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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\begin{listing}
17  \nlst{namsbc}
18  \caption{\texttt{namsbc}}
19  \label{lst:namsbc}
20\end{listing}
21%--------------------------------------------------------------------------------------------------------------
22
23The ocean needs seven fields as surface boundary condition:
24
25\begin{itemize}
26\item
27  the two components of the surface ocean stress $\left( {\tau_u \;,\;\tau_v} \right)$
28\item
29  the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
30\item
31  the surface freshwater budget $\left( {\textit{emp}} \right)$
32\item
33  the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$
34\item
35  the atmospheric pressure at the ocean surface $\left( p_a \right)$
36\end{itemize}
37
38Four different ways are available to provide the seven fields to the ocean. They are controlled by
39namelist \nam{sbc} variables:
40
41\begin{itemize}
42\item
43  a bulk formulation (\np{ln\_blk}\forcode{=.true.} with four possible bulk algorithms),
44\item
45  a flux formulation (\np{ln\_flx}\forcode{=.true.}),
46\item
47  a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler),
48(\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{=.true.}),
49\item
50  a user defined formulation (\np{ln\_usr}\forcode{=.true.}).
51\end{itemize}
52
53The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter.
54
55When the fields are supplied from data files (bulk, flux and mixed formulations),
56the input fields do not need to be supplied on the model grid.
57Instead, a file of coordinates and weights can be supplied to map the data from the input fields grid to
58the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}).
59If the "Interpolation on the Fly" option is used, input data belonging to land points (in the native grid)
60should be masked or filled to avoid spurious results in proximity of the coasts, as
61large sea-land gradients characterize most of the atmospheric variables.
62
63In addition, the resulting fields can be further modified using several namelist options.
64These options control:
65
66\begin{itemize}
67\item
68  the rotation of vector components supplied relative to an east-north coordinate system onto
69  the local grid directions in the model,
70\item
71  the use of a land/sea mask for input fields (\np{nn\_lsm}\forcode{=.true.}),
72\item
73  the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}\forcode{=.true.}),
74\item
75  the modification of fluxes below ice-covered areas (using climatological ice-cover or a sea-ice model)
76  (\np{nn\_ice}\forcode{=0..3}),
77\item
78  the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}\forcode{=.true.}),
79\item
80  the addition of ice-shelf melting as lateral inflow (parameterisation) or
81  as fluxes applied at the land-ice ocean interface (\np{ln\_isf}\forcode{=.true.}),
82\item
83  the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift
84  (\np{nn\_fwb}\forcode{=0..2}),
85\item
86  the transformation of the solar radiation (if provided as daily mean) into an analytical diurnal cycle
87  (\np{ln\_dm2dc}\forcode{=.true.}),
88\item
89  the activation of wave effects from an external wave model  (\np{ln\_wave}\forcode{=.true.}),
90\item
91  a neutral drag coefficient is read from an external wave model (\np{ln\_cdgw}\forcode{=.true.}),
92\item
93  the Stokes drift from an external wave model is accounted for (\np{ln\_sdw}\forcode{=.true.}),
94\item
95  the choice of the Stokes drift profile parameterization (\np{nn\_sdrift}\forcode{=0..2}),
96\item
97  the surface stress given to the ocean is modified by surface waves (\np{ln\_tauwoc}\forcode{=.true.}),
98\item
99  the surface stress given to the ocean is read from an external wave model (\np{ln\_tauw}\forcode{=.true.}),
100\item
101  the Stokes-Coriolis term is included (\np{ln\_stcor}\forcode{=.true.}),
102\item
103  the light penetration in the ocean (\np{ln\_traqsr}\forcode{=.true.} with namelist \nam{tra\_qsr}),
104\item
105  the atmospheric surface pressure gradient effect on ocean and ice dynamics (\np{ln\_apr\_dyn}\forcode{=.true.} with namelist \nam{sbc\_apr}),
106\item
107  the effect of sea-ice pressure on the ocean (\np{ln\_ice\_embd}\forcode{=.true.}).
108\end{itemize}
109
110In this chapter, we first discuss where the surface boundary conditions appear in the model equations.
111Then we present the three ways of providing the surface boundary conditions,
112followed by the description of the atmospheric pressure and the river runoff.
113Next, the scheme for interpolation on the fly is described.
114Finally, the different options that further modify the fluxes applied to the ocean are discussed.
115One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}),
116which act as drifting sources of fresh water.
117Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}),
118which provides additional sources of fresh water.
119
120
121
122% ================================================================
123% Surface boundary condition for the ocean
124% ================================================================
125\section{Surface boundary condition for the ocean}
126\label{sec:SBC_ocean}
127
128The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean.
129It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of
130the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}).
131As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh,
132\ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points.
133
134The surface heat flux is decomposed into two parts, a non solar and a solar heat flux,
135$Q_{ns}$ and $Q_{sr}$, respectively.
136The former is the non penetrative part of the heat flux
137(\ie\ the sum of sensible, latent and long wave heat fluxes plus
138the heat content of the mass exchange between the ocean and sea-ice).
139It is applied in \mdl{trasbc} module as a surface boundary condition trend of
140the first level temperature time evolution equation
141(see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}).
142The latter is the penetrative part of the heat flux.
143It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when
144\np{ln\_traqsr}\forcode{=.true.}.
145The way the light penetrates inside the water column is generally a sum of decreasing exponentials
146(see \autoref{subsec:TRA_qsr}).
147
148The surface freshwater budget is provided by the \textit{emp} field.
149It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and
150possibly with the sea-ice and ice shelves (freezing minus melting of ice).
151It affects the ocean in two different ways:
152$(i)$  it changes the volume of the ocean, and therefore appears in the sea surface height equation as      %GS: autoref ssh equation to be added
153a volume flux, and
154$(ii)$ it changes the surface temperature and salinity through the heat and salt contents of
155the mass exchanged with atmosphere, sea-ice and ice shelves.
156
157
158%\colorbox{yellow}{Miss: }
159%
160%A extensive description of all namsbc namelist (parameter that have to be
161%created!)
162%
163%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
164%ssv) \ie\ information required by flux computation or sea-ice
165%
166%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
167%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
168%
169%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
170%
171%Fluxes update only each nf\_sbc time step (namsbc) explain relation
172%between nf\_sbc and nf\_ice, do we define nf\_blk??? ? only one
173%nf\_sbc
174%
175%Explain here all the namlist namsbc variable{\ldots}.
176%
177% explain : use or not of surface currents
178%
179%\colorbox{yellow}{End Miss }
180
181The ocean model provides, at each time step, to the surface module (\mdl{sbcmod})
182the surface currents, temperature and salinity.
183These variables are averaged over \np{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and
184these averaged fields are used to compute the surface fluxes at the frequency of \np{nn\_fsbc} time-steps.
185
186
187%-------------------------------------------------TABLE---------------------------------------------------
188\begin{table}[tb]
189  \centering
190  \begin{tabular}{|l|l|l|l|}
191    \hline
192    Variable description                           & Model variable  & Units  & point                 \\
193    \hline
194    i-component of the surface current & ssu\_m               & $m.s^{-1}$     & U     \\
195    \hline
196    j-component of the surface current & ssv\_m               & $m.s^{-1}$     & V     \\
197    \hline
198    Sea surface temperature                  & sst\_m               & \r{}$K$              & T     \\\hline
199    Sea surface salinty                         & sss\_m               & $psu$              & T     \\   \hline
200  \end{tabular}
201  \caption[Ocean variables provided to the surface module)]{
202    Ocean variables provided to the surface module (\texttt{SBC}).
203    The variable are averaged over \protect\np{nn\_fsbc} time-step,
204    \ie\ the frequency of computation of surface fluxes.}
205  \label{tab:SBC_ssm}
206\end{table}
207%--------------------------------------------------------------------------------------------------------------
208
209%\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
210
211
212
213% ================================================================
214%       Input Data
215% ================================================================
216\section{Input data generic interface}
217\label{sec:SBC_input}
218
219A generic interface has been introduced to manage the way input data
220(2D or 3D fields, like surface forcing or ocean T and S) are specified in \NEMO.
221This task is achieved by \mdl{fldread}.
222The module is designed with four main objectives in mind:
223\begin{enumerate}
224\item
225  optionally provide a time interpolation of the input data every specified model time-step, whatever their input frequency is,
226  and according to the different calendars available in the model.
227\item
228  optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
229\item
230  make the run duration independent from the period cover by the input files.
231\item
232  provide a simple user interface and a rather simple developer interface by
233  limiting the number of prerequisite informations.
234\end{enumerate}
235
236As a result, the user has only to fill in for each variable a structure in the namelist file to
237define the input data file and variable names, the frequency of the data (in hours or months),
238whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
239and three additional parameters for the on-the-fly interpolation.
240When adding a new input variable, the developer has to add the associated structure in the namelist,
241read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example,
242and simply call \rou{fld\_read} to obtain the desired input field at the model time-step and grid points.
243
244The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
245(see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and,
246if on-the-fly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}).
247
248Note that when an input data is archived on a disc which is accessible directly from the workspace where
249the code is executed, then the user can set the \np{cn\_dir} to the pathway leading to the data.
250By default, the data are assumed to be in the same directory as the executable, so that cn\_dir='./'.
251
252
253% -------------------------------------------------------------------------------------------------------------
254% Input Data specification (\mdl{fldread})
255% -------------------------------------------------------------------------------------------------------------
256\subsection[Input data specification (\textit{fldread.F90})]
257{Input data specification (\protect\mdl{fldread})}
258\label{subsec:SBC_fldread}
259
260The structure associated with an input variable contains the following information:
261\begin{forlines}
262!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
263!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
264\end{forlines}
265where
266\begin{description}
267\item[File name]:
268  the stem name of the NetCDF file to be opened.
269  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and
270  by date information and possibly a prefix (when using AGRIF).
271  \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to
272  whether it is a climatological file or not, and to the open/close frequency (see below for definition).
273
274%--------------------------------------------------TABLE--------------------------------------------------
275  \begin{table}[htbp]
276    \centering
277    \begin{tabular}{|l|c|c|c|}
278      \hline
279                                  &  daily or weekLL     &  monthly           &  yearly        \\
280      \hline
281      \np{clim}\forcode{=.false.} &  fn\_yYYYYmMMdDD.nc  &  fn\_yYYYYmMM.nc   &  fn\_yYYYY.nc  \\
282      \hline
283      \np{clim}\forcode{=.true.}  &  not possible        &  fn\_m??.nc        &  fn            \\
284      \hline
285    \end{tabular}
286    \caption[Naming nomenclature for climatological or interannual input file]{
287      Naming nomenclature for climatological or interannual input file,
288      as a function of the open/close frequency.
289      The stem name is assumed to be 'fn'.
290      For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week
291      (\ie\ 'sun','sat','fri','thu','wed','tue','mon').
292      The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day,
293      always coded with 4 or 2 digits.
294      Note that (1) in mpp, if the file is split over each subdomain,
295      the suffix '.nc' is replaced by '\_PPPP.nc',
296      where 'PPPP' is the process number coded with 4 digits;
297      (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.
298    }
299    \label{tab:SBC_fldread}
300  \end{table}
301%--------------------------------------------------------------------------------------------------------------
302
303
304\item[Record frequency]:
305  the frequency of the records contained in the input file.
306  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
307  (for example -1 for monthly forcing or -12 for annual forcing).
308  Note that this frequency must REALLY be an integer and not a real.
309  On some computers, setting it to '24.' can be interpreted as 240!
310
311\item[Variable name]:
312  the name of the variable to be read in the input NetCDF file.
313
314\item[Time interpolation]:
315  a logical to activate, or not, the time interpolation.
316  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period.
317  For example, when using a daily forcing without time interpolation, the forcing remaining constant from
318  00h00'00'' to 23h59'59".
319  If set to 'true', the forcing will have a broken line shape.
320  Records are assumed to be dated at the middle of the forcing period.
321  For example, when using a daily forcing with time interpolation,
322  linear interpolation will be performed between mid-day of two consecutive days.
323
324\item[Climatological forcing]:
325  a logical to specify if a input file contains climatological forcing which can be cycle in time,
326  or an interannual forcing which will requires additional files if
327  the period covered by the simulation exceeds the one of the file.
328  See the above file naming strategy which impacts the expected name of the file to be opened.
329
330\item[Open/close frequency]:
331  the frequency at which forcing files must be opened/closed.
332  Four cases are coded:
333  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which
334  means the forcing files will contain data for one day, one week, one month or one year.
335  Files are assumed to contain data from the beginning of the open/close period.
336  For example, the first record of a yearly file containing daily data is Jan 1st even if
337  the experiment is not starting at the beginning of the year.
338
339\item[Others]:
340  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with
341  on-the-fly interpolation which is described in \autoref{subsec:SBC_iof}.
342
343\end{description}
344
345Additional remarks:\\
346(1) The time interpolation is a simple linear interpolation between two consecutive records of the input data.
347The only tricky point is therefore to specify the date at which we need to do the interpolation and
348the date of the records read in the input files.
349Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step.
350For example, for an experiment starting at 0h00'00" with a one-hour time-step,
351a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
352However, for forcing data related to the surface module,
353values are not needed at every time-step but at every \np{nn\_fsbc} time-step.
354For example with \np{nn\_fsbc}\forcode{=3}, the surface module will be called at time-steps 1, 4, 7, etc.
355The date used for the time interpolation is thus redefined to the middle of \np{nn\_fsbc} time-step period.
356In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
357(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar.
358The calendar associated with the forcing field is build according to the information provided by
359user in the record frequency, the open/close frequency and the type of temporal interpolation.
360For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to
361start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
362(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when
363interpolating data with the first (last) record of the open/close period.
364For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
365the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between
366Dec 31st 12h00'00" and Jan 1st 12h00'00".
367If the forcing is climatological, Dec and Jan will be keep-up from the same year.
368However, if the forcing is not climatological, at the end of
369the open/close period, the code will automatically close the current file and open the next one.
370Note that, if the experiment is starting (ending) at the beginning (end) of
371an open/close period, we do accept that the previous (next) file is not existing.
372In this case, the time interpolation will be performed between two identical values.
373For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated,
374we do accept that the file related to year Y-1 is not existing.
375The value of Jan 1st will be used as the missing one for Dec 31st of year Y-1.
376If the file of year Y-1 exists, the code will read its last record.
377Therefore, this file can contain only one record corresponding to Dec 31st,
378a useful feature for user considering that it is too heavy to manipulate the complete file for year Y-1.
379
380
381% -------------------------------------------------------------------------------------------------------------
382% Interpolation on the Fly
383% -------------------------------------------------------------------------------------------------------------
384\subsection{Interpolation on-the-fly}
385\label{subsec:SBC_iof}
386
387Interpolation on the Fly allows the user to supply input files required for the surface forcing on
388grids other than the model grid.
389To do this, he or she must supply, in addition to the source data file(s), a file of weights to be used to
390interpolate from the data grid to the model grid.
391The original development of this code used the SCRIP package
392(freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement).
393In principle, any package such as CDO can be used to generate the weights, but the variables in
394the input weights file must have the same names and meanings as assumed by the model.
395Two methods are currently available: bilinear and bicubic interpolations.
396Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from
397the input file and substitute the corresponding values with the average of the 8 neighbouring points in
398the native external grid.
399Only "sea points" are considered for the averaging.
400The land/sea mask file must be provided in the structure associated with the input variable.
401The netcdf land/sea mask variable name must be 'LSM' and must have the same horizontal and vertical dimensions as
402the associated variables and should be equal to 1 over land and 0 elsewhere.
403The procedure can be recursively applied by setting nn\_lsm > 1 in namsbc namelist.
404Note that nn\_lsm=0 forces the code to not apply the procedure, even if a land/sea mask file is supplied.
405
406
407% -------------------------------------------------------------------------------------------------------------
408% Bilinear interpolation
409% -------------------------------------------------------------------------------------------------------------
410\subsubsection{Bilinear interpolation}
411\label{subsec:SBC_iof_bilinear}
412
413The input weights file in this case has two sets of variables:
414src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04.
415The "src" variables correspond to the point in the input grid to which the weight "wgt" is applied.
416Each src value is an integer corresponding to the index of a point in the input grid when
417written as a one dimensional array.
418For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
419There are four of each variable because bilinear interpolation uses the four points defining
420the grid box containing the point to be interpolated.
421All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to
422generate a value for point (i,j) in the model.
423
424Symbolically, the algorithm used is:
425\[
426  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
427\]
428where function idx() transforms a one dimensional index src(k) into a two dimensional index,
429and wgt(1) corresponds to variable "wgt01" for example.
430
431
432% -------------------------------------------------------------------------------------------------------------
433% Bicubic interpolation
434% -------------------------------------------------------------------------------------------------------------
435\subsubsection{Bicubic interpolation}
436\label{subsec:SBC_iof_bicubic}
437
438Again, there are two sets of variables: "src" and "wgt".
439But in this case, there are 16 of each.
440The symbolic algorithm used to calculate values on the model grid is now:
441
442\[
443  \begin{split}
444    f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
445    +  \sum_{k=5 }^{8 } {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
446    +& \sum_{k=9 }^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
447    +  \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
448  \end{split}
449\]
450The gradients here are taken with respect to the horizontal indices and not distances since
451the spatial dependency has been included into the weights.
452
453
454% -------------------------------------------------------------------------------------------------------------
455% Implementation
456% -------------------------------------------------------------------------------------------------------------
457\subsubsection{Implementation}
458\label{subsec:SBC_iof_imp}
459
460To activate this option, a non-empty string should be supplied in
461the weights filename column of the relevant namelist;
462if this is left as an empty string no action is taken.
463In the model, weights files are read in and stored in a structured type (WGT) in the fldread module,
464as and when they are first required.
465This initialisation procedure determines whether the input data grid should be treated as cyclical or not by
466inspecting a global attribute stored in the weights input file.
467This attribute must be called "ew\_wrap" and be of integer type.
468If it is negative, the input non-model grid is assumed to be not cyclic.
469If zero or greater, then the value represents the number of columns that overlap.
470$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
471if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
472If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
473In this case, the \rou{fld\_read} routine defaults ew\_wrap to value 0 and
474therefore the grid is assumed to be cyclic with no overlapping columns.
475(In fact, this only matters when bicubic interpolation is required.)
476Note that no testing is done to check the validity in the model,
477since there is no way of knowing the name used for the longitude variable,
478so it is up to the user to make sure his or her data is correctly represented.
479
480Next the routine reads in the weights.
481Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used.
482The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid),
483and when required, for reading in the variable to be interpolated (on the input data grid).
484The size of the input data array is determined by examining the values in the "src" arrays to
485find the minimum and maximum i and j values required.
486Since bicubic interpolation requires the calculation of gradients at each point on the grid,
487the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
488When the array of points from the data file is adjacent to an edge of the data grid,
489the halo is either a copy of the row/column next to it (non-cyclical case),
490or is a copy of one from the first few columns on the opposite side of the grid (cyclical case).
491
492
493% -------------------------------------------------------------------------------------------------------------
494% Limitations
495% -------------------------------------------------------------------------------------------------------------
496\subsubsection{Limitations}
497\label{subsec:SBC_iof_lim}
498
499\begin{enumerate}
500\item
501  The case where input data grids are not logically rectangular (irregular grid case) has not been tested.
502\item
503  This code is not guaranteed to produce positive definite answers from positive definite inputs when
504  a bicubic interpolation method is used.
505\item
506  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
507\item
508  The gradients across the ends of a cyclical grid assume that the grid spacing between
509  the two columns involved are consistent with the weights used.
510\item
511  Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP,
512  but this has not been implemented.)
513\end{enumerate}
514
515\subsubsection{Utilities}
516\label{subsec:SBC_iof_util}
517
518% to be completed
519A set of utilities to create a weights file for a rectilinear input grid is available
520(see the directory NEMOGCM/TOOLS/WEIGHTS).
521
522
523% -------------------------------------------------------------------------------------------------------------
524% Standalone Surface Boundary Condition Scheme
525% -------------------------------------------------------------------------------------------------------------
526\subsection{Standalone surface boundary condition scheme (SAS)}
527\label{subsec:SBC_SAS}
528
529%---------------------------------------namsbc_sas--------------------------------------------------
530
531\begin{listing}
532  \nlst{namsbc_sas}
533  \caption{\texttt{namsbc\_sas}}
534  \label{lst:namsbc_sas}
535\end{listing}
536%--------------------------------------------------------------------------------------------------------------
537
538In some circumstances, it may be useful to avoid calculating the 3D temperature,
539salinity and velocity fields and simply read them in from a previous run or receive them from OASIS.
540For example:
541
542\begin{itemize}
543\item
544  Multiple runs of the model are required in code development to
545  see the effect of different algorithms in the bulk formulae.
546\item
547  The effect of different parameter sets in the ice model is to be examined.
548\item
549  Development of sea-ice algorithms or parameterizations.
550\item
551  Spinup of the iceberg floats
552\item
553  Ocean/sea-ice simulation with both models running in parallel (\np{ln\_mixcpl}\forcode{=.true.})
554\end{itemize}
555
556The Standalone Surface scheme provides this capacity.
557Its options are defined through the \nam{sbc\_sas} namelist variables.
558A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
559However, no namelist parameters need be changed from the settings of the previous run (except perhaps nn\_date0).
560In this configuration, a few routines in the standard model are overriden by new versions.
561Routines replaced are:
562
563\begin{itemize}
564\item
565  \mdl{nemogcm}:
566  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}).
567  Since the ocean state is not calculated all associated initialisations have been removed.
568\item
569  \mdl{step}:
570  The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
571\item
572  \mdl{sbcmod}:
573  This has been cut down and now only calculates surface forcing and the ice model required.
574  New surface modules that can function when only the surface level of the ocean state is defined can also be added
575  (\eg\ icebergs).
576\item
577  \mdl{daymod}:
578  No ocean restarts are read or written (though the ice model restarts are retained),
579  so calls to restart functions have been removed.
580  This also means that the calendar cannot be controlled by time in a restart file,
581  so the user must check that nn\_date0 in the model namelist is correct for his or her purposes.
582\item
583  \mdl{stpctl}:
584  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
585\item
586  \mdl{diawri}:
587  All 3D data have been removed from the output.
588  The surface temperature, salinity and velocity components (which have been read in) are written along with
589  relevant forcing and ice data.
590\end{itemize}
591
592One new routine has been added:
593
594\begin{itemize}
595\item
596  \mdl{sbcsas}:
597  This module initialises the input files needed for reading temperature, salinity and
598  velocity arrays at the surface.
599  These filenames are supplied in namelist namsbc\_sas.
600  Unfortunately, because of limitations with the \mdl{iom} module,
601  the full 3D fields from the mean files have to be read in and interpolated in time,
602  before using just the top level.
603  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
604\end{itemize}
605
606
607The 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
608 (\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.
609
610
611
612% ================================================================
613% Flux formulation
614% ================================================================
615\section[Flux formulation (\textit{sbcflx.F90})]
616{Flux formulation (\protect\mdl{sbcflx})}
617\label{sec:SBC_flx}
618%------------------------------------------namsbc_flx----------------------------------------------------
619
620\begin{listing}
621  \nlst{namsbc_flx}
622  \caption{\texttt{namsbc\_flx}}
623  \label{lst:namsbc_flx}
624\end{listing}
625%-------------------------------------------------------------------------------------------------------------
626
627In the flux formulation (\np{ln\_flx}\forcode{=.true.}),
628the surface boundary condition fields are directly read from input files.
629The user has to define in the namelist \nam{sbc\_flx} the name of the file,
630the name of the variable read in the file, the time frequency at which it is given (in hours),
631and a logical setting whether a time interpolation to the model time step is required for this field.
632See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters.
633
634Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS.
635See \autoref{subsec:SBC_ssr} for its specification.
636
637
638
639% ================================================================
640% Bulk formulation
641% ================================================================
642\section[Bulk formulation (\textit{sbcblk.F90})]
643{Bulk formulation (\protect\mdl{sbcblk})}
644\label{sec:SBC_blk}
645%---------------------------------------namsbc_blk--------------------------------------------------
646
647\begin{listing}
648  \nlst{namsbc_blk}
649  \caption{\texttt{namsbc\_blk}}
650  \label{lst:namsbc_blk}
651\end{listing}
652%--------------------------------------------------------------------------------------------------------------
653
654In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields
655and ocean (and sea-ice) variables averaged over \np{nn\_fsbc} time-step.
656
657The atmospheric fields used depend on the bulk formulae used.
658In forced mode, when a sea-ice model is used, a specific bulk formulation is used.
659Therefore, different bulk formulae are used for the turbulent fluxes computation
660over the ocean and over sea-ice surface.
661For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}):
662the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae.
663The choice is made by setting to true one of the following namelist variable:
664 \np{ln\_NCAR}, \np{ln\_COARE\_3p0}\np{ln\_COARE\_3p5} and  \np{ln\_ECMWF}.
665For sea-ice, three possibilities can be selected:
666a 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
667
668Common options are defined through the \nam{sbc\_blk} namelist variables.
669The required 9 input fields are:
670
671%--------------------------------------------------TABLE--------------------------------------------------
672\begin{table}[htbp]
673  \centering
674  \begin{tabular}{|l|c|c|c|}
675    \hline
676    Variable description                 & Model variable & Units              & point \\
677    \hline
678    i-component of the 10m air velocity  & utau           & $m.s^{-1}$         & T     \\
679    \hline
680    j-component of the 10m air velocity  & vtau           & $m.s^{-1}$         & T     \\
681    \hline
682    10m air temperature                  & tair           & \r{}$K$            & T     \\
683    \hline
684    Specific humidity                    & humi           & \%                 & T     \\
685    \hline
686    Incoming long wave radiation         & qlw            & $W.m^{-2}$         & T     \\
687    \hline
688    Incoming short wave radiation        & qsr            & $W.m^{-2}$         & T     \\
689    \hline
690    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\
691    \hline
692    Solid precipitation                  & snow           & $Kg.m^{-2}.s^{-1}$ & T     \\
693    \hline
694    Mean sea-level pressure              & slp            & $hPa$              & T     \\
695    \hline
696    \end{tabular}
697  \label{tab:SBC_BULK}
698\end{table}
699%--------------------------------------------------------------------------------------------------------------
700
701Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points).
702It is simpler and faster (less fields to be read), but it is not the recommended method when
703the ocean grid size is the same or larger than the one of the input atmospheric fields.
704
705The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, \np{sn\_prec},
706\np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used
707(spatial and temporal interpolations).
708
709\np{cn\_dir} is the directory of location of bulk files
710\np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.)
711\np{rn\_zqt}: is the height of humidity and temperature measurements (m)
712\np{rn\_zu}: is the height of wind measurements (m)
713
714Three multiplicative factors are available:
715\np{rn\_pfac} and \np{rn\_efac} allow to adjust (if necessary) the global freshwater budget by
716increasing/reducing the precipitations (total and snow) and or evaporation, respectively.
717The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in
718the calculation of surface wind stress.
719Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration).
720
721As for the flux formulation, information about the input data required by the model is provided in
722the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
723
724
725% -------------------------------------------------------------------------------------------------------------
726%        Ocean-Atmosphere Bulk formulae
727% -------------------------------------------------------------------------------------------------------------
728\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.F90,
729sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]
730{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5},
731\mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})}
732\label{subsec:SBC_blk_ocean}
733
734Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean.
735COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently
736their neutral transfer coefficients relationships with neutral wind.
737\begin{itemize}
738\item
739  NCAR (\np{ln\_NCAR}\forcode{=.true.}):
740  The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
741  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data.
742  They use an inertial dissipative method to compute the turbulent transfer coefficients
743  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity.
744  This \citet{large.yeager_rpt04} dataset is available through
745  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
746  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
747  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}.
748\item
749  COARE 3.0 (\np{ln\_COARE\_3p0}\forcode{=.true.}):
750  See \citet{fairall.bradley.ea_JC03} for more details
751\item
752  COARE 3.5 (\np{ln\_COARE\_3p5}\forcode{=.true.}):
753  See \citet{edson.jampana.ea_JPO13} for more details
754\item
755  ECMWF (\np{ln\_ECMWF}\forcode{=.true.}):
756  Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation.
757  Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}.
758\end{itemize}
759
760% -------------------------------------------------------------------------------------------------------------
761%        Ice-Atmosphere Bulk formulae
762% -------------------------------------------------------------------------------------------------------------
763\subsection{Ice-Atmosphere Bulk formulae}
764\label{subsec:SBC_blk_ice}
765
766Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
767
768\begin{itemize}
769\item
770  Constant value (\np{constant\ value}\forcode{ Cd_ice = 1.4e-3 }):
771  default constant value used for momentum and heat neutral transfer coefficients
772\item
773  \citet{lupkes.gryanik.ea_JGR12} (\np{ln\_Cd\_L12}\forcode{=.true.}):
774  This scheme adds a dependency on edges at leads, melt ponds and flows
775  of the constant neutral air-ice drag. After some approximations,
776  this can be resumed to a dependency on ice concentration (A).
777  This drag coefficient has a parabolic shape (as a function of ice concentration)
778  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.
779  It is theoretically applicable to all ice conditions (not only MIZ).
780\item
781  \citet{lupkes.gryanik_JGR15} (\np{ln\_Cd\_L15}\forcode{=.true.}):
782  Alternative turbulent transfer coefficients formulation between sea-ice
783  and atmosphere with distinct momentum and heat coefficients depending
784  on sea-ice concentration and atmospheric stability (no melt-ponds effect for now).
785  The parameterization is adapted from ECHAM6 atmospheric model.
786  Compared to Lupkes2012 scheme, it considers specific skin and form drags
787  to compute neutral transfer coefficients for both heat and momentum fluxes.
788  Atmospheric stability effect on transfer coefficient is also taken into account.
789\end{itemize}
790
791
792
793% ================================================================
794% Coupled formulation
795% ================================================================
796\section[Coupled formulation (\textit{sbccpl.F90})]
797{Coupled formulation (\protect\mdl{sbccpl})}
798\label{sec:SBC_cpl}
799%------------------------------------------namsbc_cpl----------------------------------------------------
800
801\begin{listing}
802  \nlst{namsbc_cpl}
803  \caption{\texttt{namsbc\_cpl}}
804  \label{lst:namsbc_cpl}
805\end{listing}
806%-------------------------------------------------------------------------------------------------------------
807
808In the coupled formulation of the surface boundary condition,
809the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler namelist,
810while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to
811the atmospheric component.
812
813A generalised coupled interface has been developed.
814It is currently interfaced with OASIS-3-MCT versions 1 to 4 (\key{oasis3}).
815An additional specific CPP key (\key{oa3mct\_v1v2}) is needed for OASIS-3-MCT versions 1 and 2.
816It has been successfully used to interface \NEMO\ to most of the European atmospheric GCM
817(ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrf-model.org/}{WRF}
818(Weather Research and Forecasting Model).
819
820When PISCES biogeochemical model (\key{top}) is also used in the coupled system,
821the whole carbon cycle is computed.
822In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system
823(and need to be activated in \nam{sbc\_cpl} ).
824
825The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and
826now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE).
827When indicating a multi-category coupling field in \nam{sbc\_cpl}, the number of categories will be determined by
828the number used in the sea ice model.
829In some limited cases, it may be possible to specify single category coupling fields even when
830the sea ice model is running with multiple categories -
831in this case, the user should examine the code to be sure the assumptions made are satisfactory.
832In cases where this is definitely not possible, the model should abort with an error message.
833
834
835
836% ================================================================
837%        Atmospheric pressure
838% ================================================================
839\section[Atmospheric pressure (\textit{sbcapr.F90})]
840{Atmospheric pressure (\protect\mdl{sbcapr})}
841\label{sec:SBC_apr}
842%------------------------------------------namsbc_apr----------------------------------------------------
843
844\begin{listing}
845  \nlst{namsbc_apr}
846  \caption{\texttt{namsbc\_apr}}
847  \label{lst:namsbc_apr}
848\end{listing}
849%-------------------------------------------------------------------------------------------------------------
850
851The optional atmospheric pressure can be used to force ocean and ice dynamics
852(\np{ln\_apr\_dyn}\forcode{=.true.}, \nam{sbc} namelist).
853The input atmospheric forcing defined via \np{sn\_apr} structure (\nam{sbc\_apr} namelist)
854can be interpolated in time to the model time step, and even in space when the interpolation on-the-fly is used.
855When used to force the dynamics, the atmospheric pressure is further transformed into
856an equivalent inverse barometer sea surface height, $\eta_{ib}$, using:
857\[
858  % \label{eq:SBC_ssh_ib}
859  \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
860\]
861where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
862A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true.
863In this case, $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain,
864\ie\ the mean value of $\eta_{ib}$ is kept to zero at all time steps.
865
866The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean).
867For sea-ice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta - \eta_{ib}$
868(see \mdl{sbcssr} module).
869$\eta_{ib}$ can be written in the output.
870This can simplify altimetry data and model comparison as
871inverse barometer sea surface height is usually removed from these date prior to their distribution.
872
873When using time-splitting and BDY package for open boundaries conditions,
874the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
875\np{ln\_apr\_obc}  might be set to true.
876
877
878
879% ================================================================
880%        Surface Tides Forcing
881% ================================================================
882\section[Surface tides (\textit{sbctide.F90})]
883{Surface tides (\protect\mdl{sbctide})}
884\label{sec:SBC_tide}
885
886%------------------------------------------nam_tide---------------------------------------
887
888\begin{listing}
889  \nlst{nam_tide}
890  \caption{\texttt{nam\_tide}}
891  \label{lst:nam_tide}
892\end{listing}
893%-----------------------------------------------------------------------------------------
894
895The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems,
896is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{\_tide}.
897This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that:
898\[
899  % \label{eq:SBC_PE_dyn_tides}
900  \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ...
901  +g\nabla (\Pi_{eq} + \Pi_{sal})
902\]
903where $\Pi_{eq}$ stands for the equilibrium tidal forcing and
904$\Pi_{sal}$ is a self-attraction and loading term (SAL).
905
906The equilibrium tidal forcing is expressed as a sum over a subset of
907constituents chosen from the set of available tidal constituents
908defined in file \hf{SBC/tide} (this comprises the tidal
909constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm,
910  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual
911constituents are selected by including their names in the array
912\np{clname} in \nam{\_tide} (e.g., \np{clname}\forcode{(1)='M2', }
913\np{clname}\forcode{(2)='S2'} to select solely the tidal consituents \textit{M2}
914and \textit{S2}). Optionally, when \np{ln\_tide\_ramp} is set to
915\forcode{.true.}, the equilibrium tidal forcing can be ramped up
916linearly from zero during the initial \np{rdttideramp} days of the
917model run.
918
919The SAL term should in principle be computed online as it depends on
920the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a
921discussion about the practical implementation of this term).
922Nevertheless, the complex calculations involved would make this
923computationally too expensive. Here, two options are available:
924$\Pi_{sal}$ generated by an external model can be read in
925(\np{ln\_read\_load}\forcode{ =.true.}), or a ``scalar approximation'' can be
926used (\np{ln\_scal\_load}\forcode{ =.true.}). In the latter case
927\[
928  \Pi_{sal} = \beta \eta,
929\]
930where $\beta$ (\np{rn\_scal\_load} with a default value of 0.094) is a
931spatially constant scalar, often chosen to minimize tidal prediction
932errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to
933\forcode{.false.} removes the SAL contribution.
934
935
936
937% ================================================================
938%        River runoffs
939% ================================================================
940\section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})}
941\label{sec:SBC_rnf}
942%------------------------------------------namsbc_rnf----------------------------------------------------
943
944\begin{listing}
945  \nlst{namsbc_rnf}
946  \caption{\texttt{namsbc\_rnf}}
947  \label{lst:namsbc_rnf}
948\end{listing}
949%-------------------------------------------------------------------------------------------------------------
950
951%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
952%Many models, however, have traditionally inserted river runoff to the top model cell.
953%This was the case in \NEMO\ prior to the version 3.3. The switch toward a input of runoff
954%throughout a nonzero depth has been motivated by the numerical and physical problems
955%that arise when the top grid cells are of the order of one meter. This situation is common in
956%coastal modelling and becomes more and more often open ocean and climate modelling
957%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
958%required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}.
959
960
961%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
962%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
963%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
964%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
965%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
966%emp or emps and the changes made are below:
967
968
969%Rachel:
970River runoff generally enters the ocean at a nonzero depth rather than through the surface.
971Many models, however, have traditionally inserted river runoff to the top model cell.
972This was the case in \NEMO\ prior to the version 3.3,
973and was combined with an option to increase vertical mixing near the river mouth.
974
975However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter.
976This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling
977\footnote{
978  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to
979  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}.
980  see also \autoref{fig:SBC_dcy}.}.
981
982As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth,
983and for the temperature and salinity of the river to effect the surrounding ocean.
984The user is able to specify, in a NetCDF input file, the temperature and salinity of the river,
985along with the depth (in metres) which the river should be added to.
986
987Namelist variables in \nam{sbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and
988\np{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used.
989If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu),
990and/or taken as surface temperature respectively.
991
992The runoff value and attributes are read in in sbcrnf.
993For temperature -999 is taken as missing data and the river temperature is taken to
994be the surface temperatue at the river point.
995For the depth parameter a value of -1 means the river is added to the surface box only,
996and a value of -999 means the river is added through the entire water column.
997After being read in the temperature and salinity variables are multiplied by the amount of runoff
998(converted into m/s) to give the heat and salt content of the river runoff.
999After the user specified depth is read ini,
1000the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz\_rnf}.
1001The variable \textit{h\_dep} is then calculated to be the depth (in metres) of
1002the bottom of the lowest box the river water is being added to
1003(\ie\ the total depth that river water is being added to in the model).
1004
1005The mass/volume addition due to the river runoff is, at each relevant depth level, added to
1006the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divhor}).
1007This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
1008The sea surface height is calculated using the sum of the horizontal divergence terms,
1009and so the river runoff indirectly forces an increase in sea surface height.
1010
1011The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
1012This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
1013The heat and salt content of the river runoff is not included in this step,
1014and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of
1015the box and replaced by the same volume of river water with no corresponding heat and salt addition.
1016
1017For the linear free surface case, at the surface box the tracer advection causes a flux of water
1018(of equal volume to the runoff) through the sea surface out of the domain,
1019which causes a salt and heat flux out of the model.
1020As such the volume of water does not change, but the water is diluted.
1021
1022For the non-linear free surface case, no flux is allowed through the surface.
1023Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with
1024no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
1025(The runoff addition to the top box along with the water being moved up through
1026boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size)
1027
1028In trasbc the addition of heat and salt due to the river runoff is added.
1029This is done in the same way for both vvl and non-vvl.
1030The temperature and salinity are increased through the specified depth according to
1031the heat and salt content of the river.
1032
1033In the non-linear free surface case (vvl),
1034near the end of the time step the change in sea surface height is redistrubuted through the grid boxes,
1035so that the original ratios of grid box heights are restored.
1036In doing this water is moved into boxes below, throughout the water column,
1037so the large volume addition to the surface box is spread between all the grid boxes.
1038
1039It is also possible for runnoff to be specified as a negative value for modelling flow through straits,
1040\ie\ modelling the Baltic flow in and out of the North Sea.
1041When the flow is out of the domain there is no change in temperature and salinity,
1042regardless of the namelist options used,
1043as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
1044
1045
1046%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
1047
1048%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
1049
1050%\colorbox{yellow}{river mouths{\ldots}}
1051
1052%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
1053%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
1054%ENDIF
1055
1056%\gmcomment{  word doc of runoffs:
1057%
1058%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.
1059%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.
1060
1061%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
1062
1063%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:
1064
1065
1066
1067% ================================================================
1068%        Ice shelf melting
1069% ================================================================
1070\section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})}
1071\label{sec:SBC_isf}
1072%------------------------------------------namsbc_isf----------------------------------------------------
1073
1074\begin{listing}
1075  \nlst{namsbc_isf}
1076  \caption{\texttt{namsbc\_isf}}
1077  \label{lst:namsbc_isf}
1078\end{listing}
1079%--------------------------------------------------------------------------------------------------------
1080
1081The namelist variable in \nam{sbc}, \np{nn\_isf}, controls the ice shelf representation.
1082Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}.
1083The different options are illustrated in \autoref{fig:SBC_isf}.
1084
1085\begin{description}
1086
1087  \item[\np{nn\_isf}\forcode{=1}]:
1088  The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{=.true.} needed).
1089  The fwf and heat flux are depending of the local water properties.
1090
1091  Two different bulk formulae are available:
1092
1093   \begin{description}
1094   \item[\np{nn\_isfblk}\forcode{=1}]:
1095     The melt rate is based on a balance between the upward ocean heat flux and
1096     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
1097   \item[\np{nn\_isfblk}\forcode{=2}]:
1098     The melt rate and the heat flux are based on a 3 equations formulation
1099     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
1100     A complete description is available in \citet{jenkins_JGR91}.
1101   \end{description}
1102
1103     Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}.
1104     Its thickness is defined by \np{rn\_hisf\_tbl}.
1105     The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m.
1106     Then, the fluxes are spread over the same thickness (ie over one or several cells).
1107     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.
1108     This can lead to super-cool temperature in the top cell under melting condition.
1109     If \np{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\
1110
1111     Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice.
1112     There are 3 different ways to compute the exchange coeficient:
1113   \begin{description}
1114        \item[\np{nn\_gammablk}\forcode{=0}]:
1115     The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}.
1116     \begin{gather*}
1117       % \label{eq:SBC_isf_gamma_iso}
1118       \gamma^{T} = rn\_gammat0 \\
1119       \gamma^{S} = rn\_gammas0
1120     \end{gather*}
1121     This is the recommended formulation for ISOMIP.
1122   \item[\np{nn\_gammablk}\forcode{=1}]:
1123     The salt and heat exchange coefficients are velocity dependent and defined as
1124     \begin{gather*}
1125       \gamma^{T} = rn\_gammat0 \times u_{*} \\
1126       \gamma^{S} = rn\_gammas0 \times u_{*}
1127     \end{gather*}
1128     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters).
1129     See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application.
1130   \item[\np{nn\_gammablk}\forcode{=2}]:
1131     The salt and heat exchange coefficients are velocity and stability dependent and defined as:
1132\[
1133\gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}
1134\]
1135     where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters),
1136     $\Gamma_{Turb}$ the contribution of the ocean stability and
1137     $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion.
1138     See \citet{holland.jenkins_JPO99} for all the details on this formulation.
1139     This formulation has not been extensively tested in \NEMO\ (not recommended).
1140   \end{description}
1141  \item[\np{nn\_isf}\forcode{=2}]:
1142   The ice shelf cavity is not represented.
1143   The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting.
1144   The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL)
1145   (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front
1146   (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{=3}).
1147   The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
1148  \item[\np{nn\_isf}\forcode{=3}]:
1149   The ice shelf cavity is not represented.
1150   The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between
1151   the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and
1152   the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
1153   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1154  \item[\np{nn\_isf}\forcode{=4}]:
1155   The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{=.true.} needed).
1156   However, the fwf is not computed but specified from file \np{sn\_fwfisf}).
1157   The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.
1158   As in \np{nn\_isf}\forcode{=1}, the fluxes are spread over the top boundary layer thickness (\np{rn\_hisf\_tbl})\\
1159\end{description}
1160
1161$\bullet$ \np{nn\_isf}\forcode{=1} and \np{nn\_isf}\forcode{=2} compute a melt rate based on
1162the water mass properties, ocean velocities and depth.
1163This flux is thus highly dependent of the model resolution (horizontal and vertical),
1164realism of the water masses onto the shelf ...\\
1165
1166$\bullet$ \np{nn\_isf}\forcode{=3} and \np{nn\_isf}\forcode{=4} read the melt rate from a file.
1167You have total control of the fwf forcing.
1168This can be useful if the water masses on the shelf are not realistic or
1169the resolution (horizontal/vertical) are too coarse to have realistic melting or
1170for studies where you need to control your heat and fw input.\\
1171
1172The ice shelf melt is implemented as a volume flux as for the runoff.
1173The fw addition due to the ice shelf melting is, at each relevant depth level, added to
1174the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
1175See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
1176
1177%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1178\begin{figure}[!t]
1179  \centering
1180  \includegraphics[width=0.66\textwidth]{Fig_SBC_isf}
1181  \caption[Ice shelf location and fresh water flux definition]{
1182    Illustration of the location where the fwf is injected and
1183    whether or not the fwf is interactif or not depending of \protect\np{nn\_isf}.}
1184  \label{fig:SBC_isf}
1185\end{figure}
1186%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1187
1188
1189
1190% ================================================================
1191%        Ice sheet coupling
1192% ================================================================
1193\section{Ice sheet coupling}
1194\label{sec:SBC_iscpl}
1195%------------------------------------------namsbc_iscpl----------------------------------------------------
1196
1197\begin{listing}
1198  \nlst{namsbc_iscpl}
1199  \caption{\texttt{namsbc\_iscpl}}
1200  \label{lst:namsbc_iscpl}
1201\end{listing}
1202%--------------------------------------------------------------------------------------------------------
1203
1204Ice sheet/ocean coupling is done through file exchange at the restart step.
1205At each restart step:
1206
1207\begin{description}
1208\item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file.
1209\item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools.
1210\item[Step 3]: \NEMO\ run for a specific period and output the average melt rate over the period.
1211\item[Step 4]: the ice sheet model run using the melt rate outputed in step 4.
1212\item[Step 5]: go back to 1.
1213\end{description}
1214
1215If \np{ln\_iscpl}\forcode{=.true.}, the isf draft is assume to be different at each restart step with
1216potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics.
1217The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases:
1218
1219\begin{description}
1220\item[Thin a cell down]:
1221  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant
1222  ($bt_b=bt_n$).
1223\item[Enlarge  a cell]:
1224  See case "Thin a cell down"
1225\item[Dry a cell]:
1226  mask, T/S, U/V and ssh are set to 0.
1227  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$).
1228\item[Wet a cell]:
1229  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0.
1230  If no neighbours, T/S is extrapolated from old top cell value.
1231  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0.
1232\item[Dry a column]:
1233   mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0.
1234\item[Wet a column]:
1235  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0.
1236  If no neighbour, T/S/U/V and mask set to 0.
1237\end{description}
1238
1239Furthermore, as the before and now fields are not compatible (modification of the geometry),
1240the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\
1241
1242The horizontal extrapolation to fill new cell with realistic value is called \np{nn\_drown} times.
1243It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps,
1244the code will be unable to fill all the new wet cells properly.
1245The default number is set up for the MISOMIP idealised experiments.
1246This coupling procedure is able to take into account grounding line and calving front migration.
1247However, it is a non-conservative processe.
1248This could lead to a trend in heat/salt content and volume.\\
1249
1250In order to remove the trend and keep the conservation level as close to 0 as possible,
1251a simple conservation scheme is available with \np{ln\_hsb}\forcode{=.true.}.
1252The heat/salt/vol. gain/loss is diagnosed, as well as the location.
1253A correction increment is computed and apply each time step during the next \np{rn\_fiscpl} time steps.
1254For safety, it is advised to set \np{rn\_fiscpl} equal to the coupling period (smallest increment possible).
1255The 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).
1256
1257
1258
1259% ================================================================
1260%        Handling of icebergs
1261% ================================================================
1262\section{Handling of icebergs (ICB)}
1263\label{sec:SBC_ICB_icebergs}
1264%------------------------------------------namberg----------------------------------------------------
1265
1266\begin{listing}
1267  \nlst{namberg}
1268  \caption{\texttt{namberg}}
1269  \label{lst:namberg}
1270\end{listing}
1271%-------------------------------------------------------------------------------------------------------------
1272
1273Icebergs are modelled as lagrangian particles in \NEMO\ \citep{marsh.ivchenko.ea_GMD15}.
1274Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ).
1275(Note that the authors kindly provided a copy of their code to act as a basis for implementation in \NEMO).
1276Icebergs are initially spawned into one of ten classes which have specific mass and thickness as
1277described in the \nam{berg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1278Each class has an associated scaling (\np{rn\_mass\_scaling}),
1279which is an integer representing how many icebergs of this class are being described as one lagrangian point
1280(this reduces the numerical problem of tracking every single iceberg).
1281They are enabled by setting \np{ln\_icebergs}\forcode{=.true.}.
1282
1283Two initialisation schemes are possible.
1284\begin{description}
1285\item[\np{nn\_test\_icebergs}~$>$~0]
1286  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1287  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of
1288  which an iceberg is generated at the beginning of the run.
1289  (Note that this happens each time the timestep equals \np{nn\_nit000}.)
1290  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of
1291  the geographical box: lonmin,lonmax,latmin,latmax
1292\item[\np{nn\_test\_icebergs}\forcode{=-1}]
1293  In this scheme, the model reads a calving file supplied in the \np{sn\_icb} parameter.
1294  This should be a file with a field on the configuration grid (typically ORCA)
1295  representing ice accumulation rate at each model point.
1296  These should be ocean points adjacent to land where icebergs are known to calve.
1297  Most points in this input grid are going to have value zero.
1298  When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1299  At each time step, a test is performed to see if there is enough ice mass to
1300  calve an iceberg of each class in order (1 to 10).
1301  Note that this is the initial mass multiplied by the number each particle represents (\ie\ the scaling).
1302  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1303\end{description}
1304
1305Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1306The latter act to disintegrate the iceberg.
1307This is either all melted freshwater,
1308or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1309which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1310Melt water (and other variables on the configuration grid) are written into the main \NEMO\ model output files.
1311
1312Extensive diagnostics can be produced.
1313Separate output files are maintained for human-readable iceberg information.
1314A separate file is produced for each processor (independent of \np{ln\_ctl}).
1315The amount of information is controlled by two integer parameters:
1316\begin{description}
1317\item[\np{nn\_verbose\_level}] takes a value between one and four and
1318  represents an increasing number of points in the code at which variables are written,
1319  and an increasing level of obscurity.
1320\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1321\end{description}
1322
1323Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1324A non-zero value represents how many timesteps between writes of information into the output file.
1325These output files are in NETCDF format.
1326When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1327Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1328So care is needed to recreate data for individual icebergs,
1329since its trajectory data may be spread across multiple files.
1330
1331
1332
1333% =============================================================================================================
1334%        Interactions with waves (sbcwave.F90, ln_wave)
1335% =============================================================================================================
1336\section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})}
1337\label{sec:SBC_wave}
1338%------------------------------------------namsbc_wave--------------------------------------------------------
1339
1340\begin{listing}
1341  \nlst{namsbc_wave}
1342  \caption{\texttt{namsbc\_wave}}
1343  \label{lst:namsbc_wave}
1344\end{listing}
1345%-------------------------------------------------------------------------------------------------------------
1346
1347Ocean waves represent the interface between the ocean and the atmosphere, so \NEMO\ is extended to incorporate
1348physical processes related to ocean surface waves, namely the surface stress modified by growth and
1349dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and
1350tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate
1351the wind stress.
1352
1353Physical processes related to ocean surface waves can be accounted by setting the logical variable
1354\np{ln\_wave}\forcode{=.true.} in \nam{sbc} namelist. In addition, specific flags accounting for
1355different processes should be activated as explained in the following sections.
1356
1357Wave fields can be provided either in forced or coupled mode:
1358\begin{description}
1359\item[forced mode]: wave fields should be defined through the \nam{sbc\_wave} namelist
1360for external data names, locations, frequency, interpolation and all the miscellanous options allowed by
1361Input Data generic Interface (see \autoref{sec:SBC_input}).
1362\item[coupled mode]: \NEMO\ and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.}
1363in \nam{sbc} namelist and filling the \nam{sbc\_cpl} namelist.
1364\end{description}
1365
1366
1367% ----------------------------------------------------------------
1368% Neutral drag coefficient from wave model (ln_cdgw)
1369
1370% ----------------------------------------------------------------
1371\subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})}
1372\label{subsec:SBC_wave_cdgw}
1373
1374The neutral surface drag coefficient provided from an external data source (\ie\ a wave model),
1375can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \nam{sbc} namelist.
1376Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
1377the drag coefficient is computed according to the stable/unstable conditions of the
1378air-sea interface following \citet{large.yeager_rpt04}.
1379
1380
1381% ----------------------------------------------------------------
1382% 3D Stokes Drift (ln_sdw, nn_sdrift)
1383% ----------------------------------------------------------------
1384\subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})]{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})}
1385\label{subsec:SBC_wave_sdw}
1386
1387The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}.
1388It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)
1389and the current measured at a fixed point (Eulerian velocity).
1390As waves travel, the water particles that make up the waves travel in orbital motions but
1391without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly
1392at the bottom, so the result is a net forward motion of water particles, referred to as the Stokes drift.
1393An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved
1394representation of surface physics in ocean general circulation models. %GS: reference needed
1395The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as:
1396
1397\[
1398  % \label{eq:SBC_wave_sdw}
1399  \mathbf{U}_{st} = \frac{16{\pi^3}} {g}
1400  \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3}
1401  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f
1402\]
1403
1404where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,
1405$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,
1406$k$ is the mean wavenumber defined as:
1407$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\
1408
1409In order to evaluate the Stokes drift in a realistic ocean wave field, the wave spectral shape is required
1410and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.
1411To simplify, it is customary to use approximations to the full Stokes profile.
1412Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile
1413are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift
1414$\mathbf{U}_{st |_{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra
1415and makes possible the estimation of the surface Stokes drift for random directional waves in
1416realistic wave conditions:
1417
1418\begin{description}
1419\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by
1420\citet{breivik.janssen.ea_JPO14}:
1421
1422\[
1423  % \label{eq:SBC_wave_sdw_0a}
1424  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez}
1425\]
1426
1427where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows:
1428
1429\[
1430  % \label{eq:SBC_wave_sdw_0b}
1431  k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}
1432  \quad \text{and }\
1433  T_{st} = \frac{1}{16} \bar{\omega} H_s^2
1434\]
1435
1436where $H_s$ is the significant wave height and $\omega$ is the wave frequency.
1437
1438\item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a
1439reasonable estimate of the part of the spectrum mostly contributing to the Stokes drift velocity near the surface
1440\citep{breivik.bidlot.ea_OM16}:
1441
1442\[
1443  % \label{eq:SBC_wave_sdw_1}
1444  \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz}
1445  \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big]
1446\]
1447
1448where $erf$ is the complementary error function and $k_p$ is the peak wavenumber.
1449
1450\item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1
1451but using the wave frequency from a wave model.
1452
1453\end{description}
1454
1455The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations
1456and its effect on the evolution of the sea-surface height ${\eta}$ is considered as follows:
1457
1458\[
1459  % \label{eq:SBC_wave_eta_sdw}
1460  \frac{\partial{\eta}}{\partial{t}} =
1461  -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz
1462\]
1463
1464The tracer advection equation is also modified in order for Eulerian ocean models to properly account
1465for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection
1466that is induced by the three-dimensional Stokes velocity.
1467The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves
1468can be formulated as follows:
1469
1470\[
1471  % \label{eq:SBC_wave_tra_sdw}
1472  \frac{\partial{c}}{\partial{t}} =
1473  - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c}
1474\]
1475
1476
1477% ----------------------------------------------------------------
1478% Stokes-Coriolis term (ln_stcor)
1479% ----------------------------------------------------------------
1480\subsection[Stokes-Coriolis term (\texttt{ln\_stcor})]{Stokes-Coriolis term (\protect\np{ln\_stcor})}
1481\label{subsec:SBC_wave_stcor}
1482
1483In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results
1484in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.
1485This additional force may have impact on the Ekman turning of the surface current.
1486In order to include this term, once evaluated the Stokes drift (using one of the 3 possible
1487approximations described in \autoref{subsec:SBC_wave_sdw}),
1488\np{ln\_stcor}\forcode{=.true.} has to be set.
1489
1490
1491% ----------------------------------------------------------------
1492% Waves modified stress (ln_tauwoc, ln_tauw)
1493% ----------------------------------------------------------------
1494\subsection[Wave modified stress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})]{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}
1495\label{subsec:SBC_wave_tauw}
1496
1497The surface stress felt by the ocean is the atmospheric stress minus the net stress going
1498into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
1499available for forcing the mean circulation, while in the opposite case of a decaying sea
1500state, more momentum is available for forcing the ocean.
1501Only when the sea state is in equilibrium, the ocean is forced by the atmospheric stress,
1502but in practice, an equilibrium sea state is a fairly rare event.
1503So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as:
1504
1505\[
1506  % \label{eq:SBC_wave_tauoc}
1507  \tau_{oc,a} = \tau_a - \tau_w
1508\]
1509
1510where $\tau_a$ is the atmospheric surface stress;
1511$\tau_w$ is the atmospheric stress going into the waves defined as:
1512
1513\[
1514  % \label{eq:SBC_wave_tauw}
1515  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})}
1516\]
1517
1518where: $c_p$ is the phase speed of the gravity waves,
1519$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent
1520the physics of ocean waves. The first one, $S_{in}$, describes the generation
1521of ocean waves by wind and therefore represents the momentum and energy transfer
1522from air to ocean waves; the second term $S_{nl}$ denotes
1523the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$
1524describes the dissipation of waves by processes such as white-capping, large scale breaking
1525eddy-induced damping.
1526
1527The wave stress derived from an external wave model can be provided either through the normalized
1528wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{=.true.}, or through the zonal and
1529meridional stress components by setting \np{ln\_tauw}\forcode{=.true.}.
1530
1531
1532
1533% ================================================================
1534% Miscellanea options
1535% ================================================================
1536\section{Miscellaneous options}
1537\label{sec:SBC_misc}
1538
1539
1540% -------------------------------------------------------------------------------------------------------------
1541%        Diurnal cycle
1542% -------------------------------------------------------------------------------------------------------------
1543\subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})}
1544\label{subsec:SBC_dcy}
1545%------------------------------------------namsbc-------------------------------------------------------------
1546%
1547
1548%-------------------------------------------------------------------------------------------------------------
1549
1550%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1551\begin{figure}[!t]
1552  \centering
1553  \includegraphics[width=0.66\textwidth]{Fig_SBC_diurnal}
1554  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{
1555    Example of reconstruction of the diurnal cycle variation of short wave flux from
1556    daily mean values.
1557    The reconstructed diurnal cycle (black line) is chosen as
1558    the mean value of the analytical cycle (blue line) over a time step,
1559    not as the mid time step value of the analytically cycle (red square).
1560    From \citet{bernie.guilyardi.ea_CD07}.}
1561  \label{fig:SBC_diurnal}
1562\end{figure}
1563%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1564
1565\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.
1566%Unfortunately high frequency forcing fields are rare, not to say inexistent. GS: not true anymore !
1567Nevertheless, 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}.
1568Furthermore, only the knowledge of daily mean value of SWF is needed,
1569as higher frequency variations can be reconstructed from them,
1570assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF.
1571The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO\ by
1572setting \np{ln\_dm2dc}\forcode{=.true.} (a \textit{\nam{sbc}} namelist variable) when
1573using a bulk formulation (\np{ln\_blk}\forcode{=.true.}) or
1574the flux formulation (\np{ln\_flx}\forcode{=.true.}).
1575The reconstruction is performed in the \mdl{sbcdcy} module.
1576The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}.
1577The algorithm preserves the daily mean incoming SWF as the reconstructed SWF at
1578a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}).
1579The use of diurnal cycle reconstruction requires the input SWF to be daily
1580(\ie\ a frequency of 24 hours and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1581Furthermore, it is recommended to have a least 8 surface module time steps per day,
1582that is  $\rdt \ nn\_fsbc < 10,800~s = 3~h$.
1583An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle,
1584one every 2~hours (from 1am to 11pm).
1585
1586%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1587\begin{figure}[!t]
1588  \centering
1589  \includegraphics[width=0.66\textwidth]{Fig_SBC_dcy}
1590  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{
1591    Example of reconstruction of the diurnal cycle variation of short wave flux from
1592    daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1593    The display is on (i,j) plane.}
1594  \label{fig:SBC_dcy}
1595\end{figure}
1596%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1597
1598Note also that the setting a diurnal cycle in SWF is highly recommended when
1599the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to
1600an inconsistency between the scale of the vertical resolution and the forcing acting on that scale.
1601
1602
1603% -------------------------------------------------------------------------------------------------------------
1604%        Rotation of vector pairs onto the model grid directions
1605% -------------------------------------------------------------------------------------------------------------
1606\subsection{Rotation of vector pairs onto the model grid directions}
1607\label{subsec:SBC_rotation}
1608
1609When using a flux (\np{ln\_flx}\forcode{=.true.}) or bulk (\np{ln\_blk}\forcode{=.true.}) formulation,
1610pairs of vector components can be rotated from east-north directions onto the local grid directions.
1611This is particularly useful when interpolation on the fly is used since here any vectors are likely to
1612be defined relative to a rectilinear grid.
1613To activate this option, a non-empty string is supplied in the rotation pair column of the relevant namelist.
1614The eastward component must start with "U" and the northward component with "V".
1615The remaining characters in the strings are used to identify which pair of components go together.
1616So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and
1617rotate them on to the model grid directions;
1618"U2" and "V2" could be used against a second pair of components, and so on.
1619The extra characters used in the strings are arbitrary.
1620The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1621
1622
1623% -------------------------------------------------------------------------------------------------------------
1624%        Surface restoring to observed SST and/or SSS
1625% -------------------------------------------------------------------------------------------------------------
1626\subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})}
1627\label{subsec:SBC_ssr}
1628%------------------------------------------namsbc_ssr----------------------------------------------------
1629
1630\begin{listing}
1631  \nlst{namsbc_ssr}
1632  \caption{\texttt{namsbc\_ssr}}
1633  \label{lst:namsbc_ssr}
1634\end{listing}
1635%-------------------------------------------------------------------------------------------------------------
1636
1637Options are defined through the \nam{sbc\_ssr} namelist variables.
1638On forced mode using a flux formulation (\np{ln\_flx}\forcode{=.true.}),
1639a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1640\[
1641  % \label{eq:SBC_dmp_q}
1642  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1643\]
1644where SST is a sea surface temperature field (observed or climatological),
1645$T$ is the model surface layer temperature and
1646$\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $-40~W/m^2/K$.
1647For a $50~m$ mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1648This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$.
1649
1650In the fresh water budget, a feedback term can also be added.
1651Converted into an equivalent freshwater flux, it takes the following expression :
1652
1653\begin{equation}
1654  \label{eq:SBC_dmp_emp}
1655  \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1656  {\left.S\right|_{k=1}}
1657\end{equation}
1658
1659where $\textit{emp}_{o }$ is a net surface fresh water flux
1660(observed, climatological or an atmospheric model product),
1661\textit{SSS}$_{Obs}$ is a sea surface salinity
1662(usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}),
1663$\left.S\right|_{k=1}$ is the model surface layer salinity and
1664$\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter.
1665Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as
1666the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}.
1667The SSS restoring term should be viewed as a flux correction on freshwater fluxes to
1668reduce the uncertainties we have on the observed freshwater budget.
1669
1670
1671% -------------------------------------------------------------------------------------------------------------
1672%        Handling of ice-covered area
1673% -------------------------------------------------------------------------------------------------------------
1674\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1675\label{subsec:SBC_ice-cover}
1676
1677The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean.
1678There are several way to handle sea-ice in the system depending on
1679the value of the \np{nn\_ice} namelist parameter found in \nam{sbc} namelist.
1680\begin{description}
1681\item[nn\_ice = 0]
1682  there will never be sea-ice in the computational domain.
1683  This is a typical namelist value used for tropical ocean domain.
1684  The surface fluxes are simply specified for an ice-free ocean.
1685  No specific things is done for sea-ice.
1686\item[nn\_ice = 1]
1687  sea-ice can exist in the computational domain, but no sea-ice model is used.
1688  An observed ice covered area is read in a file.
1689  Below this area, the SST is restored to the freezing point and
1690  the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere.
1691  The associated modification of the freshwater fluxes are done in such a way that
1692  the change in buoyancy fluxes remains zero.
1693  This prevents deep convection to occur when trying to reach the freezing point
1694  (and so ice covered area condition) while the SSS is too large.
1695  This manner of managing sea-ice area, just by using a IF case,
1696  is usually referred as the \textit{ice-if} model.
1697  It can be found in the \mdl{sbcice\_if} module.
1698\item[nn\_ice = 2 or more]
1699  A full sea ice model is used.
1700  This model computes the ice-ocean fluxes,
1701  that are combined with the air-sea fluxes using the ice fraction of each model cell to
1702  provide the surface averaged ocean fluxes.
1703  Note that the activation of a sea-ice model is done by defining a CPP key (\key{si3} or \key{cice}).
1704  The activation automatically overwrites the read value of nn\_ice to its appropriate value
1705  (\ie\ $2$ for SI3 or $3$ for CICE).
1706\end{description}
1707
1708% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1709%GS: ocean-ice (SI3) interface is not located in SBC directory anymore, so it should be included in SI3 doc
1710
1711
1712% -------------------------------------------------------------------------------------------------------------
1713%        CICE-ocean Interface
1714% -------------------------------------------------------------------------------------------------------------
1715\subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})}
1716\label{subsec:SBC_cice}
1717
1718It is possible to couple a regional or global \NEMO\ configuration (without AGRIF)
1719to the CICE sea-ice model by using \key{cice}.
1720The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and
1721the additional 'hadgem3' drivers will be required, even with the latest code release.
1722Input grid files consistent with those used in \NEMO\ will also be needed,
1723and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used
1724(seek advice from UKMO if necessary).
1725Currently, the code is only designed to work when using the NCAR forcing option for \NEMO\ %GS: still true ?
1726(with \textit{calc\_strair}\forcode{=.true.} and \textit{calc\_Tsfc}\forcode{=.true.} in the CICE name-list),
1727or alternatively when \NEMO\ is coupled to the HadGAM3 atmosphere model
1728(with \textit{calc\_strair}\forcode{=.false.} and \textit{calc\_Tsfc}\forcode{=false}).
1729The code is intended to be used with \np{nn\_fsbc} set to 1
1730(although coupling ocean and ice less frequently should work,
1731it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly -
1732the user should check that results are not significantly different to the standard case).
1733
1734There are two options for the technical coupling between \NEMO\ and CICE.
1735The standard version allows complete flexibility for the domain decompositions in the individual models,
1736but this is at the expense of global gather and scatter operations in the coupling which
1737become very expensive on larger numbers of processors.
1738The alternative option (using \key{nemocice\_decomp} for both \NEMO\ and CICE) ensures that
1739the domain decomposition is identical in both models (provided domain parameters are set appropriately,
1740and \textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and
1741allows much more efficient direct coupling on individual processors.
1742This solution scales much better although it is at the expense of having more idle CICE processors in areas where
1743there is no sea ice.
1744
1745
1746% -------------------------------------------------------------------------------------------------------------
1747%        Freshwater budget control
1748% -------------------------------------------------------------------------------------------------------------
1749\subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})}
1750\label{subsec:SBC_fwb}
1751
1752For global ocean simulation, it can be useful to introduce a control of the mean sea level in order to
1753prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes.
1754In \NEMO, two way of controlling the freshwater budget are proposed:
1755
1756\begin{description}
1757\item[\np{nn\_fwb}\forcode{=0}]
1758  no control at all.
1759  The mean sea level is free to drift, and will certainly do so.
1760\item[\np{nn\_fwb}\forcode{=1}]
1761  global mean \textit{emp} set to zero at each model time step.
1762  %GS: comment below still relevant ?
1763  %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).
1764\item[\np{nn\_fwb}\forcode{=2}]
1765  freshwater budget is adjusted from the previous year annual mean budget which
1766  is read in the \textit{EMPave\_old.dat} file.
1767  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from
1768  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file.
1769\end{description}
1770
1771% Griffies doc:
1772% When running ocean-ice simulations, we are not explicitly representing land processes,
1773% such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift,
1774% it is important to balance the hydrological cycle in ocean-ice models.
1775% We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff.
1776% The result of the normalization should be a global integrated zero net water input to the ocean-ice system over
1777% a chosen time scale.
1778% How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step,
1779% so that there is always a zero net input of water to the ocean-ice system.
1780% Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used
1781% to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance.
1782% Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1783% When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean
1784% and ice models when aiming to balance the hydrological cycle.
1785% 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,
1786% not the water in any one sub-component. As an extreme example to illustrate the issue,
1787% consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up,
1788% there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean.
1789% The total water contained in the ocean plus ice system is constant, but there is an exchange of water between
1790% the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle
1791% in ocean-ice models.
1792
1793
1794\biblio
1795
1796\pindex
1797
1798\end{document}
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