New URL for NEMO forge!   http://forge.nemo-ocean.eu

Since March 2022 along with NEMO 4.2 release, the code development moved to a self-hosted GitLab.
This present forge is now archived and remained online for history.
chap_SBC.tex in NEMO/trunk/doc/latex/NEMO/subfiles – NEMO

source: NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex @ 11597

Last change on this file since 11597 was 11597, checked in by nicolasmartin, 3 years ago

Continuation of coding rules application
Recovery of some sections deleted by the previous commit

File size: 91.8 KB
Line 
1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4
5\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
6\label{chap:SBC}
7
8\chaptertoc
9
10
11\begin{listing}
12  \nlst{namsbc}
13  \caption{\forcode{&namsbc}}
14  \label{lst:namsbc}
15\end{listing}
16
17The ocean needs seven fields as surface boundary condition:
18
19\begin{itemize}
20\item the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
21\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
22\item the surface freshwater budget $\left( {\textit{emp}} \right)$
23\item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
24\item the atmospheric pressure at the ocean surface $\left( p_a \right)$
25\end{itemize}
26
27Four different ways are available to provide the seven fields to the ocean. They are controlled by
28namelist \nam{sbc}{sbc} variables:
29
30\begin{itemize}
31\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk} with four possible bulk algorithms),
32\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
33\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
34(\np{ln_cpl}{ln\_cpl} or \np[=.true.]{ln_mixcpl}{ln\_mixcpl}),
35\item a user defined formulation (\np[=.true.]{ln_usr}{ln\_usr}).
36\end{itemize}
37
38The frequency at which the forcing fields have to be updated is given by the \np{nn_fsbc}{nn\_fsbc} namelist parameter.
39
40When the fields are supplied from data files (bulk, flux and mixed formulations),
41the input fields do not need to be supplied on the model grid.
42Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
43the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
44If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
45should be masked or filled to avoid spurious results in proximity of the coasts, as
46large sea-land gradients characterize most of the atmospheric variables.
47
48In addition, the resulting fields can be further modified using several namelist options.
49These options control:
50
51\begin{itemize}
52\item the rotation of vector components supplied relative to an east-north coordinate system onto
53  the local grid directions in the model,
54\item the use of a land/sea mask for input fields (\np[=.true.]{nn_lsm}{nn\_lsm}),
55\item the addition of a surface restoring term to observed SST and/or SSS (\np[=.true.]{ln_ssr}{ln\_ssr}),
56\item the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
57  (\np[=0..3]{nn_ice}{nn\_ice}),
58\item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np[=.true.]{ln_rnf}{ln\_rnf}),
59\item the addition of ice-shelf melting as lateral inflow (parameterisation) or
60  as fluxes applied at the land-ice ocean interface (\np[=.true.]{ln_isf}{ln\_isf}),
61\item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
62  (\np[=0..2]{nn_fwb}{nn\_fwb}),
63\item the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
64  (\np[=.true.]{ln_dm2dc}{ln\_dm2dc}),
65\item the activation of wave effects from an external wave model  (\np[=.true.]{ln_wave}{ln\_wave}),
66\item a neutral drag coefficient is read from an external wave model (\np[=.true.]{ln_cdgw}{ln\_cdgw}),
67\item the Stokes drift from an external wave model is accounted for (\np[=.true.]{ln_sdw}{ln\_sdw}),
68\item the choice of the Stokes drift profile parameterization (\np[=0..2]{nn_sdrift}{nn\_sdrift}),
69\item the surface stress given to the ocean is modified by surface waves (\np[=.true.]{ln_tauwoc}{ln\_tauwoc}),
70\item the surface stress given to the ocean is read from an external wave model (\np[=.true.]{ln_tauw}{ln\_tauw}),
71\item the Stokes-Coriolis term is included (\np[=.true.]{ln_stcor}{ln\_stcor}),
72\item the light penetration in the ocean (\np[=.true.]{ln_traqsr}{ln\_traqsr} with namelist \nam{tra_qsr}{tra\_qsr}),
73\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}),
74\item the effect of sea-ice pressure on the ocean (\np[=.true.]{ln_ice_embd}{ln\_ice\_embd}).
75\end{itemize}
76
77In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
78Then we present the three ways of providing the surface boundary conditions,
79followed by the description of the atmospheric pressure and the river runoff.
80Next, the scheme for interpolation on the fly is described.
81Finally, the different options that further modify the fluxes applied to the ocean are discussed.
82One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
83which act as drifting sources of fresh water.
84Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
85which provides additional sources of fresh water.
86
87%% =================================================================================================
88\section{Surface boundary condition for the ocean}
89\label{sec:SBC_ocean}
90
91The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
92It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
93the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
94As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
95\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
96
97The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
98$Q_{ns}$ and $Q_{sr}$, respectively.
99The former is the non penetrative part of the heat flux
100(\ie\ the sum of sensible, latent and long wave heat fluxes plus
101the heat content of the mass exchange between the ocean and sea-ice).
102It is applied in \mdl{trasbc} module as a surface boundary condition trend of
103the first level temperature time evolution equation
104(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
105The latter is the penetrative part of the heat flux.
106It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
107\np[=.true.]{ln_traqsr}{ln\_traqsr}.
108The way the light penetrates inside the water column is generally a sum of decreasing exponentials
109(see \autoref{subsec:TRA_qsr}).
110
111The surface freshwater budget is provided by the \textit{emp} field.
112It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
113possibly with the sea-ice and ice shelves (freezing minus melting of ice).
114It affects the ocean in two different ways:
115$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
116a volume flux, and
117$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
118the mass exchanged with atmosphere, sea-ice and ice shelves.
119
120%\colorbox{yellow}{Miss: }
121%
122%A extensive description of all namsbc namelist (parameter that have to be
123%created!)
124%
125%Especially the \np{nn_fsbc}{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
126%ssv) \ie\ information required by flux computation or sea-ice
127%
128%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
129%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
130%
131%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
132%
133%Fluxes update only each nf\_sbc time step (namsbc) explain relation
134%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
135%nf\_sbc
136%
137%Explain here all the namlist namsbc variable{\ldots}.
138%
139% explain : use or not of surface currents
140%
141%\colorbox{yellow}{End Miss }
142
143The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
144the surface currents, temperature and salinity.
145These variables are averaged over \np{nn_fsbc}{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
146these averaged fields are used to compute the surface fluxes at the frequency of \np{nn_fsbc}{nn\_fsbc} time-steps.
147
148\begin{table}[tb]
149  \centering
150  \begin{tabular}{|l|l|l|l|}
151    \hline
152    Variable description                           & Model variable  & Units  & point                 \\
153    \hline
154    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
155    \hline
156    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
157    \hline
158    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
159    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
160  \end{tabular}
161  \caption[Ocean variables provided to the surface module)]{
162    Ocean variables provided to the surface module (\texttt{SBC}).
163    The variable are averaged over \protect\np{nn_fsbc}{nn\_fsbc} time-step,
164    \ie\ the frequency of computation of surface fluxes.}
165  \label{tab:SBC_ssm}
166\end{table}
167
168%\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
169
170%% =================================================================================================
171\section{Input data generic interface}
172\label{sec:SBC_input}
173
174A generic interface has been introduced to manage the way input data
175(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
176This task is achieved by \mdl{fldread}.
177The module is designed with four main objectives in mind:
178\begin{enumerate}
179\item optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
180  and according to the different calendars available in the model.
181\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
182\item make the run duration independent from the period cover by the input files.
183\item provide a simple user interface and a rather simple developer interface by
184  limiting the number of prerequisite informations.
185\end{enumerate}
186
187As a result, the user has only to fill in for each variable a structure in the namelist file to
188define the input data file and variable names, the frequency of the data (in hours or months),
189whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
190and three additional parameters for the on-the-fly interpolation.
191When adding a new input variable, the developer has to add the associated structure in the namelist,
192read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
193and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
194
195The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
196(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
197if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
198
199Note that when an input data is archived on a disc which is accessible directly from the workspace where
200the code is executed, then the user can set the \np{cn_dir}{cn\_dir} to the pathway leading to the data.
201By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
202
203%% =================================================================================================
204\subsection[Input data specification (\textit{fldread.F90})]{Input data specification (\protect\mdl{fldread})}
205\label{subsec:SBC_fldread}
206
207The structure associated with an input variable contains the following information:
208\begin{forlines}
209!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
210!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
211\end{forlines}
212where
213\begin{description}
214\item [File name]:
215  the stem name of the NetCDF file to be opened.
216  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
217  by date information and possibly a prefix (when using AGRIF).
218  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
219  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
220
221  \begin{table}[htbp]
222    \centering
223    \begin{tabular}{|l|c|c|c|}
224      \hline
225                                  &  daily or weekLL     &  monthly           &  yearly        \\
226      \hline
227      \np[=.false.]{clim}{clim} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
228      \hline
229      \np[=.true.]{clim}{clim}  &  not possible        &  fn\_m??.nc        &  fn            \\
230      \hline
231    \end{tabular}
232    \caption[Naming nomenclature for climatological or interannual input file]{
233      Naming nomenclature for climatological or interannual input file,
234      as a function of the open/close frequency.
235      The stem name is assumed to be 'fn'.
236      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
237      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
238      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
239      always coded with 4 or 2 digits.
240      Note that (1) in mpp, if the file is split over each subdomain,
241      the suffix '.nc' is replaced by '\_PPPP.nc',
242      where 'PPPP' is the process number coded with 4 digits;
243      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
244    }
245    \label{tab:SBC_fldread}
246  \end{table}
247
248\item [Record frequency]:
249  the frequency of the records contained in the input file.
250  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
251  (for example -1 for monthly forcing or -12 for annual forcing).
252  Note that this frequency must REALLY be an integer and not a real.
253  On some computers, setting it to '24.' can be interpreted as 240!
254
255\item [Variable name]:
256  the name of the variable to be read in the input NetCDF file.
257
258\item [Time interpolation]:
259  a logical to activate, or not, the time interpolation.
260  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
261  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
262  00h00'00'' to 23h59'59".
263  If set to 'true', the forcing will have a broken line shape.
264  Records are assumed to be dated at the middle of the forcing period.
265  For example, when using a daily forcing with time interpolation,
266  linear interpolation will be performed between mid-day of two consecutive days.
267
268\item [Climatological forcing]:
269  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
274\item [Open/close frequency]:
275  the frequency at which forcing files must be opened/closed.
276  Four cases are coded:
277  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
278  means the forcing files will contain data for one day, one week, one month or one year.
279  Files are assumed to contain data from the beginning of the open/close period.
280  For example, the first record of a yearly file containing daily data is Jan 1st even if
281  the experiment is not starting at the beginning of the year.
282
283\item [Others]:
284  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
285  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
286
287\end{description}
288
289Additional remarks:\\
290(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
291The only tricky point is therefore to specify the date at which we need to do the interpolation and
292the date of the records read in the input files.
293Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
294For example, for an experiment starting at 0h00'00" with a one-hour time-step,
295a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
296However, for forcing data related to the surface module,
297values are not needed at every time-step but at every \np{nn_fsbc}{nn\_fsbc} time-step.
298For example with \np[=3]{nn_fsbc}{nn\_fsbc}, the surface module will be called at time-steps 1, 4, 7, etc.
299The date used for the time interpolation is thus redefined to the middle of \np{nn_fsbc}{nn\_fsbc} time-step period.
300In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
301(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
302The calendar associated with the forcing field is build according to the information provided by
303user in the record frequency, the open/close frequency and the type of temporal interpolation.
304For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
305start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
306(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
307interpolating data with the first (last) record of the open/close period.
308For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
309the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
310Dec 31st 12h00'00" and Jan 1st 12h00'00".
311If the forcing is climatological, Dec and Jan will be keep-up from the same year.
312However, if the forcing is not climatological, at the end of
313the open/close period, the code will automatically close the current file and open the next one.
314Note that, if the experiment is starting (ending) at the beginning (end) of
315an open/close period, we do accept that the previous (next) file is not existing.
316In this case, the time interpolation will be performed between two identical values.
317For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
318we do accept that the file related to year Y-1 is not existing.
319The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
320If the file of year Y-1 exists, the code will read its last record.
321Therefore, this file can contain only one record corresponding to Dec 31st,
322a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
323
324%% =================================================================================================
325\subsection{Interpolation on-the-fly}
326\label{subsec:SBC_iof}
327
328Interpolation on the Fly allows the user to supply input files required for the surface forcing on
329grids other than the model grid.
330To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
331interpolate from the data grid to the model grid.
332The original development of this code used the SCRIP package
333(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
334In principle, any package such as CDO can be used to generate the weights, but the variables in
335the input weights file must have the same names and meanings as assumed by the model.
336Two methods are currently available: bilinear and bicubic interpolations.
337Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
338the input file and substitute the corresponding values with the average of the 8 neighbouring points in
339the native external grid.
340Only "sea points" are considered for the averaging.
341The land/sea mask file must be provided in the structure associated with the input variable.
342The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
343the associated variables and should be equal to 1 over land and 0 elsewhere.
344The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
345Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
346
347%% =================================================================================================
348\subsubsection{Bilinear interpolation}
349\label{subsec:SBC_iof_bilinear}
350
351The input weights file in this case has two sets of variables:
352src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
353The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
354Each src value is an integer corresponding to the index of a point in the input grid when
355written as a one dimensional array.
356For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
357There are four of each variable because bilinear interpolation uses the four points defining
358the grid box containing the point to be interpolated.
359All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
360generate a value for point (i,j) in the model.
361
362Symbolically, the algorithm used is:
363\[
364  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
365\]
366where function idx() transforms a one dimensional index src(k) into a two dimensional index,
367and wgt(1) corresponds to variable "wgt01" for example.
368
369%% =================================================================================================
370\subsubsection{Bicubic interpolation}
371\label{subsec:SBC_iof_bicubic}
372
373Again, there are two sets of variables: "src" and "wgt".
374But in this case, there are 16 of each.
375The symbolic algorithm used to calculate values on the model grid is now:
376
377\[
378  \begin{split}
379    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
380    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
381    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
382    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
383  \end{split}
384\]
385The gradients here are taken with respect to the horizontal indices and not distances since
386the spatial dependency has been included into the weights.
387
388%% =================================================================================================
389\subsubsection{Implementation}
390\label{subsec:SBC_iof_imp}
391
392To activate this option, a non-empty string should be supplied in
393the weights filename column of the relevant namelist;
394if this is left as an empty string no action is taken.
395In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
396as and when they are first required.
397This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
398inspecting a global attribute stored in the weights input file.
399This attribute must be called "ew\_wrap" and be of integer type.
400If it is negative, the input non-model grid is assumed to be not cyclic.
401If zero or greater, then the value represents the number of columns that overlap.
402$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
403if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
404If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
405In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
406therefore the grid is assumed to be cyclic with no overlapping columns.
407(In fact, this only matters when bicubic interpolation is required.)
408Note that no testing is done to check the validity in the model,
409since there is no way of knowing the name used for the longitude variable,
410so it is up to the user to make sure his or her data is correctly represented.
411
412Next the routine reads in the weights.
413Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
414The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
415and when required, for reading in the variable to be interpolated (on the input data grid).
416The size of the input data array is determined by examining the values in the "src" arrays to
417find the minimum and maximum i and j values required.
418Since bicubic interpolation requires the calculation of gradients at each point on the grid,
419the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
420When the array of points from the data file is adjacent to an edge of the data grid,
421the halo is either a copy of the row/column next to it (non-cyclical case),
422or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
423
424%% =================================================================================================
425\subsubsection{Limitations}
426\label{subsec:SBC_iof_lim}
427
428\begin{enumerate}
429\item The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
430\item This code is not guaranteed to produce positive definite answers from positive definite inputs when
431  a bicubic interpolation method is used.
432\item The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
433\item The gradients across the ends of a cyclical grid assume that the grid spacing between
434  the two columns involved are consistent with the weights used.
435\item Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
436  but this has not been implemented.)
437\end{enumerate}
438
439%% =================================================================================================
440\subsubsection{Utilities}
441\label{subsec:SBC_iof_util}
442
443% to be completed
444A set of utilities to create a weights file for a rectilinear input grid is available
445(see the directory NEMOGCM/TOOLS/WEIGHTS).
446
447%% =================================================================================================
448\subsection{Standalone surface boundary condition scheme (SAS)}
449\label{subsec:SBC_SAS}
450
451
452\begin{listing}
453  \nlst{namsbc_sas}
454  \caption{\forcode{&namsbc_sas}}
455  \label{lst:namsbc_sas}
456\end{listing}
457
458In some circumstances, it may be useful to avoid calculating the 3D temperature,
459salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
460For example:
461
462\begin{itemize}
463\item Multiple runs of the model are required in code development to
464  see the effect of different algorithms in the bulk formulae.
465\item The effect of different parameter sets in the ice model is to be examined.
466\item Development of sea-ice algorithms or parameterizations.
467\item Spinup of the iceberg floats
468\item Ocean/sea-ice simulation with both models running in parallel (\np[=.true.]{ln_mixcpl}{ln\_mixcpl})
469\end{itemize}
470
471The Standalone Surface scheme provides this capacity.
472Its options are defined through the \nam{sbc_sas}{sbc\_sas} namelist variables.
473A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
474However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
475In this configuration, a few routines in the standard model are overriden by new versions.
476Routines replaced are:
477
478\begin{itemize}
479\item \mdl{nemogcm}:
480  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
481  Since the ocean state is not calculated all associated initialisations have been removed.
482\item \mdl{step}:
483  The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
484\item \mdl{sbcmod}:
485  This has been cut down and now only calculates surface forcing and the ice model required.
486  New surface modules that can function when only the surface level of the ocean state is defined can also be added
487  (\eg\ icebergs).
488\item \mdl{daymod}:
489  No ocean restarts are read or written (though the ice model restarts are retained),
490  so calls to restart functions have been removed.
491  This also means that the calendar cannot be controlled by time in a restart file,
492  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
493\item \mdl{stpctl}:
494  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
495\item \mdl{diawri}:
496  All 3D data have been removed from the output.
497  The surface temperature, salinity and velocity components (which have been read in) are written along with
498  relevant forcing and ice data.
499\end{itemize}
500
501One new routine has been added:
502
503\begin{itemize}
504\item \mdl{sbcsas}:
505  This module initialises the input files needed for reading temperature, salinity and
506  velocity arrays at the surface.
507  These filenames are supplied in namelist namsbc\_sas.
508  Unfortunately, because of limitations with the \mdl{iom} module,
509  the full 3D fields from the mean files have to be read in and interpolated in time,
510  before using just the top level.
511  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
512\end{itemize}
513
514The 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
515 (\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.
516
517%% =================================================================================================
518\section[Flux formulation (\textit{sbcflx.F90})]{Flux formulation (\protect\mdl{sbcflx})}
519\label{sec:SBC_flx}
520
521\begin{listing}
522  \nlst{namsbc_flx}
523  \caption{\forcode{&namsbc_flx}}
524  \label{lst:namsbc_flx}
525\end{listing}
526
527In the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
528the surface boundary condition fields are directly read from input files.
529The user has to define in the namelist \nam{sbc_flx}{sbc\_flx} the name of the file,
530the name of the variable read in the file, the time frequency at which it is given (in hours),
531and a logical setting whether a time interpolation to the model time step is required for this field.
532See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
533
534Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
535See \autoref{subsec:SBC_ssr} for its specification.
536
537%% =================================================================================================
538\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
539\label{sec:SBC_blk}
540
541\begin{listing}
542  \nlst{namsbc_blk}
543  \caption{\forcode{&namsbc_blk}}
544  \label{lst:namsbc_blk}
545\end{listing}
546
547In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields
548and ocean (and sea-ice) variables averaged over \np{nn_fsbc}{nn\_fsbc} time-step.
549
550The atmospheric fields used depend on the bulk formulae used.
551In forced mode, when a sea-ice model is used, a specific bulk formulation is used.
552Therefore, different bulk formulae are used for the turbulent fluxes computation
553over the ocean and over sea-ice surface.
554For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}):
555the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae.
556The choice is made by setting to true one of the following namelist variable:
557 \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}\np{ln_COARE_3p5}{ln\_COARE\_3p5} and  \np{ln_ECMWF}{ln\_ECMWF}.
558For sea-ice, three possibilities can be selected:
559a constant transfer coefficient (1.4e-3; default value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
560
561Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables.
562The required 9 input fields are:
563
564\begin{table}[htbp]
565  \centering
566  \begin{tabular}{|l|c|c|c|}
567    \hline
568    Variable description                 & Model variable & Units              & point \\
569    \hline
570    i-component of the 10m air velocity  & utau           & $m.s^{-1}$         & T     \\
571    \hline
572    j-component of the 10m air velocity  & vtau           & $m.s^{-1}$         & T     \\
573    \hline
574    10m air temperature                  & tair           & \r{}$K$            & T     \\
575    \hline
576    Specific humidity                    & humi           & \%                 & T     \\
577    \hline
578    Incoming long wave radiation         & qlw            & $W.m^{-2}$         & T     \\
579    \hline
580    Incoming short wave radiation        & qsr            & $W.m^{-2}$         & T     \\
581    \hline
582    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
583    \hline
584    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
585    \hline
586    Mean sea-level pressure              & slp            & $hPa$              & T     \\
587    \hline
588    \end{tabular}
589  \label{tab:SBC_BULK}
590\end{table}
591
592Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
593It is simpler and faster (less fields to be read), but it is not the recommended method when
594the ocean grid size is the same or larger than the one of the input atmospheric fields.
595
596The \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},
597\np{sn_snow}{sn\_snow}, \np{sn_tdif}{sn\_tdif} parameters describe the fields and the way they have to be used
598(spatial and temporal interpolations).
599
600\np{cn_dir}{cn\_dir} is the directory of location of bulk files
601\np{ln_taudif}{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
602\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m)
603\np{rn_zu}{rn\_zu}: is the height of wind measurements (m)
604
605Three multiplicative factors are available:
606\np{rn_pfac}{rn\_pfac} and \np{rn_efac}{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
607increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
608The third one,\np{rn_vfac}{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
609the calculation of surface wind stress.
610Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
611
612As for the flux formulation, information about the input data required by the model is provided in
613the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
614
615%% =================================================================================================
616\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.F90, sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}
617\label{subsec:SBC_blk_ocean}
618
619Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
620COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
621their neutral transfer coefficients relationships with neutral wind.
622\begin{itemize}
623\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}):
624  The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
625  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
626  They use an inertial dissipative method to compute the turbulent transfer coefficients
627  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
628  This \citet{large.yeager_rpt04} dataset is available through
629  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
630  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
631  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
632\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}):
633  See \citet{fairall.bradley.ea_JC03} for more details
634\item COARE 3.5 (\np[=.true.]{ln_COARE_3p5}{ln\_COARE\_3p5}):
635  See \citet{edson.jampana.ea_JPO13} for more details
636\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}):
637  Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation.
638  Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}.
639\end{itemize}
640
641%% =================================================================================================
642\subsection{Ice-Atmosphere Bulk formulae}
643\label{subsec:SBC_blk_ice}
644
645Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
646
647\begin{itemize}
648\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
649  default constant value used for momentum and heat neutral transfer coefficients
650\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
651  This scheme adds a dependency on edges at leads, melt ponds and flows
652  of the constant neutral air-ice drag. After some approximations,
653  this can be resumed to a dependency on ice concentration (A).
654  This drag coefficient has a parabolic shape (as a function of ice concentration)
655  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.
656  It is theoretically applicable to all ice conditions (not only MIZ).
657\item \citet{lupkes.gryanik_JGR15} (\np[=.true.]{ln_Cd_L15}{ln\_Cd\_L15}):
658  Alternative turbulent transfer coefficients formulation between sea-ice
659  and atmosphere with distinct momentum and heat coefficients depending
660  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
661  The parameterization is adapted from ECHAM6 atmospheric model.
662  Compared to Lupkes2012 scheme, it considers specific skin and form drags
663  to compute neutral transfer coefficients for both heat and momentum fluxes.
664  Atmospheric stability effect on transfer coefficient is also taken into account.
665\end{itemize}
666
667%% =================================================================================================
668\section[Coupled formulation (\textit{sbccpl.F90})]{Coupled formulation (\protect\mdl{sbccpl})}
669\label{sec:SBC_cpl}
670
671\begin{listing}
672  \nlst{namsbc_cpl}
673  \caption{\forcode{&namsbc_cpl}}
674  \label{lst:namsbc_cpl}
675\end{listing}
676
677In the coupled formulation of the surface boundary condition,
678the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
679while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
680the atmospheric component.
681
682A generalised coupled interface has been developed.
683It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
684An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
685It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
686(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
687(Weather Research and Forecasting Model).
688
689When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
690the whole carbon cycle is computed.
691In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
692(and need to be activated in \nam{sbc_cpl}{sbc\_cpl} ).
693
694The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
695now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
696When indicating a multi-category coupling field in \nam{sbc_cpl}{sbc\_cpl}, the number of categories will be determined by
697the number used in the sea ice model.
698In some limited cases, it may be possible to specify single category coupling fields even when
699the sea ice model is running with multiple categories -
700in this case, the user should examine the code to be sure the assumptions made are satisfactory.
701In cases where this is definitely not possible, the model should abort with an error message.
702
703%% =================================================================================================
704\section[Atmospheric pressure (\textit{sbcapr.F90})]{Atmospheric pressure (\protect\mdl{sbcapr})}
705\label{sec:SBC_apr}
706
707\begin{listing}
708  \nlst{namsbc_apr}
709  \caption{\forcode{&namsbc_apr}}
710  \label{lst:namsbc_apr}
711\end{listing}
712
713The optional atmospheric pressure can be used to force ocean and ice dynamics
714(\np[=.true.]{ln_apr_dyn}{ln\_apr\_dyn}, \nam{sbc}{sbc} namelist).
715The input atmospheric forcing defined via \np{sn_apr}{sn\_apr} structure (\nam{sbc_apr}{sbc\_apr} namelist)
716can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
717When used to force the dynamics, the atmospheric pressure is further transformed into
718an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
719\[
720  % \label{eq:SBC_ssh_ib}
721  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
722\]
723where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
724A value of $101,000~N/m^2$ is used unless \np{ln_ref_apr}{ln\_ref\_apr} is set to true.
725In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
726\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
727
728The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
729For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
730(see \mdl{sbcssr} module).
731$\eta_{ib}$ can be written in the output.
732This can simplify altimetry data and model comparison as
733inverse barometer sea surface height is usually removed from these date prior to their distribution.
734
735When using time-splitting and BDY package for open boundaries conditions,
736the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
737\np{ln_apr_obc}{ln\_apr\_obc}  might be set to true.
738
739%% =================================================================================================
740\section[Surface tides (\textit{sbctide.F90})]{Surface tides (\protect\mdl{sbctide})}
741\label{sec:SBC_tide}
742
743
744\begin{listing}
745  \nlst{nam_tide}
746  \caption{\forcode{&nam_tide}}
747  \label{lst:nam_tide}
748\end{listing}
749
750The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
751is 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}.
752This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
753\[
754  % \label{eq:SBC_PE_dyn_tides}
755  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
756  +g\nabla (\Pi_{eq} + \Pi_{sal})
757\]
758where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
759$\Pi_{sal}$ is a self-attraction and loading term (SAL).
760
761The equilibrium tidal forcing is expressed as a sum over a subset of
762constituents chosen from the set of available tidal constituents
763defined in file \hf{SBC/tide} (this comprises the tidal
764constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
765  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
766constituents are selected by including their names in the array
767\np{clname}{clname} in \nam{_tide}{\_tide} (e.g., \np{clname}{clname}\forcode{(1)='M2', }
768\np{clname}{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
769and \textit{S2}). Optionally, when \np{ln_tide_ramp}{ln\_tide\_ramp} is set to
770\forcode{.true.}, the equilibrium tidal forcing can be ramped up
771linearly from zero during the initial \np{rdttideramp}{rdttideramp} days of the
772model run.
773
774The SAL term should in principle be computed online as it depends on
775the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
776discussion about the practical implementation of this term).
777Nevertheless, the complex calculations involved would make this
778computationally too expensive. Here, two options are available:
779$\Pi_{sal}$ generated by an external model can be read in
780(\np[=.true.]{ln_read_load}{ln\_read\_load}), or a ``scalar approximation'' can be
781used (\np[=.true.]{ln_scal_load}{ln\_scal\_load}). In the latter case
782\[
783  \Pi_{sal} = \beta \eta,
784\]
785where $\beta$ (\np{rn_scal_load}{rn\_scal\_load} with a default value of 0.094) is a
786spatially constant scalar, often chosen to minimize tidal prediction
787errors. Setting both \np{ln_read_load}{ln\_read\_load} and \np{ln_scal_load}{ln\_scal\_load} to
788\forcode{.false.} removes the SAL contribution.
789
790%% =================================================================================================
791\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
792\label{sec:SBC_rnf}
793
794\begin{listing}
795  \nlst{namsbc_rnf}
796  \caption{\forcode{&namsbc_rnf}}
797  \label{lst:namsbc_rnf}
798\end{listing}
799
800%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
801%Many models, however, have traditionally inserted river runoff to the top model cell.
802%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
803%throughout a nonzero depth has been motivated by the numerical and physical problems
804%that arise when the top grid cells are of the order of one meter. This situation is common in
805%coastal modelling and becomes more and more often open ocean and climate modelling
806%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
807%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
808
809%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
810%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
811%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
812%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
813%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
814%emp or emps and the changes made are below:
815
816%Rachel:
817River runoff generally enters the ocean at a nonzero depth rather than through the surface.
818Many models, however, have traditionally inserted river runoff to the top model cell.
819This was the case in \NEMO\ prior to the version 3.3,
820and was combined with an option to increase vertical mixing near the river mouth.
821
822However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
823This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
824\footnote{
825  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
826  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
827  see also \autoref{fig:SBC_dcy}.}.
828
829As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
830and for the temperature and salinity of the river to effect the surrounding ocean.
831The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
832along with the depth (in metres) which the river should be added to.
833
834Namelist variables in \nam{sbc_rnf}{sbc\_rnf}, \np{ln_rnf_depth}{ln\_rnf\_depth}, \np{ln_rnf_sal}{ln\_rnf\_sal} and
835\np{ln_rnf_temp}{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
836If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
837and/or taken as surface temperature respectively.
838
839The runoff value and attributes are read in in sbcrnf.
840For temperature -999 is taken as missing data and the river temperature is taken to
841be the surface temperatue at the river point.
842For the depth parameter a value of -1 means the river is added to the surface box only,
843and a value of -999 means the river is added through the entire water column.
844After being read in the temperature and salinity variables are multiplied by the amount of runoff
845(converted into m/s) to give the heat and salt content of the river runoff.
846After the user specified depth is read ini,
847the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz_rnf}{nz\_rnf}.
848The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
849the bottom of the lowest box the river water is being added to
850(\ie\ the total depth that river water is being added to in the model).
851
852The mass/volume addition due to the river runoff is, at each relevant depth level, added to
853the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
854This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
855The sea surface height is calculated using the sum of the horizontal divergence terms,
856and so the river runoff indirectly forces an increase in sea surface height.
857
858The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
859This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
860The heat and salt content of the river runoff is not included in this step,
861and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
862the box and replaced by the same volume of river water with no corresponding heat and salt addition.
863
864For the linear free surface case, at the surface box the tracer advection causes a flux of water
865(of equal volume to the runoff) through the sea surface out of the domain,
866which causes a salt and heat flux out of the model.
867As such the volume of water does not change, but the water is diluted.
868
869For the non-linear free surface case, no flux is allowed through the surface.
870Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
871no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
872(The runoff addition to the top box along with the water being moved up through
873boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
874
875In trasbc the addition of heat and salt due to the river runoff is added.
876This is done in the same way for both vvl and non-vvl.
877The temperature and salinity are increased through the specified depth according to
878the heat and salt content of the river.
879
880In the non-linear free surface case (vvl),
881near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
882so that the original ratios of grid box heights are restored.
883In doing this water is moved into boxes below, throughout the water column,
884so the large volume addition to the surface box is spread between all the grid boxes.
885
886It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
887\ie\ modelling the Baltic flow in and out of the North Sea.
888When the flow is out of the domain there is no change in temperature and salinity,
889regardless of the namelist options used,
890as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
891
892%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
893
894%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
895
896%\colorbox{yellow}{river mouths{\ldots}}
897
898%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
899%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
900%ENDIF
901
902%\gmcomment{  word doc of runoffs:
903%
904%In the current \NEMO\ setup river runoff is added to emp fluxes, these are then applied at just the sea surface as a volume change (in the variable volume case this is a literal volume change, and in the linear free surface case the free surface is moved) and a salt flux due to the concentration/dilution effect.  There is also an option to increase vertical mixing near river mouths; this gives the effect of having a 3d river.  All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.
905%Our aim was to code the option to specify the temperature and salinity of river runoff, (as well as the amount), along with the depth that the river water will affect.  This would make it possible to model low salinity outflow, such as the Baltic, and would allow the ocean temperature to be affected by river runoff.
906
907%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
908
909%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the tra_sbc module.  We decided to separate them throughout the code, so that the variable emp represented solely evaporation minus precipitation fluxes, and a new 2d variable rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use emp or emps and the changes made are below:
910
911%% =================================================================================================
912\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
913\label{sec:SBC_isf}
914
915\begin{listing}
916  \nlst{namsbc_isf}
917  \caption{\forcode{&namsbc_isf}}
918  \label{lst:namsbc_isf}
919\end{listing}
920
921The namelist variable in \nam{sbc}{sbc}, \np{nn_isf}{nn\_isf}, controls the ice shelf representation.
922Description and result of sensitivity test to \np{nn_isf}{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
923The different options are illustrated in \autoref{fig:SBC_isf}.
924
925\begin{description}
926
927  \item [{\np[=1]{nn_isf}{nn\_isf}}]:
928  The ice shelf cavity is represented (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
929  The fwf and heat flux are depending of the local water properties.
930
931  Two different bulk formulae are available:
932
933   \begin{description}
934   \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]:
935     The melt rate is based on a balance between the upward ocean heat flux and
936     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
937   \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]:
938     The melt rate and the heat flux are based on a 3 equations formulation
939     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
940     A complete description is available in \citet{jenkins_JGR91}.
941   \end{description}
942
943     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
944     Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}.
945     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.
946     Then, the fluxes are spread over the same thickness (ie over one or several cells).
947     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.
948     This can lead to super-cool temperature in the top cell under melting condition.
949     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.\\
950
951     Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
952     There are 3 different ways to compute the exchange coeficient:
953   \begin{description}
954        \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]:
955     The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}.
956     \begin{gather*}
957       % \label{eq:SBC_isf_gamma_iso}
958       \gamma^{T} = rn\_gammat0 \\
959       \gamma^{S} = rn\_gammas0
960     \end{gather*}
961     This is the recommended formulation for ISOMIP.
962   \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]:
963     The salt and heat exchange coefficients are velocity dependent and defined as
964     \begin{gather*}
965       \gamma^{T} = rn\_gammat0 \times u_{*} \\
966       \gamma^{S} = rn\_gammas0 \times u_{*}
967     \end{gather*}
968     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters).
969     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
970   \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]:
971     The salt and heat exchange coefficients are velocity and stability dependent and defined as:
972\[
973\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
974\]
975     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters),
976     $\Gamma_{Turb}$ the contribution of the ocean stability and
977     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
978     See \citet{holland.jenkins_JPO99} for all the details on this formulation.
979     This formulation has not been extensively tested in \NEMO\ (not recommended).
980   \end{description}
981  \item [{\np[=2]{nn_isf}{nn\_isf}}]:
982   The ice shelf cavity is not represented.
983   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
984   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
985   (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
986   (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}).
987   The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file.
988  \item [{\np[=3]{nn_isf}{nn\_isf}}]:
989   The ice shelf cavity is not represented.
990   The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
991   the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and
992   the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}).
993   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
994  \item [{\np[=4]{nn_isf}{nn\_isf}}]:
995   The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed).
996   However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}).
997   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
998   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})\\
999\end{description}
1000
1001$\bullet$ \np[=1]{nn_isf}{nn\_isf} and \np[=2]{nn_isf}{nn\_isf} compute a melt rate based on
1002the water mass properties, ocean velocities and depth.
1003This flux is thus highly dependent of the model resolution (horizontal and vertical),
1004realism of the water masses onto the shelf ...\\
1005
1006$\bullet$ \np[=3]{nn_isf}{nn\_isf} and \np[=4]{nn_isf}{nn\_isf} read the melt rate from a file.
1007You have total control of the fwf forcing.
1008This can be useful if the water masses on the shelf are not realistic or
1009the resolution (horizontal/vertical) are too coarse to have realistic melting or
1010for studies where you need to control your heat and fw input.\\
1011
1012The ice shelf melt is implemented as a volume flux as for the runoff.
1013The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1014the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1015See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1016
1017\begin{figure}[!t]
1018  \centering
1019  \includegraphics[width=0.66\textwidth]{Fig_SBC_isf}
1020  \caption[Ice shelf location and fresh water flux definition]{
1021    Illustration of the location where the fwf is injected and
1022    whether or not the fwf is interactif or not depending of \protect\np{nn_isf}{nn\_isf}.}
1023  \label{fig:SBC_isf}
1024\end{figure}
1025
1026%% =================================================================================================
1027\section{Ice sheet coupling}
1028\label{sec:SBC_iscpl}
1029
1030\begin{listing}
1031  \nlst{namsbc_iscpl}
1032  \caption{\forcode{&namsbc_iscpl}}
1033  \label{lst:namsbc_iscpl}
1034\end{listing}
1035
1036Ice sheet/ocean coupling is done through file exchange at the restart step.
1037At each restart step:
1038
1039\begin{description}
1040\item [Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1041\item [Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools.
1042\item [Step 3]: \NEMO\ run for a specific period and output the average melt rate over the period.
1043\item [Step 4]: the ice sheet model run using the melt rate outputed in step 4.
1044\item [Step 5]: go back to 1.
1045\end{description}
1046
1047If \np[=.true.]{ln_iscpl}{ln\_iscpl}, the isf draft is assume to be different at each restart step with
1048potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1049The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1050
1051\begin{description}
1052\item [Thin a cell down]:
1053  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1054  ($bt_b=bt_n$).
1055\item [Enlarge  a cell]:
1056  See case "Thin a cell down"
1057\item [Dry a cell]:
1058  mask, T/S, U/V and ssh are set to 0.
1059  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1060\item [Wet a cell]:
1061  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1062  If no neighbours, T/S is extrapolated from old top cell value.
1063  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1064\item [Dry a column]:
1065   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1066\item [Wet a column]:
1067  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1068  If no neighbour, T/S/U/V and mask set to 0.
1069\end{description}
1070
1071Furthermore, as the before and now fields are not compatible (modification of the geometry),
1072the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1073
1074The horizontal extrapolation to fill new cell with realistic value is called \np{nn_drown}{nn\_drown} times.
1075It means that if the grounding line retreat by more than \np{nn_drown}{nn\_drown} cells between 2 coupling steps,
1076the code will be unable to fill all the new wet cells properly.
1077The default number is set up for the MISOMIP idealised experiments.
1078This coupling procedure is able to take into account grounding line and calving front migration.
1079However, it is a non-conservative processe.
1080This could lead to a trend in heat/salt content and volume.\\
1081
1082In order to remove the trend and keep the conservation level as close to 0 as possible,
1083a simple conservation scheme is available with \np[=.true.]{ln_hsb}{ln\_hsb}.
1084The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1085A correction increment is computed and apply each time step during the next \np{rn_fiscpl}{rn\_fiscpl} time steps.
1086For safety, it is advised to set \np{rn_fiscpl}{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1087The 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).
1088
1089%% =================================================================================================
1090\section{Handling of icebergs (ICB)}
1091\label{sec:SBC_ICB_icebergs}
1092
1093\begin{listing}
1094  \nlst{namberg}
1095  \caption{\forcode{&namberg}}
1096  \label{lst:namberg}
1097\end{listing}
1098
1099Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1100Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1101(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1102Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1103described in the \nam{berg}{berg} namelist: \np{rn_initial_mass}{rn\_initial\_mass} and \np{rn_initial_thickness}{rn\_initial\_thickness}.
1104Each class has an associated scaling (\np{rn_mass_scaling}{rn\_mass\_scaling}),
1105which is an integer representing how many icebergs of this class are being described as one lagrangian point
1106(this reduces the numerical problem of tracking every single iceberg).
1107They are enabled by setting \np[=.true.]{ln_icebergs}{ln\_icebergs}.
1108
1109Two initialisation schemes are possible.
1110\begin{description}
1111\item [{\np{nn_test_icebergs}{nn\_test\_icebergs}~$>$~0}]
1112  In this scheme, the value of \np{nn_test_icebergs}{nn\_test\_icebergs} represents the class of iceberg to generate
1113  (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
1114  which an iceberg is generated at the beginning of the run.
1115  (Note that this happens each time the timestep equals \np{nn_nit000}{nn\_nit000}.)
1116  \np{nn_test_icebergs}{nn\_test\_icebergs} is defined by four numbers in \np{nn_test_box}{nn\_test\_box} representing the corners of
1117  the geographical box: lonmin,lonmax,latmin,latmax
1118\item [{\np[=-1]{nn_test_icebergs}{nn\_test\_icebergs}}]
1119  In this scheme, the model reads a calving file supplied in the \np{sn_icb}{sn\_icb} parameter.
1120  This should be a file with a field on the configuration grid (typically ORCA)
1121  representing ice accumulation rate at each model point.
1122  These should be ocean points adjacent to land where icebergs are known to calve.
1123  Most points in this input grid are going to have value zero.
1124  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1125  At each time step, a test is performed to see if there is enough ice mass to
1126  calve an iceberg of each class in order (1 to 10).
1127  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1128  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1129\end{description}
1130
1131Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1132The latter act to disintegrate the iceberg.
1133This is either all melted freshwater,
1134or (if \np{rn_bits_erosion_fraction}{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1135which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1136Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1137
1138Extensive diagnostics can be produced.
1139Separate output files are maintained for human-readable iceberg information.
1140A separate file is produced for each processor (independent of \np{ln_ctl}{ln\_ctl}).
1141The amount of information is controlled by two integer parameters:
1142\begin{description}
1143\item [{\np{nn_verbose_level}{nn\_verbose\_level}}] takes a value between one and four and
1144  represents an increasing number of points in the code at which variables are written,
1145  and an increasing level of obscurity.
1146\item [{\np{nn_verbose_write}{nn\_verbose\_write}}] is the number of timesteps between writes
1147\end{description}
1148
1149Iceberg trajectories can also be written out and this is enabled by setting \np{nn_sample_rate}{nn\_sample\_rate}~$>$~0.
1150A non-zero value represents how many timesteps between writes of information into the output file.
1151These output files are in NETCDF format.
1152When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1153Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1154So care is needed to recreate data for individual icebergs,
1155since its trajectory data may be spread across multiple files.
1156
1157%% =================================================================================================
1158\section[Interactions with waves (\textit{sbcwave.F90}, \forcode{ln_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln_wave}{ln\_wave})}
1159\label{sec:SBC_wave}
1160
1161\begin{listing}
1162  \nlst{namsbc_wave}
1163  \caption{\forcode{&namsbc_wave}}
1164  \label{lst:namsbc_wave}
1165\end{listing}
1166
1167Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1168physical processes related to ocean surface waves, namely the surface stress modified by growth and
1169dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1170tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1171the wind stress.
1172
1173Physical processes related to ocean surface waves can be accounted by setting the logical variable
1174\np[=.true.]{ln_wave}{ln\_wave} in \nam{sbc}{sbc} namelist. In addition, specific flags accounting for
1175different processes should be activated as explained in the following sections.
1176
1177Wave fields can be provided either in forced or coupled mode:
1178\begin{description}
1179\item [forced mode]: wave fields should be defined through the \nam{sbc_wave}{sbc\_wave} namelist
1180for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1181Input Data generic Interface (see \autoref{sec:SBC_input}).
1182\item [coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np[=.true.]{ln_cpl}{ln\_cpl}
1183in \nam{sbc}{sbc} namelist and filling the \nam{sbc_cpl}{sbc\_cpl} namelist.
1184\end{description}
1185
1186% ----------------------------------------------------------------
1187% Neutral drag coefficient from wave model (ln_cdgw)
1188
1189% ----------------------------------------------------------------
1190%% =================================================================================================
1191\subsection[Neutral drag coefficient from wave model (\forcode{ln_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln_cdgw}{ln\_cdgw})}
1192\label{subsec:SBC_wave_cdgw}
1193
1194The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1195can be used by setting the logical variable \np[=.true.]{ln_cdgw}{ln\_cdgw} in \nam{sbc}{sbc} namelist.
1196Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1197the drag coefficient is computed according to the stable/unstable conditions of the
1198air-sea interface following \citet{large.yeager_rpt04}.
1199
1200% ----------------------------------------------------------------
1201% 3D Stokes Drift (ln_sdw, nn_sdrift)
1202% ----------------------------------------------------------------
1203%% =================================================================================================
1204\subsection[3D Stokes Drift (\forcode{ln_sdw} \& \forcode{nn_sdrift})]{3D Stokes Drift (\protect\np{ln_sdw}{ln\_sdw} \& \np{nn_sdrift}{nn\_sdrift})}
1205\label{subsec:SBC_wave_sdw}
1206
1207The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1208It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1209and the current measured at a fixed point (Eulerian velocity).
1210As waves travel, the water particles that make up the waves travel in orbital motions but
1211without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1212at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1213An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1214representation of surface physics in ocean general circulation models. %GS: reference needed
1215The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1216
1217\[
1218  % \label{eq:SBC_wave_sdw}
1219  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1220  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1221  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1222\]
1223
1224where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1225$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1226$k$ is the mean wavenumber defined as:
1227$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1228
1229In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1230and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1231To simplify, it is customary to use approximations to the full Stokes profile.
1232Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1233are included in the code through the \np{nn_sdrift}{nn\_sdrift} parameter once provided the surface Stokes drift
1234$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1235and makes possible the estimation of the surface Stokes drift for random directional waves in
1236realistic wave conditions:
1237
1238\begin{description}
1239\item [{\np{nn_sdrift}{nn\_sdrift} = 0}]: exponential integral profile parameterization proposed by
1240\citet{breivik.janssen.ea_JPO14}:
1241
1242\[
1243  % \label{eq:SBC_wave_sdw_0a}
1244  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1245\]
1246
1247where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1248
1249\[
1250  % \label{eq:SBC_wave_sdw_0b}
1251  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1252  \quad \text{and }\
1253  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1254\]
1255
1256where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1257
1258\item [{\np{nn_sdrift}{nn\_sdrift} = 1}]: velocity profile based on the Phillips spectrum which is considered to be a
1259reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1260\citep{breivik.bidlot.ea_OM16}:
1261
1262\[
1263  % \label{eq:SBC_wave_sdw_1}
1264  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1265  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1266\]
1267
1268where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1269
1270\item [{\np{nn_sdrift}{nn\_sdrift} = 2}]: velocity profile based on the Phillips spectrum as for \np{nn_sdrift}{nn\_sdrift} = 1
1271but using the wave frequency from a wave model.
1272
1273\end{description}
1274
1275The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1276and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1277
1278\[
1279  % \label{eq:SBC_wave_eta_sdw}
1280  \frac{\partial{\eta}}{\partial{t}} =
1281  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1282\]
1283
1284The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1285for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1286that is induced by the three-dimensional Stokes velocity.
1287The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1288can be formulated as follows:
1289
1290\[
1291  % \label{eq:SBC_wave_tra_sdw}
1292  \frac{\partial{c}}{\partial{t}} =
1293  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1294\]
1295
1296% ----------------------------------------------------------------
1297% Stokes-Coriolis term (ln_stcor)
1298% ----------------------------------------------------------------
1299%% =================================================================================================
1300\subsection[Stokes-Coriolis term (\forcode{ln_stcor})]{Stokes-Coriolis term (\protect\np{ln_stcor}{ln\_stcor})}
1301\label{subsec:SBC_wave_stcor}
1302
1303In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1304in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1305This additional force may have impact on the Ekman turning of the surface current.
1306In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1307approximations described in \autoref{subsec:SBC_wave_sdw}),
1308\np[=.true.]{ln_stcor}{ln\_stcor} has to be set.
1309
1310% ----------------------------------------------------------------
1311% Waves modified stress (ln_tauwoc, ln_tauw)
1312% ----------------------------------------------------------------
1313%% =================================================================================================
1314\subsection[Wave modified stress (\forcode{ln_tauwoc} \& \forcode{ln_tauw})]{Wave modified sress (\protect\np{ln_tauwoc}{ln\_tauwoc} \& \np{ln_tauw}{ln\_tauw})}
1315\label{subsec:SBC_wave_tauw}
1316
1317The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1318into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1319available for forcing the mean circulation, while in the opposite case of a decaying sea
1320state, more momentum is available for forcing the ocean.
1321Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1322but in practice, an equilibrium sea state is a fairly rare event.
1323So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1324
1325\[
1326  % \label{eq:SBC_wave_tauoc}
1327  \tau_{oc,a} = \tau_a - \tau_w
1328\]
1329
1330where $\tau_a$ is the atmospheric surface stress;
1331$\tau_w$ is the atmospheric stress going into the waves defined as:
1332
1333\[
1334  % \label{eq:SBC_wave_tauw}
1335  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1336\]
1337
1338where: $c_p$ is the phase speed of the gravity waves,
1339$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1340the physics of ocean waves. The first one, $S_{in}$, describes the generation
1341of ocean waves by wind and therefore represents the momentum and energy transfer
1342from air to ocean waves; the second term $S_{nl}$ denotes
1343the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1344describes the dissipation of waves by processes such as white-capping, large scale breaking
1345eddy-induced damping.
1346
1347The wave stress derived from an external wave model can be provided either through the normalized
1348wave stress into the ocean by setting \np[=.true.]{ln_tauwoc}{ln\_tauwoc}, or through the zonal and
1349meridional stress components by setting \np[=.true.]{ln_tauw}{ln\_tauw}.
1350
1351%% =================================================================================================
1352\section{Miscellaneous options}
1353\label{sec:SBC_misc}
1354
1355%% =================================================================================================
1356\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1357\label{subsec:SBC_dcy}
1358%
1359
1360
1361\begin{figure}[!t]
1362  \centering
1363  \includegraphics[width=0.66\textwidth]{Fig_SBC_diurnal}
1364  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1365    Example of reconstruction of the diurnal cycle variation of short wave flux from
1366    daily mean values.
1367    The reconstructed diurnal cycle (black line) is chosen as
1368    the mean value of the analytical cycle (blue line) over a time step,
1369    not as the mid time step value of the analytically cycle (red square).
1370    From \citet{bernie.guilyardi.ea_CD07}.}
1371  \label{fig:SBC_diurnal}
1372\end{figure}
1373
1374\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.
1375%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1376Nevertheless, 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}.
1377Furthermore, only the knowledge of daily mean value of SWF is needed,
1378as higher frequency variations can be reconstructed from them,
1379assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1380The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1381setting \np[=.true.]{ln_dm2dc}{ln\_dm2dc} (a \textit{\nam{sbc}{sbc}} namelist variable) when
1382using a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}) or
1383the flux formulation (\np[=.true.]{ln_flx}{ln\_flx}).
1384The reconstruction is performed in the \mdl{sbcdcy} module.
1385The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1386The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1387a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1388The use of diurnal cycle reconstruction requires the input SWF to be daily
1389(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn_qsr}{sn\_qsr} namelist parameter).
1390Furthermore, it is recommended to have a least 8 surface module time steps per day,
1391that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1392An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1393one every 2~hours (from 1am to 11pm).
1394
1395\begin{figure}[!t]
1396  \centering
1397  \includegraphics[width=0.66\textwidth]{Fig_SBC_dcy}
1398  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1399    Example of reconstruction of the diurnal cycle variation of short wave flux from
1400    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1401    The display is on (i,j) plane.}
1402  \label{fig:SBC_dcy}
1403\end{figure}
1404
1405Note also that the setting a diurnal cycle in SWF is highly recommended when
1406the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1407an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1408
1409%% =================================================================================================
1410\subsection{Rotation of vector pairs onto the model grid directions}
1411\label{subsec:SBC_rotation}
1412
1413When using a flux (\np[=.true.]{ln_flx}{ln\_flx}) or bulk (\np[=.true.]{ln_blk}{ln\_blk}) formulation,
1414pairs of vector components can be rotated from east-north directions onto the local grid directions.
1415This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1416be defined relative to a rectilinear grid.
1417To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1418The eastward component must start with "U" and the northward component with "V".
1419The remaining characters in the strings are used to identify which pair of components go together.
1420So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1421rotate them on to the model grid directions;
1422"U2" and "V2" could be used against a second pair of components, and so on.
1423The extra characters used in the strings are arbitrary.
1424The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1425
1426%% =================================================================================================
1427\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1428\label{subsec:SBC_ssr}
1429
1430\begin{listing}
1431  \nlst{namsbc_ssr}
1432  \caption{\forcode{&namsbc_ssr}}
1433  \label{lst:namsbc_ssr}
1434\end{listing}
1435
1436Options are defined through the \nam{sbc_ssr}{sbc\_ssr} namelist variables.
1437On forced mode using a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}),
1438a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1439\[
1440  % \label{eq:SBC_dmp_q}
1441  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1442\]
1443where SST is a sea surface temperature field (observed or climatological),
1444$T$ is the model surface layer temperature and
1445$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1446For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1447This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1448
1449In the fresh water budget, a feedback term can also be added.
1450Converted into an equivalent freshwater flux, it takes the following expression :
1451
1452\begin{equation}
1453  \label{eq:SBC_dmp_emp}
1454  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1455  {\left.S\right|_{k=1}}
1456\end{equation}
1457
1458where $\textit{emp}_{o }$ is a net surface fresh water flux
1459(observed, climatological or an atmospheric model product),
1460\textit{SSS}$_{Obs}$ is a sea surface salinity
1461(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1462$\left.S\right|_{k=1}$ is the model surface layer salinity and
1463$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1464Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1465the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1466The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1467reduce the uncertainties we have on the observed freshwater budget.
1468
1469%% =================================================================================================
1470\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1471\label{subsec:SBC_ice-cover}
1472
1473The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1474There are several way to handle sea-ice in the system depending on
1475the value of the \np{nn_ice}{nn\_ice} namelist parameter found in \nam{sbc}{sbc} namelist.
1476\begin{description}
1477\item [nn\_ice = 0]
1478  there will never be sea-ice in the computational domain.
1479  This is a typical namelist value used for tropical ocean domain.
1480  The surface fluxes are simply specified for an ice-free ocean.
1481  No specific things is done for sea-ice.
1482\item [nn\_ice = 1]
1483  sea-ice can exist in the computational domain, but no sea-ice model is used.
1484  An observed ice covered area is read in a file.
1485  Below this area, the SST is restored to the freezing point and
1486  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1487  The associated modification of the freshwater fluxes are done in such a way that
1488  the change in buoyancy fluxes remains zero.
1489  This prevents deep convection to occur when trying to reach the freezing point
1490  (and so ice covered area condition) while the SSS is too large.
1491  This manner of managing sea-ice area, just by using a IF case,
1492  is usually referred as the \textit{ice-if} model.
1493  It can be found in the \mdl{sbcice\_if} module.
1494\item [nn\_ice = 2 or more]
1495  A full sea ice model is used.
1496  This model computes the ice-ocean fluxes,
1497  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1498  provide the surface averaged ocean fluxes.
1499  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1500  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1501  (\ie\ $2$ for SI3 or $3$ for CICE).
1502\end{description}
1503
1504% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1505%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1506
1507%% =================================================================================================
1508\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1509\label{subsec:SBC_cice}
1510
1511It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1512to the CICE sea-ice model by using \key{cice}.
1513The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1514the additional 'hadgem3' drivers will be required, even with the latest code release.
1515Input grid files consistent with those used in \NEMO\ will also be needed,
1516and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1517(seek advice from UKMO if necessary).
1518Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1519(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1520or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1521(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1522The code is intended to be used with \np{nn_fsbc}{nn\_fsbc} set to 1
1523(although coupling ocean and ice less frequently should work,
1524it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1525the user should check that results are not significantly different to the standard case).
1526
1527There are two options for the technical coupling between \NEMO\ and CICE.
1528The standard version allows complete flexibility for the domain decompositions in the individual models,
1529but this is at the expense of global gather and scatter operations in the coupling which
1530become very expensive on larger numbers of processors.
1531The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1532the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1533and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1534allows much more efficient direct coupling on individual processors.
1535This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1536there is no sea ice.
1537
1538%% =================================================================================================
1539\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1540\label{subsec:SBC_fwb}
1541
1542For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1543prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1544In \NEMO, two way of controlling the freshwater budget are proposed:
1545
1546\begin{description}
1547\item [{\np[=0]{nn_fwb}{nn\_fwb}}]
1548  no control at all.
1549  The mean sea level is free to drift, and will certainly do so.
1550\item [{\np[=1]{nn_fwb}{nn\_fwb}}]
1551  global mean \textit{emp} set to zero at each model time step.
1552  %GS: comment below still relevant ?
1553  %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).
1554\item [{\np[=2]{nn_fwb}{nn\_fwb}}]
1555  freshwater budget is adjusted from the previous year annual mean budget which
1556  is read in the \textit{EMPave\_old.dat} file.
1557  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1558  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1559\end{description}
1560
1561% Griffies doc:
1562% When running ocean-ice simulations, we are not explicitly representing land processes,
1563% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1564% it is important to balance the hydrological cycle in ocean-ice models.
1565% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1566% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1567% a chosen time scale.
1568% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1569% so that there is always a zero net input of water to the ocean-ice system.
1570% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1571% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1572% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1573% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1574% and ice models when aiming to balance the hydrological cycle.
1575% 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,
1576% not the water in any one sub-component. As an extreme example to illustrate the issue,
1577% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1578% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1579% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1580% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1581% in ocean-ice models.
1582
1583\onlyinsubfile{\input{../../global/epilogue}}
1584
1585\end{document}
Note: See TracBrowser for help on using the repository browser.