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1\documentclass[../tex_main/NEMO_manual]{subfiles}
2\begin{document}
3% ================================================================
4% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)
5% ================================================================
6\chapter{Surface Boundary Condition (SBC, ISF, ICB) }
7\label{chap:SBC}
8\minitoc
9
10\newpage
11$\ $\newline    % force a new ligne
12%---------------------------------------namsbc--------------------------------------------------
13
14\nlst{namsbc}
15%--------------------------------------------------------------------------------------------------------------
16$\ $\newline    % force a new ligne
17
18The ocean needs six fields as surface boundary condition:
19\begin{itemize}
20\item
21  the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$
22\item
23  the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
24\item
25  the surface freshwater budget $\left( {\textit{emp}} \right)$
26\item
27  the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
28\end{itemize}
29plus an optional field:
30\begin{itemize}
31   \item the atmospheric pressure at the ocean surface $\left( p_a \right)$
32\end{itemize}
33
34Four different ways to provide the first six fields to the ocean are available which are controlled by
35namelist \ngn{namsbc} variables:
36an analytical formulation (\np{ln\_ana}\forcode{ = .true.}),
37a flux formulation (\np{ln\_flx}\forcode{ = .true.}),
38a bulk formulae formulation (CORE (\np{ln\_blk\_core}\forcode{ = .true.}),
39CLIO (\np{ln\_blk\_clio}\forcode{ = .true.}) bulk formulae) and
40a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler)
41(\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}).
42When used ($i.e.$ \np{ln\_apr\_dyn}\forcode{ = .true.}),
43the atmospheric pressure forces both ocean and ice dynamics.
44
45The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.
46When the fields are supplied from data files (flux and bulk formulations),
47the input fields need not be supplied on the model grid.
48Instead a file of coordinates and weights can be supplied which maps the data from the supplied grid to
49the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
50If the Interpolation on the Fly option is used, input data belonging to land points (in the native grid),
51can be masked to avoid spurious results in proximity of the coasts as
52large sea-land gradients characterize most of the atmospheric variables.
53
54In addition, the resulting fields can be further modified using several namelist options.
55These options control
56\begin{itemize}
57\item
58  the rotation of vector components supplied relative to an east-north coordinate system onto
59  the local grid directions in the model;
60\item
61  the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}\forcode{ = .true.});
62\item
63  the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model)
64  (\np{nn\_ice}\forcode{ = 0..3});
65\item
66  the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}\forcode{ = .true.});
67\item
68  the addition of isf melting as lateral inflow (parameterisation) or
69  as fluxes applied at the land-ice ocean interface (\np{ln\_isf}) ;
70\item
71  the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
72  (\np{nn\_fwb}\forcode{ = 0..2});
73\item
74  the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle
75  (\np{ln\_dm2dc}\forcode{ = .true.});
76\item
77  a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}\forcode{ = .true.});
78\item
79  the Stokes drift rom an external wave model can be accounted (\np{ln\_sdw}\forcode{ = .true.});
80\item
81  the Stokes-Coriolis term can be included (\np{ln\_stcor}\forcode{ = .true.});
82\item
83  the surface stress felt by the ocean can be modified by surface waves (\np{ln\_tauwoc}\forcode{ = .true.}).
84\end{itemize}
85
86In this chapter, we first discuss where the surface boundary condition appears in the model equations.
87Then we present the five ways of providing the surface boundary condition,
88followed by the description of the atmospheric pressure and the river runoff.
89Next the scheme for interpolation on the fly is described.
90Finally, the different options that further modify the fluxes applied to the ocean are discussed.
91One of these is modification by icebergs (see \autoref{sec:ICB_icebergs}),
92which act as drifting sources of fresh water.
93Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
94which provides additional sources of fresh water.
95
96
97% ================================================================
98% Surface boundary condition for the ocean
99% ================================================================
100\section{Surface boundary condition for the ocean}
101\label{sec:SBC_general}
102
103The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
104It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
105the momentum vertical mixing trend (see \autoref{eq:dynzdf_sbc} in \autoref{sec:DYN_zdf}).
106As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
107$i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
108
109The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
110$Q_{ns}$ and $Q_{sr}$, respectively.
111The former is the non penetrative part of the heat flux
112($i.e.$ the sum of sensible, latent and long wave heat fluxes plus
113the heat content of the mass exchange with the atmosphere and sea-ice).
114It is applied in \mdl{trasbc} module as a surface boundary condition trend of
115the first level temperature time evolution equation
116(see \autoref{eq:tra_sbc} and \autoref{eq:tra_sbc_lin} in \autoref{subsec:TRA_sbc}).
117The latter is the penetrative part of the heat flux.
118It is applied as a 3D trends of the temperature equation (\mdl{traqsr} module) when
119\np{ln\_traqsr}\forcode{ = .true.}.
120The way the light penetrates inside the water column is generally a sum of decreasing exponentials
121(see \autoref{subsec:TRA_qsr}).
122
123The surface freshwater budget is provided by the \textit{emp} field.
124It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
125possibly with the sea-ice and ice shelves (freezing minus melting of ice).
126It affects both the ocean in two different ways:
127$(i)$  it changes the volume of the ocean and therefore appears in the sea surface height equation as
128a volume flux, and
129$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
130the mass exchanged with the atmosphere, the sea-ice and the ice shelves.
131
132
133%\colorbox{yellow}{Miss: }
134%
135%A extensive description of all namsbc namelist (parameter that have to be
136%created!)
137%
138%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
139%ssv) i.e. information required by flux computation or sea-ice
140%
141%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
142%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
143%
144%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
145%
146%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
147%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
148%nf{\_}sbc
149%
150%Explain here all the namlist namsbc variable{\ldots}.
151%
152% explain : use or not of surface currents
153%
154%\colorbox{yellow}{End Miss }
155
156The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
157the surface currents, temperature and salinity. 
158These variables are averaged over \np{nn\_fsbc} time-step (\autoref{tab:ssm}), and
159it is these averaged fields which are used to computes the surface fluxes at a frequency of \np{nn\_fsbc} time-step.
160
161
162%-------------------------------------------------TABLE---------------------------------------------------
163\begin{table}[tb]   \begin{center}   \begin{tabular}{|l|l|l|l|}
164\hline
165Variable description             & Model variable  & Units  & point \\  \hline
166i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
167j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
168Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
169Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
170\end{tabular}
171\caption{  \protect\label{tab:ssm}
172  Ocean variables provided by the ocean to the surface module (SBC).
173  The variable are averaged over nn{\_}fsbc time step,
174  $i.e.$ the frequency of computation of surface fluxes.}
175\end{center}   \end{table}
176%--------------------------------------------------------------------------------------------------------------
177
178%\colorbox{yellow}{Penser a} mettre dans le restant l'info nn{\_}fsbc ET nn{\_}fsbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt
179
180
181% ================================================================
182%       Input Data
183% ================================================================
184\section{Input data generic interface}
185\label{sec:SBC_input}
186
187A generic interface has been introduced to manage the way input data
188(2D or 3D fields, like surface forcing or ocean T and S) are specify in \NEMO.
189This task is archieved by \mdl{fldread}.
190The module was design with four main objectives in mind:
191\begin{enumerate}
192\item
193  optionally provide a time interpolation of the input data at model time-step, whatever their input frequency is,
194  and according to the different calendars available in the model.
195\item
196  optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
197\item
198  make the run duration independent from the period cover by the input files.
199\item
200  provide a simple user interface and a rather simple developer interface by
201  limiting the number of prerequisite information.
202\end{enumerate} 
203
204As a results the user have only to fill in for each variable a structure in the namelist file to
205define the input data file and variable names, the frequency of the data (in hours or months),
206whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
207and three additional parameters for on-the-fly interpolation.
208When adding a new input variable, the developer has to add the associated structure in the namelist,
209read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
210and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
211
212The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
213(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
214if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
215
216Note that when an input data is archived on a disc which is accessible directly from the workspace where
217the code is executed, then the use can set the \np{cn\_dir} to the pathway leading to the data.
218By default, the data are assumed to have been copied so that cn\_dir='./'.
219
220% -------------------------------------------------------------------------------------------------------------
221% Input Data specification (\mdl{fldread})
222% -------------------------------------------------------------------------------------------------------------
223\subsection{Input data specification (\protect\mdl{fldread})}
224\label{subsec:SBC_fldread}
225
226The structure associated with an input variable contains the following information:
227\begin{forlines}
228!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
229!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
230\end{forlines}
231where
232\begin{description} 
233\item[File name]:
234  the stem name of the NetCDF file to be open.
235  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
236  by date information and possibly a prefix (when using AGRIF).
237  Tab.\autoref{tab:fldread} provides the resulting file name in all possible cases according to
238  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
239
240%--------------------------------------------------TABLE--------------------------------------------------
241\begin{table}[htbp]
242\begin{center}
243\begin{tabular}{|l|c|c|c|}
244\hline
245                         & daily or weekLLL          & monthly                   &   yearly          \\   \hline
246\np{clim}\forcode{ = .false.} & fn\_yYYYYmMMdDD.nc  &   fn\_yYYYYmMM.nc   &   fn\_yYYYY.nc  \\   \hline
247\np{clim}\forcode{ = .true.}        & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
248\end{tabular}
249\end{center}
250\caption{ \protect\label{tab:fldread}
251  naming nomenclature for climatological or interannual input file, as a function of the Open/close frequency.
252  The stem name is assumed to be 'fn'.
253  For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
254  ($i.e.$ 'sun','sat','fri','thu','wed','tue','mon').
255  The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits.
256  Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc',
257  where 'PPPP' is the process number coded with 4 digits;
258  (2) when using AGRIF, the prefix '\_N' is added to files, where 'N'  is the child grid number.}
259\end{table}
260%--------------------------------------------------------------------------------------------------------------
261 
262
263\item[Record frequency]:
264  the frequency of the records contained in the input file.
265  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
266  (for example -1 for monthly forcing or -12 for annual forcing).
267  Note that this frequency must really be an integer and not a real.
268  On some computers, seting it to '24.' can be interpreted as 240!
269
270\item[Variable name]:
271  the name of the variable to be read in the input NetCDF file.
272
273\item[Time interpolation]:
274  a logical to activate, or not, the time interpolation.
275  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
276  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
277  00h00'00'' to 23h59'59".
278  If set to 'true', the forcing will have a broken line shape.
279  Records are assumed to be dated the middle of the forcing period.
280  For example, when using a daily forcing with time interpolation,
281  linear interpolation will be performed between mid-day of two consecutive days.
282
283\item[Climatological forcing]:
284  a logical to specify if a input file contains climatological forcing which can be cycle in time,
285  or an interannual forcing which will requires additional files if
286  the period covered by the simulation exceed the one of the file.
287  See the above the file naming strategy which impacts the expected name of the file to be opened.
288
289\item[Open/close frequency]:
290  the frequency at which forcing files must be opened/closed.
291  Four cases are coded:
292  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
293  means the forcing files will contain data for one day, one week, one month or one year.
294  Files are assumed to contain data from the beginning of the open/close period.
295  For example, the first record of a yearly file containing daily data is Jan 1st even if
296  the experiment is not starting at the beginning of the year.
297
298\item[Others]:
299  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
300  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
301
302\end{description}
303
304Additional remarks:\\
305(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
306The only tricky point is therefore to specify the date at which we need to do the interpolation and
307the date of the records read in the input files.
308Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the time step.
309For example, for an experiment starting at 0h00'00" with a one hour time-step,
310a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
311However, for forcing data related to the surface module,
312values are not needed at every time-step but at every \np{nn\_fsbc} time-step.
313For example with \np{nn\_fsbc}\forcode{ = 3}, the surface module will be called at time-steps 1, 4, 7, etc.
314The date used for the time interpolation is thus redefined to be at the middle of \np{nn\_fsbc} time-step period.
315In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
316(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
317The calendar associated with the forcing field is build according to the information provided by
318user in the record frequency, the open/close frequency and the type of temporal interpolation.
319For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
320be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
321(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
322interpolating data with the first (last) record of the open/close period.
323For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
324the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
325Dec 31st 12h00'00" and Jan 1st 12h00'00".
326If the forcing is climatological, Dec and Jan will be keep-up from the same year.
327However, if the forcing is not climatological, at the end of
328the open/close period the code will automatically close the current file and open the next one.
329Note that, if the experiment is starting (ending) at the beginning (end) of
330an open/close period we do accept that the previous (next) file is not existing.
331In this case, the time interpolation will be performed between two identical values.
332For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
333we do accept that the file related to year Y-1 is not existing.
334The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
335If the file of year Y-1 exists, the code will read its last record.
336Therefore, this file can contain only one record corresponding to Dec 31st,
337a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
338
339
340% -------------------------------------------------------------------------------------------------------------
341% Interpolation on the Fly
342% -------------------------------------------------------------------------------------------------------------
343\subsection{Interpolation on-the-fly}
344\label{subsec:SBC_iof}
345
346Interpolation on the Fly allows the user to supply input files required for the surface forcing on
347grids other than the model grid.
348To do this he or she must supply, in addition to the source data file, a file of weights to be used to
349interpolate from the data grid to the model grid.
350The original development of this code used the SCRIP package
351(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
352In principle, any package can be used to generate the weights, but the variables in
353the input weights file must have the same names and meanings as assumed by the model.
354Two methods are currently available: bilinear and bicubic interpolation.
355Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
356the input file and substitute the corresponding values with the average of the 8 neighbouring points in
357the native external grid.
358Only "sea points" are considered for the averaging.
359The land/sea mask file must be provided in the structure associated with the input variable.
360The netcdf land/sea mask variable name must be 'LSM' it must have the same horizontal and vertical dimensions of
361the associated variable and should be equal to 1 over land and 0 elsewhere.
362The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.
363Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied.
364
365\subsubsection{Bilinear interpolation}
366\label{subsec:SBC_iof_bilinear}
367
368The input weights file in this case has two sets of variables:
369src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
370The "src" variables correspond to the point in the input grid to which the weight "wgt" is to be applied.
371Each src value is an integer corresponding to the index of a point in the input grid when
372written as a one dimensional array.
373For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
374There are four of each variable because bilinear interpolation uses the four points defining
375the grid box containing the point to be interpolated.
376All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
377generate a value for point (i,j) in the model.
378
379Symbolically, the algorithm used is:
380\begin{equation}
381f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
382\end{equation}
383where function idx() transforms a one dimensional index src(k) into a two dimensional index,
384and wgt(1) corresponds to variable "wgt01" for example.
385
386\subsubsection{Bicubic interpolation}
387\label{subsec:SBC_iof_bicubic}
388
389Again there are two sets of variables: "src" and "wgt".
390But in this case there are 16 of each.
391The symbolic algorithm used to calculate values on the model grid is now:
392
393\begin{equation*} \begin{split}
394f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}     
395              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
396              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }   
397              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
398\end{split}
399\end{equation*}
400The gradients here are taken with respect to the horizontal indices and not distances since
401the spatial dependency has been absorbed into the weights.
402
403\subsubsection{Implementation}
404\label{subsec:SBC_iof_imp}
405
406To activate this option, a non-empty string should be supplied in
407the weights filename column of the relevant namelist;
408if this is left as an empty string no action is taken.
409In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
410as and when they are first required.
411This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
412inspecting a global attribute stored in the weights input file.
413This attribute must be called "ew\_wrap" and be of integer type.
414If it is negative, the input non-model grid is assumed not to be cyclic.
415If zero or greater, then the value represents the number of columns that overlap.
416$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
417if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
418If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
419In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
420therefore the grid is assumed to be cyclic with no overlapping columns.
421(In fact this only matters when bicubic interpolation is required.)
422Note that no testing is done to check the validity in the model,
423since there is no way of knowing the name used for the longitude variable,
424so it is up to the user to make sure his or her data is correctly represented.
425
426Next the routine reads in the weights.
427Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
428The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
429and when required, for reading in the variable to be interpolated (on the input data grid).
430The size of the input data array is determined by examining the values in the "src" arrays to
431find the minimum and maximum i and j values required.
432Since bicubic interpolation requires the calculation of gradients at each point on the grid,
433the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
434When the array of points from the data file is adjacent to an edge of the data grid,
435the halo is either a copy of the row/column next to it (non-cyclical case),
436or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
437
438\subsubsection{Limitations}
439\label{subsec:SBC_iof_lim}
440
441\begin{enumerate} 
442\item
443  The case where input data grids are not logically rectangular has not been tested.
444\item
445  This code is not guaranteed to produce positive definite answers from positive definite inputs when
446  a bicubic interpolation method is used.
447\item
448  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
449\item
450  The gradients across the ends of a cyclical grid assume that the grid spacing between
451  the two columns involved are consistent with the weights used.
452\item
453  Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
454  but this has not been implemented.)
455\end{enumerate}
456
457\subsubsection{Utilities}
458\label{subsec:SBC_iof_util}
459
460% to be completed
461A set of utilities to create a weights file for a rectilinear input grid is available
462(see the directory NEMOGCM/TOOLS/WEIGHTS).
463
464% -------------------------------------------------------------------------------------------------------------
465% Standalone Surface Boundary Condition Scheme
466% -------------------------------------------------------------------------------------------------------------
467\subsection{Standalone surface boundary condition scheme}
468\label{subsec:SAS_iof}
469
470%---------------------------------------namsbc_ana--------------------------------------------------
471
472\nlst{namsbc_sas}
473%--------------------------------------------------------------------------------------------------------------
474
475In some circumstances it may be useful to avoid calculating the 3D temperature,
476salinity and velocity fields and simply read them in from a previous run or receive them from OASIS. 
477For example:
478
479\begin{itemize}
480\item
481  Multiple runs of the model are required in code development to
482  see the effect of different algorithms in the bulk formulae.
483\item
484  The effect of different parameter sets in the ice model is to be examined.
485\item
486  Development of sea-ice algorithms or parameterizations.
487\item
488  Spinup of the iceberg floats
489\item
490  Ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}\forcode{ = .true.})
491\end{itemize}
492
493The StandAlone Surface scheme provides this utility.
494Its options are defined through the \ngn{namsbc\_sas} namelist variables.
495A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
496However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0).
497In this configuration, a few routines in the standard model are overriden by new versions.
498Routines replaced are:
499
500\begin{itemize}
501\item
502  \mdl{nemogcm}:
503  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
504  Since the ocean state is not calculated all associated initialisations have been removed.
505\item
506  \mdl{step}:
507  The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
508\item
509  \mdl{sbcmod}:
510  This has been cut down and now only calculates surface forcing and the ice model required.
511  New surface modules that can function when only the surface level of the ocean state is defined can also be added
512  (e.g. icebergs).
513\item
514  \mdl{daymod}:
515  No ocean restarts are read or written (though the ice model restarts are retained),
516  so calls to restart functions have been removed.
517  This also means that the calendar cannot be controlled by time in a restart file,
518  so the user must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
519\item
520  \mdl{stpctl}:
521  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
522\item
523  \mdl{diawri}:
524  All 3D data have been removed from the output.
525  The surface temperature, salinity and velocity components (which have been read in) are written along with
526  relevant forcing and ice data.
527\end{itemize}
528
529One new routine has been added:
530
531\begin{itemize}
532\item
533  \mdl{sbcsas}:
534  This module initialises the input files needed for reading temperature, salinity and
535  velocity arrays at the surface.
536  These filenames are supplied in namelist namsbc{\_}sas.
537  Unfortunately because of limitations with the \mdl{iom} module,
538  the full 3D fields from the mean files have to be read in and interpolated in time,
539  before using just the top level.
540  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
541\end{itemize}
542
543
544% Missing the description of the 2 following variables:
545%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field
546%   ln_read_frq = .false.    !  specify whether we must read frq or not
547
548
549
550% ================================================================
551% Analytical formulation (sbcana module)
552% ================================================================
553\section{Analytical formulation (\protect\mdl{sbcana})}
554\label{sec:SBC_ana}
555
556%---------------------------------------namsbc_ana--------------------------------------------------
557%
558%\nlst{namsbc_ana}
559%--------------------------------------------------------------------------------------------------------------
560
561The analytical formulation of the surface boundary condition is the default scheme.
562In this case, all the six fluxes needed by the ocean are assumed to be uniform in space.
563They take constant values given in the namelist \ngn{namsbc{\_}ana} by
564the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0}, \np{rn\_qsr0}, and \np{rn\_emp0}
565($\textit{emp}=\textit{emp}_S$).
566The runoff is set to zero.
567In addition, the wind is allowed to reach its nominal value within a given number of time steps (\np{nn\_tau000}).
568
569If a user wants to apply a different analytical forcing,
570the \mdl{sbcana} module can be modified to use another scheme.
571As an example, the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the GYRE configuration
572(see GYRE configuration manual, in preparation).
573
574
575% ================================================================
576% Flux formulation
577% ================================================================
578\section{Flux formulation (\protect\mdl{sbcflx})}
579\label{sec:SBC_flx}
580%------------------------------------------namsbc_flx----------------------------------------------------
581
582\nlst{namsbc_flx} 
583%-------------------------------------------------------------------------------------------------------------
584
585In the flux formulation (\np{ln\_flx}\forcode{ = .true.}),
586the surface boundary condition fields are directly read from input files.
587The user has to define in the namelist \ngn{namsbc{\_}flx} the name of the file,
588the name of the variable read in the file, the time frequency at which it is given (in hours),
589and a logical setting whether a time interpolation to the model time step is required for this field.
590See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
591
592Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
593See \autoref{subsec:SBC_ssr} for its specification.
594
595
596% ================================================================
597% Bulk formulation
598% ================================================================
599\section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}]
600                        {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}}
601\label{sec:SBC_blk}
602
603In the bulk formulation, the surface boundary condition fields are computed using bulk formulae and atmospheric fields and ocean (and ice) variables.
604
605The atmospheric fields used depend on the bulk formulae used.
606Two bulk formulations are available:
607the CORE and the CLIO bulk formulea.
608The choice is made by setting to true one of the following namelist variable:
609\np{ln\_core} or \np{ln\_clio}.
610
611Note:
612in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
613Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over
614both an ocean and an ice surface.
615
616% -------------------------------------------------------------------------------------------------------------
617%        CORE Bulk formulea
618% -------------------------------------------------------------------------------------------------------------
619\subsection{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})}
620\label{subsec:SBC_blk_core}
621%------------------------------------------namsbc_core----------------------------------------------------
622%
623%\nlst{namsbc_core}
624%-------------------------------------------------------------------------------------------------------------
625
626The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
627They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data.
628They use an inertial dissipative method to compute the turbulent transfer coefficients
629(momentum, sensible heat and evaporation) from the 10 metre wind speed, air temperature and specific humidity.
630This \citet{Large_Yeager_Rep04} dataset is available through
631the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.
632
633Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
634This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
635
636Options are defined through the  \ngn{namsbc\_core} namelist variables.
637The required 8 input fields are:
638
639%--------------------------------------------------TABLE--------------------------------------------------
640\begin{table}[htbp]   \label{tab:CORE}
641\begin{center}
642\begin{tabular}{|l|c|c|c|}
643\hline
644Variable desciption              & Model variable  & Units   & point \\    \hline
645i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
646j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
64710m air temperature              & tair      & \r{}$K$            & T   \\ \hline
648Specific humidity             & humi      & \%              & T \\      \hline
649Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
650Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
651Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
652Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
653\end{tabular}
654\end{center}
655\end{table}
656%--------------------------------------------------------------------------------------------------------------
657
658Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
659It is simpler and faster (less fields to be read), but it is not the recommended method when
660the ocean grid size is the same or larger than the one of the input atmospheric fields.
661
662The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, \np{sn\_prec},
663\np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used
664(spatial and temporal interpolations).
665
666\np{cn\_dir} is the directory of location of bulk files
667\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
668\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
669\np{rn\_zu}: is the height of wind measurements (m)
670
671Three multiplicative factors are availables:
672\np{rn\_pfac} and \np{rn\_efac} allows to adjust (if necessary) the global freshwater budget by
673increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
674The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
675the calculation of surface wind stress.
676Its range should be between zero and one, and it is recommended to set it to 0.
677
678% -------------------------------------------------------------------------------------------------------------
679%        CLIO Bulk formulea
680% -------------------------------------------------------------------------------------------------------------
681\subsection{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})}
682\label{subsec:SBC_blk_clio}
683%------------------------------------------namsbc_clio----------------------------------------------------
684%
685%\nlst{namsbc_clio}
686%-------------------------------------------------------------------------------------------------------------
687
688The CLIO bulk formulae were developed several years ago for the Louvain-la-neuve coupled ice-ocean model
689(CLIO, \cite{Goosse_al_JGR99}).
690They are simpler bulk formulae.
691They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover.
692
693Options are defined through the  \ngn{namsbc\_clio} namelist variables.
694The required 7 input fields are:
695
696%--------------------------------------------------TABLE--------------------------------------------------
697\begin{table}[htbp]   \label{tab:CLIO}
698\begin{center}
699\begin{tabular}{|l|l|l|l|}
700\hline
701Variable desciption           & Model variable  & Units           & point \\  \hline
702i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
703j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
704Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
70510m air temperature              & tair         & \r{}$K$            & T \\   \hline
706Specific humidity                & humi         & \%              & T \\   \hline
707Cloud cover                   &           & \%              & T \\   \hline
708Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
709Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
710\end{tabular}
711\end{center}
712\end{table}
713%--------------------------------------------------------------------------------------------------------------
714
715As for the flux formulation, information about the input data required by the model is provided in
716the namsbc\_blk\_core or namsbc\_blk\_clio namelist (see \autoref{subsec:SBC_fldread}).
717
718% ================================================================
719% Coupled formulation
720% ================================================================
721\section{Coupled formulation (\protect\mdl{sbccpl})}
722\label{sec:SBC_cpl}
723%------------------------------------------namsbc_cpl----------------------------------------------------
724
725\nlst{namsbc_cpl} 
726%-------------------------------------------------------------------------------------------------------------
727
728In the coupled formulation of the surface boundary condition,
729the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
730while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
731the atmospheric component.
732
733A generalised coupled interface has been developed.
734It is currently interfaced with OASIS-3-MCT (\key{oasis3}).
735It has been successfully used to interface \NEMO to most of the European atmospheric GCM
736(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
737(Weather Research and Forecasting Model).
738
739Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
740The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are actually received by
741the ice-ocean system (no calculation of ice sublimation in coupled mode).
742When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
743the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}.
744In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
745(and need to be activated in \ngn{namsbc{\_}cpl} ).
746
747The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
748now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
749When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be determined by
750the number used in the sea ice model.
751In some limited cases it may be possible to specify single category coupling fields even when
752the sea ice model is running with multiple categories -
753in this case the user should examine the code to be sure the assumptions made are satisfactory.
754In cases where this is definitely not possible the model should abort with an error message.
755The new code has been tested using ECHAM with LIM2, and HadGAM3 with CICE but
756although it will compile with \key{lim3} additional minor code changes may be required to run using LIM3.
757
758
759% ================================================================
760%        Atmospheric pressure
761% ================================================================
762\section{Atmospheric pressure (\protect\mdl{sbcapr})}
763\label{sec:SBC_apr}
764%------------------------------------------namsbc_apr----------------------------------------------------
765
766\nlst{namsbc_apr} 
767%-------------------------------------------------------------------------------------------------------------
768
769The optional atmospheric pressure can be used to force ocean and ice dynamics
770(\np{ln\_apr\_dyn}\forcode{ = .true.}, \textit{\ngn{namsbc}} namelist).
771The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
772can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
773When used to force the dynamics, the atmospheric pressure is further transformed into
774an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
775\begin{equation} \label{eq:SBC_ssh_ib}
776   \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
777\end{equation}
778where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
779A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true.
780In this case $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
781$i.e.$ the mean value of $\eta_{ib}$ is kept to zero at all time step.
782
783The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
784For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
785(see \mdl{sbcssr} module).
786$\eta_{ib}$ can be set in the output.
787This can simplify altimetry data and model comparison as
788inverse barometer sea surface height is usually removed from these date prior to their distribution.
789
790When using time-splitting and BDY package for open boundaries conditions,
791the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
792\np{ln\_apr\_obc}  might be set to true.
793
794% ================================================================
795%        Surface Tides Forcing
796% ================================================================
797\section{Surface tides (\protect\mdl{sbctide})}
798\label{sec:SBC_tide}
799
800%------------------------------------------nam_tide---------------------------------------
801
802\nlst{nam_tide}
803%-----------------------------------------------------------------------------------------
804
805The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
806is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \np{.true.} in \ngn{nam\_tide}.
807This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that:
808\begin{equation}     \label{eq:PE_dyn_tides}
809\frac{\partial {\rm {\bf U}}_h }{\partial t}= ...
810+g\nabla (\Pi_{eq} + \Pi_{sal})
811\end{equation} 
812where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a self-attraction and loading term (SAL).
813 
814The equilibrium tidal forcing is expressed as a sum over the chosen constituents $l$ in \ngn{nam\_tide}.
815The constituents are defined such that \np{clname(1) = 'M2', clname(2)='S2', etc...}.
816For the three types of tidal frequencies it reads: \\
817Long period tides :
818\begin{equation}
819\Pi_{eq}(l)=A_{l}(1+k-h)(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l})
820\end{equation}
821diurnal tides :
822\begin{equation}
823\Pi_{eq}(l)=A_{l}(1+k-h)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l})
824\end{equation}
825Semi-diurnal tides:
826\begin{equation}
827\Pi_{eq}(l)=A_{l}(1+k-h)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l})
828\end{equation}
829Here $A_{l}$ is the amplitude, $\omega_{l}$ is the frequency, $\phi$ the latitude, $\lambda$ the longitude,
830$V_{0l}$ a phase shift with respect to Greenwich meridian and $t$ the time.
831The Love number factor $(1+k-h)$ is here taken as a constant (0.7).
832
833The SAL term should in principle be computed online as it depends on the model tidal prediction itself
834(see \citet{Arbic2004} for a discussion about the practical implementation of this term).
835Nevertheless, the complex calculations involved would make this computationally too expensive.
836Here, practical solutions are whether to read complex estimates $\Pi_{sal}(l)$ from an external model
837(\np{ln\_read\_load=.true.}) or use a ``scalar approximation'' (\np{ln\_scal\_load=.true.}).
838In the latter case, it reads:\\
839\begin{equation}
840\Pi_{sal} = \beta \eta
841\end{equation}
842where $\beta$ (\np{rn\_scal\_load}, $\approx0.09$) is a spatially constant scalar,
843often chosen to minimize tidal prediction errors.
844Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to false removes the SAL contribution.
845
846% ================================================================
847%        River runoffs
848% ================================================================
849\section{River runoffs (\protect\mdl{sbcrnf})}
850\label{sec:SBC_rnf}
851%------------------------------------------namsbc_rnf----------------------------------------------------
852
853\nlst{namsbc_rnf} 
854%-------------------------------------------------------------------------------------------------------------
855
856%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
857%Many models, however, have traditionally inserted river runoff to the top model cell.
858%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
859%throughout a nonzero depth has been motivated by the numerical and physical problems
860%that arise when the top grid cells are of the order of one meter. This situation is common in
861%coastal modelling and becomes more and more often open ocean and climate modelling
862%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
863%required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}.
864
865
866%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
867%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
868%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
869%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
870%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
871%emp or emps and the changes made are below:
872
873
874%Rachel:
875River runoff generally enters the ocean at a nonzero depth rather than through the surface.
876Many models, however, have traditionally inserted river runoff to the top model cell.
877This was the case in \NEMO prior to the version 3.3,
878and was combined with an option to increase vertical mixing near the river mouth.
879
880However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
881This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
882\footnote{
883  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
884  properly represent the diurnal cycle \citep{Bernie_al_JC05}.
885  see also \autoref{fig:SBC_dcy}.}.
886
887As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
888and for the temperature and salinity of the river to effect the surrounding ocean.
889The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
890along with the depth (in metres) which the river should be added to.
891
892Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and
893\np{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
894If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
895and/or taken as surface temperature respectively.
896
897The runoff value and attributes are read in in sbcrnf. 
898For temperature -999 is taken as missing data and the river temperature is taken to
899be the surface temperatue at the river point.
900For the depth parameter a value of -1 means the river is added to the surface box only,
901and a value of -999 means the river is added through the entire water column.
902After being read in the temperature and salinity variables are multiplied by the amount of runoff
903(converted into m/s) to give the heat and salt content of the river runoff.
904After the user specified depth is read ini,
905the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz\_rnf}.
906The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
907the bottom of the lowest box the river water is being added to
908(i.e. the total depth that river water is being added to in the model).
909
910The mass/volume addition due to the river runoff is, at each relevant depth level, added to
911the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
912This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
913The sea surface height is calculated using the sum of the horizontal divergence terms,
914and so the river runoff indirectly forces an increase in sea surface height.
915
916The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
917This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
918The heat and salt content of the river runoff is not included in this step,
919and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
920the box and replaced by the same volume of river water with no corresponding heat and salt addition.
921
922For the linear free surface case, at the surface box the tracer advection causes a flux of water
923(of equal volume to the runoff) through the sea surface out of the domain,
924which causes a salt and heat flux out of the model.
925As such the volume of water does not change, but the water is diluted.
926
927For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
928Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
929no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
930(The runoff addition to the top box along with the water being moved up through
931boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
932
933In trasbc the addition of heat and salt due to the river runoff is added.
934This is done in the same way for both vvl and non-vvl.
935The temperature and salinity are increased through the specified depth according to
936the heat and salt content of the river.
937
938In the non-linear free surface case (vvl),
939near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
940so that the original ratios of grid box heights are restored.
941In doing this water is moved into boxes below, throughout the water column,
942so the large volume addition to the surface box is spread between all the grid boxes.
943
944It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
945i.e. modelling the Baltic flow in and out of the North Sea.
946When the flow is out of the domain there is no change in temperature and salinity,
947regardless of the namelist options used,
948as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
949
950
951%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
952
953%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
954
955%\colorbox{yellow}{river mouths{\ldots}}
956
957%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
958%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
959%ENDIF
960
961%\gmcomment{  word doc of runoffs:
962%
963%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.
964%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. 
965
966%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
967
968%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:
969
970%}
971% ================================================================
972%        Ice shelf melting
973% ================================================================
974\section{Ice shelf melting (\protect\mdl{sbcisf})}
975\label{sec:SBC_isf}
976%------------------------------------------namsbc_isf----------------------------------------------------
977
978\nlst{namsbc_isf}
979%--------------------------------------------------------------------------------------------------------
980Namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation used.
981\begin{description}
982\item[\np{nn\_isf}\forcode{ = 1}]
983  The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{ = .true.} needed).
984  The fwf and heat flux are computed.
985  Two different bulk formula are available:
986   \begin{description}
987   \item[\np{nn\_isfblk}\forcode{ = 1}]
988     The bulk formula used to compute the melt is based the one described in \citet{Hunter2006}.
989     This formulation is based on a balance between the upward ocean heat flux and
990     the latent heat flux at the ice shelf base.
991   \item[\np{nn\_isfblk}\forcode{ = 2}]
992     The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}.
993     This formulation is based on a 3 equations formulation
994     (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation).
995   \end{description}
996   For this 2 bulk formulations, there are 3 different ways to compute the exchange coeficient:
997   \begin{description}
998   \item[\np{nn\_gammablk}\forcode{ = 0}]
999     The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}
1000   \item[\np{nn\_gammablk}\forcode{ = 1}]
1001     The salt and heat exchange coefficients are velocity dependent and defined as
1002     \np{rn\_gammas0}$ \times u_{*}$ and \np{rn\_gammat0}$ \times u_{*}$ where
1003     $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
1004     See \citet{Jenkins2010} for all the details on this formulation.
1005   \item[\np{nn\_gammablk}\forcode{ = 2}]
1006     The salt and heat exchange coefficients are velocity and stability dependent and defined as
1007     $\gamma_{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}$ where
1008     $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
1009     $\Gamma_{Turb}$ the contribution of the ocean stability and
1010     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1011     See \citet{Holland1999} for all the details on this formulation.
1012   \end{description}
1013 \item[\np{nn\_isf}\forcode{ = 2}]
1014   A parameterisation of isf is used. The ice shelf cavity is not represented.
1015   The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL)
1016   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1017   (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}).
1018   Furthermore the fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting.
1019   The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
1020 \item[\np{nn\_isf}\forcode{ = 3}]
1021   A simple parameterisation of isf is used. The ice shelf cavity is not represented.
1022   The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1023   the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and
1024   the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
1025   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1026 \item[\np{nn\_isf}\forcode{ = 4}]
1027   The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed).
1028   However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
1029   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\
1030\end{description}
1031
1032$\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on
1033the water mass properties, ocean velocities and depth.
1034This flux is thus highly dependent of the model resolution (horizontal and vertical),
1035realism of the water masses onto the shelf ...\\
1036
1037$\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file.
1038You have total control of the fwf forcing.
1039This can be useful if the water masses on the shelf are not realistic or
1040the resolution (horizontal/vertical) are too coarse to have realistic melting or
1041for studies where you need to control your heat and fw input.\\ 
1042
1043A namelist parameters control over how many meters the heat and fw fluxes are spread.
1044\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}.
1045This parameter is only used if \np{nn\_isf}\forcode{ = 1} or \np{nn\_isf}\forcode{ = 4}.
1046
1047If \np{rn\_hisf\_tbl}\forcode{ = 0}., the fluxes are put in the top level whatever is its tickness.
1048
1049If \np{rn\_hisf\_tbl} $>$ 0., the fluxes are spread over the first \np{rn\_hisf\_tbl} m
1050(ie over one or several cells).\\
1051
1052The ice shelf melt is implemented as a volume flux with in the same way as for the runoff.
1053The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1054the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}.
1055See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.
1056
1057
1058\section{Ice sheet coupling}
1059\label{sec:SBC_iscpl}
1060%------------------------------------------namsbc_iscpl----------------------------------------------------
1061
1062\nlst{namsbc_iscpl}
1063%--------------------------------------------------------------------------------------------------------
1064Ice sheet/ocean coupling is done through file exchange at the restart step.
1065NEMO, at each restart step, read the bathymetry and ice shelf draft variable in a netcdf file.
1066If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with
1067potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1068The wetting and drying scheme applied on the restart is very simple and described below for the 6 different cases:
1069\begin{description}
1070\item[Thin a cell down:]
1071  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1072  ($bt_b=bt_n$).
1073\item[Enlarge  a cell:]
1074  See case "Thin a cell down"
1075\item[Dry a cell:]
1076  mask, T/S, U/V and ssh are set to 0.
1077  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1078\item[Wet a cell:] 
1079  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1080  If no neighbours along i,j and k, T/S/U/V and mask are set to 0.
1081\item[Dry a column:]
1082   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1083\item[Wet a column:]
1084  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1085  If no neighbour, T/S/U/V and mask set to 0.
1086\end{description}
1087The extrapolation is call \np{nn\_drown} times.
1088It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,
1089the code will be unable to fill all the new wet cells properly.
1090The default number is set up for the MISOMIP idealised experiments.\\
1091This coupling procedure is able to take into account grounding line and calving front migration.
1092However, it is a non-conservative processe.
1093This could lead to a trend in heat/salt content and volume.
1094In order to remove the trend and keep the conservation level as close to 0 as possible,
1095a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}.
1096The heat/salt/vol. gain/loss is diagnose, as well as the location.
1097Based on what is done on sbcrnf to prescribed a source of heat/salt/vol.,
1098the heat/salt/vol. gain/loss is removed/added, over a period of \np{rn\_fiscpl} time step, into the system.
1099So after \np{rn\_fiscpl} time step, all the heat/salt/vol. gain/loss due to extrapolation process is canceled.\\
1100
1101As the before and now fields are not compatible (modification of the geometry),
1102the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.
1103%
1104% ================================================================
1105%        Handling of icebergs
1106% ================================================================
1107\section{Handling of icebergs (ICB)}
1108\label{sec:ICB_icebergs}
1109%------------------------------------------namberg----------------------------------------------------
1110
1111\nlst{namberg}
1112%-------------------------------------------------------------------------------------------------------------
1113
1114Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}.
1115Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ).
1116(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO).
1117Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1118described in the \ngn{namberg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1119Each class has an associated scaling (\np{rn\_mass\_scaling}),
1120which is an integer representing how many icebergs of this class are being described as one lagrangian point
1121(this reduces the numerical problem of tracking every single iceberg).
1122They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}.
1123
1124Two initialisation schemes are possible.
1125\begin{description}
1126\item[\np{nn\_test\_icebergs}~$>$~0]
1127  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1128  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1129  which an iceberg is generated at the beginning of the run.
1130  (Note that this happens each time the timestep equals \np{nn\_nit000}.)
1131  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of
1132  the geographical box: lonmin,lonmax,latmin,latmax
1133\item[\np{nn\_test\_icebergs}\forcode{ = -1}]
1134  In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
1135  This should be a file with a field on the configuration grid (typically ORCA)
1136  representing ice accumulation rate at each model point.
1137  These should be ocean points adjacent to land where icebergs are known to calve.
1138  Most points in this input grid are going to have value zero.
1139  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1140  At each time step, a test is performed to see if there is enough ice mass to
1141  calve an iceberg of each class in order (1 to 10).
1142  Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling).
1143  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1144\end{description}
1145
1146Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1147The latter act to disintegrate the iceberg.
1148This is either all melted freshwater,
1149or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1150which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1151Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
1152
1153Extensive diagnostics can be produced.
1154Separate output files are maintained for human-readable iceberg information.
1155A separate file is produced for each processor (independent of \np{ln\_ctl}).
1156The amount of information is controlled by two integer parameters:
1157\begin{description}
1158\item[\np{nn\_verbose\_level}] takes a value between one and four and
1159  represents an increasing number of points in the code at which variables are written,
1160  and an increasing level of obscurity.
1161\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1162\end{description}
1163
1164Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1165A non-zero value represents how many timesteps between writes of information into the output file.
1166These output files are in NETCDF format.
1167When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1168Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1169So care is needed to recreate data for individual icebergs,
1170since its trajectory data may be spread across multiple files.
1171
1172% -------------------------------------------------------------------------------------------------------------
1173%        Interactions with waves (sbcwave.F90, ln_wave)
1174% -------------------------------------------------------------------------------------------------------------
1175\section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
1176\label{sec:SBC_wave}
1177%------------------------------------------namsbc_wave--------------------------------------------------------
1178
1179\nlst{namsbc_wave}
1180%-------------------------------------------------------------------------------------------------------------
1181
1182Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate
1183physical processes related to ocean surface waves, namely the surface stress modified by growth and
1184dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1185tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1186the wind stress.
1187
1188Physical processes related to ocean surface waves can be accounted by setting the logical variable
1189\np{ln\_wave}\forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for
1190different porcesses should be activated as explained in the following sections.
1191
1192Wave fields can be provided either in forced or coupled mode:
1193\begin{description}
1194\item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist
1195for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1196Input Data generic Interface (see \autoref{sec:SBC_input}).
1197\item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 
1198in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist.
1199\end{description}
1200
1201
1202% ================================================================
1203% Neutral drag coefficient from wave model (ln_cdgw)

1204% ================================================================
1205\subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
1206\label{subsec:SBC_wave_cdgw}
1207
1208The neutral surface drag coefficient provided from an external data source ($i.e.$ a wave
model),
1209can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist.
1210Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,
1211the drag coefficient is computed according to the stable/unstable conditions of the
1212air-sea interface following \citet{Large_Yeager_Rep04}.
1213
1214
1215% ================================================================
1216% 3D Stokes Drift (ln_sdw, nn_sdrift)
1217% ================================================================
1218\subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
1219\label{subsec:SBC_wave_sdw}
1220
1221The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}.
1222It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1223and the current measured at a fixed point (Eulerian velocity).
1224As waves travel, the water particles that make up the waves travel in orbital motions but
1225without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1226at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift.
1227An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1228representation of surface physics in ocean general circulation models.
1229The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1230
1231\begin{equation} \label{eq:sbc_wave_sdw}
1232\mathbf{U}_{st} = \frac{16{\pi^3}} {g} 
1233                \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1234                \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1235\end{equation}
1236
1237where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1238$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1239$k$ is the mean wavenumber defined as:
1240$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1241
1242In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required
1243and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1244To simplify, it is customary to use approximations to the full Stokes profile.
1245Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1246are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift
1247$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1248and makes possible the estimation of the surface Stokes drift for random directional waves in
1249realistic wave conditions:
1250
1251\begin{description}
1252\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by
1253\citet{Breivik_al_JPO2014}:
1254
1255\begin{equation} \label{eq:sbc_wave_sdw_0a}
1256\mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez} 
1257\end{equation}
1258
1259where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1260
1261\begin{equation} \label{eq:sbc_wave_sdw_0b}
1262k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|} 
1263\quad \text{and }\
1264T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1265\end{equation}
1266
1267where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1268
1269\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a
1270reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface
1271\citep{Breivik_al_OM2016}:
1272
1273\begin{equation} \label{eq:sbc_wave_sdw_1}
1274\mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz} 
1275\textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1276\end{equation}
1277
1278where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1279
1280\item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1
1281but using the wave frequency from a wave model.
1282
1283\end{description}
1284
1285The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1286and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1287
1288\begin{equation} \label{eq:sbc_wave_eta_sdw}
1289\frac{\partial{\eta}}{\partial{t}} =
1290-\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1291\end{equation}
1292
1293The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1294for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1295that is induced by the three-dimensional Stokes velocity.
1296The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1297can be formulated as follows:
1298
1299\begin{equation} \label{eq:sbc_wave_tra_sdw}
1300\frac{\partial{c}}{\partial{t}} =
1301- (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1302\end{equation}
1303
1304
1305% ================================================================
1306% Stokes-Coriolis term (ln_stcor)
1307% ================================================================
1308\subsection{Stokes-Coriolis term (\protect\np{ln\_stcor})}
1309\label{subsec:SBC_wave_stcor}
1310
1311In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1312in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1313This additional force may have impact on the Ekman turning of the surface current.
1314In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1315approximations described in \autoref{subsec:SBC_wave_sdw}),
1316\np{ln\_stcor}\forcode{ = .true.} has to be set.
1317
1318
1319% ================================================================
1320% Waves modified stress (ln_tauwoc, ln_tauw)
1321% ================================================================
1322\subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 
1323\label{subsec:SBC_wave_tauw}
1324
1325The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1326into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not
1327available for forcing the mean circulation, while in the opposite case of a decaying sea
1328state more momentum is available for forcing the ocean.
1329Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress,
1330but in practice an equilibrium sea state is a fairly rare event.
1331So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1332
1333\begin{equation} \label{eq:sbc_wave_tauoc}
1334\tau_{oc,a} = \tau_a - \tau_w
1335\end{equation}
1336
1337where $\tau_a$ is the atmospheric surface stress;
1338$\tau_w$ is the atmospheric stress going into the waves defined as:
1339
1340\begin{equation} \label{eq:sbc_wave_tauw}
1341\tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1342\end{equation}
1343
1344where: $c_p$ is the phase speed of the gravity waves,
1345$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1346the physics of ocean waves. The first one, $S_{in}$, describes the generation
1347of ocean waves by wind and therefore represents the momentum and energy transfer
1348from air to ocean waves; the second term $S_{nl}$ denotes
1349the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$ 
1350describes the dissipation of waves by processes such as white-capping, large scale breaking
1351eddy-induced damping.
1352
1353The wave stress derived from an external wave model can be provided either through the normalized
1354wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and
1355meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}.
1356
1357
1358% ================================================================
1359% Miscellanea options
1360% ================================================================
1361\section{Miscellaneous options}
1362\label{sec:SBC_misc}
1363
1364% -------------------------------------------------------------------------------------------------------------
1365%        Diurnal cycle
1366% -------------------------------------------------------------------------------------------------------------
1367\subsection{Diurnal cycle (\protect\mdl{sbcdcy})}
1368\label{subsec:SBC_dcy}
1369%------------------------------------------namsbc_rnf----------------------------------------------------
1370%
1371\nlst{namsbc} 
1372%-------------------------------------------------------------------------------------------------------------
1373
1374%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1375\begin{figure}[!t]    \begin{center}
1376\includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal}
1377\caption{ \protect\label{fig:SBC_diurnal}
1378  Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values.
1379  The reconstructed diurnal cycle (black line) is chosen as
1380  the mean value of the analytical cycle (blue line) over a time step,
1381  not as the mid time step value of the analytically cycle (red square).
1382  From \citet{Bernie_al_CD07}.}
1383\end{center}   \end{figure}
1384%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1385
1386\cite{Bernie_al_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.
1387Unfortunately high frequency forcing fields are rare, not to say inexistent.
1388Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at
1389high frequency \citep{Bernie_al_CD07}.
1390Furthermore, only the knowledge of daily mean value of SWF is needed,
1391as higher frequency variations can be reconstructed from them,
1392assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1393The \cite{Bernie_al_CD07} reconstruction algorithm is available in \NEMO by
1394setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when
1395using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or
1396the flux formulation (\np{ln\_flx}\forcode{ = .true.}).
1397The reconstruction is performed in the \mdl{sbcdcy} module.
1398The detail of the algoritm used can be found in the appendix~A of \cite{Bernie_al_CD07}.
1399The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at
1400a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1401The use of diurnal cycle reconstruction requires the input SWF to be daily
1402($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1403Furthermore, it is recommended to have a least 8 surface module time step per day,
1404that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1405An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1406one every 2~hours (from 1am to 11pm).
1407
1408%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1409\begin{figure}[!t]  \begin{center}
1410\includegraphics[width=0.7\textwidth]{Fig_SBC_dcy}
1411\caption{ \protect\label{fig:SBC_dcy}
1412  Example of recontruction of the diurnal cycle variation of short wave flux from
1413  daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1414  The display is on (i,j) plane. }
1415\end{center}   \end{figure}
1416%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1417
1418Note also that the setting a diurnal cycle in SWF is highly recommended when
1419the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1420an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1421
1422% -------------------------------------------------------------------------------------------------------------
1423%        Rotation of vector pairs onto the model grid directions
1424% -------------------------------------------------------------------------------------------------------------
1425\subsection{Rotation of vector pairs onto the model grid directions}
1426\label{subsec:SBC_rotation}
1427
1428When using a flux (\np{ln\_flx}\forcode{ = .true.}) or
1429bulk (\np{ln\_clio}\forcode{ = .true.} or \np{ln\_core}\forcode{ = .true.}) formulation,
1430pairs of vector components can be rotated from east-north directions onto the local grid directions.
1431This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1432be defined relative to a rectilinear grid.
1433To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1434The eastward component must start with "U" and the northward component with "V". 
1435The remaining characters in the strings are used to identify which pair of components go together.
1436So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1437rotate them on to the model grid directions;
1438"U2" and "V2" could be used against a second pair of components, and so on.
1439The extra characters used in the strings are arbitrary.
1440The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1441
1442% -------------------------------------------------------------------------------------------------------------
1443%        Surface restoring to observed SST and/or SSS
1444% -------------------------------------------------------------------------------------------------------------
1445\subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1446\label{subsec:SBC_ssr}
1447%------------------------------------------namsbc_ssr----------------------------------------------------
1448
1449\nlst{namsbc_ssr} 
1450%-------------------------------------------------------------------------------------------------------------
1451
1452IOptions are defined through the \ngn{namsbc\_ssr} namelist variables.
1453On forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}),
1454a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1455\begin{equation} \label{eq:sbc_dmp_q}
1456Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1457\end{equation}
1458where SST is a sea surface temperature field (observed or climatological),
1459$T$ is the model surface layer temperature and
1460$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1461For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1462This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1463
1464In the fresh water budget, a feedback term can also be added.
1465Converted into an equivalent freshwater flux, it takes the following expression :
1466
1467\begin{equation} \label{eq:sbc_dmp_emp}
1468\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1469                                             {\left.S\right|_{k=1}}
1470\end{equation}
1471
1472where $\textit{emp}_{o }$ is a net surface fresh water flux
1473(observed, climatological or an atmospheric model product),
1474\textit{SSS}$_{Obs}$ is a sea surface salinity
1475(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
1476$\left.S\right|_{k=1}$ is the model surface layer salinity and
1477$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1478Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as
1479the atmosphere does not care about ocean surface salinity \citep{Madec1997}.
1480The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1481reduce the uncertainties we have on the observed freshwater budget.
1482
1483% -------------------------------------------------------------------------------------------------------------
1484%        Handling of ice-covered area
1485% -------------------------------------------------------------------------------------------------------------
1486\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1487\label{subsec:SBC_ice-cover}
1488
1489The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1490There are several way to handle sea-ice in the system depending on
1491the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist.
1492\begin{description}
1493\item[nn{\_}ice = 0]
1494  there will never be sea-ice in the computational domain.
1495  This is a typical namelist value used for tropical ocean domain.
1496  The surface fluxes are simply specified for an ice-free ocean.
1497  No specific things is done for sea-ice.
1498\item[nn{\_}ice = 1]
1499  sea-ice can exist in the computational domain, but no sea-ice model is used.
1500  An observed ice covered area is read in a file.
1501  Below this area, the SST is restored to the freezing point and
1502  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1503  The associated modification of the freshwater fluxes are done in such a way that
1504  the change in buoyancy fluxes remains zero.
1505  This prevents deep convection to occur when trying to reach the freezing point
1506  (and so ice covered area condition) while the SSS is too large.
1507  This manner of managing sea-ice area, just by using si IF case,
1508  is usually referred as the \textit{ice-if} model.
1509  It can be found in the \mdl{sbcice{\_}if} module.
1510\item[nn{\_}ice = 2 or more]
1511  A full sea ice model is used.
1512  This model computes the ice-ocean fluxes,
1513  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1514  provide the surface ocean fluxes.
1515  Note that the activation of a sea-ice model is is done by defining a CPP key (\key{lim3} or \key{cice}).
1516  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value
1517  ($i.e.$ $2$ for LIM-3 or $3$ for CICE).
1518\end{description}
1519
1520% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1521
1522\subsection{Interface to CICE (\protect\mdl{sbcice\_cice})}
1523\label{subsec:SBC_cice}
1524
1525It is now possible to couple a regional or global NEMO configuration (without AGRIF)
1526to the CICE sea-ice model by using \key{cice}.
1527The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1528the additional 'hadgem3' drivers will be required, even with the latest code release.
1529Input grid files consistent with those used in NEMO will also be needed,
1530and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1531(seek advice from UKMO if necessary).
1532Currently the code is only designed to work when using the CORE forcing option for NEMO
1533(with \textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE name-list),
1534or alternatively when NEMO is coupled to the HadGAM3 atmosphere model
1535(with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}).
1536The code is intended to be used with \np{nn\_fsbc} set to 1
1537(although coupling ocean and ice less frequently should work,
1538it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1539the user should check that results are not significantly different to the standard case).
1540
1541There are two options for the technical coupling between NEMO and CICE.
1542The standard version allows complete flexibility for the domain decompositions in the individual models,
1543but this is at the expense of global gather and scatter operations in the coupling which
1544become very expensive on larger numbers of processors.
1545The alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that
1546the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1547and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1548allows much more efficient direct coupling on individual processors.
1549This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1550there is no sea ice.
1551
1552% -------------------------------------------------------------------------------------------------------------
1553%        Freshwater budget control
1554% -------------------------------------------------------------------------------------------------------------
1555\subsection{Freshwater budget control (\protect\mdl{sbcfwb})}
1556\label{subsec:SBC_fwb}
1557
1558For global ocean simulation it can be useful to introduce a control of the mean sea level in order to
1559prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1560In \NEMO, two way of controlling the the freshwater budget.
1561\begin{description}
1562\item[\np{nn\_fwb}\forcode{ = 0}]
1563  no control at all.
1564  The mean sea level is free to drift, and will certainly do so.
1565\item[\np{nn\_fwb}\forcode{ = 1}]
1566  global mean \textit{emp} set to zero at each model time step.
1567%Note that with a sea-ice model, this technique only control the mean sea level with linear free surface (\key{vvl} not defined) and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling).
1568\item[\np{nn\_fwb}\forcode{ = 2}]
1569  freshwater budget is adjusted from the previous year annual mean budget which
1570  is read in the \textit{EMPave\_old.dat} file.
1571  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1572  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1573\end{description}
1574
1575
1576
1577% Griffies doc:
1578% When running ocean-ice simulations, we are not explicitly representing land processes,
1579% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1580% it is important to balance the hydrological cycle in ocean-ice models.
1581% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1582% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1583% a chosen time scale.
1584%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1585% so that there is always a zero net input of water to the ocean-ice system.
1586% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1587% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1588% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1589% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1590% and ice models when aiming to balance the hydrological cycle.
1591% 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,
1592% not the water in any one sub-component. As an extreme example to illustrate the issue,
1593% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1594% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1595% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1596% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1597% in ocean-ice models.
1598
1599
1600\end{document}
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