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1% ================================================================
2% Chapter � Surface Boundary Condition (SBC, ISF, ICB)
3% ================================================================
4\chapter{Surface Boundary Condition (SBC, ISF, ICB) }
5\label{SBC}
6\minitoc
7
8\newpage
9$\$\newline    % force a new ligne
10%---------------------------------------namsbc--------------------------------------------------
11\namdisplay{namsbc}
12%--------------------------------------------------------------------------------------------------------------
13$\$\newline    % force a new ligne
14
15The ocean needs six fields as surface boundary condition:
16\begin{itemize}
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 $\left( {\textit{emp},\;\textit{emp}_S } \right)$
20\end{itemize}
21plus an optional field:
22\begin{itemize}
23   \item the atmospheric pressure at the ocean surface $\left( p_a \right)$
24\end{itemize}
25
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}).
41If the Interpolation on the Fly option is used, input data belonging to land points (in the native grid),
42can be masked to avoid spurious results in proximity of the coasts  as large sea-land gradients characterize
43most of the atmospheric variables.
44In addition, the resulting fields can be further modified using several namelist options.
45These options control  the rotation of vector components supplied relative to an east-north
46coordinate system onto the local grid directions in the model; the addition of a surface
47restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes
48below ice-covered areas (using observed ice-cover or a sea-ice model)
49(\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater
50fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of isf melting as lateral inflow (parameterisation)
51(\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false) or as surface flux at the land-ice ocean interface
52(\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true);
53the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the
54transformation of the solar radiation (if provided as daily mean) into a diurnal
55cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave
56model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or mfs bulk formulas are selected.
57
58In this chapter, we first discuss where the surface boundary condition appears in the
59model equations. Then we present the five ways of providing the surface boundary condition,
60followed by the description of the atmospheric pressure and the river runoff.
61Next the scheme for interpolation on the fly is described.
62Finally, the different options that further modify the fluxes applied to the ocean are discussed.
63One of these is modification by icebergs (see \S\ref{ICB_icebergs}), which act as drifting sources of fresh water.
64Another example of modification is that due to the ice shelf melting/freezing (see \S\ref{SBC_isf}),
65which provides additional sources of fresh water.
66
67
68% ================================================================
69% Surface boundary condition for the ocean
70% ================================================================
71\section{Surface boundary condition for the ocean}
72\label{SBC_general}
73
74The surface ocean stress is the stress exerted by the wind and the sea-ice
75on the ocean. The two components of stress are assumed to be interpolated
76onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction
77at $u$- and $v$-points They are applied as a surface boundary condition of the
78computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
79\begin{equation} \label{Eq_sbc_dynzdf}
80\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
81    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
82\end{equation}
83where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind
84stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.
85
86The surface heat flux is decomposed into two parts, a non solar and a solar heat
87flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part
88of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes).
89It is applied as a surface boundary condition trend of the first level temperature
90time evolution equation (\mdl{trasbc} module).
91\begin{equation} \label{Eq_sbc_trasbc_q}
92\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho
93_o \;C_p \;e_{3t} }} \right|_{k=1} \quad
94\end{equation}
95$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D
96trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.
97
98\begin{equation} \label{Eq_sbc_traqsr}
99\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right]
100\end{equation}
101where $I_w$ is a non-dimensional function that describes the way the light
102penetrates inside the water column. It is generally a sum of decreasing
103exponentials (see \S\ref{TRA_qsr}).
104
105The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which
106may or may not be identical. Indeed, a surface freshwater flux has two effects:
107it changes the volume of the ocean and it changes the surface concentration of
108salt (and other tracers). Therefore it appears in the sea surface height as a volume
109flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations
110as a concentration/dilution effect,
111$\textit{emp}_{S}$ (\mdl{trasbc} module).
112\begin{equation} \label{Eq_trasbc_emp}
113\begin{aligned}
114&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad  \\
115\\
116 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\
117 \end{aligned}
118\end{equation}
119
120In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved,
121but it exist several numerical reasons why this equality should be broken.
122For example, when the ocean is coupled to a sea-ice model, the water exchanged between
123ice and ocean is slightly salty (mean sea-ice salinity is $\sim$\textit{4 psu}). In this case,
124$\textit{emp}_{S}$ take into account both concentration/dilution effect associated with
125freezing/melting and the salt flux between ice and ocean, while \textit{emp} is
126only the volume flux. In addition, in the current version of \NEMO, the sea-ice is
127assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does
128not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS.
129%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.
130
131Note that SST can also be modified by a freshwater flux. Precipitation (in
132particular solid precipitation) may have a temperature significantly different from
133the SST. Due to the lack of information about the temperature of
134precipitation, we assume it is equal to the SST. Therefore, no
135concentration/dilution term appears in the temperature equation. It has to
136be emphasised that this absence does not mean that there is no heat flux
137associated with precipitation! Precipitation can change the ocean volume and thus the
138ocean heat content. It is therefore associated with a heat flux (not yet
140
141%\colorbox{yellow}{Miss: }
142%
143%A extensive description of all namsbc namelist (parameter that have to be
144%created!)
145%
146%Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu
147%ssv) i.e. information required by flux computation or sea-ice
148%
149%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add
150%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
151%
152%Sbcmod manage the providing'' (fourniture) to the ocean the 7 fields
153%
154%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation
155%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one
156%nf{\_}sbc
157%
158%Explain here all the namlist namsbc variable{\ldots}.
159%
160%\colorbox{yellow}{End Miss }
161
162The ocean model provides the surface currents, temperature and salinity
163averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the
164mean is done in \mdl{sbcmod} module.
165
166%-------------------------------------------------TABLE---------------------------------------------------
167\begin{table}[tb]   \begin{center}   \begin{tabular}{|l|l|l|l|}
168\hline
169Variable description             & Model variable  & Units  & point \\  \hline
170i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
171j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
172Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
173Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
174\end{tabular}
175\caption{  \label{Tab_ssm}
176Ocean variables provided by the ocean to the surface module (SBC).
177The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of
178computation of surface fluxes.}
179\end{center}   \end{table}
180%--------------------------------------------------------------------------------------------------------------
181
182%\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
183
184
185% ================================================================
186%       Input Data
187% ================================================================
188\section{Input Data generic interface}
189\label{SBC_input}
190
191A generic interface has been introduced to manage the way input data (2D or 3D fields,
192like surface forcing or ocean T and S) are specify in \NEMO. This task is archieved by fldread.F90.
193The module was design with four main objectives in mind:
194\begin{enumerate}
195\item optionally provide a time interpolation of the input data at model time-step,
196whatever their input frequency is, and according to the different calendars available in the model.
197\item optionally provide an on-the-fly space interpolation from the native input data grid to the model grid.
198\item make the run duration independent from the period cover by the input files.
199\item provide a simple user interface and a rather simple developer interface by limiting the
200 number of prerequisite information.
201\end{enumerate}
202
203As a results the user have only to fill in for each variable a structure in the namelist file
204to defined the input data file and variable names, the frequency of the data (in hours or months),
205whether its is climatological data or not, the period covered by the input file (one year, month, week or day),
206and three additional parameters for on-the-fly interpolation. When adding a new input variable,
207the developer has to add the associated structure in the namelist, read this information
208by mirroring the namelist read in \rou{sbc\_blk\_init} for example, and simply call \rou{fld\_read}
209to obtain the desired input field at the model time-step and grid points.
210
211The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature
212(see \S\ref{SBC_fldread}), the period it cover is one year, month, week or day, and, if on-the-fly
213interpolation is used, a file of weights must be supplied (see \S\ref{SBC_iof}).
214
215Note that when an input data is archived on a disc which is accessible directly
216from the workspace where the code is executed, then the use can set the \np{cn\_dir}
217to the pathway leading to the data. By default, the data are assumed to have been
218copied so that cn\_dir='./'.
219
220% -------------------------------------------------------------------------------------------------------------
222% -------------------------------------------------------------------------------------------------------------
225
226The structure associated with an input variable contains the following information:
227\begin{alltt}  {{\tiny
228\begin{verbatim}
229!  file name  ! frequency (hours) ! variable  ! time interp. !  clim  ! 'yearly'/ ! weights  ! rotation ! land/sea mask !
230!             !  (if <0  months)  !   name    !   (logical)  !  (T/F) ! 'monthly' ! filename ! pairing  ! filename      !
231\end{verbatim}
232}}\end{alltt}
233where
234\begin{description}
235\item[File name]: the stem name of the NetCDF file to be open.
236This stem will be completed automatically by the model, with the addition of a '.nc' at its end
237and by date information and possibly a prefix (when using AGRIF).
238Tab.\ref{Tab_fldread} provides the resulting file name in all possible cases according to whether
239it is a climatological file or not, and to the open/close frequency (see below for definition).
240
241%--------------------------------------------------TABLE--------------------------------------------------
242\begin{table}[htbp]
243\begin{center}
244\begin{tabular}{|l|c|c|c|}
245\hline
246                         & daily or weekLLL          & monthly                   &   yearly          \\   \hline
247clim = false   & fn\_yYYYYmMMdDD  &   fn\_yYYYYmMM   &   fn\_yYYYY  \\   \hline
248clim = true       & not possible                  &  fn\_m??.nc             &   fn                \\   \hline
249\end{tabular}
250\end{center}
251\caption{ \label{Tab_fldread}   naming nomenclature for climatological or interannual input file,
252as a function of the Open/close frequency. The stem name is assumed to be 'fn'.
253For 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
254actual year/month/day, always coded with 4 or 2 digits. Note that (1) in mpp, if the file is split
255over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc', where 'PPPP' is the
256process number coded with 4 digits; (2) when using AGRIF, the prefix
258where 'N'  is the child grid number.}
259\end{table}
260%--------------------------------------------------------------------------------------------------------------
261
262
263\item[Record frequency]: the frequency of the records contained in the input file.
264Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative
265(for example -1 for monthly forcing or -12 for annual forcing).
266Note that this frequency must really be an integer and not a real.
267On some computers, seting it to '24.' can be interpreted as 240!
268
269\item[Variable name]: the name of the variable to be read in the input NetCDF file.
270
271\item[Time interpolation]: a logical to activate, or not, the time interpolation. If set to 'false',
272the forcing will have a steplike shape remaining constant during each forcing period.
273For example, when using a daily forcing without time interpolation, the forcing remaining
274constant from 00h00'00'' to 23h59'59". If set to 'true', the forcing will have a broken line shape.
275Records are assumed to be dated the middle of the forcing period.
276For example, when using a daily forcing with time interpolation, linear interpolation will
277be performed between mid-day of two consecutive days.
278
279\item[Climatological forcing]: a logical to specify if a input file contains climatological forcing
280which can be cycle in time, or an interannual forcing which will requires additional files
281if the period covered by the simulation exceed the one of the file. See the above the file
282naming strategy which impacts the expected name of the file to be opened.
283
284\item[Open/close frequency]: the frequency at which forcing files must be opened/closed.
285Four cases are coded: 'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week),
286'monthly' and 'yearly' which means the forcing files will contain data for one day, one week,
287one month or one year. Files are assumed to contain data from the beginning of the open/close period.
288For example, the first record of a yearly file containing daily data is Jan 1st even if the experiment
289is not starting at the beginning of the year.
290
291\item[Others]: 'weights filename', 'pairing rotation' and 'land/sea mask' are associted with on-the-fly interpolation
292which is described in \S\ref{SBC_iof}.
293
294\end{description}
295
297(1) The time interpolation is a simple linear interpolation between two consecutive records of
298the input data. The only tricky point is therefore to specify the date at which we need to do
299the interpolation and the date of the records read in the input files.
300Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the
301time step. For example, for an experiment starting at 0h00'00" with a one hour time-step,
302a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc.
303However, for forcing data related to the surface module, values are not needed at every
304time-step but at every \np{nn\_fsbc} time-step. For example with \np{nn\_fsbc}~=~3,
305the surface module will be called at time-steps 1, 4, 7, etc. The date used for the time interpolation
306is thus redefined to be at the middle of \np{nn\_fsbc} time-step period. In the previous example,
307this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\
308(2) For code readablility and maintenance issues, we don't take into account the NetCDF input file
309calendar. The calendar associated with the forcing field is build according to the information
310provided by user in the record frequency, the open/close frequency and the type of temporal interpolation.
311For example, the first record of a yearly file containing daily data that will be interpolated in time
312is assumed to be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\
313(3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file
314when interpolating data with the first (last) record of the open/close period.
315For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'',
316the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values
317between Dec 31st 12h00'00" and Jan 1st 12h00'00". If the forcing is climatological, Dec and Jan will
318be keep-up from the same year. However, if the forcing is not climatological, at the end of the
319open/close period the code will automatically close the current file and open the next one.
320Note that, if the experiment is starting (ending) at the beginning (end) of an open/close period
321we do accept that the previous (next) file is not existing. In this case, the time interpolation
322will be performed between two identical values. For example, when starting an experiment on
323Jan 1st of year Y with yearly files and daily data to be interpolated, we do accept that the file
324related to year Y-1 is not existing. The value of Jan 1st will be used as the missing one for
325Dec 31st of year Y-1. If the file of year Y-1 exists, the code will read its last record.
326Therefore, this file can contain only one record corresponding to Dec 31st, a useful feature for
327user considering that it is too heavy to manipulate the complete file for year Y-1.
328
329
330% -------------------------------------------------------------------------------------------------------------
331% Interpolation on the Fly
332% -------------------------------------------------------------------------------------------------------------
333\subsection [Interpolation on-the-Fly] {Interpolation on-the-Fly}
334\label{SBC_iof}
335
336Interpolation on the Fly allows the user to supply input files required
337for the surface forcing on grids other than the model grid.
338To do this he or she must supply, in addition to the source data file,
339a file of weights to be used to interpolate from the data grid to the model grid.
340The original development of this code used the SCRIP package (freely available
342In principle, any package can be used to generate the weights, but the
343variables in the input weights file must have the same names and meanings as
344assumed by the model.
345Two methods are currently available: bilinear and bicubic interpolation.
346Prior to the interpolation, providing a land/sea mask file, the user can decide to
347 remove land points from the input file and substitute the corresponding values
348with the average of the 8 neighbouring points in the native external grid.
349 Only "sea points" are considered for the averaging. The land/sea mask file must
350be provided in the structure associated with the input variable.
351 The netcdf land/sea mask variable name must be 'LSM' it must have the same
352horizontal and vertical dimensions of the associated variable and should
353be equal to 1 over land and 0 elsewhere.
354The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.
355Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied.
356
357\subsubsection{Bilinear Interpolation}
358\label{SBC_iof_bilinear}
359
360The input weights file in this case has two sets of variables: src01, src02,
361src03, src04 and wgt01, wgt02, wgt03, wgt04.
362The "src" variables correspond to the point in the input grid to which the weight
363"wgt" is to be applied. Each src value is an integer corresponding to the index of a
364point in the input grid when written as a one dimensional array.  For example, for an input grid
365of size 5x10, point (3,2) is referenced as point 8, since (2-1)*5+3=8.
366There are four of each variable because bilinear interpolation uses the four points defining
367the grid box containing the point to be interpolated.
368All of these arrays are on the model grid, so that values src01(i,j) and
369wgt01(i,j) are used to generate a value for point (i,j) in the model.
370
371Symbolically, the algorithm used is:
372
373\begin{equation}
374f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
375\end{equation}
376where function idx() transforms a one dimensional index src(k) into a two dimensional index,
377and wgt(1) corresponds to variable "wgt01" for example.
378
379\subsubsection{Bicubic Interpolation}
380\label{SBC_iof_bicubic}
381
382Again there are two sets of variables: "src" and "wgt".
383But in this case there are 16 of each.
384The symbolic algorithm used to calculate values on the model grid is now:
385
386\begin{equation*} \begin{split}
387f_{m}(i,j) =  f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))}
388              +   \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right| _{idx(src(k))} }    \\
389              +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right| _{idx(src(k))} }
390              +   \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right| _{idx(src(k))} }
391\end{split}
392\end{equation*}
393The gradients here are taken with respect to the horizontal indices and not distances since the spatial dependency has been absorbed into the weights.
394
395\subsubsection{Implementation}
396\label{SBC_iof_imp}
397
398To activate this option, a non-empty string should be supplied in the weights filename column
399of the relevant namelist; if this is left as an empty string no action is taken.
400In the model, weights files are read in and stored in a structured type (WGT) in the fldread
401module, as and when they are first required.
402This initialisation procedure determines whether the input data grid should be treated
403as cyclical or not by inspecting a global attribute stored in the weights input file.
404This attribute must be called "ew\_wrap" and be of integer type.
405If it is negative, the input non-model grid is assumed not to be cyclic.
406If zero or greater, then the value represents the number of columns that overlap.
407$E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0;
408if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2.
409If the model does not find attribute ew\_wrap, then a value of -999 is assumed.
410In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and therefore the grid
411is assumed to be cyclic with no overlapping columns.
412(In fact this only matters when bicubic interpolation is required.)
413Note that no testing is done to check the validity in the model, since there is no way
414of knowing the name used for the longitude variable,
415so it is up to the user to make sure his or her data is correctly represented.
416
417Next the routine reads in the weights.
418Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise
419bilinear interpolation is used. The WGT structure includes dynamic arrays both for
420the storage of the weights (on the model grid), and when required, for reading in
421the variable to be interpolated (on the input data grid).
422The size of the input data array is determined by examining the values in the "src"
423arrays to find the minimum and maximum i and j values required.
424Since bicubic interpolation requires the calculation of gradients at each point on the grid,
425the corresponding arrays are dimensioned with a halo of width one grid point all the way around.
426When the array of points from the data file is adjacent to an edge of the data grid,
427the halo is either a copy of the row/column next to it (non-cyclical case), or is a copy
428of one from the first few columns on the opposite side of the grid (cyclical case).
429
430\subsubsection{Limitations}
431\label{SBC_iof_lim}
432
433\begin{enumerate}
434\item  The case where input data grids are not logically rectangular has not been tested.
435\item  This code is not guaranteed to produce positive definite answers from positive definite inputs
436          when a bicubic interpolation method is used.
437\item  The cyclic condition is only applied on left and right columns, and not to top and bottom rows.
438\item  The gradients across the ends of a cyclical grid assume that the grid spacing between
439          the two columns involved are consistent with the weights used.
440\item  Neither interpolation scheme is conservative. (There is a conservative scheme available
441          in SCRIP, but this has not been implemented.)
442\end{enumerate}
443
444\subsubsection{Utilities}
445\label{SBC_iof_util}
446
447% to be completed
448A set of utilities to create a weights file for a rectilinear input grid is available
449(see the directory NEMOGCM/TOOLS/WEIGHTS).
450
451% -------------------------------------------------------------------------------------------------------------
452% Standalone Surface Boundary Condition Scheme
453% -------------------------------------------------------------------------------------------------------------
454\subsection [Standalone Surface Boundary Condition Scheme] {Standalone Surface Boundary Condition Scheme}
455\label{SAS_iof}
456
457%---------------------------------------namsbc_ana--------------------------------------------------
458\namdisplay{namsbc_sas}
459%--------------------------------------------------------------------------------------------------------------
460
461In 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.
462Options are defined through the  \ngn{namsbc\_sas} namelist variables.
463For example:
464
465\begin{enumerate}
466\item  Multiple runs of the model are required in code development to see the affect of different algorithms in
467       the bulk formulae.
468\item  The effect of different parameter sets in the ice model is to be examined.
469\end{enumerate}
470
471The StandAlone Surface scheme provides this utility.
472A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM.
473However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0)
474In this configuration, a few routines in the standard model are overriden by new versions.
475Routines replaced are:
476
477\begin{enumerate}
478\item  \mdl{nemogcm}
479
480       This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90)
481       Since the ocean state is not calculated all associated initialisations have been removed.
482\item  \mdl{step}
483
484       The main time stepping routine now only needs to call the sbc routine (and a few utility functions).
485\item  \mdl{sbcmod}
486
487       This has been cut down and now only calculates surface forcing and the ice model required.  New surface modules
488       that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs).
489\item  \mdl{daymod}
490
491       No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions
492       have been removed.  This also means that the calendar cannot be controlled by time in a restart file, so the user
493       must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes.
494\item  \mdl{stpctl}
495
496       Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module.
497\item  \mdl{diawri}
498
499       All 3D data have been removed from the output.  The surface temperature, salinity and velocity components (which
500       have been read in) are written along with relevant forcing and ice data.
501\end{enumerate}
502
503One new routine has been added:
504
505\begin{enumerate}
506\item  \mdl{sbcsas}
507       This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface.
508       These filenames are supplied in namelist namsbc{\_}sas.  Unfortunately because of limitations with the \mdl{iom} module,
509       the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level.
510       Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution.
511\end{enumerate}
512
513% ================================================================
514% Analytical formulation (sbcana module)
515% ================================================================
516\section  [Analytical formulation (\textit{sbcana}) ]
517      {Analytical formulation (\mdl{sbcana} module) }
518\label{SBC_ana}
519
520%---------------------------------------namsbc_ana--------------------------------------------------
521\namdisplay{namsbc_ana}
522%--------------------------------------------------------------------------------------------------------------
523
524The analytical formulation of the surface boundary condition is the default scheme.
525In this case, all the six fluxes needed by the ocean are assumed to
526be uniform in space. They take constant values given in the namelist
527\ngn{namsbc{\_}ana} by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0},
528\np{rn\_qsr0}, and \np{rn\_emp0} ($\textit{emp}=\textit{emp}_S$). The runoff is set to zero.
529In addition, the wind is allowed to reach its nominal value within a given number
530of time steps (\np{nn\_tau000}).
531
532If a user wants to apply a different analytical forcing, the \mdl{sbcana}
533module can be modified to use another scheme. As an example,
534the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the
535GYRE configuration (see GYRE configuration manual, in preparation).
536
537
538% ================================================================
539% Flux formulation
540% ================================================================
541\section  [Flux formulation (\textit{sbcflx}) ]
542      {Flux formulation (\mdl{sbcflx} module) }
543\label{SBC_flx}
544%------------------------------------------namsbc_flx----------------------------------------------------
545\namdisplay{namsbc_flx}
546%-------------------------------------------------------------------------------------------------------------
547
548In the flux formulation (\np{ln\_flx}=true), the surface boundary
549condition fields are directly read from input files. The user has to define
550in the namelist \ngn{namsbc{\_}flx} the name of the file, the name of the variable
551read in the file, the time frequency at which it is given (in hours), and a logical
552setting whether a time interpolation to the model time step is required
553for this field. See \S\ref{SBC_fldread} for a more detailed description of the parameters.
554
555Note that in general, a flux formulation is used in associated with a
556restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its
557specification.
558
559
560% ================================================================
561% Bulk formulation
562% ================================================================
563\section  [Bulk formulation (\textit{sbcblk\_core}, \textit{sbcblk\_clio} or \textit{sbcblk\_mfs}) ]
564      {Bulk formulation \small{(\mdl{sbcblk\_core} \mdl{sbcblk\_clio} \mdl{sbcblk\_mfs} modules)} }
565\label{SBC_blk}
566
567In the bulk formulation, the surface boundary condition fields are computed
568using bulk formulae and atmospheric fields and ocean (and ice) variables.
569
570The atmospheric fields used depend on the bulk formulae used. Three bulk formulations
571are available : the CORE, the CLIO and the MFS bulk formulea. The choice is made by setting to true
572one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or  \np{ln\_mfs}.
573
574Note : in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.
575Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over both
576an ocean and an ice surface.
577
578% -------------------------------------------------------------------------------------------------------------
579%        CORE Bulk formulea
580% -------------------------------------------------------------------------------------------------------------
581\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
582            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
583\label{SBC_blk_core}
584%------------------------------------------namsbc_core----------------------------------------------------
585\namdisplay{namsbc_core}
586%-------------------------------------------------------------------------------------------------------------
587
588The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}.
589They have been designed to handle the CORE forcing, a mixture of NCEP
590reanalysis and satellite data. They use an inertial dissipative method to compute
591the turbulent transfer coefficients (momentum, sensible heat and evaporation)
592from the 10 metre wind speed, air temperature and specific humidity.
593This \citet{Large_Yeager_Rep04} dataset is available through the
595
596Note that substituting ERA40 to NCEP reanalysis fields
597does not require changes in the bulk formulea themself.
598This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.
599
600Options are defined through the  \ngn{namsbc\_core} namelist variables.
601The required 8 input fields are:
602
603%--------------------------------------------------TABLE--------------------------------------------------
604\begin{table}[htbp]   \label{Tab_CORE}
605\begin{center}
606\begin{tabular}{|l|c|c|c|}
607\hline
608Variable desciption              & Model variable  & Units   & point \\    \hline
609i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
610j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
61110m air temperature              & tair      & \r{}$K$            & T   \\ \hline
612Specific humidity             & humi      & \%              & T \\      \hline
613Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
614Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
615Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
616Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
617\end{tabular}
618\end{center}
619\end{table}
620%--------------------------------------------------------------------------------------------------------------
621
622Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean
623point ($u$- and $v$-points). It is simpler and faster (less fields to be read),
624but it is not the recommended method when the ocean grid size is the same
625or larger than the one of the input atmospheric fields.
626
627% -------------------------------------------------------------------------------------------------------------
628%        CLIO Bulk formulea
629% -------------------------------------------------------------------------------------------------------------
630\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
631            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
632\label{SBC_blk_clio}
633%------------------------------------------namsbc_clio----------------------------------------------------
634\namdisplay{namsbc_clio}
635%-------------------------------------------------------------------------------------------------------------
636
637The CLIO bulk formulae were developed several years ago for the
638Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}).
639They are simpler bulk formulae. They assume the stress to be known and
640compute the radiative fluxes from a climatological cloud cover.
641
642Options are defined through the  \ngn{namsbc\_clio} namelist variables.
643The required 7 input fields are:
644
645%--------------------------------------------------TABLE--------------------------------------------------
646\begin{table}[htbp]   \label{Tab_CLIO}
647\begin{center}
648\begin{tabular}{|l|l|l|l|}
649\hline
650Variable desciption           & Model variable  & Units           & point \\  \hline
651i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
652j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
653Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
65410m air temperature              & tair         & \r{}$K$            & T \\   \hline
655Specific humidity                & humi         & \%              & T \\   \hline
656Cloud cover                   &           & \%              & T \\   \hline
657Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
658Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
659\end{tabular}
660\end{center}
661\end{table}
662%--------------------------------------------------------------------------------------------------------------
663
664As for the flux formulation, information about the input data required by the
665model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio
667
668% -------------------------------------------------------------------------------------------------------------
669%        MFS Bulk formulae
670% -------------------------------------------------------------------------------------------------------------
671\subsection    [MFS Bulk formulea (\np{ln\_mfs}=true)]
672            {MFS Bulk formulea (\np{ln\_mfs}=true, \mdl{sbcblk\_mfs})}
673\label{SBC_blk_mfs}
674%------------------------------------------namsbc_mfs----------------------------------------------------
675\namdisplay{namsbc_mfs}
676%----------------------------------------------------------------------------------------------------------
677
678The MFS (Mediterranean Forecasting System) bulk formulae have been developed by
679 \citet{Castellari_al_JMS1998}.
680They have been designed to handle the ECMWF operational data and are currently
681in use in the MFS operational system \citep{Tonani_al_OS08}, \citep{Oddo_al_OS09}.
682The wind stress computation uses a drag coefficient computed according to \citet{Hellerman_Rosenstein_JPO83}.
683The surface boundary condition for temperature involves the balance between surface solar radiation,
684net long-wave radiation, the latent and sensible heat fluxes.
685Solar radiation is dependent on cloud cover and is computed by means of
686an astronomical formula \citep{Reed_JPO77}. Albedo monthly values are from \citet{Payne_JAS72}
687as means of the values at $40^{o}N$ and $30^{o}N$ for the Atlantic Ocean (hence the same latitudinal
688band of the Mediterranean Sea). The net long-wave radiation flux
689\citep{Bignami_al_JGR95} is a function of
690air temperature, sea-surface temperature, cloud cover and relative humidity.
691Sensible heat and latent heat fluxes are computed by classical
692bulk formulae parameterised according to \citet{Kondo1975}.
693Details on the bulk formulae used can be found in \citet{Maggiore_al_PCE98} and \citet{Castellari_al_JMS1998}.
694
695Options are defined through the  \ngn{namsbc\_mfs} namelist variables.
696The required 7 input fields must be provided on the model Grid-T and  are:
697\begin{itemize}
698\item          Zonal Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windi})
699\item          Meridional Component of the 10m wind ($ms^{-1}$)  (\np{sn\_windj})
700\item          Total Claud Cover (\%)  (\np{sn\_clc})
701\item          2m Air Temperature ($K$) (\np{sn\_tair})
702\item          2m Dew Point Temperature ($K$)  (\np{sn\_rhm})
703\item          Total Precipitation ${Kg} m^{-2} s^{-1}$ (\np{sn\_prec})
704\item          Mean Sea Level Pressure (${Pa}$) (\np{sn\_msl})
705\end{itemize}
706% -------------------------------------------------------------------------------------------------------------
707% ================================================================
708% Coupled formulation
709% ================================================================
710\section  [Coupled formulation (\textit{sbccpl}) ]
711      {Coupled formulation (\mdl{sbccpl} module)}
712\label{SBC_cpl}
713%------------------------------------------namsbc_cpl----------------------------------------------------
714\namdisplay{namsbc_cpl}
715%-------------------------------------------------------------------------------------------------------------
716
717In the coupled formulation of the surface boundary condition, the fluxes are
718provided by the OASIS coupler at a frequency which is defined in the OASIS coupler,
719while sea and ice surface temperature, ocean and ice albedo, and ocean currents
720are sent to the atmospheric component.
721
722A generalised coupled interface has been developed. It is currently interfaced with OASIS 3
723(\key{oasis3}) and does not support OASIS 4
724\footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}.
725It has been successfully used to interface \NEMO to most of the European atmospheric
727as well as to \href{http://wrf-model.org/}{WRF} (Weather Research and Forecasting Model).
728
729Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined.
730The CPP key is mainly used in sea-ice to ensure that the atmospheric fluxes are
731actually recieved by the ice-ocean system (no calculation of ice sublimation in coupled mode).
732When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system,
733the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}. In this case,
734CO$_2$ fluxes will be exchanged between the atmosphere and the ice-ocean system (and need to be activated in \ngn{namsbc{\_}cpl} ).
735
736The namelist above allows control of various aspects of the coupling fields (particularly for
737vectors) and now allows for any coupling fields to have multiple sea ice categories (as required by LIM3
738and CICE).  When indicating a multi-category coupling field in namsbc{\_}cpl the number of categories will be
739determined by the number used in the sea ice model.  In some limited cases it may be possible to specify
740single category coupling fields even when the sea ice model is running with multiple categories - in this
741case the user should examine the code to be sure the assumptions made are satisfactory.  In cases where
742this is definitely not possible the model should abort with an error message.  The new code has been tested using
743ECHAM with LIM2, and HadGAM3 with CICE but although it will compile with \key{lim3} additional minor code changes
744may be required to run using LIM3.
745
746
747% ================================================================
748%        Atmospheric pressure
749% ================================================================
750\section   [Atmospheric pressure (\textit{sbcapr})]
751         {Atmospheric pressure (\mdl{sbcapr})}
752\label{SBC_apr}
753%------------------------------------------namsbc_apr----------------------------------------------------
754\namdisplay{namsbc_apr}
755%-------------------------------------------------------------------------------------------------------------
756
757The optional atmospheric pressure can be used to force ocean and ice dynamics
758(\np{ln\_apr\_dyn}~=~true, \textit{\ngn{namsbc}} namelist ).
759The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist)
760can be interpolated in time to the model time step, and even in space when the
761interpolation on-the-fly is used. When used to force the dynamics, the atmospheric
762pressure is further transformed into an equivalent inverse barometer sea surface height,
763$\eta_{ib}$, using:
764\begin{equation} \label{SBC_ssh_ib}
765   \eta_{ib} = -  \frac{1}{g\,\rho_o}  \left( P_{atm} - P_o \right)
766\end{equation}
767where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure.
768A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. In this case $P_o$
769is set to the value of $P_{atm}$ averaged over the ocean domain, $i.e.$ the mean value of
770$\eta_{ib}$ is kept to zero at all time step.
771
772The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation
773(see \mdl{dynspg} for the ocean). For sea-ice, the sea surface height, $\eta_m$,
774which is provided to the sea ice model is set to $\eta - \eta_{ib}$ (see \mdl{sbcssr} module).
775$\eta_{ib}$ can be set in the output. This can simplify altimetry data and model comparison
776as inverse barometer sea surface height is usually removed from these date prior to their distribution.
777
778When using time-splitting and BDY package for open boundaries conditions, the equivalent
779inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data:
780\np{ln\_apr\_obc}  might be set to true.
781
782% ================================================================
783%        Tidal Potential
784% ================================================================
785\section   [Tidal Potential (\textit{sbctide})]
786                        {Tidal Potential (\mdl{sbctide})}
787\label{SBC_tide}
788
789A module is available to use the tidal potential forcing and is activated with with \key{tide}.
790
791
792%------------------------------------------nam_tide----------------------------------------------------
793\namdisplay{nam_tide}
794%-------------------------------------------------------------------------------------------------------------
795
796Concerning the tidal potential, some parameters are available in namelist \ngn{nam\_tide}:
797
798- \np{ln\_tide\_pot} activate the tidal potential forcing
799
800- \np{nb\_harmo} is the number of constituent used
801
802- \np{clname} is the name of constituent
803
804
805The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem;
806they are expressed as the gradient of the astronomical potential ($\vec{\nabla}\Pi_{a}$). \\
807
808The potential astronomical expressed, for the three types of tidal frequencies
809following, by : \\
810Tide long period :
811\begin{equation}
812\Pi_{a}=gA_{k}(\frac{1}{2}-\frac{3}{2}sin^{2}\phi)cos(\omega_{k}t+V_{0k})
813\end{equation}
814diurnal Tide :
815\begin{equation}
816\Pi_{a}=gA_{k}(sin 2\phi)cos(\omega_{k}t+\lambda+V_{0k})
817\end{equation}
818Semi-diurnal tide:
819\begin{equation}
820\Pi_{a}=gA_{k}(cos^{2}\phi)cos(\omega_{k}t+2\lambda+V_{0k})
821\end{equation}
822
823
824$A_{k}$ is the amplitude of the wave k, $\omega_{k}$ the pulsation of the wave k, $V_{0k}$ the astronomical phase of the wave
825$k$ to Greenwich.
826
827We make corrections to the astronomical potential.
828We obtain :
829\begin{equation}
830\Pi-g\delta = (1+k-h) \Pi_{A}(\lambda,\phi)
831\end{equation}
832with $k$ a number of Love estimated to 0.6 which parameterised the astronomical tidal land,
833and $h$ a number of Love to 0.3 which parameterised the parameterisation due to the astronomical tidal land.
834
835% ================================================================
836%        River runoffs
837% ================================================================
838\section   [River runoffs (\textit{sbcrnf})]
839         {River runoffs (\mdl{sbcrnf})}
840\label{SBC_rnf}
841%------------------------------------------namsbc_rnf----------------------------------------------------
842\namdisplay{namsbc_rnf}
843%-------------------------------------------------------------------------------------------------------------
844
845%River runoff generally enters the ocean at a nonzero depth rather than through the surface.
846%Many models, however, have traditionally inserted river runoff to the top model cell.
847%This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff
848%throughout a nonzero depth has been motivated by the numerical and physical problems
849%that arise when the top grid cells are of the order of one meter. This situation is common in
850%coastal modelling and becomes more and more often open ocean and climate modelling
851%\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
853
854
855%To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the
856%\mdl{tra\_sbc} module.  We decided to separate them throughout the code, so that the variable
857%\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable
858%rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with
859%emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use
860%emp or emps and the changes made are below:
861
862
863%Rachel:
864River runoff generally enters the ocean at a nonzero depth rather than through the surface.
865Many models, however, have traditionally inserted river runoff to the top model cell.
866This was the case in \NEMO prior to the version 3.3, and was combined with an option
867to increase vertical mixing near the river mouth.
868
869However, with this method numerical and physical problems arise when the top grid cells are
870of the order of one meter. This situation is common in coastal modelling and is becoming
871more common in open ocean and climate modelling
872\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are
874
875As such from V~3.3 onwards it is possible to add river runoff through a non-zero depth, and for the
876temperature and salinity of the river to effect the surrounding ocean.
877The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, along with the
878depth (in metres) which the river should be added to.
879
880Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and \np{ln\_rnf\_temp} control whether
881the river attributes (depth, salinity and temperature) are read in and used.  If these are set
882as false the river is added to the surface box only, assumed to be fresh (0~psu), and/or
883taken as surface temperature respectively.
884
885The runoff value and attributes are read in in sbcrnf.
886For temperature -999 is taken as missing data and the river temperature is taken to be the
887surface temperatue at the river point.
888For the depth parameter a value of -1 means the river is added to the surface box only,
889and a value of -999 means the river is added through the entire water column.
890After being read in the temperature and salinity variables are multiplied by the amount of runoff (converted into m/s)
891to give the heat and salt content of the river runoff.
892After the user specified depth is read ini, the number of grid boxes this corresponds to is
893calculated and stored in the variable \np{nz\_rnf}.
894The variable \textit{h\_dep} is then calculated to be the depth (in metres) of the bottom of the
895lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model).
896
897The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence
898(\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}).
899This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux.
900The sea surface height is calculated using the sum of the horizontal divergence terms, and so the
901river runoff indirectly forces an increase in sea surface height.
902
903The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities.
904This causes a mass of water, equal to the amount of runoff, to be moved into the box above.
905The heat and salt content of the river runoff is not included in this step, and so the tracer
906concentrations are diluted as water of ocean temperature and salinity is moved upward out of the box
907and replaced by the same volume of river water with no corresponding heat and salt addition.
908
909For the linear free surface case, at the surface box the tracer advection causes a flux of water
910(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.
911As such the volume of water does not change, but the water is diluted.
912
913For the non-linear free surface case (\key{vvl}), no flux is allowed through the surface.
914Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water
915is added with no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect.
916(The runoff addition to the top box along with the water being moved up through boxes below means the surface box has a large
917increase in volume, whilst all other boxes remain the same size)
918
919In trasbc the addition of heat and salt due to the river runoff is added.
920This is done in the same way for both vvl and non-vvl.
921The temperature and salinity are increased through the specified depth according to the heat and salt content of the river.
922
923In the non-linear free surface case (vvl), near the end of the time step the change in sea surface height is redistrubuted
924through the grid boxes, so that the original ratios of grid box heights are restored.
925In 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.
926
927It 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.
928When 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.
929
930
931%\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river
932
933%All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.}
934
935%\colorbox{yellow}{river mouths{\ldots}}
936
937%IF( ln_rnf ) THEN                                     ! increase diffusivity at rivers mouths
938%        DO jk = 2, nkrnf   ;   avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:)   ;   END DO
939%ENDIF
940
941%\gmcomment{  word doc of runoffs:
942%
943%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.
944%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.
945
946%The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between.
947
948%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:
949
950%}
951% ================================================================
952%        Ice shelf melting
953% ================================================================
954\section   [Ice shelf melting (\textit{sbcisf})]
955                        {Ice shelf melting (\mdl{sbcisf})}
956\label{SBC_isf}
957%------------------------------------------namsbc_isf----------------------------------------------------
958\namdisplay{namsbc_isf}
959%--------------------------------------------------------------------------------------------------------
960Namelist variable in \ngn{namsbc}, \np{nn\_isf},  control the kind of ice shelf representation used.
961\begin{description}
962\item[\np{nn\_isf}~=~1]
963The ice shelf cavity is represented. The fwf and heat flux are computed.
964Full description, sensitivity and validation in preparation.
965
966\item[\np{nn\_isf}~=~2]
967A parameterisation of isf is used. The ice shelf cavity is not represented.
968The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL)
969(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}~=~3).
970Furthermore the fwf is computed using the \citet{Beckmann2003} parameterisation of isf melting.
971The effective melting length (\np{sn\_Leff\_isf}) is read from a file.
972
973\item[\np{nn\_isf}~=~3]
974A simple parameterisation of isf is used. The ice shelf cavity is not represented.
975The fwf (\np{sn\_rnfisf}) is distributed along the ice shelf edge between the depth of the average grounding line (GL)
976(\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}).
977Full description, sensitivity and validation in preparation.
978
979\item[\np{nn\_isf}~=~4]
980The ice shelf cavity is represented. However, the fwf (\np{sn\_fwfisf}) and heat flux (\np{sn\_qisf}) are
981not computed but specified from file.
982\end{description}
983
984\np{nn\_isf}~=~1 and \np{nn\_isf}~=~2 compute a melt rate based on the water masse properties, ocean velocities and depth.
985 This flux is thus highly dependent of the model resolution (horizontal and vertical), realism of the water masse onto the shelf ...
986
987\np{nn\_isf}~=~3 and \np{nn\_isf}~=~4 read the melt rate and heat flux from a file. You have total control of the fwf scenario.
988
989 This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too
990coarse to have realistic melting or for sensitivity studies where you want to control your input.
991Full description, sensitivity and validation in preparation.
992
993There is 2 ways to apply the fwf to NEMO. The first possibility (\np{ln\_divisf}~=~false) applied the fwf
994 and heat flux directly on the salinity and temperature tendancy. The second possibility (\np{ln\_divisf}~=~true)
995 apply the fwf as for the runoff fwf (see \S\ref{SBC_rnf}). The mass/volume addition due to the ice shelf melting is,
996 at each relevant depth level, added to the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}
997(called from \mdl{divcur}).
998%
999% ================================================================
1000%        Handling of icebergs
1001% ================================================================
1002\section{ Handling of icebergs (ICB) }
1003\label{ICB_icebergs}
1004%------------------------------------------namberg----------------------------------------------------
1005\namdisplay{namberg}
1006%-------------------------------------------------------------------------------------------------------------
1007
1008Icebergs are modelled as lagrangian particles in NEMO.
1009Their physical behaviour is controlled by equations as described in  \citet{Martin_Adcroft_OM10} ).
1010(Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO.)
1011Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described in the \ngn{namberg} namelist:
1012\np{rn\_initial\_mass} and \np{rn\_initial\_thickness}.
1013Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs
1014of this class are being described as one lagrangian point (this reduces the numerical problem of tracking every single iceberg).
1015They are enabled by setting \np{ln\_icebergs}~=~true.
1016
1017Two initialisation schemes are possible.
1018\begin{description}
1019\item[\np{nn\_test\_icebergs}~$>$~0]
1020In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate
1021(so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each
1022grid point of which an iceberg is generated at the beginning of the run.
1023(Note that this happens each time the timestep equals \np{nn\_nit000}.)
1024\np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners
1025of the geographical box: lonmin,lonmax,latmin,latmax
1026\item[\np{nn\_test\_icebergs}~=~-1]
1027In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter.
1028This should be a file with a field on the configuration grid (typically ORCA) representing ice accumulation rate at each model point.
1029These should be ocean points adjacent to land where icebergs are known to calve.
1030Most points in this input grid are going to have value zero.
1031When the model runs, ice is accumulated at each grid point which has a non-zero source term.
1032At 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).
1033Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling).
1034If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly.
1035\end{description}
1036
1037Icebergs are influenced by wind, waves and currents, bottom melt and erosion.
1038The latter act to disintegrate the iceberg. This is either all melted freshwater, or
1039(if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits
1040which are assumed to propagate with their larger parent and thus delay fluxing into the ocean.
1041Melt water (and other variables on the configuration grid) are written into the main NEMO model output files.
1042
1043Extensive diagnostics can be produced.
1044Separate output files are maintained for human-readable iceberg information.
1045A separate file is produced for each processor (independent of \np{ln\_ctl}).
1046The amount of information is controlled by two integer parameters:
1047\begin{description}
1048\item[\np{nn\_verbose\_level}]  takes a value between one and four and represents
1049an increasing number of points in the code at which variables are written, and an
1050increasing level of obscurity.
1051\item[\np{nn\_verbose\_write}] is the number of timesteps between writes
1052\end{description}
1053
1054Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0.
1055A non-zero value represents how many timesteps between writes of information into the output file.
1056These output files are in NETCDF format.
1057When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor.
1058Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs.
1059So care is needed to recreate data for individual icebergs, since its trajectory data may be spread across
1060multiple files.
1061
1062
1063% ================================================================
1064% Miscellanea options
1065% ================================================================
1066\section{Miscellaneous options}
1067\label{SBC_misc}
1068
1069% -------------------------------------------------------------------------------------------------------------
1070%        Diurnal cycle
1071% -------------------------------------------------------------------------------------------------------------
1072\subsection   [Diurnal  cycle (\textit{sbcdcy})]
1073         {Diurnal cycle (\mdl{sbcdcy})}
1074\label{SBC_dcy}
1075%------------------------------------------namsbc_rnf----------------------------------------------------
1076%\namdisplay{namsbc}
1077%-------------------------------------------------------------------------------------------------------------
1078
1079%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1080\begin{figure}[!t]    \begin{center}
1081\includegraphics[width=0.8\textwidth]{./TexFiles/Figures/Fig_SBC_diurnal.pdf}
1082\caption{ \label{Fig_SBC_diurnal}
1083Example of recontruction of the diurnal cycle variation of short wave flux
1084from daily mean values. The reconstructed diurnal cycle (black line) is chosen
1085as the mean value of the analytical cycle (blue line) over a time step, not
1086as the mid time step value of the analytically cycle (red square). From \citet{Bernie_al_CD07}.}
1087\end{center}   \end{figure}
1088%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1089
1090\cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of
1091SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution
1092of the surface fluxes of 3~h or less. Unfortunately high frequency forcing fields are rare,
1093not to say inexistent. Nevertheless, it is possible to obtain a reasonable diurnal cycle
1094of the SST knowning only short wave flux (SWF) at high frequency \citep{Bernie_al_CD07}.
1095Furthermore, only the knowledge of daily mean value of SWF is needed,
1096as higher frequency variations can be reconstructed from them, assuming that
1097the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle
1098of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available
1099in \NEMO by setting \np{ln\_dm2dc}~=~true (a \textit{\ngn{namsbc}} namelist variable) when using
1100CORE bulk formulea (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).
1101The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used
1102can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily
1103mean incomming SWF as the reconstructed SWF at a given time step is the mean value
1104of the analytical cycle over this time step (Fig.\ref{Fig_SBC_diurnal}).
1105The use of diurnal cycle reconstruction requires the input SWF to be daily
1106($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter).
1107Furthermore, it is recommended to have a least 8 surface module time step per day,
1108that is  $\rdt \ \np{nn\_fsbc} < 10,800~s = 3~h$. An example of recontructed SWF
1109is given in Fig.\ref{Fig_SBC_dcy} for a 12 reconstructed diurnal cycle, one every 2~hours
1110(from 1am to 11pm).
1111
1112%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1113\begin{figure}[!t]  \begin{center}
1114\includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_SBC_dcy.pdf}
1115\caption{ \label{Fig_SBC_dcy}
1116Example of recontruction of the diurnal cycle variation of short wave flux
1117from daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm).
1118The display is on (i,j) plane. }
1119\end{center}   \end{figure}
1120%>>>>>>>>>>>>>>>>>>>>>>>>>>>>
1121
1122Note also that the setting a diurnal cycle in SWF is highly recommended  when
1123the top layer thickness approach 1~m or less, otherwise large error in SST can
1124appear due to an inconsistency between the scale of the vertical resolution
1125and the forcing acting on that scale.
1126
1127% -------------------------------------------------------------------------------------------------------------
1128%        Rotation of vector pairs onto the model grid directions
1129% -------------------------------------------------------------------------------------------------------------
1130\subsection{Rotation of vector pairs onto the model grid directions}
1131\label{SBC_rotation}
1132
1133When using a flux (\np{ln\_flx}=true) or bulk (\np{ln\_clio}=true or \np{ln\_core}=true) formulation,
1134pairs of vector components can be rotated from east-north directions onto the local grid directions.
1135This is particularly useful when interpolation on the fly is used since here any vectors are likely to be defined
1136relative to a rectilinear grid.
1137To activate this option a non-empty string is supplied in the rotation pair column of the relevant namelist.
1138The eastward component must start with "U" and the northward component with "V".
1139The remaining characters in the strings are used to identify which pair of components go together.
1140So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together
1141and rotate them on to the model grid directions; "U2" and "V2" could be used against a second pair of components,
1142and so on.
1143The extra characters used in the strings are arbitrary.
1144The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation.
1145
1146% -------------------------------------------------------------------------------------------------------------
1147%        Surface restoring to observed SST and/or SSS
1148% -------------------------------------------------------------------------------------------------------------
1149\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
1150         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
1151\label{SBC_ssr}
1152%------------------------------------------namsbc_ssr----------------------------------------------------
1153\namdisplay{namsbc_ssr}
1154%-------------------------------------------------------------------------------------------------------------
1155
1156IOptions are defined through the  \ngn{namsbc\_ssr} namelist variables.
1157n forced mode using a flux formulation (\np{ln\_flx}~=~true), a
1158feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
1159\begin{equation} \label{Eq_sbc_dmp_q}
1160Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
1161\end{equation}
1162where SST is a sea surface temperature field (observed or climatological), $T$ is
1163the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback
1164coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$
1165mixed-layer depth, this value corresponds to a relaxation time scale of two months.
1166This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is
1167equal to $Q_o$.
1168
1169In the fresh water budget, a feedback term can also be added. Converted into an
1170equivalent freshwater flux, it takes the following expression :
1171
1172\begin{equation} \label{Eq_sbc_dmp_emp}
1173\textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
1174                                             {\left.S\right|_{k=1}}
1175\end{equation}
1176
1177where $\textit{emp}_{o }$ is a net surface fresh water flux (observed, climatological or an
1178atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time
1179interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}),
1180$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative
1181feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no
1182physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere
1184term should be viewed as a flux correction on freshwater fluxes to reduce the
1185uncertainties we have on the observed freshwater budget.
1186
1187% -------------------------------------------------------------------------------------------------------------
1188%        Handling of ice-covered area
1189% -------------------------------------------------------------------------------------------------------------
1190\subsection{Handling of ice-covered area  (\textit{sbcice\_...})}
1191\label{SBC_ice-cover}
1192
1193The presence at the sea surface of an ice covered area modifies all the fluxes
1194transmitted to the ocean. There are several way to handle sea-ice in the system
1195depending on the value of the \np{nn{\_}ice} namelist parameter.
1196\begin{description}
1197\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain.
1198This is a typical namelist value used for tropical ocean domain. The surface fluxes
1199are simply specified for an ice-free ocean. No specific things is done for sea-ice.
1200\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model
1201is used. An observed ice covered area is read in a file. Below this area, the SST is
1202restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$)
1203in the northern (southern) hemisphere. The associated modification of the freshwater
1204fluxes are done in such a way that the change in buoyancy fluxes remains zero.
1205This prevents deep convection to occur when trying to reach the freezing point
1206(and so ice covered area condition) while the SSS is too large. This manner of
1207managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if}
1208model. It can be found in the \mdl{sbcice{\_}if} module.
1209\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the
1210ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of
1211each model cell to provide the surface ocean fluxes. Note that the activation of a
1212sea-ice model is is done by defining a CPP key (\key{lim2}, \key{lim3} or \key{cice}).
1213The activation automatically overwrites the read value of nn{\_}ice to its appropriate
1214value ($i.e.$ $2$ for LIM-2, $3$ for LIM-3 or $4$ for CICE).
1215\end{description}
1216
1217% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}
1218
1219\subsection   [Interface to CICE (\textit{sbcice\_cice})]
1220         {Interface to CICE (\mdl{sbcice\_cice})}
1221\label{SBC_cice}
1222
1223It is now possible to couple a regional or global NEMO configuration (without AGRIF) to the CICE sea-ice
1224model by using \key{cice}.  The CICE code can be obtained from
1226even with the latest code release.  Input grid files consistent with those used in NEMO will also be needed,
1227and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used (seek advice from UKMO
1228if necessary).  Currently the code is only designed to work when using the CORE forcing option for NEMO (with
1229\textit{calc\_strair~=~true} and \textit{calc\_Tsfc~=~true} in the CICE name-list), or alternatively when NEMO
1230is coupled to the HadGAM3 atmosphere model (with \textit{calc\_strair~=~false} and \textit{calc\_Tsfc~=~false}).
1231The code is intended to be used with \np{nn\_fsbc} set to 1 (although coupling ocean and ice less frequently
1232should work, it is possible the calculation of some of the ocean-ice fluxes needs to be modified slightly - the
1233user should check that results are not significantly different to the standard case).
1234
1235There are two options for the technical coupling between NEMO and CICE.  The standard version allows
1236complete flexibility for the domain decompositions in the individual models, but this is at the expense of global
1237gather and scatter operations in the coupling which become very expensive on larger numbers of processors. The
1238alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that the domain decomposition is
1239identical in both models (provided domain parameters are set appropriately, and
1240\textit{processor\_shape~=~square-ice} and \textit{distribution\_wght~=~block} in the CICE name-list) and allows
1241much more efficient direct coupling on individual processors.  This solution scales much better although it is at
1242the expense of having more idle CICE processors in areas where there is no sea ice.
1243
1244% -------------------------------------------------------------------------------------------------------------
1245%        Freshwater budget control
1246% -------------------------------------------------------------------------------------------------------------
1247\subsection   [Freshwater budget control (\textit{sbcfwb})]
1248         {Freshwater budget control (\mdl{sbcfwb})}
1249\label{SBC_fwb}
1250
1251For global ocean simulation it can be useful to introduce a control of the mean sea
1252level in order to prevent unrealistic drift of the sea surface height due to inaccuracy
1253in the freshwater fluxes. In \NEMO, two way of controlling the the freshwater budget.
1254\begin{description}
1255\item[\np{nn\_fwb}=0]  no control at all. The mean sea level is free to drift, and will
1256certainly do so.
1257\item[\np{nn\_fwb}=1]  global mean \textit{emp} set to zero at each model time step.
1258%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).
1259\item[\np{nn\_fwb}=2]  freshwater budget is adjusted from the previous year annual
1260mean budget which is read in the \textit{EMPave\_old.dat} file. As the model uses the
1261Boussinesq approximation, the annual mean fresh water budget is simply evaluated
1262from the change in the mean sea level at January the first and saved in the
1263\textit{EMPav.dat} file.
1264\end{description}
1265
1266% -------------------------------------------------------------------------------------------------------------
1267%        Neutral Drag Coefficient from external wave model
1268% -------------------------------------------------------------------------------------------------------------
1269\subsection   [Neutral drag coefficient from external wave model (\textit{sbcwave})]
1270                        {Neutral drag coefficient from external wave model (\mdl{sbcwave})}
1271\label{SBC_wave}
1272%------------------------------------------namwave----------------------------------------------------
1273\namdisplay{namsbc_wave}
1274%-------------------------------------------------------------------------------------------------------------
1275\begin{description}
1276
1277\item [??] In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the
1278logical variable \np{ln\_cdgw}
1279 in $namsbc$ namelist must be defined ${.true.}$.
1280The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the
1281namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all
1282the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input})
1283and a 2D field of neutral drag coefficient. Then using the routine
1284TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according
1285to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}.
1286
1287\end{description}
1288
1289% Griffies doc:
1290% 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.
1291%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.
1292%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.
1293
1294
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