1  \documentclass[../tex_main/NEMO_manual]{subfiles} 

2  \begin{document} 

3  % ================================================================ 

4  % Chapter —— Surface Boundary Condition (SBC, ISF, ICB) 

5  % ================================================================ 

6  \chapter{Surface Boundary Condition (SBC, ISF, ICB) } 

7  \label{chap:SBC} 

8  \minitoc 

9  

10  \newpage 

11  $\ $\newline % force a new ligne 

12  %namsbc 

13  

14  \nlst{namsbc} 

15  % 

16  $\ $\newline % force a new ligne 

17  

18  The ocean needs six fields as surface boundary condition: 

19  \begin{itemize} 

20  \item 

21  the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 

22  \item 

23  the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 

24  \item 

25  the surface freshwater budget $\left( {\textit{emp}} \right)$ 

26  \item 

27  the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$ 

28  \end{itemize} 

29  plus an optional field: 

30  \begin{itemize} 

31  \item the atmospheric pressure at the ocean surface $\left( p_a \right)$ 

32  \end{itemize} 

33  

34  Four different ways to provide the first six fields to the ocean are available which are controlled by 

35  namelist \ngn{namsbc} variables: 

36  an analytical formulation (\np{ln\_ana}\forcode{ = .true.}), 

37  a flux formulation (\np{ln\_flx}\forcode{ = .true.}), 

38  a bulk formulae formulation (CORE (\np{ln\_blk\_core}\forcode{ = .true.}), 

39  CLIO (\np{ln\_blk\_clio}\forcode{ = .true.}) bulk formulae) and 

40  a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler) 

41  (\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}). 

42  When used ($i.e.$ \np{ln\_apr\_dyn}\forcode{ = .true.}), 

43  the atmospheric pressure forces both ocean and ice dynamics. 

44  

45  The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter. 

46  When the fields are supplied from data files (flux and bulk formulations), 

47  the input fields need not be supplied on the model grid. 

48  Instead a file of coordinates and weights can be supplied which maps the data from the supplied grid to 

49  the model points (so called "Interpolation on the Fly", see \autoref{subsec:SBC_iof}). 

50  If the Interpolation on the Fly option is used, input data belonging to land points (in the native grid), 

51  can be masked to avoid spurious results in proximity of the coasts as 

52  large sealand gradients characterize most of the atmospheric variables. 

53  

54  In addition, the resulting fields can be further modified using several namelist options. 

55  These options control 

56  \begin{itemize} 

57  \item 

58  the rotation of vector components supplied relative to an eastnorth coordinate system onto 

59  the local grid directions in the model; 

60  \item 

61  the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}\forcode{ = .true.}); 

62  \item 

63  the modification of fluxes below icecovered areas (using observed icecover or a seaice model) 

64  (\np{nn\_ice}\forcode{ = 0..3}); 

65  \item 

66  the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}\forcode{ = .true.}); 

67  \item 

68  the addition of isf melting as lateral inflow (parameterisation) or 

69  as fluxes applied at the landice ocean interface (\np{ln\_isf}) ; 

70  \item 

71  the addition of a freshwater flux adjustment in order to avoid a mean sealevel drift 

72  (\np{nn\_fwb}\forcode{ = 0..2}); 

73  \item 

74  the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle 

75  (\np{ln\_dm2dc}\forcode{ = .true.}); 

76  \item 

77  a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}\forcode{ = .true.}); 

78  \item 

79  the Stokes drift rom an external wave model can be accounted (\np{ln\_sdw}\forcode{ = .true.}); 

80  \item 

81  the StokesCoriolis term can be included (\np{ln\_stcor}\forcode{ = .true.}); 

82  \item 

83  the surface stress felt by the ocean can be modified by surface waves (\np{ln\_tauwoc}\forcode{ = .true.}). 

84  \end{itemize} 

85  

86  In this chapter, we first discuss where the surface boundary condition appears in the model equations. 

87  Then we present the five ways of providing the surface boundary condition, 

88  followed by the description of the atmospheric pressure and the river runoff. 

89  Next the scheme for interpolation on the fly is described. 

90  Finally, the different options that further modify the fluxes applied to the ocean are discussed. 

91  One of these is modification by icebergs (see \autoref{sec:ICB_icebergs}), 

92  which act as drifting sources of fresh water. 

93  Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}), 

94  which provides additional sources of fresh water. 

95  

96  

97  % ================================================================ 

98  % Surface boundary condition for the ocean 

99  % ================================================================ 

100  \section{Surface boundary condition for the ocean} 

101  \label{sec:SBC_general} 

102  

103  The surface ocean stress is the stress exerted by the wind and the seaice on the ocean. 

104  It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of 

105  the momentum vertical mixing trend (see \autoref{eq:dynzdf_sbc} in \autoref{sec:DYN_zdf}). 

106  As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh, 

107  $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$ and $v$points. 

108  

109  The surface heat flux is decomposed into two parts, a non solar and a solar heat flux, 

110  $Q_{ns}$ and $Q_{sr}$, respectively. 

111  The former is the non penetrative part of the heat flux 

112  ($i.e.$ the sum of sensible, latent and long wave heat fluxes plus 

113  the heat content of the mass exchange with the atmosphere and seaice). 

114  It is applied in \mdl{trasbc} module as a surface boundary condition trend of 

115  the first level temperature time evolution equation 

116  (see \autoref{eq:tra_sbc} and \autoref{eq:tra_sbc_lin} in \autoref{subsec:TRA_sbc}). 

117  The latter is the penetrative part of the heat flux. 

118  It is applied as a 3D trends of the temperature equation (\mdl{traqsr} module) when 

119  \np{ln\_traqsr}\forcode{ = .true.}. 

120  The way the light penetrates inside the water column is generally a sum of decreasing exponentials 

121  (see \autoref{subsec:TRA_qsr}). 

122  

123  The surface freshwater budget is provided by the \textit{emp} field. 

124  It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) and 

125  possibly with the seaice and ice shelves (freezing minus melting of ice). 

126  It affects both the ocean in two different ways: 

127  $(i)$ it changes the volume of the ocean and therefore appears in the sea surface height equation as 

128  a volume flux, and 

129  $(ii)$ it changes the surface temperature and salinity through the heat and salt contents of 

130  the mass exchanged with the atmosphere, the seaice and the ice shelves. 

131  

132  

133  %\colorbox{yellow}{Miss: } 

134  % 

135  %A extensive description of all namsbc namelist (parameter that have to be 

136  %created!) 

137  % 

138  %Especially the \np{nn\_fsbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu 

139  %ssv) i.e. information required by flux computation or seaice 

140  % 

141  %\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add 

142  %a word on runoff: included in surface bc or add as lateral obc{\ldots}. 

143  % 

144  %Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields 

145  % 

146  %Fluxes update only each nf{\_}sbc time step (namsbc) explain relation 

147  %between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one 

148  %nf{\_}sbc 

149  % 

150  %Explain here all the namlist namsbc variable{\ldots}. 

151  % 

152  % explain : use or not of surface currents 

153  % 

154  %\colorbox{yellow}{End Miss } 

155  

156  The ocean model provides, at each time step, to the surface module (\mdl{sbcmod}) 

157  the surface currents, temperature and salinity. 

158  These variables are averaged over \np{nn\_fsbc} timestep (\autoref{tab:ssm}), and 

159  it is these averaged fields which are used to computes the surface fluxes at a frequency of \np{nn\_fsbc} timestep. 

160  

161  

162  %TABLE 

163  \begin{table}[tb] \begin{center} \begin{tabular}{llll} 

164  \hline 

165  Variable description & Model variable & Units & point \\ \hline 

166  icomponent of the surface current & ssu\_m & $m.s^{1}$ & U \\ \hline 

167  jcomponent of the surface current & ssv\_m & $m.s^{1}$ & V \\ \hline 

168  Sea surface temperature & sst\_m & \r{}$K$ & T \\ \hline 

169  Sea surface salinty & sss\_m & $psu$ & T \\ \hline 

170  \end{tabular} 

171  \caption{ \protect\label{tab:ssm} 

172  Ocean variables provided by the ocean to the surface module (SBC). 

173  The variable are averaged over nn{\_}fsbc time step, 

174  $i.e.$ the frequency of computation of surface fluxes.} 

175  \end{center} \end{table} 

176  % 

177  

178  %\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 

179  

180  

181  % ================================================================ 

182  % Input Data 

183  % ================================================================ 

184  \section{Input data generic interface} 

185  \label{sec:SBC_input} 

186  

187  A generic interface has been introduced to manage the way input data 

188  (2D or 3D fields, like surface forcing or ocean T and S) are specify in \NEMO. 

189  This task is archieved by \mdl{fldread}. 

190  The module was design with four main objectives in mind: 

191  \begin{enumerate} 

192  \item 

193  optionally provide a time interpolation of the input data at model timestep, whatever their input frequency is, 

194  and according to the different calendars available in the model. 

195  \item 

196  optionally provide an onthefly space interpolation from the native input data grid to the model grid. 

197  \item 

198  make the run duration independent from the period cover by the input files. 

199  \item 

200  provide a simple user interface and a rather simple developer interface by 

201  limiting the number of prerequisite information. 

202  \end{enumerate} 

203  

204  As a results the user have only to fill in for each variable a structure in the namelist file to 

205  define the input data file and variable names, the frequency of the data (in hours or months), 

206  whether its is climatological data or not, the period covered by the input file (one year, month, week or day), 

207  and three additional parameters for onthefly interpolation. 

208  When adding a new input variable, the developer has to add the associated structure in the namelist, 

209  read this information by mirroring the namelist read in \rou{sbc\_blk\_init} for example, 

210  and simply call \rou{fld\_read} to obtain the desired input field at the model timestep and grid points. 

211  

212  The only constraints are that the input file is a NetCDF file, the file name follows a nomenclature 

213  (see \autoref{subsec:SBC_fldread}), the period it cover is one year, month, week or day, and, 

214  if onthefly interpolation is used, a file of weights must be supplied (see \autoref{subsec:SBC_iof}). 

215  

216  Note that when an input data is archived on a disc which is accessible directly from the workspace where 

217  the code is executed, then the use can set the \np{cn\_dir} to the pathway leading to the data. 

218  By default, the data are assumed to have been copied so that cn\_dir='./'. 

219  

220  %  

221  % Input Data specification (\mdl{fldread}) 

222  %  

223  \subsection{Input data specification (\protect\mdl{fldread})} 

224  \label{subsec:SBC_fldread} 

225  

226  The structure associated with an input variable contains the following information: 

227  \begin{forlines} 

228  ! file name ! frequency (hours) ! variable ! time interp. ! clim ! 'yearly'/ ! weights ! rotation ! land/sea mask ! 

229  ! ! (if <0 months) ! name ! (logical) ! (T/F) ! 'monthly' ! filename ! pairing ! filename ! 

230  \end{forlines} 

231  where 

232  \begin{description} 

233  \item[File name]: 

234  the stem name of the NetCDF file to be open. 

235  This stem will be completed automatically by the model, with the addition of a '.nc' at its end and 

236  by date information and possibly a prefix (when using AGRIF). 

237  Tab.\autoref{tab:fldread} provides the resulting file name in all possible cases according to 

238  whether it is a climatological file or not, and to the open/close frequency (see below for definition). 

239  

240  %TABLE 

241  \begin{table}[htbp] 

242  \begin{center} 

243  \begin{tabular}{lccc} 

244  \hline 

245  & daily or weekLLL & monthly & yearly \\ \hline 

246  \np{clim}\forcode{ = .false.} & fn\_yYYYYmMMdDD.nc & fn\_yYYYYmMM.nc & fn\_yYYYY.nc \\ \hline 

247  \np{clim}\forcode{ = .true.} & not possible & fn\_m??.nc & fn \\ \hline 

248  \end{tabular} 

249  \end{center} 

250  \caption{ \protect\label{tab:fldread} 

251  naming nomenclature for climatological or interannual input file, as a function of the Open/close frequency. 

252  The stem name is assumed to be 'fn'. 

253  For weekly files, the 'LLL' corresponds to the first three letters of the first day of the week 

254  ($i.e.$ 'sun','sat','fri','thu','wed','tue','mon'). 

255  The 'YYYY', 'MM' and 'DD' should be replaced by the actual year/month/day, always coded with 4 or 2 digits. 

256  Note that (1) in mpp, if the file is split over each subdomain, the suffix '.nc' is replaced by '\_PPPP.nc', 

257  where 'PPPP' is the process number coded with 4 digits; 

258  (2) when using AGRIF, the prefix '\_N' is added to files, where 'N' is the child grid number.} 

259  \end{table} 

260  % 

261  

262  

263  \item[Record frequency]: 

264  the frequency of the records contained in the input file. 

265  Its unit is in hours if it is positive (for example 24 for daily forcing) or in months if negative 

266  (for example 1 for monthly forcing or 12 for annual forcing). 

267  Note that this frequency must really be an integer and not a real. 

268  On some computers, seting it to '24.' can be interpreted as 240! 

269  

270  \item[Variable name]: 

271  the name of the variable to be read in the input NetCDF file. 

272  

273  \item[Time interpolation]: 

274  a logical to activate, or not, the time interpolation. 

275  If set to 'false', the forcing will have a steplike shape remaining constant during each forcing period. 

276  For example, when using a daily forcing without time interpolation, the forcing remaining constant from 

277  00h00'00'' to 23h59'59". 

278  If set to 'true', the forcing will have a broken line shape. 

279  Records are assumed to be dated the middle of the forcing period. 

280  For example, when using a daily forcing with time interpolation, 

281  linear interpolation will be performed between midday of two consecutive days. 

282  

283  \item[Climatological forcing]: 

284  a logical to specify if a input file contains climatological forcing which can be cycle in time, 

285  or an interannual forcing which will requires additional files if 

286  the period covered by the simulation exceed the one of the file. 

287  See the above the file naming strategy which impacts the expected name of the file to be opened. 

288  

289  \item[Open/close frequency]: 

290  the frequency at which forcing files must be opened/closed. 

291  Four cases are coded: 

292  'daily', 'weekLLL' (with 'LLL' the first 3 letters of the first day of the week), 'monthly' and 'yearly' which 

293  means the forcing files will contain data for one day, one week, one month or one year. 

294  Files are assumed to contain data from the beginning of the open/close period. 

295  For example, the first record of a yearly file containing daily data is Jan 1st even if 

296  the experiment is not starting at the beginning of the year. 

297  

298  \item[Others]: 

299  'weights filename', 'pairing rotation' and 'land/sea mask' are associated with 

300  onthefly interpolation which is described in \autoref{subsec:SBC_iof}. 

301  

302  \end{description} 

303  

304  Additional remarks:\\ 

305  (1) The time interpolation is a simple linear interpolation between two consecutive records of the input data. 

306  The only tricky point is therefore to specify the date at which we need to do the interpolation and 

307  the date of the records read in the input files. 

308  Following \citet{Leclair_Madec_OM09}, the date of a time step is set at the middle of the time step. 

309  For example, for an experiment starting at 0h00'00" with a one hour timestep, 

310  a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc. 

311  However, for forcing data related to the surface module, 

312  values are not needed at every timestep but at every \np{nn\_fsbc} timestep. 

313  For example with \np{nn\_fsbc}\forcode{ = 3}, the surface module will be called at timesteps 1, 4, 7, etc. 

314  The date used for the time interpolation is thus redefined to be at the middle of \np{nn\_fsbc} timestep period. 

315  In the previous example, this leads to: 1h30'00", 4h30'00", 7h30'00", etc. \\ 

316  (2) For code readablility and maintenance issues, we don't take into account the NetCDF input file calendar. 

317  The calendar associated with the forcing field is build according to the information provided by 

318  user in the record frequency, the open/close frequency and the type of temporal interpolation. 

319  For example, the first record of a yearly file containing daily data that will be interpolated in time is assumed to 

320  be start Jan 1st at 12h00'00" and end Dec 31st at 12h00'00". \\ 

321  (3) If a time interpolation is requested, the code will pick up the needed data in the previous (next) file when 

322  interpolating data with the first (last) record of the open/close period. 

323  For example, if the input file specifications are ''yearly, containing daily data to be interpolated in time'', 

324  the values given by the code between 00h00'00" and 11h59'59" on Jan 1st will be interpolated values between 

325  Dec 31st 12h00'00" and Jan 1st 12h00'00". 

326  If the forcing is climatological, Dec and Jan will be keepup from the same year. 

327  However, if the forcing is not climatological, at the end of 

328  the open/close period the code will automatically close the current file and open the next one. 

329  Note that, if the experiment is starting (ending) at the beginning (end) of 

330  an open/close period we do accept that the previous (next) file is not existing. 

331  In this case, the time interpolation will be performed between two identical values. 

332  For example, when starting an experiment on Jan 1st of year Y with yearly files and daily data to be interpolated, 

333  we do accept that the file related to year Y1 is not existing. 

334  The value of Jan 1st will be used as the missing one for Dec 31st of year Y1. 

335  If the file of year Y1 exists, the code will read its last record. 

336  Therefore, this file can contain only one record corresponding to Dec 31st, 

337  a useful feature for user considering that it is too heavy to manipulate the complete file for year Y1. 

338  

339  

340  %  

341  % Interpolation on the Fly 

342  %  

343  \subsection{Interpolation onthefly} 

344  \label{subsec:SBC_iof} 

345  

346  Interpolation on the Fly allows the user to supply input files required for the surface forcing on 

347  grids other than the model grid. 

348  To do this he or she must supply, in addition to the source data file, a file of weights to be used to 

349  interpolate from the data grid to the model grid. 

350  The original development of this code used the SCRIP package 

351  (freely available \href{http://climate.lanl.gov/Software/SCRIP}{here} under a copyright agreement). 

352  In principle, any package can be used to generate the weights, but the variables in 

353  the input weights file must have the same names and meanings as assumed by the model. 

354  Two methods are currently available: bilinear and bicubic interpolation. 

355  Prior to the interpolation, providing a land/sea mask file, the user can decide to remove land points from 

356  the input file and substitute the corresponding values with the average of the 8 neighbouring points in 

357  the native external grid. 

358  Only "sea points" are considered for the averaging. 

359  The land/sea mask file must be provided in the structure associated with the input variable. 

360  The netcdf land/sea mask variable name must be 'LSM' it must have the same horizontal and vertical dimensions of 

361  the associated variable and should be equal to 1 over land and 0 elsewhere. 

362  The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist. 

363  Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied. 

364  

365  \subsubsection{Bilinear interpolation} 

366  \label{subsec:SBC_iof_bilinear} 

367  

368  The input weights file in this case has two sets of variables: 

369  src01, src02, src03, src04 and wgt01, wgt02, wgt03, wgt04. 

370  The "src" variables correspond to the point in the input grid to which the weight "wgt" is to be applied. 

371  Each src value is an integer corresponding to the index of a point in the input grid when 

372  written as a one dimensional array. 

373  For example, for an input grid of size 5x10, point (3,2) is referenced as point 8, since (21)*5+3=8. 

374  There are four of each variable because bilinear interpolation uses the four points defining 

375  the grid box containing the point to be interpolated. 

376  All of these arrays are on the model grid, so that values src01(i,j) and wgt01(i,j) are used to 

377  generate a value for point (i,j) in the model. 

378  

379  Symbolically, the algorithm used is: 

380  \begin{equation} 

381  f_{m}(i,j) = f_{m}(i,j) + \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))} 

382  \end{equation} 

383  where function idx() transforms a one dimensional index src(k) into a two dimensional index, 

384  and wgt(1) corresponds to variable "wgt01" for example. 

385  

386  \subsubsection{Bicubic interpolation} 

387  \label{subsec:SBC_iof_bicubic} 

388  

389  Again there are two sets of variables: "src" and "wgt". 

390  But in this case there are 16 of each. 

391  The symbolic algorithm used to calculate values on the model grid is now: 

392  

393  \begin{equation*} \begin{split} 

394  f_{m}(i,j) = f_{m}(i,j) +& \sum_{k=1}^{4} {wgt(k)f(idx(src(k)))} 

395  + \sum_{k=5}^{8} {wgt(k)\left.\frac{\partial f}{\partial i}\right _{idx(src(k))} } \\ 

396  +& \sum_{k=9}^{12} {wgt(k)\left.\frac{\partial f}{\partial j}\right _{idx(src(k))} } 

397  + \sum_{k=13}^{16} {wgt(k)\left.\frac{\partial ^2 f}{\partial i \partial j}\right _{idx(src(k))} } 

398  \end{split} 

399  \end{equation*} 

400  The gradients here are taken with respect to the horizontal indices and not distances since 

401  the spatial dependency has been absorbed into the weights. 

402  

403  \subsubsection{Implementation} 

404  \label{subsec:SBC_iof_imp} 

405  

406  To activate this option, a nonempty string should be supplied in 

407  the weights filename column of the relevant namelist; 

408  if this is left as an empty string no action is taken. 

409  In the model, weights files are read in and stored in a structured type (WGT) in the fldread module, 

410  as and when they are first required. 

411  This initialisation procedure determines whether the input data grid should be treated as cyclical or not by 

412  inspecting a global attribute stored in the weights input file. 

413  This attribute must be called "ew\_wrap" and be of integer type. 

414  If it is negative, the input nonmodel grid is assumed not to be cyclic. 

415  If zero or greater, then the value represents the number of columns that overlap. 

416  $E.g.$ if the input grid has columns at longitudes 0, 1, 2, .... , 359, then ew\_wrap should be set to 0; 

417  if longitudes are 0.5, 2.5, .... , 358.5, 360.5, 362.5, ew\_wrap should be 2. 

418  If the model does not find attribute ew\_wrap, then a value of 999 is assumed. 

419  In this case the \rou{fld\_read} routine defaults ew\_wrap to value 0 and 

420  therefore the grid is assumed to be cyclic with no overlapping columns. 

421  (In fact this only matters when bicubic interpolation is required.) 

422  Note that no testing is done to check the validity in the model, 

423  since there is no way of knowing the name used for the longitude variable, 

424  so it is up to the user to make sure his or her data is correctly represented. 

425  

426  Next the routine reads in the weights. 

427  Bicubic interpolation is assumed if it finds a variable with name "src05", otherwise bilinear interpolation is used. 

428  The WGT structure includes dynamic arrays both for the storage of the weights (on the model grid), 

429  and when required, for reading in the variable to be interpolated (on the input data grid). 

430  The size of the input data array is determined by examining the values in the "src" arrays to 

431  find the minimum and maximum i and j values required. 

432  Since bicubic interpolation requires the calculation of gradients at each point on the grid, 

433  the corresponding arrays are dimensioned with a halo of width one grid point all the way around. 

434  When the array of points from the data file is adjacent to an edge of the data grid, 

435  the halo is either a copy of the row/column next to it (noncyclical case), 

436  or is a copy of one from the first few columns on the opposite side of the grid (cyclical case). 

437  

438  \subsubsection{Limitations} 

439  \label{subsec:SBC_iof_lim} 

440  

441  \begin{enumerate} 

442  \item 

443  The case where input data grids are not logically rectangular has not been tested. 

444  \item 

445  This code is not guaranteed to produce positive definite answers from positive definite inputs when 

446  a bicubic interpolation method is used. 

447  \item 

448  The cyclic condition is only applied on left and right columns, and not to top and bottom rows. 

449  \item 

450  The gradients across the ends of a cyclical grid assume that the grid spacing between 

451  the two columns involved are consistent with the weights used. 

452  \item 

453  Neither interpolation scheme is conservative. (There is a conservative scheme available in SCRIP, 

454  but this has not been implemented.) 

455  \end{enumerate} 

456  

457  \subsubsection{Utilities} 

458  \label{subsec:SBC_iof_util} 

459  

460  % to be completed 

461  A set of utilities to create a weights file for a rectilinear input grid is available 

462  (see the directory NEMOGCM/TOOLS/WEIGHTS). 

463  

464  %  

465  % Standalone Surface Boundary Condition Scheme 

466  %  

467  \subsection{Standalone surface boundary condition scheme} 

468  \label{subsec:SAS_iof} 

469  

470  %namsbc_ana 

471  

472  \nlst{namsbc_sas} 

473  % 

474  

475  In some circumstances it may be useful to avoid calculating the 3D temperature, 

476  salinity and velocity fields and simply read them in from a previous run or receive them from OASIS. 

477  For example: 

478  

479  \begin{itemize} 

480  \item 

481  Multiple runs of the model are required in code development to 

482  see the effect of different algorithms in the bulk formulae. 

483  \item 

484  The effect of different parameter sets in the ice model is to be examined. 

485  \item 

486  Development of seaice algorithms or parameterizations. 

487  \item 

488  Spinup of the iceberg floats 

489  \item 

490  Ocean/seaice simulation with both media running in parallel (\np{ln\_mixcpl}\forcode{ = .true.}) 

491  \end{itemize} 

492  

493  The StandAlone Surface scheme provides this utility. 

494  Its options are defined through the \ngn{namsbc\_sas} namelist variables. 

495  A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM. 

496  However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0). 

497  In this configuration, a few routines in the standard model are overriden by new versions. 

498  Routines replaced are: 

499  

500  \begin{itemize} 

501  \item 

502  \mdl{nemogcm}: 

503  This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (\mdl{step}). 

504  Since the ocean state is not calculated all associated initialisations have been removed. 

505  \item 

506  \mdl{step}: 

507  The main time stepping routine now only needs to call the sbc routine (and a few utility functions). 

508  \item 

509  \mdl{sbcmod}: 

510  This has been cut down and now only calculates surface forcing and the ice model required. 

511  New surface modules that can function when only the surface level of the ocean state is defined can also be added 

512  (e.g. icebergs). 

513  \item 

514  \mdl{daymod}: 

515  No ocean restarts are read or written (though the ice model restarts are retained), 

516  so calls to restart functions have been removed. 

517  This also means that the calendar cannot be controlled by time in a restart file, 

518  so the user must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes. 

519  \item 

520  \mdl{stpctl}: 

521  Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module. 

522  \item 

523  \mdl{diawri}: 

524  All 3D data have been removed from the output. 

525  The surface temperature, salinity and velocity components (which have been read in) are written along with 

526  relevant forcing and ice data. 

527  \end{itemize} 

528  

529  One new routine has been added: 

530  

531  \begin{itemize} 

532  \item 

533  \mdl{sbcsas}: 

534  This module initialises the input files needed for reading temperature, salinity and 

535  velocity arrays at the surface. 

536  These filenames are supplied in namelist namsbc{\_}sas. 

537  Unfortunately because of limitations with the \mdl{iom} module, 

538  the full 3D fields from the mean files have to be read in and interpolated in time, 

539  before using just the top level. 

540  Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution. 

541  \end{itemize} 

542  

543  

544  % Missing the description of the 2 following variables: 

545  % ln_3d_uve = .true. ! specify whether we are supplying a 3D u,v and e3 field 

546  % ln_read_frq = .false. ! specify whether we must read frq or not 

547  

548  

549  

550  % ================================================================ 

551  % Analytical formulation (sbcana module) 

552  % ================================================================ 

553  \section{Analytical formulation (\protect\mdl{sbcana})} 

554  \label{sec:SBC_ana} 

555  

556  %namsbc_ana 

557  % 

558  %\nlst{namsbc_ana} 

559  % 

560  

561  The analytical formulation of the surface boundary condition is the default scheme. 

562  In this case, all the six fluxes needed by the ocean are assumed to be uniform in space. 

563  They take constant values given in the namelist \ngn{namsbc{\_}ana} by 

564  the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0}, \np{rn\_qsr0}, and \np{rn\_emp0} 

565  ($\textit{emp}=\textit{emp}_S$). 

566  The runoff is set to zero. 

567  In addition, the wind is allowed to reach its nominal value within a given number of time steps (\np{nn\_tau000}). 

568  

569  If a user wants to apply a different analytical forcing, 

570  the \mdl{sbcana} module can be modified to use another scheme. 

571  As an example, the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the GYRE configuration 

572  (see GYRE configuration manual, in preparation). 

573  

574  

575  % ================================================================ 

576  % Flux formulation 

577  % ================================================================ 

578  \section{Flux formulation (\protect\mdl{sbcflx})} 

579  \label{sec:SBC_flx} 

580  %namsbc_flx 

581  

582  \nlst{namsbc_flx} 

583  % 

584  

585  In the flux formulation (\np{ln\_flx}\forcode{ = .true.}), 

586  the surface boundary condition fields are directly read from input files. 

587  The user has to define in the namelist \ngn{namsbc{\_}flx} the name of the file, 

588  the name of the variable read in the file, the time frequency at which it is given (in hours), 

589  and a logical setting whether a time interpolation to the model time step is required for this field. 

590  See \autoref{subsec:SBC_fldread} for a more detailed description of the parameters. 

591  

592  Note that in general, a flux formulation is used in associated with a restoring term to observed SST and/or SSS. 

593  See \autoref{subsec:SBC_ssr} for its specification. 

594  

595  

596  % ================================================================ 

597  % Bulk formulation 

598  % ================================================================ 

599  \section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}] 

600  {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}} 

601  \label{sec:SBC_blk} 

602  

603  In the bulk formulation, the surface boundary condition fields are computed using bulk formulae and atmospheric fields and ocean (and ice) variables. 

604  

605  The atmospheric fields used depend on the bulk formulae used. 

606  Two bulk formulations are available: 

607  the CORE and the CLIO bulk formulea. 

608  The choice is made by setting to true one of the following namelist variable: 

609  \np{ln\_core} or \np{ln\_clio}. 

610  

611  Note: 

612  in forced mode, when a seaice model is used, a bulk formulation (CLIO or CORE) have to be used. 

613  Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over 

614  both an ocean and an ice surface. 

615  

616  %  

617  % CORE Bulk formulea 

618  %  

619  \subsection{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})} 

620  \label{subsec:SBC_blk_core} 

621  %namsbc_core 

622  % 

623  %\nlst{namsbc_core} 

624  % 

625  

626  The CORE bulk formulae have been developed by \citet{Large_Yeager_Rep04}. 

627  They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data. 

628  They use an inertial dissipative method to compute the turbulent transfer coefficients 

629  (momentum, sensible heat and evaporation) from the 10 metre wind speed, air temperature and specific humidity. 

630  This \citet{Large_Yeager_Rep04} dataset is available through 

631  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. 

632  

633  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 

634  This is the socalled DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}. 

635  

636  Options are defined through the \ngn{namsbc\_core} namelist variables. 

637  The required 8 input fields are: 

638  

639  %TABLE 

640  \begin{table}[htbp] \label{tab:CORE} 

641  \begin{center} 

642  \begin{tabular}{lccc} 

643  \hline 

644  Variable desciption & Model variable & Units & point \\ \hline 

645  icomponent of the 10m air velocity & utau & $m.s^{1}$ & T \\ \hline 

646  jcomponent of the 10m air velocity & vtau & $m.s^{1}$ & T \\ \hline 

647  10m air temperature & tair & \r{}$K$ & T \\ \hline 

648  Specific humidity & humi & \% & T \\ \hline 

649  Incoming long wave radiation & qlw & $W.m^{2}$ & T \\ \hline 

650  Incoming short wave radiation & qsr & $W.m^{2}$ & T \\ \hline 

651  Total precipitation (liquid + solid) & precip & $Kg.m^{2}.s^{1}$ & T \\ \hline 

652  Solid precipitation & snow & $Kg.m^{2}.s^{1}$ & T \\ \hline 

653  \end{tabular} 

654  \end{center} 

655  \end{table} 

656  % 

657  

658  Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$ and $v$points). 

659  It is simpler and faster (less fields to be read), but it is not the recommended method when 

660  the ocean grid size is the same or larger than the one of the input atmospheric fields. 

661  

662  The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair}, \np{sn\_humi}, \np{sn\_prec}, 

663  \np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used 

664  (spatial and temporal interpolations). 

665  

666  \np{cn\_dir} is the directory of location of bulk files 

667  \np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.) 

668  \np{rn\_zqt}: is the height of humidity and temperature measurements (m) 

669  \np{rn\_zu}: is the height of wind measurements (m) 

670  

671  Three multiplicative factors are availables: 

672  \np{rn\_pfac} and \np{rn\_efac} allows to adjust (if necessary) the global freshwater budget by 

673  increasing/reducing the precipitations (total and snow) and or evaporation, respectively. 

674  The third one,\np{rn\_vfac}, control to which extend the ice/ocean velocities are taken into account in 

675  the calculation of surface wind stress. 

676  Its range should be between zero and one, and it is recommended to set it to 0. 

677  

678  %  

679  % CLIO Bulk formulea 

680  %  

681  \subsection{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})} 

682  \label{subsec:SBC_blk_clio} 

683  %namsbc_clio 

684  % 

685  %\nlst{namsbc_clio} 

686  % 

687  

688  The CLIO bulk formulae were developed several years ago for the Louvainlaneuve coupled iceocean model 

689  (CLIO, \cite{Goosse_al_JGR99}). 

690  They are simpler bulk formulae. 

691  They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover. 

692  

693  Options are defined through the \ngn{namsbc\_clio} namelist variables. 

694  The required 7 input fields are: 

695  

696  %TABLE 

697  \begin{table}[htbp] \label{tab:CLIO} 

698  \begin{center} 

699  \begin{tabular}{llll} 

700  \hline 

701  Variable desciption & Model variable & Units & point \\ \hline 

702  icomponent of the ocean stress & utau & $N.m^{2}$ & U \\ \hline 

703  jcomponent of the ocean stress & vtau & $N.m^{2}$ & V \\ \hline 

704  Wind speed module & vatm & $m.s^{1}$ & T \\ \hline 

705  10m air temperature & tair & \r{}$K$ & T \\ \hline 

706  Specific humidity & humi & \% & T \\ \hline 

707  Cloud cover & & \% & T \\ \hline 

708  Total precipitation (liquid + solid) & precip & $Kg.m^{2}.s^{1}$ & T \\ \hline 

709  Solid precipitation & snow & $Kg.m^{2}.s^{1}$ & T \\ \hline 

710  \end{tabular} 

711  \end{center} 

712  \end{table} 

713  % 

714  

715  As for the flux formulation, information about the input data required by the model is provided in 

716  the namsbc\_blk\_core or namsbc\_blk\_clio namelist (see \autoref{subsec:SBC_fldread}). 

717  

718  % ================================================================ 

719  % Coupled formulation 

720  % ================================================================ 

721  \section{Coupled formulation (\protect\mdl{sbccpl})} 

722  \label{sec:SBC_cpl} 

723  %namsbc_cpl 

724  

725  \nlst{namsbc_cpl} 

726  % 

727  

728  In the coupled formulation of the surface boundary condition, 

729  the fluxes are provided by the OASIS coupler at a frequency which is defined in the OASIS coupler, 

730  while sea and ice surface temperature, ocean and ice albedo, and ocean currents are sent to 

731  the atmospheric component. 

732  

733  A generalised coupled interface has been developed. 

734  It is currently interfaced with OASIS3MCT (\key{oasis3}). 

735  It has been successfully used to interface \NEMO to most of the European atmospheric GCM 

736  (ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), as well as to \href{http://wrfmodel.org/}{WRF} 

737  (Weather Research and Forecasting Model). 

738  

739  Note that in addition to the setting of \np{ln\_cpl} to true, the \key{coupled} have to be defined. 

740  The CPP key is mainly used in seaice to ensure that the atmospheric fluxes are actually received by 

741  the iceocean system (no calculation of ice sublimation in coupled mode). 

742  When PISCES biogeochemical model (\key{top} and \key{pisces}) is also used in the coupled system, 

743  the whole carbon cycle is computed by defining \key{cpl\_carbon\_cycle}. 

744  In this case, CO$_2$ fluxes will be exchanged between the atmosphere and the iceocean system 

745  (and need to be activated in \ngn{namsbc{\_}cpl} ). 

746  

747  The namelist above allows control of various aspects of the coupling fields (particularly for vectors) and 

748  now allows for any coupling fields to have multiple sea ice categories (as required by LIM3 and CICE). 

749  When indicating a multicategory coupling field in namsbc{\_}cpl the number of categories will be determined by 

750  the number used in the sea ice model. 

751  In some limited cases it may be possible to specify single category coupling fields even when 

752  the sea ice model is running with multiple categories  

753  in this case the user should examine the code to be sure the assumptions made are satisfactory. 

754  In cases where this is definitely not possible the model should abort with an error message. 

755  The new code has been tested using ECHAM with LIM2, and HadGAM3 with CICE but 

756  although it will compile with \key{lim3} additional minor code changes may be required to run using LIM3. 

757  

758  

759  % ================================================================ 

760  % Atmospheric pressure 

761  % ================================================================ 

762  \section{Atmospheric pressure (\protect\mdl{sbcapr})} 

763  \label{sec:SBC_apr} 

764  %namsbc_apr 

765  

766  \nlst{namsbc_apr} 

767  % 

768  

769  The optional atmospheric pressure can be used to force ocean and ice dynamics 

770  (\np{ln\_apr\_dyn}\forcode{ = .true.}, \textit{\ngn{namsbc}} namelist). 

771  The input atmospheric forcing defined via \np{sn\_apr} structure (\textit{namsbc\_apr} namelist) 

772  can be interpolated in time to the model time step, and even in space when the interpolation onthefly is used. 

773  When used to force the dynamics, the atmospheric pressure is further transformed into 

774  an equivalent inverse barometer sea surface height, $\eta_{ib}$, using: 

775  \begin{equation} \label{eq:SBC_ssh_ib} 

776  \eta_{ib} =  \frac{1}{g\,\rho_o} \left( P_{atm}  P_o \right) 

777  \end{equation} 

778  where $P_{atm}$ is the atmospheric pressure and $P_o$ a reference atmospheric pressure. 

779  A value of $101,000~N/m^2$ is used unless \np{ln\_ref\_apr} is set to true. 

780  In this case $P_o$ is set to the value of $P_{atm}$ averaged over the ocean domain, 

781  $i.e.$ the mean value of $\eta_{ib}$ is kept to zero at all time step. 

782  

783  The gradient of $\eta_{ib}$ is added to the RHS of the ocean momentum equation (see \mdl{dynspg} for the ocean). 

784  For seaice, the sea surface height, $\eta_m$, which is provided to the sea ice model is set to $\eta  \eta_{ib}$ 

785  (see \mdl{sbcssr} module). 

786  $\eta_{ib}$ can be set in the output. 

787  This can simplify altimetry data and model comparison as 

788  inverse barometer sea surface height is usually removed from these date prior to their distribution. 

789  

790  When using timesplitting and BDY package for open boundaries conditions, 

791  the equivalent inverse barometer sea surface height $\eta_{ib}$ can be added to BDY ssh data: 

792  \np{ln\_apr\_obc} might be set to true. 

793  

794  % ================================================================ 

795  % Surface Tides Forcing 

796  % ================================================================ 

797  \section{Surface tides (\protect\mdl{sbctide})} 

798  \label{sec:SBC_tide} 

799  

800  %nam_tide 

801  

802  \nlst{nam_tide} 

803  % 

804  

805  The tidal forcing, generated by the gravity forces of the EarthMoon and EarthSun sytems, 

806  is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \np{.true.} in \ngn{nam\_tide}. 

807  This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that: 

808  \begin{equation} \label{eq:PE_dyn_tides} 

809  \frac{\partial {\rm {\bf U}}_h }{\partial t}= ... 

810  +g\nabla (\Pi_{eq} + \Pi_{sal}) 

811  \end{equation} 

812  where $\Pi_{eq}$ stands for the equilibrium tidal forcing and $\Pi_{sal}$ a selfattraction and loading term (SAL). 

813  

814  The equilibrium tidal forcing is expressed as a sum over the chosen constituents $l$ in \ngn{nam\_tide}. 

815  The constituents are defined such that \np{clname(1) = 'M2', clname(2)='S2', etc...}. 

816  For the three types of tidal frequencies it reads: \\ 

817  Long period tides : 

818  \begin{equation} 

819  \Pi_{eq}(l)=A_{l}(1+kh)(\frac{1}{2}\frac{3}{2}sin^{2}\phi)cos(\omega_{l}t+V_{l}) 

820  \end{equation} 

821  diurnal tides : 

822  \begin{equation} 

823  \Pi_{eq}(l)=A_{l}(1+kh)(sin 2\phi)cos(\omega_{l}t+\lambda+V_{l}) 

824  \end{equation} 

825  Semidiurnal tides: 

826  \begin{equation} 

827  \Pi_{eq}(l)=A_{l}(1+kh)(cos^{2}\phi)cos(\omega_{l}t+2\lambda+V_{l}) 

828  \end{equation} 

829  Here $A_{l}$ is the amplitude, $\omega_{l}$ is the frequency, $\phi$ the latitude, $\lambda$ the longitude, 

830  $V_{0l}$ a phase shift with respect to Greenwich meridian and $t$ the time. 

831  The Love number factor $(1+kh)$ is here taken as a constant (0.7). 

832  

833  The SAL term should in principle be computed online as it depends on the model tidal prediction itself 

834  (see \citet{Arbic2004} for a discussion about the practical implementation of this term). 

835  Nevertheless, the complex calculations involved would make this computationally too expensive. 

836  Here, practical solutions are whether to read complex estimates $\Pi_{sal}(l)$ from an external model 

837  (\np{ln\_read\_load=.true.}) or use a ``scalar approximation'' (\np{ln\_scal\_load=.true.}). 

838  In the latter case, it reads:\\ 

839  \begin{equation} 

840  \Pi_{sal} = \beta \eta 

841  \end{equation} 

842  where $\beta$ (\np{rn\_scal\_load}, $\approx0.09$) is a spatially constant scalar, 

843  often chosen to minimize tidal prediction errors. 

844  Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to false removes the SAL contribution. 

845  

846  % ================================================================ 

847  % River runoffs 

848  % ================================================================ 

849  \section{River runoffs (\protect\mdl{sbcrnf})} 

850  \label{sec:SBC_rnf} 

851  %namsbc_rnf 

852  

853  \nlst{namsbc_rnf} 

854  % 

855  

856  %River runoff generally enters the ocean at a nonzero depth rather than through the surface. 

857  %Many models, however, have traditionally inserted river runoff to the top model cell. 

858  %This was the case in \NEMO prior to the version 3.3. The switch toward a input of runoff 

859  %throughout a nonzero depth has been motivated by the numerical and physical problems 

860  %that arise when the top grid cells are of the order of one meter. This situation is common in 

861  %coastal modelling and becomes more and more often open ocean and climate modelling 

862  %\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are 

863  %required to properly represent the diurnal cycle \citep{Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}. 

864  

865  

866  %To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the 

867  %\mdl{tra\_sbc} module. We decided to separate them throughout the code, so that the variable 

868  %\textit{emp} represented solely evaporation minus precipitation fluxes, and a new 2d variable 

869  %rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with 

870  %emp). This meant many uses of emp and emps needed to be changed, a list of all modules which use 

871  %emp or emps and the changes made are below: 

872  

873  

874  %Rachel: 

875  River runoff generally enters the ocean at a nonzero depth rather than through the surface. 

876  Many models, however, have traditionally inserted river runoff to the top model cell. 

877  This was the case in \NEMO prior to the version 3.3, 

878  and was combined with an option to increase vertical mixing near the river mouth. 

879  

880  However, with this method numerical and physical problems arise when the top grid cells are of the order of one meter. 

881  This situation is common in coastal modelling and is becoming more common in open ocean and climate modelling 

882  \footnote{ 

883  At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to 

884  properly represent the diurnal cycle \citep{Bernie_al_JC05}. 

885  see also \autoref{fig:SBC_dcy}.}. 

886  

887  As such from V~3.3 onwards it is possible to add river runoff through a nonzero depth, 

888  and for the temperature and salinity of the river to effect the surrounding ocean. 

889  The user is able to specify, in a NetCDF input file, the temperature and salinity of the river, 

890  along with the depth (in metres) which the river should be added to. 

891  

892  Namelist variables in \ngn{namsbc\_rnf}, \np{ln\_rnf\_depth}, \np{ln\_rnf\_sal} and 

893  \np{ln\_rnf\_temp} control whether the river attributes (depth, salinity and temperature) are read in and used. 

894  If these are set as false the river is added to the surface box only, assumed to be fresh (0~psu), 

895  and/or taken as surface temperature respectively. 

896  

897  The runoff value and attributes are read in in sbcrnf. 

898  For temperature 999 is taken as missing data and the river temperature is taken to 

899  be the surface temperatue at the river point. 

900  For the depth parameter a value of 1 means the river is added to the surface box only, 

901  and a value of 999 means the river is added through the entire water column. 

902  After being read in the temperature and salinity variables are multiplied by the amount of runoff 

903  (converted into m/s) to give the heat and salt content of the river runoff. 

904  After the user specified depth is read ini, 

905  the number of grid boxes this corresponds to is calculated and stored in the variable \np{nz\_rnf}. 

906  The variable \textit{h\_dep} is then calculated to be the depth (in metres) of 

907  the bottom of the lowest box the river water is being added to 

908  (i.e. the total depth that river water is being added to in the model). 

909  

910  The mass/volume addition due to the river runoff is, at each relevant depth level, added to 

911  the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}). 

912  This increases the diffusion term in the vicinity of the river, thereby simulating a momentum flux. 

913  The sea surface height is calculated using the sum of the horizontal divergence terms, 

914  and so the river runoff indirectly forces an increase in sea surface height. 

915  

916  The \textit{hdivn} terms are used in the tracer advection modules to force vertical velocities. 

917  This causes a mass of water, equal to the amount of runoff, to be moved into the box above. 

918  The heat and salt content of the river runoff is not included in this step, 

919  and so the tracer concentrations are diluted as water of ocean temperature and salinity is moved upward out of 

920  the box and replaced by the same volume of river water with no corresponding heat and salt addition. 

921  

922  For the linear free surface case, at the surface box the tracer advection causes a flux of water 

923  (of equal volume to the runoff) through the sea surface out of the domain, 

924  which causes a salt and heat flux out of the model. 

925  As such the volume of water does not change, but the water is diluted. 

926  

927  For the nonlinear free surface case (\key{vvl}), no flux is allowed through the surface. 

928  Instead in the surface box (as well as water moving up from the boxes below) a volume of runoff water is added with 

929  no corresponding heat and salt addition and so as happens in the lower boxes there is a dilution effect. 

930  (The runoff addition to the top box along with the water being moved up through 

931  boxes below means the surface box has a large increase in volume, whilst all other boxes remain the same size) 

932  

933  In trasbc the addition of heat and salt due to the river runoff is added. 

934  This is done in the same way for both vvl and nonvvl. 

935  The temperature and salinity are increased through the specified depth according to 

936  the heat and salt content of the river. 

937  

938  In the nonlinear free surface case (vvl), 

939  near the end of the time step the change in sea surface height is redistrubuted through the grid boxes, 

940  so that the original ratios of grid box heights are restored. 

941  In doing this water is moved into boxes below, throughout the water column, 

942  so the large volume addition to the surface box is spread between all the grid boxes. 

943  

944  It is also possible for runnoff to be specified as a negative value for modelling flow through straits, 

945  i.e. modelling the Baltic flow in and out of the North Sea. 

946  When the flow is out of the domain there is no change in temperature and salinity, 

947  regardless of the namelist options used, 

948  as the ocean water leaving the domain removes heat and salt (at the same concentration) with it. 

949  

950  

951  %\colorbox{yellow}{Nevertheless, Pb of vertical resolution and 3D input : increase vertical mixing near river mouths to mimic a 3D river 

952  

953  %All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface.} 

954  

955  %\colorbox{yellow}{river mouths{\ldots}} 

956  

957  %IF( ln_rnf ) THEN ! increase diffusivity at rivers mouths 

958  % DO jk = 2, nkrnf ; avt(:,:,jk) = avt(:,:,jk) + rn_avt_rnf * rnfmsk(:,:) ; END DO 

959  %ENDIF 

960  

961  %\gmcomment{ word doc of runoffs: 

962  % 

963  %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. 

964  %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. 

965  

966  %The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between. 

967  

968  %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: 

969  

970  %} 

971  % ================================================================ 

972  % Ice shelf melting 

973  % ================================================================ 

974  \section{Ice shelf melting (\protect\mdl{sbcisf})} 

975  \label{sec:SBC_isf} 

976  %namsbc_isf 

977  

978  \nlst{namsbc_isf} 

979  % 

980  Namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation used. 

981  \begin{description} 

982  \item[\np{nn\_isf}\forcode{ = 1}] 

983  The ice shelf cavity is represented (\np{ln\_isfcav}\forcode{ = .true.} needed). 

984  The fwf and heat flux are computed. 

985  Two different bulk formula are available: 

986  \begin{description} 

987  \item[\np{nn\_isfblk}\forcode{ = 1}] 

988  The bulk formula used to compute the melt is based the one described in \citet{Hunter2006}. 

989  This formulation is based on a balance between the upward ocean heat flux and 

990  the latent heat flux at the ice shelf base. 

991  \item[\np{nn\_isfblk}\forcode{ = 2}] 

992  The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}. 

993  This formulation is based on a 3 equations formulation 

994  (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation). 

995  \end{description} 

996  For this 2 bulk formulations, there are 3 different ways to compute the exchange coeficient: 

997  \begin{description} 

998  \item[\np{nn\_gammablk}\forcode{ = 0}] 

999  The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0} 

1000  \item[\np{nn\_gammablk}\forcode{ = 1}] 

1001  The salt and heat exchange coefficients are velocity dependent and defined as 

1002  \np{rn\_gammas0}$ \times u_{*}$ and \np{rn\_gammat0}$ \times u_{*}$ where 

1003  $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters). 

1004  See \citet{Jenkins2010} for all the details on this formulation. 

1005  \item[\np{nn\_gammablk}\forcode{ = 2}] 

1006  The salt and heat exchange coefficients are velocity and stability dependent and defined as 

1007  $\gamma_{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}$ where 

1008  $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters), 

1009  $\Gamma_{Turb}$ the contribution of the ocean stability and 

1010  $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 

1011  See \citet{Holland1999} for all the details on this formulation. 

1012  \end{description} 

1013  \item[\np{nn\_isf}\forcode{ = 2}] 

1014  A parameterisation of isf is used. The ice shelf cavity is not represented. 

1015  The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL) 

1016  (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front 

1017  (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}). 

1018  Furthermore the fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting. 

1019  The effective melting length (\np{sn\_Leff\_isf}) is read from a file. 

1020  \item[\np{nn\_isf}\forcode{ = 3}] 

1021  A simple parameterisation of isf is used. The ice shelf cavity is not represented. 

1022  The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between 

1023  the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and 

1024  the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}). 

1025  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 

1026  \item[\np{nn\_isf}\forcode{ = 4}] 

1027  The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed). 

1028  However, the fwf is not computed but specified from file \np{sn\_fwfisf}). 

1029  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\ 

1030  \end{description} 

1031  

1032  $\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on 

1033  the water mass properties, ocean velocities and depth. 

1034  This flux is thus highly dependent of the model resolution (horizontal and vertical), 

1035  realism of the water masses onto the shelf ...\\ 

1036  

1037  $\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file. 

1038  You have total control of the fwf forcing. 

1039  This can be useful if the water masses on the shelf are not realistic or 

1040  the resolution (horizontal/vertical) are too coarse to have realistic melting or 

1041  for studies where you need to control your heat and fw input.\\ 

1042  

1043  A namelist parameters control over how many meters the heat and fw fluxes are spread. 

1044  \np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}. 

1045  This parameter is only used if \np{nn\_isf}\forcode{ = 1} or \np{nn\_isf}\forcode{ = 4}. 

1046  

1047  If \np{rn\_hisf\_tbl}\forcode{ = 0}., the fluxes are put in the top level whatever is its tickness. 

1048  

1049  If \np{rn\_hisf\_tbl} $>$ 0., the fluxes are spread over the first \np{rn\_hisf\_tbl} m 

1050  (ie over one or several cells).\\ 

1051  

1052  The ice shelf melt is implemented as a volume flux with in the same way as for the runoff. 

1053  The fw addition due to the ice shelf melting is, at each relevant depth level, added to 

1054  the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}. 

1055  See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction. 

1056  

1057  

1058  \section{Ice sheet coupling} 

1059  \label{sec:SBC_iscpl} 

1060  %namsbc_iscpl 

1061  

1062  \nlst{namsbc_iscpl} 

1063  % 

1064  Ice sheet/ocean coupling is done through file exchange at the restart step. 

1065  NEMO, at each restart step, read the bathymetry and ice shelf draft variable in a netcdf file. 

1066  If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with 

1067  potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics. 

1068  The wetting and drying scheme applied on the restart is very simple and described below for the 6 different cases: 

1069  \begin{description} 

1070  \item[Thin a cell down:] 

1071  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant 

1072  ($bt_b=bt_n$). 

1073  \item[Enlarge a cell:] 

1074  See case "Thin a cell down" 

1075  \item[Dry a cell:] 

1076  mask, T/S, U/V and ssh are set to 0. 

1077  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$). 

1078  \item[Wet a cell:] 

1079  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0. 

1080  If no neighbours along i,j and k, T/S/U/V and mask are set to 0. 

1081  \item[Dry a column:] 

1082  mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0. 

1083  \item[Wet a column:] 

1084  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0. 

1085  If no neighbour, T/S/U/V and mask set to 0. 

1086  \end{description} 

1087  The extrapolation is call \np{nn\_drown} times. 

1088  It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps, 

1089  the code will be unable to fill all the new wet cells properly. 

1090  The default number is set up for the MISOMIP idealised experiments.\\ 

1091  This coupling procedure is able to take into account grounding line and calving front migration. 

1092  However, it is a nonconservative processe. 

1093  This could lead to a trend in heat/salt content and volume. 

1094  In order to remove the trend and keep the conservation level as close to 0 as possible, 

1095  a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}. 

1096  The heat/salt/vol. gain/loss is diagnose, as well as the location. 

1097  Based on what is done on sbcrnf to prescribed a source of heat/salt/vol., 

1098  the heat/salt/vol. gain/loss is removed/added, over a period of \np{rn\_fiscpl} time step, into the system. 

1099  So after \np{rn\_fiscpl} time step, all the heat/salt/vol. gain/loss due to extrapolation process is canceled.\\ 

1100  

1101  As the before and now fields are not compatible (modification of the geometry), 

1102  the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$. 

1103  % 

1104  % ================================================================ 

1105  % Handling of icebergs 

1106  % ================================================================ 

1107  \section{Handling of icebergs (ICB)} 

1108  \label{sec:ICB_icebergs} 

1109  %namberg 

1110  

1111  \nlst{namberg} 

1112  % 

1113  

1114  Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}. 

1115  Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ). 

1116  (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 

1117  Icebergs are initially spawned into one of ten classes which have specific mass and thickness as 

1118  described in the \ngn{namberg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}. 

1119  Each class has an associated scaling (\np{rn\_mass\_scaling}), 

1120  which is an integer representing how many icebergs of this class are being described as one lagrangian point 

1121  (this reduces the numerical problem of tracking every single iceberg). 

1122  They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}. 

1123  

1124  Two initialisation schemes are possible. 

1125  \begin{description} 

1126  \item[\np{nn\_test\_icebergs}~$>$~0] 

1127  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate 

1128  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of 

1129  which an iceberg is generated at the beginning of the run. 

1130  (Note that this happens each time the timestep equals \np{nn\_nit000}.) 

1131  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of 

1132  the geographical box: lonmin,lonmax,latmin,latmax 

1133  \item[\np{nn\_test\_icebergs}\forcode{ = 1}] 

1134  In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter. 

1135  This should be a file with a field on the configuration grid (typically ORCA) 

1136  representing ice accumulation rate at each model point. 

1137  These should be ocean points adjacent to land where icebergs are known to calve. 

1138  Most points in this input grid are going to have value zero. 

1139  When the model runs, ice is accumulated at each grid point which has a nonzero source term. 

1140  At each time step, a test is performed to see if there is enough ice mass to 

1141  calve an iceberg of each class in order (1 to 10). 

1142  Note that this is the initial mass multiplied by the number each particle represents ($i.e.$ the scaling). 

1143  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly. 

1144  \end{description} 

1145  

1146  Icebergs are influenced by wind, waves and currents, bottom melt and erosion. 

1147  The latter act to disintegrate the iceberg. 

1148  This is either all melted freshwater, 

1149  or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits 

1150  which are assumed to propagate with their larger parent and thus delay fluxing into the ocean. 

1151  Melt water (and other variables on the configuration grid) are written into the main NEMO model output files. 

1152  

1153  Extensive diagnostics can be produced. 

1154  Separate output files are maintained for humanreadable iceberg information. 

1155  A separate file is produced for each processor (independent of \np{ln\_ctl}). 

1156  The amount of information is controlled by two integer parameters: 

1157  \begin{description} 

1158  \item[\np{nn\_verbose\_level}] takes a value between one and four and 

1159  represents an increasing number of points in the code at which variables are written, 

1160  and an increasing level of obscurity. 

1161  \item[\np{nn\_verbose\_write}] is the number of timesteps between writes 

1162  \end{description} 

1163  

1164  Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0. 

1165  A nonzero value represents how many timesteps between writes of information into the output file. 

1166  These output files are in NETCDF format. 

1167  When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor. 

1168  Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs. 

1169  So care is needed to recreate data for individual icebergs, 

1170  since its trajectory data may be spread across multiple files. 

1171  

1172  %  

1173  % Interactions with waves (sbcwave.F90, ln_wave) 

1174  %  

1175  \section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 

1176  \label{sec:SBC_wave} 

1177  %namsbc_wave 

1178  

1179  \nlst{namsbc_wave} 

1180  % 

1181  

1182  Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate 

1183  physical processes related to ocean surface waves, namely the surface stress modified by growth and 

1184  dissipation of the oceanic wave field, the StokesCoriolis force and the Stokes drift impact on mass and 

1185  tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate 

1186  the wind stress. 

1187  

1188  Physical processes related to ocean surface waves can be accounted by setting the logical variable 

1189  \np{ln\_wave}\forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for 

1190  different porcesses should be activated as explained in the following sections. 

1191  

1192  Wave fields can be provided either in forced or coupled mode: 

1193  \begin{description} 

1194  \item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist 

1195  for external data names, locations, frequency, interpolation and all the miscellanous options allowed by 

1196  Input Data generic Interface (see \autoref{sec:SBC_input}). 

1197  \item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 

1198  in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist. 

1199  \end{description} 

1200  

1201  

1202  % ================================================================ 

1203  % Neutral drag coefficient from wave model (ln_cdgw)


1204  % ================================================================ 

1205  \subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 

1206  \label{subsec:SBC_wave_cdgw} 

1207  

1208  The neutral surface drag coefficient provided from an external data source ($i.e.$ a wave
model), 

1209  can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist. 

1210  Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided, 

1211  the drag coefficient is computed according to the stable/unstable conditions of the 

1212  airsea interface following \citet{Large_Yeager_Rep04}. 

1213  

1214  

1215  % ================================================================ 

1216  % 3D Stokes Drift (ln_sdw, nn_sdrift) 

1217  % ================================================================ 

1218  \subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 

1219  \label{subsec:SBC_wave_sdw} 

1220  

1221  The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}. 

1222  It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity) 

1223  and the current measured at a fixed point (Eulerian velocity). 

1224  As waves travel, the water particles that make up the waves travel in orbital motions but 

1225  without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly 

1226  at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift. 

1227  An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved 

1228  representation of surface physics in ocean general circulation models. 

1229  The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as: 

1230  

1231  \begin{equation} \label{eq:sbc_wave_sdw} 

1232  \mathbf{U}_{st} = \frac{16{\pi^3}} {g} 

1233  \int_0^\infty \int_{\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3} 

1234  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f 

1235  \end{equation} 

1236  

1237  where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency, 

1238  $\mathrm{S}($f$,\theta)$ is the 2D frequencydirection spectrum, 

1239  $k$ is the mean wavenumber defined as: 

1240  $k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\ 

1241  

1242  In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required 

1243  and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level. 

1244  To simplify, it is customary to use approximations to the full Stokes profile. 

1245  Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile 

1246  are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift 

1247  $\mathbf{U}_{st _{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra 

1248  and makes possible the estimation of the surface Stokes drift for random directional waves in 

1249  realistic wave conditions: 

1250  

1251  \begin{description} 

1252  \item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by 

1253  \citet{Breivik_al_JPO2014}: 

1254  

1255  \begin{equation} \label{eq:sbc_wave_sdw_0a} 

1256  \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \frac{\mathrm{e}^{2k_ez}} {18k_ez} 

1257  \end{equation} 

1258  

1259  where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows: 

1260  

1261  \begin{equation} \label{eq:sbc_wave_sdw_0b} 

1262  k_e = \frac{\mathbf{U}_{\left.st\right_{z=0}}} {T_{st}} 

1263  \quad \text{and }\ 

1264  T_{st} = \frac{1}{16} \bar{\omega} H_s^2 

1265  \end{equation} 

1266  

1267  where $H_s$ is the significant wave height and $\omega$ is the wave frequency. 

1268  

1269  \item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a 

1270  reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface 

1271  \citep{Breivik_al_OM2016}: 

1272  

1273  \begin{equation} \label{eq:sbc_wave_sdw_1} 

1274  \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \Big[exp(2k_pz)\beta \sqrt{2 \pi k_pz} 

1275  \textit{ erf } \Big(\sqrt{2 k_pz}\Big)\Big] 

1276  \end{equation} 

1277  

1278  where $erf$ is the complementary error function and $k_p$ is the peak wavenumber. 

1279  

1280  \item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1 

1281  but using the wave frequency from a wave model. 

1282  

1283  \end{description} 

1284  

1285  The Stokes drift enters the waveaveraged momentum equation, as well as the tracer advection equations 

1286  and its effect on the evolution of the seasurface height ${\eta}$ is considered as follows: 

1287  

1288  \begin{equation} \label{eq:sbc_wave_eta_sdw} 

1289  \frac{\partial{\eta}}{\partial{t}} = 

1290  \nabla_h \int_{H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz 

1291  \end{equation} 

1292  

1293  The tracer advection equation is also modified in order for Eulerian ocean models to properly account 

1294  for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection 

1295  that is induced by the threedimensional Stokes velocity. 

1296  The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves 

1297  can be formulated as follows: 

1298  

1299  \begin{equation} \label{eq:sbc_wave_tra_sdw} 

1300  \frac{\partial{c}}{\partial{t}} = 

1301   (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c} 

1302  \end{equation} 

1303  

1304  

1305  % ================================================================ 

1306  % StokesCoriolis term (ln_stcor) 

1307  % ================================================================ 

1308  \subsection{StokesCoriolis term (\protect\np{ln\_stcor})} 

1309  \label{subsec:SBC_wave_stcor} 

1310  

1311  In a rotating ocean, waves exert a waveinduced stress on the mean ocean circulation which results 

1312  in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter. 

1313  This additional force may have impact on the Ekman turning of the surface current. 

1314  In order to include this term, once evaluated the Stokes drift (using one of the 3 possible 

1315  approximations described in \autoref{subsec:SBC_wave_sdw}), 

1316  \np{ln\_stcor}\forcode{ = .true.} has to be set. 

1317  

1318  

1319  % ================================================================ 

1320  % Waves modified stress (ln_tauwoc, ln_tauw) 

1321  % ================================================================ 

1322  \subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 

1323  \label{subsec:SBC_wave_tauw} 

1324  

1325  The surface stress felt by the ocean is the atmospheric stress minus the net stress going 

1326  into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not 

1327  available for forcing the mean circulation, while in the opposite case of a decaying sea 

1328  state more momentum is available for forcing the ocean. 

1329  Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress, 

1330  but in practice an equilibrium sea state is a fairly rare event. 

1331  So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as: 

1332  

1333  \begin{equation} \label{eq:sbc_wave_tauoc} 

1334  \tau_{oc,a} = \tau_a  \tau_w 

1335  \end{equation} 

1336  

1337  where $\tau_a$ is the atmospheric surface stress; 

1338  $\tau_w$ is the atmospheric stress going into the waves defined as: 

1339  

1340  \begin{equation} \label{eq:sbc_wave_tauw} 

1341  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})} 

1342  \end{equation} 

1343  

1344  where: $c_p$ is the phase speed of the gravity waves, 

1345  $S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent 

1346  the physics of ocean waves. The first one, $S_{in}$, describes the generation 

1347  of ocean waves by wind and therefore represents the momentum and energy transfer 

1348  from air to ocean waves; the second term $S_{nl}$ denotes 

1349  the nonlinear transfer by resonant fourwave interactions; while the third term $S_{diss}$ 

1350  describes the dissipation of waves by processes such as whitecapping, large scale breaking 

1351  eddyinduced damping. 

1352  

1353  The wave stress derived from an external wave model can be provided either through the normalized 

1354  wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and 

1355  meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}. 

1356  

1357  

1358  % ================================================================ 

1359  % Miscellanea options 

1360  % ================================================================ 

1361  \section{Miscellaneous options} 

1362  \label{sec:SBC_misc} 

1363  

1364  %  

1365  % Diurnal cycle 

1366  %  

1367  \subsection{Diurnal cycle (\protect\mdl{sbcdcy})} 

1368  \label{subsec:SBC_dcy} 

1369  %namsbc_rnf 

1370  % 

1371  \nlst{namsbc} 

1372  % 

1373  

1374  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1375  \begin{figure}[!t] \begin{center} 

1376  \includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal} 

1377  \caption{ \protect\label{fig:SBC_diurnal} 

1378  Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values. 

1379  The reconstructed diurnal cycle (black line) is chosen as 

1380  the mean value of the analytical cycle (blue line) over a time step, 

1381  not as the mid time step value of the analytically cycle (red square). 

1382  From \citet{Bernie_al_CD07}.} 

1383  \end{center} \end{figure} 

1384  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1385  

1386  \cite{Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less. 

1387  Unfortunately high frequency forcing fields are rare, not to say inexistent. 

1388  Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at 

1389  high frequency \citep{Bernie_al_CD07}. 

1390  Furthermore, only the knowledge of daily mean value of SWF is needed, 

1391  as higher frequency variations can be reconstructed from them, 

1392  assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF. 

1393  The \cite{Bernie_al_CD07} reconstruction algorithm is available in \NEMO by 

1394  setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when 

1395  using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or 

1396  the flux formulation (\np{ln\_flx}\forcode{ = .true.}). 

1397  The reconstruction is performed in the \mdl{sbcdcy} module. 

1398  The detail of the algoritm used can be found in the appendix~A of \cite{Bernie_al_CD07}. 

1399  The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at 

1400  a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}). 

1401  The use of diurnal cycle reconstruction requires the input SWF to be daily 

1402  ($i.e.$ a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter). 

1403  Furthermore, it is recommended to have a least 8 surface module time step per day, 

1404  that is $\rdt \ nn\_fsbc < 10,800~s = 3~h$. 

1405  An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle, 

1406  one every 2~hours (from 1am to 11pm). 

1407  

1408  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1409  \begin{figure}[!t] \begin{center} 

1410  \includegraphics[width=0.7\textwidth]{Fig_SBC_dcy} 

1411  \caption{ \protect\label{fig:SBC_dcy} 

1412  Example of recontruction of the diurnal cycle variation of short wave flux from 

1413  daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm). 

1414  The display is on (i,j) plane. } 

1415  \end{center} \end{figure} 

1416  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1417  

1418  Note also that the setting a diurnal cycle in SWF is highly recommended when 

1419  the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to 

1420  an inconsistency between the scale of the vertical resolution and the forcing acting on that scale. 

1421  

1422  %  

1423  % Rotation of vector pairs onto the model grid directions 

1424  %  

1425  \subsection{Rotation of vector pairs onto the model grid directions} 

1426  \label{subsec:SBC_rotation} 

1427  

1428  When using a flux (\np{ln\_flx}\forcode{ = .true.}) or 

1429  bulk (\np{ln\_clio}\forcode{ = .true.} or \np{ln\_core}\forcode{ = .true.}) formulation, 

1430  pairs of vector components can be rotated from eastnorth directions onto the local grid directions. 

1431  This is particularly useful when interpolation on the fly is used since here any vectors are likely to 

1432  be defined relative to a rectilinear grid. 

1433  To activate this option a nonempty string is supplied in the rotation pair column of the relevant namelist. 

1434  The eastward component must start with "U" and the northward component with "V". 

1435  The remaining characters in the strings are used to identify which pair of components go together. 

1436  So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and 

1437  rotate them on to the model grid directions; 

1438  "U2" and "V2" could be used against a second pair of components, and so on. 

1439  The extra characters used in the strings are arbitrary. 

1440  The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation. 

1441  

1442  %  

1443  % Surface restoring to observed SST and/or SSS 

1444  %  

1445  \subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 

1446  \label{subsec:SBC_ssr} 

1447  %namsbc_ssr 

1448  

1449  \nlst{namsbc_ssr} 

1450  % 

1451  

1452  IOptions are defined through the \ngn{namsbc\_ssr} namelist variables. 

1453  On forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}), 

1454  a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$: 

1455  \begin{equation} \label{eq:sbc_dmp_q} 

1456  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right_{k=1}  SST_{Obs} \right) 

1457  \end{equation} 

1458  where SST is a sea surface temperature field (observed or climatological), 

1459  $T$ is the model surface layer temperature and 

1460  $\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $40~W/m^2/K$. 

1461  For a $50~m$ mixedlayer depth, this value corresponds to a relaxation time scale of two months. 

1462  This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$. 

1463  

1464  In the fresh water budget, a feedback term can also be added. 

1465  Converted into an equivalent freshwater flux, it takes the following expression : 

1466  

1467  \begin{equation} \label{eq:sbc_dmp_emp} 

1468  \textit{emp} = \textit{emp}_o + \gamma_s^{1} e_{3t} \frac{ \left(\left.S\right_{k=1}SSS_{Obs}\right)} 

1469  {\left.S\right_{k=1}} 

1470  \end{equation} 

1471  

1472  where $\textit{emp}_{o }$ is a net surface fresh water flux 

1473  (observed, climatological or an atmospheric model product), 

1474  \textit{SSS}$_{Obs}$ is a sea surface salinity 

1475  (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}), 

1476  $\left.S\right_{k=1}$ is the model surface layer salinity and 

1477  $\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter. 

1478  Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as 

1479  the atmosphere does not care about ocean surface salinity \citep{Madec1997}. 

1480  The SSS restoring term should be viewed as a flux correction on freshwater fluxes to 

1481  reduce the uncertainties we have on the observed freshwater budget. 

1482  

1483  %  

1484  % Handling of icecovered area 

1485  %  

1486  \subsection{Handling of icecovered area (\textit{sbcice\_...})} 

1487  \label{subsec:SBC_icecover} 

1488  

1489  The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean. 

1490  There are several way to handle seaice in the system depending on 

1491  the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist. 

1492  \begin{description} 

1493  \item[nn{\_}ice = 0] 

1494  there will never be seaice in the computational domain. 

1495  This is a typical namelist value used for tropical ocean domain. 

1496  The surface fluxes are simply specified for an icefree ocean. 

1497  No specific things is done for seaice. 

1498  \item[nn{\_}ice = 1] 

1499  seaice can exist in the computational domain, but no seaice model is used. 

1500  An observed ice covered area is read in a file. 

1501  Below this area, the SST is restored to the freezing point and 

1502  the heat fluxes are set to $4~W/m^2$ ($2~W/m^2$) in the northern (southern) hemisphere. 

1503  The associated modification of the freshwater fluxes are done in such a way that 

1504  the change in buoyancy fluxes remains zero. 

1505  This prevents deep convection to occur when trying to reach the freezing point 

1506  (and so ice covered area condition) while the SSS is too large. 

1507  This manner of managing seaice area, just by using si IF case, 

1508  is usually referred as the \textit{iceif} model. 

1509  It can be found in the \mdl{sbcice{\_}if} module. 

1510  \item[nn{\_}ice = 2 or more] 

1511  A full sea ice model is used. 

1512  This model computes the iceocean fluxes, 

1513  that are combined with the airsea fluxes using the ice fraction of each model cell to 

1514  provide the surface ocean fluxes. 

1515  Note that the activation of a seaice model is is done by defining a CPP key (\key{lim3} or \key{cice}). 

1516  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value 

1517  ($i.e.$ $2$ for LIM3 or $3$ for CICE). 

1518  \end{description} 

1519  

1520  % {Description of Iceocean interface to be added here or in LIM 2 and 3 doc ?} 

1521  

1522  \subsection{Interface to CICE (\protect\mdl{sbcice\_cice})} 

1523  \label{subsec:SBC_cice} 

1524  

1525  It is now possible to couple a regional or global NEMO configuration (without AGRIF) 

1526  to the CICE seaice model by using \key{cice}. 

1527  The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and 

1528  the additional 'hadgem3' drivers will be required, even with the latest code release. 

1529  Input grid files consistent with those used in NEMO will also be needed, 

1530  and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used 

1531  (seek advice from UKMO if necessary). 

1532  Currently the code is only designed to work when using the CORE forcing option for NEMO 

1533  (with \textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE namelist), 

1534  or alternatively when NEMO is coupled to the HadGAM3 atmosphere model 

1535  (with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}). 

1536  The code is intended to be used with \np{nn\_fsbc} set to 1 

1537  (although coupling ocean and ice less frequently should work, 

1538  it is possible the calculation of some of the oceanice fluxes needs to be modified slightly  

1539  the user should check that results are not significantly different to the standard case). 

1540  

1541  There are two options for the technical coupling between NEMO and CICE. 

1542  The standard version allows complete flexibility for the domain decompositions in the individual models, 

1543  but this is at the expense of global gather and scatter operations in the coupling which 

1544  become very expensive on larger numbers of processors. 

1545  The alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that 

1546  the domain decomposition is identical in both models (provided domain parameters are set appropriately, 

1547  and \textit{processor\_shape~=~squareice} and \textit{distribution\_wght~=~block} in the CICE namelist) and 

1548  allows much more efficient direct coupling on individual processors. 

1549  This solution scales much better although it is at the expense of having more idle CICE processors in areas where 

1550  there is no sea ice. 

1551  

1552  %  

1553  % Freshwater budget control 

1554  %  

1555  \subsection{Freshwater budget control (\protect\mdl{sbcfwb})} 

1556  \label{subsec:SBC_fwb} 

1557  

1558  For global ocean simulation it can be useful to introduce a control of the mean sea level in order to 

1559  prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes. 

1560  In \NEMO, two way of controlling the the freshwater budget. 

1561  \begin{description} 

1562  \item[\np{nn\_fwb}\forcode{ = 0}] 

1563  no control at all. 

1564  The mean sea level is free to drift, and will certainly do so. 

1565  \item[\np{nn\_fwb}\forcode{ = 1}] 

1566  global mean \textit{emp} set to zero at each model time step. 

1567  %Note that with a seaice 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 iceocean coupling). 

1568  \item[\np{nn\_fwb}\forcode{ = 2}] 

1569  freshwater budget is adjusted from the previous year annual mean budget which 

1570  is read in the \textit{EMPave\_old.dat} file. 

1571  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from 

1572  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file. 

1573  \end{description} 

1574  

1575  

1576  

1577  % Griffies doc: 

1578  % When running oceanice simulations, we are not explicitly representing land processes, 

1579  % such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, 

1580  % it is important to balance the hydrological cycle in oceanice models. 

1581  % We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. 

1582  % The result of the normalization should be a global integrated zero net water input to the oceanice system over 

1583  % a chosen time scale. 

1584  %How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, 

1585  % so that there is always a zero net input of water to the oceanice system. 

1586  % Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used 

1587  % to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. 

1588  % Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing. 

1589  % When running oceanice coupled models, it is incorrect to include the water transport between the ocean 

1590  % and ice models when aiming to balance the hydrological cycle. 

1591  % The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running oceanice models, 

1592  % not the water in any one subcomponent. As an extreme example to illustrate the issue, 

1593  % consider an oceanice model with zero initial sea ice. As the oceanice model spins up, 

1594  % there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. 

1595  % The total water contained in the ocean plus ice system is constant, but there is an exchange of water between 

1596  % the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle 

1597  % in oceanice models. 

1598  

1599  

1600  \end{document} 
