Changeset 2273
- Timestamp:
- 2010-10-15T09:20:56+02:00 (14 years ago)
- Location:
- branches/DEV_r1826_DOC/DOC
- Files:
-
- 3 edited
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NEMO_book.tex (modified) (1 diff)
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TexFiles/Chapters/Chap_LBC.tex (modified) (11 diffs)
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TexFiles/Chapters/Chap_STP.tex (modified) (9 diffs)
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branches/DEV_r1826_DOC/DOC/NEMO_book.tex
r2212 r2273 151 151 \newcommand{\key} [1] {\textbf{key\_#1}\index{CPP keys!key\_#1}} %key_cpp (key) 152 152 \newcommand{\NEMO} {\textit{NEMO }} %NEMO (nemo) 153 \newcommand{\amtcomment}[1]{#1} % command to allow "commented out" portions of 154 \newcommand{\sgacomment}[1]{#1} % command to allow "commented out" portions of 155 \newcommand{\gmcomment}[1]{} % command to allow "commented out" portions of 153 % command to "commented out" portions of text ({} argument) or not ({#1} argument) 154 \newcommand{\amtcomment}[1]{} % command to "commented out" portions of text or not (#1 in argument) 155 \newcommand{\sgacomment}[1]{} % command to "commented out" portions of 156 \newcommand{\gmcomment}[1]{} % command to "commented out" portions of 156 157 % % text that span line breaks 157 158 \newcommand{\alpbet} {\left(\alpha / \beta \right)} % alpha/beta for slp computation -
branches/DEV_r1826_DOC/DOC/TexFiles/Chapters/Chap_LBC.tex
r2213 r2273 738 738 \label{LBC_bdy} 739 739 740 %-----------------------------------------nam _obc-------------------------------------------740 %-----------------------------------------nambdy-------------------------------------------- 741 741 %- filbdy_mask = '' ! name of mask file (if ln_bdy_mask=.TRUE.) 742 742 %- filbdy_data_T = 'bdydata_grid_T.nc' ! name of data file for FRS condition (T-points) … … 758 758 %- volbdy = 0 ! = 0, the total water flux across open boundaries is zero 759 759 \namdisplay{nambdy} 760 %----------------------------------------------------------------------------------------------- 760 761 761 762 The BDY module is an alternative implementation of open boundary … … 768 769 769 770 The BDY module was modelled on the OBC module and shares many features 770 and a similar coding structure \cite t{Chanut2005}.771 and a similar coding structure \citep{Chanut2005}. 771 772 772 773 %---------------------------------------------- … … 774 775 \label{BDY_FRS_scheme} 775 776 776 The Flow Relaxation Scheme \citet{Davies_QJRMetSoc76},\citet{Engerdahl1995},777 The Flow Relaxation Scheme (FRS) \citep{Davies_QJRMS76,Engerdahl_Tel95}, 777 778 applies a simple relaxation of the model fields to 778 779 externally-specified values over a zone next to the edge of the model … … 793 794 $\alpha$ and the model time step $\Delta t$: 794 795 \begin{equation} \label{Eq_bdy_frs3} 795 \tau = \ Delta t \frac{1-\alpha}{\alpha}796 \tau = \frac{1-\alpha}{\alpha} \,\rdt 796 797 \end{equation} 797 798 Thus the model solution is completely prescribed by the external … … 803 804 The function $\alpha$ is specified as a $tanh$ function: 804 805 \begin{equation} \label{Eq_bdy_frs4} 805 \alpha(d) = 1 - \tanh\left(\frac{ 1}{2}(d-1)\right)\;\;\;\;\;d=1,N806 \alpha(d) = 1 - \tanh\left(\frac{d-1}{2}\right), \quad d=1,N 806 807 \end{equation} 807 808 The width of the FRS zone is specified in the namelist as 808 \np{nb\_rimwidth}. This is typically set to a value 809 between 8 and 10. 809 \np{nb\_rimwidth}. This is typically set to a value between 8 and 10. 810 810 811 811 %---------------------------------------------- … … 813 813 \label{BDY_flather_scheme} 814 814 815 The Flather scheme \citet{Flather1994}is a radiation condition on the normal, depth-mean815 The \citet{Flather_JPO94} scheme is a radiation condition on the normal, depth-mean 816 816 transport across the open boundary. It takes the form 817 817 \begin{equation} \label{Eq_bdy_fla1} … … 826 826 external depth-mean normal velocity, plus a correction term that 827 827 allows gravity waves generated internally to exit the model boundary. 828 Note that the sea-surface height gradient in Equation \ref{Eq_bdy_fla1}828 Note that the sea-surface height gradient in \eqref{Eq_bdy_fla1} 829 829 is a spatial gradient across the model boundary, so that $\eta_{e}$ is 830 830 defined on the $T$ points with $nbrdta=1$ and $\eta$ is defined on the 831 831 $T$ points with $nbrdta=2$. $U$ and $U_{e}$ are defined on the $U$ or 832 $V$ points with $nbrdta=1$, ie.between the two $T$ grid points.832 $V$ points with $nbrdta=1$, $i.e.$ between the two $T$ grid points. 833 833 834 834 %---------------------------------------------- … … 837 837 838 838 The Flow Relaxation Scheme may be applied separately to the 839 temperature and salinity ( set \np{ln\_bdy\_tra\_frs} to .true.) and840 the velocity fields ( set \np{ln\_bdy\_dyn\_frs} to .true.). Flather839 temperature and salinity (\np{ln\_bdy\_tra\_frs} = true) and 840 the velocity fields (\np{ln\_bdy\_dyn\_frs} = true). Flather 841 841 radiation conditions may be applied using externally defined 842 barotropic velocities and sea-surface height (set 843 \np{ln\_bdy\_dyn\_fla} to .true.) or using tidal harmonics fields (set 844 \np{ln\_bdy\_tides} to .true.) or both. FRS and Flather conditions may 845 be applied simultaneously. A typical configuration where all possible 846 conditions might be used is a tidal, shelf-seas model, where the barotropic 847 boundary conditions are fixed with the Flather scheme using tidal 848 harmonics and possibly output from a large-scale model, and FRS 849 conditions are applied to the tracers and baroclinic velocity fields, 850 using fields from a large-scale model. 842 barotropic velocities and sea-surface height (\np{ln\_bdy\_dyn\_fla} = true) 843 or using tidal harmonics fields (\np{ln\_bdy\_tides} = true) 844 or both. FRS and Flather conditions may be applied simultaneously. 845 A typical configuration where all possible conditions might be used is a tidal, 846 shelf-seas model, where the barotropic boundary conditions are fixed 847 with the Flather scheme using tidal harmonics and possibly output 848 from a large-scale model, and FRS conditions are applied to the tracers 849 and baroclinic velocity fields, using fields from a large-scale model. 851 850 852 851 Note that FRS conditions will work with the filtered … … 903 902 also have a depth dimension. 904 903 905 If \np{ln\_bdy\_clim} is set to $ .false.$, the model expects the904 If \np{ln\_bdy\_clim} is set to $false$, the model expects the 906 905 units of the time axis to have the form shown in 907 \ref{Fig_bdy_input_file}, ie.{\it ``seconds since yyyy-mm-dd906 \ref{Fig_bdy_input_file}, $i.e.$ {\it ``seconds since yyyy-mm-dd 908 907 hh:mm:ss''} The fields are then linearly interpolated to the model 909 908 time at each timestep. Note that for this option, the time axis of the … … 940 939 \label{BDY_tides} 941 940 942 943 944 945 941 To be written.... 942 943 944 945 -
branches/DEV_r1826_DOC/DOC/TexFiles/Chapters/Chap_STP.tex
r2211 r2273 137 137 constraint on the time step. Two solutions are available in \NEMO to overcome 138 138 the stability constraint: $(a)$ a forward time differencing scheme using a 139 time splitting technique (\np{ln\_zdfexp} =.true.) or $(b)$ a backward (or implicit)140 time differencing scheme (\np{ln\_zdfexp} =.false.). In $(a)$, the master139 time splitting technique (\np{ln\_zdfexp} = true) or $(b)$ a backward (or implicit) 140 time differencing scheme (\np{ln\_zdfexp} = false). In $(a)$, the master 141 141 time step $\Delta $t is cut into $N$ fractional time steps so that the 142 142 stability criterion is reduced by a factor of $N$. The computation is performed as … … 168 168 \end{equation} 169 169 where RHS is the right hand side of the equation except for the vertical diffusion term. 170 \sgacomment{why change from T to u in the following equation?}171 170 We rewrite \eqref{Eq_STP_imp} as: 172 171 \begin{equation} \label{Eq_STP_imp_mat} 173 -c(k+1)\; u^{t+1}(k+1) + d(k)\;u^{t+1}(k) - \;c(k)\;u^{t+1}(k-1) \equiv b(k)172 -c(k+1)\;T^{t+1}(k+1) + d(k)\;T^{t+1}(k) - \;c(k)\;T^{t+1}(k-1) \equiv b(k) 174 173 \end{equation} 175 174 where 176 175 \begin{align*} 177 c(k) &= A_w^{v m} (k) \, / \, e_{3uw} (k) \\178 d(k) &= e_{3 u} (k) \, / \, (2\rdt) + c_k + c_{k+1} \\179 b(k) &= e_{3 u} (k) \; \left( u^{t-1}(k) \, / \, (2\rdt) + \text{RHS} \right)176 c(k) &= A_w^{vT} (k) \, / \, e_{3w} (k) \\ 177 d(k) &= e_{3t} (k) \, / \, (2\rdt) + c_k + c_{k+1} \\ 178 b(k) &= e_{3t} (k) \; \left( T^{t-1}(k) \, / \, (2\rdt) + \text{RHS} \right) 180 179 \end{align*} 181 180 … … 226 225 as the Forward-Backward scheme used in MOM \citep{Griffies_al_OS05} and more 227 226 efficient than the LF-AM3 scheme (leapfrog time stepping combined with a third order 228 Adams-Moult on interpolation for the predictor phase) used in ROMS227 Adams-Moulthon interpolation for the predictor phase) used in ROMS 229 228 \citep{Shchepetkin_McWilliams_OM05}. 230 229 … … 234 233 frequency IGWs. Obviously, the doubling of the time-step is achievable only 235 234 if no other factors control the time-step, such as the stability limits associated 236 with advection, diffusion or Coriolis terms. For example, it is uselessin low resolution235 with advection, diffusion or Coriolis terms. For example, it is inefficient in low resolution 237 236 global ocean configurations, since inertial oscillations in the vicinity of the North Pole 238 are the limiting factor for the time step. It is also often uselessin very high237 are the limiting factor for the time step. It is also often inefficient in very high 239 238 resolution configurations where strong currents and small grid cells exert 240 239 the strongest constraint on the time step. 241 \sgacomment{ not sure "useless" is the right word here. "valueless", "inefficient"?}242 243 240 244 241 % ------------------------------------------------------------------------------------------------------------- … … 255 252 In a classical LF-RA environment, the forcing term is centred in time, $i.e.$ 256 253 it is time-stepped over a $2\rdt$ period: $x^t = x^t + 2\rdt Q^t $ where $Q$ 257 is the filtered forcing applied to $x$, and the filter is given by \eqref{Eq_STP_asselin}. 254 is the forcing applied to $x$, and the time filter is given by \eqref{Eq_STP_asselin} 255 so that $Q$ is redistributed over several time step. 258 256 In the modified LF-RA environment, these two formulations have been replaced by: 259 257 \begin{align} … … 263 261 - \gamma\,\rdt \, \left[ Q^{t+\rdt/2} - Q^{t-\rdt/2} \right] \label{Eq_STP_RA} 264 262 \end{align} 265 \sgacomment{Q(t)=f(x(t-dt),x(t),x(t+dt)), Q(t-dt/2)?}266 267 263 The change in the forcing formulation given by \eqref{Eq_STP_forcing} 268 264 (see Fig.\ref{Fig_MLF_forcing}) has a significant effect: the forcing term no 269 265 longer excites the divergence of odd and even time steps \citep{Leclair_Madec_OM09}. 266 % forcing seen by the model.... 270 267 This property improves the LF-RA scheme in two respects. 271 First, the LF-RA becomes a truly quasi-second order scheme. Indeed, 268 First, the LF-RA can now ensure the local and global conservation of tracers. 269 Indeed, time filtering is no longer required on the forcing part. The influence of 270 the Asselin filter on the forcing is be removed by adding a new term in the filter 271 (last term in \eqref{Eq_STP_RA} compared to \eqref{Eq_STP_asselin}). Since 272 the filtering of the forcing was the source of non-conservation in the classical 273 LF-RA scheme, the modified formulation becomes conservative \citep{Leclair_Madec_OM09}. 274 Second, the LF-RA becomes a truly quasi-second order scheme. Indeed, 272 275 \eqref{Eq_STP_forcing} used in combination with a careful treatment of static 273 276 instability (\S\ref{ZDF_evd}) and of the TKE physics (\S\ref{ZDF_tke_ene}), 274 the two other main sources of time step divergence, allows a reduction by two orders 275 of magnitude of the Asselin filter parameter. 276 Second, the LF-RA can now ensure the local and global conservation of tracers. 277 Indeed, time filtering is no longer required on the forcing part. 278 \sgacomment{ but Q is described above as the forcing part!} The influence of 279 the forcing in the Asselin filter can be removed by adding a new term in the filter 280 (last term in \eqref{Eq_STP_RA} compared to \eqref{Eq_STP_asselin}). Since 281 the filtering of the forcing was the source of non-conservation in the LF-RA 282 scheme, it becomes conservative \citep{Leclair_Madec_OM09}. 277 the two other main sources of time step divergence, allows a reduction by 278 two orders of magnitude of the Asselin filter parameter. 283 279 284 280 Note that the forcing is now provided at the middle of a time step: $Q^{t+\rdt/2}$ … … 292 288 \begin{figure}[!t] \label{Fig_MLF_forcing} \begin{center} 293 289 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_MLF_forcing.pdf} 294 \caption{Illustration of forcing integration methods. ''Traditional'' formulation (top) 295 where a centred forcing is applied over a $2\rdt$ period and modified formulation 296 (bottom) where a mean forcing over the two successive time step is applied over a $2\rdt$ period.} 290 \caption{Illustration of forcing integration methods. 291 (top) ''Traditional'' formulation : the forcing is defined at the same time as the variable 292 on which it is applied (integer value of the time step index) and it is applied over a $2\rdt$ period. 293 (bottom) modified formulation : the forcing is defined in the mid of the time (integer and a half 294 value of the time step index) and the mean of two successive forcing ($n-1/2$, $n+1/2$). 295 is applied over a $2\rdt$ period.} 297 296 \end{center} \end{figure} 298 297 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 299 298 300 \sgacomment{two methods in caption sound the same }299 \sgacomment{two methods in caption sound the same ==> gm: I try to change this, but I'm not happy with the result} 301 300 302 301 % ------------------------------------------------------------------------------------------------------------- … … 314 313 x^1 = x^0 + \rdt \ \text{RHS}^0 315 314 \end{equation} 316 This is done simply by keeping the leapfrog environment but setting all $x^0$ (\textit{before}) 317 and $x^{1/2}$ (\textit{now}) fields equal at the first time step. 315 This is done simply by keeping the leapfrog environment ($i.e.$ the \eqref{Eq_STP} 316 three level time stepping) but setting all $x^0$ (\textit{before}) and $x^{1}$ (\textit{now}) fields 317 equal at the first time step and using half the value of $\rdt$. 318 318 319 319 It is also possible to restart from a previous computation, by using a … … 328 328 gradient (see \S\ref{DYN_hpg_imp}), an extra three-dimensional field has to be 329 329 added to the restart file to ensure an exact restartability. This is done optionally 330 via the namelist parameter \np{nn\_dynhpg\_rst}, so that the size of the330 via the \np{nn\_dynhpg\_rst} namelist parameter, so that the size of the 331 331 restart file can be reduced when restartability is not a key issue (operational 332 332 oceanography or in ensemble simulations for seasonal forecasting).
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