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

2  

3  \begin{document} 

4  % ================================================================ 

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

6  % ================================================================ 

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

8  \label{chap:SBC} 

9  \minitoc 

10  

11  \newpage 

12  

13  %namsbc 

14  

15  \nlst{namsbc} 

16  % 

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 (\ie \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  \ie 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  (\ie 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) \ie 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] 

164  \begin{center} 

165  \begin{tabular}{llll} 

166  \hline 

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

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

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

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

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

172  \end{tabular} 

173  \caption{ 

174  \protect\label{tab:ssm} 

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

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

177  \ie the frequency of computation of surface fluxes. 

178  } 

179  \end{center} 

180  \end{table} 

181  % 

182  

183  %\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 

184  

185  

186  % ================================================================ 

187  % Input Data 

188  % ================================================================ 

189  \section{Input data generic interface} 

190  \label{sec:SBC_input} 

191  

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

193  (2D or 3D fields, like surface forcing or ocean T and S) are specify in \NEMO. 

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

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

196  \begin{enumerate} 

197  \item 

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

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

200  \item 

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

202  \item 

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

204  \item 

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

206  limiting the number of prerequisite information. 

207  \end{enumerate} 

208  

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

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

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

212  and three additional parameters for onthefly interpolation. 

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

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

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

216  

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

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

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

220  

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

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

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

224  

225  %  

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

227  %  

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

229  \label{subsec:SBC_fldread} 

230  

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

232  \begin{forlines} 

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

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

235  \end{forlines} 

236  where 

237  \begin{description} 

238  \item[File name]: 

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

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

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

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

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

244  

245  %TABLE 

246  \begin{table}[htbp] 

247  \begin{center} 

248  \begin{tabular}{lccc} 

249  \hline 

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

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

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

253  \end{tabular} 

254  \end{center} 

255  \caption{ 

256  \protect\label{tab:fldread} 

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

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

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

260  (\ie 'sun','sat','fri','thu','wed','tue','mon'). 

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

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

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

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

265  } 

266  \end{table} 

267  % 

268  

269  

270  \item[Record frequency]: 

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

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

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

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

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

276  

277  \item[Variable name]: 

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

279  

280  \item[Time interpolation]: 

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

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

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

284  00h00'00'' to 23h59'59". 

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

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

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

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

289  

290  \item[Climatological forcing]: 

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

292  or an interannual forcing which will requires additional files if 

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

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

295  

296  \item[Open/close frequency]: 

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

298  Four cases are coded: 

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

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

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

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

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

304  

305  \item[Others]: 

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

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

308  

309  \end{description} 

310  

311  Additional remarks:\\ 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

345  

346  

347  %  

348  % Interpolation on the Fly 

349  %  

350  \subsection{Interpolation onthefly} 

351  \label{subsec:SBC_iof} 

352  

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

354  grids other than the model grid. 

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

356  interpolate from the data grid to the model grid. 

357  The original development of this code used the SCRIP package 

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

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

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

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

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

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

364  the native external grid. 

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

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

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

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

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

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

371  

372  \subsubsection{Bilinear interpolation} 

373  \label{subsec:SBC_iof_bilinear} 

374  

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

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

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

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

379  written as a one dimensional array. 

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

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

382  the grid box containing the point to be interpolated. 

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

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

385  

386  Symbolically, the algorithm used is: 

387  \[ 

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

389  \] 

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

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

392  

393  \subsubsection{Bicubic interpolation} 

394  \label{subsec:SBC_iof_bicubic} 

395  

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

397  But in this case there are 16 of each. 

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

399  

400  \[ 

401  \begin{split} 

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

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

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

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

406  \end{split} 

407  \] 

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

409  the spatial dependency has been absorbed into the weights. 

410  

411  \subsubsection{Implementation} 

412  \label{subsec:SBC_iof_imp} 

413  

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

415  the weights filename column of the relevant namelist; 

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

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

418  as and when they are first required. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

433  

434  Next the routine reads in the weights. 

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

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

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

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

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

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

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

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

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

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

445  

446  \subsubsection{Limitations} 

447  \label{subsec:SBC_iof_lim} 

448  

449  \begin{enumerate} 

450  \item 

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

452  \item 

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

454  a bicubic interpolation method is used. 

455  \item 

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

457  \item 

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

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

460  \item 

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

462  but this has not been implemented.) 

463  \end{enumerate} 

464  

465  \subsubsection{Utilities} 

466  \label{subsec:SBC_iof_util} 

467  

468  % to be completed 

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

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

471  

472  %  

473  % Standalone Surface Boundary Condition Scheme 

474  %  

475  \subsection{Standalone surface boundary condition scheme} 

476  \label{subsec:SAS_iof} 

477  

478  %namsbc_ana 

479  

480  \nlst{namsbc_sas} 

481  % 

482  

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

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

485  For example: 

486  

487  \begin{itemize} 

488  \item 

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

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

491  \item 

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

493  \item 

494  Development of seaice algorithms or parameterizations. 

495  \item 

496  Spinup of the iceberg floats 

497  \item 

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

499  \end{itemize} 

500  

501  The StandAlone Surface scheme provides this utility. 

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

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

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

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

506  Routines replaced are: 

507  

508  \begin{itemize} 

509  \item 

510  \mdl{nemogcm}: 

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

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

513  \item 

514  \mdl{step}: 

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

516  \item 

517  \mdl{sbcmod}: 

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

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

520  (\eg icebergs). 

521  \item 

522  \mdl{daymod}: 

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

524  so calls to restart functions have been removed. 

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

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

527  \item 

528  \mdl{stpctl}: 

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

530  \item 

531  \mdl{diawri}: 

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

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

534  relevant forcing and ice data. 

535  \end{itemize} 

536  

537  One new routine has been added: 

538  

539  \begin{itemize} 

540  \item 

541  \mdl{sbcsas}: 

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

543  velocity arrays at the surface. 

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

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

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

547  before using just the top level. 

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

549  \end{itemize} 

550  

551  

552  % Missing the description of the 2 following variables: 

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

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

555  

556  

557  

558  % ================================================================ 

559  % Analytical formulation (sbcana module) 

560  % ================================================================ 

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

562  \label{sec:SBC_ana} 

563  

564  %namsbc_ana 

565  % 

566  %\nlst{namsbc_ana} 

567  % 

568  

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

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

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

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

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

574  The runoff is set to zero. 

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

576  

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

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

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

580  (see GYRE configuration manual, in preparation). 

581  

582  

583  % ================================================================ 

584  % Flux formulation 

585  % ================================================================ 

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

587  \label{sec:SBC_flx} 

588  %namsbc_flx 

589  

590  \nlst{namsbc_flx} 

591  % 

592  

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

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

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

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

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

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

599  

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

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

602  

603  

604  % ================================================================ 

605  % Bulk formulation 

606  % ================================================================ 

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

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

609  \label{sec:SBC_blk} 

610  

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

612  

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

614  Two bulk formulations are available: 

615  the CORE and the CLIO bulk formulea. 

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

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

618  

619  Note: 

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

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

622  both an ocean and an ice surface. 

623  

624  %  

625  % CORE Bulk formulea 

626  %  

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

628  \label{subsec:SBC_blk_core} 

629  %namsbc_core 

630  % 

631  %\nlst{namsbc_core} 

632  % 

633  

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

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

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

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

638  This \citet{Large_Yeager_Rep04} dataset is available through 

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

640  

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

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

643  

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

645  The required 8 input fields are: 

646  

647  %TABLE 

648  \begin{table}[htbp] 

649  \label{tab:CORE} 

650  \begin{center} 

651  \begin{tabular}{lccc} 

652  \hline 

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

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

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

656  10m air temperature & tair & \r{}$K$ & T \\ \hline 

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

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

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

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

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

662  \end{tabular} 

663  \end{center} 

664  \end{table} 

665  % 

666  

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

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

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

670  

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

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

673  (spatial and temporal interpolations). 

674  

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

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

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

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

679  

680  Three multiplicative factors are availables: 

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

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

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

684  the calculation of surface wind stress. 

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

686  

687  %  

688  % CLIO Bulk formulea 

689  %  

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

691  \label{subsec:SBC_blk_clio} 

692  %namsbc_clio 

693  % 

694  %\nlst{namsbc_clio} 

695  % 

696  

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

698  (CLIO, \cite{Goosse_al_JGR99}). 

699  They are simpler bulk formulae. 

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

701  

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

703  The required 7 input fields are: 

704  

705  %TABLE 

706  \begin{table}[htbp] 

707  \label{tab:CLIO} 

708  \begin{center} 

709  \begin{tabular}{llll} 

710  \hline 

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

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

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

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

715  10m air temperature & tair & \r{}$K$ & T \\ \hline 

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

717  Cloud cover & & \% & T \\ \hline 

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

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

720  \end{tabular} 

721  \end{center} 

722  \end{table} 

723  % 

724  

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

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

727  

728  % ================================================================ 

729  % Coupled formulation 

730  % ================================================================ 

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

732  \label{sec:SBC_cpl} 

733  %namsbc_cpl 

734  

735  \nlst{namsbc_cpl} 

736  % 

737  

738  In the coupled formulation of the surface boundary condition, 

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

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

741  the atmospheric component. 

742  

743  A generalised coupled interface has been developed. 

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

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

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

747  (Weather Research and Forecasting Model). 

748  

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

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

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

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

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

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

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

756  

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

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

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

760  the number used in the sea ice model. 

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

762  the sea ice model is running with multiple categories  

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

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

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

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

767  

768  

769  % ================================================================ 

770  % Atmospheric pressure 

771  % ================================================================ 

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

773  \label{sec:SBC_apr} 

774  %namsbc_apr 

775  

776  \nlst{namsbc_apr} 

777  % 

778  

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

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

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

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

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

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

785  \[ 

786  % \label{eq:SBC_ssh_ib} 

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

788  \] 

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

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

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

792  \ie the mean value of $\eta_{ib}$ is kept to zero at all time step. 

793  

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

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

796  (see \mdl{sbcssr} module). 

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

798  This can simplify altimetry data and model comparison as 

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

800  

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

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

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

804  

805  % ================================================================ 

806  % Surface Tides Forcing 

807  % ================================================================ 

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

809  \label{sec:SBC_tide} 

810  

811  %nam_tide 

812  

813  \nlst{nam_tide} 

814  % 

815  

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

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

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

819  \[ 

820  % \label{eq:PE_dyn_tides} 

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

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

823  \] 

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

825  

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

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

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

829  Long period tides : 

830  \[ 

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

832  \] 

833  diurnal tides : 

834  \[ 

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

836  \] 

837  Semidiurnal tides: 

838  \[ 

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

840  \] 

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

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

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

844  

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

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

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

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

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

850  In the latter case, it reads:\\ 

851  \[ 

852  \Pi_{sal} = \beta \eta 

853  \] 

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

855  often chosen to minimize tidal prediction errors. 

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

857  

858  % ================================================================ 

859  % River runoffs 

860  % ================================================================ 

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

862  \label{sec:SBC_rnf} 

863  %namsbc_rnf 

864  

865  \nlst{namsbc_rnf} 

866  % 

867  

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

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

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

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

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

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

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

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

876  

877  

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

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

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

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

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

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

884  

885  

886  %Rachel: 

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

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

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

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

891  

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

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

894  \footnote{ 

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

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

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

898  

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

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

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

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

903  

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

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

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

907  and/or taken as surface temperature respectively. 

908  

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

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

911  be the surface temperatue at the river point. 

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

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

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

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

916  After the user specified depth is read ini, 

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

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

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

920  (\ie the total depth that river water is being added to in the model). 

921  

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

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

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

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

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

927  

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

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

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

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

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

933  

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

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

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

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

938  

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

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

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

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

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

944  

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

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

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

948  the heat and salt content of the river. 

949  

950  In the nonlinear free surface case (vvl), 

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

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

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

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

955  

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

957  \ie modelling the Baltic flow in and out of the North Sea. 

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

959  regardless of the namelist options used, 

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

961  

962  

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

964  

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

966  

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

968  

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

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

971  %ENDIF 

972  

973  %\gmcomment{ word doc of runoffs: 

974  % 

975  %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. 

976  %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. 

977  

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

979  

980  %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: 

981  

982  %} 

983  % ================================================================ 

984  % Ice shelf melting 

985  % ================================================================ 

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

987  \label{sec:SBC_isf} 

988  %namsbc_isf 

989  

990  \nlst{namsbc_isf} 

991  % 

992  The namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation. 

993  Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{Mathiot2017}. 

994  The different options are illustrated in \autoref{fig:SBC_isf}. 

995  

996  \begin{description} 

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

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

999  The fwf and heat flux are depending of the local water properties. 

1000  Two different bulk formulae are available: 

1001  

1002  \begin{description} 

1003  \item[\np{nn\_isfblk}\forcode{ = 1}]: 

1004  The melt rate is based on a balance between the upward ocean heat flux and 

1005  the latent heat flux at the ice shelf base. A complete description is available in \citet{Hunter2006}. 

1006  \item[\np{nn\_isfblk}\forcode{ = 2}]: 

1007  The melt rate and the heat flux are based on a 3 equations formulation 

1008  (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation). 

1009  A complete description is available in \citet{Jenkins1991}. 

1010  \end{description} 

1011  

1012  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{Losch2008}. 

1013  Its thickness is defined by \np{rn\_hisf\_tbl}. 

1014  The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m. 

1015  Then, the fluxes are spread over the same thickness (ie over one or several cells). 

1016  If \np{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature. 

1017  This can lead to supercool temperature in the top cell under melting condition. 

1018  If \np{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\ 

1019  

1020  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice. 

1021  There are 3 different ways to compute the exchange coeficient: 

1022  \begin{description} 

1023  \item[\np{nn\_gammablk}\forcode{ = 0}]: 

1024  The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}. 

1025  \[ 

1026  % \label{eq:sbc_isf_gamma_iso} 

1027  \gamma^{T} = \np{rn\_gammat0} 

1028  \] 

1029  \[ 

1030  \gamma^{S} = \np{rn\_gammas0} 

1031  \] 

1032  This is the recommended formulation for ISOMIP. 

1033  \item[\np{nn\_gammablk}\forcode{ = 1}]: 

1034  The salt and heat exchange coefficients are velocity dependent and defined as 

1035  \[ 

1036  \gamma^{T} = \np{rn\_gammat0} \times u_{*} 

1037  \] 

1038  \[ 

1039  \gamma^{S} = \np{rn\_gammas0} \times u_{*} 

1040  \] 

1041  where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters). 

1042  See \citet{Jenkins2010} for all the details on this formulation. It is the recommended formulation for realistic application. 

1043  \item[\np{nn\_gammablk}\forcode{ = 2}]: 

1044  The salt and heat exchange coefficients are velocity and stability dependent and defined as: 

1045  \[ 

1046  \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}} 

1047  \] 

1048  where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters), 

1049  $\Gamma_{Turb}$ the contribution of the ocean stability and 

1050  $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 

1051  See \citet{Holland1999} for all the details on this formulation. 

1052  This formulation has not been extensively tested in NEMO (not recommended). 

1053  \end{description} 

1054  \item[\np{nn\_isf}\forcode{ = 2}]: 

1055  The ice shelf cavity is not represented. 

1056  The fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting. 

1057  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL) 

1058  (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front 

1059  (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}). 

1060  The effective melting length (\np{sn\_Leff\_isf}) is read from a file. 

1061  \item[\np{nn\_isf}\forcode{ = 3}]: 

1062  The ice shelf cavity is not represented. 

1063  The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between 

1064  the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and 

1065  the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}). 

1066  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 

1067  \item[\np{nn\_isf}\forcode{ = 4}]: 

1068  The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed). 

1069  However, the fwf is not computed but specified from file \np{sn\_fwfisf}). 

1070  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 

1071  As in \np{nn\_isf}\forcode{ = 1}, the fluxes are spread over the top boundary layer thickness (\np{rn\_hisf\_tbl})\\ 

1072  \end{description} 

1073  

1074  $\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on 

1075  the water mass properties, ocean velocities and depth. 

1076  This flux is thus highly dependent of the model resolution (horizontal and vertical), 

1077  realism of the water masses onto the shelf ...\\ 

1078  

1079  $\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file. 

1080  You have total control of the fwf forcing. 

1081  This can be useful if the water masses on the shelf are not realistic or 

1082  the resolution (horizontal/vertical) are too coarse to have realistic melting or 

1083  for studies where you need to control your heat and fw input.\\ 

1084  

1085  The ice shelf melt is implemented as a volume flux as for the runoff. 

1086  The fw addition due to the ice shelf melting is, at each relevant depth level, added to 

1087  the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}. 

1088  See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\ 

1089  

1090  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1091  \begin{figure}[!t] 

1092  \begin{center} 

1093  \includegraphics[width=0.8\textwidth]{Fig_SBC_isf} 

1094  \caption{ 

1095  \protect\label{fig:SBC_isf} 

1096  Illustration the location where the fwf is injected and whether or not the fwf is interactif or not depending of \np{nn\_isf}. 

1097  } 

1098  \end{center} 

1099  \end{figure} 

1100  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1101  

1102  \section{Ice sheet coupling} 

1103  \label{sec:SBC_iscpl} 

1104  %namsbc_iscpl 

1105  

1106  \nlst{namsbc_iscpl} 

1107  % 

1108  Ice sheet/ocean coupling is done through file exchange at the restart step. 

1109  At each restart step: 

1110  \begin{description} 

1111  \item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file. 

1112  \item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools. 

1113  \item[Step 3]: NEMO run for a specific period and output the average melt rate over the period. 

1114  \item[Step 4]: the ice sheet model run using the melt rate outputed in step 4. 

1115  \item[Step 5]: go back to 1. 

1116  \end{description} 

1117  

1118  If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with 

1119  potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics. 

1120  The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases: 

1121  \begin{description} 

1122  \item[Thin a cell down]: 

1123  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant 

1124  ($bt_b=bt_n$). 

1125  \item[Enlarge a cell]: 

1126  See case "Thin a cell down" 

1127  \item[Dry a cell]: 

1128  mask, T/S, U/V and ssh are set to 0. 

1129  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$). 

1130  \item[Wet a cell]: 

1131  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0. 

1132  If no neighbours, T/S is extrapolated from old top cell value. 

1133  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0. 

1134  \item[Dry a column]: 

1135  mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0. 

1136  \item[Wet a column]: 

1137  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0. 

1138  If no neighbour, T/S/U/V and mask set to 0. 

1139  \end{description} 

1140  

1141  Furthermore, as the before and now fields are not compatible (modification of the geometry), 

1142  the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\ 

1143  

1144  The horizontal extrapolation to fill new cell with realistic value is called \np{nn\_drown} times. 

1145  It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps, 

1146  the code will be unable to fill all the new wet cells properly. 

1147  The default number is set up for the MISOMIP idealised experiments. 

1148  This coupling procedure is able to take into account grounding line and calving front migration. 

1149  However, it is a nonconservative processe. 

1150  This could lead to a trend in heat/salt content and volume.\\ 

1151  

1152  In order to remove the trend and keep the conservation level as close to 0 as possible, 

1153  a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}. 

1154  The heat/salt/vol. gain/loss is diagnosed, as well as the location. 

1155  A correction increment is computed and apply each time step during the next \np{rn\_fiscpl} time steps. 

1156  For safety, it is advised to set \np{rn\_fiscpl} equal to the coupling period (smallest increment possible). 

1157  The corrective increment is apply into the cell itself (if it is a wet cell), the neigbouring cells or the closest wet cell (if the cell is now dry). 

1158  

1159  % 

1160  % ================================================================ 

1161  % Handling of icebergs 

1162  % ================================================================ 

1163  \section{Handling of icebergs (ICB)} 

1164  \label{sec:ICB_icebergs} 

1165  %namberg 

1166  

1167  \nlst{namberg} 

1168  % 

1169  

1170  Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}. 

1171  Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ). 

1172  (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 

1173  Icebergs are initially spawned into one of ten classes which have specific mass and thickness as 

1174  described in the \ngn{namberg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}. 

1175  Each class has an associated scaling (\np{rn\_mass\_scaling}), 

1176  which is an integer representing how many icebergs of this class are being described as one lagrangian point 

1177  (this reduces the numerical problem of tracking every single iceberg). 

1178  They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}. 

1179  

1180  Two initialisation schemes are possible. 

1181  \begin{description} 

1182  \item[\np{nn\_test\_icebergs}~$>$~0] 

1183  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate 

1184  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of 

1185  which an iceberg is generated at the beginning of the run. 

1186  (Note that this happens each time the timestep equals \np{nn\_nit000}.) 

1187  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of 

1188  the geographical box: lonmin,lonmax,latmin,latmax 

1189  \item[\np{nn\_test\_icebergs}\forcode{ = 1}] 

1190  In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter. 

1191  This should be a file with a field on the configuration grid (typically ORCA) 

1192  representing ice accumulation rate at each model point. 

1193  These should be ocean points adjacent to land where icebergs are known to calve. 

1194  Most points in this input grid are going to have value zero. 

1195  When the model runs, ice is accumulated at each grid point which has a nonzero source term. 

1196  At each time step, a test is performed to see if there is enough ice mass to 

1197  calve an iceberg of each class in order (1 to 10). 

1198  Note that this is the initial mass multiplied by the number each particle represents (\ie the scaling). 

1199  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly. 

1200  \end{description} 

1201  

1202  Icebergs are influenced by wind, waves and currents, bottom melt and erosion. 

1203  The latter act to disintegrate the iceberg. 

1204  This is either all melted freshwater, 

1205  or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits 

1206  which are assumed to propagate with their larger parent and thus delay fluxing into the ocean. 

1207  Melt water (and other variables on the configuration grid) are written into the main NEMO model output files. 

1208  

1209  Extensive diagnostics can be produced. 

1210  Separate output files are maintained for humanreadable iceberg information. 

1211  A separate file is produced for each processor (independent of \np{ln\_ctl}). 

1212  The amount of information is controlled by two integer parameters: 

1213  \begin{description} 

1214  \item[\np{nn\_verbose\_level}] takes a value between one and four and 

1215  represents an increasing number of points in the code at which variables are written, 

1216  and an increasing level of obscurity. 

1217  \item[\np{nn\_verbose\_write}] is the number of timesteps between writes 

1218  \end{description} 

1219  

1220  Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0. 

1221  A nonzero value represents how many timesteps between writes of information into the output file. 

1222  These output files are in NETCDF format. 

1223  When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor. 

1224  Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs. 

1225  So care is needed to recreate data for individual icebergs, 

1226  since its trajectory data may be spread across multiple files. 

1227  

1228  %  

1229  % Interactions with waves (sbcwave.F90, ln_wave) 

1230  %  

1231  \section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 

1232  \label{sec:SBC_wave} 

1233  %namsbc_wave 

1234  

1235  \nlst{namsbc_wave} 

1236  % 

1237  

1238  Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate 

1239  physical processes related to ocean surface waves, namely the surface stress modified by growth and 

1240  dissipation of the oceanic wave field, the StokesCoriolis force and the Stokes drift impact on mass and 

1241  tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate 

1242  the wind stress. 

1243  

1244  Physical processes related to ocean surface waves can be accounted by setting the logical variable 

1245  \np{ln\_wave}\forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for 

1246  different porcesses should be activated as explained in the following sections. 

1247  

1248  Wave fields can be provided either in forced or coupled mode: 

1249  \begin{description} 

1250  \item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist 

1251  for external data names, locations, frequency, interpolation and all the miscellanous options allowed by 

1252  Input Data generic Interface (see \autoref{sec:SBC_input}). 

1253  \item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 

1254  in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist. 

1255  \end{description} 

1256  

1257  

1258  % ================================================================ 

1259  % Neutral drag coefficient from wave model (ln_cdgw)


1260  % ================================================================ 

1261  \subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 

1262  \label{subsec:SBC_wave_cdgw} 

1263  

1264  The neutral surface drag coefficient provided from an external data source (\ie a wave model), 

1265  can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist. 

1266  Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided, 

1267  the drag coefficient is computed according to the stable/unstable conditions of the 

1268  airsea interface following \citet{Large_Yeager_Rep04}. 

1269  

1270  

1271  % ================================================================ 

1272  % 3D Stokes Drift (ln_sdw, nn_sdrift) 

1273  % ================================================================ 

1274  \subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 

1275  \label{subsec:SBC_wave_sdw} 

1276  

1277  The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}. 

1278  It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity) 

1279  and the current measured at a fixed point (Eulerian velocity). 

1280  As waves travel, the water particles that make up the waves travel in orbital motions but 

1281  without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly 

1282  at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift. 

1283  An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved 

1284  representation of surface physics in ocean general circulation models. 

1285  The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as: 

1286  

1287  \[ 

1288  % \label{eq:sbc_wave_sdw} 

1289  \mathbf{U}_{st} = \frac{16{\pi^3}} {g} 

1290  \int_0^\infty \int_{\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3} 

1291  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f 

1292  \] 

1293  

1294  where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency, 

1295  $\mathrm{S}($f$,\theta)$ is the 2D frequencydirection spectrum, 

1296  $k$ is the mean wavenumber defined as: 

1297  $k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\ 

1298  

1299  In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required 

1300  and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level. 

1301  To simplify, it is customary to use approximations to the full Stokes profile. 

1302  Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile 

1303  are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift 

1304  $\mathbf{U}_{st _{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra 

1305  and makes possible the estimation of the surface Stokes drift for random directional waves in 

1306  realistic wave conditions: 

1307  

1308  \begin{description} 

1309  \item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by 

1310  \citet{Breivik_al_JPO2014}: 

1311  

1312  \[ 

1313  % \label{eq:sbc_wave_sdw_0a} 

1314  \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \frac{\mathrm{e}^{2k_ez}} {18k_ez} 

1315  \] 

1316  

1317  where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows: 

1318  

1319  \[ 

1320  % \label{eq:sbc_wave_sdw_0b} 

1321  k_e = \frac{\mathbf{U}_{\left.st\right_{z=0}}} {T_{st}} 

1322  \quad \text{and }\ 

1323  T_{st} = \frac{1}{16} \bar{\omega} H_s^2 

1324  \] 

1325  

1326  where $H_s$ is the significant wave height and $\omega$ is the wave frequency. 

1327  

1328  \item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a 

1329  reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface 

1330  \citep{Breivik_al_OM2016}: 

1331  

1332  \[ 

1333  % \label{eq:sbc_wave_sdw_1} 

1334  \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \Big[exp(2k_pz)\beta \sqrt{2 \pi k_pz} 

1335  \textit{ erf } \Big(\sqrt{2 k_pz}\Big)\Big] 

1336  \] 

1337  

1338  where $erf$ is the complementary error function and $k_p$ is the peak wavenumber. 

1339  

1340  \item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1 

1341  but using the wave frequency from a wave model. 

1342  

1343  \end{description} 

1344  

1345  The Stokes drift enters the waveaveraged momentum equation, as well as the tracer advection equations 

1346  and its effect on the evolution of the seasurface height ${\eta}$ is considered as follows: 

1347  

1348  \[ 

1349  % \label{eq:sbc_wave_eta_sdw} 

1350  \frac{\partial{\eta}}{\partial{t}} = 

1351  \nabla_h \int_{H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz 

1352  \] 

1353  

1354  The tracer advection equation is also modified in order for Eulerian ocean models to properly account 

1355  for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection 

1356  that is induced by the threedimensional Stokes velocity. 

1357  The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves 

1358  can be formulated as follows: 

1359  

1360  \[ 

1361  % \label{eq:sbc_wave_tra_sdw} 

1362  \frac{\partial{c}}{\partial{t}} = 

1363   (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c} 

1364  \] 

1365  

1366  

1367  % ================================================================ 

1368  % StokesCoriolis term (ln_stcor) 

1369  % ================================================================ 

1370  \subsection{StokesCoriolis term (\protect\np{ln\_stcor})} 

1371  \label{subsec:SBC_wave_stcor} 

1372  

1373  In a rotating ocean, waves exert a waveinduced stress on the mean ocean circulation which results 

1374  in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter. 

1375  This additional force may have impact on the Ekman turning of the surface current. 

1376  In order to include this term, once evaluated the Stokes drift (using one of the 3 possible 

1377  approximations described in \autoref{subsec:SBC_wave_sdw}), 

1378  \np{ln\_stcor}\forcode{ = .true.} has to be set. 

1379  

1380  

1381  % ================================================================ 

1382  % Waves modified stress (ln_tauwoc, ln_tauw) 

1383  % ================================================================ 

1384  \subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 

1385  \label{subsec:SBC_wave_tauw} 

1386  

1387  The surface stress felt by the ocean is the atmospheric stress minus the net stress going 

1388  into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not 

1389  available for forcing the mean circulation, while in the opposite case of a decaying sea 

1390  state more momentum is available for forcing the ocean. 

1391  Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress, 

1392  but in practice an equilibrium sea state is a fairly rare event. 

1393  So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as: 

1394  

1395  \[ 

1396  % \label{eq:sbc_wave_tauoc} 

1397  \tau_{oc,a} = \tau_a  \tau_w 

1398  \] 

1399  

1400  where $\tau_a$ is the atmospheric surface stress; 

1401  $\tau_w$ is the atmospheric stress going into the waves defined as: 

1402  

1403  \[ 

1404  % \label{eq:sbc_wave_tauw} 

1405  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})} 

1406  \] 

1407  

1408  where: $c_p$ is the phase speed of the gravity waves, 

1409  $S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent 

1410  the physics of ocean waves. The first one, $S_{in}$, describes the generation 

1411  of ocean waves by wind and therefore represents the momentum and energy transfer 

1412  from air to ocean waves; the second term $S_{nl}$ denotes 

1413  the nonlinear transfer by resonant fourwave interactions; while the third term $S_{diss}$ 

1414  describes the dissipation of waves by processes such as whitecapping, large scale breaking 

1415  eddyinduced damping. 

1416  

1417  The wave stress derived from an external wave model can be provided either through the normalized 

1418  wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and 

1419  meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}. 

1420  

1421  

1422  % ================================================================ 

1423  % Miscellanea options 

1424  % ================================================================ 

1425  \section{Miscellaneous options} 

1426  \label{sec:SBC_misc} 

1427  

1428  %  

1429  % Diurnal cycle 

1430  %  

1431  \subsection{Diurnal cycle (\protect\mdl{sbcdcy})} 

1432  \label{subsec:SBC_dcy} 

1433  %namsbc_rnf 

1434  % 

1435  \nlst{namsbc} 

1436  % 

1437  

1438  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1439  \begin{figure}[!t] 

1440  \begin{center} 

1441  \includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal} 

1442  \caption{ 

1443  \protect\label{fig:SBC_diurnal} 

1444  Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values. 

1445  The reconstructed diurnal cycle (black line) is chosen as 

1446  the mean value of the analytical cycle (blue line) over a time step, 

1447  not as the mid time step value of the analytically cycle (red square). 

1448  From \citet{Bernie_al_CD07}. 

1449  } 

1450  \end{center} 

1451  \end{figure} 

1452  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1453  

1454  \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. 

1455  Unfortunately high frequency forcing fields are rare, not to say inexistent. 

1456  Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at 

1457  high frequency \citep{Bernie_al_CD07}. 

1458  Furthermore, only the knowledge of daily mean value of SWF is needed, 

1459  as higher frequency variations can be reconstructed from them, 

1460  assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF. 

1461  The \cite{Bernie_al_CD07} reconstruction algorithm is available in \NEMO by 

1462  setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when 

1463  using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or 

1464  the flux formulation (\np{ln\_flx}\forcode{ = .true.}). 

1465  The reconstruction is performed in the \mdl{sbcdcy} module. 

1466  The detail of the algoritm used can be found in the appendix~A of \cite{Bernie_al_CD07}. 

1467  The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at 

1468  a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}). 

1469  The use of diurnal cycle reconstruction requires the input SWF to be daily 

1470  (\ie a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter). 

1471  Furthermore, it is recommended to have a least 8 surface module time step per day, 

1472  that is $\rdt \ nn\_fsbc < 10,800~s = 3~h$. 

1473  An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle, 

1474  one every 2~hours (from 1am to 11pm). 

1475  

1476  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1477  \begin{figure}[!t] 

1478  \begin{center} 

1479  \includegraphics[width=0.7\textwidth]{Fig_SBC_dcy} 

1480  \caption{ 

1481  \protect\label{fig:SBC_dcy} 

1482  Example of recontruction of the diurnal cycle variation of short wave flux from 

1483  daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm). 

1484  The display is on (i,j) plane. 

1485  } 

1486  \end{center} 

1487  \end{figure} 

1488  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1489  

1490  Note also that the setting a diurnal cycle in SWF is highly recommended when 

1491  the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to 

1492  an inconsistency between the scale of the vertical resolution and the forcing acting on that scale. 

1493  

1494  %  

1495  % Rotation of vector pairs onto the model grid directions 

1496  %  

1497  \subsection{Rotation of vector pairs onto the model grid directions} 

1498  \label{subsec:SBC_rotation} 

1499  

1500  When using a flux (\np{ln\_flx}\forcode{ = .true.}) or 

1501  bulk (\np{ln\_clio}\forcode{ = .true.} or \np{ln\_core}\forcode{ = .true.}) formulation, 

1502  pairs of vector components can be rotated from eastnorth directions onto the local grid directions. 

1503  This is particularly useful when interpolation on the fly is used since here any vectors are likely to 

1504  be defined relative to a rectilinear grid. 

1505  To activate this option a nonempty string is supplied in the rotation pair column of the relevant namelist. 

1506  The eastward component must start with "U" and the northward component with "V". 

1507  The remaining characters in the strings are used to identify which pair of components go together. 

1508  So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and 

1509  rotate them on to the model grid directions; 

1510  "U2" and "V2" could be used against a second pair of components, and so on. 

1511  The extra characters used in the strings are arbitrary. 

1512  The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation. 

1513  

1514  %  

1515  % Surface restoring to observed SST and/or SSS 

1516  %  

1517  \subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 

1518  \label{subsec:SBC_ssr} 

1519  %namsbc_ssr 

1520  

1521  \nlst{namsbc_ssr} 

1522  % 

1523  

1524  IOptions are defined through the \ngn{namsbc\_ssr} namelist variables. 

1525  On forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}), 

1526  a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$: 

1527  \[ 

1528  % \label{eq:sbc_dmp_q} 

1529  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right_{k=1}  SST_{Obs} \right) 

1530  \] 

1531  where SST is a sea surface temperature field (observed or climatological), 

1532  $T$ is the model surface layer temperature and 

1533  $\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $40~W/m^2/K$. 

1534  For a $50~m$ mixedlayer depth, this value corresponds to a relaxation time scale of two months. 

1535  This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$. 

1536  

1537  In the fresh water budget, a feedback term can also be added. 

1538  Converted into an equivalent freshwater flux, it takes the following expression : 

1539  

1540  \begin{equation} 

1541  \label{eq:sbc_dmp_emp} 

1542  \textit{emp} = \textit{emp}_o + \gamma_s^{1} e_{3t} \frac{ \left(\left.S\right_{k=1}SSS_{Obs}\right)} 

1543  {\left.S\right_{k=1}} 

1544  \end{equation} 

1545  

1546  where $\textit{emp}_{o }$ is a net surface fresh water flux 

1547  (observed, climatological or an atmospheric model product), 

1548  \textit{SSS}$_{Obs}$ is a sea surface salinity 

1549  (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}), 

1550  $\left.S\right_{k=1}$ is the model surface layer salinity and 

1551  $\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter. 

1552  Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as 

1553  the atmosphere does not care about ocean surface salinity \citep{Madec1997}. 

1554  The SSS restoring term should be viewed as a flux correction on freshwater fluxes to 

1555  reduce the uncertainties we have on the observed freshwater budget. 

1556  

1557  %  

1558  % Handling of icecovered area 

1559  %  

1560  \subsection{Handling of icecovered area (\textit{sbcice\_...})} 

1561  \label{subsec:SBC_icecover} 

1562  

1563  The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean. 

1564  There are several way to handle seaice in the system depending on 

1565  the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist. 

1566  \begin{description} 

1567  \item[nn{\_}ice = 0] 

1568  there will never be seaice in the computational domain. 

1569  This is a typical namelist value used for tropical ocean domain. 

1570  The surface fluxes are simply specified for an icefree ocean. 

1571  No specific things is done for seaice. 

1572  \item[nn{\_}ice = 1] 

1573  seaice can exist in the computational domain, but no seaice model is used. 

1574  An observed ice covered area is read in a file. 

1575  Below this area, the SST is restored to the freezing point and 

1576  the heat fluxes are set to $4~W/m^2$ ($2~W/m^2$) in the northern (southern) hemisphere. 

1577  The associated modification of the freshwater fluxes are done in such a way that 

1578  the change in buoyancy fluxes remains zero. 

1579  This prevents deep convection to occur when trying to reach the freezing point 

1580  (and so ice covered area condition) while the SSS is too large. 

1581  This manner of managing seaice area, just by using si IF case, 

1582  is usually referred as the \textit{iceif} model. 

1583  It can be found in the \mdl{sbcice{\_}if} module. 

1584  \item[nn{\_}ice = 2 or more] 

1585  A full sea ice model is used. 

1586  This model computes the iceocean fluxes, 

1587  that are combined with the airsea fluxes using the ice fraction of each model cell to 

1588  provide the surface ocean fluxes. 

1589  Note that the activation of a seaice model is is done by defining a CPP key (\key{lim3} or \key{cice}). 

1590  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value 

1591  (\ie $2$ for LIM3 or $3$ for CICE). 

1592  \end{description} 

1593  

1594  % {Description of Iceocean interface to be added here or in LIM 2 and 3 doc ?} 

1595  

1596  \subsection{Interface to CICE (\protect\mdl{sbcice\_cice})} 

1597  \label{subsec:SBC_cice} 

1598  

1599  It is now possible to couple a regional or global NEMO configuration (without AGRIF) 

1600  to the CICE seaice model by using \key{cice}. 

1601  The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and 

1602  the additional 'hadgem3' drivers will be required, even with the latest code release. 

1603  Input grid files consistent with those used in NEMO will also be needed, 

1604  and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used 

1605  (seek advice from UKMO if necessary). 

1606  Currently the code is only designed to work when using the CORE forcing option for NEMO 

1607  (with \textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE namelist), 

1608  or alternatively when NEMO is coupled to the HadGAM3 atmosphere model 

1609  (with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}). 

1610  The code is intended to be used with \np{nn\_fsbc} set to 1 

1611  (although coupling ocean and ice less frequently should work, 

1612  it is possible the calculation of some of the oceanice fluxes needs to be modified slightly  

1613  the user should check that results are not significantly different to the standard case). 

1614  

1615  There are two options for the technical coupling between NEMO and CICE. 

1616  The standard version allows complete flexibility for the domain decompositions in the individual models, 

1617  but this is at the expense of global gather and scatter operations in the coupling which 

1618  become very expensive on larger numbers of processors. 

1619  The alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that 

1620  the domain decomposition is identical in both models (provided domain parameters are set appropriately, 

1621  and \textit{processor\_shape~=~squareice} and \textit{distribution\_wght~=~block} in the CICE namelist) and 

1622  allows much more efficient direct coupling on individual processors. 

1623  This solution scales much better although it is at the expense of having more idle CICE processors in areas where 

1624  there is no sea ice. 

1625  

1626  %  

1627  % Freshwater budget control 

1628  %  

1629  \subsection{Freshwater budget control (\protect\mdl{sbcfwb})} 

1630  \label{subsec:SBC_fwb} 

1631  

1632  For global ocean simulation it can be useful to introduce a control of the mean sea level in order to 

1633  prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes. 

1634  In \NEMO, two way of controlling the the freshwater budget. 

1635  \begin{description} 

1636  \item[\np{nn\_fwb}\forcode{ = 0}] 

1637  no control at all. 

1638  The mean sea level is free to drift, and will certainly do so. 

1639  \item[\np{nn\_fwb}\forcode{ = 1}] 

1640  global mean \textit{emp} set to zero at each model time step. 

1641  %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). 

1642  \item[\np{nn\_fwb}\forcode{ = 2}] 

1643  freshwater budget is adjusted from the previous year annual mean budget which 

1644  is read in the \textit{EMPave\_old.dat} file. 

1645  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from 

1646  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file. 

1647  \end{description} 

1648  

1649  

1650  

1651  % Griffies doc: 

1652  % When running oceanice simulations, we are not explicitly representing land processes, 

1653  % such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, 

1654  % it is important to balance the hydrological cycle in oceanice models. 

1655  % We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. 

1656  % The result of the normalization should be a global integrated zero net water input to the oceanice system over 

1657  % a chosen time scale. 

1658  %How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, 

1659  % so that there is always a zero net input of water to the oceanice system. 

1660  % Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used 

1661  % to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. 

1662  % Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing. 

1663  % When running oceanice coupled models, it is incorrect to include the water transport between the ocean 

1664  % and ice models when aiming to balance the hydrological cycle. 

1665  % The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running oceanice models, 

1666  % not the water in any one subcomponent. As an extreme example to illustrate the issue, 

1667  % consider an oceanice model with zero initial sea ice. As the oceanice model spins up, 

1668  % there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. 

1669  % The total water contained in the ocean plus ice system is constant, but there is an exchange of water between 

1670  % the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle 

1671  % in oceanice models. 

1672  

1673  \biblio 

1674  

1675  \pindex 

1676  

1677  \end{document} 
