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1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4
5\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
6\label{chap:SBC}
7
8\thispagestyle{plain}
9
10\chaptertoc
11
12\paragraph{Changes record} ~\\
13
14{\footnotesize
15  \begin{tabularx}{\textwidth}{l||X|X}
16    Release & Author(s) & Modifications \\
17    \hline
18    {\em   4.0} & {\em ...} & {\em ...} \\
19    {\em   3.6} & {\em ...} & {\em ...} \\
20    {\em   3.4} & {\em ...} & {\em ...} \\
21    {\em <=3.4} & {\em ...} & {\em ...}
22  \end{tabularx}
23}
24
25\clearpage
26
27\begin{listing}
28  \nlst{namsbc}
29  \caption{\forcode{&namsbc}}
30  \label{lst:namsbc}
31\end{listing}
32
33The ocean needs seven fields as surface boundary condition:
34
35\begin{itemize}
36\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
37\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
38\item the surface freshwater budget $\left( {\textit{emp}} \right)$
39\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
40\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
41\end{itemize}
42
43Four different ways are available to provide the seven fields to the ocean. They are controlled by
44namelist \nam{sbc}{sbc} variables:
45
46\begin{itemize}
47\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk} with four possible bulk algorithms),
48\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
49\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
50(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
51\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
52\end{itemize}
53
54The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
55
56When the fields are supplied from data files (bulk, flux and mixed formulations),
57the input fields do not need to be supplied on the model grid.
58Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
59the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
60If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
61should be masked or filled to avoid spurious results in proximity of the coasts, as
62large sea-land gradients characterize most of the atmospheric variables.
63
64In addition, the resulting fields can be further modified using several namelist options.
65These options control:
66
67\begin{itemize}
68\item the rotation of vector components supplied relative to an east-north coordinate system onto
69  the local grid directions in the model,
70\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
71\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
72\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
73  (\np[=0..3]{nn_ice}{nn\_ice}),
74\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
75\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
76  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
77\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
78  (\np[=0..2]{nn_fwb}{nn\_fwb}),
79\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
80  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
81\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
82\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
83\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
84\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
85\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
86\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
87\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
88\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
89\item the atmospheric surface pressure gradient effect on ocean and ice dynamics (\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn} with namelist \nam{sbc_apr}{sbc\_apr}),
90\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
91\end{itemize}
92
93In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
94Then we present the three ways of providing the surface boundary conditions,
95followed by the description of the atmospheric pressure and the river runoff.
96Next, the scheme for interpolation on the fly is described.
97Finally, the different options that further modify the fluxes applied to the ocean are discussed.
98One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
99which act as drifting sources of fresh water.
100Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
101which provides additional sources of fresh water.
102
103%% =================================================================================================
104\section{Surface boundary condition for the ocean}
105\label{sec:SBC_ocean}
106
107The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
108It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
109the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
110As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
111\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
112
113The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
114$Q_{ns}$ and $Q_{sr}$, respectively.
115The former is the non penetrative part of the heat flux
116(\ie\ the sum of sensible, latent and long wave heat fluxes plus
117the heat content of the mass exchange between the ocean and sea-ice).
118It is applied in \mdl{trasbc} module as a surface boundary condition trend of
119the first level temperature time evolution equation
120(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
121The latter is the penetrative part of the heat flux.
122It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
123\np[=.true.]{ln_traqsr}{ln\_traqsr}.
124The way the light penetrates inside the water column is generally a sum of decreasing exponentials
125(see \autoref{subsec:TRA_qsr}).
126
127The surface freshwater budget is provided by the \textit{emp} field.
128It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
129possibly with the sea-ice and ice shelves (freezing minus melting of ice).
130It affects the ocean in two different ways:
131$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
132a volume flux, and
133$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
134the mass exchanged with atmosphere, sea-ice and ice shelves.
135
136%\colorbox{yellow}{Miss: }
137%A extensive description of all namsbc namelist (parameter that have to be
138%created!)
139%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
140%ssv) \ie\ information required by flux computation or sea-ice
141%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
142%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
143%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
144%Fluxes update only each nf\_sbc time step (namsbc) explain relation
145%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
146%nf\_sbc
147%Explain here all the namlist namsbc variable{\ldots}.
148% explain : use or not of surface currents
149%\colorbox{yellow}{End Miss }
150
151The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
152the surface currents, temperature and salinity.
153These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
154these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
155
156\begin{table}[tb]
157  \centering
158  \begin{tabular}{|l|l|l|l|}
159    \hline
160    Variable description                           & Model variable  & Units  & point                 \\
161    \hline
162    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
163    \hline
164    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
165    \hline
166    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
167    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
168  \end{tabular}
169  \caption[Ocean variables provided to the surface module)]{
170    Ocean variables provided to the surface module (\texttt{SBC}).
171    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
172    \ie\ the frequency of computation of surface fluxes.}
173  \label{tab:SBC_ssm}
174\end{table}
175
176%\colorbox{yellow}{Penser a} mettre dans le restant l'info nn\_fsbc ET nn\_fsbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt
177
178%% =================================================================================================
179\section{Input data generic interface}
180\label{sec:SBC_input}
181
182A generic interface has been introduced to manage the way input data
183(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
184This task is achieved by \mdl{fldread}.
185The module is designed with four main objectives in mind:
186\begin{enumerate}
187\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
188  and according to the different calendars available in the model.
189\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
190\item make the run duration independent from the period cover by the input files.
191\item provide a simple user interface and a rather simple developer interface by
192  limiting the number of prerequisite informations.
193\end{enumerate}
194
195As a result, the user has only to fill in for each variable a structure in the namelist file to
196define the input data file and variable names, the frequency of the data (in hours or months),
197whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
198and three additional parameters for the on-the-fly interpolation.
199When adding a new input variable, the developer has to add the associated structure in the namelist,
200read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
201and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
202
203The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
204(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
205if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
206
207Note that when an input data is archived on a disc which is accessible directly from the workspace where
208the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
209By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
210
211%% =================================================================================================
212\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
213\label{subsec:SBC_fldread}
214
215The structure associated with an input variable contains the following information:
216\begin{forlines}
217!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
218!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
219\end{forlines}
220where
221\begin{description}
222\item [File name]: the stem name of the NetCDF file to be opened.
223  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
224  by date information and possibly a prefix (when using AGRIF).
225  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
226  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
227  \begin{table}[htbp]
228    \centering
229    \begin{tabular}{|l|c|c|c|}
230      \hline
231                                  &  daily or weekLL     &  monthly           &  yearly        \\
232      \hline
233      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
234      \hline
235      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
236      \hline
237    \end{tabular}
238    \caption[Naming nomenclature for climatological or interannual input file]{
239      Naming nomenclature for climatological or interannual input file,
240      as a function of the open/close frequency.
241      The stem name is assumed to be 'fn'.
242      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
243      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
244      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
245      always coded with 4 or 2 digits.
246      Note that (1) in mpp, if the file is split over each subdomain,
247      the suffix '.nc' is replaced by '\_PPPP.nc',
248      where 'PPPP' is the process number coded with 4 digits;
249      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
250    }
251    \label{tab:SBC_fldread}
252  \end{table}
253\item [Record frequency]: the frequency of the records contained in the input file.
254  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
255  (for example -1 for monthly forcing or -12 for annual forcing).
256  Note that this frequency must REALLY be an integer and not a real.
257  On some computers, setting it to '24.' can be interpreted as 240!
258\item [Variable name]: the name of the variable to be read in the input NetCDF file.
259\item [Time interpolation]: a logical to activate, or not, the time interpolation.
260  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
261  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
262  00h00'00'' to 23h59'59".
263  If set to 'true', the forcing will have a broken line shape.
264  Records are assumed to be dated at the middle of the forcing period.
265  For example, when using a daily forcing with time interpolation,
266  linear interpolation will be performed between mid-day of two consecutive days.
267\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
268  or an interannual forcing which will requires additional files if
269  the period covered by the simulation exceeds the one of the file.
270  See the above file naming strategy which impacts the expected name of the file to be opened.
271\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
272  Four cases are coded:
273  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
274  means the forcing files will contain data for one day, one week, one month or one year.
275  Files are assumed to contain data from the beginning of the open/close period.
276  For example, the first record of a yearly file containing daily data is Jan 1st even if
277  the experiment is not starting at the beginning of the year.
278\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
279  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
280\end{description}
281
282Additional remarks:\\
283(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
284The only tricky point is therefore to specify the date at which we need to do the interpolation and
285the date of the records read in the input files.
286Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
287For example, for an experiment starting at 0h00'00" with a one-hour time-step,
288a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
289However, for forcing data related to the surface module,
290values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
291For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
292The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
293In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
294(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
295The calendar associated with the forcing field is build according to the information provided by
296user in the record frequency, the open/close frequency and the type of temporal interpolation.
297For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
298start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
299(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
300interpolating data with the first (last) record of the open/close period.
301For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
302the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
303Dec 31st 12h00'00" and Jan 1st 12h00'00".
304If the forcing is climatological, Dec and Jan will be keep-up from the same year.
305However, if the forcing is not climatological, at the end of
306the open/close period, the code will automatically close the current file and open the next one.
307Note that, if the experiment is starting (ending) at the beginning (end) of
308an open/close period, we do accept that the previous (next) file is not existing.
309In this case, the time interpolation will be performed between two identical values.
310For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
311we do accept that the file related to year Y-1 is not existing.
312The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
313If the file of year Y-1 exists, the code will read its last record.
314Therefore, this file can contain only one record corresponding to Dec 31st,
315a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
316
317%% =================================================================================================
318\subsection{Interpolation on-the-fly}
319\label{subsec:SBC_iof}
320
321Interpolation on the Fly allows the user to supply input files required for the surface forcing on
322grids other than the model grid.
323To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
324interpolate from the data grid to the model grid.
325The original development of this code used the SCRIP package
326(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
327In principle, any package such as CDO can be used to generate the weights, but the variables in
328the input weights file must have the same names and meanings as assumed by the model.
329Two methods are currently available: bilinear and bicubic interpolations.
330Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
331the input file and substitute the corresponding values with the average of the 8 neighbouring points in
332the native external grid.
333Only "sea points" are considered for the averaging.
334The land/sea mask file must be provided in the structure associated with the input variable.
335The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
336the associated variables and should be equal to 1 over land and 0 elsewhere.
337The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
338Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
339
340%% =================================================================================================
341\subsubsection{Bilinear interpolation}
342\label{subsec:SBC_iof_bilinear}
343
344The input weights file in this case has two sets of variables:
345src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
346The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
347Each src value is an integer corresponding to the index of a point in the input grid when
348written as a one dimensional array.
349For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
350There are four of each variable because bilinear interpolation uses the four points defining
351the grid box containing the point to be interpolated.
352All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
353generate a value for point (i,j) in the model.
354
355Symbolically, the algorithm used is:
356\[
357  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
358\]
359where function idx() transforms a one dimensional index src(k) into a two dimensional index,
360and wgt(1) corresponds to variable "wgt01" for example.
361
362%% =================================================================================================
363\subsubsection{Bicubic interpolation}
364\label{subsec:SBC_iof_bicubic}
365
366Again, there are two sets of variables: "src" and "wgt".
367But in this case, there are 16 of each.
368The symbolic algorithm used to calculate values on the model grid is now:
369
370\[
371  \begin{split}
372    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
373    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
374    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
375    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
376  \end{split}
377\]
378The gradients here are taken with respect to the horizontal indices and not distances since
379the spatial dependency has been included into the weights.
380
381%% =================================================================================================
382\subsubsection{Implementation}
383\label{subsec:SBC_iof_imp}
384
385To activate this option, a non-empty string should be supplied in
386the weights filename column of the relevant namelist;
387if this is left as an empty string no action is taken.
388In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
389as and when they are first required.
390This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
391inspecting a global attribute stored in the weights input file.
392This attribute must be called "ew\_wrap" and be of integer type.
393If it is negative, the input non-model grid is assumed to be not cyclic.
394If zero or greater, then the value represents the number of columns that overlap.
395$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
396if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
397If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
398In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
399therefore the grid is assumed to be cyclic with no overlapping columns.
400(In fact, this only matters when bicubic interpolation is required.)
401Note that no testing is done to check the validity in the model,
402since there is no way of knowing the name used for the longitude variable,
403so it is up to the user to make sure his or her data is correctly represented.
404
405Next the routine reads in the weights.
406Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
407The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
408and when required, for reading in the variable to be interpolated (on the input data grid).
409The size of the input data array is determined by examining the values in the "src" arrays to
410find the minimum and maximum i and j values required.
411Since bicubic interpolation requires the calculation of gradients at each point on the grid,
412the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
413When the array of points from the data file is adjacent to an edge of the data grid,
414the halo is either a copy of the row/column next to it (non-cyclical case),
415or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
416
417%% =================================================================================================
418\subsubsection{Limitations}
419\label{subsec:SBC_iof_lim}
420
421\begin{enumerate}
422\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
423\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
424  a bicubic interpolation method is used.
425\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
426\item The gradients across the ends of a cyclical grid assume that the grid spacing between
427  the two columns involved are consistent with the weights used.
428\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
429  but this has not been implemented.)
430\end{enumerate}
431
432%% =================================================================================================
433\subsubsection{Utilities}
434\label{subsec:SBC_iof_util}
435
436% to be completed
437A set of utilities to create a weights file for a rectilinear input grid is available
438(see the directory NEMOGCM/TOOLS/WEIGHTS).
439
440%% =================================================================================================
441\subsection{Standalone surface boundary condition scheme (SAS)}
442\label{subsec:SBC_SAS}
443
444\begin{listing}
445  \nlst{namsbc_sas}
446  \caption{\forcode{&namsbc_sas}}
447  \label{lst:namsbc_sas}
448\end{listing}
449
450In some circumstances, it may be useful to avoid calculating the 3D temperature,
451salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
452For example:
453
454\begin{itemize}
455\item Multiple runs of the model are required in code development to
456  see the effect of different algorithms in the bulk formulae.
457\item The effect of different parameter sets in the ice model is to be examined.
458\item Development of sea-ice algorithms or parameterizations.
459\item Spinup of the iceberg floats
460\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
461\end{itemize}
462
463The Standalone Surface scheme provides this capacity.
464Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
465A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
466However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
467In this configuration, a few routines in the standard model are overriden by new versions.
468Routines replaced are:
469
470\begin{itemize}
471\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
472  Since the ocean state is not calculated all associated initialisations have been removed.
473\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
474\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
475  New surface modules that can function when only the surface level of the ocean state is defined can also be added
476  (\eg\ icebergs).
477\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
478  so calls to restart functions have been removed.
479  This also means that the calendar cannot be controlled by time in a restart file,
480  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
481\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
482\item \mdl{diawri}: All 3D data have been removed from the output.
483  The surface temperature, salinity and velocity components (which have been read in) are written along with
484  relevant forcing and ice data.
485\end{itemize}
486
487One new routine has been added:
488
489\begin{itemize}
490\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
491  velocity arrays at the surface.
492  These filenames are supplied in namelist namsbc\_sas.
493  Unfortunately, because of limitations with the \mdl{iom} module,
494  the full 3D fields from the mean files have to be read in and interpolated in time,
495  before using just the top level.
496  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
497\end{itemize}
498
499The user can also choose in the \nam{sbc_sas}{sbc\_sas} namelist to read the mean (nn\_fsbc time-step) fraction of solar net radiation absorbed in the 1st T level using
500 (\np[=.true.]{ln_flx}{ln\_flx}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln_flx}{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in.
501
502%% =================================================================================================
503\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
504\label{sec:SBC_flx}
505
506\begin{listing}
507  \nlst{namsbc_flx}
508  \caption{\forcode{&namsbc_flx}}
509  \label{lst:namsbc_flx}
510\end{listing}
511
512In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
513the surface boundary condition fields are directly read from input files.
514The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
515the name of the variable read in the file, the time frequency at which it is given (in hours),
516and a logical setting whether a time interpolation to the model time step is required for this field.
517See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
518
519Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
520See \autoref{subsec:SBC_ssr} for its specification.
521
522%% =================================================================================================
523\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
524\label{sec:SBC_blk}
525
526\begin{listing}
527  \nlst{namsbc_blk}
528  \caption{\forcode{&namsbc_blk}}
529  \label{lst:namsbc_blk}
530\end{listing}
531
532In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields
533and ocean (and sea-ice) variables averaged over \np{nn_fsbc}{nn\_fsbc} time-step.
534
535The atmospheric fields used depend on the bulk formulae used.
536In forced mode, when a sea-ice model is used, a specific bulk formulation is used.
537Therefore, different bulk formulae are used for the turbulent fluxes computation
538over the ocean and over sea-ice surface.
539For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}):
540the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae.
541The choice is made by setting to true one of the following namelist variable:
542 \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}\np{ln_COARE_3p5}{ln\_COARE\_3p5} and  \np{ln_ECMWF}{ln\_ECMWF}.
543For sea-ice, three possibilities can be selected:
544a constant transfer coefficient (1.4e-3; default value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
545
546Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
547The required 9 input fields are:
548
549\begin{table}[htbp]
550  \centering
551  \begin{tabular}{|l|c|c|c|}
552    \hline
553    Variable description                 & Model variable & Units              & point \\
554    \hline
555    i-component of the 10m air velocity  & utau           & $m.s^{-1}$         & T     \\
556    \hline
557    j-component of the 10m air velocity  & vtau           & $m.s^{-1}$         & T     \\
558    \hline
559    10m air temperature                  & tair           & \r{}$K$            & T     \\
560    \hline
561    Specific humidity                    & humi           & \%                 & T     \\
562    \hline
563    Incoming long wave radiation         & qlw            & $W.m^{-2}$         & T     \\
564    \hline
565    Incoming short wave radiation        & qsr            & $W.m^{-2}$         & T     \\
566    \hline
567    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
568    \hline
569    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
570    \hline
571    Mean sea-level pressure              & slp            & $hPa$              & T     \\
572    \hline
573    \end{tabular}
574  \label{tab:SBC_BULK}
575\end{table}
576
577Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
578It is simpler and faster (less fields to be read), but it is not the recommended method when
579the ocean grid size is the same or larger than the one of the input atmospheric fields.
580
581The \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},
582\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
583(spatial and temporal interpolations).
584
585\np{cn_dir}{cn\_dir} is the directory of location of bulk files
586\np{ln_taudif}{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
587\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
588\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
589
590Three multiplicative factors are available:
591\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
592increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
593The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
594the calculation of surface wind stress.
595Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
596
597As for the flux formulation, information about the input data required by the model is provided in
598the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
599
600%% =================================================================================================
601\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.F90, sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}
602\label{subsec:SBC_blk_ocean}
603
604Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
605COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
606their neutral transfer coefficients relationships with neutral wind.
607\begin{itemize}
608\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
609  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
610  They use an inertial dissipative method to compute the turbulent transfer coefficients
611  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
612  This \citet{large.yeager_rpt04} dataset is available through
613  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
614  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
615  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
616\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
617\item COARE 3.5 (\np[=.true.]{ln_COARE_3p5}{ln\_COARE\_3p5}): See \citet{edson.jampana.ea_JPO13} for more details
618\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation.
619  Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}.
620\end{itemize}
621
622%% =================================================================================================
623\subsection{Ice-Atmosphere Bulk formulae}
624\label{subsec:SBC_blk_ice}
625
626Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
627
628\begin{itemize}
629\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
630  default constant value used for momentum and heat neutral transfer coefficients
631\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
632  This scheme adds a dependency on edges at leads, melt ponds and flows
633  of the constant neutral air-ice drag. After some approximations,
634  this can be resumed to a dependency on ice concentration (A).
635  This drag coefficient has a parabolic shape (as a function of ice concentration)
636  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.
637  It is theoretically applicable to all ice conditions (not only MIZ).
638\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
639  Alternative turbulent transfer coefficients formulation between sea-ice
640  and atmosphere with distinct momentum and heat coefficients depending
641  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
642  The parameterization is adapted from ECHAM6 atmospheric model.
643  Compared to Lupkes2012 scheme, it considers specific skin and form drags
644  to compute neutral transfer coefficients for both heat and momentum fluxes.
645  Atmospheric stability effect on transfer coefficient is also taken into account.
646\end{itemize}
647
648%% =================================================================================================
649\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
650\label{sec:SBC_cpl}
651
652\begin{listing}
653  \nlst{namsbc_cpl}
654  \caption{\forcode{&namsbc_cpl}}
655  \label{lst:namsbc_cpl}
656\end{listing}
657
658In the coupled formulation of the surface boundary condition,
659the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
660while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
661the atmospheric component.
662
663A generalised coupled interface has been developed.
664It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
665An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
666It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
667(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
668(Weather Research and Forecasting Model).
669
670When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
671the whole carbon cycle is computed.
672In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
673(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
674
675The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
676now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
677When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
678the number used in the sea ice model.
679In some limited cases, it may be possible to specify single category coupling fields even when
680the sea ice model is running with multiple categories -
681in this case, the user should examine the code to be sure the assumptions made are satisfactory.
682In cases where this is definitely not possible, the model should abort with an error message.
683
684%% =================================================================================================
685\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
686\label{sec:SBC_apr}
687
688\begin{listing}
689  \nlst{namsbc_apr}
690  \caption{\forcode{&namsbc_apr}}
691  \label{lst:namsbc_apr}
692\end{listing}
693
694The optional atmospheric pressure can be used to force ocean and ice dynamics
695(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
696The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
697can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
698When used to force the dynamics, the atmospheric pressure is further transformed into
699an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
700\[
701  % \label{eq:SBC_ssh_ib}
702  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
703\]
704where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
705A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
706In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
707\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
708
709The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
710For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
711(see \mdl{sbcssr} module).
712$\eta_{ib}$ can be written in the output.
713This can simplify altimetry data and model comparison as
714inverse barometer sea surface height is usually removed from these date prior to their distribution.
715
716When using time-splitting and BDY package for open boundaries conditions,
717the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
718\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
719
720%% =================================================================================================
721\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
722\label{sec:SBC_tide}
723
724\begin{listing}
725  \nlst{nam_tide}
726  \caption{\forcode{&nam_tide}}
727  \label{lst:nam_tide}
728\end{listing}
729
730The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
731is 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}.
732This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
733\[
734  % \label{eq:SBC_PE_dyn_tides}
735  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
736  +g\nabla (\Pi_{eq} + \Pi_{sal})
737\]
738where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
739$\Pi_{sal}$ is a self-attraction and loading term (SAL).
740
741The equilibrium tidal forcing is expressed as a sum over a subset of
742constituents chosen from the set of available tidal constituents
743defined in file \hf{SBC/tide} (this comprises the tidal
744constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
745  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
746constituents are selected by including their names in the array
747\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
748\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
749and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
750\forcode{.true.}, the equilibrium tidal forcing can be ramped up
751linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
752model run.
753
754The SAL term should in principle be computed online as it depends on
755the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
756discussion about the practical implementation of this term).
757Nevertheless, the complex calculations involved would make this
758computationally too expensive. Here, two options are available:
759$\Pi_{sal}$ generated by an external model can be read in
760(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
761used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
762\[
763  \Pi_{sal} = \beta \eta,
764\]
765where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
766spatially constant scalar, often chosen to minimize tidal prediction
767errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
768\forcode{.false.} removes the SAL contribution.
769
770%% =================================================================================================
771\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
772\label{sec:SBC_rnf}
773
774\begin{listing}
775  \nlst{namsbc_rnf}
776  \caption{\forcode{&namsbc_rnf}}
777  \label{lst:namsbc_rnf}
778\end{listing}
779
780%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
781%Many models, however, have traditionally inserted river runoff to the top model cell.
782%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
783%throughout a nonzero depth has been motivated by the numerical and physical problems
784%that arise when the top grid cells are of the order of one meter. This situation is common in
785%coastal modelling and becomes more and more often open ocean and climate modelling
786%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
787%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
788
789%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
790%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
791%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
792%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
793%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
794%emp or emps and the changes made are below:
795
796%Rachel:
797River runoff generally enters the ocean at a nonzero depth rather than through the surface.
798Many models, however, have traditionally inserted river runoff to the top model cell.
799This was the case in \NEMO\ prior to the version 3.3,
800and was combined with an option to increase vertical mixing near the river mouth.
801
802However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
803This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
804\footnote{
805  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
806  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
807  see also \autoref{fig:SBC_dcy}.}.
808
809As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
810and for the temperature and salinity of the river to effect the surrounding ocean.
811The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
812along with the depth (in metres) which the river should be added to.
813
814Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
815\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
816If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
817and/or taken as surface temperature respectively.
818
819The runoff value and attributes are read in in sbcrnf.
820For temperature -999 is taken as missing data and the river temperature is taken to
821be the surface temperatue at the river point.
822For the depth parameter a value of -1 means the river is added to the surface box only,
823and a value of -999 means the river is added through the entire water column.
824After being read in the temperature and salinity variables are multiplied by the amount of runoff
825(converted into m/s) to give the heat and salt content of the river runoff.
826After the user specified depth is read ini,
827the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
828The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
829the bottom of the lowest box the river water is being added to
830(\ie\ the total depth that river water is being added to in the model).
831
832The mass/volume addition due to the river runoff is, at each relevant depth level, added to
833the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
834This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
835The sea surface height is calculated using the sum of the horizontal divergence terms,
836and so the river runoff indirectly forces an increase in sea surface height.
837
838The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
839This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
840The heat and salt content of the river runoff is not included in this step,
841and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
842the box and replaced by the same volume of river water with no corresponding heat and salt addition.
843
844For the linear free surface case, at the surface box the tracer advection causes a flux of water
845(of equal volume to the runoff) through the sea surface out of the domain,
846which causes a salt and heat flux out of the model.
847As such the volume of water does not change, but the water is diluted.
848
849For the non-linear free surface case, no flux is allowed through the surface.
850Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
851no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
852(The runoff addition to the top box along with the water being moved up through
853boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
854
855In trasbc the addition of heat and salt due to the river runoff is added.
856This is done in the same way for both vvl and non-vvl.
857The temperature and salinity are increased through the specified depth according to
858the heat and salt content of the river.
859
860In the non-linear free surface case (vvl),
861near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
862so that the original ratios of grid box heights are restored.
863In doing this water is moved into boxes below, throughout the water column,
864so the large volume addition to the surface box is spread between all the grid boxes.
865
866It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
867\ie\ modelling the Baltic flow in and out of the North Sea.
868When the flow is out of the domain there is no change in temperature and salinity,
869regardless of the namelist options used,
870as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
871
872%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
873
874%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
875
876%\colorbox{yellow}{river mouths{\ldots}}
877
878%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
879%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
880%ENDIF
881
882\cmtgm{  word doc of runoffs:
883In the current \NEMO\ setup river runoff is added to emp fluxes,
884these are then applied at just the sea surface as a volume change (in the variable volume case
885this is a literal volume change, and in the linear free surface case the free surface is moved)
886and a salt flux due to the concentration/dilution effect.
887There is also an option to increase vertical mixing near river mouths;
888this gives the effect of having a 3d river.
889All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
890at the same temperature as the sea surface.
891Our aim was to code the option to specify the temperature and salinity of river runoff,
892(as well as the amount), along with the depth that the river water will affect.
893This would make it possible to model low salinity outflow, such as the Baltic,
894and would allow the ocean temperature to be affected by river runoff.
895
896The depth option makes it possible to have the river water affecting just the surface layer,
897throughout depth, or some specified point in between.
898
899To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
900the \mdl{tra_sbc} module.
901We decided to separate them throughout the code,
902so that the variable emp represented solely evaporation minus precipitation fluxes,
903and a new 2d variable rnf was added which represents the volume flux of river runoff
904(in $kg/m^2s$ to remain consistent with $emp$).
905This meant many uses of emp and emps needed to be changed,
906a list of all modules which use $emp$ or $emps$ and the changes made are below:}
907
908%% =================================================================================================
909\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
910\label{sec:SBC_isf}
911
912\begin{listing}
913  \nlst{namsbc_isf}
914  \caption{\forcode{&namsbc_isf}}
915  \label{lst:namsbc_isf}
916\end{listing}
917
918The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
919Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
920The different options are illustrated in \autoref{fig:SBC_isf}.
921
922\begin{description}
923  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
924  The fwf and heat flux are depending of the local water properties.
925
926  Two different bulk formulae are available:
927
928  \begin{description}
929  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
930    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
931  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
932    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
933    A complete description is available in \citet{jenkins_JGR91}.
934  \end{description}
935
936  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
937  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
938  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.
939  Then, the fluxes are spread over the same thickness (ie over one or several cells).
940  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.
941  This can lead to super-cool temperature in the top cell under melting condition.
942  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.\\
943
944  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
945  There are 3 different ways to compute the exchange coeficient:
946  \begin{description}
947  \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}.
948    \begin{gather*}
949       % \label{eq:SBC_isf_gamma_iso}
950      \gamma^{T} = rn\_gammat0 \\
951      \gamma^{S} = rn\_gammas0
952    \end{gather*}
953    This is the recommended formulation for ISOMIP.
954  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
955    \begin{gather*}
956      \gamma^{T} = rn\_gammat0 \times u_{*} \\
957      \gamma^{S} = rn\_gammas0 \times u_{*}
958    \end{gather*}
959    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
960    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
961  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
962    \[
963      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
964    \]
965    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
966    $\Gamma_{Turb}$ the contribution of the ocean stability and
967    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
968    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
969    This formulation has not been extensively tested in \NEMO\ (not recommended).
970  \end{description}
971\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
972  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
973  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
974  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
975  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
976  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
977\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
978  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
979  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
980  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
981  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
982\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
983  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
984  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
985  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})
986\end{description}
987
988$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
989the water mass properties, ocean velocities and depth.
990This flux is thus highly dependent of the model resolution (horizontal and vertical),
991realism of the water masses onto the shelf ...\\
992
993$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
994You have total control of the fwf forcing.
995This can be useful if the water masses on the shelf are not realistic or
996the resolution (horizontal/vertical) are too coarse to have realistic melting or
997for studies where you need to control your heat and fw input.\\
998
999The ice shelf melt is implemented as a volume flux as for the runoff.
1000The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1001the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1002See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1003
1004\begin{figure}[!t]
1005  \centering
1006  \includegraphics[width=0.66\textwidth]{SBC_isf}
1007  \caption[Ice shelf location and fresh water flux definition]{
1008    Illustration of the location where the fwf is injected and
1009    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1010  \label{fig:SBC_isf}
1011\end{figure}
1012
1013%% =================================================================================================
1014\section{Ice sheet coupling}
1015\label{sec:SBC_iscpl}
1016
1017\begin{listing}
1018  \nlst{namsbc_iscpl}
1019  \caption{\forcode{&namsbc_iscpl}}
1020  \label{lst:namsbc_iscpl}
1021\end{listing}
1022
1023Ice sheet/ocean coupling is done through file exchange at the restart step.
1024At each restart step:
1025
1026\begin{enumerate}
1027\item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1028\item a new domcfg.nc file is built using the DOMAINcfg tools.
1029\item \NEMO\ run for a specific period and output the average melt rate over the period.
1030\item the ice sheet model run using the melt rate outputed in step 4.
1031\item go back to 1.
1032\end{enumerate}
1033
1034If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1035potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1036The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1037
1038\begin{description}
1039\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
1040  ($bt_b=bt_n$).
1041\item [Enlarge  a cell]: See case "Thin a cell down"
1042\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
1043  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1044\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.
1045  If no neighbours, T/S is extrapolated from old top cell value.
1046  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1047\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1048\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.
1049  If no neighbour, T/S/U/V and mask set to 0.
1050\end{description}
1051
1052Furthermore, as the before and now fields are not compatible (modification of the geometry),
1053the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1054
1055The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1056It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1057the code will be unable to fill all the new wet cells properly.
1058The default number is set up for the MISOMIP idealised experiments.
1059This coupling procedure is able to take into account grounding line and calving front migration.
1060However, it is a non-conservative processe.
1061This could lead to a trend in heat/salt content and volume.\\
1062
1063In order to remove the trend and keep the conservation level as close to 0 as possible,
1064a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1065The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1066A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1067For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1068The 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).
1069
1070%% =================================================================================================
1071\section{Handling of icebergs (ICB)}
1072\label{sec:SBC_ICB_icebergs}
1073
1074\begin{listing}
1075  \nlst{namberg}
1076  \caption{\forcode{&namberg}}
1077  \label{lst:namberg}
1078\end{listing}
1079
1080Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1081Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1082(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1083Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1084described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1085Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1086which is an integer representing how many icebergs of this class are being described as one lagrangian point
1087(this reduces the numerical problem of tracking every single iceberg).
1088They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1089
1090Two initialisation schemes are possible.
1091\begin{description}
1092\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
1093  (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
1094  which an iceberg is generated at the beginning of the run.
1095  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1096  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1097  the geographical box: lonmin,lonmax,latmin,latmax
1098\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.
1099  This should be a file with a field on the configuration grid (typically ORCA)
1100  representing ice accumulation rate at each model point.
1101  These should be ocean points adjacent to land where icebergs are known to calve.
1102  Most points in this input grid are going to have value zero.
1103  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1104  At each time step, a test is performed to see if there is enough ice mass to
1105  calve an iceberg of each class in order (1 to 10).
1106  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1107  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1108\end{description}
1109
1110Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1111The latter act to disintegrate the iceberg.
1112This is either all melted freshwater,
1113or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1114which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1115Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1116
1117Extensive diagnostics can be produced.
1118Separate output files are maintained for human-readable iceberg information.
1119A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1120The amount of information is controlled by two integer parameters:
1121\begin{description}
1122\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1123  represents an increasing number of points in the code at which variables are written,
1124  and an increasing level of obscurity.
1125\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1126\end{description}
1127
1128Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1129A non-zero value represents how many timesteps between writes of information into the output file.
1130These output files are in NETCDF format.
1131When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1132Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1133So care is needed to recreate data for individual icebergs,
1134since its trajectory data may be spread across multiple files.
1135
1136%% =================================================================================================
1137\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1138\label{sec:SBC_wave}
1139
1140\begin{listing}
1141  \nlst{namsbc_wave}
1142  \caption{\forcode{&namsbc_wave}}
1143  \label{lst:namsbc_wave}
1144\end{listing}
1145
1146Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1147physical processes related to ocean surface waves, namely the surface stress modified by growth and
1148dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1149tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1150the wind stress.
1151
1152Physical processes related to ocean surface waves can be accounted by setting the logical variable
1153\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1154different processes should be activated as explained in the following sections.
1155
1156Wave fields can be provided either in forced or coupled mode:
1157\begin{description}
1158\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1159for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1160Input Data generic Interface (see \autoref{sec:SBC_input}).
1161\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1162in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1163\end{description}
1164
1165%% =================================================================================================
1166\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1167\label{subsec:SBC_wave_cdgw}
1168
1169The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1170can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1171Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1172the drag coefficient is computed according to the stable/unstable conditions of the
1173air-sea interface following \citet{large.yeager_rpt04}.
1174
1175%% =================================================================================================
1176\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1177\label{subsec:SBC_wave_sdw}
1178
1179The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1180It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1181and the current measured at a fixed point (Eulerian velocity).
1182As waves travel, the water particles that make up the waves travel in orbital motions but
1183without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1184at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1185An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1186representation of surface physics in ocean general circulation models. %GS: reference needed
1187The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1188
1189\[
1190  % \label{eq:SBC_wave_sdw}
1191  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1192  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1193  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1194\]
1195
1196where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1197$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1198$k$ is the mean wavenumber defined as:
1199$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1200
1201In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1202and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1203To simplify, it is customary to use approximations to the full Stokes profile.
1204Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1205are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1206$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1207and makes possible the estimation of the surface Stokes drift for random directional waves in
1208realistic wave conditions:
1209
1210\begin{description}
1211\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1212\citet{breivik.janssen.ea_JPO14}:
1213
1214\[
1215  % \label{eq:SBC_wave_sdw_0a}
1216  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1217\]
1218
1219where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1220
1221\[
1222  % \label{eq:SBC_wave_sdw_0b}
1223  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1224  \quad \text{and }\
1225  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1226\]
1227
1228where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1229
1230\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1231reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1232\citep{breivik.bidlot.ea_OM16}:
1233
1234\[
1235  % \label{eq:SBC_wave_sdw_1}
1236  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1237  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1238\]
1239
1240where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1241
1242\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1243but using the wave frequency from a wave model.
1244
1245\end{description}
1246
1247The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1248and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1249
1250\[
1251  % \label{eq:SBC_wave_eta_sdw}
1252  \frac{\partial{\eta}}{\partial{t}} =
1253  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1254\]
1255
1256The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1257for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1258that is induced by the three-dimensional Stokes velocity.
1259The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1260can be formulated as follows:
1261
1262\[
1263  % \label{eq:SBC_wave_tra_sdw}
1264  \frac{\partial{c}}{\partial{t}} =
1265  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1266\]
1267
1268%% =================================================================================================
1269\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1270\label{subsec:SBC_wave_stcor}
1271
1272In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1273in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1274This additional force may have impact on the Ekman turning of the surface current.
1275In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1276approximations described in \autoref{subsec:SBC_wave_sdw}),
1277\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1278
1279%% =================================================================================================
1280\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1281\label{subsec:SBC_wave_tauw}
1282
1283The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1284into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1285available for forcing the mean circulation, while in the opposite case of a decaying sea
1286state, more momentum is available for forcing the ocean.
1287Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1288but in practice, an equilibrium sea state is a fairly rare event.
1289So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1290
1291\[
1292  % \label{eq:SBC_wave_tauoc}
1293  \tau_{oc,a} = \tau_a - \tau_w
1294\]
1295
1296where $\tau_a$ is the atmospheric surface stress;
1297$\tau_w$ is the atmospheric stress going into the waves defined as:
1298
1299\[
1300  % \label{eq:SBC_wave_tauw}
1301  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1302\]
1303
1304where: $c_p$ is the phase speed of the gravity waves,
1305$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1306the physics of ocean waves. The first one, $S_{in}$, describes the generation
1307of ocean waves by wind and therefore represents the momentum and energy transfer
1308from air to ocean waves; the second term $S_{nl}$ denotes
1309the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1310describes the dissipation of waves by processes such as white-capping, large scale breaking
1311eddy-induced damping.
1312
1313The wave stress derived from an external wave model can be provided either through the normalized
1314wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1315meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1316
1317%% =================================================================================================
1318\section{Miscellaneous options}
1319\label{sec:SBC_misc}
1320
1321%% =================================================================================================
1322\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1323\label{subsec:SBC_dcy}
1324
1325\begin{figure}[!t]
1326  \centering
1327  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
1328  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1329    Example of reconstruction of the diurnal cycle variation of short wave flux from
1330    daily mean values.
1331    The reconstructed diurnal cycle (black line) is chosen as
1332    the mean value of the analytical cycle (blue line) over a time step,
1333    not as the mid time step value of the analytically cycle (red square).
1334    From \citet{bernie.guilyardi.ea_CD07}.}
1335  \label{fig:SBC_diurnal}
1336\end{figure}
1337
1338\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.
1339%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1340Nevertheless, 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}.
1341Furthermore, only the knowledge of daily mean value of SWF is needed,
1342as higher frequency variations can be reconstructed from them,
1343assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1344The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1345setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1346using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1347the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1348The reconstruction is performed in the \mdl{sbcdcy} module.
1349The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1350The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1351a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1352The use of diurnal cycle reconstruction requires the input SWF to be daily
1353(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1354Furthermore, it is recommended to have a least 8 surface module time steps per day,
1355that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1356An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1357one every 2~hours (from 1am to 11pm).
1358
1359\begin{figure}[!t]
1360  \centering
1361  \includegraphics[width=0.66\textwidth]{SBC_dcy}
1362  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1363    Example of reconstruction of the diurnal cycle variation of short wave flux from
1364    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1365    The display is on (i,j) plane.}
1366  \label{fig:SBC_dcy}
1367\end{figure}
1368
1369Note also that the setting a diurnal cycle in SWF is highly recommended when
1370the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1371an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1372
1373%% =================================================================================================
1374\subsection{Rotation of vector pairs onto the model grid directions}
1375\label{subsec:SBC_rotation}
1376
1377When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1378pairs of vector components can be rotated from east-north directions onto the local grid directions.
1379This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1380be defined relative to a rectilinear grid.
1381To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1382The eastward component must start with "U" and the northward component with "V".
1383The remaining characters in the strings are used to identify which pair of components go together.
1384So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1385rotate them on to the model grid directions;
1386"U2" and "V2" could be used against a second pair of components, and so on.
1387The extra characters used in the strings are arbitrary.
1388The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1389
1390%% =================================================================================================
1391\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1392\label{subsec:SBC_ssr}
1393
1394\begin{listing}
1395  \nlst{namsbc_ssr}
1396  \caption{\forcode{&namsbc_ssr}}
1397  \label{lst:namsbc_ssr}
1398\end{listing}
1399
1400Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1401On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1402a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1403\[
1404  % \label{eq:SBC_dmp_q}
1405  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1406\]
1407where SST is a sea surface temperature field (observed or climatological),
1408$T$ is the model surface layer temperature and
1409$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1410For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1411This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1412
1413In the fresh water budget, a feedback term can also be added.
1414Converted into an equivalent freshwater flux, it takes the following expression :
1415
1416\begin{equation}
1417  \label{eq:SBC_dmp_emp}
1418  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1419  {\left.S\right|_{k=1}}
1420\end{equation}
1421
1422where $\textit{emp}_{o }$ is a net surface fresh water flux
1423(observed, climatological or an atmospheric model product),
1424\textit{SSS}$_{Obs}$ is a sea surface salinity
1425(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1426$\left.S\right|_{k=1}$ is the model surface layer salinity and
1427$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1428Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1429the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1430The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1431reduce the uncertainties we have on the observed freshwater budget.
1432
1433%% =================================================================================================
1434\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1435\label{subsec:SBC_ice-cover}
1436
1437The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1438There are several way to handle sea-ice in the system depending on
1439the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1440\begin{description}
1441\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1442  This is a typical namelist value used for tropical ocean domain.
1443  The surface fluxes are simply specified for an ice-free ocean.
1444  No specific things is done for sea-ice.
1445\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1446  An observed ice covered area is read in a file.
1447  Below this area, the SST is restored to the freezing point and
1448  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1449  The associated modification of the freshwater fluxes are done in such a way that
1450  the change in buoyancy fluxes remains zero.
1451  This prevents deep convection to occur when trying to reach the freezing point
1452  (and so ice covered area condition) while the SSS is too large.
1453  This manner of managing sea-ice area, just by using a IF case,
1454  is usually referred as the \textit{ice-if} model.
1455  It can be found in the \mdl{sbcice\_if} module.
1456\item [nn\_ice = 2 or more] A full sea ice model is used.
1457  This model computes the ice-ocean fluxes,
1458  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1459  provide the surface averaged ocean fluxes.
1460  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1461  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1462  (\ie\ $2$ for SI3 or $3$ for CICE).
1463\end{description}
1464
1465% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1466%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1467
1468%% =================================================================================================
1469\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1470\label{subsec:SBC_cice}
1471
1472It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1473to the CICE sea-ice model by using \key{cice}.
1474The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1475the additional 'hadgem3' drivers will be required, even with the latest code release.
1476Input grid files consistent with those used in \NEMO\ will also be needed,
1477and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1478(seek advice from UKMO if necessary).
1479Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1480(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1481or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1482(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1483The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1484(although coupling ocean and ice less frequently should work,
1485it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1486the user should check that results are not significantly different to the standard case).
1487
1488There are two options for the technical coupling between \NEMO\ and CICE.
1489The standard version allows complete flexibility for the domain decompositions in the individual models,
1490but this is at the expense of global gather and scatter operations in the coupling which
1491become very expensive on larger numbers of processors.
1492The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1493the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1494and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1495allows much more efficient direct coupling on individual processors.
1496This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1497there is no sea ice.
1498
1499%% =================================================================================================
1500\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1501\label{subsec:SBC_fwb}
1502
1503For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1504prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1505In \NEMO, two way of controlling the freshwater budget are proposed:
1506
1507\begin{description}
1508\item [{\np[=0]{nn_fwb}{nn\_fwb}}] no control at all.
1509  The mean sea level is free to drift, and will certainly do so.
1510\item [{\np[=1]{nn_fwb}{nn\_fwb}}] global mean \textit{emp} set to zero at each model time step.
1511  %GS: comment below still relevant ?
1512  %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).
1513\item [{\np[=2]{nn_fwb}{nn\_fwb}}] freshwater budget is adjusted from the previous year annual mean budget which
1514  is read in the \textit{EMPave\_old.dat} file.
1515  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1516  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1517\end{description}
1518
1519% Griffies doc:
1520% When running ocean-ice simulations, we are not explicitly representing land processes,
1521% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1522% it is important to balance the hydrological cycle in ocean-ice models.
1523% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1524% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1525% a chosen time scale.
1526% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1527% so that there is always a zero net input of water to the ocean-ice system.
1528% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1529% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1530% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1531% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1532% and ice models when aiming to balance the hydrological cycle.
1533% 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,
1534% not the water in any one sub-component. As an extreme example to illustrate the issue,
1535% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1536% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1537% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1538% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1539% in ocean-ice models.
1540
1541\subinc{\input{../../global/epilogue}}
1542
1543\end{document}
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