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1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4
5% ================================================================
6% Chapter —— Surface Boundary Condition (SBC, SAS, ISF, ICB)
7% ================================================================
8\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
9\label{chap:SBC}
10\minitoc
11
12\newpage
13
14%---------------------------------------namsbc--------------------------------------------------
15
16\nlst{namsbc}
17%--------------------------------------------------------------------------------------------------------------
18
19The ocean needs seven fields as surface boundary condition:
20
21\begin{itemize}
22\item
23  the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
24\item
25  the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
26\item
27  the surface freshwater budget $\left( {\textit{emp}} \right)$
28\item
29  the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
30\item
31  the atmospheric pressure at the ocean surface $\left( p_a \right)$
32\end{itemize}
33
34Four different ways are available to provide the seven fields to the ocean. They are controlled by
35namelist \ngn{namsbc} variables:
36
37\begin{itemize}
38\item
39  a bulk formulation (\np{ln\_blk}\forcode{ = .true.} with four possible bulk algorithms),
40\item
41  a flux formulation (\np{ln\_flx}\forcode{ = .true.}),
42\item
43  a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
44(\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}),
45\item
46  a user defined formulation (\np{ln\_usr}\forcode{ = .true.}).
47\end{itemize}
48
49
50The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.
51
52When the fields are supplied from data files (bulk, flux and mixed formulations),
53the input fields do not need to be supplied on the model grid.
54Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
55the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
56If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
57should be masked or filled to avoid spurious results in proximity of the coasts, as
58large sea-land gradients characterize most of the atmospheric variables.
59
60In addition, the resulting fields can be further modified using several namelist options.
61These options control:
62
63\begin{itemize}
64\item
65  the rotation of vector components supplied relative to an east-north coordinate system onto
66  the local grid directions in the model,
67\item
68  the use of a land/sea mask for input fields (\np{nn\_lsm}\forcode{ = .true.}),
69\item
70  the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}\forcode{ = .true.}),
71\item
72  the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
73  (\np{nn\_ice}\forcode{ = 0..3}),
74\item
75  the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}\forcode{ = .true.}),
76\item
77  the addition of ice-shelf melting as lateral inflow (parameterisation) or
78  as fluxes applied at the land-ice ocean interface (\np{ln\_isf}\forcode{ = .true.}),
79\item
80  the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
81  (\np{nn\_fwb}\forcode{ = 0..2}),
82\item
83  the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
84  (\np{ln\_dm2dc}\forcode{ = .true.}),
85\item
86  the activation of wave effects from an external wave model  (\np{ln\_wave}\forcode{ = .true.}),
87\item
88  a neutral drag coefficient is read from an external wave model (\np{ln\_cdgw}\forcode{ = .true.}),
89\item
90  the Stokes drift from an external wave model is accounted for (\np{ln\_sdw}\forcode{ = .true.}),
91\item
92  the choice of the Stokes drift profile parameterization (\np{nn\_sdrift}\forcode{ = 0..2}),
93\item
94  the surface stress given to the ocean is modified by surface waves (\np{ln\_tauwoc}\forcode{ = .true.}),
95\item
96  the surface stress given to the ocean is read from an external wave model (\np{ln\_tauw}\forcode{ = .true.}),
97\item
98  the Stokes-Coriolis term is included (\np{ln\_stcor}\forcode{ = .true.}),
99\item
100  the light penetration in the ocean (\np{ln\_traqsr}\forcode{ = .true.} with namelist \ngn{namtra\_qsr}),
101\item
102  the atmospheric surface pressure gradient effect on ocean and ice dynamics (\np{ln\_apr\_dyn}\forcode{ = .true.} with namelist \ngn{namsbc\_apr}),
103\item
104  the effect of sea-ice pressure on the ocean (\np{ln\_ice\_embd}\forcode{ = .true.}).
105\end{itemize}
106
107In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
108Then we present the three ways of providing the surface boundary conditions,
109followed by the description of the atmospheric pressure and the river runoff.
110Next, the scheme for interpolation on the fly is described.
111Finally, the different options that further modify the fluxes applied to the ocean are discussed.
112One of these is modification by icebergs (see \autoref{sec:ICB_icebergs}),
113which act as drifting sources of fresh water.
114Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
115which provides additional sources of fresh water.
116
117
118
119% ================================================================
120% Surface boundary condition for the ocean
121% ================================================================
122\section{Surface boundary condition for the ocean}
123\label{sec:SBC_ocean}
124
125The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
126It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
127the momentum vertical mixing trend (see \autoref{eq:dynzdf_sbc} in \autoref{sec:DYN_zdf}).
128As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
129\ie resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
130
131The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
132$Q_{ns}$ and $Q_{sr}$, respectively.
133The former is the non penetrative part of the heat flux
134(\ie the sum of sensible, latent and long wave heat fluxes plus
135the heat content of the mass exchange between the ocean and sea-ice).
136It is applied in \mdl{trasbc} module as a surface boundary condition trend of
137the first level temperature time evolution equation
138(see \autoref{eq:tra_sbc} and \autoref{eq:tra_sbc_lin} in \autoref{subsec:TRA_sbc}).
139The latter is the penetrative part of the heat flux.
140It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
141\np{ln\_traqsr}\forcode{ = .true.}.
142The way the light penetrates inside the water column is generally a sum of decreasing exponentials
143(see \autoref{subsec:TRA_qsr}).
144
145The surface freshwater budget is provided by the \textit{emp} field.
146It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
147possibly with the sea-ice and ice shelves (freezing minus melting of ice).
148It affects the ocean in two different ways:
149$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
150a volume flux, and
151$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
152the mass exchanged with atmosphere, sea-ice and ice shelves.
153
154
155%\colorbox{yellow}{Miss: }
156%
157%A extensive description of all namsbc namelist (parameter that have to be
158%created!)
159%
160%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
161%ssv) \ie information required by flux computation or sea-ice
162%
163%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
164%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
165%
166%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
167%
168%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
169%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
170%nf{\_}sbc
171%
172%Explain here all the namlist namsbc variable{\ldots}.
173%
174% explain : use or not of surface currents
175%
176%\colorbox{yellow}{End Miss }
177
178The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
179the surface currents, temperature and salinity. 
180These variables are averaged over \np{nn\_fsbc} time-step (\autoref{tab:ssm}), and
181these averaged fields are used to compute the surface fluxes at the frequency of \np{nn\_fsbc} time-steps.
182
183
184%-------------------------------------------------TABLE---------------------------------------------------
185\begin{table}[tb]
186  \begin{center}
187    \begin{tabular}{|l|l|l|l|}
188      \hline
189      Variable description                         & Model variable  & Units  & point                 \\\hline
190      i-component of the surface current  & ssu\_m               & $m.s^{-1}$     & U     \\\hline
191      j-component of the surface current  & ssv\_m               & $m.s^{-1}$     & V     \\ \hline
192      Sea surface temperature                & sst\_m               & \r{}$K$              & T     \\\hline
193      Sea surface salinty                          & sss\_m               & $psu$              & T     \\   \hline
194    \end{tabular}
195    \caption{
196      \protect\label{tab:ssm}
197      Ocean variables provided by the ocean to the surface module (SBC).
198      The variable are averaged over \np{nn\_fsbc} time-step,
199      \ie the frequency of computation of surface fluxes.
200    }
201  \end{center}
202\end{table}
203%--------------------------------------------------------------------------------------------------------------
204
205%\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
206
207
208
209% ================================================================
210%       Input Data
211% ================================================================
212\section{Input data generic interface}
213\label{sec:SBC_input}
214
215A generic interface has been introduced to manage the way input data
216(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
217This task is achieved by \mdl{fldread}.
218The module is designed with four main objectives in mind:
219\begin{enumerate}
220\item
221  optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
222  and according to the different calendars available in the model.
223\item
224  optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
225\item
226  make the run duration independent from the period cover by the input files.
227\item
228  provide a simple user interface and a rather simple developer interface by
229  limiting the number of prerequisite informations.
230\end{enumerate}
231
232As a result, the user has only to fill in for each variable a structure in the namelist file to
233define the input data file and variable names, the frequency of the data (in hours or months),
234whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
235and three additional parameters for the on-the-fly interpolation.
236When adding a new input variable, the developer has to add the associated structure in the namelist,
237read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
238and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
239
240The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
241(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
242if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
243
244Note that when an input data is archived on a disc which is accessible directly from the workspace where
245the code is executed, then the user can set the \np{cn\_dir} to the pathway leading to the data.
246By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
247
248
249% -------------------------------------------------------------------------------------------------------------
250% Input Data specification (\mdl{fldread})
251% -------------------------------------------------------------------------------------------------------------
252\subsection[Input data specification (\textit{fldread.F90})]
253{Input data specification (\protect\mdl{fldread})}
254\label{subsec:SBC_fldread}
255
256The structure associated with an input variable contains the following information:
257\begin{forlines}
258!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
259!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
260\end{forlines}
261where
262\begin{description} 
263\item[File name]:
264  the stem name of the NetCDF file to be opened.
265  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
266  by date information and possibly a prefix (when using AGRIF).
267  Tab.\autoref{tab:fldread} provides the resulting file name in all possible cases according to
268  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
269
270%--------------------------------------------------TABLE--------------------------------------------------
271  \begin{table}[htbp]
272    \begin{center}
273      \begin{tabular}{|l|c|c|c|}
274        \hline
275                                        &  daily or weekLL     &  monthly           &  yearly        \\   \hline
276        \np{clim}\forcode{ = .false.}  &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\   \hline
277        \np{clim}\forcode{ = .true.}   &  not possible        &  fn\_m??.nc        &  fn            \\   \hline
278      \end{tabular}
279    \end{center}
280    \caption{
281      \protect\label{tab:fldread}
282      naming nomenclature for climatological or interannual input file(s), as a function of the open/close frequency.
283      The stem name is assumed to be 'fn'.
284      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
285      (\ie 'sun','sat','fri','thu','wed','tue','mon').
286      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits.
287      Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc',
288      where 'PPPP' is the process number coded with 4 digits;
289      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
290    }
291  \end{table}
292%--------------------------------------------------------------------------------------------------------------
293 
294
295\item[Record frequency]:
296  the frequency of the records contained in the input file.
297  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
298  (for example -1 for monthly forcing or -12 for annual forcing).
299  Note that this frequency must REALLY be an integer and not a real.
300  On some computers, setting it to '24.' can be interpreted as 240!
301
302\item[Variable name]:
303  the name of the variable to be read in the input NetCDF file.
304
305\item[Time interpolation]:
306  a logical to activate, or not, the time interpolation.
307  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
308  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
309  00h00'00'' to 23h59'59".
310  If set to 'true', the forcing will have a broken line shape.
311  Records are assumed to be dated at the middle of the forcing period.
312  For example, when using a daily forcing with time interpolation,
313  linear interpolation will be performed between mid-day of two consecutive days.
314
315\item[Climatological forcing]:
316  a logical to specify if a input file contains climatological forcing which can be cycle in time,
317  or an interannual forcing which will requires additional files if
318  the period covered by the simulation exceeds the one of the file.
319  See the above file naming strategy which impacts the expected name of the file to be opened.
320
321\item[Open/close frequency]:
322  the frequency at which forcing files must be opened/closed.
323  Four cases are coded:
324  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
325  means the forcing files will contain data for one day, one week, one month or one year.
326  Files are assumed to contain data from the beginning of the open/close period.
327  For example, the first record of a yearly file containing daily data is Jan 1st even if
328  the experiment is not starting at the beginning of the year.
329
330\item[Others]:
331  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
332  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
333
334\end{description}
335
336Additional remarks:\\
337(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
338The only tricky point is therefore to specify the date at which we need to do the interpolation and
339the date of the records read in the input files.
340Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
341For example, for an experiment starting at 0h00'00" with a one-hour time-step,
342a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
343However, for forcing data related to the surface module,
344values are not needed at every time-step but at every \np{nn\_fsbc} time-step.
345For example with \np{nn\_fsbc}\forcode{ = 3}, the surface module will be called at time-steps 1, 4, 7, etc.
346The date used for the time interpolation is thus redefined to the middle of \np{nn\_fsbc} time-step period.
347In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
348(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
349The calendar associated with the forcing field is build according to the information provided by
350user in the record frequency, the open/close frequency and the type of temporal interpolation.
351For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
352start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
353(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
354interpolating data with the first (last) record of the open/close period.
355For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
356the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
357Dec 31st 12h00'00" and Jan 1st 12h00'00".
358If the forcing is climatological, Dec and Jan will be keep-up from the same year.
359However, if the forcing is not climatological, at the end of
360the open/close period, the code will automatically close the current file and open the next one.
361Note that, if the experiment is starting (ending) at the beginning (end) of
362an open/close period, we do accept that the previous (next) file is not existing.
363In this case, the time interpolation will be performed between two identical values.
364For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
365we do accept that the file related to year Y-1 is not existing.
366The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
367If the file of year Y-1 exists, the code will read its last record.
368Therefore, this file can contain only one record corresponding to Dec 31st,
369a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
370
371
372% -------------------------------------------------------------------------------------------------------------
373% Interpolation on the Fly
374% -------------------------------------------------------------------------------------------------------------
375\subsection{Interpolation on-the-fly}
376\label{subsec:SBC_iof}
377
378Interpolation on the Fly allows the user to supply input files required for the surface forcing on
379grids other than the model grid.
380To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
381interpolate from the data grid to the model grid.
382The original development of this code used the SCRIP package
383(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
384In principle, any package such as CDO can be used to generate the weights, but the variables in
385the input weights file must have the same names and meanings as assumed by the model.
386Two methods are currently available: bilinear and bicubic interpolations.
387Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
388the input file and substitute the corresponding values with the average of the 8 neighbouring points in
389the native external grid.
390Only "sea points" are considered for the averaging.
391The land/sea mask file must be provided in the structure associated with the input variable.
392The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
393the associated variables and should be equal to 1 over land and 0 elsewhere.
394The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
395Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
396
397
398% -------------------------------------------------------------------------------------------------------------
399% Bilinear interpolation
400% -------------------------------------------------------------------------------------------------------------
401\subsubsection{Bilinear interpolation}
402\label{subsec:SBC_iof_bilinear}
403
404The input weights file in this case has two sets of variables:
405src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
406The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
407Each src value is an integer corresponding to the index of a point in the input grid when
408written as a one dimensional array.
409For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
410There are four of each variable because bilinear interpolation uses the four points defining
411the grid box containing the point to be interpolated.
412All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
413generate a value for point (i,j) in the model.
414
415Symbolically, the algorithm used is:
416\[
417  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
418\]
419where function idx() transforms a one dimensional index src(k) into a two dimensional index,
420and wgt(1) corresponds to variable "wgt01" for example.
421
422
423% -------------------------------------------------------------------------------------------------------------
424% Bicubic interpolation
425% -------------------------------------------------------------------------------------------------------------
426\subsubsection{Bicubic interpolation}
427\label{subsec:SBC_iof_bicubic}
428
429Again, there are two sets of variables: "src" and "wgt".
430But in this case, there are 16 of each.
431The symbolic algorithm used to calculate values on the model grid is now:
432
433\[
434  \begin{split}
435    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
436    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
437    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
438    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
439  \end{split}
440\]
441The gradients here are taken with respect to the horizontal indices and not distances since
442the spatial dependency has been included into the weights.
443
444
445% -------------------------------------------------------------------------------------------------------------
446% Implementation
447% -------------------------------------------------------------------------------------------------------------
448\subsubsection{Implementation}
449\label{subsec:SBC_iof_imp}
450
451To activate this option, a non-empty string should be supplied in
452the weights filename column of the relevant namelist;
453if this is left as an empty string no action is taken.
454In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
455as and when they are first required.
456This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
457inspecting a global attribute stored in the weights input file.
458This attribute must be called "ew\_wrap" and be of integer type.
459If it is negative, the input non-model grid is assumed to be not cyclic.
460If zero or greater, then the value represents the number of columns that overlap.
461$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
462if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
463If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
464In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
465therefore the grid is assumed to be cyclic with no overlapping columns.
466(In fact, this only matters when bicubic interpolation is required.)
467Note that no testing is done to check the validity in the model,
468since there is no way of knowing the name used for the longitude variable,
469so it is up to the user to make sure his or her data is correctly represented.
470
471Next the routine reads in the weights.
472Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
473The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
474and when required, for reading in the variable to be interpolated (on the input data grid).
475The size of the input data array is determined by examining the values in the "src" arrays to
476find the minimum and maximum i and j values required.
477Since bicubic interpolation requires the calculation of gradients at each point on the grid,
478the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
479When the array of points from the data file is adjacent to an edge of the data grid,
480the halo is either a copy of the row/column next to it (non-cyclical case),
481or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
482
483
484% -------------------------------------------------------------------------------------------------------------
485% Limitations
486% -------------------------------------------------------------------------------------------------------------
487\subsubsection{Limitations}
488\label{subsec:SBC_iof_lim}
489
490\begin{enumerate} 
491\item
492  The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
493\item
494  This code is not guaranteed to produce positive definite answers from positive definite inputs when
495  a bicubic interpolation method is used.
496\item
497  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
498\item
499  The gradients across the ends of a cyclical grid assume that the grid spacing between
500  the two columns involved are consistent with the weights used.
501\item
502  Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
503  but this has not been implemented.)
504\end{enumerate}
505
506\subsubsection{Utilities}
507\label{subsec:SBC_iof_util}
508
509% to be completed
510A set of utilities to create a weights file for a rectilinear input grid is available
511(see the directory NEMOGCM/TOOLS/WEIGHTS).
512
513
514% -------------------------------------------------------------------------------------------------------------
515% Standalone Surface Boundary Condition Scheme
516% -------------------------------------------------------------------------------------------------------------
517\subsection{Standalone surface boundary condition scheme (SAS)}
518\label{subsec:SAS}
519
520%---------------------------------------namsbc_sas--------------------------------------------------
521
522\nlst{namsbc_sas}
523%--------------------------------------------------------------------------------------------------------------
524
525In some circumstances, it may be useful to avoid calculating the 3D temperature,
526salinity and velocity fields and simply read them in from a previous run or receive them from OASIS. 
527For example:
528
529\begin{itemize}
530\item
531  Multiple runs of the model are required in code development to
532  see the effect of different algorithms in the bulk formulae.
533\item
534  The effect of different parameter sets in the ice model is to be examined.
535\item
536  Development of sea-ice algorithms or parameterizations.
537\item
538  Spinup of the iceberg floats
539\item
540  Ocean/sea-ice simulation with both models running in parallel (\np{ln\_mixcpl}\forcode{ = .true.})
541\end{itemize}
542
543The Standalone Surface scheme provides this capacity.
544Its options are defined through the \ngn{namsbc\_sas} namelist variables.
545A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
546However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0).
547In this configuration, a few routines in the standard model are overriden by new versions.
548Routines replaced are:
549
550\begin{itemize}
551\item
552  \mdl{nemogcm}:
553  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
554  Since the ocean state is not calculated all associated initialisations have been removed.
555\item
556  \mdl{step}:
557  The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
558\item
559  \mdl{sbcmod}:
560  This has been cut down and now only calculates surface forcing and the ice model required.
561  New surface modules that can function when only the surface level of the ocean state is defined can also be added
562  (\eg icebergs).
563\item
564  \mdl{daymod}:
565  No ocean restarts are read or written (though the ice model restarts are retained),
566  so calls to restart functions have been removed.
567  This also means that the calendar cannot be controlled by time in a restart file,
568  so the user must check that nn{\_}date0 in the model namelist is correct for his or her purposes.
569\item
570  \mdl{stpctl}:
571  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
572\item
573  \mdl{diawri}:
574  All 3D data have been removed from the output.
575  The surface temperature, salinity and velocity components (which have been read in) are written along with
576  relevant forcing and ice data.
577\end{itemize}
578
579One new routine has been added:
580
581\begin{itemize}
582\item
583  \mdl{sbcsas}:
584  This module initialises the input files needed for reading temperature, salinity and
585  velocity arrays at the surface.
586  These filenames are supplied in namelist namsbc{\_}sas.
587  Unfortunately, because of limitations with the \mdl{iom} module,
588  the full 3D fields from the mean files have to be read in and interpolated in time,
589  before using just the top level.
590  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
591\end{itemize}
592
593
594The user can also choose in the \ngn{namsbc\_sas} namelist to read the mean (nn\_fsbc time-step) fraction of solar net radiation absorbed in the 1st T level using
595 (\np{ln\_flx}\forcode{ = .true.}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln\_flx}\forcode{ = .true.}). In that last case, only the 1st level will be read in.
596
597
598
599% ================================================================
600% Flux formulation
601% ================================================================
602\section[Flux formulation (\textit{sbcflx.F90})]
603{Flux formulation (\protect\mdl{sbcflx})}
604\label{sec:SBC_flx}
605%------------------------------------------namsbc_flx----------------------------------------------------
606
607\nlst{namsbc_flx} 
608%-------------------------------------------------------------------------------------------------------------
609
610In the flux formulation (\np{ln\_flx}\forcode{ = .true.}),
611the surface boundary condition fields are directly read from input files.
612The user has to define in the namelist \ngn{namsbc{\_}flx} the name of the file,
613the name of the variable read in the file, the time frequency at which it is given (in hours),
614and a logical setting whether a time interpolation to the model time step is required for this field.
615See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
616
617Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
618See \autoref{subsec:SBC_ssr} for its specification.
619
620
621
622% ================================================================
623% Bulk formulation
624% ================================================================
625\section[Bulk formulation (\textit{sbcblk.F90})]
626{Bulk formulation (\protect\mdl{sbcblk})}
627\label{sec:SBC_blk}
628%---------------------------------------namsbc_blk--------------------------------------------------
629
630\nlst{namsbc_blk}
631%--------------------------------------------------------------------------------------------------------------
632
633In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields
634and ocean (and sea-ice) variables averaged over \np{nn\_fsbc} time-step.
635
636The atmospheric fields used depend on the bulk formulae used.
637In forced mode, when a sea-ice model is used, a specific bulk formulation is used.
638Therefore, different bulk formulae are used for the turbulent fluxes computation
639over the ocean and over sea-ice surface.
640For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}):
641the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae.
642The choice is made by setting to true one of the following namelist variable:
643 \np{ln\_NCAR}, \np{ln\_COARE\_3p0}\np{ln\_COARE\_3p5} and  \np{ln\_ECMWF}.
644For sea-ice, three possibilities can be selected:
645a constant transfer coefficient (1.4e-3; default value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln\_Cd\_L12}), and \citet{lupkes.gryanik_JGR15} (\np{ln\_Cd\_L15}) parameterizations
646
647Common options are defined through the \ngn{namsbc\_blk} namelist variables.
648The required 9 input fields are:
649
650%--------------------------------------------------TABLE--------------------------------------------------
651\begin{table}[htbp]
652  \label{tab:BULK}
653  \begin{center}
654    \begin{tabular}{|l|c|c|c|}
655      \hline
656      Variable description                           & Model variable   & Units                         & point \\   \hline
657      i-component of the 10m air velocity   & utau                   & $m.s^{-1}$                   & T         \\   \hline
658      j-component of the 10m air velocity   & vtau                & $m.s^{-1}$                   & T         \\   \hline
659      10m air temperature                      & tair                & \r{}$K$                        & T       \\   \hline
660      Specific humidity                        & humi           & \%                             & T      \\   \hline
661      Incoming long wave radiation          & qlw                & $W.m^{-2}$            & T        \\   \hline
662      Incoming short wave radiation          & qsr               & $W.m^{-2}$            & T        \\   \hline
663      Total precipitation (liquid + solid)         & precip            & $Kg.m^{-2}.s^{-1}$      & T      \\   \hline
664      Solid precipitation                           & snow               & $Kg.m^{-2}.s^{-1}$       & T      \\   \hline
665      Mean sea-level pressure                     & slp                     & $hPa$                          & T       \\ \hline
666    \end{tabular}
667  \end{center}
668\end{table}
669%--------------------------------------------------------------------------------------------------------------
670
671Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
672It is simpler and faster (less fields to be read), but it is not the recommended method when
673the ocean grid size is the same or larger than the one of the input atmospheric fields.
674
675The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, \np{sn\_prec},
676\np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used
677(spatial and temporal interpolations).
678
679\np{cn\_dir} is the directory of location of bulk files
680\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
681\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
682\np{rn\_zu}: is the height of wind measurements (m)
683
684Three multiplicative factors are available:
685\np{rn\_pfac} and \np{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
686increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
687The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
688the calculation of surface wind stress.
689Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
690
691As for the flux formulation, information about the input data required by the model is provided in
692the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
693
694
695% -------------------------------------------------------------------------------------------------------------
696%        Ocean-Atmosphere Bulk formulae
697% -------------------------------------------------------------------------------------------------------------
698\subsection{Ocean-Atmosphere Bulk formulae}
699%\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk_algo\{\_ncar,\_coare,\_coare3p5,\_ecmwf}.F90})]
700\label{subsec:SBC_blk_ocean}
701
702Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
703COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
704their neutral transfer coefficients relationships with neutral wind.
705\begin{itemize}
706\item
707  NCAR (\np{ln\_NCAR}\forcode{ = .true.}):
708  The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
709  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
710  They use an inertial dissipative method to compute the turbulent transfer coefficients
711  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
712  This \citet{large.yeager_rpt04} dataset is available through
713  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
714  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
715  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
716\item
717  COARE 3.0 (\np{ln\_COARE\_3p0}\forcode{ = .true.}):
718  See \citet{fairall.bradley.ea_JC03} for more details
719\item
720  COARE 3.5 (\np{ln\_COARE\_3p5}\forcode{ = .true.}):
721  See \citet{edson.jampana.ea_JPO13} for more details
722\item
723  ECMWF (\np{ln\_ECMWF}\forcode{ = .true.}):
724  Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation.
725  Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}.
726\end{itemize}
727
728
729% -------------------------------------------------------------------------------------------------------------
730%        Ice-Atmosphere Bulk formulae
731% -------------------------------------------------------------------------------------------------------------
732\subsection{ Ice-Atmosphere Bulk formulae }
733\label{subsec:SBC_blk_ice}
734
735Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
736
737\begin{itemize}
738\item
739  Constant value (\np{constant\ value}\forcode{ Cd_ice = 1.4e-3 }):
740  default constant value used for momentum and heat neutral transfer coefficients
741\item
742  \citet{lupkes.gryanik.ea_JGR12} (\np{ln\_Cd\_L12}\forcode{ = .true.}):
743  This scheme adds a dependency on edges at leads, melt ponds and flows
744  of the constant neutral air-ice drag. After some approximations,
745  this can be resumed to a dependency on ice concentration (A).
746  This drag coefficient has a parabolic shape (as a function of ice concentration)
747  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.
748  It is theoretically applicable to all ice conditions (not only MIZ).
749\item
750  \citet{lupkes.gryanik_JGR15} (\np{ln\_Cd\_L15}\forcode{ = .true.}):
751  Alternative turbulent transfer coefficients formulation between sea-ice
752  and atmosphere with distinct momentum and heat coefficients depending
753  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
754  The parameterization is adapted from ECHAM6 atmospheric model.
755  Compared to Lupkes2012 scheme, it considers specific skin and form drags
756  to compute neutral transfer coefficients for both heat and momentum fluxes.
757  Atmospheric stability effect on transfer coefficient is also taken into account.
758\end{itemize}
759
760
761
762% ================================================================
763% Coupled formulation
764% ================================================================
765\section[Coupled formulation (\textit{sbccpl.F90})]
766{Coupled formulation (\protect\mdl{sbccpl})}
767\label{sec:SBC_cpl}
768%------------------------------------------namsbc_cpl----------------------------------------------------
769
770\nlst{namsbc_cpl} 
771%-------------------------------------------------------------------------------------------------------------
772
773In the coupled formulation of the surface boundary condition,
774the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
775while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
776the atmospheric component.
777
778A generalised coupled interface has been developed.
779It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
780It has been successfully used to interface \NEMO to most of the European atmospheric GCM
781(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
782(Weather Research and Forecasting Model).
783
784When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
785the whole carbon cycle is computed.
786In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
787(and need to be activated in \ngn{namsbc{\_}cpl} ).
788
789The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
790now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
791When indicating a multi-category coupling field in \ngn{namsbc{\_}cpl}, the number of categories will be determined by
792the number used in the sea ice model.
793In some limited cases, it may be possible to specify single category coupling fields even when
794the sea ice model is running with multiple categories -
795in this case, the user should examine the code to be sure the assumptions made are satisfactory.
796In cases where this is definitely not possible, the model should abort with an error message.
797
798
799
800% ================================================================
801%        Atmospheric pressure
802% ================================================================
803\section[Atmospheric pressure (\textit{sbcapr.F90})]
804{Atmospheric pressure (\protect\mdl{sbcapr})}
805\label{sec:SBC_apr}
806%------------------------------------------namsbc_apr----------------------------------------------------
807
808\nlst{namsbc_apr} 
809%-------------------------------------------------------------------------------------------------------------
810
811The optional atmospheric pressure can be used to force ocean and ice dynamics
812(\np{ln\_apr\_dyn}\forcode{ = .true.}, \ngn{namsbc} namelist).
813The input atmospheric forcing defined via \np{sn\_apr} structure (\ngn{namsbc\_apr} namelist)
814can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
815When used to force the dynamics, the atmospheric pressure is further transformed into
816an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
817\[
818  % \label{eq:SBC_ssh_ib}
819  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
820\]
821where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
822A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true.
823In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
824\ie the mean value of $\eta_{ib}$ is kept to zero at all time steps.
825
826The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
827For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
828(see \mdl{sbcssr} module).
829$\eta_{ib}$ can be written in the output.
830This can simplify altimetry data and model comparison as
831inverse barometer sea surface height is usually removed from these date prior to their distribution.
832
833When using time-splitting and BDY package for open boundaries conditions,
834the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
835\np{ln\_apr\_obc}  might be set to true.
836
837
838
839% ================================================================
840%        Surface Tides Forcing
841% ================================================================
842\section[Surface tides (\textit{sbctide.F90})]
843{Surface tides (\protect\mdl{sbctide})}
844\label{sec:SBC_tide}
845
846%------------------------------------------nam_tide---------------------------------------
847
848\nlst{nam_tide}
849%-----------------------------------------------------------------------------------------
850
851The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
852is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \forcode{.true.} in \ngn{nam\_tide}.
853This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that:
854\[
855  % \label{eq:PE_dyn_tides}
856  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
857  +g\nabla (\Pi_{eq} + \Pi_{sal})
858\]
859where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
860$\Pi_{sal}$ is a self-attraction and loading term (SAL).
861 
862The equilibrium tidal forcing is expressed as a sum over a subset of
863constituents chosen from the set of available tidal constituents
864defined in file \textit{SBC/tide.h90} (this comprises the tidal
865constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
866  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
867constituents are selected by including their names in the array
868\np{clname} in \ngn{nam\_tide} (e.g., \np{clname(1) = 'M2',
869  clname(2)='S2'} to select solely the tidal consituents \textit{M2}
870and \textit{S2}). Optionally, when \np{ln\_tide\_ramp} is set to
871\forcode{.true.}, the equilibrium tidal forcing can be ramped up
872linearly from zero during the initial \np{rdttideramp} days of the
873model run.
874
875The SAL term should in principle be computed online as it depends on
876the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
877discussion about the practical implementation of this term).
878Nevertheless, the complex calculations involved would make this
879computationally too expensive. Here, two options are available:
880$\Pi_{sal}$ generated by an external model can be read in
881(\np{ln\_read\_load=.true.}), or a ``scalar approximation'' can be
882used (\np{ln\_scal\_load=.true.}). In the latter case
883\[
884  \Pi_{sal} = \beta \eta,
885\]
886where $\beta$ (\np{rn\_scal\_load} with a default value of 0.094) is a
887spatially constant scalar, often chosen to minimize tidal prediction
888errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to
889\forcode{.false.} removes the SAL contribution.
890
891
892
893% ================================================================
894%        River runoffs
895% ================================================================
896\section[River runoffs (\textit{sbcrnf.F90})]
897{River runoffs (\protect\mdl{sbcrnf})}
898\label{sec:SBC_rnf}
899%------------------------------------------namsbc_rnf----------------------------------------------------
900
901\nlst{namsbc_rnf} 
902%-------------------------------------------------------------------------------------------------------------
903
904%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
905%Many models, however, have traditionally inserted river runoff to the top model cell.
906%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
907%throughout a nonzero depth has been motivated by the numerical and physical problems
908%that arise when the top grid cells are of the order of one meter. This situation is common in
909%coastal modelling and becomes more and more often open ocean and climate modelling
910%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
911%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
912
913
914%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
915%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
916%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
917%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
918%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
919%emp or emps and the changes made are below:
920
921
922%Rachel:
923River runoff generally enters the ocean at a nonzero depth rather than through the surface.
924Many models, however, have traditionally inserted river runoff to the top model cell.
925This was the case in \NEMO prior to the version 3.3,
926and was combined with an option to increase vertical mixing near the river mouth.
927
928However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
929This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
930\footnote{
931  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
932  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
933  see also \autoref{fig:SBC_dcy}.}.
934
935As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
936and for the temperature and salinity of the river to effect the surrounding ocean.
937The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
938along with the depth (in metres) which the river should be added to.
939
940Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and
941\np{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
942If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
943and/or taken as surface temperature respectively.
944
945The runoff value and attributes are read in in sbcrnf. 
946For temperature -999 is taken as missing data and the river temperature is taken to
947be the surface temperatue at the river point.
948For the depth parameter a value of -1 means the river is added to the surface box only,
949and a value of -999 means the river is added through the entire water column.
950After being read in the temperature and salinity variables are multiplied by the amount of runoff
951(converted into m/s) to give the heat and salt content of the river runoff.
952After the user specified depth is read ini,
953the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz\_rnf}.
954The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
955the bottom of the lowest box the river water is being added to
956(\ie the total depth that river water is being added to in the model).
957
958The mass/volume addition due to the river runoff is, at each relevant depth level, added to
959the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
960This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
961The sea surface height is calculated using the sum of the horizontal divergence terms,
962and so the river runoff indirectly forces an increase in sea surface height.
963
964The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
965This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
966The heat and salt content of the river runoff is not included in this step,
967and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
968the box and replaced by the same volume of river water with no corresponding heat and salt addition.
969
970For the linear free surface case, at the surface box the tracer advection causes a flux of water
971(of equal volume to the runoff) through the sea surface out of the domain,
972which causes a salt and heat flux out of the model.
973As such the volume of water does not change, but the water is diluted.
974
975For the non-linear free surface case, no flux is allowed through the surface.
976Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
977no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
978(The runoff addition to the top box along with the water being moved up through
979boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
980
981In trasbc the addition of heat and salt due to the river runoff is added.
982This is done in the same way for both vvl and non-vvl.
983The temperature and salinity are increased through the specified depth according to
984the heat and salt content of the river.
985
986In the non-linear free surface case (vvl),
987near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
988so that the original ratios of grid box heights are restored.
989In doing this water is moved into boxes below, throughout the water column,
990so the large volume addition to the surface box is spread between all the grid boxes.
991
992It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
993\ie modelling the Baltic flow in and out of the North Sea.
994When the flow is out of the domain there is no change in temperature and salinity,
995regardless of the namelist options used,
996as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
997
998
999%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1000
1001%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1002
1003%\colorbox{yellow}{river mouths{\ldots}}
1004
1005%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1006%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1007%ENDIF
1008
1009%\gmcomment{  word doc of runoffs:
1010%
1011%In the current \NEMO setup river runoff is added to emp fluxes, these are then applied at just the sea surface as a volume change (in the variable volume case this is a literal volume change, and in the linear free surface case the free surface is moved) and a salt flux due to the concentration/dilution effect.  There is also an option to increase vertical mixing near river mouths; this gives the effect of having a 3d river.  All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.
1012%Our aim was to code the option to specify the temperature and salinity of river runoff, (as well as the amount), along with the depth that the river water will affect.  This would make it possible to model low salinity outflow, such as the Baltic, and would allow the ocean temperature to be affected by river runoff. 
1013
1014%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
1015
1016%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the tra_sbc module.  We decided to separate them throughout the code, so that the variable emp represented solely evaporation minus precipitation fluxes, and a new 2d variable rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use emp or emps and the changes made are below:
1017
1018
1019
1020% ================================================================
1021%        Ice shelf melting
1022% ================================================================
1023\section[Ice shelf melting (\textit{sbcisf.F90})]
1024{Ice shelf melting (\protect\mdl{sbcisf})}
1025\label{sec:SBC_isf}
1026%------------------------------------------namsbc_isf----------------------------------------------------
1027
1028\nlst{namsbc_isf}
1029%--------------------------------------------------------------------------------------------------------
1030
1031The namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation.
1032Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1033The different options are illustrated in \autoref{fig:SBC_isf}.
1034
1035\begin{description}
1036
1037  \item[\np{nn\_isf}\forcode{ = 1}]:
1038  The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{ = .true.} needed).
1039  The fwf and heat flux are depending of the local water properties.
1040 
1041  Two different bulk formulae are available:
1042
1043   \begin{description}
1044   \item[\np{nn\_isfblk}\forcode{ = 1}]:
1045     The melt rate is based on a balance between the upward ocean heat flux and
1046     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
1047   \item[\np{nn\_isfblk}\forcode{ = 2}]:
1048     The melt rate and the heat flux are based on a 3 equations formulation
1049     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1050     A complete description is available in \citet{jenkins_JGR91}.
1051   \end{description}
1052
1053     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1054     Its thickness is defined by \np{rn\_hisf\_tbl}.
1055     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m.
1056     Then, the fluxes are spread over the same thickness (ie over one or several cells).
1057     If \np{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.
1058     This can lead to super-cool temperature in the top cell under melting condition.
1059     If \np{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
1060
1061     Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1062     There are 3 different ways to compute the exchange coeficient:
1063   \begin{description}
1064        \item[\np{nn\_gammablk}\forcode{ = 0}]:
1065     The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}.
1066\[
1067  % \label{eq:sbc_isf_gamma_iso}
1068\gamma^{T} = \np{rn\_gammat0}
1069\]
1070\[
1071\gamma^{S} = \np{rn\_gammas0}
1072\]
1073     This is the recommended formulation for ISOMIP.
1074   \item[\np{nn\_gammablk}\forcode{ = 1}]:
1075     The salt and heat exchange coefficients are velocity dependent and defined as
1076\[
1077\gamma^{T} = \np{rn\_gammat0} \times u_{*}
1078\]
1079\[
1080\gamma^{S} = \np{rn\_gammas0} \times u_{*}
1081\]
1082     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
1083     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1084   \item[\np{nn\_gammablk}\forcode{ = 2}]:
1085     The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1086\[
1087\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1088\]
1089     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
1090     $\Gamma_{Turb}$ the contribution of the ocean stability and
1091     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1092     See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1093     This formulation has not been extensively tested in NEMO (not recommended).
1094   \end{description}
1095  \item[\np{nn\_isf}\forcode{ = 2}]:
1096   The ice shelf cavity is not represented.
1097   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1098   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1099   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1100   (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}).
1101   The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
1102  \item[\np{nn\_isf}\forcode{ = 3}]:
1103   The ice shelf cavity is not represented.
1104   The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1105   the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and
1106   the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
1107   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1108  \item[\np{nn\_isf}\forcode{ = 4}]:
1109   The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed).
1110   However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
1111   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1112   As in \np{nn\_isf}\forcode{ = 1}, the fluxes are spread over the top boundary layer thickness (\np{rn\_hisf\_tbl})\\
1113\end{description}
1114
1115$\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on
1116the water mass properties, ocean velocities and depth.
1117This flux is thus highly dependent of the model resolution (horizontal and vertical),
1118realism of the water masses onto the shelf ...\\
1119
1120$\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file.
1121You have total control of the fwf forcing.
1122This can be useful if the water masses on the shelf are not realistic or
1123the resolution (horizontal/vertical) are too coarse to have realistic melting or
1124for studies where you need to control your heat and fw input.\\ 
1125
1126The ice shelf melt is implemented as a volume flux as for the runoff.
1127The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1128the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1129See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1130
1131%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1132\begin{figure}[!t]
1133  \begin{center}
1134    \includegraphics[width=\textwidth]{Fig_SBC_isf}
1135    \caption{
1136      \protect\label{fig:SBC_isf}
1137      Illustration the location where the fwf is injected and whether or not the fwf is interactif or not depending of \np{nn\_isf}.
1138    }
1139  \end{center}
1140\end{figure}
1141%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1142
1143
1144
1145% ================================================================
1146%        Ice sheet coupling
1147% ================================================================
1148\section{Ice sheet coupling}
1149\label{sec:SBC_iscpl}
1150%------------------------------------------namsbc_iscpl----------------------------------------------------
1151
1152\nlst{namsbc_iscpl}
1153%--------------------------------------------------------------------------------------------------------
1154
1155Ice sheet/ocean coupling is done through file exchange at the restart step.
1156At each restart step:
1157
1158\begin{description}
1159\item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1160\item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools.
1161\item[Step 3]: NEMO run for a specific period and output the average melt rate over the period.
1162\item[Step 4]: the ice sheet model run using the melt rate outputed in step 4.
1163\item[Step 5]: go back to 1.
1164\end{description}
1165
1166If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with
1167potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1168The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1169
1170\begin{description}
1171\item[Thin a cell down]:
1172  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1173  ($bt_b=bt_n$).
1174\item[Enlarge  a cell]:
1175  See case "Thin a cell down"
1176\item[Dry a cell]:
1177  mask, T/S, U/V and ssh are set to 0.
1178  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1179\item[Wet a cell]:
1180  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1181  If no neighbours, T/S is extrapolated from old top cell value.
1182  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1183\item[Dry a column]:
1184   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1185\item[Wet a column]:
1186  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1187  If no neighbour, T/S/U/V and mask set to 0.
1188\end{description}
1189
1190Furthermore, as the before and now fields are not compatible (modification of the geometry),
1191the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1192
1193The horizontal extrapolation to fill new cell with realistic value is called \np{nn\_drown} times.
1194It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,
1195the code will be unable to fill all the new wet cells properly.
1196The default number is set up for the MISOMIP idealised experiments.
1197This coupling procedure is able to take into account grounding line and calving front migration.
1198However, it is a non-conservative processe.
1199This could lead to a trend in heat/salt content and volume.\\
1200
1201In order to remove the trend and keep the conservation level as close to 0 as possible,
1202a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}.
1203The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1204A correction increment is computed and apply each time step during the next \np{rn\_fiscpl} time steps.
1205For safety, it is advised to set \np{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1206The 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).
1207
1208
1209
1210% ================================================================
1211%        Handling of icebergs
1212% ================================================================
1213\section{Handling of icebergs (ICB)}
1214\label{sec:ICB_icebergs}
1215%------------------------------------------namberg----------------------------------------------------
1216
1217\nlst{namberg}
1218%-------------------------------------------------------------------------------------------------------------
1219
1220Icebergs are modelled as lagrangian particles in NEMO \citep{marsh.ivchenko.ea_GMD15}.
1221Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1222(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO).
1223Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1224described in the \ngn{namberg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1225Each class has an associated scaling (\np{rn\_mass\_scaling}),
1226which is an integer representing how many icebergs of this class are being described as one lagrangian point
1227(this reduces the numerical problem of tracking every single iceberg).
1228They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}.
1229
1230Two initialisation schemes are possible.
1231\begin{description}
1232\item[\np{nn\_test\_icebergs}~$>$~0]
1233  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1234  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1235  which an iceberg is generated at the beginning of the run.
1236  (Note that this happens each time the timestep equals \np{nn\_nit000}.)
1237  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of
1238  the geographical box: lonmin,lonmax,latmin,latmax
1239\item[\np{nn\_test\_icebergs}\forcode{ = -1}]
1240  In this scheme, the model reads a calving file supplied in the \np{sn\_icb} parameter.
1241  This should be a file with a field on the configuration grid (typically ORCA)
1242  representing ice accumulation rate at each model point.
1243  These should be ocean points adjacent to land where icebergs are known to calve.
1244  Most points in this input grid are going to have value zero.
1245  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1246  At each time step, a test is performed to see if there is enough ice mass to
1247  calve an iceberg of each class in order (1 to 10).
1248  Note that this is the initial mass multiplied by the number each particle represents (\ie the scaling).
1249  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1250\end{description}
1251
1252Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1253The latter act to disintegrate the iceberg.
1254This is either all melted freshwater,
1255or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1256which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1257Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
1258
1259Extensive diagnostics can be produced.
1260Separate output files are maintained for human-readable iceberg information.
1261A separate file is produced for each processor (independent of \np{ln\_ctl}).
1262The amount of information is controlled by two integer parameters:
1263\begin{description}
1264\item[\np{nn\_verbose\_level}] takes a value between one and four and
1265  represents an increasing number of points in the code at which variables are written,
1266  and an increasing level of obscurity.
1267\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1268\end{description}
1269
1270Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1271A non-zero value represents how many timesteps between writes of information into the output file.
1272These output files are in NETCDF format.
1273When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1274Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1275So care is needed to recreate data for individual icebergs,
1276since its trajectory data may be spread across multiple files.
1277
1278
1279
1280% =============================================================================================================
1281%        Interactions with waves (sbcwave.F90, ln_wave)
1282% =============================================================================================================
1283\section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})]
1284{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
1285\label{sec:SBC_wave}
1286%------------------------------------------namsbc_wave--------------------------------------------------------
1287
1288\nlst{namsbc_wave}
1289%-------------------------------------------------------------------------------------------------------------
1290
1291Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate
1292physical processes related to ocean surface waves, namely the surface stress modified by growth and
1293dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1294tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1295the wind stress.
1296
1297Physical processes related to ocean surface waves can be accounted by setting the logical variable
1298\np{ln\_wave} \forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for
1299different processes should be activated as explained in the following sections.
1300
1301Wave fields can be provided either in forced or coupled mode:
1302\begin{description}
1303\item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist
1304for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1305Input Data generic Interface (see \autoref{sec:SBC_input}).
1306\item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 
1307in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist.
1308\end{description}
1309
1310
1311% ----------------------------------------------------------------
1312% Neutral drag coefficient from wave model (ln_cdgw)
1313
1314% ----------------------------------------------------------------
1315\subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})]
1316{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
1317\label{subsec:SBC_wave_cdgw}
1318
1319The neutral surface drag coefficient provided from an external data source (\ie a wave model),
1320can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist.
1321Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1322the drag coefficient is computed according to the stable/unstable conditions of the
1323air-sea interface following \citet{large.yeager_rpt04}.
1324
1325
1326% ----------------------------------------------------------------
1327% 3D Stokes Drift (ln_sdw, nn_sdrift)
1328% ----------------------------------------------------------------
1329\subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})]
1330{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
1331\label{subsec:SBC_wave_sdw}
1332
1333The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1334It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1335and the current measured at a fixed point (Eulerian velocity).
1336As waves travel, the water particles that make up the waves travel in orbital motions but
1337without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1338at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1339An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1340representation of surface physics in ocean general circulation models. %GS: reference needed
1341The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1342
1343\[
1344  % \label{eq:sbc_wave_sdw}
1345  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1346  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1347  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1348\]
1349
1350where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1351$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1352$k$ is the mean wavenumber defined as:
1353$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1354
1355In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1356and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1357To simplify, it is customary to use approximations to the full Stokes profile.
1358Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1359are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift
1360$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1361and makes possible the estimation of the surface Stokes drift for random directional waves in
1362realistic wave conditions:
1363
1364\begin{description}
1365\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by
1366\citet{breivik.janssen.ea_JPO14}:
1367
1368\[
1369  % \label{eq:sbc_wave_sdw_0a}
1370  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1371\]
1372
1373where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1374
1375\[
1376  % \label{eq:sbc_wave_sdw_0b}
1377  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1378  \quad \text{and }\
1379  T_{st} = \frac{1}{16} \bar{\omega} H_s^2 
1380\]
1381
1382where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1383
1384\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a
1385reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1386\citep{breivik.bidlot.ea_OM16}:
1387
1388\[
1389  % \label{eq:sbc_wave_sdw_1}
1390  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1391  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1392\]
1393
1394where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1395
1396\item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1
1397but using the wave frequency from a wave model.
1398
1399\end{description}
1400
1401The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1402and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1403
1404\[
1405  % \label{eq:sbc_wave_eta_sdw}
1406  \frac{\partial{\eta}}{\partial{t}} =
1407  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1408\]
1409
1410The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1411for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1412that is induced by the three-dimensional Stokes velocity.
1413The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1414can be formulated as follows:
1415
1416\[
1417  % \label{eq:sbc_wave_tra_sdw}
1418  \frac{\partial{c}}{\partial{t}} =
1419  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1420\]
1421
1422
1423% ----------------------------------------------------------------
1424% Stokes-Coriolis term (ln_stcor)
1425% ----------------------------------------------------------------
1426\subsection[Stokes-Coriolis term (\texttt{ln\_stcor})]
1427{Stokes-Coriolis term (\protect\np{ln\_stcor})}
1428\label{subsec:SBC_wave_stcor}
1429
1430In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1431in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1432This additional force may have impact on the Ekman turning of the surface current.
1433In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1434approximations described in \autoref{subsec:SBC_wave_sdw}),
1435\np{ln\_stcor}\forcode{ = .true.} has to be set.
1436
1437
1438% ----------------------------------------------------------------
1439% Waves modified stress (ln_tauwoc, ln_tauw)
1440% ----------------------------------------------------------------
1441\subsection[Wave modified stress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})]
1442{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}
1443\label{subsec:SBC_wave_tauw}
1444
1445The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1446into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1447available for forcing the mean circulation, while in the opposite case of a decaying sea
1448state, more momentum is available for forcing the ocean.
1449Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1450but in practice, an equilibrium sea state is a fairly rare event.
1451So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1452
1453\[
1454  % \label{eq:sbc_wave_tauoc}
1455  \tau_{oc,a} = \tau_a - \tau_w
1456\]
1457
1458where $\tau_a$ is the atmospheric surface stress;
1459$\tau_w$ is the atmospheric stress going into the waves defined as:
1460
1461\[
1462  % \label{eq:sbc_wave_tauw}
1463  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1464\]
1465
1466where: $c_p$ is the phase speed of the gravity waves,
1467$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1468the physics of ocean waves. The first one, $S_{in}$, describes the generation
1469of ocean waves by wind and therefore represents the momentum and energy transfer
1470from air to ocean waves; the second term $S_{nl}$ denotes
1471the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$ 
1472describes the dissipation of waves by processes such as white-capping, large scale breaking
1473eddy-induced damping.
1474
1475The wave stress derived from an external wave model can be provided either through the normalized
1476wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and
1477meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}.
1478
1479
1480
1481% ================================================================
1482% Miscellanea options
1483% ================================================================
1484\section{Miscellaneous options}
1485\label{sec:SBC_misc}
1486
1487
1488% -------------------------------------------------------------------------------------------------------------
1489%        Diurnal cycle
1490% -------------------------------------------------------------------------------------------------------------
1491\subsection[Diurnal cycle (\textit{sbcdcy.F90})]
1492{Diurnal cycle (\protect\mdl{sbcdcy})}
1493\label{subsec:SBC_dcy}
1494%------------------------------------------namsbc-------------------------------------------------------------
1495%
1496\nlst{namsbc} 
1497%-------------------------------------------------------------------------------------------------------------
1498
1499%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1500\begin{figure}[!t]
1501  \begin{center}
1502    \includegraphics[width=\textwidth]{Fig_SBC_diurnal}
1503    \caption{
1504      \protect\label{fig:SBC_diurnal}
1505      Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values.
1506      The reconstructed diurnal cycle (black line) is chosen as
1507      the mean value of the analytical cycle (blue line) over a time step,
1508      not as the mid time step value of the analytically cycle (red square).
1509      From \citet{bernie.guilyardi.ea_CD07}.
1510    }
1511  \end{center}
1512\end{figure}
1513%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1514
1515\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.
1516%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1517Nevertheless, 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}.
1518Furthermore, only the knowledge of daily mean value of SWF is needed,
1519as higher frequency variations can be reconstructed from them,
1520assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1521The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO by
1522setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when
1523using a bulk formulation (\np{ln\_blk}\forcode{ = .true.}) or
1524the flux formulation (\np{ln\_flx}\forcode{ = .true.}).
1525The reconstruction is performed in the \mdl{sbcdcy} module.
1526The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1527The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1528a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1529The use of diurnal cycle reconstruction requires the input SWF to be daily
1530(\ie a frequency of 24 hours and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1531Furthermore, it is recommended to have a least 8 surface module time steps per day,
1532that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1533An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1534one every 2~hours (from 1am to 11pm).
1535
1536%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1537\begin{figure}[!t]
1538  \begin{center}
1539    \includegraphics[width=\textwidth]{Fig_SBC_dcy}
1540    \caption{
1541      \protect\label{fig:SBC_dcy}
1542      Example of recontruction of the diurnal cycle variation of short wave flux from
1543      daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1544      The display is on (i,j) plane.
1545    }
1546  \end{center}
1547\end{figure}
1548%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1549
1550Note also that the setting a diurnal cycle in SWF is highly recommended when
1551the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1552an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1553
1554
1555% -------------------------------------------------------------------------------------------------------------
1556%        Rotation of vector pairs onto the model grid directions
1557% -------------------------------------------------------------------------------------------------------------
1558\subsection{Rotation of vector pairs onto the model grid directions}
1559\label{subsec:SBC_rotation}
1560
1561When using a flux (\np{ln\_flx}\forcode{ = .true.}) or bulk (\np{ln\_blk}\forcode{ = .true.}) formulation,
1562pairs of vector components can be rotated from east-north directions onto the local grid directions.
1563This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1564be defined relative to a rectilinear grid.
1565To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1566The eastward component must start with "U" and the northward component with "V". 
1567The remaining characters in the strings are used to identify which pair of components go together.
1568So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1569rotate them on to the model grid directions;
1570"U2" and "V2" could be used against a second pair of components, and so on.
1571The extra characters used in the strings are arbitrary.
1572The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1573
1574
1575% -------------------------------------------------------------------------------------------------------------
1576%        Surface restoring to observed SST and/or SSS
1577% -------------------------------------------------------------------------------------------------------------
1578\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]
1579{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1580\label{subsec:SBC_ssr}
1581%------------------------------------------namsbc_ssr----------------------------------------------------
1582
1583\nlst{namsbc_ssr} 
1584%-------------------------------------------------------------------------------------------------------------
1585
1586Options are defined through the \ngn{namsbc\_ssr} namelist variables.
1587On forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}),
1588a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1589\[
1590  % \label{eq:sbc_dmp_q}
1591  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1592\]
1593where SST is a sea surface temperature field (observed or climatological),
1594$T$ is the model surface layer temperature and
1595$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1596For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1597This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1598
1599In the fresh water budget, a feedback term can also be added.
1600Converted into an equivalent freshwater flux, it takes the following expression :
1601
1602\begin{equation}
1603  \label{eq:sbc_dmp_emp}
1604  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1605  {\left.S\right|_{k=1}}
1606\end{equation}
1607
1608where $\textit{emp}_{o }$ is a net surface fresh water flux
1609(observed, climatological or an atmospheric model product),
1610\textit{SSS}$_{Obs}$ is a sea surface salinity
1611(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1612$\left.S\right|_{k=1}$ is the model surface layer salinity and
1613$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1614Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as
1615the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1616The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1617reduce the uncertainties we have on the observed freshwater budget.
1618
1619
1620% -------------------------------------------------------------------------------------------------------------
1621%        Handling of ice-covered area
1622% -------------------------------------------------------------------------------------------------------------
1623\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1624\label{subsec:SBC_ice-cover}
1625
1626The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1627There are several way to handle sea-ice in the system depending on
1628the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist.
1629\begin{description}
1630\item[nn{\_}ice = 0]
1631  there will never be sea-ice in the computational domain.
1632  This is a typical namelist value used for tropical ocean domain.
1633  The surface fluxes are simply specified for an ice-free ocean.
1634  No specific things is done for sea-ice.
1635\item[nn{\_}ice = 1]
1636  sea-ice can exist in the computational domain, but no sea-ice model is used.
1637  An observed ice covered area is read in a file.
1638  Below this area, the SST is restored to the freezing point and
1639  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1640  The associated modification of the freshwater fluxes are done in such a way that
1641  the change in buoyancy fluxes remains zero.
1642  This prevents deep convection to occur when trying to reach the freezing point
1643  (and so ice covered area condition) while the SSS is too large.
1644  This manner of managing sea-ice area, just by using a IF case,
1645  is usually referred as the \textit{ice-if} model.
1646  It can be found in the \mdl{sbcice{\_}if} module.
1647\item[nn{\_}ice = 2 or more]
1648  A full sea ice model is used.
1649  This model computes the ice-ocean fluxes,
1650  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1651  provide the surface averaged ocean fluxes.
1652  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1653  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value
1654  (\ie $2$ for SI3 or $3$ for CICE).
1655\end{description}
1656
1657% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1658%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1659
1660
1661% -------------------------------------------------------------------------------------------------------------
1662%        CICE-ocean Interface
1663% -------------------------------------------------------------------------------------------------------------
1664\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]
1665{Interface to CICE (\protect\mdl{sbcice\_cice})}
1666\label{subsec:SBC_cice}
1667
1668It is possible to couple a regional or global NEMO configuration (without AGRIF)
1669to the CICE sea-ice model by using \key{cice}.
1670The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1671the additional 'hadgem3' drivers will be required, even with the latest code release.
1672Input grid files consistent with those used in NEMO will also be needed,
1673and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1674(seek advice from UKMO if necessary).
1675Currently, the code is only designed to work when using the NCAR forcing option for NEMO %GS: still true ?
1676(with \textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE name-list),
1677or alternatively when NEMO is coupled to the HadGAM3 atmosphere model
1678(with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}).
1679The code is intended to be used with \np{nn\_fsbc} set to 1
1680(although coupling ocean and ice less frequently should work,
1681it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1682the user should check that results are not significantly different to the standard case).
1683
1684There are two options for the technical coupling between NEMO and CICE.
1685The standard version allows complete flexibility for the domain decompositions in the individual models,
1686but this is at the expense of global gather and scatter operations in the coupling which
1687become very expensive on larger numbers of processors.
1688The alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that
1689the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1690and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1691allows much more efficient direct coupling on individual processors.
1692This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1693there is no sea ice.
1694
1695
1696% -------------------------------------------------------------------------------------------------------------
1697%        Freshwater budget control
1698% -------------------------------------------------------------------------------------------------------------
1699\subsection[Freshwater budget control (\textit{sbcfwb.F90})]
1700{Freshwater budget control (\protect\mdl{sbcfwb})}
1701\label{subsec:SBC_fwb}
1702
1703For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1704prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1705In \NEMO, two way of controlling the freshwater budget are proposed:
1706 
1707\begin{description}
1708\item[\np{nn\_fwb}\forcode{ = 0}]
1709  no control at all.
1710  The mean sea level is free to drift, and will certainly do so.
1711\item[\np{nn\_fwb}\forcode{ = 1}]
1712  global mean \textit{emp} set to zero at each model time step.
1713  %GS: comment below still relevant ?
1714  %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).
1715\item[\np{nn\_fwb}\forcode{ = 2}]
1716  freshwater budget is adjusted from the previous year annual mean budget which
1717  is read in the \textit{EMPave\_old.dat} file.
1718  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1719  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1720\end{description}
1721
1722% Griffies doc:
1723% When running ocean-ice simulations, we are not explicitly representing land processes,
1724% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1725% it is important to balance the hydrological cycle in ocean-ice models.
1726% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1727% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1728% a chosen time scale.
1729% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1730% so that there is always a zero net input of water to the ocean-ice system.
1731% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1732% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1733% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1734% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1735% and ice models when aiming to balance the hydrological cycle.
1736% 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,
1737% not the water in any one sub-component. As an extreme example to illustrate the issue,
1738% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1739% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1740% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1741% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1742% in ocean-ice models.
1743
1744
1745\biblio
1746
1747\pindex
1748
1749\end{document}
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