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chap_SBC.tex in NEMO/trunk/doc/latex/NEMO/subfiles – NEMO

source: NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex @ 11598

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1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4
5\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
6\label{chap:SBC}
7
8\thispagestyle{plain}
9
10\chaptertoc
11
12\paragraph{Changes record} ~\\
13
14{\footnotesize
15  \begin{tabularx}{\textwidth}{l||X|X}
16    Release & Author(s) & Modifications \\
17    \hline
18    {\em   4.0} & {\em ...} & {\em ...} \\
19    {\em   3.6} & {\em ...} & {\em ...} \\
20    {\em   3.4} & {\em ...} & {\em ...} \\
21    {\em <=3.4} & {\em ...} & {\em ...}
22  \end{tabularx}
23}
24
25\clearpage
26
27\begin{listing}
28  \nlst{namsbc}
29  \caption{\forcode{&namsbc}}
30  \label{lst:namsbc}
31\end{listing}
32
33The ocean needs seven fields as surface boundary condition:
34
35\begin{itemize}
36\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
37\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
38\item the surface freshwater budget $\left( {\textit{emp}} \right)$
39\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
40\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
41\end{itemize}
42
43Four different ways are available to provide the seven fields to the ocean. They are controlled by
44namelist \nam{sbc}{sbc} variables:
45
46\begin{itemize}
47\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk} with four possible bulk algorithms),
48\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
49\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
50(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
51\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
52\end{itemize}
53
54The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
55
56When the fields are supplied from data files (bulk, flux and mixed formulations),
57the input fields do not need to be supplied on the model grid.
58Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
59the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
60If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
61should be masked or filled to avoid spurious results in proximity of the coasts, as
62large sea-land gradients characterize most of the atmospheric variables.
63
64In addition, the resulting fields can be further modified using several namelist options.
65These options control:
66
67\begin{itemize}
68\item the rotation of vector components supplied relative to an east-north coordinate system onto
69  the local grid directions in the model,
70\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
71\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
72\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
73  (\np[=0..3]{nn_ice}{nn\_ice}),
74\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
75\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
76  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
77\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
78  (\np[=0..2]{nn_fwb}{nn\_fwb}),
79\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
80  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
81\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
82\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
83\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
84\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
85\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
86\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
87\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
88\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
89\item the atmospheric surface pressure gradient effect on ocean and ice dynamics (\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn} with namelist \nam{sbc_apr}{sbc\_apr}),
90\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
91\end{itemize}
92
93In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
94Then we present the three ways of providing the surface boundary conditions,
95followed by the description of the atmospheric pressure and the river runoff.
96Next, the scheme for interpolation on the fly is described.
97Finally, the different options that further modify the fluxes applied to the ocean are discussed.
98One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
99which act as drifting sources of fresh water.
100Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
101which provides additional sources of fresh water.
102
103%% =================================================================================================
104\section{Surface boundary condition for the ocean}
105\label{sec:SBC_ocean}
106
107The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
108It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
109the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
110As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
111\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
112
113The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
114$Q_{ns}$ and $Q_{sr}$, respectively.
115The former is the non penetrative part of the heat flux
116(\ie\ the sum of sensible, latent and long wave heat fluxes plus
117the heat content of the mass exchange between the ocean and sea-ice).
118It is applied in \mdl{trasbc} module as a surface boundary condition trend of
119the first level temperature time evolution equation
120(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
121The latter is the penetrative part of the heat flux.
122It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
123\np[=.true.]{ln_traqsr}{ln\_traqsr}.
124The way the light penetrates inside the water column is generally a sum of decreasing exponentials
125(see \autoref{subsec:TRA_qsr}).
126
127The surface freshwater budget is provided by the \textit{emp} field.
128It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
129possibly with the sea-ice and ice shelves (freezing minus melting of ice).
130It affects the ocean in two different ways:
131$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
132a volume flux, and
133$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
134the mass exchanged with atmosphere, sea-ice and ice shelves.
135
136%\colorbox{yellow}{Miss: }
137%
138%A extensive description of all namsbc namelist (parameter that have to be
139%created!)
140%
141%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
142%ssv) \ie\ information required by flux computation or sea-ice
143%
144%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
145%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
146%
147%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
148%
149%Fluxes update only each nf\_sbc time step (namsbc) explain relation
150%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
151%nf\_sbc
152%
153%Explain here all the namlist namsbc variable{\ldots}.
154%
155% explain : use or not of surface currents
156%
157%\colorbox{yellow}{End Miss }
158
159The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
160the surface currents, temperature and salinity.
161These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
162these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
163
164\begin{table}[tb]
165  \centering
166  \begin{tabular}{|l|l|l|l|}
167    \hline
168    Variable description                           & Model variable  & Units  & point                 \\
169    \hline
170    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
171    \hline
172    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
173    \hline
174    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
175    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
176  \end{tabular}
177  \caption[Ocean variables provided to the surface module)]{
178    Ocean variables provided to the surface module (\texttt{SBC}).
179    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
180    \ie\ the frequency of computation of surface fluxes.}
181  \label{tab:SBC_ssm}
182\end{table}
183
184%\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
185
186%% =================================================================================================
187\section{Input data generic interface}
188\label{sec:SBC_input}
189
190A generic interface has been introduced to manage the way input data
191(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
192This task is achieved by \mdl{fldread}.
193The module is designed with four main objectives in mind:
194\begin{enumerate}
195\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
196  and according to the different calendars available in the model.
197\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
198\item make the run duration independent from the period cover by the input files.
199\item provide a simple user interface and a rather simple developer interface by
200  limiting the number of prerequisite informations.
201\end{enumerate}
202
203As a result, the user has only to fill in for each variable a structure in the namelist file to
204define the input data file and variable names, the frequency of the data (in hours or months),
205whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
206and three additional parameters for the on-the-fly interpolation.
207When adding a new input variable, the developer has to add the associated structure in the namelist,
208read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
209and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
210
211The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
212(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
213if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
214
215Note that when an input data is archived on a disc which is accessible directly from the workspace where
216the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
217By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
218
219%% =================================================================================================
220\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
221\label{subsec:SBC_fldread}
222
223The structure associated with an input variable contains the following information:
224\begin{forlines}
225!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
226!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
227\end{forlines}
228where
229\begin{description}
230\item [File name]: the stem name of the NetCDF file to be opened.
231  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
232  by date information and possibly a prefix (when using AGRIF).
233  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
234  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
235  \begin{table}[htbp]
236    \centering
237    \begin{tabular}{|l|c|c|c|}
238      \hline
239                                  &  daily or weekLL     &  monthly           &  yearly        \\
240      \hline
241      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
242      \hline
243      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
244      \hline
245    \end{tabular}
246    \caption[Naming nomenclature for climatological or interannual input file]{
247      Naming nomenclature for climatological or interannual input file,
248      as a function of the open/close frequency.
249      The stem name is assumed to be 'fn'.
250      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
251      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
252      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
253      always coded with 4 or 2 digits.
254      Note that (1) in mpp, if the file is split over each subdomain,
255      the suffix '.nc' is replaced by '\_PPPP.nc',
256      where 'PPPP' is the process number coded with 4 digits;
257      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
258    }
259    \label{tab:SBC_fldread}
260  \end{table}
261\item [Record frequency]: the frequency of the records contained in the input file.
262  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
263  (for example -1 for monthly forcing or -12 for annual forcing).
264  Note that this frequency must REALLY be an integer and not a real.
265  On some computers, setting it to '24.' can be interpreted as 240!
266\item [Variable name]: the name of the variable to be read in the input NetCDF file.
267\item [Time interpolation]: a logical to activate, or not, the time interpolation.
268  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
269  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
270  00h00'00'' to 23h59'59".
271  If set to 'true', the forcing will have a broken line shape.
272  Records are assumed to be dated at the middle of the forcing period.
273  For example, when using a daily forcing with time interpolation,
274  linear interpolation will be performed between mid-day of two consecutive days.
275\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
276  or an interannual forcing which will requires additional files if
277  the period covered by the simulation exceeds the one of the file.
278  See the above file naming strategy which impacts the expected name of the file to be opened.
279\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
280  Four cases are coded:
281  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
282  means the forcing files will contain data for one day, one week, one month or one year.
283  Files are assumed to contain data from the beginning of the open/close period.
284  For example, the first record of a yearly file containing daily data is Jan 1st even if
285  the experiment is not starting at the beginning of the year.
286\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
287  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
288\end{description}
289
290Additional remarks:\\
291(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
292The only tricky point is therefore to specify the date at which we need to do the interpolation and
293the date of the records read in the input files.
294Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
295For example, for an experiment starting at 0h00'00" with a one-hour time-step,
296a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
297However, for forcing data related to the surface module,
298values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
299For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
300The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
301In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
302(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
303The calendar associated with the forcing field is build according to the information provided by
304user in the record frequency, the open/close frequency and the type of temporal interpolation.
305For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
306start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
307(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
308interpolating data with the first (last) record of the open/close period.
309For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
310the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
311Dec 31st 12h00'00" and Jan 1st 12h00'00".
312If the forcing is climatological, Dec and Jan will be keep-up from the same year.
313However, if the forcing is not climatological, at the end of
314the open/close period, the code will automatically close the current file and open the next one.
315Note that, if the experiment is starting (ending) at the beginning (end) of
316an open/close period, we do accept that the previous (next) file is not existing.
317In this case, the time interpolation will be performed between two identical values.
318For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
319we do accept that the file related to year Y-1 is not existing.
320The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
321If the file of year Y-1 exists, the code will read its last record.
322Therefore, this file can contain only one record corresponding to Dec 31st,
323a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
324
325%% =================================================================================================
326\subsection{Interpolation on-the-fly}
327\label{subsec:SBC_iof}
328
329Interpolation on the Fly allows the user to supply input files required for the surface forcing on
330grids other than the model grid.
331To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
332interpolate from the data grid to the model grid.
333The original development of this code used the SCRIP package
334(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
335In principle, any package such as CDO can be used to generate the weights, but the variables in
336the input weights file must have the same names and meanings as assumed by the model.
337Two methods are currently available: bilinear and bicubic interpolations.
338Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
339the input file and substitute the corresponding values with the average of the 8 neighbouring points in
340the native external grid.
341Only "sea points" are considered for the averaging.
342The land/sea mask file must be provided in the structure associated with the input variable.
343The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
344the associated variables and should be equal to 1 over land and 0 elsewhere.
345The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
346Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
347
348%% =================================================================================================
349\subsubsection{Bilinear interpolation}
350\label{subsec:SBC_iof_bilinear}
351
352The input weights file in this case has two sets of variables:
353src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
354The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
355Each src value is an integer corresponding to the index of a point in the input grid when
356written as a one dimensional array.
357For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
358There are four of each variable because bilinear interpolation uses the four points defining
359the grid box containing the point to be interpolated.
360All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
361generate a value for point (i,j) in the model.
362
363Symbolically, the algorithm used is:
364\[
365  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
366\]
367where function idx() transforms a one dimensional index src(k) into a two dimensional index,
368and wgt(1) corresponds to variable "wgt01" for example.
369
370%% =================================================================================================
371\subsubsection{Bicubic interpolation}
372\label{subsec:SBC_iof_bicubic}
373
374Again, there are two sets of variables: "src" and "wgt".
375But in this case, there are 16 of each.
376The symbolic algorithm used to calculate values on the model grid is now:
377
378\[
379  \begin{split}
380    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
381    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
382    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
383    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
384  \end{split}
385\]
386The gradients here are taken with respect to the horizontal indices and not distances since
387the spatial dependency has been included into the weights.
388
389%% =================================================================================================
390\subsubsection{Implementation}
391\label{subsec:SBC_iof_imp}
392
393To activate this option, a non-empty string should be supplied in
394the weights filename column of the relevant namelist;
395if this is left as an empty string no action is taken.
396In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
397as and when they are first required.
398This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
399inspecting a global attribute stored in the weights input file.
400This attribute must be called "ew\_wrap" and be of integer type.
401If it is negative, the input non-model grid is assumed to be not cyclic.
402If zero or greater, then the value represents the number of columns that overlap.
403$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
404if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
405If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
406In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
407therefore the grid is assumed to be cyclic with no overlapping columns.
408(In fact, this only matters when bicubic interpolation is required.)
409Note that no testing is done to check the validity in the model,
410since there is no way of knowing the name used for the longitude variable,
411so it is up to the user to make sure his or her data is correctly represented.
412
413Next the routine reads in the weights.
414Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
415The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
416and when required, for reading in the variable to be interpolated (on the input data grid).
417The size of the input data array is determined by examining the values in the "src" arrays to
418find the minimum and maximum i and j values required.
419Since bicubic interpolation requires the calculation of gradients at each point on the grid,
420the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
421When the array of points from the data file is adjacent to an edge of the data grid,
422the halo is either a copy of the row/column next to it (non-cyclical case),
423or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
424
425%% =================================================================================================
426\subsubsection{Limitations}
427\label{subsec:SBC_iof_lim}
428
429\begin{enumerate}
430\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
431\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
432  a bicubic interpolation method is used.
433\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
434\item The gradients across the ends of a cyclical grid assume that the grid spacing between
435  the two columns involved are consistent with the weights used.
436\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
437  but this has not been implemented.)
438\end{enumerate}
439
440%% =================================================================================================
441\subsubsection{Utilities}
442\label{subsec:SBC_iof_util}
443
444% to be completed
445A set of utilities to create a weights file for a rectilinear input grid is available
446(see the directory NEMOGCM/TOOLS/WEIGHTS).
447
448%% =================================================================================================
449\subsection{Standalone surface boundary condition scheme (SAS)}
450\label{subsec:SBC_SAS}
451
452\begin{listing}
453  \nlst{namsbc_sas}
454  \caption{\forcode{&namsbc_sas}}
455  \label{lst:namsbc_sas}
456\end{listing}
457
458In some circumstances, it may be useful to avoid calculating the 3D temperature,
459salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
460For example:
461
462\begin{itemize}
463\item Multiple runs of the model are required in code development to
464  see the effect of different algorithms in the bulk formulae.
465\item The effect of different parameter sets in the ice model is to be examined.
466\item Development of sea-ice algorithms or parameterizations.
467\item Spinup of the iceberg floats
468\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
469\end{itemize}
470
471The Standalone Surface scheme provides this capacity.
472Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
473A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
474However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
475In this configuration, a few routines in the standard model are overriden by new versions.
476Routines replaced are:
477
478\begin{itemize}
479\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
480  Since the ocean state is not calculated all associated initialisations have been removed.
481\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
482\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
483  New surface modules that can function when only the surface level of the ocean state is defined can also be added
484  (\eg\ icebergs).
485\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
486  so calls to restart functions have been removed.
487  This also means that the calendar cannot be controlled by time in a restart file,
488  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
489\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
490\item \mdl{diawri}: All 3D data have been removed from the output.
491  The surface temperature, salinity and velocity components (which have been read in) are written along with
492  relevant forcing and ice data.
493\end{itemize}
494
495One new routine has been added:
496
497\begin{itemize}
498\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
499  velocity arrays at the surface.
500  These filenames are supplied in namelist namsbc\_sas.
501  Unfortunately, because of limitations with the \mdl{iom} module,
502  the full 3D fields from the mean files have to be read in and interpolated in time,
503  before using just the top level.
504  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
505\end{itemize}
506
507The user can also choose in the \nam{sbc_sas}{sbc\_sas} namelist to read the mean (nn\_fsbc time-step) fraction of solar net radiation absorbed in the 1st T level using
508 (\np[=.true.]{ln_flx}{ln\_flx}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln_flx}{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in.
509
510%% =================================================================================================
511\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
512\label{sec:SBC_flx}
513
514\begin{listing}
515  \nlst{namsbc_flx}
516  \caption{\forcode{&namsbc_flx}}
517  \label{lst:namsbc_flx}
518\end{listing}
519
520In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
521the surface boundary condition fields are directly read from input files.
522The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
523the name of the variable read in the file, the time frequency at which it is given (in hours),
524and a logical setting whether a time interpolation to the model time step is required for this field.
525See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
526
527Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
528See \autoref{subsec:SBC_ssr} for its specification.
529
530%% =================================================================================================
531\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
532\label{sec:SBC_blk}
533
534\begin{listing}
535  \nlst{namsbc_blk}
536  \caption{\forcode{&namsbc_blk}}
537  \label{lst:namsbc_blk}
538\end{listing}
539
540In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields
541and ocean (and sea-ice) variables averaged over \np{nn_fsbc}{nn\_fsbc} time-step.
542
543The atmospheric fields used depend on the bulk formulae used.
544In forced mode, when a sea-ice model is used, a specific bulk formulation is used.
545Therefore, different bulk formulae are used for the turbulent fluxes computation
546over the ocean and over sea-ice surface.
547For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}):
548the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae.
549The choice is made by setting to true one of the following namelist variable:
550 \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}\np{ln_COARE_3p5}{ln\_COARE\_3p5} and  \np{ln_ECMWF}{ln\_ECMWF}.
551For sea-ice, three possibilities can be selected:
552a constant transfer coefficient (1.4e-3; default value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
553
554Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
555The required 9 input fields are:
556
557\begin{table}[htbp]
558  \centering
559  \begin{tabular}{|l|c|c|c|}
560    \hline
561    Variable description                 & Model variable & Units              & point \\
562    \hline
563    i-component of the 10m air velocity  & utau           & $m.s^{-1}$         & T     \\
564    \hline
565    j-component of the 10m air velocity  & vtau           & $m.s^{-1}$         & T     \\
566    \hline
567    10m air temperature                  & tair           & \r{}$K$            & T     \\
568    \hline
569    Specific humidity                    & humi           & \%                 & T     \\
570    \hline
571    Incoming long wave radiation         & qlw            & $W.m^{-2}$         & T     \\
572    \hline
573    Incoming short wave radiation        & qsr            & $W.m^{-2}$         & T     \\
574    \hline
575    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
576    \hline
577    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
578    \hline
579    Mean sea-level pressure              & slp            & $hPa$              & T     \\
580    \hline
581    \end{tabular}
582  \label{tab:SBC_BULK}
583\end{table}
584
585Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
586It is simpler and faster (less fields to be read), but it is not the recommended method when
587the ocean grid size is the same or larger than the one of the input atmospheric fields.
588
589The \np{sn_wndi}{sn\_wndi}, \np{sn_wndj}{sn\_wndj}, \np{sn_qsr}{sn\_qsr}, \np{sn_qlw}{sn\_qlw}, \np{sn_tair}{sn\_tair}, \np{sn_humi}{sn\_humi}, \np{sn_prec}{sn\_prec},
590\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
591(spatial and temporal interpolations).
592
593\np{cn_dir}{cn\_dir} is the directory of location of bulk files
594\np{ln_taudif}{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
595\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
596\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
597
598Three multiplicative factors are available:
599\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
600increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
601The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
602the calculation of surface wind stress.
603Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
604
605As for the flux formulation, information about the input data required by the model is provided in
606the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
607
608%% =================================================================================================
609\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.F90, sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}
610\label{subsec:SBC_blk_ocean}
611
612Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
613COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
614their neutral transfer coefficients relationships with neutral wind.
615\begin{itemize}
616\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
617  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
618  They use an inertial dissipative method to compute the turbulent transfer coefficients
619  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
620  This \citet{large.yeager_rpt04} dataset is available through
621  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
622  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
623  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
624\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
625\item COARE 3.5 (\np[=.true.]{ln_COARE_3p5}{ln\_COARE\_3p5}): See \citet{edson.jampana.ea_JPO13} for more details
626\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation.
627  Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}.
628\end{itemize}
629
630%% =================================================================================================
631\subsection{Ice-Atmosphere Bulk formulae}
632\label{subsec:SBC_blk_ice}
633
634Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
635
636\begin{itemize}
637\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
638  default constant value used for momentum and heat neutral transfer coefficients
639\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
640  This scheme adds a dependency on edges at leads, melt ponds and flows
641  of the constant neutral air-ice drag. After some approximations,
642  this can be resumed to a dependency on ice concentration (A).
643  This drag coefficient has a parabolic shape (as a function of ice concentration)
644  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.
645  It is theoretically applicable to all ice conditions (not only MIZ).
646\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
647  Alternative turbulent transfer coefficients formulation between sea-ice
648  and atmosphere with distinct momentum and heat coefficients depending
649  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
650  The parameterization is adapted from ECHAM6 atmospheric model.
651  Compared to Lupkes2012 scheme, it considers specific skin and form drags
652  to compute neutral transfer coefficients for both heat and momentum fluxes.
653  Atmospheric stability effect on transfer coefficient is also taken into account.
654\end{itemize}
655
656%% =================================================================================================
657\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
658\label{sec:SBC_cpl}
659
660\begin{listing}
661  \nlst{namsbc_cpl}
662  \caption{\forcode{&namsbc_cpl}}
663  \label{lst:namsbc_cpl}
664\end{listing}
665
666In the coupled formulation of the surface boundary condition,
667the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
668while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
669the atmospheric component.
670
671A generalised coupled interface has been developed.
672It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
673An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
674It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
675(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
676(Weather Research and Forecasting Model).
677
678When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
679the whole carbon cycle is computed.
680In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
681(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
682
683The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
684now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
685When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
686the number used in the sea ice model.
687In some limited cases, it may be possible to specify single category coupling fields even when
688the sea ice model is running with multiple categories -
689in this case, the user should examine the code to be sure the assumptions made are satisfactory.
690In cases where this is definitely not possible, the model should abort with an error message.
691
692%% =================================================================================================
693\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
694\label{sec:SBC_apr}
695
696\begin{listing}
697  \nlst{namsbc_apr}
698  \caption{\forcode{&namsbc_apr}}
699  \label{lst:namsbc_apr}
700\end{listing}
701
702The optional atmospheric pressure can be used to force ocean and ice dynamics
703(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
704The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
705can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
706When used to force the dynamics, the atmospheric pressure is further transformed into
707an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
708\[
709  % \label{eq:SBC_ssh_ib}
710  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
711\]
712where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
713A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
714In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
715\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
716
717The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
718For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
719(see \mdl{sbcssr} module).
720$\eta_{ib}$ can be written in the output.
721This can simplify altimetry data and model comparison as
722inverse barometer sea surface height is usually removed from these date prior to their distribution.
723
724When using time-splitting and BDY package for open boundaries conditions,
725the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
726\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
727
728%% =================================================================================================
729\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
730\label{sec:SBC_tide}
731
732\begin{listing}
733  \nlst{nam_tide}
734  \caption{\forcode{&nam_tide}}
735  \label{lst:nam_tide}
736\end{listing}
737
738The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
739is activated if \np{ln_tide}{ln\_tide} and \np{ln_tide_pot}{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{_tide}{\_tide}.
740This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
741\[
742  % \label{eq:SBC_PE_dyn_tides}
743  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
744  +g\nabla (\Pi_{eq} + \Pi_{sal})
745\]
746where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
747$\Pi_{sal}$ is a self-attraction and loading term (SAL).
748
749The equilibrium tidal forcing is expressed as a sum over a subset of
750constituents chosen from the set of available tidal constituents
751defined in file \hf{SBC/tide} (this comprises the tidal
752constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
753  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
754constituents are selected by including their names in the array
755\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
756\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
757and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
758\forcode{.true.}, the equilibrium tidal forcing can be ramped up
759linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
760model run.
761
762The SAL term should in principle be computed online as it depends on
763the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
764discussion about the practical implementation of this term).
765Nevertheless, the complex calculations involved would make this
766computationally too expensive. Here, two options are available:
767$\Pi_{sal}$ generated by an external model can be read in
768(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
769used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
770\[
771  \Pi_{sal} = \beta \eta,
772\]
773where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
774spatially constant scalar, often chosen to minimize tidal prediction
775errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
776\forcode{.false.} removes the SAL contribution.
777
778%% =================================================================================================
779\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
780\label{sec:SBC_rnf}
781
782\begin{listing}
783  \nlst{namsbc_rnf}
784  \caption{\forcode{&namsbc_rnf}}
785  \label{lst:namsbc_rnf}
786\end{listing}
787
788%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
789%Many models, however, have traditionally inserted river runoff to the top model cell.
790%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
791%throughout a nonzero depth has been motivated by the numerical and physical problems
792%that arise when the top grid cells are of the order of one meter. This situation is common in
793%coastal modelling and becomes more and more often open ocean and climate modelling
794%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
795%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
796
797%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
798%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
799%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
800%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
801%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
802%emp or emps and the changes made are below:
803
804%Rachel:
805River runoff generally enters the ocean at a nonzero depth rather than through the surface.
806Many models, however, have traditionally inserted river runoff to the top model cell.
807This was the case in \NEMO\ prior to the version 3.3,
808and was combined with an option to increase vertical mixing near the river mouth.
809
810However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
811This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
812\footnote{
813  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
814  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
815  see also \autoref{fig:SBC_dcy}.}.
816
817As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
818and for the temperature and salinity of the river to effect the surrounding ocean.
819The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
820along with the depth (in metres) which the river should be added to.
821
822Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
823\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
824If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
825and/or taken as surface temperature respectively.
826
827The runoff value and attributes are read in in sbcrnf.
828For temperature -999 is taken as missing data and the river temperature is taken to
829be the surface temperatue at the river point.
830For the depth parameter a value of -1 means the river is added to the surface box only,
831and a value of -999 means the river is added through the entire water column.
832After being read in the temperature and salinity variables are multiplied by the amount of runoff
833(converted into m/s) to give the heat and salt content of the river runoff.
834After the user specified depth is read ini,
835the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
836The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
837the bottom of the lowest box the river water is being added to
838(\ie\ the total depth that river water is being added to in the model).
839
840The mass/volume addition due to the river runoff is, at each relevant depth level, added to
841the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
842This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
843The sea surface height is calculated using the sum of the horizontal divergence terms,
844and so the river runoff indirectly forces an increase in sea surface height.
845
846The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
847This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
848The heat and salt content of the river runoff is not included in this step,
849and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
850the box and replaced by the same volume of river water with no corresponding heat and salt addition.
851
852For the linear free surface case, at the surface box the tracer advection causes a flux of water
853(of equal volume to the runoff) through the sea surface out of the domain,
854which causes a salt and heat flux out of the model.
855As such the volume of water does not change, but the water is diluted.
856
857For the non-linear free surface case, no flux is allowed through the surface.
858Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
859no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
860(The runoff addition to the top box along with the water being moved up through
861boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
862
863In trasbc the addition of heat and salt due to the river runoff is added.
864This is done in the same way for both vvl and non-vvl.
865The temperature and salinity are increased through the specified depth according to
866the heat and salt content of the river.
867
868In the non-linear free surface case (vvl),
869near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
870so that the original ratios of grid box heights are restored.
871In doing this water is moved into boxes below, throughout the water column,
872so the large volume addition to the surface box is spread between all the grid boxes.
873
874It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
875\ie\ modelling the Baltic flow in and out of the North Sea.
876When the flow is out of the domain there is no change in temperature and salinity,
877regardless of the namelist options used,
878as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
879
880%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
881
882%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
883
884%\colorbox{yellow}{river mouths{\ldots}}
885
886%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
887%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
888%ENDIF
889
890%\gmcomment{  word doc of runoffs:
891%
892%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.
893%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.
894
895%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
896
897%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:
898
899%% =================================================================================================
900\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
901\label{sec:SBC_isf}
902
903\begin{listing}
904  \nlst{namsbc_isf}
905  \caption{\forcode{&namsbc_isf}}
906  \label{lst:namsbc_isf}
907\end{listing}
908
909The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
910Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
911The different options are illustrated in \autoref{fig:SBC_isf}.
912
913\begin{description}
914  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
915  The fwf and heat flux are depending of the local water properties.
916
917  Two different bulk formulae are available:
918
919   \begin{description}
920   \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
921     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
922   \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
923     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
924     A complete description is available in \citet{jenkins_JGR91}.
925   \end{description}
926
927     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
928     Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
929     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m.
930     Then, the fluxes are spread over the same thickness (ie over one or several cells).
931     If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature.
932     This can lead to super-cool temperature in the top cell under melting condition.
933     If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
934
935     Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
936     There are 3 different ways to compute the exchange coeficient:
937   \begin{description}
938        \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}.
939     \begin{gather*}
940       % \label{eq:SBC_isf_gamma_iso}
941       \gamma^{T} = rn\_gammat0 \\
942       \gamma^{S} = rn\_gammas0
943     \end{gather*}
944     This is the recommended formulation for ISOMIP.
945   \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
946     \begin{gather*}
947       \gamma^{T} = rn\_gammat0 \times u_{*} \\
948       \gamma^{S} = rn\_gammas0 \times u_{*}
949     \end{gather*}
950     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
951     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
952   \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
953\[
954\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
955\]
956     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
957     $\Gamma_{Turb}$ the contribution of the ocean stability and
958     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
959     See \citet{holland.jenkins_JPO99} for all the details on this formulation.
960     This formulation has not been extensively tested in \NEMO\ (not recommended).
961   \end{description}
962  \item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
963   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
964   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
965   (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
966   (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
967   The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
968  \item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
969   The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
970   the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
971   the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
972   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
973  \item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
974   However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
975   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
976   As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl})\\
977\end{description}
978
979$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
980the water mass properties, ocean velocities and depth.
981This flux is thus highly dependent of the model resolution (horizontal and vertical),
982realism of the water masses onto the shelf ...\\
983
984$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
985You have total control of the fwf forcing.
986This can be useful if the water masses on the shelf are not realistic or
987the resolution (horizontal/vertical) are too coarse to have realistic melting or
988for studies where you need to control your heat and fw input.\\
989
990The ice shelf melt is implemented as a volume flux as for the runoff.
991The fw addition due to the ice shelf melting is, at each relevant depth level, added to
992the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
993See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
994
995\begin{figure}[!t]
996  \centering
997  \includegraphics[width=0.66\textwidth]{Fig_SBC_isf}
998  \caption[Ice shelf location and fresh water flux definition]{
999    Illustration of the location where the fwf is injected and
1000    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1001  \label{fig:SBC_isf}
1002\end{figure}
1003
1004%% =================================================================================================
1005\section{Ice sheet coupling}
1006\label{sec:SBC_iscpl}
1007
1008\begin{listing}
1009  \nlst{namsbc_iscpl}
1010  \caption{\forcode{&namsbc_iscpl}}
1011  \label{lst:namsbc_iscpl}
1012\end{listing}
1013
1014Ice sheet/ocean coupling is done through file exchange at the restart step.
1015At each restart step:
1016
1017\begin{enumerate}
1018\item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1019\item a new domcfg.nc file is built using the DOMAINcfg tools.
1020\item \NEMO\ run for a specific period and output the average melt rate over the period.
1021\item the ice sheet model run using the melt rate outputed in step 4.
1022\item go back to 1.
1023\end{enumerate}
1024
1025If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1026potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1027The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1028
1029\begin{description}
1030\item [Thin a cell down]: T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1031  ($bt_b=bt_n$).
1032\item [Enlarge  a cell]: See case "Thin a cell down"
1033\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
1034  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1035\item [Wet a cell]: mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1036  If no neighbours, T/S is extrapolated from old top cell value.
1037  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1038\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1039\item [Wet a column]: set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1040  If no neighbour, T/S/U/V and mask set to 0.
1041\end{description}
1042
1043Furthermore, as the before and now fields are not compatible (modification of the geometry),
1044the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1045
1046The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1047It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1048the code will be unable to fill all the new wet cells properly.
1049The default number is set up for the MISOMIP idealised experiments.
1050This coupling procedure is able to take into account grounding line and calving front migration.
1051However, it is a non-conservative processe.
1052This could lead to a trend in heat/salt content and volume.\\
1053
1054In order to remove the trend and keep the conservation level as close to 0 as possible,
1055a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1056The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1057A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1058For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1059The 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).
1060
1061%% =================================================================================================
1062\section{Handling of icebergs (ICB)}
1063\label{sec:SBC_ICB_icebergs}
1064
1065\begin{listing}
1066  \nlst{namberg}
1067  \caption{\forcode{&namberg}}
1068  \label{lst:namberg}
1069\end{listing}
1070
1071Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1072Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1073(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1074Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1075described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1076Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1077which is an integer representing how many icebergs of this class are being described as one lagrangian point
1078(this reduces the numerical problem of tracking every single iceberg).
1079They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1080
1081Two initialisation schemes are possible.
1082\begin{description}
1083\item [{\np{nn_test_icebergs}{nn\_test\_icebergs}~$>$~0}] In this scheme, the value of \np{nn_test_icebergs}{nn\_test\_icebergs} represents the class of iceberg to generate
1084  (so between 1 and 10), and \np{nn_test_icebergs}{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1085  which an iceberg is generated at the beginning of the run.
1086  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1087  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1088  the geographical box: lonmin,lonmax,latmin,latmax
1089\item [{\np[=-1]{nn_test_icebergs}{nn\_test\_icebergs}}] In this scheme, the model reads a calving file supplied in the \np{sn_icb}{sn\_icb} parameter.
1090  This should be a file with a field on the configuration grid (typically ORCA)
1091  representing ice accumulation rate at each model point.
1092  These should be ocean points adjacent to land where icebergs are known to calve.
1093  Most points in this input grid are going to have value zero.
1094  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1095  At each time step, a test is performed to see if there is enough ice mass to
1096  calve an iceberg of each class in order (1 to 10).
1097  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1098  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1099\end{description}
1100
1101Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1102The latter act to disintegrate the iceberg.
1103This is either all melted freshwater,
1104or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1105which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1106Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1107
1108Extensive diagnostics can be produced.
1109Separate output files are maintained for human-readable iceberg information.
1110A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1111The amount of information is controlled by two integer parameters:
1112\begin{description}
1113\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1114  represents an increasing number of points in the code at which variables are written,
1115  and an increasing level of obscurity.
1116\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1117\end{description}
1118
1119Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1120A non-zero value represents how many timesteps between writes of information into the output file.
1121These output files are in NETCDF format.
1122When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1123Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1124So care is needed to recreate data for individual icebergs,
1125since its trajectory data may be spread across multiple files.
1126
1127%% =================================================================================================
1128\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1129\label{sec:SBC_wave}
1130
1131\begin{listing}
1132  \nlst{namsbc_wave}
1133  \caption{\forcode{&namsbc_wave}}
1134  \label{lst:namsbc_wave}
1135\end{listing}
1136
1137Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1138physical processes related to ocean surface waves, namely the surface stress modified by growth and
1139dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1140tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1141the wind stress.
1142
1143Physical processes related to ocean surface waves can be accounted by setting the logical variable
1144\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1145different processes should be activated as explained in the following sections.
1146
1147Wave fields can be provided either in forced or coupled mode:
1148\begin{description}
1149\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1150for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1151Input Data generic Interface (see \autoref{sec:SBC_input}).
1152\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1153in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1154\end{description}
1155
1156%% =================================================================================================
1157\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1158\label{subsec:SBC_wave_cdgw}
1159
1160The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1161can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1162Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1163the drag coefficient is computed according to the stable/unstable conditions of the
1164air-sea interface following \citet{large.yeager_rpt04}.
1165
1166%% =================================================================================================
1167\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1168\label{subsec:SBC_wave_sdw}
1169
1170The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1171It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1172and the current measured at a fixed point (Eulerian velocity).
1173As waves travel, the water particles that make up the waves travel in orbital motions but
1174without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1175at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1176An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1177representation of surface physics in ocean general circulation models. %GS: reference needed
1178The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1179
1180\[
1181  % \label{eq:SBC_wave_sdw}
1182  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1183  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1184  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1185\]
1186
1187where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1188$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1189$k$ is the mean wavenumber defined as:
1190$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1191
1192In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1193and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1194To simplify, it is customary to use approximations to the full Stokes profile.
1195Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1196are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1197$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1198and makes possible the estimation of the surface Stokes drift for random directional waves in
1199realistic wave conditions:
1200
1201\begin{description}
1202\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1203\citet{breivik.janssen.ea_JPO14}:
1204
1205\[
1206  % \label{eq:SBC_wave_sdw_0a}
1207  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1208\]
1209
1210where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1211
1212\[
1213  % \label{eq:SBC_wave_sdw_0b}
1214  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1215  \quad \text{and }\
1216  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1217\]
1218
1219where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1220
1221\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1222reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1223\citep{breivik.bidlot.ea_OM16}:
1224
1225\[
1226  % \label{eq:SBC_wave_sdw_1}
1227  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1228  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1229\]
1230
1231where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1232
1233\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1234but using the wave frequency from a wave model.
1235
1236\end{description}
1237
1238The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1239and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1240
1241\[
1242  % \label{eq:SBC_wave_eta_sdw}
1243  \frac{\partial{\eta}}{\partial{t}} =
1244  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1245\]
1246
1247The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1248for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1249that is induced by the three-dimensional Stokes velocity.
1250The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1251can be formulated as follows:
1252
1253\[
1254  % \label{eq:SBC_wave_tra_sdw}
1255  \frac{\partial{c}}{\partial{t}} =
1256  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1257\]
1258
1259%% =================================================================================================
1260\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1261\label{subsec:SBC_wave_stcor}
1262
1263In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1264in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1265This additional force may have impact on the Ekman turning of the surface current.
1266In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1267approximations described in \autoref{subsec:SBC_wave_sdw}),
1268\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1269
1270%% =================================================================================================
1271\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1272\label{subsec:SBC_wave_tauw}
1273
1274The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1275into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1276available for forcing the mean circulation, while in the opposite case of a decaying sea
1277state, more momentum is available for forcing the ocean.
1278Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1279but in practice, an equilibrium sea state is a fairly rare event.
1280So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1281
1282\[
1283  % \label{eq:SBC_wave_tauoc}
1284  \tau_{oc,a} = \tau_a - \tau_w
1285\]
1286
1287where $\tau_a$ is the atmospheric surface stress;
1288$\tau_w$ is the atmospheric stress going into the waves defined as:
1289
1290\[
1291  % \label{eq:SBC_wave_tauw}
1292  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1293\]
1294
1295where: $c_p$ is the phase speed of the gravity waves,
1296$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1297the physics of ocean waves. The first one, $S_{in}$, describes the generation
1298of ocean waves by wind and therefore represents the momentum and energy transfer
1299from air to ocean waves; the second term $S_{nl}$ denotes
1300the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1301describes the dissipation of waves by processes such as white-capping, large scale breaking
1302eddy-induced damping.
1303
1304The wave stress derived from an external wave model can be provided either through the normalized
1305wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1306meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1307
1308%% =================================================================================================
1309\section{Miscellaneous options}
1310\label{sec:SBC_misc}
1311
1312%% =================================================================================================
1313\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1314\label{subsec:SBC_dcy}
1315%
1316
1317\begin{figure}[!t]
1318  \centering
1319  \includegraphics[width=0.66\textwidth]{Fig_SBC_diurnal}
1320  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1321    Example of reconstruction of the diurnal cycle variation of short wave flux from
1322    daily mean values.
1323    The reconstructed diurnal cycle (black line) is chosen as
1324    the mean value of the analytical cycle (blue line) over a time step,
1325    not as the mid time step value of the analytically cycle (red square).
1326    From \citet{bernie.guilyardi.ea_CD07}.}
1327  \label{fig:SBC_diurnal}
1328\end{figure}
1329
1330\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.
1331%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1332Nevertheless, 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}.
1333Furthermore, only the knowledge of daily mean value of SWF is needed,
1334as higher frequency variations can be reconstructed from them,
1335assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1336The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1337setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1338using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1339the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1340The reconstruction is performed in the \mdl{sbcdcy} module.
1341The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1342The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1343a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1344The use of diurnal cycle reconstruction requires the input SWF to be daily
1345(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1346Furthermore, it is recommended to have a least 8 surface module time steps per day,
1347that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1348An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1349one every 2~hours (from 1am to 11pm).
1350
1351\begin{figure}[!t]
1352  \centering
1353  \includegraphics[width=0.66\textwidth]{Fig_SBC_dcy}
1354  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1355    Example of reconstruction of the diurnal cycle variation of short wave flux from
1356    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1357    The display is on (i,j) plane.}
1358  \label{fig:SBC_dcy}
1359\end{figure}
1360
1361Note also that the setting a diurnal cycle in SWF is highly recommended when
1362the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1363an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1364
1365%% =================================================================================================
1366\subsection{Rotation of vector pairs onto the model grid directions}
1367\label{subsec:SBC_rotation}
1368
1369When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1370pairs of vector components can be rotated from east-north directions onto the local grid directions.
1371This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1372be defined relative to a rectilinear grid.
1373To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1374The eastward component must start with "U" and the northward component with "V".
1375The remaining characters in the strings are used to identify which pair of components go together.
1376So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1377rotate them on to the model grid directions;
1378"U2" and "V2" could be used against a second pair of components, and so on.
1379The extra characters used in the strings are arbitrary.
1380The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1381
1382%% =================================================================================================
1383\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1384\label{subsec:SBC_ssr}
1385
1386\begin{listing}
1387  \nlst{namsbc_ssr}
1388  \caption{\forcode{&namsbc_ssr}}
1389  \label{lst:namsbc_ssr}
1390\end{listing}
1391
1392Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1393On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1394a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1395\[
1396  % \label{eq:SBC_dmp_q}
1397  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1398\]
1399where SST is a sea surface temperature field (observed or climatological),
1400$T$ is the model surface layer temperature and
1401$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1402For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1403This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1404
1405In the fresh water budget, a feedback term can also be added.
1406Converted into an equivalent freshwater flux, it takes the following expression :
1407
1408\begin{equation}
1409  \label{eq:SBC_dmp_emp}
1410  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1411  {\left.S\right|_{k=1}}
1412\end{equation}
1413
1414where $\textit{emp}_{o }$ is a net surface fresh water flux
1415(observed, climatological or an atmospheric model product),
1416\textit{SSS}$_{Obs}$ is a sea surface salinity
1417(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1418$\left.S\right|_{k=1}$ is the model surface layer salinity and
1419$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1420Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1421the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1422The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1423reduce the uncertainties we have on the observed freshwater budget.
1424
1425%% =================================================================================================
1426\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1427\label{subsec:SBC_ice-cover}
1428
1429The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1430There are several way to handle sea-ice in the system depending on
1431the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1432\begin{description}
1433\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1434  This is a typical namelist value used for tropical ocean domain.
1435  The surface fluxes are simply specified for an ice-free ocean.
1436  No specific things is done for sea-ice.
1437\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1438  An observed ice covered area is read in a file.
1439  Below this area, the SST is restored to the freezing point and
1440  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1441  The associated modification of the freshwater fluxes are done in such a way that
1442  the change in buoyancy fluxes remains zero.
1443  This prevents deep convection to occur when trying to reach the freezing point
1444  (and so ice covered area condition) while the SSS is too large.
1445  This manner of managing sea-ice area, just by using a IF case,
1446  is usually referred as the \textit{ice-if} model.
1447  It can be found in the \mdl{sbcice\_if} module.
1448\item [nn\_ice = 2 or more] A full sea ice model is used.
1449  This model computes the ice-ocean fluxes,
1450  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1451  provide the surface averaged ocean fluxes.
1452  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1453  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1454  (\ie\ $2$ for SI3 or $3$ for CICE).
1455\end{description}
1456
1457% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1458%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1459
1460%% =================================================================================================
1461\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1462\label{subsec:SBC_cice}
1463
1464It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1465to the CICE sea-ice model by using \key{cice}.
1466The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1467the additional 'hadgem3' drivers will be required, even with the latest code release.
1468Input grid files consistent with those used in \NEMO\ will also be needed,
1469and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1470(seek advice from UKMO if necessary).
1471Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1472(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1473or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1474(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1475The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1476(although coupling ocean and ice less frequently should work,
1477it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1478the user should check that results are not significantly different to the standard case).
1479
1480There are two options for the technical coupling between \NEMO\ and CICE.
1481The standard version allows complete flexibility for the domain decompositions in the individual models,
1482but this is at the expense of global gather and scatter operations in the coupling which
1483become very expensive on larger numbers of processors.
1484The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1485the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1486and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1487allows much more efficient direct coupling on individual processors.
1488This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1489there is no sea ice.
1490
1491%% =================================================================================================
1492\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1493\label{subsec:SBC_fwb}
1494
1495For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1496prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1497In \NEMO, two way of controlling the freshwater budget are proposed:
1498
1499\begin{description}
1500\item [{\np[=0]{nn_fwb}{nn\_fwb}}] no control at all.
1501  The mean sea level is free to drift, and will certainly do so.
1502\item [{\np[=1]{nn_fwb}{nn\_fwb}}] global mean \textit{emp} set to zero at each model time step.
1503  %GS: comment below still relevant ?
1504  %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).
1505\item [{\np[=2]{nn_fwb}{nn\_fwb}}] freshwater budget is adjusted from the previous year annual mean budget which
1506  is read in the \textit{EMPave\_old.dat} file.
1507  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1508  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1509\end{description}
1510
1511% Griffies doc:
1512% When running ocean-ice simulations, we are not explicitly representing land processes,
1513% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1514% it is important to balance the hydrological cycle in ocean-ice models.
1515% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1516% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1517% a chosen time scale.
1518% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1519% so that there is always a zero net input of water to the ocean-ice system.
1520% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1521% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1522% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1523% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1524% and ice models when aiming to balance the hydrological cycle.
1525% 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,
1526% not the water in any one sub-component. As an extreme example to illustrate the issue,
1527% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1528% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1529% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1530% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1531% in ocean-ice models.
1532
1533\onlyinsubfile{\input{../../global/epilogue}}
1534
1535\end{document}
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