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_rpt04}. 

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_rpt04} 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.barnier.ea_OM10}. 

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.deleersnijder.ea_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 \forcode{.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 {\mathrm {\mathbf U}}_h }{\partial t}= ... 

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

823  \] 

824  where $\Pi_{eq}$ stands for the equilibrium tidal forcing and 

825  $\Pi_{sal}$ is a selfattraction and loading term (SAL). 

826  

827  The equilibrium tidal forcing is expressed as a sum over a subset of 

828  constituents chosen from the set of available tidal constituents 

829  defined in file \rou{SBC/tide.h90} (this comprises the tidal 

830  constituents \textit{M2, N2, 2N2, S2, K2, K1, O1, Q1, P1, M4, Mf, Mm, 

831  Msqm, Mtm, S1, MU2, NU2, L2}, and \textit{T2}). Individual 

832  constituents are selected by including their names in the array 

833  \np{clname} in \ngn{nam\_tide} (e.g., \np{clname(1) = 'M2', 

834  clname(2)='S2'} to select solely the tidal consituents \textit{M2} 

835  and \textit{S2}). Optionally, when \np{ln\_tide\_ramp} is set to 

836  \forcode{.true.}, the equilibrium tidal forcing can be ramped up 

837  linearly from zero during the initial \np{rdttideramp} days of the 

838  model run. 

839  

840  The SAL term should in principle be computed online as it depends on 

841  the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a 

842  discussion about the practical implementation of this term). 

843  Nevertheless, the complex calculations involved would make this 

844  computationally too expensive. Here, two options are available: 

845  $\Pi_{sal}$ generated by an external model can be read in 

846  (\np{ln\_read\_load=.true.}), or a ``scalar approximation'' can be 

847  used (\np{ln\_scal\_load=.true.}). In the latter case 

848  \[ 

849  \Pi_{sal} = \beta \eta, 

850  \] 

851  where $\beta$ (\np{rn\_scal\_load} with a default value of 0.094) is a 

852  spatially constant scalar, often chosen to minimize tidal prediction 

853  errors. Setting both \np{ln\_read\_load} and \np{ln\_scal\_load} to 

854  \forcode{.false.} removes the SAL contribution. 

855  

856  % ================================================================ 

857  % River runoffs 

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

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

860  \label{sec:SBC_rnf} 

861  %namsbc_rnf 

862  

863  \nlst{namsbc_rnf} 

864  % 

865  

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

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

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

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

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

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

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

873  %required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}. 

874  

875  

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

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

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

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

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

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

882  

883  

884  %Rachel: 

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

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

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

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

889  

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

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

892  \footnote{ 

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

894  properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. 

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

896  

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

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

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

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

901  

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

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

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

905  and/or taken as surface temperature respectively. 

906  

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

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

909  be the surface temperatue at the river point. 

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

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

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

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

914  After the user specified depth is read ini, 

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

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

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

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

919  

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

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

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

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

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

925  

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

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

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

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

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

931  

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

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

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

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

936  

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

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

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

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

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

942  

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

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

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

946  the heat and salt content of the river. 

947  

948  In the nonlinear free surface case (vvl), 

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

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

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

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

953  

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

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

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

957  regardless of the namelist options used, 

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

959  

960  

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

962  

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

964  

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

966  

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

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

969  %ENDIF 

970  

971  %\gmcomment{ word doc of runoffs: 

972  % 

973  %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. 

974  %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. 

975  

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

977  

978  %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: 

979  

980  %} 

981  % ================================================================ 

982  % Ice shelf melting 

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

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

985  \label{sec:SBC_isf} 

986  %namsbc_isf 

987  

988  \nlst{namsbc_isf} 

989  % 

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

991  Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}. 

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

993  

994  \begin{description} 

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

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

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

998  Two different bulk formulae are available: 

999  

1000  \begin{description} 

1001  \item[\np{nn\_isfblk}\forcode{ = 1}]: 

1002  The melt rate is based on a balance between the upward ocean heat flux and 

1003  the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}. 

1004  \item[\np{nn\_isfblk}\forcode{ = 2}]: 

1005  The melt rate and the heat flux are based on a 3 equations formulation 

1006  (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation). 

1007  A complete description is available in \citet{jenkins_JGR91}. 

1008  \end{description} 

1009  

1010  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}. 

1011  Its thickness is defined by \np{rn\_hisf\_tbl}. 

1012  The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m. 

1013  Then, the fluxes are spread over the same thickness (ie over one or several cells). 

1014  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. 

1015  This can lead to supercool temperature in the top cell under melting condition. 

1016  If \np{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\ 

1017  

1018  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice. 

1019  There are 3 different ways to compute the exchange coeficient: 

1020  \begin{description} 

1021  \item[\np{nn\_gammablk}\forcode{ = 0}]: 

1022  The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}. 

1023  \[ 

1024  % \label{eq:sbc_isf_gamma_iso} 

1025  \gamma^{T} = \np{rn\_gammat0} 

1026  \] 

1027  \[ 

1028  \gamma^{S} = \np{rn\_gammas0} 

1029  \] 

1030  This is the recommended formulation for ISOMIP. 

1031  \item[\np{nn\_gammablk}\forcode{ = 1}]: 

1032  The salt and heat exchange coefficients are velocity dependent and defined as 

1033  \[ 

1034  \gamma^{T} = \np{rn\_gammat0} \times u_{*} 

1035  \] 

1036  \[ 

1037  \gamma^{S} = \np{rn\_gammas0} \times u_{*} 

1038  \] 

1039  where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters). 

1040  See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application. 

1041  \item[\np{nn\_gammablk}\forcode{ = 2}]: 

1042  The salt and heat exchange coefficients are velocity and stability dependent and defined as: 

1043  \[ 

1044  \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}} 

1045  \] 

1046  where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters), 

1047  $\Gamma_{Turb}$ the contribution of the ocean stability and 

1048  $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 

1049  See \citet{holland.jenkins_JPO99} for all the details on this formulation. 

1050  This formulation has not been extensively tested in NEMO (not recommended). 

1051  \end{description} 

1052  \item[\np{nn\_isf}\forcode{ = 2}]: 

1053  The ice shelf cavity is not represented. 

1054  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting. 

1055  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL) 

1056  (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front 

1057  (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}\forcode{ = 3}). 

1058  The effective melting length (\np{sn\_Leff\_isf}) is read from a file. 

1059  \item[\np{nn\_isf}\forcode{ = 3}]: 

1060  The ice shelf cavity is not represented. 

1061  The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between 

1062  the depth of the average grounding line (GL) (\np{sn\_depmax\_isf}) and 

1063  the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}). 

1064  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 

1065  \item[\np{nn\_isf}\forcode{ = 4}]: 

1066  The ice shelf cavity is opened (\np{ln\_isfcav}\forcode{ = .true.} needed). 

1067  However, the fwf is not computed but specified from file \np{sn\_fwfisf}). 

1068  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 

1069  As in \np{nn\_isf}\forcode{ = 1}, the fluxes are spread over the top boundary layer thickness (\np{rn\_hisf\_tbl})\\ 

1070  \end{description} 

1071  

1072  $\bullet$ \np{nn\_isf}\forcode{ = 1} and \np{nn\_isf}\forcode{ = 2} compute a melt rate based on 

1073  the water mass properties, ocean velocities and depth. 

1074  This flux is thus highly dependent of the model resolution (horizontal and vertical), 

1075  realism of the water masses onto the shelf ...\\ 

1076  

1077  $\bullet$ \np{nn\_isf}\forcode{ = 3} and \np{nn\_isf}\forcode{ = 4} read the melt rate from a file. 

1078  You have total control of the fwf forcing. 

1079  This can be useful if the water masses on the shelf are not realistic or 

1080  the resolution (horizontal/vertical) are too coarse to have realistic melting or 

1081  for studies where you need to control your heat and fw input.\\ 

1082  

1083  The ice shelf melt is implemented as a volume flux as for the runoff. 

1084  The fw addition due to the ice shelf melting is, at each relevant depth level, added to 

1085  the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}. 

1086  See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\ 

1087  

1088  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1089  \begin{figure}[!t] 

1090  \begin{center} 

1091  \includegraphics[width=\textwidth]{Fig_SBC_isf} 

1092  \caption{ 

1093  \protect\label{fig:SBC_isf} 

1094  Illustration the location where the fwf is injected and whether or not the fwf is interactif or not depending of \np{nn\_isf}. 

1095  } 

1096  \end{center} 

1097  \end{figure} 

1098  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1099  

1100  \section{Ice sheet coupling} 

1101  \label{sec:SBC_iscpl} 

1102  %namsbc_iscpl 

1103  

1104  \nlst{namsbc_iscpl} 

1105  % 

1106  Ice sheet/ocean coupling is done through file exchange at the restart step. 

1107  At each restart step: 

1108  \begin{description} 

1109  \item[Step 1]: the ice sheet model send a new bathymetry and ice shelf draft netcdf file. 

1110  \item[Step 2]: a new domcfg.nc file is built using the DOMAINcfg tools. 

1111  \item[Step 3]: NEMO run for a specific period and output the average melt rate over the period. 

1112  \item[Step 4]: the ice sheet model run using the melt rate outputed in step 4. 

1113  \item[Step 5]: go back to 1. 

1114  \end{description} 

1115  

1116  If \np{ln\_iscpl}\forcode{ = .true.}, the isf draft is assume to be different at each restart step with 

1117  potentially some new wet/dry cells due to the ice sheet dynamics/thermodynamics. 

1118  The wetting and drying scheme applied on the restart is very simple and described below for the 6 different possible cases: 

1119  \begin{description} 

1120  \item[Thin a cell down]: 

1121  T/S/ssh are unchanged and U/V in the top cell are corrected to keep the barotropic transport (bt) constant 

1122  ($bt_b=bt_n$). 

1123  \item[Enlarge a cell]: 

1124  See case "Thin a cell down" 

1125  \item[Dry a cell]: 

1126  mask, T/S, U/V and ssh are set to 0. 

1127  Furthermore, U/V into the water column are modified to satisfy ($bt_b=bt_n$). 

1128  \item[Wet a cell]: 

1129  mask is set to 1, T/S is extrapolated from neighbours, $ssh_n = ssh_b$ and U/V set to 0. 

1130  If no neighbours, T/S is extrapolated from old top cell value. 

1131  If no neighbours along i,j and k (both previous test failed), T/S/U/V/ssh and mask are set to 0. 

1132  \item[Dry a column]: 

1133  mask, T/S, U/V are set to 0 everywhere in the column and ssh set to 0. 

1134  \item[Wet a column]: 

1135  set mask to 1, T/S is extrapolated from neighbours, ssh is extrapolated from neighbours and U/V set to 0. 

1136  If no neighbour, T/S/U/V and mask set to 0. 

1137  \end{description} 

1138  

1139  Furthermore, as the before and now fields are not compatible (modification of the geometry), 

1140  the restart time step is prescribed to be an euler time step instead of a leap frog and $fields_b = fields_n$.\\ 

1141  

1142  The horizontal extrapolation to fill new cell with realistic value is called \np{nn\_drown} times. 

1143  It means that if the grounding line retreat by more than \np{nn\_drown} cells between 2 coupling steps, 

1144  the code will be unable to fill all the new wet cells properly. 

1145  The default number is set up for the MISOMIP idealised experiments. 

1146  This coupling procedure is able to take into account grounding line and calving front migration. 

1147  However, it is a nonconservative processe. 

1148  This could lead to a trend in heat/salt content and volume.\\ 

1149  

1150  In order to remove the trend and keep the conservation level as close to 0 as possible, 

1151  a simple conservation scheme is available with \np{ln\_hsb}\forcode{ = .true.}. 

1152  The heat/salt/vol. gain/loss is diagnosed, as well as the location. 

1153  A correction increment is computed and apply each time step during the next \np{rn\_fiscpl} time steps. 

1154  For safety, it is advised to set \np{rn\_fiscpl} equal to the coupling period (smallest increment possible). 

1155  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). 

1156  

1157  % 

1158  % ================================================================ 

1159  % Handling of icebergs 

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

1161  \section{Handling of icebergs (ICB)} 

1162  \label{sec:ICB_icebergs} 

1163  %namberg 

1164  

1165  \nlst{namberg} 

1166  % 

1167  

1168  Icebergs are modelled as lagrangian particles in NEMO \citep{marsh.ivchenko.ea_GMD15}. 

1169  Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ). 

1170  (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 

1171  Icebergs are initially spawned into one of ten classes which have specific mass and thickness as 

1172  described in the \ngn{namberg} namelist: \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}. 

1173  Each class has an associated scaling (\np{rn\_mass\_scaling}), 

1174  which is an integer representing how many icebergs of this class are being described as one lagrangian point 

1175  (this reduces the numerical problem of tracking every single iceberg). 

1176  They are enabled by setting \np{ln\_icebergs}\forcode{ = .true.}. 

1177  

1178  Two initialisation schemes are possible. 

1179  \begin{description} 

1180  \item[\np{nn\_test\_icebergs}~$>$~0] 

1181  In this scheme, the value of \np{nn\_test\_icebergs} represents the class of iceberg to generate 

1182  (so between 1 and 10), and \np{nn\_test\_icebergs} provides a lon/lat box in the domain at each grid point of 

1183  which an iceberg is generated at the beginning of the run. 

1184  (Note that this happens each time the timestep equals \np{nn\_nit000}.) 

1185  \np{nn\_test\_icebergs} is defined by four numbers in \np{nn\_test\_box} representing the corners of 

1186  the geographical box: lonmin,lonmax,latmin,latmax 

1187  \item[\np{nn\_test\_icebergs}\forcode{ = 1}] 

1188  In this scheme the model reads a calving file supplied in the \np{sn\_icb} parameter. 

1189  This should be a file with a field on the configuration grid (typically ORCA) 

1190  representing ice accumulation rate at each model point. 

1191  These should be ocean points adjacent to land where icebergs are known to calve. 

1192  Most points in this input grid are going to have value zero. 

1193  When the model runs, ice is accumulated at each grid point which has a nonzero source term. 

1194  At each time step, a test is performed to see if there is enough ice mass to 

1195  calve an iceberg of each class in order (1 to 10). 

1196  Note that this is the initial mass multiplied by the number each particle represents (\ie the scaling). 

1197  If there is enough ice, a new iceberg is spawned and the total available ice reduced accordingly. 

1198  \end{description} 

1199  

1200  Icebergs are influenced by wind, waves and currents, bottom melt and erosion. 

1201  The latter act to disintegrate the iceberg. 

1202  This is either all melted freshwater, 

1203  or (if \np{rn\_bits\_erosion\_fraction}~$>$~0) into melt and additionally small ice bits 

1204  which are assumed to propagate with their larger parent and thus delay fluxing into the ocean. 

1205  Melt water (and other variables on the configuration grid) are written into the main NEMO model output files. 

1206  

1207  Extensive diagnostics can be produced. 

1208  Separate output files are maintained for humanreadable iceberg information. 

1209  A separate file is produced for each processor (independent of \np{ln\_ctl}). 

1210  The amount of information is controlled by two integer parameters: 

1211  \begin{description} 

1212  \item[\np{nn\_verbose\_level}] takes a value between one and four and 

1213  represents an increasing number of points in the code at which variables are written, 

1214  and an increasing level of obscurity. 

1215  \item[\np{nn\_verbose\_write}] is the number of timesteps between writes 

1216  \end{description} 

1217  

1218  Iceberg trajectories can also be written out and this is enabled by setting \np{nn\_sample\_rate}~$>$~0. 

1219  A nonzero value represents how many timesteps between writes of information into the output file. 

1220  These output files are in NETCDF format. 

1221  When \key{mpp\_mpi} is defined, each output file contains only those icebergs in the corresponding processor. 

1222  Trajectory points are written out in the order of their parent iceberg in the model's "linked list" of icebergs. 

1223  So care is needed to recreate data for individual icebergs, 

1224  since its trajectory data may be spread across multiple files. 

1225  

1226  %  

1227  % Interactions with waves (sbcwave.F90, ln_wave) 

1228  %  

1229  \section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 

1230  \label{sec:SBC_wave} 

1231  %namsbc_wave 

1232  

1233  \nlst{namsbc_wave} 

1234  % 

1235  

1236  Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate 

1237  physical processes related to ocean surface waves, namely the surface stress modified by growth and 

1238  dissipation of the oceanic wave field, the StokesCoriolis force and the Stokes drift impact on mass and 

1239  tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate 

1240  the wind stress. 

1241  

1242  Physical processes related to ocean surface waves can be accounted by setting the logical variable 

1243  \np{ln\_wave}\forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for 

1244  different porcesses should be activated as explained in the following sections. 

1245  

1246  Wave fields can be provided either in forced or coupled mode: 

1247  \begin{description} 

1248  \item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist 

1249  for external data names, locations, frequency, interpolation and all the miscellanous options allowed by 

1250  Input Data generic Interface (see \autoref{sec:SBC_input}). 

1251  \item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 

1252  in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist. 

1253  \end{description} 

1254  

1255  

1256  % ================================================================ 

1257  % Neutral drag coefficient from wave model (ln_cdgw)


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

1259  \subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 

1260  \label{subsec:SBC_wave_cdgw} 

1261  

1262  The neutral surface drag coefficient provided from an external data source (\ie a wave model), 

1263  can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist. 

1264  Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided, 

1265  the drag coefficient is computed according to the stable/unstable conditions of the 

1266  airsea interface following \citet{large.yeager_rpt04}. 

1267  

1268  

1269  % ================================================================ 

1270  % 3D Stokes Drift (ln_sdw, nn_sdrift) 

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

1272  \subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 

1273  \label{subsec:SBC_wave_sdw} 

1274  

1275  The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}. 

1276  It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity) 

1277  and the current measured at a fixed point (Eulerian velocity). 

1278  As waves travel, the water particles that make up the waves travel in orbital motions but 

1279  without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly 

1280  at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift. 

1281  An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved 

1282  representation of surface physics in ocean general circulation models. 

1283  The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as: 

1284  

1285  \[ 

1286  % \label{eq:sbc_wave_sdw} 

1287  \mathbf{U}_{st} = \frac{16{\pi^3}} {g} 

1288  \int_0^\infty \int_{\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3} 

1289  \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f 

1290  \] 

1291  

1292  where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency, 

1293  $\mathrm{S}($f$,\theta)$ is the 2D frequencydirection spectrum, 

1294  $k$ is the mean wavenumber defined as: 

1295  $k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\ 

1296  

1297  In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required 

1298  and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level. 

1299  To simplify, it is customary to use approximations to the full Stokes profile. 

1300  Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile 

1301  are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift 

1302  $\mathbf{U}_{st _{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra 

1303  and makes possible the estimation of the surface Stokes drift for random directional waves in 

1304  realistic wave conditions: 

1305  

1306  \begin{description} 

1307  \item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by 

1308  \citet{breivik.janssen.ea_JPO14}: 

1309  

1310  \[ 

1311  % \label{eq:sbc_wave_sdw_0a} 

1312  \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \frac{\mathrm{e}^{2k_ez}} {18k_ez} 

1313  \] 

1314  

1315  where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows: 

1316  

1317  \[ 

1318  % \label{eq:sbc_wave_sdw_0b} 

1319  k_e = \frac{\mathbf{U}_{\left.st\right_{z=0}}} {T_{st}} 

1320  \quad \text{and }\ 

1321  T_{st} = \frac{1}{16} \bar{\omega} H_s^2 

1322  \] 

1323  

1324  where $H_s$ is the significant wave height and $\omega$ is the wave frequency. 

1325  

1326  \item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a 

1327  reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface 

1328  \citep{breivik.bidlot.ea_OM16}: 

1329  

1330  \[ 

1331  % \label{eq:sbc_wave_sdw_1} 

1332  \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \Big[exp(2k_pz)\beta \sqrt{2 \pi k_pz} 

1333  \textit{ erf } \Big(\sqrt{2 k_pz}\Big)\Big] 

1334  \] 

1335  

1336  where $erf$ is the complementary error function and $k_p$ is the peak wavenumber. 

1337  

1338  \item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1 

1339  but using the wave frequency from a wave model. 

1340  

1341  \end{description} 

1342  

1343  The Stokes drift enters the waveaveraged momentum equation, as well as the tracer advection equations 

1344  and its effect on the evolution of the seasurface height ${\eta}$ is considered as follows: 

1345  

1346  \[ 

1347  % \label{eq:sbc_wave_eta_sdw} 

1348  \frac{\partial{\eta}}{\partial{t}} = 

1349  \nabla_h \int_{H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz 

1350  \] 

1351  

1352  The tracer advection equation is also modified in order for Eulerian ocean models to properly account 

1353  for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection 

1354  that is induced by the threedimensional Stokes velocity. 

1355  The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves 

1356  can be formulated as follows: 

1357  

1358  \[ 

1359  % \label{eq:sbc_wave_tra_sdw} 

1360  \frac{\partial{c}}{\partial{t}} = 

1361   (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c} 

1362  \] 

1363  

1364  

1365  % ================================================================ 

1366  % StokesCoriolis term (ln_stcor) 

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

1368  \subsection{StokesCoriolis term (\protect\np{ln\_stcor})} 

1369  \label{subsec:SBC_wave_stcor} 

1370  

1371  In a rotating ocean, waves exert a waveinduced stress on the mean ocean circulation which results 

1372  in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter. 

1373  This additional force may have impact on the Ekman turning of the surface current. 

1374  In order to include this term, once evaluated the Stokes drift (using one of the 3 possible 

1375  approximations described in \autoref{subsec:SBC_wave_sdw}), 

1376  \np{ln\_stcor}\forcode{ = .true.} has to be set. 

1377  

1378  

1379  % ================================================================ 

1380  % Waves modified stress (ln_tauwoc, ln_tauw) 

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

1382  \subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 

1383  \label{subsec:SBC_wave_tauw} 

1384  

1385  The surface stress felt by the ocean is the atmospheric stress minus the net stress going 

1386  into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not 

1387  available for forcing the mean circulation, while in the opposite case of a decaying sea 

1388  state more momentum is available for forcing the ocean. 

1389  Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress, 

1390  but in practice an equilibrium sea state is a fairly rare event. 

1391  So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as: 

1392  

1393  \[ 

1394  % \label{eq:sbc_wave_tauoc} 

1395  \tau_{oc,a} = \tau_a  \tau_w 

1396  \] 

1397  

1398  where $\tau_a$ is the atmospheric surface stress; 

1399  $\tau_w$ is the atmospheric stress going into the waves defined as: 

1400  

1401  \[ 

1402  % \label{eq:sbc_wave_tauw} 

1403  \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})} 

1404  \] 

1405  

1406  where: $c_p$ is the phase speed of the gravity waves, 

1407  $S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent 

1408  the physics of ocean waves. The first one, $S_{in}$, describes the generation 

1409  of ocean waves by wind and therefore represents the momentum and energy transfer 

1410  from air to ocean waves; the second term $S_{nl}$ denotes 

1411  the nonlinear transfer by resonant fourwave interactions; while the third term $S_{diss}$ 

1412  describes the dissipation of waves by processes such as whitecapping, large scale breaking 

1413  eddyinduced damping. 

1414  

1415  The wave stress derived from an external wave model can be provided either through the normalized 

1416  wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and 

1417  meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}. 

1418  

1419  

1420  % ================================================================ 

1421  % Miscellanea options 

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

1423  \section{Miscellaneous options} 

1424  \label{sec:SBC_misc} 

1425  

1426  %  

1427  % Diurnal cycle 

1428  %  

1429  \subsection{Diurnal cycle (\protect\mdl{sbcdcy})} 

1430  \label{subsec:SBC_dcy} 

1431  %namsbc_rnf 

1432  % 

1433  \nlst{namsbc} 

1434  % 

1435  

1436  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1437  \begin{figure}[!t] 

1438  \begin{center} 

1439  \includegraphics[width=\textwidth]{Fig_SBC_diurnal} 

1440  \caption{ 

1441  \protect\label{fig:SBC_diurnal} 

1442  Example of recontruction of the diurnal cycle variation of short wave flux from daily mean values. 

1443  The reconstructed diurnal cycle (black line) is chosen as 

1444  the mean value of the analytical cycle (blue line) over a time step, 

1445  not as the mid time step value of the analytically cycle (red square). 

1446  From \citet{bernie.guilyardi.ea_CD07}. 

1447  } 

1448  \end{center} 

1449  \end{figure} 

1450  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1451  

1452  \cite{bernie.woolnough.ea_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less. 

1453  Unfortunately high frequency forcing fields are rare, not to say inexistent. 

1454  Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at 

1455  high frequency \citep{bernie.guilyardi.ea_CD07}. 

1456  Furthermore, only the knowledge of daily mean value of SWF is needed, 

1457  as higher frequency variations can be reconstructed from them, 

1458  assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF. 

1459  The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO by 

1460  setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when 

1461  using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or 

1462  the flux formulation (\np{ln\_flx}\forcode{ = .true.}). 

1463  The reconstruction is performed in the \mdl{sbcdcy} module. 

1464  The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}. 

1465  The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at 

1466  a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}). 

1467  The use of diurnal cycle reconstruction requires the input SWF to be daily 

1468  (\ie a frequency of 24 and a time interpolation set to true in \np{sn\_qsr} namelist parameter). 

1469  Furthermore, it is recommended to have a least 8 surface module time step per day, 

1470  that is $\rdt \ nn\_fsbc < 10,800~s = 3~h$. 

1471  An example of recontructed SWF is given in \autoref{fig:SBC_dcy} for a 12 reconstructed diurnal cycle, 

1472  one every 2~hours (from 1am to 11pm). 

1473  

1474  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1475  \begin{figure}[!t] 

1476  \begin{center} 

1477  \includegraphics[width=\textwidth]{Fig_SBC_dcy} 

1478  \caption{ 

1479  \protect\label{fig:SBC_dcy} 

1480  Example of recontruction of the diurnal cycle variation of short wave flux from 

1481  daily mean values on an ORCA2 grid with a time sampling of 2~hours (from 1am to 11pm). 

1482  The display is on (i,j) plane. 

1483  } 

1484  \end{center} 

1485  \end{figure} 

1486  %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 

1487  

1488  Note also that the setting a diurnal cycle in SWF is highly recommended when 

1489  the top layer thickness approach 1~m or less, otherwise large error in SST can appear due to 

1490  an inconsistency between the scale of the vertical resolution and the forcing acting on that scale. 

1491  

1492  %  

1493  % Rotation of vector pairs onto the model grid directions 

1494  %  

1495  \subsection{Rotation of vector pairs onto the model grid directions} 

1496  \label{subsec:SBC_rotation} 

1497  

1498  When using a flux (\np{ln\_flx}\forcode{ = .true.}) or 

1499  bulk (\np{ln\_clio}\forcode{ = .true.} or \np{ln\_core}\forcode{ = .true.}) formulation, 

1500  pairs of vector components can be rotated from eastnorth directions onto the local grid directions. 

1501  This is particularly useful when interpolation on the fly is used since here any vectors are likely to 

1502  be defined relative to a rectilinear grid. 

1503  To activate this option a nonempty string is supplied in the rotation pair column of the relevant namelist. 

1504  The eastward component must start with "U" and the northward component with "V". 

1505  The remaining characters in the strings are used to identify which pair of components go together. 

1506  So for example, strings "U1" and "V1" next to "utau" and "vtau" would pair the wind stress components together and 

1507  rotate them on to the model grid directions; 

1508  "U2" and "V2" could be used against a second pair of components, and so on. 

1509  The extra characters used in the strings are arbitrary. 

1510  The rot\_rep routine from the \mdl{geo2ocean} module is used to perform the rotation. 

1511  

1512  %  

1513  % Surface restoring to observed SST and/or SSS 

1514  %  

1515  \subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 

1516  \label{subsec:SBC_ssr} 

1517  %namsbc_ssr 

1518  

1519  \nlst{namsbc_ssr} 

1520  % 

1521  

1522  IOptions are defined through the \ngn{namsbc\_ssr} namelist variables. 

1523  On forced mode using a flux formulation (\np{ln\_flx}\forcode{ = .true.}), 

1524  a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$: 

1525  \[ 

1526  % \label{eq:sbc_dmp_q} 

1527  Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right_{k=1}  SST_{Obs} \right) 

1528  \] 

1529  where SST is a sea surface temperature field (observed or climatological), 

1530  $T$ is the model surface layer temperature and 

1531  $\frac{dQ}{dT}$ is a negative feedback coefficient usually taken equal to $40~W/m^2/K$. 

1532  For a $50~m$ mixedlayer depth, this value corresponds to a relaxation time scale of two months. 

1533  This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is equal to $Q_o$. 

1534  

1535  In the fresh water budget, a feedback term can also be added. 

1536  Converted into an equivalent freshwater flux, it takes the following expression : 

1537  

1538  \begin{equation} 

1539  \label{eq:sbc_dmp_emp} 

1540  \textit{emp} = \textit{emp}_o + \gamma_s^{1} e_{3t} \frac{ \left(\left.S\right_{k=1}SSS_{Obs}\right)} 

1541  {\left.S\right_{k=1}} 

1542  \end{equation} 

1543  

1544  where $\textit{emp}_{o }$ is a net surface fresh water flux 

1545  (observed, climatological or an atmospheric model product), 

1546  \textit{SSS}$_{Obs}$ is a sea surface salinity 

1547  (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}), 

1548  $\left.S\right_{k=1}$ is the model surface layer salinity and 

1549  $\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter. 

1550  Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as 

1551  the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}. 

1552  The SSS restoring term should be viewed as a flux correction on freshwater fluxes to 

1553  reduce the uncertainties we have on the observed freshwater budget. 

1554  

1555  %  

1556  % Handling of icecovered area 

1557  %  

1558  \subsection{Handling of icecovered area (\textit{sbcice\_...})} 

1559  \label{subsec:SBC_icecover} 

1560  

1561  The presence at the sea surface of an ice covered area modifies all the fluxes transmitted to the ocean. 

1562  There are several way to handle seaice in the system depending on 

1563  the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist. 

1564  \begin{description} 

1565  \item[nn{\_}ice = 0] 

1566  there will never be seaice in the computational domain. 

1567  This is a typical namelist value used for tropical ocean domain. 

1568  The surface fluxes are simply specified for an icefree ocean. 

1569  No specific things is done for seaice. 

1570  \item[nn{\_}ice = 1] 

1571  seaice can exist in the computational domain, but no seaice model is used. 

1572  An observed ice covered area is read in a file. 

1573  Below this area, the SST is restored to the freezing point and 

1574  the heat fluxes are set to $4~W/m^2$ ($2~W/m^2$) in the northern (southern) hemisphere. 

1575  The associated modification of the freshwater fluxes are done in such a way that 

1576  the change in buoyancy fluxes remains zero. 

1577  This prevents deep convection to occur when trying to reach the freezing point 

1578  (and so ice covered area condition) while the SSS is too large. 

1579  This manner of managing seaice area, just by using si IF case, 

1580  is usually referred as the \textit{iceif} model. 

1581  It can be found in the \mdl{sbcice{\_}if} module. 

1582  \item[nn{\_}ice = 2 or more] 

1583  A full sea ice model is used. 

1584  This model computes the iceocean fluxes, 

1585  that are combined with the airsea fluxes using the ice fraction of each model cell to 

1586  provide the surface ocean fluxes. 

1587  Note that the activation of a seaice model is is done by defining a CPP key (\key{lim3} or \key{cice}). 

1588  The activation automatically overwrites the read value of nn{\_}ice to its appropriate value 

1589  (\ie $2$ for LIM3 or $3$ for CICE). 

1590  \end{description} 

1591  

1592  % {Description of Iceocean interface to be added here or in LIM 2 and 3 doc ?} 

1593  

1594  \subsection{Interface to CICE (\protect\mdl{sbcice\_cice})} 

1595  \label{subsec:SBC_cice} 

1596  

1597  It is now possible to couple a regional or global NEMO configuration (without AGRIF) 

1598  to the CICE seaice model by using \key{cice}. 

1599  The CICE code can be obtained from \href{http://oceans11.lanl.gov/trac/CICE/}{LANL} and 

1600  the additional 'hadgem3' drivers will be required, even with the latest code release. 

1601  Input grid files consistent with those used in NEMO will also be needed, 

1602  and CICE CPP keys \textbf{ORCA\_GRID}, \textbf{CICE\_IN\_NEMO} and \textbf{coupled} should be used 

1603  (seek advice from UKMO if necessary). 

1604  Currently the code is only designed to work when using the CORE forcing option for NEMO 

1605  (with \textit{calc\_strair}\forcode{ = .true.} and \textit{calc\_Tsfc}\forcode{ = .true.} in the CICE namelist), 

1606  or alternatively when NEMO is coupled to the HadGAM3 atmosphere model 

1607  (with \textit{calc\_strair}\forcode{ = .false.} and \textit{calc\_Tsfc}\forcode{ = false}). 

1608  The code is intended to be used with \np{nn\_fsbc} set to 1 

1609  (although coupling ocean and ice less frequently should work, 

1610  it is possible the calculation of some of the oceanice fluxes needs to be modified slightly  

1611  the user should check that results are not significantly different to the standard case). 

1612  

1613  There are two options for the technical coupling between NEMO and CICE. 

1614  The standard version allows complete flexibility for the domain decompositions in the individual models, 

1615  but this is at the expense of global gather and scatter operations in the coupling which 

1616  become very expensive on larger numbers of processors. 

1617  The alternative option (using \key{nemocice\_decomp} for both NEMO and CICE) ensures that 

1618  the domain decomposition is identical in both models (provided domain parameters are set appropriately, 

1619  and \textit{processor\_shape~=~squareice} and \textit{distribution\_wght~=~block} in the CICE namelist) and 

1620  allows much more efficient direct coupling on individual processors. 

1621  This solution scales much better although it is at the expense of having more idle CICE processors in areas where 

1622  there is no sea ice. 

1623  

1624  %  

1625  % Freshwater budget control 

1626  %  

1627  \subsection{Freshwater budget control (\protect\mdl{sbcfwb})} 

1628  \label{subsec:SBC_fwb} 

1629  

1630  For global ocean simulation it can be useful to introduce a control of the mean sea level in order to 

1631  prevent unrealistic drift of the sea surface height due to inaccuracy in the freshwater fluxes. 

1632  In \NEMO, two way of controlling the the freshwater budget. 

1633  \begin{description} 

1634  \item[\np{nn\_fwb}\forcode{ = 0}] 

1635  no control at all. 

1636  The mean sea level is free to drift, and will certainly do so. 

1637  \item[\np{nn\_fwb}\forcode{ = 1}] 

1638  global mean \textit{emp} set to zero at each model time step. 

1639  %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). 

1640  \item[\np{nn\_fwb}\forcode{ = 2}] 

1641  freshwater budget is adjusted from the previous year annual mean budget which 

1642  is read in the \textit{EMPave\_old.dat} file. 

1643  As the model uses the Boussinesq approximation, the annual mean fresh water budget is simply evaluated from 

1644  the change in the mean sea level at January the first and saved in the \textit{EMPav.dat} file. 

1645  \end{description} 

1646  

1647  

1648  

1649  % Griffies doc: 

1650  % When running oceanice simulations, we are not explicitly representing land processes, 

1651  % such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, 

1652  % it is important to balance the hydrological cycle in oceanice models. 

1653  % We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. 

1654  % The result of the normalization should be a global integrated zero net water input to the oceanice system over 

1655  % a chosen time scale. 

1656  %How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, 

1657  % so that there is always a zero net input of water to the oceanice system. 

1658  % Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used 

1659  % to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. 

1660  % Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing. 

1661  % When running oceanice coupled models, it is incorrect to include the water transport between the ocean 

1662  % and ice models when aiming to balance the hydrological cycle. 

1663  % The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running oceanice models, 

1664  % not the water in any one subcomponent. As an extreme example to illustrate the issue, 

1665  % consider an oceanice model with zero initial sea ice. As the oceanice model spins up, 

1666  % there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. 

1667  % The total water contained in the ocean plus ice system is constant, but there is an exchange of water between 

1668  % the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle 

1669  % in oceanice models. 

1670  

1671  \biblio 

1672  

1673  \pindex 

1674  

1675  \end{document} 
