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1% ================================================================
2% Chapter � Surface Boundary Condition (SBC, ICB)
3% ================================================================
4\chapter{Surface Boundary Condition (SBC, ICB) }
9$\ $\newline    % force a new ligne
13$\ $\newline    % force a new ligne
15The ocean needs six fields as surface boundary condition:
17   \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$
18   \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
19   \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$
21plus an optional field:
23   \item the atmospheric pressure at the ocean surface $\left( p_a \right)$
26Five different ways to provide the first six fields to the ocean are available which
27are controlled by namelist \ngn{namsbc} variables: an analytical formulation (\np{ln\_ana}~=~true),
28a flux formulation (\np{ln\_flx}~=~true), a bulk formulae formulation (CORE
29(\np{ln\_core}~=~true), CLIO (\np{ln\_clio}~=~true) or MFS
30\footnote { Note that MFS bulk formulae compute fluxes only for the ocean component}
31(\np{ln\_mfs}~=~true) bulk formulae) and a coupled
32formulation (exchanges with a atmospheric model via the OASIS coupler)
33(\np{ln\_cpl}~=~true). When used, the atmospheric pressure forces both
34ocean and ice dynamics (\np{ln\_apr\_dyn}~=~true).
35The frequency at which the six or seven fields have to be updated is the \np{nn\_fsbc} 
36namelist parameter.
37When the fields are supplied from data files (flux and bulk formulations), the input fields
38need not be supplied on the model grid.  Instead a file of coordinates and weights can
39be supplied which maps the data from the supplied grid to the model points
40(so called "Interpolation on the Fly", see \S\ref{SBC_iof}).
41In addition, the resulting fields can be further modified using several namelist options.
42These options control  the rotation of vector components supplied relative to an east-north
43coordinate system onto the local grid directions in the model; the addition of a surface
44restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes
45below ice-covered areas (using observed ice-cover or a sea-ice model)
46(\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater
47fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of a freshwater flux adjustment
48in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the
49transformation of the solar radiation (if provided as daily mean) into a diurnal
50cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave
51model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or mfs bulk formulas are selected.
53In this chapter, we first discuss where the surface boundary condition appears in the
54model equations. Then we present the five ways of providing the surface boundary condition,
55followed by the description of the atmospheric pressure and the river runoff.
56Next the scheme for interpolation on the fly is described.
57Finally, the different options that further modify the fluxes applied to the ocean are discussed.
58One of these is modification by icebergs (see \S\ref{ICB_icebergs}), which act as drifting sources of fresh water.
61% ================================================================
62% Surface boundary condition for the ocean
63% ================================================================
64\section{Surface boundary condition for the ocean}
67The surface ocean stress is the stress exerted by the wind and the sea-ice
68on the ocean. The two components of stress are assumed to be interpolated
69onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
70at $u$- and $v$-points They are applied as a surface boundary condition of the
71computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
72\begin{equation} \label{Eq_sbc_dynzdf}
73\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
74    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
76where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
77stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
79The surface heat flux is decomposed into two parts, a non solar and a solar heat
80flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
81of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
82It is applied as a surface boundary condition trend of the first level temperature
83time evolution equation (\mdl{trasbc} module).
84\begin{equation} \label{Eq_sbc_trasbc_q}
85\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 
86_o \;C_p \;e_{3t} }} \right|_{k=1} \quad
88$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
89trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
91\begin{equation} \label{Eq_sbc_traqsr}
92\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right]
94where $I_w$ is a non-dimensional function that describes the way the light
95penetrates inside the water column. It is generally a sum of decreasing
96exponentials (see \S\ref{TRA_qsr}).
98The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which
99may or may not be identical. Indeed, a surface freshwater flux has two effects:
100it changes the volume of the ocean and it changes the surface concentration of
101salt (and other tracers). Therefore it appears in the sea surface height as a volume
102flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
103as a concentration/dilution effect,
104$\textit{emp}_{S}$ (\mdl{trasbc} module).
105\begin{equation} \label{Eq_trasbc_emp}
107&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\ 
109 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\ 
110 \end{aligned}
113In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,
114but it exist several numerical reasons why this equality should be broken.
115For example, when the ocean is coupled to a sea-ice model, the water exchanged between
116ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case,
117$\textit{emp}_{S}$ take into account both concentration/dilution effect associated with
118freezing/melting and the salt flux between ice and ocean, while \textit{emp} is
119only the volume flux. In addition, in the current version of \NEMO, the sea-ice is
120assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does
121not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS.
122%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
124Note that SST can also be modified by a freshwater flux. Precipitation (in
125particular solid precipitation) may have a temperature significantly different from
126the SST. Due to the lack of information about the temperature of
127precipitation, we assume it is equal to the SST. Therefore, no
128concentration/dilution term appears in the temperature equation. It has to
129be emphasised that this absence does not mean that there is no heat flux
130associated with precipitation! Precipitation can change the ocean volume and thus the
131ocean heat content. It is therefore associated with a heat flux (not yet 
132diagnosed in the model) \citep{Roullet_Madec_JGR00}).
134%\colorbox{yellow}{Miss: }
136%A extensive description of all namsbc namelist (parameter that have to be
139%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
140%ssv) i.e. information required by flux computation or sea-ice
142%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
143%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
145%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
147%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
148%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
151%Explain here all the namlist namsbc variable{\ldots}.
153%\colorbox{yellow}{End Miss }
155The ocean model provides the surface currents, temperature and salinity
156averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
157mean is done in \mdl{sbcmod} module.
160\begin{table}[tb]   \begin{center}   \begin{tabular}{|l|l|l|l|}
162Variable description             & Model variable  & Units  & point \\  \hline
163i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
164j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
165Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
166Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
168\caption{  \label{Tab_ssm}   
169Ocean variables provided by the ocean to the surface module (SBC).
170The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of
171computation of surface fluxes.}
172\end{center}   \end{table}
175%\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
178% ================================================================
179%       Input Data
180% ================================================================
181\section{Input Data generic interface}
184A generic interface has been introduced to manage the way input data (2D or 3D fields,
185like surface forcing or ocean T and S) are specify in \NEMO. This task is archieved by fldread.F90.
186The module was design with four main objectives in mind:
188\item optionally provide a time interpolation of the input data at model time-step,
189whatever their input frequency is, and according to the different calendars available in the model.
190\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
191\item make the run duration independent from the period cover by the input files.
192\item provide a simple user interface and a rather simple developer interface by limiting the
193 number of prerequisite information.
196As a results the user have only to fill in for each variable a structure in the namelist file
197to defined the input data file and variable names, the frequency of the data (in hours or months),
198whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
199and two additional parameters for on-the-fly interpolation. When adding a new input variable,
200the developer has to add the associated structure in the namelist, read this information
201by mirroring the namelist read in \rou{sbc\_blk\_init} for example, and simply call \rou{fld\_read} 
202to obtain the desired input field at the model time-step and grid points.
204The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
205(see \S\ref{SBC_fldread}), the period it cover is one year, month, week or day, and, if on-the-fly
206interpolation is used, a file of weights must be supplied (see \S\ref{SBC_iof}).
208Note that when an input data is archived on a disc which is accessible directly
209from the workspace where the code is executed, then the use can set the \np{cn\_dir} 
210to the pathway leading to the data. By default, the data are assumed to have been
211copied so that cn\_dir='./'.
213% -------------------------------------------------------------------------------------------------------------
214% Input Data specification (\mdl{fldread})
215% -------------------------------------------------------------------------------------------------------------
216\subsection{Input Data specification (\mdl{fldread})}
219The structure associated with an input variable contains the following information:
220\begin{alltt}  {{\tiny   
222!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation !
223!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  !
228\item[File name]: the stem name of the NetCDF file to be open.
229This stem will be completed automatically by the model, with the addition of a '.nc' at its end
230and by date information and possibly a prefix (when using AGRIF).
231Tab.\ref{Tab_fldread} provides the resulting file name in all possible cases according to whether
232it is a climatological file or not, and to the open/close frequency (see below for definition).
239                         & daily or weekLLL          & monthly                   &   yearly          \\   \hline
240clim = false   & fn\_yYYYYmMMdDD  &   fn\_yYYYYmMM   &   fn\_yYYYY  \\   \hline
241clim = true       & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
244\caption{ \label{Tab_fldread}   naming nomenclature for climatological or interannual input file,
245as a function of the Open/close frequency. The stem name is assumed to be 'fn'.
246For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week ($i.e.$ 'sun','sat','fri','thu','wed','tue','mon'). The 'YYYY', 'MM' and 'DD' should be replaced by the
247actual year/month/day, always coded with 4 or 2 digits. Note that (1) in mpp, if the file is split
248over each subdomain, the suffix '.nc' is replaced by '\', where 'PPPP' is the
249process number coded with 4 digits; (2) when using AGRIF, the prefix
250'\_N' is added to files,
251where 'N'  is the child grid number.}
256\item[Record frequency]: the frequency of the records contained in the input file.
257Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
258(for example -1 for monthly forcing or -12 for annual forcing).
259Note that this frequency must really be an integer and not a real.
260On some computers, seting it to '24.' can be interpreted as 240!
262\item[Variable name]: the name of the variable to be read in the input NetCDF file.
264\item[Time interpolation]: a logical to activate, or not, the time interpolation. If set to 'false',
265the forcing will have a steplike shape remaining constant during each forcing period.
266For example, when using a daily forcing without time interpolation, the forcing remaining
267constant from 00h00'00'' to 23h59'59". If set to 'true', the forcing will have a broken line shape.
268Records are assumed to be dated the middle of the forcing period.
269For example, when using a daily forcing with time interpolation, linear interpolation will
270be performed between mid-day of two consecutive days.
272\item[Climatological forcing]: a logical to specify if a input file contains climatological forcing
273which can be cycle in time, or an interannual forcing which will requires additional files
274if the period covered by the simulation exceed the one of the file. See the above the file
275naming strategy which impacts the expected name of the file to be opened.
277\item[Open/close frequency]: the frequency at which forcing files must be opened/closed.
278Four cases are coded: 'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week),
279'monthly' and 'yearly' which means the forcing files will contain data for one day, one week,
280one month or one year. Files are assumed to contain data from the beginning of the open/close period.
281For example, the first record of a yearly file containing daily data is Jan 1st even if the experiment
282is not starting at the beginning of the year.
284\item[Others]: 'weights filename' and 'pairing rotation' are associted with on-the-fly interpolation
285which is described in \S\ref{SBC_iof}.
289Additional remarks:\\
290(1) The time interpolation is a simple linear interpolation between two consecutive records of
291the input data. The only tricky point is therefore to specify the date at which we need to do
292the interpolation and the date of the records read in the input files.
293Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the
294time step. For example, for an experiment starting at 0h00'00" with a one hour time-step,
295a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
296However, for forcing data related to the surface module, values are not needed at every
297time-step but at every \np{nn\_fsbc} time-step. For example with \np{nn\_fsbc}~=~3,
298the surface module will be called at time-steps 1, 4, 7, etc. The date used for the time interpolation
299is thus redefined to be at the middle of \np{nn\_fsbc} time-step period. In the previous example,
300this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 
301(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file
302calendar. The calendar associated with the forcing field is build according to the information
303provided by user in the record frequency, the open/close frequency and the type of temporal interpolation.
304For example, the first record of a yearly file containing daily data that will be interpolated in time
305is assumed to be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
306(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file
307when interpolating data with the first (last) record of the open/close period.
308For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
309the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values
310between Dec 31st 12h00'00" and Jan 1st 12h00'00". If the forcing is climatological, Dec and Jan will
311be keep-up from the same year. However, if the forcing is not climatological, at the end of the
312open/close period the code will automatically close the current file and open the next one.
313Note that, if the experiment is starting (ending) at the beginning (end) of an open/close period
314we do accept that the previous (next) file is not existing. In this case, the time interpolation
315will be performed between two identical values. For example, when starting an experiment on
316Jan 1st of year Y with yearly files and daily data to be interpolated, we do accept that the file
317related to year Y-1 is not existing. The value of Jan 1st will be used as the missing one for
318Dec 31st of year Y-1. If the file of year Y-1 exists, the code will read its last record.
319Therefore, this file can contain only one record corresponding to Dec 31st, a useful feature for
320user considering that it is too heavy to manipulate the complete file for year Y-1.
323% -------------------------------------------------------------------------------------------------------------
324% Interpolation on the Fly
325% -------------------------------------------------------------------------------------------------------------
326\subsection [Interpolation on-the-Fly] {Interpolation on-the-Fly}
329Interpolation on the Fly allows the user to supply input files required
330for the surface forcing on grids other than the model grid.
331To do this he or she must supply, in addition to the source data file,
332a file of weights to be used to interpolate from the data grid to the model grid.
333The original development of this code used the SCRIP package (freely available
334\href{}{here} under a copyright agreement).
335In principle, any package can be used to generate the weights, but the
336variables in the input weights file must have the same names and meanings as
337assumed by the model.
338Two methods are currently available: bilinear and bicubic interpolation.
340\subsubsection{Bilinear Interpolation}
343The input weights file in this case has two sets of variables: src01, src02,
344src03, src04 and wgt01, wgt02, wgt03, wgt04.
345The "src" variables correspond to the point in the input grid to which the weight
346"wgt" is to be applied. Each src value is an integer corresponding to the index of a
347point in the input grid when written as a one dimensional array.  For example, for an input grid
348of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
349There are four of each variable because bilinear interpolation uses the four points defining
350the grid box containing the point to be interpolated.
351All of these arrays are on the model grid, so that values src01(i,j) and
352wgt01(i,j) are used to generate a value for point (i,j) in the model.
354Symbolically, the algorithm used is:
357f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
359where function idx() transforms a one dimensional index src(k) into a two dimensional index,
360and wgt(1) corresponds to variable "wgt01" for example.
362\subsubsection{Bicubic Interpolation}
365Again there are two sets of variables: "src" and "wgt".
366But in this case there are 16 of each.
367The symbolic algorithm used to calculate values on the model grid is now:
369\begin{equation*} \begin{split}
370f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}     
371              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
372              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }   
373              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
376The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
381To activate this option, a non-empty string should be supplied in the weights filename column
382of the relevant namelist; if this is left as an empty string no action is taken.
383In the model, weights files are read in and stored in a structured type (WGT) in the fldread
384module, as and when they are first required.
385This initialisation procedure determines whether the input data grid should be treated
386as cyclical or not by inspecting a global attribute stored in the weights input file.
387This attribute must be called "ew\_wrap" and be of integer type.
388If it is negative, the input non-model grid is assumed not to be cyclic.
389If zero or greater, then the value represents the number of columns that overlap.
390$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
391if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
392If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
393In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and therefore the grid
394is assumed to be cyclic with no overlapping columns.
395(In fact this only matters when bicubic interpolation is required.)
396Note that no testing is done to check the validity in the model, since there is no way
397of knowing the name used for the longitude variable,
398so it is up to the user to make sure his or her data is correctly represented.
400Next the routine reads in the weights.
401Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise
402bilinear interpolation is used. The WGT structure includes dynamic arrays both for
403the storage of the weights (on the model grid), and when required, for reading in
404the variable to be interpolated (on the input data grid).
405The size of the input data array is determined by examining the values in the "src"
406arrays to find the minimum and maximum i and j values required.
407Since bicubic interpolation requires the calculation of gradients at each point on the grid,
408the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
409When the array of points from the data file is adjacent to an edge of the data grid,
410the halo is either a copy of the row/column next to it (non-cyclical case), or is a copy
411of one from the first few columns on the opposite side of the grid (cyclical case).
417\item  The case where input data grids are not logically rectangular has not been tested.
418\item  This code is not guaranteed to produce positive definite answers from positive definite inputs
419          when a bicubic interpolation method is used.
420\item  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
421\item  The gradients across the ends of a cyclical grid assume that the grid spacing between
422          the two columns involved are consistent with the weights used.
423\item  Neither interpolation scheme is conservative. (There is a conservative scheme available
424          in SCRIP, but this has not been implemented.)
430% to be completed
431A set of utilities to create a weights file for a rectilinear input grid is available
432(see the directory NEMOGCM/TOOLS/WEIGHTS).
434% -------------------------------------------------------------------------------------------------------------
435% Standalone Surface Boundary Condition Scheme
436% -------------------------------------------------------------------------------------------------------------
437\subsection [Standalone Surface Boundary Condition Scheme] {Standalone Surface Boundary Condition Scheme}
444In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields and simply read them in from  a previous run. 
445Options are defined through the  \ngn{namsbc\_sas} namelist variables.
446For example:
449\item  Multiple runs of the model are required in code development to see the affect of different algorithms in
450       the bulk formulae.
451\item  The effect of different parameter sets in the ice model is to be examined.
454The StandAlone Surface scheme provides this utility.
455A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
456However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0)
457In this configuration, a few routines in the standard model are overriden by new versions.
458Routines replaced are:
461\item  \mdl{nemogcm}
463       This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90)
464       Since the ocean state is not calculated all associated initialisations have been removed.
465\item  \mdl{step}
467       The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
468\item  \mdl{sbcmod}
470       This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules
471       that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs).
472\item  \mdl{daymod}
474       No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions
475       have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user
476       must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
477\item  \mdl{stpctl}
479       Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
480\item  \mdl{diawri}
482       All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which
483       have been read in) are written along with relevant forcing and ice data.
486One new routine has been added:
489\item  \mdl{sbcsas}
490       This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface.
491       These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module,
492       the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level.
493       Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
496% ================================================================
497% Analytical formulation (sbcana module)
498% ================================================================
499\section  [Analytical formulation (\textit{sbcana}) ]
500      {Analytical formulation (\mdl{sbcana} module) }
507The analytical formulation of the surface boundary condition is the default scheme.
508In this case, all the six fluxes needed by the ocean are assumed to
509be uniform in space. They take constant values given in the namelist
510\ngn{namsbc{\_}ana} by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
511\np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero.
512In addition, the wind is allowed to reach its nominal value within a given number
513of time steps (\np{nn\_tau000}).
515If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
516module can be modified to use another scheme. As an example,
517the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
518GYRE configuration (see GYRE configuration manual, in preparation).
521% ================================================================
522% Flux formulation
523% ================================================================
524\section  [Flux formulation (\textit{sbcflx}) ]
525      {Flux formulation (\mdl{sbcflx} module) }
531In the flux formulation (\np{ln\_flx}=true), the surface boundary
532condition fields are directly read from input files. The user has to define
533in the namelist \ngn{namsbc{\_}flx} the name of the file, the name of the variable
534read in the file, the time frequency at which it is given (in hours), and a logical
535setting whether a time interpolation to the model time step is required
536for this field. See \S\ref{SBC_fldread} for a more detailed description of the parameters.
538Note that in general, a flux formulation is used in associated with a
539restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
543% ================================================================
544% Bulk formulation
545% ================================================================
546\section  [Bulk formulation (\textit{sbcblk\_core}, \textit{sbcblk\_clio} or \textit{sbcblk\_mfs}) ]
547      {Bulk formulation \small{(\mdl{sbcblk\_core} \mdl{sbcblk\_clio} \mdl{sbcblk\_mfs} modules)} }
550In the bulk formulation, the surface boundary condition fields are computed
551using bulk formulae and atmospheric fields and ocean (and ice) variables.
553The atmospheric fields used depend on the bulk formulae used. Three bulk formulations
554are available : the CORE, the CLIO and the MFS bulk formulea. The choice is made by setting to true
555one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or  \np{ln\_mfs}.
557Note : in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
558Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over both
559an ocean and an ice surface.
561% -------------------------------------------------------------------------------------------------------------
562%        CORE Bulk formulea
563% -------------------------------------------------------------------------------------------------------------
564\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
565            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
571The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
572They have been designed to handle the CORE forcing, a mixture of NCEP
573reanalysis and satellite data. They use an inertial dissipative method to compute
574the turbulent transfer coefficients (momentum, sensible heat and evaporation)
575from the 10 metre wind speed, air temperature and specific humidity.
576This \citet{Large_Yeager_Rep04} dataset is available through the
577\href{}{GFDL web site}.
579Note that substituting ERA40 to NCEP reanalysis fields
580does not require changes in the bulk formulea themself.
581This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
583Options are defined through the  \ngn{namsbc\_core} namelist variables.
584The required 8 input fields are:
587\begin{table}[htbp]   \label{Tab_CORE}
591Variable desciption              & Model variable  & Units   & point \\    \hline
592i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
593j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
59410m air temperature              & tair      & \r{}$K$            & T   \\ \hline
595Specific humidity             & humi      & \%              & T \\      \hline
596Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
597Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
598Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
599Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
605Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean
606point ($u$- and $v$-points). It is simpler and faster (less fields to be read),
607but it is not the recommended method when the ocean grid size is the same
608or larger than the one of the input atmospheric fields.
610% -------------------------------------------------------------------------------------------------------------
611%        CLIO Bulk formulea
612% -------------------------------------------------------------------------------------------------------------
613\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
614            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
620The CLIO bulk formulae were developed several years ago for the
621Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
622They are simpler bulk formulae. They assume the stress to be known and
623compute the radiative fluxes from a climatological cloud cover.
625Options are defined through the  \ngn{namsbc\_clio} namelist variables.
626The required 7 input fields are:
629\begin{table}[htbp]   \label{Tab_CLIO}
633Variable desciption           & Model variable  & Units           & point \\  \hline
634i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
635j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
636Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
63710m air temperature              & tair         & \r{}$K$            & T \\   \hline
638Specific humidity                & humi         & \%              & T \\   \hline
639Cloud cover                   &           & \%              & T \\   \hline
640Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
641Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
647As for the flux formulation, information about the input data required by the
648model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
649namelist (see \S\ref{SBC_fldread}).
651% -------------------------------------------------------------------------------------------------------------
652%        MFS Bulk formulae
653% -------------------------------------------------------------------------------------------------------------
654\subsection    [MFS Bulk formulea (\np{ln\_mfs}=true)]
655            {MFS Bulk formulea (\np{ln\_mfs}=true, \mdl{sbcblk\_mfs})}
661The MFS (Mediterranean Forecasting System) bulk formulae have been developed by
662 \citet{Castellari_al_JMS1998}.
663They have been designed to handle the ECMWF operational data and are currently
664in use in the MFS operational system \citep{Tonani_al_OS08}, \citep{Oddo_al_OS09}.
665The wind stress computation uses a drag coefficient computed according to \citet{Hellerman_Rosenstein_JPO83}.
666The surface boundary condition for temperature involves the balance between surface solar radiation,
667net long-wave radiation, the latent and sensible heat fluxes.
668Solar radiation is dependent on cloud cover and is computed by means of
669an astronomical formula \citep{Reed_JPO77}. Albedo monthly values are from \citet{Payne_JAS72} 
670as means of the values at $40^{o}N$ and $30^{o}N$ for the Atlantic Ocean (hence the same latitudinal
671band of the Mediterranean Sea). The net long-wave radiation flux
672\citep{Bignami_al_JGR95} is a function of
673air temperature, sea-surface temperature, cloud cover and relative humidity.
674Sensible heat and latent heat fluxes are computed by classical
675bulk formulae parameterized according to \citet{Kondo1975}.
676Details on the bulk formulae used can be found in \citet{Maggiore_al_PCE98} and \citet{Castellari_al_JMS1998}.
678Options are defined through the  \ngn{namsbc\_mfs} namelist variables.
679The required 7 input fields must be provided on the model Grid-T and  are:
681\item          Zonal Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windi})
682\item          Meridional Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windj})
683\item          Total Claud Cover (\%)  (\np{sn\_clc})
684\item          2m Air Temperature ($K$) (\np{sn\_tair})
685\item          2m Dew Point Temperature ($K$)  (\np{sn\_rhm})
686\item          Total Precipitation ${Kg} m^{-2} s^{-1}$ (\np{sn\_prec})
687\item          Mean Sea Level Pressure (${Pa}$) (\np{sn\_msl})
689% -------------------------------------------------------------------------------------------------------------
690% ================================================================
691% Coupled formulation
692% ================================================================
693\section  [Coupled formulation (\textit{sbccpl}) ]
694      {Coupled formulation (\mdl{sbccpl} module)}
700In the coupled formulation of the surface boundary condition, the fluxes are
701provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
702while sea and ice surface temperature, ocean and ice albedo, and ocean currents
703are sent to the atmospheric component.
705A generalised coupled interface has been developed. It is currently interfaced with OASIS 3
706(\key{oasis3}) and does not support OASIS 4
707\footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}.
708It has been successfully used to interface \NEMO to most of the European atmospheric
710as well as to \href{}{WRF} (Weather Research and Forecasting Model).
712Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
713The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are
714actually recieved by the ice-ocean system (no calculation of ice sublimation in coupled mode).
715When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
716the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}. In this case,
717CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system (and need to be activated in \ngn{namsbc{\_}cpl} ).
719The namelist above allows control of various aspects of the coupling fields (particularly for
720vectors) and now allows for any coupling fields to have multiple sea ice categories (as required by LIM3
721and CICE).  When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be
722determined by the number used in the sea ice model.  In some limited cases it may be possible to specify
723single category coupling fields even when the sea ice model is running with multiple categories - in this
724case the user should examine the code to be sure the assumptions made are satisfactory.  In cases where
725this is definitely not possible the model should abort with an error message.  The new code has been tested using
726ECHAM with LIM2, and HadGAM3 with CICE but although it will compile with \key{lim3} additional minor code changes
727may be required to run using LIM3.
730% ================================================================
731%        Atmospheric pressure
732% ================================================================
733\section   [Atmospheric pressure (\textit{sbcapr})]
734         {Atmospheric pressure (\mdl{sbcapr})}
740The optional atmospheric pressure can be used to force ocean and ice dynamics
741(\np{ln\_apr\_dyn}~=~true, \textit{\ngn{namsbc}} namelist ).
742The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
743can be interpolated in time to the model time step, and even in space when the
744interpolation on-the-fly is used. When used to force the dynamics, the atmospheric
745pressure is further transformed into an equivalent inverse barometer sea surface height,
746$\eta_{ib}$, using:
747\begin{equation} \label{SBC_ssh_ib}
748   \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
750where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
751A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. In this case $P_o$ 
752is set to the value of $P_{atm}$ averaged over the ocean domain, $i.e.$ the mean value of
753$\eta_{ib}$ is kept to zero at all time step.
755The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation
756(see \mdl{dynspg} for the ocean). For sea-ice, the sea surface height, $\eta_m$,
757which is provided to the sea ice model is set to $\eta - \eta_{ib}$ (see \mdl{sbcssr} module).
758$\eta_{ib}$ can be set in the output. This can simplify altimetry data and model comparison
759as inverse barometer sea surface height is usually removed from these date prior to their distribution.
761When using time-splitting and BDY package for open boundaries conditions, the equivalent
762inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
763\np{ln\_apr\_obc}  might be set to true.
765% ================================================================
766%        Tidal Potential
767% ================================================================
768\section   [Tidal Potential (\textit{sbctide})]
769                        {Tidal Potential (\mdl{sbctide})}
772A module is available to use the tidal potential forcing and is activated with with \key{tide}.
779Concerning the tidal potential, some parameters are available in namelist \ngn{nam\_tide}:
781- \np{ln\_tide\_pot} activate the tidal potential forcing
783- \np{nb\_harmo} is the number of constituent used
785- \np{clname} is the name of constituent
788The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem;
789they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\
791The potential astronomical expressed, for the three types of tidal frequencies
792following, by : \\
793Tide long period :
797diurnal Tide :
799\Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k})
801Semi-diurnal tide:
807$A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave
808$k$ to Greenwich.
810We make corrections to the astronomical potential.
811We obtain :
813\Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi)
815with $k$ a number of Love estimated to 0.6 which parametrized the astronomical tidal land,
816and $h$ a number of Love to 0.3 which parametrized the parametrization due to the astronomical tidal land.
818% ================================================================
819%        River runoffs
820% ================================================================
821\section   [River runoffs (\textit{sbcrnf})]
822         {River runoffs (\mdl{sbcrnf})}
828%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
829%Many models, however, have traditionally inserted river runoff to the top model cell.
830%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
831%throughout a nonzero depth has been motivated by the numerical and physical problems
832%that arise when the top grid cells are of the order of one meter. This situation is common in
833%coastal modelling and becomes more and more often open ocean and climate modelling
834%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
835%required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
838%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
839%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
840%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
841%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
842%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
843%emp or emps and the changes made are below:
847River runoff generally enters the ocean at a nonzero depth rather than through the surface.
848Many models, however, have traditionally inserted river runoff to the top model cell.
849This was the case in \NEMO prior to the version 3.3, and was combined with an option
850to increase vertical mixing near the river mouth.
852However, with this method numerical and physical problems arise when the top grid cells are
853of the order of one meter. This situation is common in coastal modelling and is becoming
854more common in open ocean and climate modelling
855\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
856required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \S\ref{SBC_dcy}.}.
858As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth, and for the
859temperature and salinity of the river to effect the surrounding ocean.
860The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, along with the   
861depth (in metres) which the river should be added to.
863Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and \np{ln\_rnf\_temp} control whether
864the river attributes (depth, salinity and temperature) are read in and used.  If these are set
865as false the river is added to the surface box only, assumed to be fresh (0~psu), and/or
866taken as surface temperature respectively.
868The runoff value and attributes are read in in sbcrnf. 
869For temperature -999 is taken as missing data and the river temperature is taken to be the
870surface temperatue at the river point.
871For the depth parameter a value of -1 means the river is added to the surface box only,
872and a value of -999 means the river is added through the entire water column.
873After being read in the temperature and salinity variables are multiplied by the amount of runoff (converted into m/s)
874to give the heat and salt content of the river runoff.
875After the user specified depth is read ini, the number of grid boxes this corresponds to is
876calculated and stored in the variable \np{nz\_rnf}.
877The variable \textit{h\_dep} is then calculated to be the depth (in metres) of the bottom of the
878lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model).
880The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence
881(\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
882This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
883The sea surface height is calculated using the sum of the horizontal divergence terms, and so the
884river runoff indirectly forces an increase in sea surface height.
886The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
887This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
888The heat and salt content of the river runoff is not included in this step, and so the tracer
889concentrations are diluted as water of ocean temperature and salinity is moved upward out of the box
890and replaced by the same volume of river water with no corresponding heat and salt addition.
892For the linear free surface case, at the surface box the tracer advection causes a flux of water
893(of equal volume to the runoff) through the sea surface out of the domain, which causes a salt and heat flux out of the model.
894As such the volume of water does not change, but the water is diluted.
896For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
897Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water
898is added with no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
899(The runoff addition to the top box along with the water being moved up through boxes below means the surface box has a large
900increase in volume, whilst all other boxes remain the same size)
902In trasbc the addition of heat and salt due to the river runoff is added.
903This is done in the same way for both vvl and non-vvl.
904The temperature and salinity are increased through the specified depth according to the heat and salt content of the river.
906In the non-linear free surface case (vvl), near the end of the time step the change in sea surface height is redistrubuted
907through the grid boxes, so that the original ratios of grid box heights are restored.
908In doing this water is moved into boxes below, throughout the water column, so the large volume addition to the surface box is spread between all the grid boxes.
910It is also possible for runnoff to be specified as a negative value for modelling flow through straits, i.e. modelling the Baltic flow in and out of the North Sea.
911When the flow is out of the domain there is no change in temperature and salinity, regardless of the namelist options used, as the ocean water leaving the domain removes heat and salt (at the same concentration) with it.
914%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
916%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
918%\colorbox{yellow}{river mouths{\ldots}}
920%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
921%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
924%\gmcomment{  word doc of runoffs:
926%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.
927%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. 
929%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
931%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:
936% ================================================================
937%        Handling of icebergs
938% ================================================================
939\section{ Handling of icebergs (ICB) }
945Icebergs are modelled as lagrangian particles in NEMO.
946Their physical behaviour is controlled by equations as described in  \citet{Martin_Adcroft_OM10} ).
947(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO.)
948Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described in the \ngn{namberg} namelist:
949\np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
950Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs
951of this class are being described as one lagrangian point (this reduces the numerical problem of tracking every single iceberg).
952They are enabled by setting \np{ln\_icebergs}~=~true.
954Two initialisation schemes are possible.
957In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
958(so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each
959grid point of which an iceberg is generated at the beginning of the run.
960(Note that this happens each time the timestep equals \np{nn\_nit000}.)
961\np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners
962of the geographical box: lonmin,lonmax,latmin,latmax
964In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
965This should be a file with a field on the configuration grid (typically ORCA) representing ice accumulation rate at each model point.
966These should be ocean points adjacent to land where icebergs are known to calve.
967Most points in this input grid are going to have value zero.
968When the model runs, ice is accumulated at each grid point which has a non-zero source term.
969At each time step, a test is performed to see if there is enough ice mass to calve an iceberg of each class in order (1 to 10).
970Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling).
971If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
974Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
975The latter act to disintegrate the iceberg. This is either all melted freshwater, or
976(if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
977which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
978Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
980Extensive diagnostics can be produced.
981Separate output files are maintained for human-readable iceberg information.
982A separate file is produced for each processor (independent of \np{ln\_ctl}).
983The amount of information is controlled by two integer parameters:
985\item[\np{nn\_verbose\_level}]  takes a value between one and four and represents
986an increasing number of points in the code at which variables are written, and an
987increasing level of obscurity.
988\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
991Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
992A non-zero value represents how many timesteps between writes of information into the output file.
993These output files are in NETCDF format.
994When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
995Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
996So care is needed to recreate data for individual icebergs, since its trajectory data may be spread across
997multiple files.
1000% ================================================================
1001% Miscellanea options
1002% ================================================================
1003\section{Miscellaneous options}
1006% -------------------------------------------------------------------------------------------------------------
1007%        Diurnal cycle
1008% -------------------------------------------------------------------------------------------------------------
1009\subsection   [Diurnal  cycle (\textit{sbcdcy})]
1010         {Diurnal cycle (\mdl{sbcdcy})}
1017\begin{figure}[!t]    \begin{center}
1019\caption{ \label{Fig_SBC_diurnal}   
1020Example of recontruction of the diurnal cycle variation of short wave flux 
1021from daily mean values. The reconstructed diurnal cycle (black line) is chosen
1022as the mean value of the analytical cycle (blue line) over a time step, not
1023as the mid time step value of the analytically cycle (red square). From \citet{Bernie_al_CD07}.}
1024\end{center}   \end{figure}
1027\cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of
1028SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution
1029of the surface fluxes of 3~h or less. Unfortunately high frequency forcing fields are rare,
1030not to say inexistent. Nevertheless, it is possible to obtain a reasonable diurnal cycle
1031of the SST knowning only short wave flux (SWF) at high frequency \citep{Bernie_al_CD07}.
1032Furthermore, only the knowledge of daily mean value of SWF is needed,
1033as higher frequency variations can be reconstructed from them, assuming that
1034the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle
1035of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available
1036in \NEMO by setting \np{ln\_dm2dc}~=~true (a \textit{\ngn{namsbc}} namelist variable) when using
1037CORE bulk formulea (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).
1038The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used
1039can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily
1040mean incomming SWF as the reconstructed SWF at a given time step is the mean value
1041of the analytical cycle over this time step (Fig.\ref{Fig_SBC_diurnal}).
1042The use of diurnal cycle reconstruction requires the input SWF to be daily
1043($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1044Furthermore, it is recommended to have a least 8 surface module time step per day,
1045that is  $\rdt \ \np{nn\_fsbc} < 10,800~s = 3~h$. An example of recontructed SWF
1046is given in Fig.\ref{Fig_SBC_dcy} for a 12 reconstructed diurnal cycle, one every 2~hours
1047(from 1am to 11pm).
1050\begin{figure}[!t]  \begin{center}
1052\caption{ \label{Fig_SBC_dcy}   
1053Example of recontruction of the diurnal cycle variation of short wave flux 
1054from daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1055The display is on (i,j) plane. }
1056\end{center}   \end{figure}
1059Note also that the setting a diurnal cycle in SWF is highly recommended  when
1060the top layer thickness approach 1~m or less, otherwise large error in SST can
1061appear due to an inconsistency between the scale of the vertical resolution
1062and the forcing acting on that scale.
1064% -------------------------------------------------------------------------------------------------------------
1065%        Rotation of vector pairs onto the model grid directions
1066% -------------------------------------------------------------------------------------------------------------
1067\subsection{Rotation of vector pairs onto the model grid directions}
1070When using a flux (\np{ln\_flx}=true) or bulk (\np{ln\_clio}=true or \np{ln\_core}=true) formulation,
1071pairs of vector components can be rotated from east-north directions onto the local grid directions. 
1072This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
1073relative to a rectilinear grid.
1074To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1075The eastward component must start with "U" and the northward component with "V". 
1076The remaining characters in the strings are used to identify which pair of components go together.
1077So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
1078and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
1079and so on.
1080The extra characters used in the strings are arbitrary.
1081The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1083% -------------------------------------------------------------------------------------------------------------
1084%        Surface restoring to observed SST and/or SSS
1085% -------------------------------------------------------------------------------------------------------------
1086\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
1087         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
1093IOptions are defined through the  \ngn{namsbc\_ssr} namelist variables.
1094n forced mode using a flux formulation (\np{ln\_flx}~=~true), a
1095feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1096\begin{equation} \label{Eq_sbc_dmp_q}
1097Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1099where SST is a sea surface temperature field (observed or climatological), $T$ is
1100the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
1101coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
1102mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1103This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
1104equal to $Q_o$.
1106In the fresh water budget, a feedback term can also be added. Converted into an
1107equivalent freshwater flux, it takes the following expression :
1109\begin{equation} \label{Eq_sbc_dmp_emp}
1110\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1111                                             {\left.S\right|_{k=1}}
1114where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an
1115atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
1116interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
1117$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
1118feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
1119physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
1120does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring
1121term should be viewed as a flux correction on freshwater fluxes to reduce the
1122uncertainties we have on the observed freshwater budget.
1124% -------------------------------------------------------------------------------------------------------------
1125%        Handling of ice-covered area
1126% -------------------------------------------------------------------------------------------------------------
1127\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1130The presence at the sea surface of an ice covered area modifies all the fluxes
1131transmitted to the ocean. There are several way to handle sea-ice in the system
1132depending on the value of the \np{nn{\_}ice} namelist parameter. 
1134\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
1135This is a typical namelist value used for tropical ocean domain. The surface fluxes
1136are simply specified for an ice-free ocean. No specific things is done for sea-ice.
1137\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
1138is used. An observed ice covered area is read in a file. Below this area, the SST is
1139restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
1140in the northern (southern) hemisphere. The associated modification of the freshwater
1141fluxes are done in such a way that the change in buoyancy fluxes remains zero.
1142This prevents deep convection to occur when trying to reach the freezing point
1143(and so ice covered area condition) while the SSS is too large. This manner of
1144managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if} 
1145model. It can be found in the \mdl{sbcice{\_}if} module.
1146\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
1147ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
1148each model cell to provide the surface ocean fluxes. Note that the activation of a
1149sea-ice model is is done by defining a CPP key (\key{lim2}, \key{lim3} or \key{cice}).
1150The activation automatically overwrites the read value of nn{\_}ice to its appropriate
1151value ($i.e.$ $2$ for LIM-2, $3$ for LIM-3 or $4$ for CICE).
1154% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1156\subsection   [Interface to CICE (\textit{sbcice\_cice})]
1157         {Interface to CICE (\mdl{sbcice\_cice})}
1160It is now possible to couple a regional or global NEMO configuration (without AGRIF) to the CICE sea-ice
1161model by using \key{cice}.  The CICE code can be obtained from
1162\href{}{LANL} and the additional 'hadgem3' drivers will be required,
1163even with the latest code release.  Input grid files consistent with those used in NEMO will also be needed,
1164and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used (seek advice from UKMO
1165if necessary).  Currently the code is only designed to work when using the CORE forcing option for NEMO (with
1166\textit{calc\_strair~=~true} and \textit{calc\_Tsfc~=~true} in the CICE name-list), or alternatively when NEMO
1167is coupled to the HadGAM3 atmosphere model (with \textit{calc\_strair~=~false} and \textit{calc\_Tsfc~=~false}).
1168The code is intended to be used with \np{nn\_fsbc} set to 1 (although coupling ocean and ice less frequently
1169should work, it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly - the
1170user should check that results are not significantly different to the standard case).
1172There are two options for the technical coupling between NEMO and CICE.  The standard version allows
1173complete flexibility for the domain decompositions in the individual models, but this is at the expense of global
1174gather and scatter operations in the coupling which become very expensive on larger numbers of processors. The
1175alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that the domain decomposition is
1176identical in both models (provided domain parameters are set appropriately, and
1177\textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and allows
1178much more efficient direct coupling on individual processors.  This solution scales much better although it is at
1179the expense of having more idle CICE processors in areas where there is no sea ice.
1181% -------------------------------------------------------------------------------------------------------------
1182%        Freshwater budget control
1183% -------------------------------------------------------------------------------------------------------------
1184\subsection   [Freshwater budget control (\textit{sbcfwb})]
1185         {Freshwater budget control (\mdl{sbcfwb})}
1188For global ocean simulation it can be useful to introduce a control of the mean sea
1189level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
1190in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
1192\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
1193certainly do so.
1194\item[\np{nn\_fwb}=1]  global mean \textit{emp} set to zero at each model time step.
1195%Note that with a sea-ice model, this technique only control the mean sea level with linear free surface (\key{vvl} not defined) and no mass flux between ocean and ice (as it is implemented in the current ice-ocean coupling).
1196\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
1197mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
1198Boussinesq approximation, the annual mean fresh water budget is simply evaluated
1199from the change in the mean sea level at January the first and saved in the
1200\textit{EMPav.dat} file.
1203% -------------------------------------------------------------------------------------------------------------
1204%        Neutral Drag Coefficient from external wave model
1205% -------------------------------------------------------------------------------------------------------------
1206\subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})]
1207                        {Neutral drag coefficient from external wave model (\mdl{sbcwave})}
1214\item [??] In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the
1215logical variable \np{ln\_cdgw}
1216 in $namsbc$ namelist must be defined ${.true.}$.
1217The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the
1218namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all
1219the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input})
1220and a 2D field of neutral drag coefficient. Then using the routine
1221TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according
1222to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
1226% Griffies doc:
1227% When running ocean-ice simulations, we are not explicitly representing land processes, such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, it is important to balance the hydrological cycle in ocean-ice models. We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. The result of the normalization should be a global integrated zero net water input to the ocean-ice system over a chosen time scale.
1228%How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, so that there is always a zero net input of water to the ocean-ice system. Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing.
1229%When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean and ice models when aiming to balance the hydrological cycle. 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, not the water in any one sub-component. As an extreme example to illustrate the issue, consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up, there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. The total water contained in the ocean plus ice system is constant, but there is an exchange of water between the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle in ocean-ice models.
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