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1\documentclass[../main/NEMO_manual]{subfiles}
2\usepackage{fontspec}
3\usepackage{fontawesome}
4
5\begin{document}
6
7\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
8\label{chap:SBC}
9
10\thispagestyle{plain}
11
12\chaptertoc
13
14\paragraph{Changes record} ~\\
15
16{\footnotesize
17  \begin{tabularx}{\textwidth}{l||X|X}
18    Release & Author(s) & Modifications \\
19    \hline
20    {\em   4.0} & {\em ...} & {\em ...} \\
21    {\em   3.6} & {\em ...} & {\em ...} \\
22    {\em   3.4} & {\em ...} & {\em ...} \\
23    {\em <=3.4} & {\em ...} & {\em ...}
24  \end{tabularx}
25}
26
27\clearpage
28
29\begin{listing}
30  \nlst{namsbc}
31  \caption{\forcode{&namsbc}}
32  \label{lst:namsbc}
33\end{listing}
34
35The ocean needs seven fields as surface boundary condition:
36
37\begin{itemize}
38\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
39\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
40\item the surface freshwater budget $\left( {\textit{emp}} \right)$
41\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
42\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
43\end{itemize}
44
45Four different ways are available to provide the seven fields to the ocean. They are controlled by
46namelist \nam{sbc}{sbc} variables:
47
48\begin{itemize}
49\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms,
50\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
51\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
52(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
53\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
54\end{itemize}
55
56The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
57
58When the fields are supplied from data files (bulk, flux and mixed formulations),
59the input fields do not need to be supplied on the model grid.
60Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
61the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
62If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
63should be masked or filled to avoid spurious results in proximity of the coasts, as
64large sea-land gradients characterize most of the atmospheric variables.
65
66In addition, the resulting fields can be further modified using several namelist options.
67These options control:
68
69\begin{itemize}
70\item the rotation of vector components supplied relative to an east-north coordinate system onto
71  the local grid directions in the model,
72\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
73\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
74\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
75  (\np[=0..3]{nn_ice}{nn\_ice}),
76\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
77\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
78  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
79\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
80  (\np[=0..2]{nn_fwb}{nn\_fwb}),
81\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
82  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
83\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
84\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
85\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
86\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
87\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
88\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
89\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
90\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
91\item the atmospheric surface pressure gradient effect on ocean and ice dynamics (\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn} with namelist \nam{sbc_apr}{sbc\_apr}),
92\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
93\end{itemize}
94
95In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
96Then we present the three ways of providing the surface boundary conditions,
97followed by the description of the atmospheric pressure and the river runoff.
98Next, the scheme for interpolation on the fly is described.
99Finally, the different options that further modify the fluxes applied to the ocean are discussed.
100One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
101which act as drifting sources of fresh water.
102Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
103which provides additional sources of fresh water.
104
105%% =================================================================================================
106\section{Surface boundary condition for the ocean}
107\label{sec:SBC_ocean}
108
109The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
110It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
111the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
112As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
113\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
114
115The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
116$Q_{ns}$ and $Q_{sr}$, respectively.
117The former is the non penetrative part of the heat flux
118(\ie\ the sum of sensible, latent and long wave heat fluxes plus
119the heat content of the mass exchange between the ocean and sea-ice).
120It is applied in \mdl{trasbc} module as a surface boundary condition trend of
121the first level temperature time evolution equation
122(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
123The latter is the penetrative part of the heat flux.
124It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
125\np[=.true.]{ln_traqsr}{ln\_traqsr}.
126The way the light penetrates inside the water column is generally a sum of decreasing exponentials
127(see \autoref{subsec:TRA_qsr}).
128
129The surface freshwater budget is provided by the \textit{emp} field.
130It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
131possibly with the sea-ice and ice shelves (freezing minus melting of ice).
132It affects the ocean in two different ways:
133$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
134a volume flux, and
135$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
136the mass exchanged with atmosphere, sea-ice and ice shelves.
137
138%\colorbox{yellow}{Miss: }
139%A extensive description of all namsbc namelist (parameter that have to be
140%created!)
141%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
142%ssv) \ie\ information required by flux computation or sea-ice
143%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
144%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
145%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
146%Fluxes update only each nf\_sbc time step (namsbc) explain relation
147%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
148%nf\_sbc
149%Explain here all the namlist namsbc variable{\ldots}.
150% explain : use or not of surface currents
151%\colorbox{yellow}{End Miss }
152
153The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
154the surface currents, temperature and salinity.
155These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
156these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
157
158\begin{table}[tb]
159  \centering
160  \begin{tabular}{|l|l|l|l|}
161    \hline
162    Variable description                           & Model variable  & Units  & point                 \\
163    \hline
164    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
165    \hline
166    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
167    \hline
168    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
169    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
170  \end{tabular}
171  \caption[Ocean variables provided to the surface module)]{
172    Ocean variables provided to the surface module (\texttt{SBC}).
173    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
174    \ie\ the frequency of computation of surface fluxes.}
175  \label{tab:SBC_ssm}
176\end{table}
177
178%\colorbox{yellow}{Penser a} mettre dans le restant l'info nn\_fsbc ET nn\_fsbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt
179
180%% =================================================================================================
181\section{Input data generic interface}
182\label{sec:SBC_input}
183
184A generic interface has been introduced to manage the way input data
185(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
186This task is achieved by \mdl{fldread}.
187The module is designed with four main objectives in mind:
188\begin{enumerate}
189\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
190  and according to the different calendars available in the model.
191\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
192\item make the run duration independent from the period cover by the input files.
193\item provide a simple user interface and a rather simple developer interface by
194  limiting the number of prerequisite informations.
195\end{enumerate}
196
197As a result, the user has only to fill in for each variable a structure in the namelist file to
198define the input data file and variable names, the frequency of the data (in hours or months),
199whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
200and three additional parameters for the on-the-fly interpolation.
201When adding a new input variable, the developer has to add the associated structure in the namelist,
202read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
203and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
204
205The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
206(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
207if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
208
209Note that when an input data is archived on a disc which is accessible directly from the workspace where
210the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
211By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
212
213%% =================================================================================================
214\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
215\label{subsec:SBC_fldread}
216
217The structure associated with an input variable contains the following information:
218\begin{forlines}
219!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
220!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
221\end{forlines}
222where
223\begin{description}
224\item [File name]: the stem name of the NetCDF file to be opened.
225  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
226  by date information and possibly a prefix (when using AGRIF).
227  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
228  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
229  \begin{table}[htbp]
230    \centering
231    \begin{tabular}{|l|c|c|c|}
232      \hline
233                                  &  daily or weekLL     &  monthly           &  yearly        \\
234      \hline
235      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
236      \hline
237      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
238      \hline
239    \end{tabular}
240    \caption[Naming nomenclature for climatological or interannual input file]{
241      Naming nomenclature for climatological or interannual input file,
242      as a function of the open/close frequency.
243      The stem name is assumed to be 'fn'.
244      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
245      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
246      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
247      always coded with 4 or 2 digits.
248      Note that (1) in mpp, if the file is split over each subdomain,
249      the suffix '.nc' is replaced by '\_PPPP.nc',
250      where 'PPPP' is the process number coded with 4 digits;
251      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
252    }
253    \label{tab:SBC_fldread}
254  \end{table}
255\item [Record frequency]: the frequency of the records contained in the input file.
256  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
257  (for example -1 for monthly forcing or -12 for annual forcing).
258  Note that this frequency must REALLY be an integer and not a real.
259  On some computers, setting it to '24.' can be interpreted as 240!
260\item [Variable name]: the name of the variable to be read in the input NetCDF file.
261\item [Time interpolation]: a logical to activate, or not, the time interpolation.
262  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
263  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
264  00h00'00'' to 23h59'59".
265  If set to 'true', the forcing will have a broken line shape.
266  Records are assumed to be dated at the middle of the forcing period.
267  For example, when using a daily forcing with time interpolation,
268  linear interpolation will be performed between mid-day of two consecutive days.
269\item [Climatological forcing]: a logical to specify if a input file contains climatological forcing which can be cycle in time,
270  or an interannual forcing which will requires additional files if
271  the period covered by the simulation exceeds the one of the file.
272  See the above file naming strategy which impacts the expected name of the file to be opened.
273\item [Open/close frequency]: the frequency at which forcing files must be opened/closed.
274  Four cases are coded:
275  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
276  means the forcing files will contain data for one day, one week, one month or one year.
277  Files are assumed to contain data from the beginning of the open/close period.
278  For example, the first record of a yearly file containing daily data is Jan 1st even if
279  the experiment is not starting at the beginning of the year.
280\item [Others]:  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
281  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
282\end{description}
283
284Additional remarks:\\
285(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
286The only tricky point is therefore to specify the date at which we need to do the interpolation and
287the date of the records read in the input files.
288Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
289For example, for an experiment starting at 0h00'00" with a one-hour time-step,
290a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
291However, for forcing data related to the surface module,
292values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
293For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
294The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
295In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
296(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
297The calendar associated with the forcing field is build according to the information provided by
298user in the record frequency, the open/close frequency and the type of temporal interpolation.
299For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
300start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
301(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
302interpolating data with the first (last) record of the open/close period.
303For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
304the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
305Dec 31st 12h00'00" and Jan 1st 12h00'00".
306If the forcing is climatological, Dec and Jan will be keep-up from the same year.
307However, if the forcing is not climatological, at the end of
308the open/close period, the code will automatically close the current file and open the next one.
309Note that, if the experiment is starting (ending) at the beginning (end) of
310an open/close period, we do accept that the previous (next) file is not existing.
311In this case, the time interpolation will be performed between two identical values.
312For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
313we do accept that the file related to year Y-1 is not existing.
314The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
315If the file of year Y-1 exists, the code will read its last record.
316Therefore, this file can contain only one record corresponding to Dec 31st,
317a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
318
319%% =================================================================================================
320\subsection{Interpolation on-the-fly}
321\label{subsec:SBC_iof}
322
323Interpolation on the Fly allows the user to supply input files required for the surface forcing on
324grids other than the model grid.
325To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
326interpolate from the data grid to the model grid.
327The original development of this code used the SCRIP package
328(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
329In principle, any package such as CDO can be used to generate the weights, but the variables in
330the input weights file must have the same names and meanings as assumed by the model.
331Two methods are currently available: bilinear and bicubic interpolations.
332Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
333the input file and substitute the corresponding values with the average of the 8 neighbouring points in
334the native external grid.
335Only "sea points" are considered for the averaging.
336The land/sea mask file must be provided in the structure associated with the input variable.
337The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
338the associated variables and should be equal to 1 over land and 0 elsewhere.
339The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
340Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
341
342%% =================================================================================================
343\subsubsection{Bilinear interpolation}
344\label{subsec:SBC_iof_bilinear}
345
346The input weights file in this case has two sets of variables:
347src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
348The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
349Each src value is an integer corresponding to the index of a point in the input grid when
350written as a one dimensional array.
351For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
352There are four of each variable because bilinear interpolation uses the four points defining
353the grid box containing the point to be interpolated.
354All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
355generate a value for point (i,j) in the model.
356
357Symbolically, the algorithm used is:
358\[
359  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
360\]
361where function idx() transforms a one dimensional index src(k) into a two dimensional index,
362and wgt(1) corresponds to variable "wgt01" for example.
363
364%% =================================================================================================
365\subsubsection{Bicubic interpolation}
366\label{subsec:SBC_iof_bicubic}
367
368Again, there are two sets of variables: "src" and "wgt".
369But in this case, there are 16 of each.
370The symbolic algorithm used to calculate values on the model grid is now:
371
372\[
373  \begin{split}
374    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
375    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
376    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
377    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
378  \end{split}
379\]
380The gradients here are taken with respect to the horizontal indices and not distances since
381the spatial dependency has been included into the weights.
382
383%% =================================================================================================
384\subsubsection{Implementation}
385\label{subsec:SBC_iof_imp}
386
387To activate this option, a non-empty string should be supplied in
388the weights filename column of the relevant namelist;
389if this is left as an empty string no action is taken.
390In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
391as and when they are first required.
392This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
393inspecting a global attribute stored in the weights input file.
394This attribute must be called "ew\_wrap" and be of integer type.
395If it is negative, the input non-model grid is assumed to be not cyclic.
396If zero or greater, then the value represents the number of columns that overlap.
397$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
398if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
399If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
400In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
401therefore the grid is assumed to be cyclic with no overlapping columns.
402(In fact, this only matters when bicubic interpolation is required.)
403Note that no testing is done to check the validity in the model,
404since there is no way of knowing the name used for the longitude variable,
405so it is up to the user to make sure his or her data is correctly represented.
406
407Next the routine reads in the weights.
408Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
409The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
410and when required, for reading in the variable to be interpolated (on the input data grid).
411The size of the input data array is determined by examining the values in the "src" arrays to
412find the minimum and maximum i and j values required.
413Since bicubic interpolation requires the calculation of gradients at each point on the grid,
414the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
415When the array of points from the data file is adjacent to an edge of the data grid,
416the halo is either a copy of the row/column next to it (non-cyclical case),
417or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
418
419%% =================================================================================================
420\subsubsection{Limitations}
421\label{subsec:SBC_iof_lim}
422
423\begin{enumerate}
424\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
425\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
426  a bicubic interpolation method is used.
427\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
428\item The gradients across the ends of a cyclical grid assume that the grid spacing between
429  the two columns involved are consistent with the weights used.
430\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
431  but this has not been implemented.)
432\end{enumerate}
433
434%% =================================================================================================
435\subsubsection{Utilities}
436\label{subsec:SBC_iof_util}
437
438% to be completed
439A set of utilities to create a weights file for a rectilinear input grid is available
440(see the directory NEMOGCM/TOOLS/WEIGHTS).
441
442%% =================================================================================================
443\subsection{Standalone surface boundary condition scheme (SAS)}
444\label{subsec:SBC_SAS}
445
446\begin{listing}
447  \nlst{namsbc_sas}
448  \caption{\forcode{&namsbc_sas}}
449  \label{lst:namsbc_sas}
450\end{listing}
451
452In some circumstances, it may be useful to avoid calculating the 3D temperature,
453salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
454For example:
455
456\begin{itemize}
457\item Multiple runs of the model are required in code development to
458  see the effect of different algorithms in the bulk formulae.
459\item The effect of different parameter sets in the ice model is to be examined.
460\item Development of sea-ice algorithms or parameterizations.
461\item Spinup of the iceberg floats
462\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
463\end{itemize}
464
465The Standalone Surface scheme provides this capacity.
466Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
467A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
468However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
469In this configuration, a few routines in the standard model are overriden by new versions.
470Routines replaced are:
471
472\begin{itemize}
473\item \mdl{nemogcm}: This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
474  Since the ocean state is not calculated all associated initialisations have been removed.
475\item \mdl{step}: The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
476\item \mdl{sbcmod}: This has been cut down and now only calculates surface forcing and the ice model required.
477  New surface modules that can function when only the surface level of the ocean state is defined can also be added
478  (\eg\ icebergs).
479\item \mdl{daymod}: No ocean restarts are read or written (though the ice model restarts are retained),
480  so calls to restart functions have been removed.
481  This also means that the calendar cannot be controlled by time in a restart file,
482  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
483\item \mdl{stpctl}: Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
484\item \mdl{diawri}: All 3D data have been removed from the output.
485  The surface temperature, salinity and velocity components (which have been read in) are written along with
486  relevant forcing and ice data.
487\end{itemize}
488
489One new routine has been added:
490
491\begin{itemize}
492\item \mdl{sbcsas}: This module initialises the input files needed for reading temperature, salinity and
493  velocity arrays at the surface.
494  These filenames are supplied in namelist namsbc\_sas.
495  Unfortunately, because of limitations with the \mdl{iom} module,
496  the full 3D fields from the mean files have to be read in and interpolated in time,
497  before using just the top level.
498  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
499\end{itemize}
500
501The user can also choose in the \nam{sbc_sas}{sbc\_sas} namelist to read the mean (nn\_fsbc time-step) fraction of solar net radiation absorbed in the 1st T level using
502 (\np[=.true.]{ln_flx}{ln\_flx}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln_flx}{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in.
503
504%% =================================================================================================
505\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
506\label{sec:SBC_flx}
507
508% Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk
509% parameterization'' (i.e NCAR, COARE, ECMWF...)
510
511\begin{listing}
512  \nlst{namsbc_flx}
513  \caption{\forcode{&namsbc_flx}}
514  \label{lst:namsbc_flx}
515\end{listing}
516
517In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
518the surface boundary condition fields are directly read from input files.
519The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
520the name of the variable read in the file, the time frequency at which it is given (in hours),
521and a logical setting whether a time interpolation to the model time step is required for this field.
522See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
523
524Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
525See \autoref{subsec:SBC_ssr} for its specification.
526
527
528
529
530
531
532
533%% =================================================================================================
534\pagebreak
535\newpage
536\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
537\label{sec:SBC_blk}
538
539% L. Brodeau, December 2019... %
540
541\begin{listing}
542  \nlst{namsbc_blk}
543  \caption{\forcode{&namsbc_blk}}
544  \label{lst:namsbc_blk}
545\end{listing}
546
547If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea
548fluxes associated with surface boundary conditions are estimated by means of the
549traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed
550near-surface atmosphere state (typically extracted from a weather reanalysis)
551and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc}
552time-step(s).
553
554% Turbulent air-sea fluxes are computed using the sea surface properties and
555% atmospheric SSVs at height $z$ above the sea surface, with the traditional
556% aerodynamic bulk formulae:
557
558Note: all the NEMO Fortran routines involved in the present section have been
559 initially developed (and are still developed in parallel) in
560 the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} open-source project
561\citep{brodeau.barnier.ea_JPO17}.
562
563%%% Bulk formulae are this:
564\subsection{Bulk formulae}\label{subsec:SBC_blkform}
565%
566In NEMO, the set of equations that relate each component of the surface fluxes
567to the near-surface atmosphere and sea surface states writes
568%
569\begin{subequations}\label{eq_bulk}
570  \label{eq:SBC_bulk_form}
571  \begin{eqnarray}
572    \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
573    Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
574    E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
575    Q_L           &=& -L_v \, E \\
576    %
577    Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\
578    Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4)
579  \end{eqnarray}
580\end{subequations}
581%
582with
583   \[ \theta_z \simeq T_z+\gamma z \]
584   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
585%
586from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
587%
588where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
589$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
590flux.
591%
592$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
593and longwave radiative fluxes, respectively.
594%
595Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$
596implies a gain of the relevant quantity for the ocean, while a positive $E$
597implies a freshwater loss for the ocean.
598%
599$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
600coefficients for momentum, sensible heat, and moisture, respectively.
601%
602$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
603vaporization of water.
604%
605$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
606and specific humidity of air at height $z$ above the sea surface,
607respectively. $\gamma z$ is a temperature correction term which accounts for the
608adiabatic lapse rate and approximates the potential temperature at height
609$z$ \citep{josey.gulev.ea_2013}.
610%
611$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
612(possibly referenced to the surface current $\mathbf{u_0}$,
613section \ref{s_res1}.\ref{ss_current}).
614%
615The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
616$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution.
617%
618$a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\
619%
620%$p_a$ is the mean sea-level pressure (SLP).
621%
622$T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity
623of air at temperature $T_s$; it includes a 2\% reduction to account for the
624presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}.
625Depending on the bulk parametrization used, $T_s$ can either be the temperature
626at the air-sea interface (skin temperature, hereafter SSST) or at typically a
627few tens of centimeters below the surface (bulk sea surface temperature,
628hereafter SST).
629%
630The SSST differs from the SST due to the contributions of two effects of
631opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL,
632respectively, see section\,\ref{subsec:SBC_skin}).
633%
634Technically, when the ECMWF or COARE* bulk parametrizations are selected
635(\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}),
636$T_s$ is the SSST, as opposed to the NCAR bulk parametrization
637(\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature
638at first T-point level).
639
640For more details on all these aspects the reader is invited to refer
641to \citet{brodeau.barnier.ea_JPO17}.
642
643
644
645\subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean}
646%%%\label{subsec:SBC_param}
647
648Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae
649strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and
650$C_E$. They are estimated with what we refer to as a \emph{bulk
651parametrization} algorithm. When relevant, these algorithms also perform the
652height adjustment of humidity and temperature to the wind reference measurement
653height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}).
654
655
656
657For the open ocean, four bulk parametrization algorithms are available in NEMO:
658\begin{itemize}
659\item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09}
660\item COARE 3.0 \citep{fairall.bradley.ea_JC03}
661\item COARE 3.6 \citep{edson.jampana.ea_JPO13}
662\item ECMWF (IFS documentation, cy45)
663\end{itemize}
664
665
666With respect to version 3, the principal advances in version 3.6 of the COARE
667bulk parametrization are built around improvements in the representation of the
668effects of waves on
669fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes
670improved relationships of surface roughness, and whitecap fraction on wave
671parameters. It is therefore recommended to chose version 3.6 over 3.
672
673
674
675
676\subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin}
677%\subsection[Cool-skin and warm-layer parameterizations
678%(\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})}
679%\label{subsec:SBC_skin}
680%
681As opposed to the NCAR bulk parametrization, more advanced bulk
682parametrizations such as COARE3.x and ECMWF are meant to be used with the skin
683temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
684the first T-point level, see section\,\ref{subsec:SBC_blkform}).
685%
686As such, the relevant cool-skin and warm-layer parametrization must be
687activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs}
688and \np[=T]{ln_skin_wl}{ln\_skin\_wl} to use COARE3.x or ECMWF in a consistent
689way.
690
691\texttt{\#LB: ADD BLBLA ABOUT THE TWO CS/WL PARAMETRIZATIONS (ECMWF and COARE) !!!}
692
693For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same
694basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based
695on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE
6963.6.
697
698For the warm-layer scheme, ECMWF is based on \citet{zeng.beljaars_GRL05} with a
699recent update from \citet{takaya.bidlot.ea_JGR10} (consideration of the
700turbulence input from Langmuir circulation).
701
702Importantly, COARE warm-layer scheme \citep{fairall.ea_19} includes a prognostic
703equation for the thickness of the warm-layer, while it is considered as constant
704in the ECWMF algorithm.
705
706
707\subsection{Appropriate use of each bulk parametrization}
708
709\subsubsection{NCAR}
710
711NCAR bulk parametrizations (formerly known as CORE) is meant to be used with the
712CORE II atmospheric forcing \citep{large.yeager_CD09}. The expected sea surface
713temperature is the bulk SST. Hence the following namelist parameters must be
714set:
715%
716\begin{verbatim}
717  ...
718  ln_NCAR    = .true.
719  ...
720  rn_zqt     = 10.     ! Air temperature & humidity reference height (m)
721  rn_zu      = 10.     ! Wind vector reference height (m)
722  ...
723  ln_skin_cs = .false. ! use the cool-skin parameterization
724  ln_skin_wl = .false. ! use the warm-layer parameterization
725  ...
726  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
727\end{verbatim}
728
729
730\subsubsection{ECMWF}
731%
732With an atmospheric forcing based on a reanalysis of the ECMWF, such as the
733Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to
734use the ECMWF bulk parametrizations with the cool-skin and warm-layer
735parametrizations activated. In ECMWF reanalyzes, since air temperature and
736humidity are provided at the 2\,m height, and given that the humidity is
737distributed as the dew-point temperature, the namelist must be tuned as follows:
738%
739\begin{verbatim}
740  ...
741  ln_ECMWF   = .true.
742  ...     
743  rn_zqt     =  2.     ! Air temperature & humidity reference height (m)
744  rn_zu      = 10.     ! Wind vector reference height (m)
745  ...
746  ln_skin_cs = .true. ! use the cool-skin parameterization
747  ln_skin_wl = .true. ! use the warm-layer parameterization
748  ...
749  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
750  ...
751\end{verbatim}
752%
753Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
754of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
755triggers the use of the ECMWF cool-skin and warm-layer parametrizations,
756respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
757
758
759\subsubsection{COARE 3.x}
760%
761Since the ECMWF parametrization is largely based on the COARE* parametrization,
762the two algorithms are very similar in terms of structure and closure
763approach. As such, the namelist tuning for COARE 3.x is identical to that of
764ECMWF:
765%
766\begin{verbatim}
767  ...
768  ln_COARE3p6 = .true.
769  ...     
770  ln_skin_cs = .true. ! use the cool-skin parameterization
771  ln_skin_wl = .true. ! use the warm-layer parameterization
772  ...
773\end{verbatim}
774
775Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection
776of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
777triggers the use of the COARE cool-skin and warm-layer parametrizations,
778respectively (found in \textit{sbcblk\_skin\_coare.F90}).
779
780
781%lulu
782
783
784
785% In a typical bulk algorithm, the BTCs under neutral stability conditions are
786% defined using \emph{in-situ} flux measurements while their dependence on the
787% stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and
788% the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are
789% functions of the wind speed and the near-surface stability of the atmospheric
790% surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$
791% and $q_z$.
792
793
794
795\subsection{Prescribed near-surface atmospheric state}
796
797The atmospheric fields used depend on the bulk formulae used.  In forced mode,
798when a sea-ice model is used, a specific bulk formulation is used.  Therefore,
799different bulk formulae are used for the turbulent fluxes computation over the
800ocean and over sea-ice surface.
801%
802
803%The choice is made by setting to true one of the following namelist
804%variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6}
805%and \np{ln_ECMWF}{ln\_ECMWF}.
806
807Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
808The required 9 input fields are:
809
810\begin{table}[htbp]
811  \centering
812  \begin{tabular}{|l|c|c|c|}
813    \hline
814    Variable description                 & Model variable & Units              & point \\
815    \hline
816    i-component of the 10m air velocity  & wndi           & $m.s^{-1}$         & T     \\
817    \hline
818    j-component of the 10m air velocity  & wndj           & $m.s^{-1}$         & T     \\
819    \hline
820    10m air temperature                  & tair           & $K$               & T     \\
821    \hline
822    Specific humidity                    & humi           & $-$               & T     \\
823    Relative humidity                    & ~              & $\%$              & T     \\
824    Dew-point temperature                & ~              & $K$               & T     \\   
825    \hline
826    Downwelling longwave radiation       & qlw            & $W.m^{-2}$         & T     \\
827    \hline
828    Downwelling shortwave radiation      & qsr            & $W.m^{-2}$         & T     \\
829    \hline
830    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
831    \hline
832    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
833    \hline
834    Mean sea-level pressure              & slp            & $Pa$              & T     \\
835    \hline
836    \end{tabular}
837  \label{tab:SBC_BULK}
838\end{table}
839
840Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
841It is simpler and faster (less fields to be read), but it is not the recommended method when
842the ocean grid size is the same or larger than the one of the input atmospheric fields.
843
844The \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},
845\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
846(spatial and temporal interpolations).
847
848\np{cn_dir}{cn\_dir} is the directory of location of bulk files
849%\np{ln_taudif}{ln\_taudif} is the flag to specify if we use High Frequency (HF) tau information (.true.) or not (.false.)
850\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
851\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
852
853Three multiplicative factors are available:
854\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
855increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
856The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
857the calculation of surface wind stress.
858Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
859
860As for the flux parametrization, information about the input data required by the model is provided in
861the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
862
863
864\subsubsection{Air humidity}
865
866Air humidity can be provided as three different parameters: specific humidity
867[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
868parameters)...
869
870
871~\\
872
873
874
875
876
877
878
879
880
881
882%% =================================================================================================
883%\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare3p0.F90, sbcblk\_algo\_coare3p6.F90, %sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare3p0}, %\mdl{sbcblk\_algo\_coare3p6}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}
884%\label{subsec:SBC_blk_ocean}
885
886%Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
887%COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
888%their neutral transfer coefficients relationships with neutral wind.
889%\begin{itemize}
890%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
891%  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
892%  They use an inertial dissipative method to compute the turbulent transfer coefficients
893%  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
894%  This \citet{large.yeager_rpt04} dataset is available through
895%  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
896%  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
897%  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
898%\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details
899%\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details
900%\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9204}{IFS (Cy40r1)} %implementation and documentation.
901%  Surface roughness lengths needed for the Obukhov length are computed
902%  following \citet{beljaars_QJRMS95}.
903%\end{itemize}
904
905%% =================================================================================================
906\subsection{Ice-Atmosphere Bulk formulae}
907\label{subsec:SBC_blk_ice}
908
909
910\texttt{\#out\_of\_place:}
911 For sea-ice, three possibilities can be selected:
912a constant transfer coefficient (1.4e-3; default
913value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
914and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
915\texttt{\#out\_of\_place.}
916
917
918
919
920Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
921
922\begin{itemize}
923\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
924  default constant value used for momentum and heat neutral transfer coefficients
925\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
926  This scheme adds a dependency on edges at leads, melt ponds and flows
927  of the constant neutral air-ice drag. After some approximations,
928  this can be resumed to a dependency on ice concentration (A).
929  This drag coefficient has a parabolic shape (as a function of ice concentration)
930  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.
931  It is theoretically applicable to all ice conditions (not only MIZ).
932\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
933  Alternative turbulent transfer coefficients formulation between sea-ice
934  and atmosphere with distinct momentum and heat coefficients depending
935  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
936  The parameterization is adapted from ECHAM6 atmospheric model.
937  Compared to Lupkes2012 scheme, it considers specific skin and form drags
938  to compute neutral transfer coefficients for both heat and momentum fluxes.
939  Atmospheric stability effect on transfer coefficient is also taken into account.
940\end{itemize}
941
942%% =================================================================================================
943\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
944\label{sec:SBC_cpl}
945
946\begin{listing}
947  \nlst{namsbc_cpl}
948  \caption{\forcode{&namsbc_cpl}}
949  \label{lst:namsbc_cpl}
950\end{listing}
951
952In the coupled formulation of the surface boundary condition,
953the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
954while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
955the atmospheric component.
956
957A generalised coupled interface has been developed.
958It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
959An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
960It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
961(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
962(Weather Research and Forecasting Model).
963
964When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
965the whole carbon cycle is computed.
966In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
967(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
968
969The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
970now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
971When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
972the number used in the sea ice model.
973In some limited cases, it may be possible to specify single category coupling fields even when
974the sea ice model is running with multiple categories -
975in this case, the user should examine the code to be sure the assumptions made are satisfactory.
976In cases where this is definitely not possible, the model should abort with an error message.
977
978%% =================================================================================================
979\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
980\label{sec:SBC_apr}
981
982\begin{listing}
983  \nlst{namsbc_apr}
984  \caption{\forcode{&namsbc_apr}}
985  \label{lst:namsbc_apr}
986\end{listing}
987
988The optional atmospheric pressure can be used to force ocean and ice dynamics
989(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
990The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
991can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
992When used to force the dynamics, the atmospheric pressure is further transformed into
993an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
994\[
995  % \label{eq:SBC_ssh_ib}
996  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
997\]
998where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
999A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
1000In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
1001\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
1002
1003The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
1004For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
1005(see \mdl{sbcssr} module).
1006$\eta_{ib}$ can be written in the output.
1007This can simplify altimetry data and model comparison as
1008inverse barometer sea surface height is usually removed from these date prior to their distribution.
1009
1010When using time-splitting and BDY package for open boundaries conditions,
1011the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
1012\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
1013
1014%% =================================================================================================
1015\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
1016\label{sec:SBC_tide}
1017
1018\begin{listing}
1019  \nlst{nam_tide}
1020  \caption{\forcode{&nam_tide}}
1021  \label{lst:nam_tide}
1022\end{listing}
1023
1024The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
1025is 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}.
1026This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
1027\[
1028  % \label{eq:SBC_PE_dyn_tides}
1029  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
1030  +g\nabla (\Pi_{eq} + \Pi_{sal})
1031\]
1032where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
1033$\Pi_{sal}$ is a self-attraction and loading term (SAL).
1034
1035The equilibrium tidal forcing is expressed as a sum over a subset of
1036constituents chosen from the set of available tidal constituents
1037defined in file \hf{SBC/tide} (this comprises the tidal
1038constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
1039  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
1040constituents are selected by including their names in the array
1041\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
1042\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
1043and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
1044\forcode{.true.}, the equilibrium tidal forcing can be ramped up
1045linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
1046model run.
1047
1048The SAL term should in principle be computed online as it depends on
1049the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
1050discussion about the practical implementation of this term).
1051Nevertheless, the complex calculations involved would make this
1052computationally too expensive. Here, two options are available:
1053$\Pi_{sal}$ generated by an external model can be read in
1054(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
1055used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
1056\[
1057  \Pi_{sal} = \beta \eta,
1058\]
1059where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
1060spatially constant scalar, often chosen to minimize tidal prediction
1061errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
1062\forcode{.false.} removes the SAL contribution.
1063
1064%% =================================================================================================
1065\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
1066\label{sec:SBC_rnf}
1067
1068\begin{listing}
1069  \nlst{namsbc_rnf}
1070  \caption{\forcode{&namsbc_rnf}}
1071  \label{lst:namsbc_rnf}
1072\end{listing}
1073
1074%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1075%Many models, however, have traditionally inserted river runoff to the top model cell.
1076%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
1077%throughout a nonzero depth has been motivated by the numerical and physical problems
1078%that arise when the top grid cells are of the order of one meter. This situation is common in
1079%coastal modelling and becomes more and more often open ocean and climate modelling
1080%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
1081%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
1082
1083%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
1084%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
1085%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
1086%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
1087%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
1088%emp or emps and the changes made are below:
1089
1090%Rachel:
1091River runoff generally enters the ocean at a nonzero depth rather than through the surface.
1092Many models, however, have traditionally inserted river runoff to the top model cell.
1093This was the case in \NEMO\ prior to the version 3.3,
1094and was combined with an option to increase vertical mixing near the river mouth.
1095
1096However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
1097This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
1098\footnote{
1099  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
1100  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
1101  see also \autoref{fig:SBC_dcy}.}.
1102
1103As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
1104and for the temperature and salinity of the river to effect the surrounding ocean.
1105The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
1106along with the depth (in metres) which the river should be added to.
1107
1108Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
1109\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
1110If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
1111and/or taken as surface temperature respectively.
1112
1113The runoff value and attributes are read in in sbcrnf.
1114For temperature -999 is taken as missing data and the river temperature is taken to
1115be the surface temperatue at the river point.
1116For the depth parameter a value of -1 means the river is added to the surface box only,
1117and a value of -999 means the river is added through the entire water column.
1118After being read in the temperature and salinity variables are multiplied by the amount of runoff
1119(converted into m/s) to give the heat and salt content of the river runoff.
1120After the user specified depth is read ini,
1121the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
1122The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
1123the bottom of the lowest box the river water is being added to
1124(\ie\ the total depth that river water is being added to in the model).
1125
1126The mass/volume addition due to the river runoff is, at each relevant depth level, added to
1127the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
1128This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
1129The sea surface height is calculated using the sum of the horizontal divergence terms,
1130and so the river runoff indirectly forces an increase in sea surface height.
1131
1132The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
1133This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
1134The heat and salt content of the river runoff is not included in this step,
1135and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
1136the box and replaced by the same volume of river water with no corresponding heat and salt addition.
1137
1138For the linear free surface case, at the surface box the tracer advection causes a flux of water
1139(of equal volume to the runoff) through the sea surface out of the domain,
1140which causes a salt and heat flux out of the model.
1141As such the volume of water does not change, but the water is diluted.
1142
1143For the non-linear free surface case, no flux is allowed through the surface.
1144Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
1145no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
1146(The runoff addition to the top box along with the water being moved up through
1147boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
1148
1149In trasbc the addition of heat and salt due to the river runoff is added.
1150This is done in the same way for both vvl and non-vvl.
1151The temperature and salinity are increased through the specified depth according to
1152the heat and salt content of the river.
1153
1154In the non-linear free surface case (vvl),
1155near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
1156so that the original ratios of grid box heights are restored.
1157In doing this water is moved into boxes below, throughout the water column,
1158so the large volume addition to the surface box is spread between all the grid boxes.
1159
1160It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
1161\ie\ modelling the Baltic flow in and out of the North Sea.
1162When the flow is out of the domain there is no change in temperature and salinity,
1163regardless of the namelist options used,
1164as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
1165
1166%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1167
1168%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1169
1170%\colorbox{yellow}{river mouths{\ldots}}
1171
1172%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1173%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1174%ENDIF
1175
1176\cmtgm{  word doc of runoffs:
1177In the current \NEMO\ setup river runoff is added to emp fluxes,
1178these are then applied at just the sea surface as a volume change (in the variable volume case
1179this is a literal volume change, and in the linear free surface case the free surface is moved)
1180and a salt flux due to the concentration/dilution effect.
1181There is also an option to increase vertical mixing near river mouths;
1182this gives the effect of having a 3d river.
1183All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and
1184at the same temperature as the sea surface.
1185Our aim was to code the option to specify the temperature and salinity of river runoff,
1186(as well as the amount), along with the depth that the river water will affect.
1187This would make it possible to model low salinity outflow, such as the Baltic,
1188and would allow the ocean temperature to be affected by river runoff.
1189
1190The depth option makes it possible to have the river water affecting just the surface layer,
1191throughout depth, or some specified point in between.
1192
1193To do this we need to treat evaporation/precipitation fluxes and river runoff differently in
1194the \mdl{tra_sbc} module.
1195We decided to separate them throughout the code,
1196so that the variable emp represented solely evaporation minus precipitation fluxes,
1197and a new 2d variable rnf was added which represents the volume flux of river runoff
1198(in $kg/m^2s$ to remain consistent with $emp$).
1199This meant many uses of emp and emps needed to be changed,
1200a list of all modules which use $emp$ or $emps$ and the changes made are below:}
1201
1202%% =================================================================================================
1203\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
1204\label{sec:SBC_isf}
1205
1206\begin{listing}
1207  \nlst{namsbc_isf}
1208  \caption{\forcode{&namsbc_isf}}
1209  \label{lst:namsbc_isf}
1210\end{listing}
1211
1212The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
1213Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1214The different options are illustrated in \autoref{fig:SBC_isf}.
1215
1216\begin{description}
1217  \item [{\np[=1]{nn_isf}{nn\_isf}}]: The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1218  The fwf and heat flux are depending of the local water properties.
1219
1220  Two different bulk formulae are available:
1221
1222  \begin{description}
1223  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
1224    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
1225  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
1226    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1227    A complete description is available in \citet{jenkins_JGR91}.
1228  \end{description}
1229
1230  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1231  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
1232  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.
1233  Then, the fluxes are spread over the same thickness (ie over one or several cells).
1234  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.
1235  This can lead to super-cool temperature in the top cell under melting condition.
1236  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.\\
1237
1238  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1239  There are 3 different ways to compute the exchange coeficient:
1240  \begin{description}
1241  \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}.
1242    \begin{gather*}
1243       % \label{eq:SBC_isf_gamma_iso}
1244      \gamma^{T} = rn\_gammat0 \\
1245      \gamma^{S} = rn\_gammas0
1246    \end{gather*}
1247    This is the recommended formulation for ISOMIP.
1248  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as
1249    \begin{gather*}
1250      \gamma^{T} = rn\_gammat0 \times u_{*} \\
1251      \gamma^{S} = rn\_gammas0 \times u_{*}
1252    \end{gather*}
1253    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
1254    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1255  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1256    \[
1257      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1258    \]
1259    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
1260    $\Gamma_{Turb}$ the contribution of the ocean stability and
1261    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1262    See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1263    This formulation has not been extensively tested in \NEMO\ (not recommended).
1264  \end{description}
1265\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1266  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1267  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1268  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1269  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
1270  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
1271\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented.
1272  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1273  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
1274  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
1275  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1276\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
1277  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
1278  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1279  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})
1280\end{description}
1281
1282$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
1283the water mass properties, ocean velocities and depth.
1284This flux is thus highly dependent of the model resolution (horizontal and vertical),
1285realism of the water masses onto the shelf ...\\
1286
1287$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
1288You have total control of the fwf forcing.
1289This can be useful if the water masses on the shelf are not realistic or
1290the resolution (horizontal/vertical) are too coarse to have realistic melting or
1291for studies where you need to control your heat and fw input.\\
1292
1293The ice shelf melt is implemented as a volume flux as for the runoff.
1294The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1295the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1296See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1297
1298\begin{figure}[!t]
1299  \centering
1300  \includegraphics[width=0.66\textwidth]{SBC_isf}
1301  \caption[Ice shelf location and fresh water flux definition]{
1302    Illustration of the location where the fwf is injected and
1303    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1304  \label{fig:SBC_isf}
1305\end{figure}
1306
1307%% =================================================================================================
1308\section{Ice sheet coupling}
1309\label{sec:SBC_iscpl}
1310
1311\begin{listing}
1312  \nlst{namsbc_iscpl}
1313  \caption{\forcode{&namsbc_iscpl}}
1314  \label{lst:namsbc_iscpl}
1315\end{listing}
1316
1317Ice sheet/ocean coupling is done through file exchange at the restart step.
1318At each restart step:
1319
1320\begin{enumerate}
1321\item the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1322\item a new domcfg.nc file is built using the DOMAINcfg tools.
1323\item \NEMO\ run for a specific period and output the average melt rate over the period.
1324\item the ice sheet model run using the melt rate outputed in step 4.
1325\item go back to 1.
1326\end{enumerate}
1327
1328If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1329potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1330The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1331
1332\begin{description}
1333\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
1334  ($bt_b=bt_n$).
1335\item [Enlarge  a cell]: See case "Thin a cell down"
1336\item [Dry a cell]: mask, T/S, U/V and ssh are set to 0.
1337  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1338\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.
1339  If no neighbours, T/S is extrapolated from old top cell value.
1340  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1341\item [Dry a column]: mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1342\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.
1343  If no neighbour, T/S/U/V and mask set to 0.
1344\end{description}
1345
1346Furthermore, as the before and now fields are not compatible (modification of the geometry),
1347the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1348
1349The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1350It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1351the code will be unable to fill all the new wet cells properly.
1352The default number is set up for the MISOMIP idealised experiments.
1353This coupling procedure is able to take into account grounding line and calving front migration.
1354However, it is a non-conservative processe.
1355This could lead to a trend in heat/salt content and volume.\\
1356
1357In order to remove the trend and keep the conservation level as close to 0 as possible,
1358a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1359The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1360A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1361For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1362The 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).
1363
1364%% =================================================================================================
1365\section{Handling of icebergs (ICB)}
1366\label{sec:SBC_ICB_icebergs}
1367
1368\begin{listing}
1369  \nlst{namberg}
1370  \caption{\forcode{&namberg}}
1371  \label{lst:namberg}
1372\end{listing}
1373
1374Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1375Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1376(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1377Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1378described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1379Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1380which is an integer representing how many icebergs of this class are being described as one lagrangian point
1381(this reduces the numerical problem of tracking every single iceberg).
1382They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1383
1384Two initialisation schemes are possible.
1385\begin{description}
1386\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
1387  (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
1388  which an iceberg is generated at the beginning of the run.
1389  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1390  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1391  the geographical box: lonmin,lonmax,latmin,latmax
1392\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.
1393  This should be a file with a field on the configuration grid (typically ORCA)
1394  representing ice accumulation rate at each model point.
1395  These should be ocean points adjacent to land where icebergs are known to calve.
1396  Most points in this input grid are going to have value zero.
1397  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1398  At each time step, a test is performed to see if there is enough ice mass to
1399  calve an iceberg of each class in order (1 to 10).
1400  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1401  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1402\end{description}
1403
1404Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1405The latter act to disintegrate the iceberg.
1406This is either all melted freshwater,
1407or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1408which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1409Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1410
1411Extensive diagnostics can be produced.
1412Separate output files are maintained for human-readable iceberg information.
1413A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1414The amount of information is controlled by two integer parameters:
1415\begin{description}
1416\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1417  represents an increasing number of points in the code at which variables are written,
1418  and an increasing level of obscurity.
1419\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1420\end{description}
1421
1422Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1423A non-zero value represents how many timesteps between writes of information into the output file.
1424These output files are in NETCDF format.
1425When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1426Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1427So care is needed to recreate data for individual icebergs,
1428since its trajectory data may be spread across multiple files.
1429
1430%% =================================================================================================
1431\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1432\label{sec:SBC_wave}
1433
1434\begin{listing}
1435  \nlst{namsbc_wave}
1436  \caption{\forcode{&namsbc_wave}}
1437  \label{lst:namsbc_wave}
1438\end{listing}
1439
1440Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1441physical processes related to ocean surface waves, namely the surface stress modified by growth and
1442dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1443tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1444the wind stress.
1445
1446Physical processes related to ocean surface waves can be accounted by setting the logical variable
1447\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1448different processes should be activated as explained in the following sections.
1449
1450Wave fields can be provided either in forced or coupled mode:
1451\begin{description}
1452\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1453for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1454Input Data generic Interface (see \autoref{sec:SBC_input}).
1455\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1456in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1457\end{description}
1458
1459%% =================================================================================================
1460\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1461\label{subsec:SBC_wave_cdgw}
1462
1463The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1464can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1465Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1466the drag coefficient is computed according to the stable/unstable conditions of the
1467air-sea interface following \citet{large.yeager_rpt04}.
1468
1469%% =================================================================================================
1470\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1471\label{subsec:SBC_wave_sdw}
1472
1473The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1474It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1475and the current measured at a fixed point (Eulerian velocity).
1476As waves travel, the water particles that make up the waves travel in orbital motions but
1477without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1478at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1479An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1480representation of surface physics in ocean general circulation models. %GS: reference needed
1481The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1482
1483\[
1484  % \label{eq:SBC_wave_sdw}
1485  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1486  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1487  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1488\]
1489
1490where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1491$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1492$k$ is the mean wavenumber defined as:
1493$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1494
1495In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1496and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1497To simplify, it is customary to use approximations to the full Stokes profile.
1498Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1499are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1500$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1501and makes possible the estimation of the surface Stokes drift for random directional waves in
1502realistic wave conditions:
1503
1504\begin{description}
1505\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1506\citet{breivik.janssen.ea_JPO14}:
1507
1508\[
1509  % \label{eq:SBC_wave_sdw_0a}
1510  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1511\]
1512
1513where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1514
1515\[
1516  % \label{eq:SBC_wave_sdw_0b}
1517  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1518  \quad \text{and }\
1519  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1520\]
1521
1522where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1523
1524\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1525reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1526\citep{breivik.bidlot.ea_OM16}:
1527
1528\[
1529  % \label{eq:SBC_wave_sdw_1}
1530  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1531  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1532\]
1533
1534where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1535
1536\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1537but using the wave frequency from a wave model.
1538
1539\end{description}
1540
1541The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1542and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1543
1544\[
1545  % \label{eq:SBC_wave_eta_sdw}
1546  \frac{\partial{\eta}}{\partial{t}} =
1547  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1548\]
1549
1550The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1551for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1552that is induced by the three-dimensional Stokes velocity.
1553The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1554can be formulated as follows:
1555
1556\[
1557  % \label{eq:SBC_wave_tra_sdw}
1558  \frac{\partial{c}}{\partial{t}} =
1559  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1560\]
1561
1562%% =================================================================================================
1563\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1564\label{subsec:SBC_wave_stcor}
1565
1566In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1567in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1568This additional force may have impact on the Ekman turning of the surface current.
1569In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1570approximations described in \autoref{subsec:SBC_wave_sdw}),
1571\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1572
1573%% =================================================================================================
1574\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1575\label{subsec:SBC_wave_tauw}
1576
1577The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1578into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1579available for forcing the mean circulation, while in the opposite case of a decaying sea
1580state, more momentum is available for forcing the ocean.
1581Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1582but in practice, an equilibrium sea state is a fairly rare event.
1583So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1584
1585\[
1586  % \label{eq:SBC_wave_tauoc}
1587  \tau_{oc,a} = \tau_a - \tau_w
1588\]
1589
1590where $\tau_a$ is the atmospheric surface stress;
1591$\tau_w$ is the atmospheric stress going into the waves defined as:
1592
1593\[
1594  % \label{eq:SBC_wave_tauw}
1595  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1596\]
1597
1598where: $c_p$ is the phase speed of the gravity waves,
1599$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1600the physics of ocean waves. The first one, $S_{in}$, describes the generation
1601of ocean waves by wind and therefore represents the momentum and energy transfer
1602from air to ocean waves; the second term $S_{nl}$ denotes
1603the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1604describes the dissipation of waves by processes such as white-capping, large scale breaking
1605eddy-induced damping.
1606
1607The wave stress derived from an external wave model can be provided either through the normalized
1608wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1609meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1610
1611%% =================================================================================================
1612\section{Miscellaneous options}
1613\label{sec:SBC_misc}
1614
1615%% =================================================================================================
1616\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1617\label{subsec:SBC_dcy}
1618
1619\begin{figure}[!t]
1620  \centering
1621  \includegraphics[width=0.66\textwidth]{SBC_diurnal}
1622  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1623    Example of reconstruction of the diurnal cycle variation of short wave flux from
1624    daily mean values.
1625    The reconstructed diurnal cycle (black line) is chosen as
1626    the mean value of the analytical cycle (blue line) over a time step,
1627    not as the mid time step value of the analytically cycle (red square).
1628    From \citet{bernie.guilyardi.ea_CD07}.}
1629  \label{fig:SBC_diurnal}
1630\end{figure}
1631
1632\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.
1633%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1634Nevertheless, 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}.
1635Furthermore, only the knowledge of daily mean value of SWF is needed,
1636as higher frequency variations can be reconstructed from them,
1637assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1638The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1639setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1640using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1641the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1642The reconstruction is performed in the \mdl{sbcdcy} module.
1643The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1644The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1645a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1646The use of diurnal cycle reconstruction requires the input SWF to be daily
1647(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1648Furthermore, it is recommended to have a least 8 surface module time steps per day,
1649that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1650An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1651one every 2~hours (from 1am to 11pm).
1652
1653\begin{figure}[!t]
1654  \centering
1655  \includegraphics[width=0.66\textwidth]{SBC_dcy}
1656  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1657    Example of reconstruction of the diurnal cycle variation of short wave flux from
1658    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1659    The display is on (i,j) plane.}
1660  \label{fig:SBC_dcy}
1661\end{figure}
1662
1663Note also that the setting a diurnal cycle in SWF is highly recommended when
1664the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1665an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1666
1667%% =================================================================================================
1668\subsection{Rotation of vector pairs onto the model grid directions}
1669\label{subsec:SBC_rotation}
1670
1671When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1672pairs of vector components can be rotated from east-north directions onto the local grid directions.
1673This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1674be defined relative to a rectilinear grid.
1675To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1676The eastward component must start with "U" and the northward component with "V".
1677The remaining characters in the strings are used to identify which pair of components go together.
1678So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1679rotate them on to the model grid directions;
1680"U2" and "V2" could be used against a second pair of components, and so on.
1681The extra characters used in the strings are arbitrary.
1682The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1683
1684%% =================================================================================================
1685\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1686\label{subsec:SBC_ssr}
1687
1688\begin{listing}
1689  \nlst{namsbc_ssr}
1690  \caption{\forcode{&namsbc_ssr}}
1691  \label{lst:namsbc_ssr}
1692\end{listing}
1693
1694Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1695On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1696a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1697\[
1698  % \label{eq:SBC_dmp_q}
1699  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1700\]
1701where SST is a sea surface temperature field (observed or climatological),
1702$T$ is the model surface layer temperature and
1703$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1704For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1705This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1706
1707In the fresh water budget, a feedback term can also be added.
1708Converted into an equivalent freshwater flux, it takes the following expression :
1709
1710\begin{equation}
1711  \label{eq:SBC_dmp_emp}
1712  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1713  {\left.S\right|_{k=1}}
1714\end{equation}
1715
1716where $\textit{emp}_{o }$ is a net surface fresh water flux
1717(observed, climatological or an atmospheric model product),
1718\textit{SSS}$_{Obs}$ is a sea surface salinity
1719(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1720$\left.S\right|_{k=1}$ is the model surface layer salinity and
1721$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1722Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1723the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1724The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1725reduce the uncertainties we have on the observed freshwater budget.
1726
1727%% =================================================================================================
1728\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1729\label{subsec:SBC_ice-cover}
1730
1731The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1732There are several way to handle sea-ice in the system depending on
1733the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1734\begin{description}
1735\item [nn\_ice = 0] there will never be sea-ice in the computational domain.
1736  This is a typical namelist value used for tropical ocean domain.
1737  The surface fluxes are simply specified for an ice-free ocean.
1738  No specific things is done for sea-ice.
1739\item [nn\_ice = 1] sea-ice can exist in the computational domain, but no sea-ice model is used.
1740  An observed ice covered area is read in a file.
1741  Below this area, the SST is restored to the freezing point and
1742  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1743  The associated modification of the freshwater fluxes are done in such a way that
1744  the change in buoyancy fluxes remains zero.
1745  This prevents deep convection to occur when trying to reach the freezing point
1746  (and so ice covered area condition) while the SSS is too large.
1747  This manner of managing sea-ice area, just by using a IF case,
1748  is usually referred as the \textit{ice-if} model.
1749  It can be found in the \mdl{sbcice\_if} module.
1750\item [nn\_ice = 2 or more] A full sea ice model is used.
1751  This model computes the ice-ocean fluxes,
1752  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1753  provide the surface averaged ocean fluxes.
1754  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1755  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1756  (\ie\ $2$ for SI3 or $3$ for CICE).
1757\end{description}
1758
1759% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1760%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1761
1762%% =================================================================================================
1763\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1764\label{subsec:SBC_cice}
1765
1766It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1767to the CICE sea-ice model by using \key{cice}.
1768The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1769the additional 'hadgem3' drivers will be required, even with the latest code release.
1770Input grid files consistent with those used in \NEMO\ will also be needed,
1771and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1772(seek advice from UKMO if necessary).
1773Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1774(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1775or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1776(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1777The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1778(although coupling ocean and ice less frequently should work,
1779it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1780the user should check that results are not significantly different to the standard case).
1781
1782There are two options for the technical coupling between \NEMO\ and CICE.
1783The standard version allows complete flexibility for the domain decompositions in the individual models,
1784but this is at the expense of global gather and scatter operations in the coupling which
1785become very expensive on larger numbers of processors.
1786The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1787the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1788and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1789allows much more efficient direct coupling on individual processors.
1790This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1791there is no sea ice.
1792
1793%% =================================================================================================
1794\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1795\label{subsec:SBC_fwb}
1796
1797For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1798prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1799In \NEMO, two way of controlling the freshwater budget are proposed:
1800
1801\begin{description}
1802\item [{\np[=0]{nn_fwb}{nn\_fwb}}] no control at all.
1803  The mean sea level is free to drift, and will certainly do so.
1804\item [{\np[=1]{nn_fwb}{nn\_fwb}}] global mean \textit{emp} set to zero at each model time step.
1805  %GS: comment below still relevant ?
1806  %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).
1807\item [{\np[=2]{nn_fwb}{nn\_fwb}}] freshwater budget is adjusted from the previous year annual mean budget which
1808  is read in the \textit{EMPave\_old.dat} file.
1809  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1810  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1811\end{description}
1812
1813% Griffies doc:
1814% When running ocean-ice simulations, we are not explicitly representing land processes,
1815% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1816% it is important to balance the hydrological cycle in ocean-ice models.
1817% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1818% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1819% a chosen time scale.
1820% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1821% so that there is always a zero net input of water to the ocean-ice system.
1822% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1823% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1824% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1825% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1826% and ice models when aiming to balance the hydrological cycle.
1827% 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,
1828% not the water in any one sub-component. As an extreme example to illustrate the issue,
1829% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1830% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1831% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1832% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1833% in ocean-ice models.
1834
1835\subinc{\input{../../global/epilogue}}
1836
1837\end{document}
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