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1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4% ================================================================
5% Chapter —— Surface Boundary Condition (SBC, ISF, ICB)
6% ================================================================
7\chapter{Surface Boundary Condition (SBC, ISF, ICB) }
8\label{chap:SBC}
9\minitoc
10
11\newpage
12
13%---------------------------------------namsbc--------------------------------------------------
14
15\nlst{namsbc}
16%--------------------------------------------------------------------------------------------------------------
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 (\ie \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\ie 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(\ie 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) \ie 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]
164  \begin{center}
165    \begin{tabular}{|l|l|l|l|}
166      \hline
167      Variable description             & Model variable  & Units  & point \\  \hline
168      i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
169      j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
170      Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
171      Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
172    \end{tabular}
173    \caption{
174      \protect\label{tab:ssm}
175      Ocean variables provided by the ocean to the surface module (SBC).
176      The variable are averaged over nn{\_}fsbc time step,
177      \ie the frequency of computation of surface fluxes.
178    }
179  \end{center}
180\end{table}
181%--------------------------------------------------------------------------------------------------------------
182
183%\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
184
185
186% ================================================================
187%       Input Data
188% ================================================================
189\section{Input data generic interface}
190\label{sec:SBC_input}
191
192A generic interface has been introduced to manage the way input data
193(2D or 3D fields, like surface forcing or ocean T and S) are specify in \NEMO.
194This task is archieved by \mdl{fldread}.
195The module was design with four main objectives in mind:
196\begin{enumerate}
197\item
198  optionally provide a time interpolation of the input data at model time-step, whatever their input frequency is,
199  and according to the different calendars available in the model.
200\item
201  optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
202\item
203  make the run duration independent from the period cover by the input files.
204\item
205  provide a simple user interface and a rather simple developer interface by
206  limiting the number of prerequisite information.
207\end{enumerate} 
208
209As a results the user have only to fill in for each variable a structure in the namelist file to
210define the input data file and variable names, the frequency of the data (in hours or months),
211whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
212and three additional parameters for on-the-fly interpolation.
213When adding a new input variable, the developer has to add the associated structure in the namelist,
214read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
215and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
216
217The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
218(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
219if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
220
221Note that when an input data is archived on a disc which is accessible directly from the workspace where
222the code is executed, then the use can set the \np{cn\_dir} to the pathway leading to the data.
223By default, the data are assumed to have been copied so that cn\_dir='./'.
224
225% -------------------------------------------------------------------------------------------------------------
226% Input Data specification (\mdl{fldread})
227% -------------------------------------------------------------------------------------------------------------
228\subsection{Input data specification (\protect\mdl{fldread})}
229\label{subsec:SBC_fldread}
230
231The structure associated with an input variable contains the following information:
232\begin{forlines}
233!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
234!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
235\end{forlines}
236where
237\begin{description} 
238\item[File name]:
239  the stem name of the NetCDF file to be open.
240  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
241  by date information and possibly a prefix (when using AGRIF).
242  Tab.\autoref{tab:fldread} provides the resulting file name in all possible cases according to
243  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
244
245%--------------------------------------------------TABLE--------------------------------------------------
246  \begin{table}[htbp]
247    \begin{center}
248      \begin{tabular}{|l|c|c|c|}
249        \hline
250        & daily or weekLLL         & monthly                   &   yearly          \\   \hline
251        \np{clim}\forcode{ = .false.}  & fn\_yYYYYmMMdDD.nc  &   fn\_yYYYYmMM.nc   &   fn\_yYYYY.nc  \\   \hline
252        \np{clim}\forcode{ = .true.}         & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
253      \end{tabular}
254    \end{center}
255    \caption{
256      \protect\label{tab:fldread}
257      naming nomenclature for climatological or interannual input file, as a function of the Open/close frequency.
258      The stem name is assumed to be 'fn'.
259      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
260      (\ie 'sun','sat','fri','thu','wed','tue','mon').
261      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits.
262      Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc',
263      where 'PPPP' is the process number coded with 4 digits;
264      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N'  is the child grid number.
265    }
266  \end{table}
267%--------------------------------------------------------------------------------------------------------------
268 
269
270\item[Record frequency]:
271  the frequency of the records contained in the input file.
272  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
273  (for example -1 for monthly forcing or -12 for annual forcing).
274  Note that this frequency must really be an integer and not a real.
275  On some computers, seting it to '24.' can be interpreted as 240!
276
277\item[Variable name]:
278  the name of the variable to be read in the input NetCDF file.
279
280\item[Time interpolation]:
281  a logical to activate, or not, the time interpolation.
282  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
283  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
284  00h00'00'' to 23h59'59".
285  If set to 'true', the forcing will have a broken line shape.
286  Records are assumed to be dated the middle of the forcing period.
287  For example, when using a daily forcing with time interpolation,
288  linear interpolation will be performed between mid-day of two consecutive days.
289
290\item[Climatological forcing]:
291  a logical to specify if a input file contains climatological forcing which can be cycle in time,
292  or an interannual forcing which will requires additional files if
293  the period covered by the simulation exceed the one of the file.
294  See the above the file naming strategy which impacts the expected name of the file to be opened.
295
296\item[Open/close frequency]:
297  the frequency at which forcing files must be opened/closed.
298  Four cases are coded:
299  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
300  means the forcing files will contain data for one day, one week, one month or one year.
301  Files are assumed to contain data from the beginning of the open/close period.
302  For example, the first record of a yearly file containing daily data is Jan 1st even if
303  the experiment is not starting at the beginning of the year.
304
305\item[Others]:
306  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
307  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
308
309\end{description}
310
311Additional remarks:\\
312(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
313The only tricky point is therefore to specify the date at which we need to do the interpolation and
314the date of the records read in the input files.
315Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the time step.
316For example, for an experiment starting at 0h00'00" with a one hour time-step,
317a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
318However, for forcing data related to the surface module,
319values are not needed at every time-step but at every \np{nn\_fsbc} time-step.
320For example with \np{nn\_fsbc}\forcode{ = 3}, the surface module will be called at time-steps 1, 4, 7, etc.
321The date used for the time interpolation is thus redefined to be at the middle of \np{nn\_fsbc} time-step period.
322In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
323(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
324The calendar associated with the forcing field is build according to the information provided by
325user in the record frequency, the open/close frequency and the type of temporal interpolation.
326For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
327be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
328(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
329interpolating data with the first (last) record of the open/close period.
330For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
331the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
332Dec 31st 12h00'00" and Jan 1st 12h00'00".
333If the forcing is climatological, Dec and Jan will be keep-up from the same year.
334However, if the forcing is not climatological, at the end of
335the open/close period the code will automatically close the current file and open the next one.
336Note that, if the experiment is starting (ending) at the beginning (end) of
337an open/close period we do accept that the previous (next) file is not existing.
338In this case, the time interpolation will be performed between two identical values.
339For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
340we do accept that the file related to year Y-1 is not existing.
341The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
342If the file of year Y-1 exists, the code will read its last record.
343Therefore, this file can contain only one record corresponding to Dec 31st,
344a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
345
346
347% -------------------------------------------------------------------------------------------------------------
348% Interpolation on the Fly
349% -------------------------------------------------------------------------------------------------------------
350\subsection{Interpolation on-the-fly}
351\label{subsec:SBC_iof}
352
353Interpolation on the Fly allows the user to supply input files required for the surface forcing on
354grids other than the model grid.
355To do this he or she must supply, in addition to the source data file, a file of weights to be used to
356interpolate from the data grid to the model grid.
357The original development of this code used the SCRIP package
358(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
359In principle, any package can be used to generate the weights, but the variables in
360the input weights file must have the same names and meanings as assumed by the model.
361Two methods are currently available: bilinear and bicubic interpolation.
362Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
363the input file and substitute the corresponding values with the average of the 8 neighbouring points in
364the native external grid.
365Only "sea points" are considered for the averaging.
366The land/sea mask file must be provided in the structure associated with the input variable.
367The netcdf land/sea mask variable name must be 'LSM' it must have the same horizontal and vertical dimensions of
368the associated variable and should be equal to 1 over land and 0 elsewhere.
369The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.
370Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied.
371
372\subsubsection{Bilinear interpolation}
373\label{subsec:SBC_iof_bilinear}
374
375The input weights file in this case has two sets of variables:
376src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
377The "src" variables correspond to the point in the input grid to which the weight "wgt" is to be applied.
378Each src value is an integer corresponding to the index of a point in the input grid when
379written as a one dimensional array.
380For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
381There are four of each variable because bilinear interpolation uses the four points defining
382the grid box containing the point to be interpolated.
383All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
384generate a value for point (i,j) in the model.
385
386Symbolically, the algorithm used is:
387\[
388  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
389\]
390where function idx() transforms a one dimensional index src(k) into a two dimensional index,
391and wgt(1) corresponds to variable "wgt01" for example.
392
393\subsubsection{Bicubic interpolation}
394\label{subsec:SBC_iof_bicubic}
395
396Again there are two sets of variables: "src" and "wgt".
397But in this case there are 16 of each.
398The symbolic algorithm used to calculate values on the model grid is now:
399
400\[
401  \begin{split}
402    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
403    +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
404    +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
405    +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
406  \end{split}
407\]
408The gradients here are taken with respect to the horizontal indices and not distances since
409the spatial dependency has been absorbed into the weights.
410
411\subsubsection{Implementation}
412\label{subsec:SBC_iof_imp}
413
414To activate this option, a non-empty string should be supplied in
415the weights filename column of the relevant namelist;
416if this is left as an empty string no action is taken.
417In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
418as and when they are first required.
419This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
420inspecting a global attribute stored in the weights input file.
421This attribute must be called "ew\_wrap" and be of integer type.
422If it is negative, the input non-model grid is assumed not to be cyclic.
423If zero or greater, then the value represents the number of columns that overlap.
424$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
425if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
426If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
427In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
428therefore the grid is assumed to be cyclic with no overlapping columns.
429(In fact this only matters when bicubic interpolation is required.)
430Note that no testing is done to check the validity in the model,
431since there is no way of knowing the name used for the longitude variable,
432so it is up to the user to make sure his or her data is correctly represented.
433
434Next the routine reads in the weights.
435Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
436The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
437and when required, for reading in the variable to be interpolated (on the input data grid).
438The size of the input data array is determined by examining the values in the "src" arrays to
439find the minimum and maximum i and j values required.
440Since bicubic interpolation requires the calculation of gradients at each point on the grid,
441the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
442When the array of points from the data file is adjacent to an edge of the data grid,
443the halo is either a copy of the row/column next to it (non-cyclical case),
444or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
445
446\subsubsection{Limitations}
447\label{subsec:SBC_iof_lim}
448
449\begin{enumerate} 
450\item
451  The case where input data grids are not logically rectangular has not been tested.
452\item
453  This code is not guaranteed to produce positive definite answers from positive definite inputs when
454  a bicubic interpolation method is used.
455\item
456  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
457\item
458  The gradients across the ends of a cyclical grid assume that the grid spacing between
459  the two columns involved are consistent with the weights used.
460\item
461  Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
462  but this has not been implemented.)
463\end{enumerate}
464
465\subsubsection{Utilities}
466\label{subsec:SBC_iof_util}
467
468% to be completed
469A set of utilities to create a weights file for a rectilinear input grid is available
470(see the directory NEMOGCM/TOOLS/WEIGHTS).
471
472% -------------------------------------------------------------------------------------------------------------
473% Standalone Surface Boundary Condition Scheme
474% -------------------------------------------------------------------------------------------------------------
475\subsection{Standalone surface boundary condition scheme}
476\label{subsec:SAS_iof}
477
478%---------------------------------------namsbc_ana--------------------------------------------------
479
480\nlst{namsbc_sas}
481%--------------------------------------------------------------------------------------------------------------
482
483In some circumstances it may be useful to avoid calculating the 3D temperature,
484salinity and velocity fields and simply read them in from a previous run or receive them from OASIS. 
485For example:
486
487\begin{itemize}
488\item
489  Multiple runs of the model are required in code development to
490  see the effect of different algorithms in the bulk formulae.
491\item
492  The effect of different parameter sets in the ice model is to be examined.
493\item
494  Development of sea-ice algorithms or parameterizations.
495\item
496  Spinup of the iceberg floats
497\item
498  Ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}\forcode{ = .true.})
499\end{itemize}
500
501The StandAlone Surface scheme provides this utility.
502Its options are defined through the \ngn{namsbc\_sas} namelist variables.
503A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
504However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0).
505In this configuration, a few routines in the standard model are overriden by new versions.
506Routines replaced are:
507
508\begin{itemize}
509\item
510  \mdl{nemogcm}:
511  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
512  Since the ocean state is not calculated all associated initialisations have been removed.
513\item
514  \mdl{step}:
515  The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
516\item
517  \mdl{sbcmod}:
518  This has been cut down and now only calculates surface forcing and the ice model required.
519  New surface modules that can function when only the surface level of the ocean state is defined can also be added
520  (\eg icebergs).
521\item
522  \mdl{daymod}:
523  No ocean restarts are read or written (though the ice model restarts are retained),
524  so calls to restart functions have been removed.
525  This also means that the calendar cannot be controlled by time in a restart file,
526  so the user must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
527\item
528  \mdl{stpctl}:
529  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
530\item
531  \mdl{diawri}:
532  All 3D data have been removed from the output.
533  The surface temperature, salinity and velocity components (which have been read in) are written along with
534  relevant forcing and ice data.
535\end{itemize}
536
537One new routine has been added:
538
539\begin{itemize}
540\item
541  \mdl{sbcsas}:
542  This module initialises the input files needed for reading temperature, salinity and
543  velocity arrays at the surface.
544  These filenames are supplied in namelist namsbc{\_}sas.
545  Unfortunately because of limitations with the \mdl{iom} module,
546  the full 3D fields from the mean files have to be read in and interpolated in time,
547  before using just the top level.
548  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
549\end{itemize}
550
551
552% Missing the description of the 2 following variables:
553%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field
554%   ln_read_frq = .false.    !  specify whether we must read frq or not
555
556
557
558% ================================================================
559% Analytical formulation (sbcana module)
560% ================================================================
561\section{Analytical formulation (\protect\mdl{sbcana})}
562\label{sec:SBC_ana}
563
564%---------------------------------------namsbc_ana--------------------------------------------------
565%
566%\nlst{namsbc_ana}
567%--------------------------------------------------------------------------------------------------------------
568
569The analytical formulation of the surface boundary condition is the default scheme.
570In this case, all the six fluxes needed by the ocean are assumed to be uniform in space.
571They take constant values given in the namelist \ngn{namsbc{\_}ana} by
572the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0}, \np{rn\_qsr0}, and \np{rn\_emp0}
573($\textit{emp}=\textit{emp}_S$).
574The runoff is set to zero.
575In addition, the wind is allowed to reach its nominal value within a given number of time steps (\np{nn\_tau000}).
576
577If a user wants to apply a different analytical forcing,
578the \mdl{sbcana} module can be modified to use another scheme.
579As an example, the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the GYRE configuration
580(see GYRE configuration manual, in preparation).
581
582
583% ================================================================
584% Flux formulation
585% ================================================================
586\section{Flux formulation (\protect\mdl{sbcflx})}
587\label{sec:SBC_flx}
588%------------------------------------------namsbc_flx----------------------------------------------------
589
590\nlst{namsbc_flx} 
591%-------------------------------------------------------------------------------------------------------------
592
593In the flux formulation (\np{ln\_flx}\forcode{ = .true.}),
594the surface boundary condition fields are directly read from input files.
595The user has to define in the namelist \ngn{namsbc{\_}flx} the name of the file,
596the name of the variable read in the file, the time frequency at which it is given (in hours),
597and a logical setting whether a time interpolation to the model time step is required for this field.
598See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
599
600Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
601See \autoref{subsec:SBC_ssr} for its specification.
602
603
604% ================================================================
605% Bulk formulation
606% ================================================================
607\section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}]
608                        {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}}
609\label{sec:SBC_blk}
610
611In the bulk formulation, the surface boundary condition fields are computed using bulk formulae and atmospheric fields and ocean (and ice) variables.
612
613The atmospheric fields used depend on the bulk formulae used.
614Two bulk formulations are available:
615the CORE and the CLIO bulk formulea.
616The choice is made by setting to true one of the following namelist variable:
617\np{ln\_core} or \np{ln\_clio}.
618
619Note:
620in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
621Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over
622both an ocean and an ice surface.
623
624% -------------------------------------------------------------------------------------------------------------
625%        CORE Bulk formulea
626% -------------------------------------------------------------------------------------------------------------
627\subsection{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})}
628\label{subsec:SBC_blk_core}
629%------------------------------------------namsbc_core----------------------------------------------------
630%
631%\nlst{namsbc_core}
632%-------------------------------------------------------------------------------------------------------------
633
634The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
635They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data.
636They use an inertial dissipative method to compute the turbulent transfer coefficients
637(momentum, sensible heat and evaporation) from the 10 metre wind speed, air temperature and specific humidity.
638This \citet{Large_Yeager_Rep04} dataset is available through
639the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.
640
641Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
642This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
643
644Options are defined through the  \ngn{namsbc\_core} namelist variables.
645The required 8 input fields are:
646
647%--------------------------------------------------TABLE--------------------------------------------------
648\begin{table}[htbp]
649  \label{tab:CORE}
650  \begin{center}
651    \begin{tabular}{|l|c|c|c|}
652      \hline
653      Variable desciption              & Model variable  & Units   & point \\    \hline
654      i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
655      j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
656      10m air temperature              & tair      & \r{}$K$            & T   \\ \hline
657      Specific humidity             & humi      & \%              & T \\      \hline
658      Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
659      Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
660      Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
661      Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
662    \end{tabular}
663  \end{center}
664\end{table}
665%--------------------------------------------------------------------------------------------------------------
666
667Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
668It is simpler and faster (less fields to be read), but it is not the recommended method when
669the ocean grid size is the same or larger than the one of the input atmospheric fields.
670
671The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, \np{sn\_prec},
672\np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used
673(spatial and temporal interpolations).
674
675\np{cn\_dir} is the directory of location of bulk files
676\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
677\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
678\np{rn\_zu}: is the height of wind measurements (m)
679
680Three multiplicative factors are availables:
681\np{rn\_pfac} and \np{rn\_efac} allows to adjust (if necessary) the global freshwater budget by
682increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
683The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
684the calculation of surface wind stress.
685Its range should be between zero and one, and it is recommended to set it to 0.
686
687% -------------------------------------------------------------------------------------------------------------
688%        CLIO Bulk formulea
689% -------------------------------------------------------------------------------------------------------------
690\subsection{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})}
691\label{subsec:SBC_blk_clio}
692%------------------------------------------namsbc_clio----------------------------------------------------
693%
694%\nlst{namsbc_clio}
695%-------------------------------------------------------------------------------------------------------------
696
697The CLIO bulk formulae were developed several years ago for the Louvain-la-neuve coupled ice-ocean model
698(CLIO, \cite{Goosse_al_JGR99}).
699They are simpler bulk formulae.
700They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover.
701
702Options are defined through the  \ngn{namsbc\_clio} namelist variables.
703The required 7 input fields are:
704
705%--------------------------------------------------TABLE--------------------------------------------------
706\begin{table}[htbp]
707  \label{tab:CLIO}
708  \begin{center}
709    \begin{tabular}{|l|l|l|l|}
710      \hline
711      Variable desciption           & Model variable  & Units           & point \\  \hline
712      i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
713      j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
714      Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
715      10m air temperature              & tair         & \r{}$K$            & T \\   \hline
716      Specific humidity                & humi         & \%              & T \\   \hline
717      Cloud cover                   &           & \%              & T \\   \hline
718      Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
719      Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
720    \end{tabular}
721  \end{center}
722\end{table}
723%--------------------------------------------------------------------------------------------------------------
724
725As for the flux formulation, information about the input data required by the model is provided in
726the namsbc\_blk\_core or namsbc\_blk\_clio namelist (see \autoref{subsec:SBC_fldread}).
727
728% ================================================================
729% Coupled formulation
730% ================================================================
731\section{Coupled formulation (\protect\mdl{sbccpl})}
732\label{sec:SBC_cpl}
733%------------------------------------------namsbc_cpl----------------------------------------------------
734
735\nlst{namsbc_cpl} 
736%-------------------------------------------------------------------------------------------------------------
737
738In the coupled formulation of the surface boundary condition,
739the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
740while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
741the atmospheric component.
742
743A generalised coupled interface has been developed.
744It is currently interfaced with OASIS-3-MCT (\key{oasis3}).
745It has been successfully used to interface \NEMO to most of the European atmospheric GCM
746(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
747(Weather Research and Forecasting Model).
748
749Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
750The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are actually received by
751the ice-ocean system (no calculation of ice sublimation in coupled mode).
752When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
753the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}.
754In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
755(and need to be activated in \ngn{namsbc{\_}cpl} ).
756
757The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
758now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
759When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be determined by
760the number used in the sea ice model.
761In some limited cases it may be possible to specify single category coupling fields even when
762the sea ice model is running with multiple categories -
763in this case the user should examine the code to be sure the assumptions made are satisfactory.
764In cases where this is definitely not possible the model should abort with an error message.
765The new code has been tested using ECHAM with LIM2, and HadGAM3 with CICE but
766although it will compile with \key{lim3} additional minor code changes may be required to run using LIM3.
767
768
769% ================================================================
770%        Atmospheric pressure
771% ================================================================
772\section{Atmospheric pressure (\protect\mdl{sbcapr})}
773\label{sec:SBC_apr}
774%------------------------------------------namsbc_apr----------------------------------------------------
775
776\nlst{namsbc_apr} 
777%-------------------------------------------------------------------------------------------------------------
778
779The optional atmospheric pressure can be used to force ocean and ice dynamics
780(\np{ln\_apr\_dyn}\forcode{ = .true.}, \textit{\ngn{namsbc}} namelist).
781The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
782can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
783When used to force the dynamics, the atmospheric pressure is further transformed into
784an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
785\[
786  % \label{eq:SBC_ssh_ib}
787  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
788\]
789where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
790A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true.
791In this case $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
792\ie the mean value of $\eta_{ib}$ is kept to zero at all time step.
793
794The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
795For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
796(see \mdl{sbcssr} module).
797$\eta_{ib}$ can be set in the output.
798This can simplify altimetry data and model comparison as
799inverse barometer sea surface height is usually removed from these date prior to their distribution.
800
801When using time-splitting and BDY package for open boundaries conditions,
802the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
803\np{ln\_apr\_obc}  might be set to true.
804
805% ================================================================
806%        Surface Tides Forcing
807% ================================================================
808\section{Surface tides (\protect\mdl{sbctide})}
809\label{sec:SBC_tide}
810
811%------------------------------------------nam_tide---------------------------------------
812
813\nlst{nam_tide}
814%-----------------------------------------------------------------------------------------
815
816The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
817is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \np{.true.} in \ngn{nam\_tide}.
818This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that:
819\[
820  % \label{eq:PE_dyn_tides}
821  \frac{\partial {\rm {\bf U}}_h }{\partial t}= ...
822  +g\nabla (\Pi_{eq} + \Pi_{sal})
823\]
824where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a self-attraction and loading term (SAL).
825 
826The equilibrium tidal forcing is expressed as a sum over the chosen constituents $l$ in \ngn{nam\_tide}.
827The constituents are defined such that \np{clname(1) = 'M2', clname(2)='S2', etc...}.
828For the three types of tidal frequencies it reads: \\
829Long period tides :
830\[
831  \Pi_{eq}(l)=A_{l}(1+k-h)(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l})
832\]
833diurnal tides :
834\[
835  \Pi_{eq}(l)=A_{l}(1+k-h)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l})
836\]
837Semi-diurnal tides:
838\[
839  \Pi_{eq}(l)=A_{l}(1+k-h)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l})
840\]
841Here $A_{l}$ is the amplitude, $\omega_{l}$ is the frequency, $\phi$ the latitude, $\lambda$ the longitude,
842$V_{0l}$ a phase shift with respect to Greenwich meridian and $t$ the time.
843The Love number factor $(1+k-h)$ is here taken as a constant (0.7).
844
845The SAL term should in principle be computed online as it depends on the model tidal prediction itself
846(see \citet{Arbic2004} for a discussion about the practical implementation of this term).
847Nevertheless, the complex calculations involved would make this computationally too expensive.
848Here, practical solutions are whether to read complex estimates $\Pi_{sal}(l)$ from an external model
849(\np{ln\_read\_load=.true.}) or use a ``scalar approximation'' (\np{ln\_scal\_load=.true.}).
850In the latter case, it reads:\\
851\[
852  \Pi_{sal} = \beta \eta
853\]
854where $\beta$ (\np{rn\_scal\_load}, $\approx0.09$) is a spatially constant scalar,
855often chosen to minimize tidal prediction errors.
856Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to false removes the SAL contribution.
857
858% ================================================================
859%        River runoffs
860% ================================================================
861\section{River runoffs (\protect\mdl{sbcrnf})}
862\label{sec:SBC_rnf}
863%------------------------------------------namsbc_rnf----------------------------------------------------
864
865\nlst{namsbc_rnf} 
866%-------------------------------------------------------------------------------------------------------------
867
868%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
869%Many models, however, have traditionally inserted river runoff to the top model cell.
870%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
871%throughout a nonzero depth has been motivated by the numerical and physical problems
872%that arise when the top grid cells are of the order of one meter. This situation is common in
873%coastal modelling and becomes more and more often open ocean and climate modelling
874%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
875%required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}.
876
877
878%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
879%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
880%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
881%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
882%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
883%emp or emps and the changes made are below:
884
885
886%Rachel:
887River runoff generally enters the ocean at a nonzero depth rather than through the surface.
888Many models, however, have traditionally inserted river runoff to the top model cell.
889This was the case in \NEMO prior to the version 3.3,
890and was combined with an option to increase vertical mixing near the river mouth.
891
892However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
893This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
894\footnote{
895  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
896  properly represent the diurnal cycle \citep{Bernie_al_JC05}.
897  see also \autoref{fig:SBC_dcy}.}.
898
899As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
900and for the temperature and salinity of the river to effect the surrounding ocean.
901The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
902along with the depth (in metres) which the river should be added to.
903
904Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and
905\np{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
906If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
907and/or taken as surface temperature respectively.
908
909The runoff value and attributes are read in in sbcrnf. 
910For temperature -999 is taken as missing data and the river temperature is taken to
911be the surface temperatue at the river point.
912For the depth parameter a value of -1 means the river is added to the surface box only,
913and a value of -999 means the river is added through the entire water column.
914After being read in the temperature and salinity variables are multiplied by the amount of runoff
915(converted into m/s) to give the heat and salt content of the river runoff.
916After the user specified depth is read ini,
917the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz\_rnf}.
918The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
919the bottom of the lowest box the river water is being added to
920(\ie the total depth that river water is being added to in the model).
921
922The mass/volume addition due to the river runoff is, at each relevant depth level, added to
923the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
924This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
925The sea surface height is calculated using the sum of the horizontal divergence terms,
926and so the river runoff indirectly forces an increase in sea surface height.
927
928The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
929This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
930The heat and salt content of the river runoff is not included in this step,
931and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
932the box and replaced by the same volume of river water with no corresponding heat and salt addition.
933
934For the linear free surface case, at the surface box the tracer advection causes a flux of water
935(of equal volume to the runoff) through the sea surface out of the domain,
936which causes a salt and heat flux out of the model.
937As such the volume of water does not change, but the water is diluted.
938
939For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
940Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
941no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
942(The runoff addition to the top box along with the water being moved up through
943boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
944
945In trasbc the addition of heat and salt due to the river runoff is added.
946This is done in the same way for both vvl and non-vvl.
947The temperature and salinity are increased through the specified depth according to
948the heat and salt content of the river.
949
950In the non-linear free surface case (vvl),
951near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
952so that the original ratios of grid box heights are restored.
953In doing this water is moved into boxes below, throughout the water column,
954so the large volume addition to the surface box is spread between all the grid boxes.
955
956It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
957\ie modelling the Baltic flow in and out of the North Sea.
958When the flow is out of the domain there is no change in temperature and salinity,
959regardless of the namelist options used,
960as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
961
962
963%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
964
965%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
966
967%\colorbox{yellow}{river mouths{\ldots}}
968
969%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
970%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
971%ENDIF
972
973%\gmcomment{  word doc of runoffs:
974%
975%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.
976%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. 
977
978%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
979
980%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:
981
982%}
983% ================================================================
984%        Ice shelf melting
985% ================================================================
986\section{Ice shelf melting (\protect\mdl{sbcisf})}
987\label{sec:SBC_isf}
988%------------------------------------------namsbc_isf----------------------------------------------------
989
990\nlst{namsbc_isf}
991%--------------------------------------------------------------------------------------------------------
992Namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation used.
993\begin{description}
994\item[\np{nn\_isf}\forcode{ = 1}]
995  The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{ = .true.} needed).
996  The fwf and heat flux are computed.
997  Two different bulk formula are available:
998   \begin{description}
999   \item[\np{nn\_isfblk}\forcode{ = 1}]
1000     The bulk formula used to compute the melt is based the one described in \citet{Hunter2006}.
1001     This formulation is based on a balance between the upward ocean heat flux and
1002     the latent heat flux at the ice shelf base.
1003   \item[\np{nn\_isfblk}\forcode{ = 2}]
1004     The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}.
1005     This formulation is based on a 3 equations formulation
1006     (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation).
1007   \end{description}
1008   For this 2 bulk formulations, there are 3 different ways to compute the exchange coeficient:
1009   \begin{description}
1010   \item[\np{nn\_gammablk}\forcode{ = 0}]
1011     The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}
1012   \item[\np{nn\_gammablk}\forcode{ = 1}]
1013     The salt and heat exchange coefficients are velocity dependent and defined as
1014     \np{rn\_gammas0}$ \times u_{*}$ and \np{rn\_gammat0}$ \times u_{*}$ where
1015     $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
1016     See \citet{Jenkins2010} for all the details on this formulation.
1017   \item[\np{nn\_gammablk}\forcode{ = 2}]
1018     The salt and heat exchange coefficients are velocity and stability dependent and defined as
1019     $\gamma_{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}$ where
1020     $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
1021     $\Gamma_{Turb}$ the contribution of the ocean stability and
1022     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1023     See \citet{Holland1999} for all the details on this formulation.
1024   \end{description}
1025 \item[\np{nn\_isf}\forcode{ = 2}]
1026   A parameterisation of isf is used. The ice shelf cavity is not represented.
1027   The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL)
1028   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1029   (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}).
1030   Furthermore the fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting.
1031   The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
1032 \item[\np{nn\_isf}\forcode{ = 3}]
1033   A simple parameterisation of isf is used. The ice shelf cavity is not represented.
1034   The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1035   the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and
1036   the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
1037   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1038 \item[\np{nn\_isf}\forcode{ = 4}]
1039   The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed).
1040   However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
1041   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\
1042\end{description}
1043
1044$\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on
1045the water mass properties, ocean velocities and depth.
1046This flux is thus highly dependent of the model resolution (horizontal and vertical),
1047realism of the water masses onto the shelf ...\\
1048
1049$\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file.
1050You have total control of the fwf forcing.
1051This can be useful if the water masses on the shelf are not realistic or
1052the resolution (horizontal/vertical) are too coarse to have realistic melting or
1053for studies where you need to control your heat and fw input.\\ 
1054
1055A namelist parameters control over how many meters the heat and fw fluxes are spread.
1056\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}.
1057This parameter is only used if \np{nn\_isf}\forcode{ = 1} or \np{nn\_isf}\forcode{ = 4}.
1058
1059If \np{rn\_hisf\_tbl}\forcode{ = 0}., the fluxes are put in the top level whatever is its tickness.
1060
1061If \np{rn\_hisf\_tbl} $>$ 0., the fluxes are spread over the first \np{rn\_hisf\_tbl} m
1062(ie over one or several cells).\\
1063
1064The ice shelf melt is implemented as a volume flux with in the same way as for the runoff.
1065The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1066the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}.
1067See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.
1068
1069
1070\section{Ice sheet coupling}
1071\label{sec:SBC_iscpl}
1072%------------------------------------------namsbc_iscpl----------------------------------------------------
1073
1074\nlst{namsbc_iscpl}
1075%--------------------------------------------------------------------------------------------------------
1076Ice sheet/ocean coupling is done through file exchange at the restart step.
1077NEMO, at each restart step, read the bathymetry and ice shelf draft variable in a netcdf file.
1078If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with
1079potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1080The wetting and drying scheme applied on the restart is very simple and described below for the 6 different cases:
1081\begin{description}
1082\item[Thin a cell down:]
1083  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1084  ($bt_b=bt_n$).
1085\item[Enlarge  a cell:]
1086  See case "Thin a cell down"
1087\item[Dry a cell:]
1088  mask, T/S, U/V and ssh are set to 0.
1089  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1090\item[Wet a cell:] 
1091  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1092  If no neighbours along i,j and k, T/S/U/V and mask are set to 0.
1093\item[Dry a column:]
1094   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1095\item[Wet a column:]
1096  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1097  If no neighbour, T/S/U/V and mask set to 0.
1098\end{description}
1099The extrapolation is call \np{nn\_drown} times.
1100It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,
1101the code will be unable to fill all the new wet cells properly.
1102The default number is set up for the MISOMIP idealised experiments.\\
1103This coupling procedure is able to take into account grounding line and calving front migration.
1104However, it is a non-conservative processe.
1105This could lead to a trend in heat/salt content and volume.
1106In order to remove the trend and keep the conservation level as close to 0 as possible,
1107a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}.
1108The heat/salt/vol. gain/loss is diagnose, as well as the location.
1109Based on what is done on sbcrnf to prescribed a source of heat/salt/vol.,
1110the heat/salt/vol. gain/loss is removed/added, over a period of \np{rn\_fiscpl} time step, into the system.
1111So after \np{rn\_fiscpl} time step, all the heat/salt/vol. gain/loss due to extrapolation process is canceled.\\
1112
1113As the before and now fields are not compatible (modification of the geometry),
1114the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.
1115%
1116% ================================================================
1117%        Handling of icebergs
1118% ================================================================
1119\section{Handling of icebergs (ICB)}
1120\label{sec:ICB_icebergs}
1121%------------------------------------------namberg----------------------------------------------------
1122
1123\nlst{namberg}
1124%-------------------------------------------------------------------------------------------------------------
1125
1126Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}.
1127Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ).
1128(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO).
1129Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1130described in the \ngn{namberg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1131Each class has an associated scaling (\np{rn\_mass\_scaling}),
1132which is an integer representing how many icebergs of this class are being described as one lagrangian point
1133(this reduces the numerical problem of tracking every single iceberg).
1134They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}.
1135
1136Two initialisation schemes are possible.
1137\begin{description}
1138\item[\np{nn\_test\_icebergs}~$>$~0]
1139  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1140  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1141  which an iceberg is generated at the beginning of the run.
1142  (Note that this happens each time the timestep equals \np{nn\_nit000}.)
1143  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of
1144  the geographical box: lonmin,lonmax,latmin,latmax
1145\item[\np{nn\_test\_icebergs}\forcode{ = -1}]
1146  In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
1147  This should be a file with a field on the configuration grid (typically ORCA)
1148  representing ice accumulation rate at each model point.
1149  These should be ocean points adjacent to land where icebergs are known to calve.
1150  Most points in this input grid are going to have value zero.
1151  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1152  At each time step, a test is performed to see if there is enough ice mass to
1153  calve an iceberg of each class in order (1 to 10).
1154  Note that this is the initial mass multiplied by the number each particle represents (\ie the scaling).
1155  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1156\end{description}
1157
1158Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1159The latter act to disintegrate the iceberg.
1160This is either all melted freshwater,
1161or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1162which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1163Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
1164
1165Extensive diagnostics can be produced.
1166Separate output files are maintained for human-readable iceberg information.
1167A separate file is produced for each processor (independent of \np{ln\_ctl}).
1168The amount of information is controlled by two integer parameters:
1169\begin{description}
1170\item[\np{nn\_verbose\_level}] takes a value between one and four and
1171  represents an increasing number of points in the code at which variables are written,
1172  and an increasing level of obscurity.
1173\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1174\end{description}
1175
1176Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1177A non-zero value represents how many timesteps between writes of information into the output file.
1178These output files are in NETCDF format.
1179When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1180Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1181So care is needed to recreate data for individual icebergs,
1182since its trajectory data may be spread across multiple files.
1183
1184% -------------------------------------------------------------------------------------------------------------
1185%        Interactions with waves (sbcwave.F90, ln_wave)
1186% -------------------------------------------------------------------------------------------------------------
1187\section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
1188\label{sec:SBC_wave}
1189%------------------------------------------namsbc_wave--------------------------------------------------------
1190
1191\nlst{namsbc_wave}
1192%-------------------------------------------------------------------------------------------------------------
1193
1194Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate
1195physical processes related to ocean surface waves, namely the surface stress modified by growth and
1196dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1197tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1198the wind stress.
1199
1200Physical processes related to ocean surface waves can be accounted by setting the logical variable
1201\np{ln\_wave}\forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for
1202different porcesses should be activated as explained in the following sections.
1203
1204Wave fields can be provided either in forced or coupled mode:
1205\begin{description}
1206\item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist
1207for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1208Input Data generic Interface (see \autoref{sec:SBC_input}).
1209\item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 
1210in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist.
1211\end{description}
1212
1213
1214% ================================================================
1215% Neutral drag coefficient from wave model (ln_cdgw)

1216% ================================================================
1217\subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
1218\label{subsec:SBC_wave_cdgw}
1219
1220The neutral surface drag coefficient provided from an external data source (\ie a wave model),
1221can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist.
1222Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,
1223the drag coefficient is computed according to the stable/unstable conditions of the
1224air-sea interface following \citet{Large_Yeager_Rep04}.
1225
1226
1227% ================================================================
1228% 3D Stokes Drift (ln_sdw, nn_sdrift)
1229% ================================================================
1230\subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
1231\label{subsec:SBC_wave_sdw}
1232
1233The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}.
1234It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1235and the current measured at a fixed point (Eulerian velocity).
1236As waves travel, the water particles that make up the waves travel in orbital motions but
1237without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1238at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift.
1239An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1240representation of surface physics in ocean general circulation models.
1241The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1242
1243\[
1244  % \label{eq:sbc_wave_sdw}
1245  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1246  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1247  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1248\]
1249
1250where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1251$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1252$k$ is the mean wavenumber defined as:
1253$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1254
1255In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required
1256and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1257To simplify, it is customary to use approximations to the full Stokes profile.
1258Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1259are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift
1260$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1261and makes possible the estimation of the surface Stokes drift for random directional waves in
1262realistic wave conditions:
1263
1264\begin{description}
1265\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by
1266\citet{Breivik_al_JPO2014}:
1267
1268\[
1269  % \label{eq:sbc_wave_sdw_0a}
1270  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1271\]
1272
1273where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1274
1275\[
1276  % \label{eq:sbc_wave_sdw_0b}
1277  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1278  \quad \text{and }\
1279  T_{st} = \frac{1}{16} \bar{\omega} H_s^2 
1280\]
1281
1282where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1283
1284\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a
1285reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface
1286\citep{Breivik_al_OM2016}:
1287
1288\[
1289  % \label{eq:sbc_wave_sdw_1}
1290  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1291  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1292\]
1293
1294where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1295
1296\item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1
1297but using the wave frequency from a wave model.
1298
1299\end{description}
1300
1301The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1302and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1303
1304\[
1305  % \label{eq:sbc_wave_eta_sdw}
1306  \frac{\partial{\eta}}{\partial{t}} =
1307  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1308\]
1309
1310The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1311for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1312that is induced by the three-dimensional Stokes velocity.
1313The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1314can be formulated as follows:
1315
1316\[
1317  % \label{eq:sbc_wave_tra_sdw}
1318  \frac{\partial{c}}{\partial{t}} =
1319  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1320\]
1321
1322
1323% ================================================================
1324% Stokes-Coriolis term (ln_stcor)
1325% ================================================================
1326\subsection{Stokes-Coriolis term (\protect\np{ln\_stcor})}
1327\label{subsec:SBC_wave_stcor}
1328
1329In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1330in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1331This additional force may have impact on the Ekman turning of the surface current.
1332In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1333approximations described in \autoref{subsec:SBC_wave_sdw}),
1334\np{ln\_stcor}\forcode{ = .true.} has to be set.
1335
1336
1337% ================================================================
1338% Waves modified stress (ln_tauwoc, ln_tauw)
1339% ================================================================
1340\subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 
1341\label{subsec:SBC_wave_tauw}
1342
1343The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1344into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not
1345available for forcing the mean circulation, while in the opposite case of a decaying sea
1346state more momentum is available for forcing the ocean.
1347Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress,
1348but in practice an equilibrium sea state is a fairly rare event.
1349So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1350
1351\[
1352  % \label{eq:sbc_wave_tauoc}
1353  \tau_{oc,a} = \tau_a - \tau_w
1354\]
1355
1356where $\tau_a$ is the atmospheric surface stress;
1357$\tau_w$ is the atmospheric stress going into the waves defined as:
1358
1359\[
1360  % \label{eq:sbc_wave_tauw}
1361  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1362\]
1363
1364where: $c_p$ is the phase speed of the gravity waves,
1365$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1366the physics of ocean waves. The first one, $S_{in}$, describes the generation
1367of ocean waves by wind and therefore represents the momentum and energy transfer
1368from air to ocean waves; the second term $S_{nl}$ denotes
1369the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$ 
1370describes the dissipation of waves by processes such as white-capping, large scale breaking
1371eddy-induced damping.
1372
1373The wave stress derived from an external wave model can be provided either through the normalized
1374wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and
1375meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}.
1376
1377
1378% ================================================================
1379% Miscellanea options
1380% ================================================================
1381\section{Miscellaneous options}
1382\label{sec:SBC_misc}
1383
1384% -------------------------------------------------------------------------------------------------------------
1385%        Diurnal cycle
1386% -------------------------------------------------------------------------------------------------------------
1387\subsection{Diurnal cycle (\protect\mdl{sbcdcy})}
1388\label{subsec:SBC_dcy}
1389%------------------------------------------namsbc_rnf----------------------------------------------------
1390%
1391\nlst{namsbc} 
1392%-------------------------------------------------------------------------------------------------------------
1393
1394%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1395\begin{figure}[!t]
1396  \begin{center}
1397    \includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal}
1398    \caption{
1399      \protect\label{fig:SBC_diurnal}
1400      Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values.
1401      The reconstructed diurnal cycle (black line) is chosen as
1402      the mean value of the analytical cycle (blue line) over a time step,
1403      not as the mid time step value of the analytically cycle (red square).
1404      From \citet{Bernie_al_CD07}.
1405    }
1406  \end{center}
1407\end{figure}
1408%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1409
1410\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.
1411Unfortunately high frequency forcing fields are rare, not to say inexistent.
1412Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at
1413high frequency \citep{Bernie_al_CD07}.
1414Furthermore, only the knowledge of daily mean value of SWF is needed,
1415as higher frequency variations can be reconstructed from them,
1416assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1417The \cite{Bernie_al_CD07} reconstruction algorithm is available in \NEMO by
1418setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when
1419using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or
1420the flux formulation (\np{ln\_flx}\forcode{ = .true.}).
1421The reconstruction is performed in the \mdl{sbcdcy} module.
1422The detail of the algoritm used can be found in the appendix~A of \cite{Bernie_al_CD07}.
1423The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at
1424a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1425The use of diurnal cycle reconstruction requires the input SWF to be daily
1426(\ie a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1427Furthermore, it is recommended to have a least 8 surface module time step per day,
1428that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1429An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1430one every 2~hours (from 1am to 11pm).
1431
1432%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1433\begin{figure}[!t]
1434  \begin{center}
1435    \includegraphics[width=0.7\textwidth]{Fig_SBC_dcy}
1436    \caption{
1437      \protect\label{fig:SBC_dcy}
1438      Example of recontruction of the diurnal cycle variation of short wave flux from
1439      daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1440      The display is on (i,j) plane.
1441    }
1442  \end{center}
1443\end{figure}
1444%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1445
1446Note also that the setting a diurnal cycle in SWF is highly recommended when
1447the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1448an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1449
1450% -------------------------------------------------------------------------------------------------------------
1451%        Rotation of vector pairs onto the model grid directions
1452% -------------------------------------------------------------------------------------------------------------
1453\subsection{Rotation of vector pairs onto the model grid directions}
1454\label{subsec:SBC_rotation}
1455
1456When using a flux (\np{ln\_flx}\forcode{ = .true.}) or
1457bulk (\np{ln\_clio}\forcode{ = .true.} or \np{ln\_core}\forcode{ = .true.}) formulation,
1458pairs of vector components can be rotated from east-north directions onto the local grid directions.
1459This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1460be defined relative to a rectilinear grid.
1461To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1462The eastward component must start with "U" and the northward component with "V". 
1463The remaining characters in the strings are used to identify which pair of components go together.
1464So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1465rotate them on to the model grid directions;
1466"U2" and "V2" could be used against a second pair of components, and so on.
1467The extra characters used in the strings are arbitrary.
1468The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1469
1470% -------------------------------------------------------------------------------------------------------------
1471%        Surface restoring to observed SST and/or SSS
1472% -------------------------------------------------------------------------------------------------------------
1473\subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1474\label{subsec:SBC_ssr}
1475%------------------------------------------namsbc_ssr----------------------------------------------------
1476
1477\nlst{namsbc_ssr} 
1478%-------------------------------------------------------------------------------------------------------------
1479
1480IOptions are defined through the \ngn{namsbc\_ssr} namelist variables.
1481On forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}),
1482a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1483\[
1484  % \label{eq:sbc_dmp_q}
1485  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1486\]
1487where SST is a sea surface temperature field (observed or climatological),
1488$T$ is the model surface layer temperature and
1489$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1490For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1491This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1492
1493In the fresh water budget, a feedback term can also be added.
1494Converted into an equivalent freshwater flux, it takes the following expression :
1495
1496\begin{equation}
1497  \label{eq:sbc_dmp_emp}
1498  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1499  {\left.S\right|_{k=1}}
1500\end{equation}
1501
1502where $\textit{emp}_{o }$ is a net surface fresh water flux
1503(observed, climatological or an atmospheric model product),
1504\textit{SSS}$_{Obs}$ is a sea surface salinity
1505(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
1506$\left.S\right|_{k=1}$ is the model surface layer salinity and
1507$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1508Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as
1509the atmosphere does not care about ocean surface salinity \citep{Madec1997}.
1510The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1511reduce the uncertainties we have on the observed freshwater budget.
1512
1513% -------------------------------------------------------------------------------------------------------------
1514%        Handling of ice-covered area
1515% -------------------------------------------------------------------------------------------------------------
1516\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1517\label{subsec:SBC_ice-cover}
1518
1519The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1520There are several way to handle sea-ice in the system depending on
1521the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist.
1522\begin{description}
1523\item[nn{\_}ice = 0]
1524  there will never be sea-ice in the computational domain.
1525  This is a typical namelist value used for tropical ocean domain.
1526  The surface fluxes are simply specified for an ice-free ocean.
1527  No specific things is done for sea-ice.
1528\item[nn{\_}ice = 1]
1529  sea-ice can exist in the computational domain, but no sea-ice model is used.
1530  An observed ice covered area is read in a file.
1531  Below this area, the SST is restored to the freezing point and
1532  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1533  The associated modification of the freshwater fluxes are done in such a way that
1534  the change in buoyancy fluxes remains zero.
1535  This prevents deep convection to occur when trying to reach the freezing point
1536  (and so ice covered area condition) while the SSS is too large.
1537  This manner of managing sea-ice area, just by using si IF case,
1538  is usually referred as the \textit{ice-if} model.
1539  It can be found in the \mdl{sbcice{\_}if} module.
1540\item[nn{\_}ice = 2 or more]
1541  A full sea ice model is used.
1542  This model computes the ice-ocean fluxes,
1543  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1544  provide the surface ocean fluxes.
1545  Note that the activation of a sea-ice model is is done by defining a CPP key (\key{lim3} or \key{cice}).
1546  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value
1547  (\ie $2$ for LIM-3 or $3$ for CICE).
1548\end{description}
1549
1550% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1551
1552\subsection{Interface to CICE (\protect\mdl{sbcice\_cice})}
1553\label{subsec:SBC_cice}
1554
1555It is now possible to couple a regional or global NEMO configuration (without AGRIF)
1556to the CICE sea-ice model by using \key{cice}.
1557The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1558the additional 'hadgem3' drivers will be required, even with the latest code release.
1559Input grid files consistent with those used in NEMO will also be needed,
1560and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1561(seek advice from UKMO if necessary).
1562Currently the code is only designed to work when using the CORE forcing option for NEMO
1563(with \textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE name-list),
1564or alternatively when NEMO is coupled to the HadGAM3 atmosphere model
1565(with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}).
1566The code is intended to be used with \np{nn\_fsbc} set to 1
1567(although coupling ocean and ice less frequently should work,
1568it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1569the user should check that results are not significantly different to the standard case).
1570
1571There are two options for the technical coupling between NEMO and CICE.
1572The standard version allows complete flexibility for the domain decompositions in the individual models,
1573but this is at the expense of global gather and scatter operations in the coupling which
1574become very expensive on larger numbers of processors.
1575The alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that
1576the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1577and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1578allows much more efficient direct coupling on individual processors.
1579This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1580there is no sea ice.
1581
1582% -------------------------------------------------------------------------------------------------------------
1583%        Freshwater budget control
1584% -------------------------------------------------------------------------------------------------------------
1585\subsection{Freshwater budget control (\protect\mdl{sbcfwb})}
1586\label{subsec:SBC_fwb}
1587
1588For global ocean simulation it can be useful to introduce a control of the mean sea level in order to
1589prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1590In \NEMO, two way of controlling the the freshwater budget.
1591\begin{description}
1592\item[\np{nn\_fwb}\forcode{ = 0}]
1593  no control at all.
1594  The mean sea level is free to drift, and will certainly do so.
1595\item[\np{nn\_fwb}\forcode{ = 1}]
1596  global mean \textit{emp} set to zero at each model time step.
1597%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).
1598\item[\np{nn\_fwb}\forcode{ = 2}]
1599  freshwater budget is adjusted from the previous year annual mean budget which
1600  is read in the \textit{EMPave\_old.dat} file.
1601  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1602  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1603\end{description}
1604
1605
1606
1607% Griffies doc:
1608% When running ocean-ice simulations, we are not explicitly representing land processes,
1609% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1610% it is important to balance the hydrological cycle in ocean-ice models.
1611% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1612% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1613% a chosen time scale.
1614%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1615% so that there is always a zero net input of water to the ocean-ice system.
1616% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1617% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1618% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1619% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1620% and ice models when aiming to balance the hydrological cycle.
1621% 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,
1622% not the water in any one sub-component. As an extreme example to illustrate the issue,
1623% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1624% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1625% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1626% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1627% in ocean-ice models.
1628
1629\biblio
1630
1631\pindex
1632
1633\end{document}
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