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chap_SBC.tex in NEMO/trunk/doc/latex/NEMO/subfiles – NEMO

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1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4
5% ================================================================
6% Chapter —— Surface Boundary Condition (SBC, SAS, ISF, ICB)
7% ================================================================
8\chapter{Surface Boundary Condition (SBC, SAS, ISF, ICB)}
9\label{chap:SBC}
10\chaptertoc
11
12\newpage
13
14%---------------------------------------namsbc--------------------------------------------------
15
16\nlst{namsbc}
17%--------------------------------------------------------------------------------------------------------------
18
19The ocean needs seven fields as surface boundary condition:
20
21\begin{itemize}
22\item
23  the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
24\item
25  the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
26\item
27  the surface freshwater budget $\left( {\textit{emp}} \right)$
28\item
29  the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
30\item
31  the atmospheric pressure at the ocean surface $\left( p_a \right)$
32\end{itemize}
33
34Four different ways are available to provide the seven fields to the ocean. They are controlled by
35namelist \nam{sbc} variables:
36
37\begin{itemize}
38\item
39  a bulk formulation (\np{ln\_blk}\forcode{=.true.} with four possible bulk algorithms),
40\item
41  a flux formulation (\np{ln\_flx}\forcode{=.true.}),
42\item
43  a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
44(\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{=.true.}),
45\item
46  a user defined formulation (\np{ln\_usr}\forcode{=.true.}).
47\end{itemize}
48
49The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.
50
51When the fields are supplied from data files (bulk, flux and mixed formulations),
52the input fields do not need to be supplied on the model grid.
53Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
54the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
55If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
56should be masked or filled to avoid spurious results in proximity of the coasts, as
57large sea-land gradients characterize most of the atmospheric variables.
58
59In addition, the resulting fields can be further modified using several namelist options.
60These options control:
61
62\begin{itemize}
63\item
64  the rotation of vector components supplied relative to an east-north coordinate system onto
65  the local grid directions in the model,
66\item
67  the use of a land/sea mask for input fields (\np{nn\_lsm}\forcode{=.true.}),
68\item
69  the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}\forcode{=.true.}),
70\item
71  the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
72  (\np{nn\_ice}\forcode{=0..3}),
73\item
74  the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}\forcode{=.true.}),
75\item
76  the addition of ice-shelf melting as lateral inflow (parameterisation) or
77  as fluxes applied at the land-ice ocean interface (\np{ln\_isf}\forcode{=.true.}),
78\item
79  the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
80  (\np{nn\_fwb}\forcode{=0..2}),
81\item
82  the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
83  (\np{ln\_dm2dc}\forcode{=.true.}),
84\item
85  the activation of wave effects from an external wave model  (\np{ln\_wave}\forcode{=.true.}),
86\item
87  a neutral drag coefficient is read from an external wave model (\np{ln\_cdgw}\forcode{=.true.}),
88\item
89  the Stokes drift from an external wave model is accounted for (\np{ln\_sdw}\forcode{=.true.}),
90\item
91  the choice of the Stokes drift profile parameterization (\np{nn\_sdrift}\forcode{=0..2}),
92\item
93  the surface stress given to the ocean is modified by surface waves (\np{ln\_tauwoc}\forcode{=.true.}),
94\item
95  the surface stress given to the ocean is read from an external wave model (\np{ln\_tauw}\forcode{=.true.}),
96\item
97  the Stokes-Coriolis term is included (\np{ln\_stcor}\forcode{=.true.}),
98\item
99  the light penetration in the ocean (\np{ln\_traqsr}\forcode{=.true.} with namelist \nam{tra\_qsr}),
100\item
101  the atmospheric surface pressure gradient effect on ocean and ice dynamics (\np{ln\_apr\_dyn}\forcode{=.true.} with namelist \nam{sbc\_apr}),
102\item
103  the effect of sea-ice pressure on the ocean (\np{ln\_ice\_embd}\forcode{=.true.}).
104\end{itemize}
105
106In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
107Then we present the three ways of providing the surface boundary conditions,
108followed by the description of the atmospheric pressure and the river runoff.
109Next, the scheme for interpolation on the fly is described.
110Finally, the different options that further modify the fluxes applied to the ocean are discussed.
111One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
112which act as drifting sources of fresh water.
113Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
114which provides additional sources of fresh water.
115
116
117
118% ================================================================
119% Surface boundary condition for the ocean
120% ================================================================
121\section{Surface boundary condition for the ocean}
122\label{sec:SBC_ocean}
123
124The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
125It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
126the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
127As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
128\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
129
130The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
131$Q_{ns}$ and $Q_{sr}$, respectively.
132The former is the non penetrative part of the heat flux
133(\ie\ the sum of sensible, latent and long wave heat fluxes plus
134the heat content of the mass exchange between the ocean and sea-ice).
135It is applied in \mdl{trasbc} module as a surface boundary condition trend of
136the first level temperature time evolution equation
137(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
138The latter is the penetrative part of the heat flux.
139It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
140\np{ln\_traqsr}\forcode{=.true.}.
141The way the light penetrates inside the water column is generally a sum of decreasing exponentials
142(see \autoref{subsec:TRA_qsr}).
143
144The surface freshwater budget is provided by the \textit{emp} field.
145It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
146possibly with the sea-ice and ice shelves (freezing minus melting of ice).
147It affects the ocean in two different ways:
148$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
149a volume flux, and
150$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
151the mass exchanged with atmosphere, sea-ice and ice shelves.
152
153
154%\colorbox{yellow}{Miss: }
155%
156%A extensive description of all namsbc namelist (parameter that have to be
157%created!)
158%
159%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
160%ssv) \ie\ information required by flux computation or sea-ice
161%
162%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
163%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
164%
165%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
166%
167%Fluxes update only each nf\_sbc time step (namsbc) explain relation
168%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
169%nf\_sbc
170%
171%Explain here all the namlist namsbc variable{\ldots}.
172%
173% explain : use or not of surface currents
174%
175%\colorbox{yellow}{End Miss }
176
177The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
178the surface currents, temperature and salinity.
179These variables are averaged over \np{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
180these averaged fields are used to compute the surface fluxes at the frequency of \np{nn\_fsbc} time-steps.
181
182
183%-------------------------------------------------TABLE---------------------------------------------------
184\begin{table}[tb]
185  \begin{center}
186    \begin{tabular}{|l|l|l|l|}
187      \hline
188      Variable description                         & Model variable  & Units  & point                 \\\hline
189      i-component of the surface current  & ssu\_m               & $m.s^{-1}$     & U     \\\hline
190      j-component of the surface current  & ssv\_m               & $m.s^{-1}$     & V     \\ \hline
191      Sea surface temperature                & sst\_m               & \r{}$K$              & T     \\\hline
192      Sea surface salinty                          & sss\_m               & $psu$              & T     \\   \hline
193    \end{tabular}
194    \caption{
195      \protect\label{tab:SBC_ssm}
196      Ocean variables provided by the ocean to the surface module (SBC).
197      The variable are averaged over \np{nn\_fsbc} time-step,
198      \ie\ the frequency of computation of surface fluxes.
199    }
200  \end{center}
201\end{table}
202%--------------------------------------------------------------------------------------------------------------
203
204%\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
205
206
207
208% ================================================================
209%       Input Data
210% ================================================================
211\section{Input data generic interface}
212\label{sec:SBC_input}
213
214A generic interface has been introduced to manage the way input data
215(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
216This task is achieved by \mdl{fldread}.
217The module is designed with four main objectives in mind:
218\begin{enumerate}
219\item
220  optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
221  and according to the different calendars available in the model.
222\item
223  optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
224\item
225  make the run duration independent from the period cover by the input files.
226\item
227  provide a simple user interface and a rather simple developer interface by
228  limiting the number of prerequisite informations.
229\end{enumerate}
230
231As a result, the user has only to fill in for each variable a structure in the namelist file to
232define the input data file and variable names, the frequency of the data (in hours or months),
233whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
234and three additional parameters for the on-the-fly interpolation.
235When adding a new input variable, the developer has to add the associated structure in the namelist,
236read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
237and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
238
239The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
240(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
241if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
242
243Note that when an input data is archived on a disc which is accessible directly from the workspace where
244the code is executed, then the user can set the \np{cn\_dir} to the pathway leading to the data.
245By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
246
247
248% -------------------------------------------------------------------------------------------------------------
249% Input Data specification (\mdl{fldread})
250% -------------------------------------------------------------------------------------------------------------
251\subsection[Input data specification (\textit{fldread.F90})]
252{Input data specification (\protect\mdl{fldread})}
253\label{subsec:SBC_fldread}
254
255The structure associated with an input variable contains the following information:
256\begin{forlines}
257!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
258!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
259\end{forlines}
260where
261\begin{description}
262\item[File name]:
263  the stem name of the NetCDF file to be opened.
264  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
265  by date information and possibly a prefix (when using AGRIF).
266  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
267  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
268
269%--------------------------------------------------TABLE--------------------------------------------------
270  \begin{table}[htbp]
271    \begin{center}
272      \begin{tabular}{|l|c|c|c|}
273        \hline
274                                        &  daily or weekLL     &  monthly           &  yearly        \\   \hline
275        \np{clim}\forcode{=.false.} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\   \hline
276        \np{clim}\forcode{=.true.}  &  not possible        &  fn\_m??.nc        &  fn            \\   \hline
277      \end{tabular}
278    \end{center}
279    \caption{
280      \protect\label{tab:SBC_fldread}
281      naming nomenclature for climatological or interannual input file(s), as a function of the open/close frequency.
282      The stem name is assumed to be 'fn'.
283      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
284      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
285      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits.
286      Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc',
287      where 'PPPP' is the process number coded with 4 digits;
288      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
289    }
290  \end{table}
291%--------------------------------------------------------------------------------------------------------------
292
293
294\item[Record frequency]:
295  the frequency of the records contained in the input file.
296  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
297  (for example -1 for monthly forcing or -12 for annual forcing).
298  Note that this frequency must REALLY be an integer and not a real.
299  On some computers, setting it to '24.' can be interpreted as 240!
300
301\item[Variable name]:
302  the name of the variable to be read in the input NetCDF file.
303
304\item[Time interpolation]:
305  a logical to activate, or not, the time interpolation.
306  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
307  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
308  00h00'00'' to 23h59'59".
309  If set to 'true', the forcing will have a broken line shape.
310  Records are assumed to be dated at the middle of the forcing period.
311  For example, when using a daily forcing with time interpolation,
312  linear interpolation will be performed between mid-day of two consecutive days.
313
314\item[Climatological forcing]:
315  a logical to specify if a input file contains climatological forcing which can be cycle in time,
316  or an interannual forcing which will requires additional files if
317  the period covered by the simulation exceeds the one of the file.
318  See the above file naming strategy which impacts the expected name of the file to be opened.
319
320\item[Open/close frequency]:
321  the frequency at which forcing files must be opened/closed.
322  Four cases are coded:
323  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
324  means the forcing files will contain data for one day, one week, one month or one year.
325  Files are assumed to contain data from the beginning of the open/close period.
326  For example, the first record of a yearly file containing daily data is Jan 1st even if
327  the experiment is not starting at the beginning of the year.
328
329\item[Others]:
330  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
331  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
332
333\end{description}
334
335Additional remarks:\\
336(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
337The only tricky point is therefore to specify the date at which we need to do the interpolation and
338the date of the records read in the input files.
339Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
340For example, for an experiment starting at 0h00'00" with a one-hour time-step,
341a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
342However, for forcing data related to the surface module,
343values are not needed at every time-step but at every \np{nn\_fsbc} time-step.
344For example with \np{nn\_fsbc}\forcode{=3}, the surface module will be called at time-steps 1, 4, 7, etc.
345The date used for the time interpolation is thus redefined to the middle of \np{nn\_fsbc} time-step period.
346In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
347(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
348The calendar associated with the forcing field is build according to the information provided by
349user in the record frequency, the open/close frequency and the type of temporal interpolation.
350For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
351start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
352(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
353interpolating data with the first (last) record of the open/close period.
354For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
355the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
356Dec 31st 12h00'00" and Jan 1st 12h00'00".
357If the forcing is climatological, Dec and Jan will be keep-up from the same year.
358However, if the forcing is not climatological, at the end of
359the open/close period, the code will automatically close the current file and open the next one.
360Note that, if the experiment is starting (ending) at the beginning (end) of
361an open/close period, we do accept that the previous (next) file is not existing.
362In this case, the time interpolation will be performed between two identical values.
363For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
364we do accept that the file related to year Y-1 is not existing.
365The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
366If the file of year Y-1 exists, the code will read its last record.
367Therefore, this file can contain only one record corresponding to Dec 31st,
368a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
369
370
371% -------------------------------------------------------------------------------------------------------------
372% Interpolation on the Fly
373% -------------------------------------------------------------------------------------------------------------
374\subsection{Interpolation on-the-fly}
375\label{subsec:SBC_iof}
376
377Interpolation on the Fly allows the user to supply input files required for the surface forcing on
378grids other than the model grid.
379To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
380interpolate from the data grid to the model grid.
381The original development of this code used the SCRIP package
382(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
383In principle, any package such as CDO can be used to generate the weights, but the variables in
384the input weights file must have the same names and meanings as assumed by the model.
385Two methods are currently available: bilinear and bicubic interpolations.
386Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
387the input file and substitute the corresponding values with the average of the 8 neighbouring points in
388the native external grid.
389Only "sea points" are considered for the averaging.
390The land/sea mask file must be provided in the structure associated with the input variable.
391The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
392the associated variables and should be equal to 1 over land and 0 elsewhere.
393The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
394Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
395
396
397% -------------------------------------------------------------------------------------------------------------
398% Bilinear interpolation
399% -------------------------------------------------------------------------------------------------------------
400\subsubsection{Bilinear interpolation}
401\label{subsec:SBC_iof_bilinear}
402
403The input weights file in this case has two sets of variables:
404src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
405The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
406Each src value is an integer corresponding to the index of a point in the input grid when
407written as a one dimensional array.
408For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
409There are four of each variable because bilinear interpolation uses the four points defining
410the grid box containing the point to be interpolated.
411All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
412generate a value for point (i,j) in the model.
413
414Symbolically, the algorithm used is:
415\[
416  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
417\]
418where function idx() transforms a one dimensional index src(k) into a two dimensional index,
419and wgt(1) corresponds to variable "wgt01" for example.
420
421
422% -------------------------------------------------------------------------------------------------------------
423% Bicubic interpolation
424% -------------------------------------------------------------------------------------------------------------
425\subsubsection{Bicubic interpolation}
426\label{subsec:SBC_iof_bicubic}
427
428Again, there are two sets of variables: "src" and "wgt".
429But in this case, there are 16 of each.
430The symbolic algorithm used to calculate values on the model grid is now:
431
432\[
433  \begin{split}
434    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
435    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
436    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
437    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
438  \end{split}
439\]
440The gradients here are taken with respect to the horizontal indices and not distances since
441the spatial dependency has been included into the weights.
442
443
444% -------------------------------------------------------------------------------------------------------------
445% Implementation
446% -------------------------------------------------------------------------------------------------------------
447\subsubsection{Implementation}
448\label{subsec:SBC_iof_imp}
449
450To activate this option, a non-empty string should be supplied in
451the weights filename column of the relevant namelist;
452if this is left as an empty string no action is taken.
453In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
454as and when they are first required.
455This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
456inspecting a global attribute stored in the weights input file.
457This attribute must be called "ew\_wrap" and be of integer type.
458If it is negative, the input non-model grid is assumed to be not cyclic.
459If zero or greater, then the value represents the number of columns that overlap.
460$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
461if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
462If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
463In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
464therefore the grid is assumed to be cyclic with no overlapping columns.
465(In fact, this only matters when bicubic interpolation is required.)
466Note that no testing is done to check the validity in the model,
467since there is no way of knowing the name used for the longitude variable,
468so it is up to the user to make sure his or her data is correctly represented.
469
470Next the routine reads in the weights.
471Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
472The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
473and when required, for reading in the variable to be interpolated (on the input data grid).
474The size of the input data array is determined by examining the values in the "src" arrays to
475find the minimum and maximum i and j values required.
476Since bicubic interpolation requires the calculation of gradients at each point on the grid,
477the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
478When the array of points from the data file is adjacent to an edge of the data grid,
479the halo is either a copy of the row/column next to it (non-cyclical case),
480or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
481
482
483% -------------------------------------------------------------------------------------------------------------
484% Limitations
485% -------------------------------------------------------------------------------------------------------------
486\subsubsection{Limitations}
487\label{subsec:SBC_iof_lim}
488
489\begin{enumerate}
490\item
491  The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
492\item
493  This code is not guaranteed to produce positive definite answers from positive definite inputs when
494  a bicubic interpolation method is used.
495\item
496  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
497\item
498  The gradients across the ends of a cyclical grid assume that the grid spacing between
499  the two columns involved are consistent with the weights used.
500\item
501  Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
502  but this has not been implemented.)
503\end{enumerate}
504
505\subsubsection{Utilities}
506\label{subsec:SBC_iof_util}
507
508% to be completed
509A set of utilities to create a weights file for a rectilinear input grid is available
510(see the directory NEMOGCM/TOOLS/WEIGHTS).
511
512
513% -------------------------------------------------------------------------------------------------------------
514% Standalone Surface Boundary Condition Scheme
515% -------------------------------------------------------------------------------------------------------------
516\subsection{Standalone surface boundary condition scheme (SAS)}
517\label{subsec:SBC_SAS}
518
519%---------------------------------------namsbc_sas--------------------------------------------------
520
521\nlst{namsbc_sas}
522%--------------------------------------------------------------------------------------------------------------
523
524In some circumstances, it may be useful to avoid calculating the 3D temperature,
525salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
526For example:
527
528\begin{itemize}
529\item
530  Multiple runs of the model are required in code development to
531  see the effect of different algorithms in the bulk formulae.
532\item
533  The effect of different parameter sets in the ice model is to be examined.
534\item
535  Development of sea-ice algorithms or parameterizations.
536\item
537  Spinup of the iceberg floats
538\item
539  Ocean/sea-ice simulation with both models running in parallel (\np{ln\_mixcpl}\forcode{=.true.})
540\end{itemize}
541
542The Standalone Surface scheme provides this capacity.
543Its options are defined through the \nam{sbc\_sas} namelist variables.
544A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
545However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
546In this configuration, a few routines in the standard model are overriden by new versions.
547Routines replaced are:
548
549\begin{itemize}
550\item
551  \mdl{nemogcm}:
552  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
553  Since the ocean state is not calculated all associated initialisations have been removed.
554\item
555  \mdl{step}:
556  The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
557\item
558  \mdl{sbcmod}:
559  This has been cut down and now only calculates surface forcing and the ice model required.
560  New surface modules that can function when only the surface level of the ocean state is defined can also be added
561  (\eg\ icebergs).
562\item
563  \mdl{daymod}:
564  No ocean restarts are read or written (though the ice model restarts are retained),
565  so calls to restart functions have been removed.
566  This also means that the calendar cannot be controlled by time in a restart file,
567  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
568\item
569  \mdl{stpctl}:
570  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
571\item
572  \mdl{diawri}:
573  All 3D data have been removed from the output.
574  The surface temperature, salinity and velocity components (which have been read in) are written along with
575  relevant forcing and ice data.
576\end{itemize}
577
578One new routine has been added:
579
580\begin{itemize}
581\item
582  \mdl{sbcsas}:
583  This module initialises the input files needed for reading temperature, salinity and
584  velocity arrays at the surface.
585  These filenames are supplied in namelist namsbc\_sas.
586  Unfortunately, because of limitations with the \mdl{iom} module,
587  the full 3D fields from the mean files have to be read in and interpolated in time,
588  before using just the top level.
589  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
590\end{itemize}
591
592
593The user can also choose in the \nam{sbc\_sas} namelist to read the mean (nn\_fsbc time-step) fraction of solar net radiation absorbed in the 1st T level using
594 (\np{ln\_flx}\forcode{=.true.}) and to provide 3D oceanic velocities instead of 2D ones (\np{ln\_flx}\forcode{=.true.}). In that last case, only the 1st level will be read in.
595
596
597
598% ================================================================
599% Flux formulation
600% ================================================================
601\section[Flux formulation (\textit{sbcflx.F90})]
602{Flux formulation (\protect\mdl{sbcflx})}
603\label{sec:SBC_flx}
604%------------------------------------------namsbc_flx----------------------------------------------------
605
606\nlst{namsbc_flx}
607%-------------------------------------------------------------------------------------------------------------
608
609In the flux formulation (\np{ln\_flx}\forcode{=.true.}),
610the surface boundary condition fields are directly read from input files.
611The user has to define in the namelist \nam{sbc\_flx} the name of the file,
612the name of the variable read in the file, the time frequency at which it is given (in hours),
613and a logical setting whether a time interpolation to the model time step is required for this field.
614See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
615
616Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
617See \autoref{subsec:SBC_ssr} for its specification.
618
619
620
621% ================================================================
622% Bulk formulation
623% ================================================================
624\section[Bulk formulation (\textit{sbcblk.F90})]
625{Bulk formulation (\protect\mdl{sbcblk})}
626\label{sec:SBC_blk}
627%---------------------------------------namsbc_blk--------------------------------------------------
628
629\nlst{namsbc_blk}
630%--------------------------------------------------------------------------------------------------------------
631
632In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields
633and ocean (and sea-ice) variables averaged over \np{nn\_fsbc} time-step.
634
635The atmospheric fields used depend on the bulk formulae used.
636In forced mode, when a sea-ice model is used, a specific bulk formulation is used.
637Therefore, different bulk formulae are used for the turbulent fluxes computation
638over the ocean and over sea-ice surface.
639For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}):
640the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae.
641The choice is made by setting to true one of the following namelist variable:
642 \np{ln\_NCAR}, \np{ln\_COARE\_3p0}\np{ln\_COARE\_3p5} and  \np{ln\_ECMWF}.
643For sea-ice, three possibilities can be selected:
644a constant transfer coefficient (1.4e-3; default value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln\_Cd\_L12}), and \citet{lupkes.gryanik_JGR15} (\np{ln\_Cd\_L15}) parameterizations
645
646Common options are defined through the \nam{sbc\_blk} namelist variables.
647The required 9 input fields are:
648
649%--------------------------------------------------TABLE--------------------------------------------------
650\begin{table}[htbp]
651  \label{tab:SBC_BULK}
652  \begin{center}
653    \begin{tabular}{|l|c|c|c|}
654      \hline
655      Variable description                           & Model variable   & Units                         & point \\   \hline
656      i-component of the 10m air velocity   & utau                   & $m.s^{-1}$                   & T         \\   \hline
657      j-component of the 10m air velocity   & vtau                & $m.s^{-1}$                   & T         \\   \hline
658      10m air temperature                      & tair                & \r{}$K$                        & T       \\   \hline
659      Specific humidity                        & humi           & \%                             & T      \\   \hline
660      Incoming long wave radiation          & qlw                & $W.m^{-2}$            & T        \\   \hline
661      Incoming short wave radiation          & qsr               & $W.m^{-2}$            & T        \\   \hline
662      Total precipitation (liquid + solid)         & precip            & $Kg.m^{-2}.s^{-1}$      & T      \\   \hline
663      Solid precipitation                           & snow               & $Kg.m^{-2}.s^{-1}$       & T      \\   \hline
664      Mean sea-level pressure                     & slp                     & $hPa$                          & T       \\ \hline
665    \end{tabular}
666  \end{center}
667\end{table}
668%--------------------------------------------------------------------------------------------------------------
669
670Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
671It is simpler and faster (less fields to be read), but it is not the recommended method when
672the ocean grid size is the same or larger than the one of the input atmospheric fields.
673
674The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, \np{sn\_prec},
675\np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used
676(spatial and temporal interpolations).
677
678\np{cn\_dir} is the directory of location of bulk files
679\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
680\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
681\np{rn\_zu}: is the height of wind measurements (m)
682
683Three multiplicative factors are available:
684\np{rn\_pfac} and \np{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
685increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
686The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
687the calculation of surface wind stress.
688Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
689
690As for the flux formulation, information about the input data required by the model is provided in
691the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
692
693
694% -------------------------------------------------------------------------------------------------------------
695%        Ocean-Atmosphere Bulk formulae
696% -------------------------------------------------------------------------------------------------------------
697\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.F90,
698sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]
699{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5},
700\mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}
701\label{subsec:SBC_blk_ocean}
702
703Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
704COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
705their neutral transfer coefficients relationships with neutral wind.
706\begin{itemize}
707\item
708  NCAR (\np{ln\_NCAR}\forcode{=.true.}):
709  The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
710  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
711  They use an inertial dissipative method to compute the turbulent transfer coefficients
712  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
713  This \citet{large.yeager_rpt04} dataset is available through
714  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
715  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
716  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
717\item
718  COARE 3.0 (\np{ln\_COARE\_3p0}\forcode{=.true.}):
719  See \citet{fairall.bradley.ea_JC03} for more details
720\item
721  COARE 3.5 (\np{ln\_COARE\_3p5}\forcode{=.true.}):
722  See \citet{edson.jampana.ea_JPO13} for more details
723\item
724  ECMWF (\np{ln\_ECMWF}\forcode{=.true.}):
725  Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation.
726  Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}.
727\end{itemize}
728
729% -------------------------------------------------------------------------------------------------------------
730%        Ice-Atmosphere Bulk formulae
731% -------------------------------------------------------------------------------------------------------------
732\subsection{Ice-Atmosphere Bulk formulae}
733\label{subsec:SBC_blk_ice}
734
735Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
736
737\begin{itemize}
738\item
739  Constant value (\np{constant\ value}\forcode{ Cd_ice = 1.4e-3 }):
740  default constant value used for momentum and heat neutral transfer coefficients
741\item
742  \citet{lupkes.gryanik.ea_JGR12} (\np{ln\_Cd\_L12}\forcode{=.true.}):
743  This scheme adds a dependency on edges at leads, melt ponds and flows
744  of the constant neutral air-ice drag. After some approximations,
745  this can be resumed to a dependency on ice concentration (A).
746  This drag coefficient has a parabolic shape (as a function of ice concentration)
747  starting at 1.5e-3 for A=0, reaching 1.97e-3 for A=0.5 and going down 1.4e-3 for A=1.
748  It is theoretically applicable to all ice conditions (not only MIZ).
749\item
750  \citet{lupkes.gryanik_JGR15} (\np{ln\_Cd\_L15}\forcode{=.true.}):
751  Alternative turbulent transfer coefficients formulation between sea-ice
752  and atmosphere with distinct momentum and heat coefficients depending
753  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
754  The parameterization is adapted from ECHAM6 atmospheric model.
755  Compared to Lupkes2012 scheme, it considers specific skin and form drags
756  to compute neutral transfer coefficients for both heat and momentum fluxes.
757  Atmospheric stability effect on transfer coefficient is also taken into account.
758\end{itemize}
759
760
761
762% ================================================================
763% Coupled formulation
764% ================================================================
765\section[Coupled formulation (\textit{sbccpl.F90})]
766{Coupled formulation (\protect\mdl{sbccpl})}
767\label{sec:SBC_cpl}
768%------------------------------------------namsbc_cpl----------------------------------------------------
769
770\nlst{namsbc_cpl}
771%-------------------------------------------------------------------------------------------------------------
772
773In the coupled formulation of the surface boundary condition,
774the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
775while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
776the atmospheric component.
777
778A generalised coupled interface has been developed.
779It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
780An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
781It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
782(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
783(Weather Research and Forecasting Model).
784
785When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
786the whole carbon cycle is computed.
787In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
788(and need to be activated in \nam{sbc\_cpl} ).
789
790The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
791now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
792When indicating a multi-category coupling field in \nam{sbc\_cpl}, the number of categories will be determined by
793the number used in the sea ice model.
794In some limited cases, it may be possible to specify single category coupling fields even when
795the sea ice model is running with multiple categories -
796in this case, the user should examine the code to be sure the assumptions made are satisfactory.
797In cases where this is definitely not possible, the model should abort with an error message.
798
799
800
801% ================================================================
802%        Atmospheric pressure
803% ================================================================
804\section[Atmospheric pressure (\textit{sbcapr.F90})]
805{Atmospheric pressure (\protect\mdl{sbcapr})}
806\label{sec:SBC_apr}
807%------------------------------------------namsbc_apr----------------------------------------------------
808
809\nlst{namsbc_apr}
810%-------------------------------------------------------------------------------------------------------------
811
812The optional atmospheric pressure can be used to force ocean and ice dynamics
813(\np{ln\_apr\_dyn}\forcode{=.true.}, \nam{sbc} namelist).
814The input atmospheric forcing defined via \np{sn\_apr} structure (\nam{sbc\_apr} namelist)
815can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
816When used to force the dynamics, the atmospheric pressure is further transformed into
817an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
818\[
819  % \label{eq:SBC_ssh_ib}
820  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
821\]
822where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
823A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true.
824In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
825\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
826
827The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
828For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
829(see \mdl{sbcssr} module).
830$\eta_{ib}$ can be written in the output.
831This can simplify altimetry data and model comparison as
832inverse barometer sea surface height is usually removed from these date prior to their distribution.
833
834When using time-splitting and BDY package for open boundaries conditions,
835the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
836\np{ln\_apr\_obc}  might be set to true.
837
838
839
840% ================================================================
841%        Surface Tides Forcing
842% ================================================================
843\section[Surface tides (\textit{sbctide.F90})]
844{Surface tides (\protect\mdl{sbctide})}
845\label{sec:SBC_tide}
846
847%------------------------------------------nam_tide---------------------------------------
848
849\nlst{nam_tide}
850%-----------------------------------------------------------------------------------------
851
852The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
853is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{\_tide}.
854This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
855\[
856  % \label{eq:SBC_PE_dyn_tides}
857  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
858  +g\nabla (\Pi_{eq} + \Pi_{sal})
859\]
860where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
861$\Pi_{sal}$ is a self-attraction and loading term (SAL).
862
863The equilibrium tidal forcing is expressed as a sum over a subset of
864constituents chosen from the set of available tidal constituents
865defined in file \hf{SBC/tide} (this comprises the tidal
866constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
867  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
868constituents are selected by including their names in the array
869\np{clname} in \nam{\_tide} (e.g., \np{clname}\forcode{(1)='M2', }
870\np{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
871and \textit{S2}). Optionally, when \np{ln\_tide\_ramp} is set to
872\forcode{.true.}, the equilibrium tidal forcing can be ramped up
873linearly from zero during the initial \np{rdttideramp} days of the
874model run.
875
876The SAL term should in principle be computed online as it depends on
877the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
878discussion about the practical implementation of this term).
879Nevertheless, the complex calculations involved would make this
880computationally too expensive. Here, two options are available:
881$\Pi_{sal}$ generated by an external model can be read in
882(\np{ln\_read\_load}\forcode{ =.true.}), or a ``scalar approximation'' can be
883used (\np{ln\_scal\_load}\forcode{ =.true.}). In the latter case
884\[
885  \Pi_{sal} = \beta \eta,
886\]
887where $\beta$ (\np{rn\_scal\_load} with a default value of 0.094) is a
888spatially constant scalar, often chosen to minimize tidal prediction
889errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to
890\forcode{.false.} removes the SAL contribution.
891
892
893
894% ================================================================
895%        River runoffs
896% ================================================================
897\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
898\label{sec:SBC_rnf}
899%------------------------------------------namsbc_rnf----------------------------------------------------
900
901\nlst{namsbc_rnf}
902%-------------------------------------------------------------------------------------------------------------
903
904%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
905%Many models, however, have traditionally inserted river runoff to the top model cell.
906%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
907%throughout a nonzero depth has been motivated by the numerical and physical problems
908%that arise when the top grid cells are of the order of one meter. This situation is common in
909%coastal modelling and becomes more and more often open ocean and climate modelling
910%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
911%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
912
913
914%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
915%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
916%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
917%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
918%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
919%emp or emps and the changes made are below:
920
921
922%Rachel:
923River runoff generally enters the ocean at a nonzero depth rather than through the surface.
924Many models, however, have traditionally inserted river runoff to the top model cell.
925This was the case in \NEMO\ prior to the version 3.3,
926and was combined with an option to increase vertical mixing near the river mouth.
927
928However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
929This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
930\footnote{
931  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
932  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
933  see also \autoref{fig:SBC_dcy}.}.
934
935As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
936and for the temperature and salinity of the river to effect the surrounding ocean.
937The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
938along with the depth (in metres) which the river should be added to.
939
940Namelist variables in \nam{sbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and
941\np{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
942If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
943and/or taken as surface temperature respectively.
944
945The runoff value and attributes are read in in sbcrnf.
946For temperature -999 is taken as missing data and the river temperature is taken to
947be the surface temperatue at the river point.
948For the depth parameter a value of -1 means the river is added to the surface box only,
949and a value of -999 means the river is added through the entire water column.
950After being read in the temperature and salinity variables are multiplied by the amount of runoff
951(converted into m/s) to give the heat and salt content of the river runoff.
952After the user specified depth is read ini,
953the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz\_rnf}.
954The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
955the bottom of the lowest box the river water is being added to
956(\ie\ the total depth that river water is being added to in the model).
957
958The mass/volume addition due to the river runoff is, at each relevant depth level, added to
959the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
960This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
961The sea surface height is calculated using the sum of the horizontal divergence terms,
962and so the river runoff indirectly forces an increase in sea surface height.
963
964The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
965This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
966The heat and salt content of the river runoff is not included in this step,
967and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
968the box and replaced by the same volume of river water with no corresponding heat and salt addition.
969
970For the linear free surface case, at the surface box the tracer advection causes a flux of water
971(of equal volume to the runoff) through the sea surface out of the domain,
972which causes a salt and heat flux out of the model.
973As such the volume of water does not change, but the water is diluted.
974
975For the non-linear free surface case, no flux is allowed through the surface.
976Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
977no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
978(The runoff addition to the top box along with the water being moved up through
979boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
980
981In trasbc the addition of heat and salt due to the river runoff is added.
982This is done in the same way for both vvl and non-vvl.
983The temperature and salinity are increased through the specified depth according to
984the heat and salt content of the river.
985
986In the non-linear free surface case (vvl),
987near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
988so that the original ratios of grid box heights are restored.
989In doing this water is moved into boxes below, throughout the water column,
990so the large volume addition to the surface box is spread between all the grid boxes.
991
992It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
993\ie\ modelling the Baltic flow in and out of the North Sea.
994When the flow is out of the domain there is no change in temperature and salinity,
995regardless of the namelist options used,
996as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
997
998
999%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1000
1001%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1002
1003%\colorbox{yellow}{river mouths{\ldots}}
1004
1005%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1006%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1007%ENDIF
1008
1009%\gmcomment{  word doc of runoffs:
1010%
1011%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.
1012%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.
1013
1014%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
1015
1016%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:
1017
1018
1019
1020% ================================================================
1021%        Ice shelf melting
1022% ================================================================
1023\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
1024\label{sec:SBC_isf}
1025%------------------------------------------namsbc_isf----------------------------------------------------
1026
1027\nlst{namsbc_isf}
1028%--------------------------------------------------------------------------------------------------------
1029
1030The namelist variable in \nam{sbc}, \np{nn\_isf}, controls the ice shelf representation.
1031Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1032The different options are illustrated in \autoref{fig:SBC_isf}.
1033
1034\begin{description}
1035
1036  \item[\np{nn\_isf}\forcode{=1}]:
1037  The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{=.true.} needed).
1038  The fwf and heat flux are depending of the local water properties.
1039
1040  Two different bulk formulae are available:
1041
1042   \begin{description}
1043   \item[\np{nn\_isfblk}\forcode{=1}]:
1044     The melt rate is based on a balance between the upward ocean heat flux and
1045     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
1046   \item[\np{nn\_isfblk}\forcode{=2}]:
1047     The melt rate and the heat flux are based on a 3 equations formulation
1048     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1049     A complete description is available in \citet{jenkins_JGR91}.
1050   \end{description}
1051
1052     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1053     Its thickness is defined by \np{rn\_hisf\_tbl}.
1054     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m.
1055     Then, the fluxes are spread over the same thickness (ie over one or several cells).
1056     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.
1057     This can lead to super-cool temperature in the top cell under melting condition.
1058     If \np{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
1059
1060     Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1061     There are 3 different ways to compute the exchange coeficient:
1062   \begin{description}
1063        \item[\np{nn\_gammablk}\forcode{=0}]:
1064     The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}.
1065     \begin{gather*}
1066       % \label{eq:SBC_isf_gamma_iso}
1067       \gamma^{T} = rn\_gammat0 \\
1068       \gamma^{S} = rn\_gammas0
1069     \end{gather*}
1070     This is the recommended formulation for ISOMIP.
1071   \item[\np{nn\_gammablk}\forcode{=1}]:
1072     The salt and heat exchange coefficients are velocity dependent and defined as
1073     \begin{gather*}
1074       \gamma^{T} = rn\_gammat0 \times u_{*} \\
1075       \gamma^{S} = rn\_gammas0 \times u_{*}
1076     \end{gather*}
1077     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
1078     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1079   \item[\np{nn\_gammablk}\forcode{=2}]:
1080     The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1081\[
1082\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1083\]
1084     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
1085     $\Gamma_{Turb}$ the contribution of the ocean stability and
1086     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1087     See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1088     This formulation has not been extensively tested in \NEMO\ (not recommended).
1089   \end{description}
1090  \item[\np{nn\_isf}\forcode{=2}]:
1091   The ice shelf cavity is not represented.
1092   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1093   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1094   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1095   (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{=3}).
1096   The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
1097  \item[\np{nn\_isf}\forcode{=3}]:
1098   The ice shelf cavity is not represented.
1099   The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1100   the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and
1101   the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
1102   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1103  \item[\np{nn\_isf}\forcode{=4}]:
1104   The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{=.true.} needed).
1105   However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
1106   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1107   As in \np{nn\_isf}\forcode{=1}, the fluxes are spread over the top boundary layer thickness (\np{rn\_hisf\_tbl})\\
1108\end{description}
1109
1110$\bullet$ \np{nn\_isf}\forcode{=1} and \np{nn\_isf}\forcode{=2} compute a melt rate based on
1111the water mass properties, ocean velocities and depth.
1112This flux is thus highly dependent of the model resolution (horizontal and vertical),
1113realism of the water masses onto the shelf ...\\
1114
1115$\bullet$ \np{nn\_isf}\forcode{=3} and \np{nn\_isf}\forcode{=4} read the melt rate from a file.
1116You have total control of the fwf forcing.
1117This can be useful if the water masses on the shelf are not realistic or
1118the resolution (horizontal/vertical) are too coarse to have realistic melting or
1119for studies where you need to control your heat and fw input.\\
1120
1121The ice shelf melt is implemented as a volume flux as for the runoff.
1122The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1123the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1124See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1125
1126%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1127\begin{figure}[!t]
1128  \begin{center}
1129    \includegraphics[width=\textwidth]{Fig_SBC_isf}
1130    \caption{
1131      \protect\label{fig:SBC_isf}
1132      Illustration the location where the fwf is injected and whether or not the fwf is interactif or not depending of \np{nn\_isf}.
1133    }
1134  \end{center}
1135\end{figure}
1136%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1137
1138
1139
1140% ================================================================
1141%        Ice sheet coupling
1142% ================================================================
1143\section{Ice sheet coupling}
1144\label{sec:SBC_iscpl}
1145%------------------------------------------namsbc_iscpl----------------------------------------------------
1146
1147\nlst{namsbc_iscpl}
1148%--------------------------------------------------------------------------------------------------------
1149
1150Ice sheet/ocean coupling is done through file exchange at the restart step.
1151At each restart step:
1152
1153\begin{description}
1154\item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1155\item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools.
1156\item[Step 3]: \NEMO\ run for a specific period and output the average melt rate over the period.
1157\item[Step 4]: the ice sheet model run using the melt rate outputed in step 4.
1158\item[Step 5]: go back to 1.
1159\end{description}
1160
1161If \np{ln\_iscpl}\forcode{=.true.}, the isf draft is assume to be different at each restart step with
1162potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1163The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1164
1165\begin{description}
1166\item[Thin a cell down]:
1167  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1168  ($bt_b=bt_n$).
1169\item[Enlarge  a cell]:
1170  See case "Thin a cell down"
1171\item[Dry a cell]:
1172  mask, T/S, U/V and ssh are set to 0.
1173  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1174\item[Wet a cell]:
1175  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1176  If no neighbours, T/S is extrapolated from old top cell value.
1177  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1178\item[Dry a column]:
1179   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1180\item[Wet a column]:
1181  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1182  If no neighbour, T/S/U/V and mask set to 0.
1183\end{description}
1184
1185Furthermore, as the before and now fields are not compatible (modification of the geometry),
1186the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1187
1188The horizontal extrapolation to fill new cell with realistic value is called \np{nn\_drown} times.
1189It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,
1190the code will be unable to fill all the new wet cells properly.
1191The default number is set up for the MISOMIP idealised experiments.
1192This coupling procedure is able to take into account grounding line and calving front migration.
1193However, it is a non-conservative processe.
1194This could lead to a trend in heat/salt content and volume.\\
1195
1196In order to remove the trend and keep the conservation level as close to 0 as possible,
1197a simple conservation scheme is available with \np{ln\_hsb}\forcode{=.true.}.
1198The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1199A correction increment is computed and apply each time step during the next \np{rn\_fiscpl} time steps.
1200For safety, it is advised to set \np{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1201The 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).
1202
1203
1204
1205% ================================================================
1206%        Handling of icebergs
1207% ================================================================
1208\section{Handling of icebergs (ICB)}
1209\label{sec:SBC_ICB_icebergs}
1210%------------------------------------------namberg----------------------------------------------------
1211
1212\nlst{namberg}
1213%-------------------------------------------------------------------------------------------------------------
1214
1215Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1216Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1217(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1218Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1219described in the \nam{berg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1220Each class has an associated scaling (\np{rn\_mass\_scaling}),
1221which is an integer representing how many icebergs of this class are being described as one lagrangian point
1222(this reduces the numerical problem of tracking every single iceberg).
1223They are enabled by setting \np{ln\_icebergs}\forcode{=.true.}.
1224
1225Two initialisation schemes are possible.
1226\begin{description}
1227\item[\np{nn\_test\_icebergs}~$>$~0]
1228  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1229  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1230  which an iceberg is generated at the beginning of the run.
1231  (Note that this happens each time the timestep equals \np{nn\_nit000}.)
1232  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of
1233  the geographical box: lonmin,lonmax,latmin,latmax
1234\item[\np{nn\_test\_icebergs}\forcode{=-1}]
1235  In this scheme, the model reads a calving file supplied in the \np{sn\_icb} parameter.
1236  This should be a file with a field on the configuration grid (typically ORCA)
1237  representing ice accumulation rate at each model point.
1238  These should be ocean points adjacent to land where icebergs are known to calve.
1239  Most points in this input grid are going to have value zero.
1240  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1241  At each time step, a test is performed to see if there is enough ice mass to
1242  calve an iceberg of each class in order (1 to 10).
1243  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1244  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1245\end{description}
1246
1247Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1248The latter act to disintegrate the iceberg.
1249This is either all melted freshwater,
1250or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1251which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1252Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1253
1254Extensive diagnostics can be produced.
1255Separate output files are maintained for human-readable iceberg information.
1256A separate file is produced for each processor (independent of \np{ln\_ctl}).
1257The amount of information is controlled by two integer parameters:
1258\begin{description}
1259\item[\np{nn\_verbose\_level}] takes a value between one and four and
1260  represents an increasing number of points in the code at which variables are written,
1261  and an increasing level of obscurity.
1262\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1263\end{description}
1264
1265Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1266A non-zero value represents how many timesteps between writes of information into the output file.
1267These output files are in NETCDF format.
1268When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1269Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1270So care is needed to recreate data for individual icebergs,
1271since its trajectory data may be spread across multiple files.
1272
1273
1274
1275% =============================================================================================================
1276%        Interactions with waves (sbcwave.F90, ln_wave)
1277% =============================================================================================================
1278\section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
1279\label{sec:SBC_wave}
1280%------------------------------------------namsbc_wave--------------------------------------------------------
1281
1282\nlst{namsbc_wave}
1283%-------------------------------------------------------------------------------------------------------------
1284
1285Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1286physical processes related to ocean surface waves, namely the surface stress modified by growth and
1287dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1288tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1289the wind stress.
1290
1291Physical processes related to ocean surface waves can be accounted by setting the logical variable
1292\np{ln\_wave}\forcode{=.true.} in \nam{sbc} namelist. In addition, specific flags accounting for
1293different processes should be activated as explained in the following sections.
1294
1295Wave fields can be provided either in forced or coupled mode:
1296\begin{description}
1297\item[forced mode]: wave fields should be defined through the \nam{sbc\_wave} namelist
1298for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1299Input Data generic Interface (see \autoref{sec:SBC_input}).
1300\item[coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.}
1301in \nam{sbc} namelist and filling the \nam{sbc\_cpl} namelist.
1302\end{description}
1303
1304
1305% ----------------------------------------------------------------
1306% Neutral drag coefficient from wave model (ln_cdgw)
1307
1308% ----------------------------------------------------------------
1309\subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
1310\label{subsec:SBC_wave_cdgw}
1311
1312The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1313can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \nam{sbc} namelist.
1314Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1315the drag coefficient is computed according to the stable/unstable conditions of the
1316air-sea interface following \citet{large.yeager_rpt04}.
1317
1318
1319% ----------------------------------------------------------------
1320% 3D Stokes Drift (ln_sdw, nn_sdrift)
1321% ----------------------------------------------------------------
1322\subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})]{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
1323\label{subsec:SBC_wave_sdw}
1324
1325The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1326It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1327and the current measured at a fixed point (Eulerian velocity).
1328As waves travel, the water particles that make up the waves travel in orbital motions but
1329without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1330at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1331An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1332representation of surface physics in ocean general circulation models. %GS: reference needed
1333The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1334
1335\[
1336  % \label{eq:SBC_wave_sdw}
1337  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1338  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1339  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1340\]
1341
1342where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1343$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1344$k$ is the mean wavenumber defined as:
1345$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1346
1347In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1348and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1349To simplify, it is customary to use approximations to the full Stokes profile.
1350Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1351are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift
1352$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1353and makes possible the estimation of the surface Stokes drift for random directional waves in
1354realistic wave conditions:
1355
1356\begin{description}
1357\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by
1358\citet{breivik.janssen.ea_JPO14}:
1359
1360\[
1361  % \label{eq:SBC_wave_sdw_0a}
1362  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1363\]
1364
1365where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1366
1367\[
1368  % \label{eq:SBC_wave_sdw_0b}
1369  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1370  \quad \text{and }\
1371  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1372\]
1373
1374where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1375
1376\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a
1377reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1378\citep{breivik.bidlot.ea_OM16}:
1379
1380\[
1381  % \label{eq:SBC_wave_sdw_1}
1382  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1383  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1384\]
1385
1386where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1387
1388\item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1
1389but using the wave frequency from a wave model.
1390
1391\end{description}
1392
1393The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1394and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1395
1396\[
1397  % \label{eq:SBC_wave_eta_sdw}
1398  \frac{\partial{\eta}}{\partial{t}} =
1399  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1400\]
1401
1402The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1403for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1404that is induced by the three-dimensional Stokes velocity.
1405The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1406can be formulated as follows:
1407
1408\[
1409  % \label{eq:SBC_wave_tra_sdw}
1410  \frac{\partial{c}}{\partial{t}} =
1411  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1412\]
1413
1414
1415% ----------------------------------------------------------------
1416% Stokes-Coriolis term (ln_stcor)
1417% ----------------------------------------------------------------
1418\subsection[Stokes-Coriolis term (\texttt{ln\_stcor})]{Stokes-Coriolis term (\protect\np{ln\_stcor})}
1419\label{subsec:SBC_wave_stcor}
1420
1421In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1422in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1423This additional force may have impact on the Ekman turning of the surface current.
1424In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1425approximations described in \autoref{subsec:SBC_wave_sdw}),
1426\np{ln\_stcor}\forcode{=.true.} has to be set.
1427
1428
1429% ----------------------------------------------------------------
1430% Waves modified stress (ln_tauwoc, ln_tauw)
1431% ----------------------------------------------------------------
1432\subsection[Wave modified stress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})]{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}
1433\label{subsec:SBC_wave_tauw}
1434
1435The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1436into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1437available for forcing the mean circulation, while in the opposite case of a decaying sea
1438state, more momentum is available for forcing the ocean.
1439Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1440but in practice, an equilibrium sea state is a fairly rare event.
1441So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1442
1443\[
1444  % \label{eq:SBC_wave_tauoc}
1445  \tau_{oc,a} = \tau_a - \tau_w
1446\]
1447
1448where $\tau_a$ is the atmospheric surface stress;
1449$\tau_w$ is the atmospheric stress going into the waves defined as:
1450
1451\[
1452  % \label{eq:SBC_wave_tauw}
1453  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1454\]
1455
1456where: $c_p$ is the phase speed of the gravity waves,
1457$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1458the physics of ocean waves. The first one, $S_{in}$, describes the generation
1459of ocean waves by wind and therefore represents the momentum and energy transfer
1460from air to ocean waves; the second term $S_{nl}$ denotes
1461the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1462describes the dissipation of waves by processes such as white-capping, large scale breaking
1463eddy-induced damping.
1464
1465The wave stress derived from an external wave model can be provided either through the normalized
1466wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{=.true.}, or through the zonal and
1467meridional stress components by setting \np{ln\_tauw}\forcode{=.true.}.
1468
1469
1470
1471% ================================================================
1472% Miscellanea options
1473% ================================================================
1474\section{Miscellaneous options}
1475\label{sec:SBC_misc}
1476
1477
1478% -------------------------------------------------------------------------------------------------------------
1479%        Diurnal cycle
1480% -------------------------------------------------------------------------------------------------------------
1481\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1482\label{subsec:SBC_dcy}
1483%------------------------------------------namsbc-------------------------------------------------------------
1484%
1485\nlst{namsbc}
1486%-------------------------------------------------------------------------------------------------------------
1487
1488%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1489\begin{figure}[!t]
1490  \begin{center}
1491    \includegraphics[width=\textwidth]{Fig_SBC_diurnal}
1492    \caption{
1493      \protect\label{fig:SBC_diurnal}
1494      Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values.
1495      The reconstructed diurnal cycle (black line) is chosen as
1496      the mean value of the analytical cycle (blue line) over a time step,
1497      not as the mid time step value of the analytically cycle (red square).
1498      From \citet{bernie.guilyardi.ea_CD07}.
1499    }
1500  \end{center}
1501\end{figure}
1502%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1503
1504\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.
1505%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1506Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at high frequency \citep{bernie.guilyardi.ea_CD07}.
1507Furthermore, only the knowledge of daily mean value of SWF is needed,
1508as higher frequency variations can be reconstructed from them,
1509assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1510The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1511setting \np{ln\_dm2dc}\forcode{=.true.} (a \textit{\nam{sbc}} namelist variable) when
1512using a bulk formulation (\np{ln\_blk}\forcode{=.true.}) or
1513the flux formulation (\np{ln\_flx}\forcode{=.true.}).
1514The reconstruction is performed in the \mdl{sbcdcy} module.
1515The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1516The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1517a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1518The use of diurnal cycle reconstruction requires the input SWF to be daily
1519(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1520Furthermore, it is recommended to have a least 8 surface module time steps per day,
1521that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1522An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1523one every 2~hours (from 1am to 11pm).
1524
1525%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1526\begin{figure}[!t]
1527  \begin{center}
1528    \includegraphics[width=\textwidth]{Fig_SBC_dcy}
1529    \caption{
1530      \protect\label{fig:SBC_dcy}
1531      Example of recontruction of the diurnal cycle variation of short wave flux from
1532      daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1533      The display is on (i,j) plane.
1534    }
1535  \end{center}
1536\end{figure}
1537%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1538
1539Note also that the setting a diurnal cycle in SWF is highly recommended when
1540the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1541an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1542
1543
1544% -------------------------------------------------------------------------------------------------------------
1545%        Rotation of vector pairs onto the model grid directions
1546% -------------------------------------------------------------------------------------------------------------
1547\subsection{Rotation of vector pairs onto the model grid directions}
1548\label{subsec:SBC_rotation}
1549
1550When using a flux (\np{ln\_flx}\forcode{=.true.}) or bulk (\np{ln\_blk}\forcode{=.true.}) formulation,
1551pairs of vector components can be rotated from east-north directions onto the local grid directions.
1552This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1553be defined relative to a rectilinear grid.
1554To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1555The eastward component must start with "U" and the northward component with "V".
1556The remaining characters in the strings are used to identify which pair of components go together.
1557So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1558rotate them on to the model grid directions;
1559"U2" and "V2" could be used against a second pair of components, and so on.
1560The extra characters used in the strings are arbitrary.
1561The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1562
1563
1564% -------------------------------------------------------------------------------------------------------------
1565%        Surface restoring to observed SST and/or SSS
1566% -------------------------------------------------------------------------------------------------------------
1567\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1568\label{subsec:SBC_ssr}
1569%------------------------------------------namsbc_ssr----------------------------------------------------
1570
1571\nlst{namsbc_ssr}
1572%-------------------------------------------------------------------------------------------------------------
1573
1574Options are defined through the \nam{sbc\_ssr} namelist variables.
1575On forced mode using a flux formulation (\np{ln\_flx}\forcode{=.true.}),
1576a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1577\[
1578  % \label{eq:SBC_dmp_q}
1579  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1580\]
1581where SST is a sea surface temperature field (observed or climatological),
1582$T$ is the model surface layer temperature and
1583$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1584For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1585This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1586
1587In the fresh water budget, a feedback term can also be added.
1588Converted into an equivalent freshwater flux, it takes the following expression :
1589
1590\begin{equation}
1591  \label{eq:SBC_dmp_emp}
1592  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1593  {\left.S\right|_{k=1}}
1594\end{equation}
1595
1596where $\textit{emp}_{o }$ is a net surface fresh water flux
1597(observed, climatological or an atmospheric model product),
1598\textit{SSS}$_{Obs}$ is a sea surface salinity
1599(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1600$\left.S\right|_{k=1}$ is the model surface layer salinity and
1601$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1602Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1603the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1604The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1605reduce the uncertainties we have on the observed freshwater budget.
1606
1607
1608% -------------------------------------------------------------------------------------------------------------
1609%        Handling of ice-covered area
1610% -------------------------------------------------------------------------------------------------------------
1611\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1612\label{subsec:SBC_ice-cover}
1613
1614The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1615There are several way to handle sea-ice in the system depending on
1616the value of the \np{nn\_ice} namelist parameter found in \nam{sbc} namelist.
1617\begin{description}
1618\item[nn\_ice = 0]
1619  there will never be sea-ice in the computational domain.
1620  This is a typical namelist value used for tropical ocean domain.
1621  The surface fluxes are simply specified for an ice-free ocean.
1622  No specific things is done for sea-ice.
1623\item[nn\_ice = 1]
1624  sea-ice can exist in the computational domain, but no sea-ice model is used.
1625  An observed ice covered area is read in a file.
1626  Below this area, the SST is restored to the freezing point and
1627  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1628  The associated modification of the freshwater fluxes are done in such a way that
1629  the change in buoyancy fluxes remains zero.
1630  This prevents deep convection to occur when trying to reach the freezing point
1631  (and so ice covered area condition) while the SSS is too large.
1632  This manner of managing sea-ice area, just by using a IF case,
1633  is usually referred as the \textit{ice-if} model.
1634  It can be found in the \mdl{sbcice\_if} module.
1635\item[nn\_ice = 2 or more]
1636  A full sea ice model is used.
1637  This model computes the ice-ocean fluxes,
1638  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1639  provide the surface averaged ocean fluxes.
1640  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1641  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1642  (\ie\ $2$ for SI3 or $3$ for CICE).
1643\end{description}
1644
1645% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1646%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1647
1648
1649% -------------------------------------------------------------------------------------------------------------
1650%        CICE-ocean Interface
1651% -------------------------------------------------------------------------------------------------------------
1652\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1653\label{subsec:SBC_cice}
1654
1655It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1656to the CICE sea-ice model by using \key{cice}.
1657The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1658the additional 'hadgem3' drivers will be required, even with the latest code release.
1659Input grid files consistent with those used in \NEMO\ will also be needed,
1660and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1661(seek advice from UKMO if necessary).
1662Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1663(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1664or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1665(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1666The code is intended to be used with \np{nn\_fsbc} set to 1
1667(although coupling ocean and ice less frequently should work,
1668it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1669the user should check that results are not significantly different to the standard case).
1670
1671There are two options for the technical coupling between \NEMO\ and CICE.
1672The standard version allows complete flexibility for the domain decompositions in the individual models,
1673but this is at the expense of global gather and scatter operations in the coupling which
1674become very expensive on larger numbers of processors.
1675The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1676the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1677and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1678allows much more efficient direct coupling on individual processors.
1679This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1680there is no sea ice.
1681
1682
1683% -------------------------------------------------------------------------------------------------------------
1684%        Freshwater budget control
1685% -------------------------------------------------------------------------------------------------------------
1686\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1687\label{subsec:SBC_fwb}
1688
1689For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1690prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1691In \NEMO, two way of controlling the freshwater budget are proposed:
1692
1693\begin{description}
1694\item[\np{nn\_fwb}\forcode{=0}]
1695  no control at all.
1696  The mean sea level is free to drift, and will certainly do so.
1697\item[\np{nn\_fwb}\forcode{=1}]
1698  global mean \textit{emp} set to zero at each model time step.
1699  %GS: comment below still relevant ?
1700  %Note that with a sea-ice model, this technique only controls the mean sea level with linear free surface and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling).
1701\item[\np{nn\_fwb}\forcode{=2}]
1702  freshwater budget is adjusted from the previous year annual mean budget which
1703  is read in the \textit{EMPave\_old.dat} file.
1704  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1705  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1706\end{description}
1707
1708% Griffies doc:
1709% When running ocean-ice simulations, we are not explicitly representing land processes,
1710% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1711% it is important to balance the hydrological cycle in ocean-ice models.
1712% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1713% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1714% a chosen time scale.
1715% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1716% so that there is always a zero net input of water to the ocean-ice system.
1717% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1718% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1719% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1720% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1721% and ice models when aiming to balance the hydrological cycle.
1722% 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,
1723% not the water in any one sub-component. As an extreme example to illustrate the issue,
1724% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1725% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1726% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1727% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1728% in ocean-ice models.
1729
1730
1731\biblio
1732
1733\pindex
1734
1735\end{document}
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