coupling on individual processors.
1731This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1732there is no sea ice.
1733
1734%% =================================================================================================
1735\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1736\label{subsec:SBC_fwb}
1737
1738For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1739prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1740In \NEMO, two way of controlling the freshwater budget are proposed:
1741
1742\begin{description}
1743\item [{\np[=0]{nn_fwb}{nn\_fwb}}] no control at all.
1744  The mean sea level is free to drift, and will certainly do so.
1745\item [{\np[=1]{nn_fwb}{nn\_fwb}}] global mean \textit{emp} set to zero at each model time step.
1746  %GS: comment below still relevant ?
1747  %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).
1748\item [{\np[=2]{nn_fwb}{nn\_fwb}}] freshwater budget is adjusted from the previous year annual mean budget which
1749  is read in the \textit{EMPave\_old.dat} file.
1750  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1751  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1752\end{description}
1753
1754% Griffies doc:
1755% When running ocean-ice simulations, we are not explicitly representing land processes,
1756% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1757% it is important to balance the hydrological cycle in ocean-ice models.
1758% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1759% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1760% a chosen time scale.
1761% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1762% so that there is always a zero net input of water to the ocean-ice system.
1763% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1764% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1765% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1766% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1767% and ice models when aiming to balance the hydrological cycle.
1768% 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,
1769% not the water in any one sub-component. As an extreme example to illustrate the issue,
1770% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1771% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1772% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1773% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1774% in ocean-ice models.
1775
1776\subinc{\input{../../global/epilogue}}
1777
1778\end{document}
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