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branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_LBC.tex
r1224 r2282 15 15 % Boundary Condition at the Coast 16 16 % ================================================================ 17 \section{Boundary Condition at the Coast (\np{ shlat})}17 \section{Boundary Condition at the Coast (\np{rn\_shlat})} 18 18 \label{LBC_coast} 19 19 %--------------------------------------------nam_lbc------------------------------------------------------- 20 \namdisplay{nam _lbc}20 \namdisplay{namlbc} 21 21 %-------------------------------------------------------------------------------------------------------------- 22 22 … … 69 69 condition influences the relative vorticity and momentum diffusive trends, and is 70 70 required in order to compute the vorticity at the coast. Four different types of 71 lateral boundary condition are available, controlled by the value of the \np{ shlat}71 lateral boundary condition are available, controlled by the value of the \np{rn\_shlat} 72 72 namelist parameter. (The value of the mask$_{f}$ array along the coastline is set 73 73 equal to this parameter.) These are: … … 76 76 \begin{figure}[!p] \label{Fig_LBC_shlat} \begin{center} 77 77 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_LBC_shlat.pdf} 78 \caption {lateral boundary condition (a) free-slip ($ shlat=0$) ; (b) no-slip ($shlat=2$)79 ; (c) "partial" free-slip ($0< shlat<2$) and (d) "strong" no-slip ($2<shlat$).78 \caption {lateral boundary condition (a) free-slip ($rn\_shlat=0$) ; (b) no-slip ($rn\_shlat=2$) 79 ; (c) "partial" free-slip ($0<rn\_shlat<2$) and (d) "strong" no-slip ($2<rn\_shlat$). 80 80 Implied "ghost" velocity inside land area is display in grey. } 81 81 \end{center} \end{figure} … … 84 84 \begin{description} 85 85 86 \item[free-slip boundary condition (\np{ shlat}=0): ] the tangential velocity at the86 \item[free-slip boundary condition (\np{rn\_shlat}=0): ] the tangential velocity at the 87 87 coastline is equal to the offshore velocity, $i.e.$ the normal derivative of the 88 88 tangential velocity is zero at the coast, so the vorticity: mask$_{f}$ array is set 89 89 to zero inside the land and just at the coast (Fig.~\ref{Fig_LBC_shlat}-a). 90 90 91 \item[no-slip boundary condition (\np{ shlat}=2): ] the tangential velocity vanishes91 \item[no-slip boundary condition (\np{rn\_shlat}=2): ] the tangential velocity vanishes 92 92 at the coastline. Assuming that the tangential velocity decreases linearly from 93 93 the closest ocean velocity grid point to the coastline, the normal derivative is … … 108 108 \end{equation} 109 109 110 \item["partial" free-slip boundary condition (0$<$\np{ shlat}$<$2): ] the tangential110 \item["partial" free-slip boundary condition (0$<$\np{rn\_shlat}$<$2): ] the tangential 111 111 velocity at the coastline is smaller than the offshore velocity, $i.e.$ there is a lateral 112 112 friction but not strong enough to make the tangential velocity at the coast vanish … … 114 114 strictly inbetween $0$ and $2$. 115 115 116 \item["strong" no-slip boundary condition (2$<$\np{ shlat}): ] the viscous boundary116 \item["strong" no-slip boundary condition (2$<$\np{rn\_shlat}): ] the viscous boundary 117 117 layer is assumed to be smaller than half the grid size (Fig.~\ref{Fig_LBC_shlat}-d). 118 118 The friction is thus larger than in the no-slip case. … … 134 134 spectacular improvements have not been found in the half-degree global ocean 135 135 (ORCA05), but significant reductions of numerically induced coastal upwellings were 136 found in an eddy resolving simulation of the Alboran Sea \citep{Olivier Ph2001}.136 found in an eddy resolving simulation of the Alboran Sea \citep{Olivier_PhD01}. 137 137 Nevertheless, since a no-slip boundary condition is not recommended in an eddy 138 permitting or resolving simulation \citep{Penduff 2007}, the use of this option is also138 permitting or resolving simulation \citep{Penduff_al_OS07}, the use of this option is also 139 139 not recommended. 140 140 … … 355 355 ($e1t$, $e2t$, etc) and do not expect the grid size to be zero, even on land. It may be 356 356 best not to eliminate land processors when running the model especially to write the 357 mesh files as outputs (when \np{nmsh} namelist parameter differs from 0). 357 mesh files as outputs (when \np{nn\_msh} namelist parameter differs from 0). 358 %% 358 359 \gmcomment{Steven : dont understand this, no land processor means no output file 359 360 covering this part of globe; its only when files are stitched together into one that you 360 361 can leave a hole} 362 %% 361 363 362 364 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 380 382 %- nobc_dta = 0 ! = 0 the obc data are equal to the initial state 381 383 %- ! = 1 the obc data are read in 'obc .dta' files 382 %- rdpein = 1. ! ??? 383 %- rdpwin = 1. ! ??? 384 %- rdpnin = 30. ! ??? 385 %- rdpsin = 1. ! ??? 386 %- rdpeob = 1500. ! time relaxation (days) for the east open boundary 387 %- rdpwob = 15. ! " " for the west open boundary 388 %- rdpnob = 150. ! " " for the north open boundary 389 %- rdpsob = 15. ! " " for the south open boundary 390 %- zbsic1 = 140.e+6 ! barotropic stream function on first isolated coastline 391 %- zbsic2 = 1.e+6 ! " " on second isolated coastline 392 %- zbsic3 = 0. ! " " on thrid isolated coastline 384 %- rn_dpein = 1. ! ??? 385 %- rn_dpwin = 1. ! ??? 386 %- rn_dpnin = 30. ! ??? 387 %- rn_dpsin = 1. ! ??? 388 %- rn_dpeob = 1500. ! time relaxation (days) for the east open boundary 389 %- rn_dpwob = 15. ! " " for the west open boundary 390 %- rn_dpnob = 150. ! " " for the north open boundary 391 %- rn_dpsob = 15. ! " " for the south open boundary 393 392 %- ln_obc_clim = .true. ! climatological obc data files (default T) 394 393 %- ln_vol_cst = .true. ! total volume conserved … … 428 427 of the domain, for example at Gibraltar Straits if one wants to avoid including 429 428 the Mediterranean in an Atlantic domain. This flexibility has been found necessary 430 for the CLIPPER project \citep{Treguier 2001}. Because of the complexity of the429 for the CLIPPER project \citep{Treguier_al_JGR01}. Because of the complexity of the 431 430 geometry of ocean basins, it may even be necessary to have more than one 432 431 ''west'' open boundary, more than one ''north'', etc. This is not possible with … … 520 519 It is necessary to provide information at the boundaries. The simplest case is 521 520 when this information does not change in time and is equal to the initial conditions 522 (namelist variable \np{n obc\_dta}=0). This is the case for the standard configuration523 EEL5 with open boundaries. When (\np{n obc\_dta}=1), open boundary information521 (namelist variable \np{nn\_obcdta}=0). This is the case for the standard configuration 522 EEL5 with open boundaries. When (\np{nn\_obcdta}=1), open boundary information 524 523 is read from netcdf files. For convenience the input files are supposed to be similar 525 524 to the ''history'' NEMO output files, for dimension names and variable names. … … 529 528 530 529 When ocean observations are used to generate the boundary data (a hydrographic 531 section for example, as in \citet{Treguier 2001}) it happens often that only the velocity530 section for example, as in \citet{Treguier_al_JGR01}) it happens often that only the velocity 532 531 normal to the boundary is known, which is the reason why the initial OBC code 533 532 assumes that only $T$, $S$, and the normal velocity ($u$ or $v$) needs to be … … 548 547 remain in NEMO v2.3. Users should read the code carefully before using it. Finally, 549 548 in the case of the rigid lid approximation the barotropic streamfunction must be 550 provided, as documented in \citet{Treguier 2001}). This option is no longer549 provided, as documented in \citet{Treguier_al_JGR01}). This option is no longer 551 550 recommended but remains in NEMO V2.3. 552 551 … … 596 595 data is held fixed in time. If the files contain 12 values, it is assumed that the input 597 596 is a climatology for a repeated annual cycle (corresponding to the case \np{ln\_obc\_clim} 598 = .True.). The case of an arbitrary number of time frames is not yet implemented597 =true). The case of an arbitrary number of time frames is not yet implemented 599 598 correctly; the user is required to write his own code in the module \mdl{obc\_dta} 600 599 to deal with this situation. … … 608 607 of energy. The constraints are specified separately at each boundary as time 609 608 scales for ''inflow'' and ''outflow'' as defined below. The time scales are set (in days) 610 by namelist parameters such as \np{r dpein}, \np{rdpeob} for the eastern open609 by namelist parameters such as \np{rn\_dpein}, \np{rn\_dpeob} for the eastern open 611 610 boundary for example. When both time scales are zero for a given boundary 612 ($e.g.$ for the western boundary, \jp{lp\_obc\_west}= .True., \np{rdpwob}=0 and613 \np{r dpwin}=0) this means that the boundary in question is a ''fixed '' boundary611 ($e.g.$ for the western boundary, \jp{lp\_obc\_west}=true, \np{rn\_dpwob}=0 and 612 \np{rn\_dpwin}=0) this means that the boundary in question is a ''fixed '' boundary 614 613 where the solution is set exactly by the boundary data. This is not recommended, 615 614 except in combination with increased viscosity in a ''sponge'' layer next to the … … 623 622 $s$-coordinate model on an Arakawa C-grid. Although the algorithm has 624 623 been numerically successful in the CLIPPER Atlantic models, the physics 625 do not work as expected \citep{Treguier 2001}. Users are invited to consider624 do not work as expected \citep{Treguier_al_JGR01}. Users are invited to consider 626 625 open boundary conditions (OBC hereafter) with some scepticism 627 626 \citep{Durran2001, Blayo2005}. … … 637 636 C_{\phi y} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{y}. 638 637 \end{equation} 639 Following \citet{Treguier 2001} and \citet{Marchesiello2001} we retain only638 Following \citet{Treguier_al_JGR01} and \citet{Marchesiello2001} we retain only 640 639 the normal component of the velocity, $C_{\phi x}$, setting $C_{\phi y} =0$ 641 640 (but unlike the original Orlanski radiation algorithm we retain $\phi_{y}$ in … … 665 664 propagation), the radiation condition (\ref{Eq_obc_rado}) is used. 666 665 When $C_{\phi x}$ is westward (inward propagation), (\ref{Eq_obc_radi}) is 667 used with a strong relaxation to climatology (usually $\tau_{i}=\np{r dpein}=$1~day).666 used with a strong relaxation to climatology (usually $\tau_{i}=\np{rn\_dpein}=$1~day). 668 667 Equation (\ref{Eq_obc_radi}) is solved with a Euler time-stepping scheme. As a 669 668 consequence, setting $\tau_{i}$ smaller than, or equal to the time step is equivalent … … 672 671 numerical stability. 673 672 674 In the case of a western boundary located in the Eastern Atlantic, \citet{Penduff 2000}673 In the case of a western boundary located in the Eastern Atlantic, \citet{Penduff_al_JGR00} 675 674 have been able to implement the radiation algorithm without any boundary data, 676 675 using persistence from the previous time step instead. This solution has not worked 677 in other cases \citep{Treguier 2001}, so that the use of boundary data is recommended.676 in other cases \citep{Treguier_al_JGR01}, so that the use of boundary data is recommended. 678 677 Even in the outflow condition (\ref{Eq_obc_rado}), we have found it desirable to 679 678 maintain a weak relaxation to climatology. The time step is usually chosen so as to … … 733 732 \colorbox{yellow}{OBC rigid lid? {\ldots}} 734 733 735 736 737 738 734 % ==================================================================== 739 % Flow Relaxation Scheme735 % Unstructured open boundaries BDY 740 736 % ==================================================================== 741 \section{ Flow Relaxation Scheme (???)}737 \section{Unstructured Open Boundary Conditions (\key{bdy})} 742 738 \label{LBC_bdy} 743 739 744 %gm% to be updated by Met Office 740 %-----------------------------------------nambdy-------------------------------------------- 741 %- filbdy_mask = '' ! name of mask file (if ln_bdy_mask=.TRUE.) 742 %- filbdy_data_T = 'bdydata_grid_T.nc' ! name of data file for FRS condition (T-points) 743 %- filbdy_data_U = 'bdydata_grid_U.nc' ! name of data file for FRS condition (U-points) 744 %- filbdy_data_V = 'bdydata_grid_V.nc' ! name of data file for FRS condition (V-points) 745 %- filbdy_data_bt_T = 'bdydata_bt_grid_T.nc' ! name of data file for Flather condition (T-points) 746 %- filbdy_data_bt_U = 'bdydata_bt_grid_U.nc' ! name of data file for Flather condition (U-points) 747 %- filbdy_data_bt_V = 'bdydata_bt_grid_V.nc' ! name of data file for Flather condition (V-points) 748 %- ln_bdy_clim = .false. ! contain 1 (T) or 12 (F) time dumps and be cyclic 749 %- ln_bdy_vol = .true. ! total volume correction (see volbdy parameter) 750 %- ln_bdy_mask = .false. ! boundary mask from filbdy_mask (T) or boundaries are on edges of domain (F) 751 %- ln_bdy_tides = .true. ! Apply tidal harmonic forcing with Flather condition 752 %- ln_bdy_dyn_fla = .true. ! Apply Flather condition to velocities 753 %- ln_bdy_tra_frs = .false. ! Apply FRS condition to temperature and salinity 754 %- ln_bdy_dyn_frs = .false. ! Apply FRS condition to velocities 755 %- nbdy_dta = 1 ! = 0, bdy data are equal to the initial state 756 %- ! = 1, bdy data are read in 'bdydata .nc' files 757 %- nb_rimwidth = 9 ! width of the relaxation zone 758 %- volbdy = 0 ! = 0, the total water flux across open boundaries is zero 759 \namdisplay{nambdy} 760 %----------------------------------------------------------------------------------------------- 761 762 The BDY module is an alternative implementation of open boundary 763 conditions for regional configurations. It implements the Flow 764 Relaxation Scheme algorithm for temperature, salinity, velocities and 765 ice fields, and the Flather radiation condition for the depth-mean 766 transports. The specification of the location of the open boundary is 767 completely flexible and allows for example the open boundary to follow 768 an isobath or other irregular contour. 769 770 The BDY module was modelled on the OBC module and shares many features 771 and a similar coding structure \citep{Chanut2005}. 772 773 %---------------------------------------------- 774 \subsection{The Flow Relaxation Scheme} 775 \label{BDY_FRS_scheme} 776 777 The Flow Relaxation Scheme (FRS) \citep{Davies_QJRMS76,Engerdahl_Tel95}, 778 applies a simple relaxation of the model fields to 779 externally-specified values over a zone next to the edge of the model 780 domain. Given a model prognostic variable $\Phi$ 781 \begin{equation} \label{Eq_bdy_frs1} 782 \Phi(d) = \alpha(d)\Phi_{e}(d) + (1-\alpha(d))\Phi_{m}(d)\;\;\;\;\; d=1,N 783 \end{equation} 784 where $\Phi_{m}$ is the model solution and $\Phi_{e}$ is the specified 785 external field, $d$ gives the discrete distance from the model 786 boundary and $\alpha$ is a parameter that varies from $1$ at $d=1$ to 787 a small value at $d=N$. It can be shown that this scheme is equivalent 788 to adding a relaxation term to the prognostic equation for $\Phi$ of 789 the form: 790 \begin{equation} \label{Eq_bdy_frs2} 791 -\frac{1}{\tau}\left(\Phi - \Phi_{e}\right) 792 \end{equation} 793 where the relaxation time scale $\tau$ is given by a function of 794 $\alpha$ and the model time step $\Delta t$: 795 \begin{equation} \label{Eq_bdy_frs3} 796 \tau = \frac{1-\alpha}{\alpha} \,\rdt 797 \end{equation} 798 Thus the model solution is completely prescribed by the external 799 conditions at the edge of the model domain and is relaxed towards the 800 external conditions over the rest of the FRS zone. The application of 801 a relaxation zone helps to prevent spurious reflection of outgoing 802 signals from the model boundary. 803 804 The function $\alpha$ is specified as a $tanh$ function: 805 \begin{equation} \label{Eq_bdy_frs4} 806 \alpha(d) = 1 - \tanh\left(\frac{d-1}{2}\right), \quad d=1,N 807 \end{equation} 808 The width of the FRS zone is specified in the namelist as 809 \np{nb\_rimwidth}. This is typically set to a value between 8 and 10. 810 811 %---------------------------------------------- 812 \subsection{The Flather radiation scheme} 813 \label{BDY_flather_scheme} 814 815 The \citet{Flather_JPO94} scheme is a radiation condition on the normal, depth-mean 816 transport across the open boundary. It takes the form 817 \begin{equation} \label{Eq_bdy_fla1} 818 U = U_{e} + \frac{c}{h}\left(\eta - \eta_{e}\right), 819 \end{equation} 820 where $U$ is the depth-mean velocity normal to the boundary and $\eta$ 821 is the sea surface height, both from the model. The subscript $e$ 822 indicates the same fields from external sources. The speed of external 823 gravity waves is given by $c = \sqrt{gh}$, and $h$ is the depth of the 824 water column. The depth-mean normal velocity along the edge of the 825 model domain is set equal to the 826 external depth-mean normal velocity, plus a correction term that 827 allows gravity waves generated internally to exit the model boundary. 828 Note that the sea-surface height gradient in \eqref{Eq_bdy_fla1} 829 is a spatial gradient across the model boundary, so that $\eta_{e}$ is 830 defined on the $T$ points with $nbrdta=1$ and $\eta$ is defined on the 831 $T$ points with $nbrdta=2$. $U$ and $U_{e}$ are defined on the $U$ or 832 $V$ points with $nbrdta=1$, $i.e.$ between the two $T$ grid points. 833 834 %---------------------------------------------- 835 \subsection{Choice of schemes} 836 \label{BDY_choice_of_schemes} 837 838 The Flow Relaxation Scheme may be applied separately to the 839 temperature and salinity (\np{ln\_bdy\_tra\_frs} = true) and 840 the velocity fields (\np{ln\_bdy\_dyn\_frs} = true). Flather 841 radiation conditions may be applied using externally defined 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. 850 851 Note that FRS conditions will work with the filtered 852 (\key{dynspg\_flt}) or time-split (\key{dynspg\_ts}) solutions for the 853 surface pressure gradient. The Flather condition will only work for 854 the time-split solution (\key{dynspg\_ts}). FRS conditions are applied 855 at the end of the main model time step. Flather conditions are applied 856 during the barotropic subcycle in the time-split solution. 857 858 %---------------------------------------------- 859 \subsection{Boundary geometry} 860 \label{BDY_geometry} 861 862 The definition of the open boundary is completely flexible. An example 863 is shown in Fig.~\ref{Fig_LBC_bdy_geom}. The boundary zone is 864 defined by a series of index arrays read in from the input boundary 865 data files: $nbidta$, $nbjdta$, and $nbrdta$. The first two of these 866 define the global $(i,j)$ indices of each point in the boundary zone 867 and the $nbrdta$ array defines the discrete distance from the boundary 868 with $nbrdta=1$ meaning that the point is next to the edge of the 869 model domain and $nbrdta>1$ showing that the point is increasingly 870 further away from the edge of the model domain. These arrays are 871 defined separately for each of the $T$, $U$ and $V$ grids, but the 872 relationship between the points is assumed to be as in Fig. 873 \ref{Fig_LBC_bdy_geom} with the $T$ points forming the outermost row 874 of the boundary and the first row of velocities normal to the boundary 875 being inside the first row of $T$ points. The order in which the 876 points are defined is unimportant. 877 878 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 879 \begin{figure}[!t] \label{Fig_LBC_bdy_geom} \begin{center} 880 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_LBC_bdy_geom.pdf} 881 \caption {Example of geometry of unstructured open boundary} 882 \end{center} \end{figure} 883 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 884 885 %---------------------------------------------- 886 \subsection{Input boundary data files} 887 \label{BDY_data} 888 889 The input data files for the FRS conditions are defined in the 890 namelist as \np{filbdy\_data\_T}, \np{filbdy\_data\_U}, 891 \np{filbdy\_data\_V}. The input data files for the Flather conditions 892 are defined in the namelist as \np{filbdy\_data\_bt\_T}, 893 \np{filbdy\_data\_bt\_U}, \np{filbdy\_data\_bt\_V}. 894 895 The netcdf header of a typical input data file is shown in Figure 896 \ref{Fig_LBC_nc_header}. The file contains the index arrays which 897 define the boundary geometry as noted above and the data arrays for 898 each field. The data arrays are dimensioned on: a time 899 dimension; $xb$ which is the index of the boundary data point in the 900 horizontal; and $yb$ which is a degenerate dimension of 1 to enable 901 the file to be read by the standard NEMO I/O routines. The 3D fields 902 also have a depth dimension. 903 904 If \np{ln\_bdy\_clim} is set to $false$, the model expects the 905 units of the time axis to have the form shown in 906 \ref{Fig_bdy_input_file}, $i.e.$ {\it ``seconds since yyyy-mm-dd 907 hh:mm:ss''} The fields are then linearly interpolated to the model 908 time at each timestep. Note that for this option, the time axis of the 909 input files must completely span the time period of the model 910 integration. If \np{ln\_bdy\_clim} is set to $.true.$ (climatological 911 boundary forcing), the model will expect either a single set of annual 912 mean fields (constant boundary forcing) or 12 sets of monthly mean 913 fields in the input files. 914 915 As in the OBC module there is an option to use initial conditions as 916 boundary conditions. This is chosen by setting 917 $\np{nb\_dta}=0$. However, since the model defines the boundary 918 geometry by reading the boundary index arrays from the input files, 919 it is still necessary to provide a set of input files in this 920 case. They need only contain the boundary index arrays, $nbidta$, 921 $nbjdta$, $nbrdta$. 922 923 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 924 \begin{figure}[!t] \label{Fig_LBC_nc_header} \begin{center} 925 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_LBC_nc_header.pdf} 926 \caption {Example of header of netcdf input data file for BDY} 927 \end{center} \end{figure} 928 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 929 930 %---------------------------------------------- 931 \subsection{Volume correction} 932 \label{BDY_vol_corr} 933 934 There is an option to force the total volume in the regional model to be constant, similar to the option in the OBC module. This is controlled by the \np{volbdy} parameter in the namelist. A value of $\np{volbdy} = 0$ indicates that this option is not used. If $\np{volbdy} = 1$ then a correction is applied to the normal velocities around the boundary at each timestep to ensure that the integrated volume flow through the boundary is zero. If $\np{volbdy} = 2$ then the calculation of the volume change on the timestep includes the change due to the freshwater flux across the surface and the correction velocity corrects for this as well. 935 936 937 %---------------------------------------------- 938 \subsection{Tidal harmonic forcing} 939 \label{BDY_tides} 940 941 To be written.... 942 943 944 945
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