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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 (\textit{fldread.F90})]
229{Input data specification (\protect\mdl{fldread})}
230\label{subsec:SBC_fldread}
231
232The structure associated with an input variable contains the following information:
233\begin{forlines}
234!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
235!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
236\end{forlines}
237where
238\begin{description} 
239\item[File name]:
240  the stem name of the NetCDF file to be open.
241  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
242  by date information and possibly a prefix (when using AGRIF).
243  Tab.\autoref{tab:fldread} provides the resulting file name in all possible cases according to
244  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
245
246%--------------------------------------------------TABLE--------------------------------------------------
247  \begin{table}[htbp]
248    \begin{center}
249      \begin{tabular}{|l|c|c|c|}
250        \hline
251        & daily or weekLLL         & monthly                   &   yearly          \\   \hline
252        \np{clim}\forcode{ = .false.}  & fn\_yYYYYmMMdDD.nc  &   fn\_yYYYYmMM.nc   &   fn\_yYYYY.nc  \\   \hline
253        \np{clim}\forcode{ = .true.}         & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
254      \end{tabular}
255    \end{center}
256    \caption{
257      \protect\label{tab:fldread}
258      naming nomenclature for climatological or interannual input file, as a function of the Open/close frequency.
259      The stem name is assumed to be 'fn'.
260      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
261      (\ie 'sun','sat','fri','thu','wed','tue','mon').
262      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits.
263      Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc',
264      where 'PPPP' is the process number coded with 4 digits;
265      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N'  is the child grid number.
266    }
267  \end{table}
268%--------------------------------------------------------------------------------------------------------------
269 
270
271\item[Record frequency]:
272  the frequency of the records contained in the input file.
273  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
274  (for example -1 for monthly forcing or -12 for annual forcing).
275  Note that this frequency must really be an integer and not a real.
276  On some computers, seting it to '24.' can be interpreted as 240!
277
278\item[Variable name]:
279  the name of the variable to be read in the input NetCDF file.
280
281\item[Time interpolation]:
282  a logical to activate, or not, the time interpolation.
283  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
284  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
285  00h00'00'' to 23h59'59".
286  If set to 'true', the forcing will have a broken line shape.
287  Records are assumed to be dated the middle of the forcing period.
288  For example, when using a daily forcing with time interpolation,
289  linear interpolation will be performed between mid-day of two consecutive days.
290
291\item[Climatological forcing]:
292  a logical to specify if a input file contains climatological forcing which can be cycle in time,
293  or an interannual forcing which will requires additional files if
294  the period covered by the simulation exceed the one of the file.
295  See the above the file naming strategy which impacts the expected name of the file to be opened.
296
297\item[Open/close frequency]:
298  the frequency at which forcing files must be opened/closed.
299  Four cases are coded:
300  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
301  means the forcing files will contain data for one day, one week, one month or one year.
302  Files are assumed to contain data from the beginning of the open/close period.
303  For example, the first record of a yearly file containing daily data is Jan 1st even if
304  the experiment is not starting at the beginning of the year.
305
306\item[Others]:
307  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
308  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
309
310\end{description}
311
312Additional remarks:\\
313(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
314The only tricky point is therefore to specify the date at which we need to do the interpolation and
315the date of the records read in the input files.
316Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
317For example, for an experiment starting at 0h00'00" with a one hour time-step,
318a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
319However, for forcing data related to the surface module,
320values are not needed at every time-step but at every \np{nn\_fsbc} time-step.
321For example with \np{nn\_fsbc}\forcode{ = 3}, the surface module will be called at time-steps 1, 4, 7, etc.
322The date used for the time interpolation is thus redefined to be at the middle of \np{nn\_fsbc} time-step period.
323In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
324(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
325The calendar associated with the forcing field is build according to the information provided by
326user in the record frequency, the open/close frequency and the type of temporal interpolation.
327For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
328be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
329(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
330interpolating data with the first (last) record of the open/close period.
331For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
332the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
333Dec 31st 12h00'00" and Jan 1st 12h00'00".
334If the forcing is climatological, Dec and Jan will be keep-up from the same year.
335However, if the forcing is not climatological, at the end of
336the open/close period the code will automatically close the current file and open the next one.
337Note that, if the experiment is starting (ending) at the beginning (end) of
338an open/close period we do accept that the previous (next) file is not existing.
339In this case, the time interpolation will be performed between two identical values.
340For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
341we do accept that the file related to year Y-1 is not existing.
342The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
343If the file of year Y-1 exists, the code will read its last record.
344Therefore, this file can contain only one record corresponding to Dec 31st,
345a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
346
347
348% -------------------------------------------------------------------------------------------------------------
349% Interpolation on the Fly
350% -------------------------------------------------------------------------------------------------------------
351\subsection{Interpolation on-the-fly}
352\label{subsec:SBC_iof}
353
354Interpolation on the Fly allows the user to supply input files required for the surface forcing on
355grids other than the model grid.
356To do this he or she must supply, in addition to the source data file, a file of weights to be used to
357interpolate from the data grid to the model grid.
358The original development of this code used the SCRIP package
359(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
360In principle, any package can be used to generate the weights, but the variables in
361the input weights file must have the same names and meanings as assumed by the model.
362Two methods are currently available: bilinear and bicubic interpolation.
363Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
364the input file and substitute the corresponding values with the average of the 8 neighbouring points in
365the native external grid.
366Only "sea points" are considered for the averaging.
367The land/sea mask file must be provided in the structure associated with the input variable.
368The netcdf land/sea mask variable name must be 'LSM' it must have the same horizontal and vertical dimensions of
369the associated variable and should be equal to 1 over land and 0 elsewhere.
370The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.
371Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied.
372
373\subsubsection{Bilinear interpolation}
374\label{subsec:SBC_iof_bilinear}
375
376The input weights file in this case has two sets of variables:
377src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
378The "src" variables correspond to the point in the input grid to which the weight "wgt" is to be applied.
379Each src value is an integer corresponding to the index of a point in the input grid when
380written as a one dimensional array.
381For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
382There are four of each variable because bilinear interpolation uses the four points defining
383the grid box containing the point to be interpolated.
384All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
385generate a value for point (i,j) in the model.
386
387Symbolically, the algorithm used is:
388\[
389  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
390\]
391where function idx() transforms a one dimensional index src(k) into a two dimensional index,
392and wgt(1) corresponds to variable "wgt01" for example.
393
394\subsubsection{Bicubic interpolation}
395\label{subsec:SBC_iof_bicubic}
396
397Again there are two sets of variables: "src" and "wgt".
398But in this case there are 16 of each.
399The symbolic algorithm used to calculate values on the model grid is now:
400
401\[
402  \begin{split}
403    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
404    +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
405    +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
406    +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
407  \end{split}
408\]
409The gradients here are taken with respect to the horizontal indices and not distances since
410the spatial dependency has been absorbed into the weights.
411
412\subsubsection{Implementation}
413\label{subsec:SBC_iof_imp}
414
415To activate this option, a non-empty string should be supplied in
416the weights filename column of the relevant namelist;
417if this is left as an empty string no action is taken.
418In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
419as and when they are first required.
420This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
421inspecting a global attribute stored in the weights input file.
422This attribute must be called "ew\_wrap" and be of integer type.
423If it is negative, the input non-model grid is assumed not to be cyclic.
424If zero or greater, then the value represents the number of columns that overlap.
425$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
426if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
427If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
428In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
429therefore the grid is assumed to be cyclic with no overlapping columns.
430(In fact this only matters when bicubic interpolation is required.)
431Note that no testing is done to check the validity in the model,
432since there is no way of knowing the name used for the longitude variable,
433so it is up to the user to make sure his or her data is correctly represented.
434
435Next the routine reads in the weights.
436Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
437The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
438and when required, for reading in the variable to be interpolated (on the input data grid).
439The size of the input data array is determined by examining the values in the "src" arrays to
440find the minimum and maximum i and j values required.
441Since bicubic interpolation requires the calculation of gradients at each point on the grid,
442the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
443When the array of points from the data file is adjacent to an edge of the data grid,
444the halo is either a copy of the row/column next to it (non-cyclical case),
445or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
446
447\subsubsection{Limitations}
448\label{subsec:SBC_iof_lim}
449
450\begin{enumerate} 
451\item
452  The case where input data grids are not logically rectangular has not been tested.
453\item
454  This code is not guaranteed to produce positive definite answers from positive definite inputs when
455  a bicubic interpolation method is used.
456\item
457  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
458\item
459  The gradients across the ends of a cyclical grid assume that the grid spacing between
460  the two columns involved are consistent with the weights used.
461\item
462  Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
463  but this has not been implemented.)
464\end{enumerate}
465
466\subsubsection{Utilities}
467\label{subsec:SBC_iof_util}
468
469% to be completed
470A set of utilities to create a weights file for a rectilinear input grid is available
471(see the directory NEMOGCM/TOOLS/WEIGHTS).
472
473% -------------------------------------------------------------------------------------------------------------
474% Standalone Surface Boundary Condition Scheme
475% -------------------------------------------------------------------------------------------------------------
476\subsection{Standalone surface boundary condition scheme}
477\label{subsec:SAS_iof}
478
479%---------------------------------------namsbc_ana--------------------------------------------------
480
481\nlst{namsbc_sas}
482%--------------------------------------------------------------------------------------------------------------
483
484In some circumstances it may be useful to avoid calculating the 3D temperature,
485salinity and velocity fields and simply read them in from a previous run or receive them from OASIS. 
486For example:
487
488\begin{itemize}
489\item
490  Multiple runs of the model are required in code development to
491  see the effect of different algorithms in the bulk formulae.
492\item
493  The effect of different parameter sets in the ice model is to be examined.
494\item
495  Development of sea-ice algorithms or parameterizations.
496\item
497  Spinup of the iceberg floats
498\item
499  Ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}\forcode{ = .true.})
500\end{itemize}
501
502The StandAlone Surface scheme provides this utility.
503Its options are defined through the \ngn{namsbc\_sas} namelist variables.
504A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
505However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0).
506In this configuration, a few routines in the standard model are overriden by new versions.
507Routines replaced are:
508
509\begin{itemize}
510\item
511  \mdl{nemogcm}:
512  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
513  Since the ocean state is not calculated all associated initialisations have been removed.
514\item
515  \mdl{step}:
516  The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
517\item
518  \mdl{sbcmod}:
519  This has been cut down and now only calculates surface forcing and the ice model required.
520  New surface modules that can function when only the surface level of the ocean state is defined can also be added
521  (\eg icebergs).
522\item
523  \mdl{daymod}:
524  No ocean restarts are read or written (though the ice model restarts are retained),
525  so calls to restart functions have been removed.
526  This also means that the calendar cannot be controlled by time in a restart file,
527  so the user must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
528\item
529  \mdl{stpctl}:
530  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
531\item
532  \mdl{diawri}:
533  All 3D data have been removed from the output.
534  The surface temperature, salinity and velocity components (which have been read in) are written along with
535  relevant forcing and ice data.
536\end{itemize}
537
538One new routine has been added:
539
540\begin{itemize}
541\item
542  \mdl{sbcsas}:
543  This module initialises the input files needed for reading temperature, salinity and
544  velocity arrays at the surface.
545  These filenames are supplied in namelist namsbc{\_}sas.
546  Unfortunately because of limitations with the \mdl{iom} module,
547  the full 3D fields from the mean files have to be read in and interpolated in time,
548  before using just the top level.
549  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
550\end{itemize}
551
552
553% Missing the description of the 2 following variables:
554%   ln_3d_uve   = .true.    !  specify whether we are supplying a 3D u,v and e3 field
555%   ln_read_frq = .false.    !  specify whether we must read frq or not
556
557
558
559% ================================================================
560% Analytical formulation (sbcana module)
561% ================================================================
562\section[Analytical formulation (\textit{sbcana.F90})]
563{Analytical formulation (\protect\mdl{sbcana})}
564\label{sec:SBC_ana}
565
566%---------------------------------------namsbc_ana--------------------------------------------------
567%
568%\nlst{namsbc_ana}
569%--------------------------------------------------------------------------------------------------------------
570
571The analytical formulation of the surface boundary condition is the default scheme.
572In this case, all the six fluxes needed by the ocean are assumed to be uniform in space.
573They take constant values given in the namelist \ngn{namsbc{\_}ana} by
574the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0}, \np{rn\_qsr0}, and \np{rn\_emp0}
575($\textit{emp}=\textit{emp}_S$).
576The runoff is set to zero.
577In addition, the wind is allowed to reach its nominal value within a given number of time steps (\np{nn\_tau000}).
578
579If a user wants to apply a different analytical forcing,
580the \mdl{sbcana} module can be modified to use another scheme.
581As an example, the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the GYRE configuration
582(see GYRE configuration manual, in preparation).
583
584
585% ================================================================
586% Flux formulation
587% ================================================================
588\section[Flux formulation (\textit{sbcflx.F90})]
589{Flux formulation (\protect\mdl{sbcflx})}
590\label{sec:SBC_flx}
591%------------------------------------------namsbc_flx----------------------------------------------------
592
593\nlst{namsbc_flx} 
594%-------------------------------------------------------------------------------------------------------------
595
596In the flux formulation (\np{ln\_flx}\forcode{ = .true.}),
597the surface boundary condition fields are directly read from input files.
598The user has to define in the namelist \ngn{namsbc{\_}flx} the name of the file,
599the name of the variable read in the file, the time frequency at which it is given (in hours),
600and a logical setting whether a time interpolation to the model time step is required for this field.
601See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
602
603Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
604See \autoref{subsec:SBC_ssr} for its specification.
605
606
607% ================================================================
608% Bulk formulation
609% ================================================================
610\section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}]
611{Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}}
612\label{sec:SBC_blk}
613
614In the bulk formulation, the surface boundary condition fields are computed using bulk formulae and atmospheric fields and ocean (and ice) variables.
615
616The atmospheric fields used depend on the bulk formulae used.
617Two bulk formulations are available:
618the CORE and the CLIO bulk formulea.
619The choice is made by setting to true one of the following namelist variable:
620\np{ln\_core} or \np{ln\_clio}.
621
622Note:
623in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
624Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over
625both an ocean and an ice surface.
626
627% -------------------------------------------------------------------------------------------------------------
628%        CORE Bulk formulea
629% -------------------------------------------------------------------------------------------------------------
630\subsection[CORE formulea (\textit{sbcblk\_core.F90}, \forcode{ln_core = .true.})]
631{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})}
632\label{subsec:SBC_blk_core}
633%------------------------------------------namsbc_core----------------------------------------------------
634%
635%\nlst{namsbc_core}
636%-------------------------------------------------------------------------------------------------------------
637
638The CORE bulk formulae have been developed by \citet{large.yeager_rpt04}.
639They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data.
640They use an inertial dissipative method to compute the turbulent transfer coefficients
641(momentum, sensible heat and evaporation) from the 10 metre wind speed, air temperature and specific humidity.
642This \citet{large.yeager_rpt04} dataset is available through
643the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}.
644
645Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
646This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
647
648Options are defined through the  \ngn{namsbc\_core} namelist variables.
649The required 8 input fields are:
650
651%--------------------------------------------------TABLE--------------------------------------------------
652\begin{table}[htbp]
653  \label{tab:CORE}
654  \begin{center}
655    \begin{tabular}{|l|c|c|c|}
656      \hline
657      Variable desciption              & Model variable  & Units   & point \\    \hline
658      i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
659      j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
660      10m air temperature              & tair      & \r{}$K$            & T   \\ \hline
661      Specific humidity             & humi      & \%              & T \\      \hline
662      Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
663      Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
664      Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
665      Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
666    \end{tabular}
667  \end{center}
668\end{table}
669%--------------------------------------------------------------------------------------------------------------
670
671Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
672It is simpler and faster (less fields to be read), but it is not the recommended method when
673the ocean grid size is the same or larger than the one of the input atmospheric fields.
674
675The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, \np{sn\_prec},
676\np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used
677(spatial and temporal interpolations).
678
679\np{cn\_dir} is the directory of location of bulk files
680\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
681\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
682\np{rn\_zu}: is the height of wind measurements (m)
683
684Three multiplicative factors are availables:
685\np{rn\_pfac} and \np{rn\_efac} allows to adjust (if necessary) the global freshwater budget by
686increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
687The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
688the calculation of surface wind stress.
689Its range should be between zero and one, and it is recommended to set it to 0.
690
691% -------------------------------------------------------------------------------------------------------------
692%        CLIO Bulk formulea
693% -------------------------------------------------------------------------------------------------------------
694\subsection[CLIO formulea (\textit{sbcblk\_clio.F90}, \forcode{ln_clio = .true.})]
695{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})}
696\label{subsec:SBC_blk_clio}
697%------------------------------------------namsbc_clio----------------------------------------------------
698%
699%\nlst{namsbc_clio}
700%-------------------------------------------------------------------------------------------------------------
701
702The CLIO bulk formulae were developed several years ago for the Louvain-la-neuve coupled ice-ocean model
703(CLIO, \cite{goosse.deleersnijder.ea_JGR99}).
704They are simpler bulk formulae.
705They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover.
706
707Options are defined through the  \ngn{namsbc\_clio} namelist variables.
708The required 7 input fields are:
709
710%--------------------------------------------------TABLE--------------------------------------------------
711\begin{table}[htbp]
712  \label{tab:CLIO}
713  \begin{center}
714    \begin{tabular}{|l|l|l|l|}
715      \hline
716      Variable desciption           & Model variable  & Units           & point \\  \hline
717      i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
718      j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
719      Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
720      10m air temperature              & tair         & \r{}$K$            & T \\   \hline
721      Specific humidity                & humi         & \%              & T \\   \hline
722      Cloud cover                   &           & \%              & T \\   \hline
723      Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
724      Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
725    \end{tabular}
726  \end{center}
727\end{table}
728%--------------------------------------------------------------------------------------------------------------
729
730As for the flux formulation, information about the input data required by the model is provided in
731the namsbc\_blk\_core or namsbc\_blk\_clio namelist (see \autoref{subsec:SBC_fldread}).
732
733% ================================================================
734% Coupled formulation
735% ================================================================
736\section[Coupled formulation (\textit{sbccpl.F90})]
737{Coupled formulation (\protect\mdl{sbccpl})}
738\label{sec:SBC_cpl}
739%------------------------------------------namsbc_cpl----------------------------------------------------
740
741\nlst{namsbc_cpl} 
742%-------------------------------------------------------------------------------------------------------------
743
744In the coupled formulation of the surface boundary condition,
745the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
746while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
747the atmospheric component.
748
749A generalised coupled interface has been developed.
750It is currently interfaced with OASIS-3-MCT (\key{oasis3}).
751It has been successfully used to interface \NEMO to most of the European atmospheric GCM
752(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
753(Weather Research and Forecasting Model).
754
755Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
756The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are actually received by
757the ice-ocean system (no calculation of ice sublimation in coupled mode).
758When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
759the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}.
760In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
761(and need to be activated in \ngn{namsbc{\_}cpl} ).
762
763The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
764now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
765When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be determined by
766the number used in the sea ice model.
767In some limited cases it may be possible to specify single category coupling fields even when
768the sea ice model is running with multiple categories -
769in this case the user should examine the code to be sure the assumptions made are satisfactory.
770In cases where this is definitely not possible the model should abort with an error message.
771The new code has been tested using ECHAM with LIM2, and HadGAM3 with CICE but
772although it will compile with \key{lim3} additional minor code changes may be required to run using LIM3.
773
774
775% ================================================================
776%        Atmospheric pressure
777% ================================================================
778\section[Atmospheric pressure (\textit{sbcapr.F90})]
779{Atmospheric pressure (\protect\mdl{sbcapr})}
780\label{sec:SBC_apr}
781%------------------------------------------namsbc_apr----------------------------------------------------
782
783\nlst{namsbc_apr} 
784%-------------------------------------------------------------------------------------------------------------
785
786The optional atmospheric pressure can be used to force ocean and ice dynamics
787(\np{ln\_apr\_dyn}\forcode{ = .true.}, \textit{\ngn{namsbc}} namelist).
788The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
789can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
790When used to force the dynamics, the atmospheric pressure is further transformed into
791an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
792\[
793  % \label{eq:SBC_ssh_ib}
794  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
795\]
796where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
797A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true.
798In this case $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
799\ie the mean value of $\eta_{ib}$ is kept to zero at all time step.
800
801The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
802For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
803(see \mdl{sbcssr} module).
804$\eta_{ib}$ can be set in the output.
805This can simplify altimetry data and model comparison as
806inverse barometer sea surface height is usually removed from these date prior to their distribution.
807
808When using time-splitting and BDY package for open boundaries conditions,
809the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
810\np{ln\_apr\_obc}  might be set to true.
811
812% ================================================================
813%        Surface Tides Forcing
814% ================================================================
815\section[Surface tides (\textit{sbctide.F90})]
816{Surface tides (\protect\mdl{sbctide})}
817\label{sec:SBC_tide}
818
819%------------------------------------------nam_tide---------------------------------------
820
821\nlst{nam_tide}
822%-----------------------------------------------------------------------------------------
823
824The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
825is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \forcode{.true.} in \ngn{nam\_tide}.
826This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that:
827\[
828  % \label{eq:PE_dyn_tides}
829  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
830  +g\nabla (\Pi_{eq} + \Pi_{sal})
831\]
832where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
833$\Pi_{sal}$ is a self-attraction and loading term (SAL).
834 
835The equilibrium tidal forcing is expressed as a sum over a subset of
836constituents chosen from the set of available tidal constituents
837defined in file \rou{SBC/tide.h90} (this comprises the tidal
838constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
839  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
840constituents are selected by including their names in the array
841\np{clname} in \ngn{nam\_tide} (e.g., \np{clname(1) = 'M2',
842  clname(2)='S2'} to select solely the tidal consituents \textit{M2}
843and \textit{S2}). Optionally, when \np{ln\_tide\_ramp} is set to
844\forcode{.true.}, the equilibrium tidal forcing can be ramped up
845linearly from zero during the initial \np{rdttideramp} days of the
846model run.
847
848The SAL term should in principle be computed online as it depends on
849the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
850discussion about the practical implementation of this term).
851Nevertheless, the complex calculations involved would make this
852computationally too expensive.  Here, two options are available:
853$\Pi_{sal}$ generated by an external model can be read in
854(\np{ln\_read\_load=.true.}), or a ``scalar approximation'' can be
855used (\np{ln\_scal\_load=.true.}). In the latter case
856\[
857  \Pi_{sal} = \beta \eta,
858\]
859where $\beta$ (\np{rn\_scal\_load} with a default value of 0.094) is a
860spatially constant scalar, often chosen to minimize tidal prediction
861errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to
862\forcode{.false.} removes the SAL contribution.
863
864% ================================================================
865%        River runoffs
866% ================================================================
867\section[River runoffs (\textit{sbcrnf.F90})]
868{River runoffs (\protect\mdl{sbcrnf})}
869\label{sec:SBC_rnf}
870%------------------------------------------namsbc_rnf----------------------------------------------------
871
872\nlst{namsbc_rnf} 
873%-------------------------------------------------------------------------------------------------------------
874
875%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
876%Many models, however, have traditionally inserted river runoff to the top model cell.
877%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
878%throughout a nonzero depth has been motivated by the numerical and physical problems
879%that arise when the top grid cells are of the order of one meter. This situation is common in
880%coastal modelling and becomes more and more often open ocean and climate modelling
881%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
882%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
883
884
885%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
886%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
887%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
888%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
889%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
890%emp or emps and the changes made are below:
891
892
893%Rachel:
894River runoff generally enters the ocean at a nonzero depth rather than through the surface.
895Many models, however, have traditionally inserted river runoff to the top model cell.
896This was the case in \NEMO prior to the version 3.3,
897and was combined with an option to increase vertical mixing near the river mouth.
898
899However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
900This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
901\footnote{
902  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
903  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
904  see also \autoref{fig:SBC_dcy}.}.
905
906As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
907and for the temperature and salinity of the river to effect the surrounding ocean.
908The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
909along with the depth (in metres) which the river should be added to.
910
911Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and
912\np{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
913If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
914and/or taken as surface temperature respectively.
915
916The runoff value and attributes are read in in sbcrnf. 
917For temperature -999 is taken as missing data and the river temperature is taken to
918be the surface temperatue at the river point.
919For the depth parameter a value of -1 means the river is added to the surface box only,
920and a value of -999 means the river is added through the entire water column.
921After being read in the temperature and salinity variables are multiplied by the amount of runoff
922(converted into m/s) to give the heat and salt content of the river runoff.
923After the user specified depth is read ini,
924the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz\_rnf}.
925The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
926the bottom of the lowest box the river water is being added to
927(\ie the total depth that river water is being added to in the model).
928
929The mass/volume addition due to the river runoff is, at each relevant depth level, added to
930the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
931This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
932The sea surface height is calculated using the sum of the horizontal divergence terms,
933and so the river runoff indirectly forces an increase in sea surface height.
934
935The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
936This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
937The heat and salt content of the river runoff is not included in this step,
938and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
939the box and replaced by the same volume of river water with no corresponding heat and salt addition.
940
941For the linear free surface case, at the surface box the tracer advection causes a flux of water
942(of equal volume to the runoff) through the sea surface out of the domain,
943which causes a salt and heat flux out of the model.
944As such the volume of water does not change, but the water is diluted.
945
946For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
947Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
948no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
949(The runoff addition to the top box along with the water being moved up through
950boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
951
952In trasbc the addition of heat and salt due to the river runoff is added.
953This is done in the same way for both vvl and non-vvl.
954The temperature and salinity are increased through the specified depth according to
955the heat and salt content of the river.
956
957In the non-linear free surface case (vvl),
958near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
959so that the original ratios of grid box heights are restored.
960In doing this water is moved into boxes below, throughout the water column,
961so the large volume addition to the surface box is spread between all the grid boxes.
962
963It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
964\ie modelling the Baltic flow in and out of the North Sea.
965When the flow is out of the domain there is no change in temperature and salinity,
966regardless of the namelist options used,
967as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
968
969
970%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
971
972%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
973
974%\colorbox{yellow}{river mouths{\ldots}}
975
976%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
977%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
978%ENDIF
979
980%\gmcomment{  word doc of runoffs:
981%
982%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.
983%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. 
984
985%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
986
987%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:
988
989%}
990% ================================================================
991%        Ice shelf melting
992% ================================================================
993\section[Ice shelf melting (\textit{sbcisf.F90})]
994{Ice shelf melting (\protect\mdl{sbcisf})}
995\label{sec:SBC_isf}
996%------------------------------------------namsbc_isf----------------------------------------------------
997
998\nlst{namsbc_isf}
999%--------------------------------------------------------------------------------------------------------
1000The namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation.
1001Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1002The different options are illustrated in \autoref{fig:SBC_isf}.
1003
1004\begin{description}
1005\item[\np{nn\_isf}\forcode{ = 1}]:
1006  The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{ = .true.} needed).
1007  The fwf and heat flux are depending of the local water properties.
1008  Two different bulk formulae are available:
1009
1010   \begin{description}
1011   \item[\np{nn\_isfblk}\forcode{ = 1}]:
1012     The melt rate is based on a balance between the upward ocean heat flux and
1013     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
1014   \item[\np{nn\_isfblk}\forcode{ = 2}]:
1015     The melt rate and the heat flux are based on a 3 equations formulation
1016     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1017     A complete description is available in \citet{jenkins_JGR91}.
1018   \end{description}
1019
1020     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1021     Its thickness is defined by \np{rn\_hisf\_tbl}.
1022     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m.
1023     Then, the fluxes are spread over the same thickness (ie over one or several cells).
1024     If \np{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature.
1025     This can lead to super-cool temperature in the top cell under melting condition.
1026     If \np{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
1027
1028     Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1029     There are 3 different ways to compute the exchange coeficient:
1030   \begin{description}
1031        \item[\np{nn\_gammablk}\forcode{ = 0}]:
1032     The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}.
1033\[
1034  % \label{eq:sbc_isf_gamma_iso}
1035\gamma^{T} = \np{rn\_gammat0}
1036\]
1037\[
1038\gamma^{S} = \np{rn\_gammas0}
1039\]
1040     This is the recommended formulation for ISOMIP.
1041   \item[\np{nn\_gammablk}\forcode{ = 1}]:
1042     The salt and heat exchange coefficients are velocity dependent and defined as
1043\[
1044\gamma^{T} = \np{rn\_gammat0} \times u_{*}
1045\]
1046\[
1047\gamma^{S} = \np{rn\_gammas0} \times u_{*}
1048\]
1049     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
1050     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1051   \item[\np{nn\_gammablk}\forcode{ = 2}]:
1052     The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1053\[
1054\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1055\]
1056     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
1057     $\Gamma_{Turb}$ the contribution of the ocean stability and
1058     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1059     See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1060     This formulation has not been extensively tested in NEMO (not recommended).
1061   \end{description}
1062 \item[\np{nn\_isf}\forcode{ = 2}]:
1063   The ice shelf cavity is not represented.
1064   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1065   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1066   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1067   (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}).
1068   The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
1069 \item[\np{nn\_isf}\forcode{ = 3}]:
1070   The ice shelf cavity is not represented.
1071   The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1072   the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and
1073   the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
1074   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1075 \item[\np{nn\_isf}\forcode{ = 4}]:
1076   The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed).
1077   However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
1078   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1079   As in \np{nn\_isf}\forcode{ = 1}, the fluxes are spread over the top boundary layer thickness (\np{rn\_hisf\_tbl})\\
1080\end{description}
1081
1082$\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on
1083the water mass properties, ocean velocities and depth.
1084This flux is thus highly dependent of the model resolution (horizontal and vertical),
1085realism of the water masses onto the shelf ...\\
1086
1087$\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file.
1088You have total control of the fwf forcing.
1089This can be useful if the water masses on the shelf are not realistic or
1090the resolution (horizontal/vertical) are too coarse to have realistic melting or
1091for studies where you need to control your heat and fw input.\\ 
1092
1093The ice shelf melt is implemented as a volume flux as for the runoff.
1094The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1095the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1096See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1097
1098%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1099\begin{figure}[!t]
1100  \begin{center}
1101    \includegraphics[width=\textwidth]{Fig_SBC_isf}
1102    \caption{
1103      \protect\label{fig:SBC_isf}
1104      Illustration the location where the fwf is injected and whether or not the fwf is interactif or not depending of \np{nn\_isf}.
1105    }
1106  \end{center}
1107\end{figure}
1108%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1109
1110\section{Ice sheet coupling}
1111\label{sec:SBC_iscpl}
1112%------------------------------------------namsbc_iscpl----------------------------------------------------
1113
1114\nlst{namsbc_iscpl}
1115%--------------------------------------------------------------------------------------------------------
1116Ice sheet/ocean coupling is done through file exchange at the restart step.
1117At each restart step:
1118\begin{description}
1119\item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1120\item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools.
1121\item[Step 3]: NEMO run for a specific period and output the average melt rate over the period.
1122\item[Step 4]: the ice sheet model run using the melt rate outputed in step 4.
1123\item[Step 5]: go back to 1.
1124\end{description}
1125
1126If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with
1127potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1128The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1129\begin{description}
1130\item[Thin a cell down]:
1131  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1132  ($bt_b=bt_n$).
1133\item[Enlarge  a cell]:
1134  See case "Thin a cell down"
1135\item[Dry a cell]:
1136  mask, T/S, U/V and ssh are set to 0.
1137  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1138\item[Wet a cell]:
1139  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1140  If no neighbours, T/S is extrapolated from old top cell value.
1141  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1142\item[Dry a column]:
1143   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1144\item[Wet a column]:
1145  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1146  If no neighbour, T/S/U/V and mask set to 0.
1147\end{description}
1148
1149Furthermore, as the before and now fields are not compatible (modification of the geometry),
1150the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1151
1152The horizontal extrapolation to fill new cell with realistic value is called \np{nn\_drown} times.
1153It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,
1154the code will be unable to fill all the new wet cells properly.
1155The default number is set up for the MISOMIP idealised experiments.
1156This coupling procedure is able to take into account grounding line and calving front migration.
1157However, it is a non-conservative processe.
1158This could lead to a trend in heat/salt content and volume.\\
1159
1160In order to remove the trend and keep the conservation level as close to 0 as possible,
1161a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}.
1162The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1163A correction increment is computed and apply each time step during the next \np{rn\_fiscpl} time steps.
1164For safety, it is advised to set \np{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1165The corrective increment is apply into the cell itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry).
1166
1167%
1168% ================================================================
1169%        Handling of icebergs
1170% ================================================================
1171\section{Handling of icebergs (ICB)}
1172\label{sec:ICB_icebergs}
1173%------------------------------------------namberg----------------------------------------------------
1174
1175\nlst{namberg}
1176%-------------------------------------------------------------------------------------------------------------
1177
1178Icebergs are modelled as lagrangian particles in NEMO \citep{marsh.ivchenko.ea_GMD15}.
1179Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1180(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO).
1181Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1182described in the \ngn{namberg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1183Each class has an associated scaling (\np{rn\_mass\_scaling}),
1184which is an integer representing how many icebergs of this class are being described as one lagrangian point
1185(this reduces the numerical problem of tracking every single iceberg).
1186They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}.
1187
1188Two initialisation schemes are possible.
1189\begin{description}
1190\item[\np{nn\_test\_icebergs}~$>$~0]
1191  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1192  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1193  which an iceberg is generated at the beginning of the run.
1194  (Note that this happens each time the timestep equals \np{nn\_nit000}.)
1195  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of
1196  the geographical box: lonmin,lonmax,latmin,latmax
1197\item[\np{nn\_test\_icebergs}\forcode{ = -1}]
1198  In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
1199  This should be a file with a field on the configuration grid (typically ORCA)
1200  representing ice accumulation rate at each model point.
1201  These should be ocean points adjacent to land where icebergs are known to calve.
1202  Most points in this input grid are going to have value zero.
1203  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1204  At each time step, a test is performed to see if there is enough ice mass to
1205  calve an iceberg of each class in order (1 to 10).
1206  Note that this is the initial mass multiplied by the number each particle represents (\ie the scaling).
1207  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1208\end{description}
1209
1210Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1211The latter act to disintegrate the iceberg.
1212This is either all melted freshwater,
1213or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1214which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1215Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
1216
1217Extensive diagnostics can be produced.
1218Separate output files are maintained for human-readable iceberg information.
1219A separate file is produced for each processor (independent of \np{ln\_ctl}).
1220The amount of information is controlled by two integer parameters:
1221\begin{description}
1222\item[\np{nn\_verbose\_level}] takes a value between one and four and
1223  represents an increasing number of points in the code at which variables are written,
1224  and an increasing level of obscurity.
1225\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1226\end{description}
1227
1228Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1229A non-zero value represents how many timesteps between writes of information into the output file.
1230These output files are in NETCDF format.
1231When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1232Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1233So care is needed to recreate data for individual icebergs,
1234since its trajectory data may be spread across multiple files.
1235
1236% -------------------------------------------------------------------------------------------------------------
1237%        Interactions with waves (sbcwave.F90, ln_wave)
1238% -------------------------------------------------------------------------------------------------------------
1239\section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})]
1240{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
1241\label{sec:SBC_wave}
1242%------------------------------------------namsbc_wave--------------------------------------------------------
1243
1244\nlst{namsbc_wave}
1245%-------------------------------------------------------------------------------------------------------------
1246
1247Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate
1248physical processes related to ocean surface waves, namely the surface stress modified by growth and
1249dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1250tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1251the wind stress.
1252
1253Physical processes related to ocean surface waves can be accounted by setting the logical variable
1254\np{ln\_wave}\forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for
1255different porcesses should be activated as explained in the following sections.
1256
1257Wave fields can be provided either in forced or coupled mode:
1258\begin{description}
1259\item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist
1260for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1261Input Data generic Interface (see \autoref{sec:SBC_input}).
1262\item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 
1263in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist.
1264\end{description}
1265
1266
1267% ================================================================
1268% Neutral drag coefficient from wave model (ln_cdgw)

1269% ================================================================
1270\subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})]
1271{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
1272\label{subsec:SBC_wave_cdgw}
1273
1274The neutral surface drag coefficient provided from an external data source (\ie a wave model),
1275can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist.
1276Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,
1277the drag coefficient is computed according to the stable/unstable conditions of the
1278air-sea interface following \citet{large.yeager_rpt04}.
1279
1280
1281% ================================================================
1282% 3D Stokes Drift (ln_sdw, nn_sdrift)
1283% ================================================================
1284\subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})]
1285{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
1286\label{subsec:SBC_wave_sdw}
1287
1288The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1289It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1290and the current measured at a fixed point (Eulerian velocity).
1291As waves travel, the water particles that make up the waves travel in orbital motions but
1292without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1293at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift.
1294An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1295representation of surface physics in ocean general circulation models.
1296The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1297
1298\[
1299  % \label{eq:sbc_wave_sdw}
1300  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1301  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1302  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1303\]
1304
1305where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1306$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1307$k$ is the mean wavenumber defined as:
1308$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1309
1310In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required
1311and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1312To simplify, it is customary to use approximations to the full Stokes profile.
1313Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1314are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift
1315$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1316and makes possible the estimation of the surface Stokes drift for random directional waves in
1317realistic wave conditions:
1318
1319\begin{description}
1320\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by
1321\citet{breivik.janssen.ea_JPO14}:
1322
1323\[
1324  % \label{eq:sbc_wave_sdw_0a}
1325  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1326\]
1327
1328where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1329
1330\[
1331  % \label{eq:sbc_wave_sdw_0b}
1332  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1333  \quad \text{and }\
1334  T_{st} = \frac{1}{16} \bar{\omega} H_s^2 
1335\]
1336
1337where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1338
1339\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a
1340reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface
1341\citep{breivik.bidlot.ea_OM16}:
1342
1343\[
1344  % \label{eq:sbc_wave_sdw_1}
1345  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1346  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1347\]
1348
1349where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1350
1351\item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1
1352but using the wave frequency from a wave model.
1353
1354\end{description}
1355
1356The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1357and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1358
1359\[
1360  % \label{eq:sbc_wave_eta_sdw}
1361  \frac{\partial{\eta}}{\partial{t}} =
1362  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1363\]
1364
1365The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1366for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1367that is induced by the three-dimensional Stokes velocity.
1368The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1369can be formulated as follows:
1370
1371\[
1372  % \label{eq:sbc_wave_tra_sdw}
1373  \frac{\partial{c}}{\partial{t}} =
1374  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1375\]
1376
1377
1378% ================================================================
1379% Stokes-Coriolis term (ln_stcor)
1380% ================================================================
1381\subsection[Stokes-Coriolis term (\texttt{ln\_stcor})]
1382{Stokes-Coriolis term (\protect\np{ln\_stcor})}
1383\label{subsec:SBC_wave_stcor}
1384
1385In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1386in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1387This additional force may have impact on the Ekman turning of the surface current.
1388In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1389approximations described in \autoref{subsec:SBC_wave_sdw}),
1390\np{ln\_stcor}\forcode{ = .true.} has to be set.
1391
1392
1393% ================================================================
1394% Waves modified stress (ln_tauwoc, ln_tauw)
1395% ================================================================
1396\subsection[Wave modified sress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})]
1397{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}
1398\label{subsec:SBC_wave_tauw}
1399
1400The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1401into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1402available for forcing the mean circulation, while in the opposite case of a decaying sea
1403state more momentum is available for forcing the ocean.
1404Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress,
1405but in practice an equilibrium sea state is a fairly rare event.
1406So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1407
1408\[
1409  % \label{eq:sbc_wave_tauoc}
1410  \tau_{oc,a} = \tau_a - \tau_w
1411\]
1412
1413where $\tau_a$ is the atmospheric surface stress;
1414$\tau_w$ is the atmospheric stress going into the waves defined as:
1415
1416\[
1417  % \label{eq:sbc_wave_tauw}
1418  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1419\]
1420
1421where: $c_p$ is the phase speed of the gravity waves,
1422$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1423the physics of ocean waves. The first one, $S_{in}$, describes the generation
1424of ocean waves by wind and therefore represents the momentum and energy transfer
1425from air to ocean waves; the second term $S_{nl}$ denotes
1426the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$ 
1427describes the dissipation of waves by processes such as white-capping, large scale breaking
1428eddy-induced damping.
1429
1430The wave stress derived from an external wave model can be provided either through the normalized
1431wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and
1432meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}.
1433
1434
1435% ================================================================
1436% Miscellanea options
1437% ================================================================
1438\section{Miscellaneous options}
1439\label{sec:SBC_misc}
1440
1441% -------------------------------------------------------------------------------------------------------------
1442%        Diurnal cycle
1443% -------------------------------------------------------------------------------------------------------------
1444\subsection[Diurnal cycle (\textit{sbcdcy.F90})]
1445{Diurnal cycle (\protect\mdl{sbcdcy})}
1446\label{subsec:SBC_dcy}
1447%------------------------------------------namsbc_rnf----------------------------------------------------
1448%
1449\nlst{namsbc} 
1450%-------------------------------------------------------------------------------------------------------------
1451
1452%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1453\begin{figure}[!t]
1454  \begin{center}
1455    \includegraphics[width=\textwidth]{Fig_SBC_diurnal}
1456    \caption{
1457      \protect\label{fig:SBC_diurnal}
1458      Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values.
1459      The reconstructed diurnal cycle (black line) is chosen as
1460      the mean value of the analytical cycle (blue line) over a time step,
1461      not as the mid time step value of the analytically cycle (red square).
1462      From \citet{bernie.guilyardi.ea_CD07}.
1463    }
1464  \end{center}
1465\end{figure}
1466%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1467
1468\cite{bernie.woolnough.ea_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less.
1469Unfortunately high frequency forcing fields are rare, not to say inexistent.
1470Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at
1471high frequency \citep{bernie.guilyardi.ea_CD07}.
1472Furthermore, only the knowledge of daily mean value of SWF is needed,
1473as higher frequency variations can be reconstructed from them,
1474assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1475The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO by
1476setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when
1477using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or
1478the flux formulation (\np{ln\_flx}\forcode{ = .true.}).
1479The reconstruction is performed in the \mdl{sbcdcy} module.
1480The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1481The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at
1482a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1483The use of diurnal cycle reconstruction requires the input SWF to be daily
1484(\ie a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1485Furthermore, it is recommended to have a least 8 surface module time step per day,
1486that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1487An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1488one every 2~hours (from 1am to 11pm).
1489
1490%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1491\begin{figure}[!t]
1492  \begin{center}
1493    \includegraphics[width=\textwidth]{Fig_SBC_dcy}
1494    \caption{
1495      \protect\label{fig:SBC_dcy}
1496      Example of recontruction of the diurnal cycle variation of short wave flux from
1497      daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1498      The display is on (i,j) plane.
1499    }
1500  \end{center}
1501\end{figure}
1502%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1503
1504Note also that the setting a diurnal cycle in SWF is highly recommended when
1505the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1506an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1507
1508% -------------------------------------------------------------------------------------------------------------
1509%        Rotation of vector pairs onto the model grid directions
1510% -------------------------------------------------------------------------------------------------------------
1511\subsection{Rotation of vector pairs onto the model grid directions}
1512\label{subsec:SBC_rotation}
1513
1514When using a flux (\np{ln\_flx}\forcode{ = .true.}) or
1515bulk (\np{ln\_clio}\forcode{ = .true.} or \np{ln\_core}\forcode{ = .true.}) formulation,
1516pairs of vector components can be rotated from east-north directions onto the local grid directions.
1517This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1518be defined relative to a rectilinear grid.
1519To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1520The eastward component must start with "U" and the northward component with "V". 
1521The remaining characters in the strings are used to identify which pair of components go together.
1522So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1523rotate them on to the model grid directions;
1524"U2" and "V2" could be used against a second pair of components, and so on.
1525The extra characters used in the strings are arbitrary.
1526The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1527
1528% -------------------------------------------------------------------------------------------------------------
1529%        Surface restoring to observed SST and/or SSS
1530% -------------------------------------------------------------------------------------------------------------
1531\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]
1532{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1533\label{subsec:SBC_ssr}
1534%------------------------------------------namsbc_ssr----------------------------------------------------
1535
1536\nlst{namsbc_ssr} 
1537%-------------------------------------------------------------------------------------------------------------
1538
1539IOptions are defined through the \ngn{namsbc\_ssr} namelist variables.
1540On forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}),
1541a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1542\[
1543  % \label{eq:sbc_dmp_q}
1544  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1545\]
1546where SST is a sea surface temperature field (observed or climatological),
1547$T$ is the model surface layer temperature and
1548$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1549For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1550This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1551
1552In the fresh water budget, a feedback term can also be added.
1553Converted into an equivalent freshwater flux, it takes the following expression :
1554
1555\begin{equation}
1556  \label{eq:sbc_dmp_emp}
1557  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1558  {\left.S\right|_{k=1}}
1559\end{equation}
1560
1561where $\textit{emp}_{o }$ is a net surface fresh water flux
1562(observed, climatological or an atmospheric model product),
1563\textit{SSS}$_{Obs}$ is a sea surface salinity
1564(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1565$\left.S\right|_{k=1}$ is the model surface layer salinity and
1566$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1567Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as
1568the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1569The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1570reduce the uncertainties we have on the observed freshwater budget.
1571
1572% -------------------------------------------------------------------------------------------------------------
1573%        Handling of ice-covered area
1574% -------------------------------------------------------------------------------------------------------------
1575\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1576\label{subsec:SBC_ice-cover}
1577
1578The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1579There are several way to handle sea-ice in the system depending on
1580the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist.
1581\begin{description}
1582\item[nn{\_}ice = 0]
1583  there will never be sea-ice in the computational domain.
1584  This is a typical namelist value used for tropical ocean domain.
1585  The surface fluxes are simply specified for an ice-free ocean.
1586  No specific things is done for sea-ice.
1587\item[nn{\_}ice = 1]
1588  sea-ice can exist in the computational domain, but no sea-ice model is used.
1589  An observed ice covered area is read in a file.
1590  Below this area, the SST is restored to the freezing point and
1591  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1592  The associated modification of the freshwater fluxes are done in such a way that
1593  the change in buoyancy fluxes remains zero.
1594  This prevents deep convection to occur when trying to reach the freezing point
1595  (and so ice covered area condition) while the SSS is too large.
1596  This manner of managing sea-ice area, just by using si IF case,
1597  is usually referred as the \textit{ice-if} model.
1598  It can be found in the \mdl{sbcice{\_}if} module.
1599\item[nn{\_}ice = 2 or more]
1600  A full sea ice model is used.
1601  This model computes the ice-ocean fluxes,
1602  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1603  provide the surface ocean fluxes.
1604  Note that the activation of a sea-ice model is is done by defining a CPP key (\key{lim3} or \key{cice}).
1605  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value
1606  (\ie $2$ for LIM-3 or $3$ for CICE).
1607\end{description}
1608
1609% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1610
1611\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]
1612{Interface to CICE (\protect\mdl{sbcice\_cice})}
1613\label{subsec:SBC_cice}
1614
1615It is now possible to couple a regional or global NEMO configuration (without AGRIF)
1616to the CICE sea-ice model by using \key{cice}.
1617The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1618the additional 'hadgem3' drivers will be required, even with the latest code release.
1619Input grid files consistent with those used in NEMO will also be needed,
1620and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1621(seek advice from UKMO if necessary).
1622Currently the code is only designed to work when using the CORE forcing option for NEMO
1623(with \textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE name-list),
1624or alternatively when NEMO is coupled to the HadGAM3 atmosphere model
1625(with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}).
1626The code is intended to be used with \np{nn\_fsbc} set to 1
1627(although coupling ocean and ice less frequently should work,
1628it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1629the user should check that results are not significantly different to the standard case).
1630
1631There are two options for the technical coupling between NEMO and CICE.
1632The standard version allows complete flexibility for the domain decompositions in the individual models,
1633but this is at the expense of global gather and scatter operations in the coupling which
1634become very expensive on larger numbers of processors.
1635The alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that
1636the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1637and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1638allows much more efficient direct coupling on individual processors.
1639This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1640there is no sea ice.
1641
1642% -------------------------------------------------------------------------------------------------------------
1643%        Freshwater budget control
1644% -------------------------------------------------------------------------------------------------------------
1645\subsection[Freshwater budget control (\textit{sbcfwb.F90})]
1646{Freshwater budget control (\protect\mdl{sbcfwb})}
1647\label{subsec:SBC_fwb}
1648
1649For global ocean simulation it can be useful to introduce a control of the mean sea level in order to
1650prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1651In \NEMO, two way of controlling the the freshwater budget.
1652\begin{description}
1653\item[\np{nn\_fwb}\forcode{ = 0}]
1654  no control at all.
1655  The mean sea level is free to drift, and will certainly do so.
1656\item[\np{nn\_fwb}\forcode{ = 1}]
1657  global mean \textit{emp} set to zero at each model time step.
1658%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).
1659\item[\np{nn\_fwb}\forcode{ = 2}]
1660  freshwater budget is adjusted from the previous year annual mean budget which
1661  is read in the \textit{EMPave\_old.dat} file.
1662  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1663  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1664\end{description}
1665
1666
1667
1668% Griffies doc:
1669% When running ocean-ice simulations, we are not explicitly representing land processes,
1670% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1671% it is important to balance the hydrological cycle in ocean-ice models.
1672% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1673% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1674% a chosen time scale.
1675%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1676% so that there is always a zero net input of water to the ocean-ice system.
1677% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1678% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1679% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1680% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1681% and ice models when aiming to balance the hydrological cycle.
1682% 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,
1683% not the water in any one sub-component. As an extreme example to illustrate the issue,
1684% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1685% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1686% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1687% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1688% in ocean-ice models.
1689
1690\biblio
1691
1692\pindex
1693
1694\end{document}
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