Changeset 3507


Ignore:
Timestamp:
2012-10-17T12:54:32+02:00 (8 years ago)
Author:
rfurner
Message:

documentation and namelist updates and inclusion of a hydrostatic consistency parameter

Location:
branches/2012/dev_r3435_UKMO7_SCOORDS
Files:
1 added
13 edited

Legend:

Unmodified
Added
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  • branches/2012/dev_r3435_UKMO7_SCOORDS/DOC/TexFiles/Biblio/Biblio.bib

    r3294 r3507  
    25242524} 
    25252525 
     2526@ARTICLE{Siddorn_Furner_OM12, 
     2527  author = {J. Siddorn and R. Furner}, 
     2528  title = {An analytical stretching function that combines the best attributes of geopotential and terrain-following vertical coordinates}, 
     2529  journal = OM, 
     2530  year = {2012}, 
     2531  pages = {submitted}, 
     2532} 
    25262533@ARTICLE{Simmons_al_OM04, 
    25272534  author = {H. L. Simmons and S. R. Jayne and L. C. {St. Laurent} and A. J. Weaver}, 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/DOC/TexFiles/Chapters/Chap_DOM.tex

    r3294 r3507  
    502502time-variation of the free surface so that the transformation is time dependent:  
    503503$z(i,j,k,t)$ (Fig.~\ref{Fig_z_zps_s_sps}f). This option can be used with full step  
    504 bathymetry or $s$-coordinate (hybride and partial step coordinates have not  
     504bathymetry or $s$-coordinate (hybrid and partial step coordinates have not  
    505505yet been tested in NEMO v2.3).  
    506506 
     
    743743levels are defined from the product of a depth field and either a stretching  
    744744function or its derivative, respectively: 
     745 
    745746\begin{equation} \label{DOM_sco_ana} 
    746747\begin{split} 
     
    749750\end{split} 
    750751\end{equation} 
     752 
    751753where $h$ is the depth of the last $w$-level ($z_0(k)$) defined at the $t$-point  
    752754location in the horizontal and $z_0(k)$ is a function which varies from $0$ at the sea  
    753755surface to $1$ at the ocean bottom. The depth field $h$ is not necessary the ocean  
    754756depth, since a mixed step-like and bottom-following representation of the  
    755 topography can be used (Fig.~\ref{Fig_z_zps_s_sps}d-e). In the example provided  
    756 (\rou{zgr\_sco} routine, see \mdl{domzgr}) $h$ is a smooth envelope bathymetry  
    757 and steps are used to represent sharp bathymetric gradients. 
    758  
    759 A new flexible stretching function, modified from \citet{Song_Haidvogel_JCP94} is provided as an example: 
     757topography can be used (Fig.~\ref{Fig_z_zps_s_sps}d-e) or an envelop bathymetry can be defined (Fig.~\ref{Fig_z_zps_s_sps}f). 
     758The namelist parameter \np{rn\_rmax} determines the slope at which the terrain-following coordinate intersects the sea bed and becomes a pseudo z-coordinate. The coordinate can also be hybridised by specifying \np{rn\_sbot\_min} and \np{rn\_sbot\_max} as the minimum and maximum depths at which the terrain-following vertical coordinate is calculated. 
     759 
     760Options for stretching the coordinate are provided as examples, but care must be taken to ensure that the vertical stretch used is appropriate for the application. 
     761A stretching function, modified from the commonly used \citet{Song_Haidvogel_JCP94} stretching (\np{ln\_sco\_SH94}~=~true), is provided as an example: 
     762 
    760763\begin{equation} \label{DOM_sco_function} 
    761764\begin{split} 
    762 z  &= h_c +( h-h_c)\;c s)  \\ 
     765z  &= h_c +( h-h_c)\;c s   \\ 
    763766c(s)  &=  \frac{ \left[   \tanh{ \left( \theta \, (s+b) \right)}  
    764767               - \tanh{ \left(  \theta \, b      \right)}  \right]} 
     
    766769\end{split} 
    767770\end{equation} 
    768 where $h_c$ is the thermocline depth and $\theta$ and $b$ are the surface and  
     771 
     772 
     773%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     774\begin{figure}[!ht]    \begin{center} 
     775\includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_sco_function.pdf} 
     776\caption{  \label{Fig_sco_function}    
     777Examples of the stretching function applied to a seamount; from left to right:  
     778surface, surface and bottom, and bottom intensified resolutions} 
     779\end{center}   \end{figure} 
     780%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     781 
     782where $h_c$ is the critical depth (\np{rn\_hc}) total depth at which the coordinate transitions from pure $\sigma$ to the stretched coordinate,  and $\theta$ (\np{rn\_theta}) and $b$ (\np{rn\_bb}) are the surface and  
    769783bottom control parameters such that $0\leqslant \theta \leqslant 20$, and  
    770784$0\leqslant b\leqslant 1$. $b$ has been designed to allow surface and/or bottom  
    771785increase of the vertical resolution (Fig.~\ref{Fig_sco_function}). 
    772786 
    773 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
    774 \begin{figure}[!tb]    \begin{center} 
    775 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_sco_function.pdf} 
    776 \caption{  \label{Fig_sco_function}    
    777 Examples of the stretching function applied to a sea mont; from left to right:  
    778 surface, surface and bottom, and bottom intensified resolutions} 
    779 \end{center}   \end{figure} 
    780 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     787Another example has been provided at version 3.5 (\np{ln\_sco\_SF12}) that allows a fixed surface resolution in an analytical terrain-following stretching \citet{Siddorn_Furner_OM12}. In this case the a stretching function $\gamma$ is defined such that: 
     788 
     789\begin{equation} 
     790z = \gamma\left(h+\zeta\right) \quad \text{ with } \quad 0 \leq \gamma \leq 1 
     791\label{eq:z} 
     792\end{equation} 
     793 
     794The function is defined with respect to $\sigma$, the unstretched terrain-following coordinate: 
     795 
     796\begin{equation} \label{DOM_gamma_deriv} 
     797\gamma= A\left(\sigma-\frac{1}{2}\left(\sigma^{2}+f\left(\sigma\right)\right)\right)+B\left(\sigma^{3}-f\left(\sigma\right)\right)+f\left(\sigma\right) 
     798\end{equation} 
     799 
     800Where: 
     801\begin{equation} \label{DOM_gamma} 
     802f\left(\sigma\right)=\left(\alpha+2\right)\sigma^{\alpha+1}-\left(\alpha+1\right)\sigma^{\alpha+2} 
     803\end{equation} 
     804 
     805This gives an analytical stretching of $\sigma$ that is solvable in $A$ and $B$ as a function of the user prescribed stretching parameter $\alpha$ (\np{rn\_alpha}) that stretches towards the surface ($\alpha > 1.0$) or the bottom ($\alpha < 1.0$) and user prescribed surface (\np{rn\_zs}) and bottom depths. The bottom cell depth in this example is given as a function of water depth: 
     806 
     807\begin{equation} \label{DOM_zb} 
     808Z_b= h a + b 
     809\end{equation} 
     810 
     811where the namelist parameters \np{rn\_zb\_a} and \np{rn\_zb\_b} are $a$ and $b$ respectively. 
     812 
     813%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     814\begin{figure}[!ht] 
     815   \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/FIG_DOM_compare_coordinates_surface.pdf} 
     816        \caption{A comparison of the \citet{Song_Haidvogel_JCP94} $S$-coordinate (solid lines), a 50 level $Z$-coordinate (contoured surfaces) and the \citet{Siddorn_Furner_OM12} $S$-coordinate (dashed lines) in the surface 100m for a idealised bathymetry that goes from 50m to 5500m depth. For clarity every third coordinate surface is shown.} 
     817    \label{fig_compare_coordinates_surface} 
     818\end{figure} 
     819%>>>>>>>>>>>>>>>>>>>>>>>>>>>> 
     820 
     821This gives a smooth analytical stretching in computational space that is constrained to given specified surface and bottom grid cell depths in real space. This is not to be confused with the hybrid schemes that superimpose geopotential coordinates on terrain following coordinates thus creating a non-analytical vertical coordinate that therefore may suffer from large gradients in the vertical resolutions. This stretching is less straightforward to implement than the \citet{Song_Haidvogel_JCP94} stretching, but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes. 
     822 
     823As with the \citet{Song_Haidvogel_JCP94} stretching the stretch is only applied at depths greater than the critical depth $h_c$. In this example two options are available in depths shallower than $h_c$, with pure sigma being applied if the \np{ln\_sigcrit} is true and pure z-coordinates if it is false (the z-coordinate being equal to the depths of the stretched coordinate at $h_c$. 
     824 
     825Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as large slopes lead to hydrostatic consistency. A hydrostatic consistency parameter diagnostic following \citet{Haney1991} has been implemented, and is output as part of the model mesh file at the start of the run. 
    781826 
    782827% ------------------------------------------------------------------------------------------------------------- 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/DOC/TexFiles/Namelist/namzgr_sco

    r3294 r3507  
    22&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate 
    33!----------------------------------------------------------------------- 
    4    rn_sbot_min =  300.     !  minimum depth of s-bottom surface (>0) (m) 
    5    rn_sbot_max = 5250.     !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
    6    rn_theta    =    6.0    !  surface control parameter (0<=rn_theta<=20) 
    7    rn_thetb    =    0.75   !  bottom control parameter  (0<=rn_thetb<= 1) 
    8    rn_rmax     =    0.15   !  maximum cut-off r-value allowed (0<rn_max<1) 
    9    ln_s_sigma  = .false.   !  hybrid s-sigma coordinates 
    10    rn_bb       =    0.8    !  stretching with s-sigma 
    11    rn_hc       =  150.0    !  critical depth with s-sigma  
     4   ln_s_sh94   = .true.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
     5   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
     6   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch 
     7                           !  stretching coefficients for all functions 
     8   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m) 
     9   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
     10   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates 
     11                        !!!!!!!  Envelop bathymetry 
     12   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1) 
     13                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.) 
     14   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20) 
     15   rn_bb       =    0.8    !  stretching with SH94 s-sigma    
     16                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.) 
     17   rn_alpha    =    4.4    !  stretching with SF12 s-sigma 
     18   rn_efold    =    0.0    !  efold length scale for transition to stretched coord 
     19   rn_zs       =    1.0    !  depth of surface grid box 
     20                           !  bottom cell depth (Zb) is a linear function of water depth Zb = H*a + b 
     21   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb 
     22   rn_zb_b     =   -0.2    !  offset for calculating Zb 
     23                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above] 
     24   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)  
    1225/ 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/CONFIG/AMM12/EXP00/namelist

    r3453 r3507  
    2727   cn_exp      =  "AMM12"  !  experience name  
    2828   nn_it000    =       1   !  first time step 
    29    nn_itend    =     576   !  last  time step (std 1 day = 576) 
     29   nn_itend    =    2880   !  last  time step (std 1 day = 288) 
    3030   nn_date0    =  20070101 !  date at nit_0000 (format yyyymmdd) used if ln_rstart=F or (ln_rstart=T and nn_rstctl=0 or 1) 
    3131   nn_leapy    =       1   !  Leap year calendar (1) or not (0) 
    32    ln_rstart   =  .false.  !  start from rest (F) or from a restart file (T) 
     32   ln_rstart   =  .true.  !  start from rest (F) or from a restart file (T) 
    3333   nn_rstctl   =       0   !  restart control => activated only if ln_rstart = T 
    3434                           !    = 0 nn_date0 read in namelist ; nn_it000 : read in namelist 
     
    3737   cn_ocerst_in  = "restart"   !  suffix of ocean restart name (input) 
    3838   cn_ocerst_out = "restart"   !  suffix of ocean restart name (output) 
    39    nn_istate   =       0   !  output the initial state (1) or not (0) 
    40    nn_stock    =     576   !  frequency of creation of a restart file (modulo referenced to 1) 
    41    nn_write    =      12   !  frequency of write in the output file   (modulo referenced to nit000) 
     39   nn_istate   =       1   !  output the initial state (1) or not (0) 
     40   nn_stock    =     2880  !  frequency of creation of a restart file (modulo referenced to 1) 
     41   nn_write    =     144   !  frequency of write in the output file   (modulo referenced to nit000)  
    4242   ln_dimgnnn  = .false.   !  DIMG file format: 1 file for all processors (F) or by processor (T) 
    4343   ln_mskland  = .false.   !  mask land points in NetCDF outputs (costly: + ~15%) 
     
    6565&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate 
    6666!----------------------------------------------------------------------- 
    67    ln_s_sh94   = .false.   !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
    68    ln_s_sf12   = .true.    !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
    69    ln_sigcrit  = .true.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch  
     67   ln_s_sh94   = .true.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
     68   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
     69   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch 
     70                           !  stretching coefficients for all functions 
    7071   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m) 
    7172   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
    72    rn_hc       =   50.0    !  critical depth for transition to stretched coordinates 
     73   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates 
     74                        !!!!!!!  Envelop bathymetry 
    7375   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1) 
    74                            !  SH94 stretching coefficients  
     76                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.) 
    7577   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20) 
    76    rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1) 
    77    rn_bb       =    0.8    !  stretching with SH94 s-sigma 
    78                            !  SF12 stretching coefficient  
    79    rn_alpha    =    4.4    !  stretching with SH94 s-sigma 
     78   rn_bb       =    0.8    !  stretching with SH94 s-sigma    
     79                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.) 
     80   rn_alpha    =    4.4    !  stretching with SF12 s-sigma 
    8081   rn_efold    =    0.0    !  efold length scale for transition to stretched coord 
    8182   rn_zs       =    1.0    !  depth of surface grid box 
     
    8384   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb 
    8485   rn_zb_b     =   -0.2    !  offset for calculating Zb 
     86                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above] 
     87   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)  
    8588/ 
    8689!----------------------------------------------------------------------- 
     
    9497   rn_e3zps_rat=    0.1    !  rn_e3zps_min and rn_e3zps_rat*e3t, with 0<rn_e3zps_rat<1 
    9598                           ! 
    96    rn_rdt      =  150.     !  time step for the dynamics (and tracer if nn_acc=0) 
     99   rn_rdt      =  300.     !  time step for the dynamics (and tracer if nn_acc=0) 
    97100   nn_baro     =   30      !  number of barotropic time step            ("key_dynspg_ts") 
    98101   rn_atfp     =    0.1    !  asselin time filter parameter 
     
    404407    cn_mask_file = ''                     !  name of mask file (if ln_mask_file=.TRUE.) 
    405408    nn_dyn2d      =  2                    !  boundary conditions for barotropic fields 
    406     nn_dyn2d_dta  =  2                    !  = 0, bdy data are equal to the initial state 
     409    nn_dyn2d_dta  =  3                    !  = 0, bdy data are equal to the initial state 
    407410                                          !  = 1, bdy data are read in 'bdydata   .nc' files 
    408411                                          !  = 2, use tidal harmonic forcing data from files 
     
    412415                           !  = 1, bdy data are read in 'bdydata   .nc' files 
    413416    nn_tra        =  1                    !  boundary conditions for T and S 
    414     nn_tra_dta    =  0                    !  = 0, bdy data are equal to the initial state 
     417    nn_tra_dta    =  1                    !  = 0, bdy data are equal to the initial state 
    415418                           !  = 1, bdy data are read in 'bdydata   .nc' files 
    416419    nn_rimwidth  = 10                      !  width of the relaxation zone 
     
    429432   bn_v3d  =    'amm12_bdyV_u3d' ,         24        , 'vomecrty' ,     .true.     , .false. ,  'daily'  ,    ''    ,   '' 
    430433   bn_tem  =    'amm12_bdyT_tra' ,         24        , 'votemper' ,     .true.     , .false. ,  'daily'  ,    ''    ,   '' 
    431    bn_tem  =    'amm12_bdyT_tra' ,         24        , 'vosaline' ,     .true.     , .false. ,  'daily'  ,    ''    ,   '' 
     434   bn_sal  =    'amm12_bdyT_tra' ,         24        , 'vosaline' ,     .true.     , .false. ,  'daily'  ,    ''    ,   '' 
    432435   cn_dir  =    'bdydta/' 
    433436   ln_full_vel = .false. 
     
    606609   ln_hpg_zco  = .false.   !  z-coordinate - full steps                    
    607610   ln_hpg_zps  = .false.   !  z-coordinate - partial steps (interpolation) 
    608    ln_hpg_sco  = .true.    !  s-coordinate (standard jacobian formulation) 
     611   ln_hpg_sco  = .false.    !  s-coordinate (standard jacobian formulation) 
    609612   ln_hpg_djc  = .false.   !  s-coordinate (Density Jacobian with Cubic polynomial) 
    610    ln_hpg_prj  = .false.   !  s-coordinate (Pressure Jacobian scheme) 
     613   ln_hpg_prj  = .true.   !  s-coordinate (Pressure Jacobian scheme) 
    611614   ln_dynhpg_imp = .false. !  time stepping: semi-implicit time scheme  (T) 
    612615                                 !           centered      time scheme  (F) 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/CONFIG/AMM12_PISCES/EXP00/namelist

    r3309 r3507  
    2727   cn_exp      =  "AMM12"  !  experience name  
    2828   nn_it000    =       1   !  first time step 
    29    nn_itend    =     576   !  last  time step (std 1 day = 576) 
     29   nn_itend    =    2880   !  last  time step (std 1 day = 288) 
    3030   nn_date0    =  20070101 !  date at nit_0000 (format yyyymmdd) used if ln_rstart=F or (ln_rstart=T and nn_rstctl=0 or 1) 
    3131   nn_leapy    =       1   !  Leap year calendar (1) or not (0) 
    32    ln_rstart   =  .false.  !  start from rest (F) or from a restart file (T) 
     32   ln_rstart   =  .true.  !  start from rest (F) or from a restart file (T) 
    3333   nn_rstctl   =       0   !  restart control => activated only if ln_rstart = T 
    3434                           !    = 0 nn_date0 read in namelist ; nn_it000 : read in namelist 
     
    3737   cn_ocerst_in  = "restart"   !  suffix of ocean restart name (input) 
    3838   cn_ocerst_out = "restart"   !  suffix of ocean restart name (output) 
    39    nn_istate   =       0   !  output the initial state (1) or not (0) 
    40    nn_stock    =     576   !  frequency of creation of a restart file (modulo referenced to 1) 
    41    nn_write    =      12   !  frequency of write in the output file   (modulo referenced to nit000) 
     39   nn_istate   =       1   !  output the initial state (1) or not (0) 
     40   nn_stock    =     2880  !  frequency of creation of a restart file (modulo referenced to 1) 
     41   nn_write    =     144   !  frequency of write in the output file   (modulo referenced to nit000)  
    4242   ln_dimgnnn  = .false.   !  DIMG file format: 1 file for all processors (F) or by processor (T) 
    4343   ln_mskland  = .false.   !  mask land points in NetCDF outputs (costly: + ~15%) 
     
    6565&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate 
    6666!----------------------------------------------------------------------- 
    67    rn_sbot_min =   10.     !  minimum depth of s-bottom surface (>0) (m) 
    68    rn_sbot_max = 7000.     !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
     67   ln_s_sh94   = .true.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
     68   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
     69   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch 
     70                           !  stretching coefficients for all functions 
     71   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m) 
     72   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
     73   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates 
     74                        !!!!!!!  Envelop bathymetry 
     75   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1) 
     76                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.) 
    6977   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20) 
    70    rn_thetb    =    1.00   !  bottom control parameter  (0<=thetb<= 1) 
    71    rn_rmax     =    0.30   !  maximum cut-off r-value allowed (0<r_max<1) 
    72    ln_s_sigma  = .true.    !  hybrid s-sigma coordinates 
    73    rn_bb       =    0.8    !  stretching with s-sigma 
    74    rn_hc       =  150.0    !  critical depth with s-sigma  
    75 / 
     78   rn_bb       =    0.8    !  stretching with SH94 s-sigma    
     79                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.) 
     80   rn_alpha    =    4.4    !  stretching with SF12 s-sigma 
     81   rn_efold    =    0.0    !  efold length scale for transition to stretched coord 
     82   rn_zs       =    1.0    !  depth of surface grid box 
     83                           !  bottom cell depth (Zb) is a linear function of water depth Zb = H*a + b 
     84   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb 
     85   rn_zb_b     =   -0.2    !  offset for calculating Zb 
     86                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above] 
     87   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)  
     88/ 
     89 
    7690!----------------------------------------------------------------------- 
    7791&namdom        !   space and time domain (bathymetry, mesh, timestep) 
     
    7993   nn_bathy    =    1      !  compute (=0) or read (=1) the bathymetry file 
    8094   nn_closea    =   0      !  remove (=0) or keep (=1) closed seas and lakes (ORCA) 
    81    nn_msh      =    0      !  create (=1) a mesh file or not (=0) 
     95   nn_msh      =    1      !  create (=1) a mesh file or not (=0) 
    8296   rn_hmin     =   -3.     !  min depth of the ocean (>0) or min number of ocean level (<0) 
    8397   rn_e3zps_min=   20.     !  partial step thickness is set larger than the minimum of 
    8498   rn_e3zps_rat=    0.1    !  rn_e3zps_min and rn_e3zps_rat*e3t, with 0<rn_e3zps_rat<1 
    8599                           ! 
    86    rn_rdt      =  150.     !  time step for the dynamics (and tracer if nn_acc=0) 
     100   rn_rdt      =  300.     !  time step for the dynamics (and tracer if nn_acc=0) 
    87101   nn_baro     =   30      !  number of barotropic time step            ("key_dynspg_ts") 
    88102   rn_atfp     =    0.1    !  asselin time filter parameter 
     
    102116   ! 
    103117   cn_dir        = './'     !  root directory for the location of the runoff files 
    104    ln_tsd_init   = .false.  !  Initialisation of ocean T & S with T &S input data (T) or not (F) 
    105    ln_tsd_tradmp = .false.  !  damping of ocean T & S toward T &S input data (T) or not (F) 
     118   ln_tsd_init   = .false.   !  Initialisation of ocean T & S with T &S input data (T) or not (F) 
     119   ln_tsd_tradmp = .false.   !  damping of ocean T & S toward T &S input data (T) or not (F) 
    106120/ 
    107121!!====================================================================== 
     
    302316                           !  or to SSS only (=1) or no damping term (=0) 
    303317   rn_dqdt     =   -40.    !  magnitude of the retroaction on temperature   [W/m2/K] 
    304    rn_deds     =  -166.67  !  magnitude of the damping on salinity   [mm/day] 
     318   rn_deds     =  -27.7    !  magnitude of the damping on salinity   [mm/day] 
    305319   ln_sssr_bnd =   .true.  !  flag to bound erp term (associated with nn_sssr=2) 
    306320   rn_sssr_bnd =   4.e0    !  ABS(Max/Min) value of the damping erp term [mm/day] 
     
    596610   ln_hpg_zco  = .false.   !  z-coordinate - full steps                    
    597611   ln_hpg_zps  = .false.   !  z-coordinate - partial steps (interpolation) 
    598    ln_hpg_sco  = .true.    !  s-coordinate (standard jacobian formulation) 
     612   ln_hpg_sco  = .false.    !  s-coordinate (standard jacobian formulation) 
    599613   ln_hpg_djc  = .false.   !  s-coordinate (Density Jacobian with Cubic polynomial) 
    600    ln_hpg_prj  = .false.   !  s-coordinate (Pressure Jacobian scheme) 
     614   ln_hpg_prj  = .true.   !  s-coordinate (Pressure Jacobian scheme) 
    601615   ln_dynhpg_imp = .false. !  time stepping: semi-implicit time scheme  (T) 
    602616                                 !           centered      time scheme  (F) 
     
    875889                           !  0 < n : debug section number n 
    876890/ 
    877  
    878891!!====================================================================== 
    879892!!            ***  Observation & Assimilation namelists *** 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/CONFIG/GYRE/EXP00/namelist

    r3306 r3507  
    6565&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate 
    6666!----------------------------------------------------------------------- 
    67    rn_sbot_min =  300.     !  minimum depth of s-bottom surface (>0) (m) 
    68    rn_sbot_max = 5250.     !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
    69    rn_theta    =    6.0    !  surface control parameter (0<=rn_theta<=20) 
    70    rn_thetb    =    0.75   !  bottom control parameter  (0<=rn_thetb<= 1) 
    71    rn_rmax     =    0.15   !  maximum cut-off r-value allowed (0<rn_max<1) 
    72    ln_s_sigma  = .false.   !  hybrid s-sigma coordinates 
    73    rn_bb       =    0.8    !  stretching with s-sigma 
    74    rn_hc       =  150.0    !  critical depth with s-sigma  
     67   ln_s_sh94   = .true.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
     68   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
     69   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch 
     70                           !  stretching coefficients for all functions 
     71   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m) 
     72   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
     73   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates 
     74                        !!!!!!!  Envelop bathymetry 
     75   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1) 
     76                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.) 
     77   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20) 
     78   rn_bb       =    0.8    !  stretching with SH94 s-sigma    
     79                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.) 
     80   rn_alpha    =    4.4    !  stretching with SF12 s-sigma 
     81   rn_efold    =    0.0    !  efold length scale for transition to stretched coord 
     82   rn_zs       =    1.0    !  depth of surface grid box 
     83                           !  bottom cell depth (Zb) is a linear function of water depth Zb = H*a + b 
     84   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb 
     85   rn_zb_b     =   -0.2    !  offset for calculating Zb 
     86                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above] 
     87   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)  
    7588/ 
    7689!----------------------------------------------------------------------- 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/CONFIG/ORCA2_LIM/EXP00/1_namelist

    r3306 r3507  
    6666&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate 
    6767!----------------------------------------------------------------------- 
    68    rn_sbot_min =  300.     !  minimum depth of s-bottom surface (>0) (m) 
    69    rn_sbot_max = 5250.     !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
    70    rn_theta    =    6.0    !  surface control parameter (0<=rn_theta<=20) 
    71    rn_thetb    =    0.75   !  bottom control parameter  (0<=rn_thetb<= 1) 
    72    rn_rmax     =    0.15   !  maximum cut-off r-value allowed (0<rn_max<1) 
    73    ln_s_sigma  = .false.   !  hybrid s-sigma coordinates 
    74    rn_bb       =    0.8    !  stretching with s-sigma 
    75    rn_hc       =  150.0    !  critical depth with s-sigma  
     68   ln_s_sh94   = .true.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
     69   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
     70   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch 
     71                           !  stretching coefficients for all functions 
     72   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m) 
     73   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
     74   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates 
     75                        !!!!!!!  Envelop bathymetry 
     76   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1) 
     77                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.) 
     78   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20) 
     79   rn_bb       =    0.8    !  stretching with SH94 s-sigma    
     80                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.) 
     81   rn_alpha    =    4.4    !  stretching with SF12 s-sigma 
     82   rn_efold    =    0.0    !  efold length scale for transition to stretched coord 
     83   rn_zs       =    1.0    !  depth of surface grid box 
     84                           !  bottom cell depth (Zb) is a linear function of water depth Zb = H*a + b 
     85   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb 
     86   rn_zb_b     =   -0.2    !  offset for calculating Zb 
     87                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above] 
     88   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)  
    7689/ 
    7790!----------------------------------------------------------------------- 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/CONFIG/ORCA2_LIM/EXP00/namelist

    r3306 r3507  
    6565&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate 
    6666!----------------------------------------------------------------------- 
    67    rn_sbot_min =  300.     !  minimum depth of s-bottom surface (>0) (m) 
    68    rn_sbot_max = 5250.     !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
    69    rn_theta    =    6.0    !  surface control parameter (0<=rn_theta<=20) 
    70    rn_thetb    =    0.75   !  bottom control parameter  (0<=rn_thetb<= 1) 
    71    rn_rmax     =    0.15   !  maximum cut-off r-value allowed (0<rn_max<1) 
    72    ln_s_sigma  = .false.   !  hybrid s-sigma coordinates 
    73    rn_bb       =    0.8    !  stretching with s-sigma 
    74    rn_hc       =  150.0    !  critical depth with s-sigma  
     67   ln_s_sh94   = .true.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
     68   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
     69   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch 
     70                           !  stretching coefficients for all functions 
     71   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m) 
     72   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
     73   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates 
     74                        !!!!!!!  Envelop bathymetry 
     75   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1) 
     76                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.) 
     77   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20) 
     78   rn_bb       =    0.8    !  stretching with SH94 s-sigma    
     79                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.) 
     80   rn_alpha    =    4.4    !  stretching with SF12 s-sigma 
     81   rn_efold    =    0.0    !  efold length scale for transition to stretched coord 
     82   rn_zs       =    1.0    !  depth of surface grid box 
     83                           !  bottom cell depth (Zb) is a linear function of water depth Zb = H*a + b 
     84   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb 
     85   rn_zb_b     =   -0.2    !  offset for calculating Zb 
     86                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above] 
     87   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)  
    7588/ 
    7689!----------------------------------------------------------------------- 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/CONFIG/ORCA2_OFF_PISCES/EXP00/namelist

    r3306 r3507  
    6565&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate 
    6666!----------------------------------------------------------------------- 
    67    rn_sbot_min =  300.     !  minimum depth of s-bottom surface (>0) (m) 
    68    rn_sbot_max = 5250.     !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
    69    rn_theta    =    6.0    !  surface control parameter (0<=rn_theta<=20) 
    70    rn_thetb    =    0.75   !  bottom control parameter  (0<=rn_thetb<= 1) 
    71    rn_rmax     =    0.15   !  maximum cut-off r-value allowed (0<rn_max<1) 
    72    ln_s_sigma  = .false.   !  hybrid s-sigma coordinates 
    73    rn_bb       =    0.8    !  stretching with s-sigma 
    74    rn_hc       =  150.0    !  critical depth with s-sigma  
     67   ln_s_sh94   = .true.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)| 
     68   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied 
     69   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch 
     70                           !  stretching coefficients for all functions 
     71   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m) 
     72   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m) 
     73   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates 
     74                        !!!!!!!  Envelop bathymetry 
     75   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1) 
     76                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.) 
     77   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20) 
     78   rn_bb       =    0.8    !  stretching with SH94 s-sigma    
     79                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.) 
     80   rn_alpha    =    4.4    !  stretching with SF12 s-sigma 
     81   rn_efold    =    0.0    !  efold length scale for transition to stretched coord 
     82   rn_zs       =    1.0    !  depth of surface grid box 
     83                           !  bottom cell depth (Zb) is a linear function of water depth Zb = H*a + b 
     84   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb 
     85   rn_zb_b     =   -0.2    !  offset for calculating Zb 
     86                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above] 
     87   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)  
    7588/ 
    7689!----------------------------------------------------------------------- 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/NEMO/OPA_SRC/DOM/dom_oce.F90

    r3421 r3507  
    174174   REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) ::   hifv  , hiff     !: interface depth between stretching at  V--F 
    175175   REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) ::   hift  , hifu     !: and quasi-uniform spacing              T--U  points (m) 
     176   REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:) ::   rx1              !: Maximum grid stiffness ratio 
    176177 
    177178   !!---------------------------------------------------------------------- 
     
    294295         &      scosrf(jpi,jpj) , scobot(jpi,jpj) ,     & 
    295296         &      hifv  (jpi,jpj) , hiff  (jpi,jpj) ,     & 
    296          &      hift  (jpi,jpj) , hifu  (jpi,jpj) , STAT=ierr(8) ) 
     297         &      hift  (jpi,jpj) , hifu  (jpi,jpj) , rx1 (jpi,jpj) , STAT=ierr(8) ) 
    297298 
    298299      ALLOCATE( mbathy(jpi,jpj) , bathy(jpi,jpj) ,                     & 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/NEMO/OPA_SRC/DOM/domain.F90

    r3421 r3507  
    3636   USE dyncor_c1d      ! Coriolis term (c1d case)         (cor_c1d routine) 
    3737   USE timing          ! Timing 
     38   USE lbclnk          ! ocean lateral boundary condition (or mpp link) 
    3839 
    3940   IMPLICIT NONE 
     
    8485                             CALL dom_zgr      ! Vertical mesh and bathymetry 
    8586                             CALL dom_msk      ! Masks 
     87      IF( ln_sco )           CALL dom_stiff    ! Maximum stiffness ratio/hydrostatic consistency 
    8688      IF( lk_vvl         )   CALL dom_vvl      ! Vertical variable mesh 
    8789      ! 
     
    322324   END SUBROUTINE dom_ctl 
    323325 
     326   SUBROUTINE dom_stiff 
     327      !!---------------------------------------------------------------------- 
     328      !!                  ***  ROUTINE dom_stiff  *** 
     329      !!                      
     330      !! ** Purpose :   Diagnose maximum grid stiffness/hydrostatic consistency 
     331      !! 
     332      !! ** Method  :   Compute Haney (1991) hydrostatic condition ratio 
     333      !!                Save the maximum in the vertical direction 
     334      !!                (this number is only relevant in s-coordinates) 
     335      !! 
     336      !!                Haney, R. L., 1991: On the pressure gradient force 
     337      !!                over steep topography in sigma coordinate ocean models.  
     338      !!                J. Phys. Oceanogr., 21, 610???619. 
     339      !!---------------------------------------------------------------------- 
     340      INTEGER  ::   ji, jj, jk  
     341      REAL(wp) ::   zrxmax 
     342      REAL(wp), DIMENSION(4) :: zr1 
     343      !!---------------------------------------------------------------------- 
     344      rx1(:,:) = 0.e0 
     345      zrxmax   = 0.e0 
     346      zr1(:)   = 0.e0 
     347       
     348      DO ji = 2, jpim1 
     349         DO jj = 2, jpjm1 
     350            DO jk = 1, jpkm1 
     351               zr1(1) = umask(ji-1,jj  ,jk) *abs( (gdepw(ji  ,jj  ,jk  )-gdepw(ji-1,jj  ,jk  )  &  
     352                    &                         +gdepw(ji  ,jj  ,jk+1)-gdepw(ji-1,jj  ,jk+1)) & 
     353                    &                        /(gdepw(ji  ,jj  ,jk  )+gdepw(ji-1,jj  ,jk  )  & 
     354                    &                         -gdepw(ji  ,jj  ,jk+1)-gdepw(ji-1,jj  ,jk+1) + rsmall) ) 
     355               zr1(2) = umask(ji  ,jj  ,jk) *abs( (gdepw(ji+1,jj  ,jk  )-gdepw(ji  ,jj  ,jk  )  & 
     356                    &                         +gdepw(ji+1,jj  ,jk+1)-gdepw(ji  ,jj  ,jk+1)) & 
     357                    &                        /(gdepw(ji+1,jj  ,jk  )+gdepw(ji  ,jj  ,jk  )  & 
     358                    &                         -gdepw(ji+1,jj  ,jk+1)-gdepw(ji  ,jj  ,jk+1) + rsmall) ) 
     359               zr1(3) = vmask(ji  ,jj  ,jk) *abs( (gdepw(ji  ,jj+1,jk  )-gdepw(ji  ,jj  ,jk  )  & 
     360                    &                         +gdepw(ji  ,jj+1,jk+1)-gdepw(ji  ,jj  ,jk+1)) & 
     361                    &                        /(gdepw(ji  ,jj+1,jk  )+gdepw(ji  ,jj  ,jk  )  & 
     362                    &                         -gdepw(ji  ,jj+1,jk+1)-gdepw(ji  ,jj  ,jk+1) + rsmall) ) 
     363               zr1(4) = vmask(ji  ,jj-1,jk) *abs( (gdepw(ji  ,jj  ,jk  )-gdepw(ji  ,jj-1,jk  )  & 
     364                    &                         +gdepw(ji  ,jj  ,jk+1)-gdepw(ji  ,jj-1,jk+1)) & 
     365                    &                        /(gdepw(ji  ,jj  ,jk  )+gdepw(ji  ,jj-1,jk  )  & 
     366                    &                         -gdepw(ji,  jj  ,jk+1)-gdepw(ji  ,jj-1,jk+1) + rsmall) ) 
     367               zrxmax = MAXVAL(zr1(1:4)) 
     368               rx1(ji,jj) = MAX(rx1(ji,jj), zrxmax) 
     369            END DO 
     370         END DO 
     371      END DO 
     372 
     373      CALL lbc_lnk( rx1, 'T', 1. ) 
     374 
     375      zrxmax = MAXVAL(rx1) 
     376 
     377      IF( lk_mpp )   CALL mpp_max( zrxmax ) ! max over the global domain 
     378 
     379      IF(lwp) THEN 
     380         WRITE(numout,*) 
     381         WRITE(numout,*) 'dom_stiff : maximum grid stiffness ratio: ', zrxmax 
     382         WRITE(numout,*) '~~~~~~~~~' 
     383      ENDIF 
     384 
     385   END SUBROUTINE dom_stiff 
     386 
     387 
     388 
    324389   !!====================================================================== 
    325390END MODULE domain 
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/NEMO/OPA_SRC/DOM/domwri.F90

    r3453 r3507  
    172172             
    173173      IF( ln_sco ) THEN                                         ! s-coordinate 
    174          CALL iom_rstput( 0, 0, inum4, 'hbatt', hbatt )         !    ! depth 
    175          CALL iom_rstput( 0, 0, inum4, 'hbatu', hbatu )  
     174         CALL iom_rstput( 0, 0, inum4, 'hbatt', hbatt ) 
     175         CALL iom_rstput( 0, 0, inum4, 'hbatu', hbatu ) 
    176176         CALL iom_rstput( 0, 0, inum4, 'hbatv', hbatv ) 
    177177         CALL iom_rstput( 0, 0, inum4, 'hbatf', hbatf ) 
     
    187187         CALL iom_rstput( 0, 0, inum4, 'e3v', e3v ) 
    188188         CALL iom_rstput( 0, 0, inum4, 'e3w', e3w ) 
     189         CALL iom_rstput( 0, 0, inum4, 'rx1', rx1 )             !    ! Max. grid stiffness ratio 
    189190         ! 
    190191         CALL iom_rstput( 0, 0, inum4, 'gdept' , gdept )    !    ! stretched system 
    191          CALL iom_rstput( 0, 0, inum4, 'gdepw' , gdepw )  
     192         CALL iom_rstput( 0, 0, inum4, 'gdepw' , gdepw ) 
    192193      ENDIF 
    193194       
  • branches/2012/dev_r3435_UKMO7_SCOORDS/NEMOGCM/NEMO/OPA_SRC/DOM/domzgr.F90

    r3453 r3507  
    17271727      !! ** Purpose :   stretch the s-coordinate system 
    17281728      !! 
    1729       !! ** Method  :   s-coordinate stretch using the Siddorn and Furner 2012? 
    1730       !!                mixed S/sigma/Z coordinate 
    1731       !! 
     1729      !! ** Method  :   s-coordinate stretch  
    17321730      !! 
    17331731      !! Reference : Madec, Lott, Delecluse and Crepon, 1996. JPO, 26, 1393-1408. 
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