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1\documentclass[../main/NEMO_manual]{subfiles}
2
3\begin{document}
4
5\chapter{A brief guide to the DOMAINcfg tool}
6\label{apdx:DOMCFG}
7
8\chaptertoc
9
10\paragraph{Changes record} ~\\
11
12{\footnotesize
13  \begin{tabularx}{\textwidth}{l||X|X}
14    Release     & Author(s)            & Modifications                                                 \\
15    \hline
16    {\em  next} & {\em Pierre Mathiot} & {\em Add ice shelf and closed sea option description        } \\
17    {\em   4.0} & {\em  Andrew Coward} & {\em Creation from materials removed from \autoref{chap:DOM}
18                                              that are still relevant to the DOMAINcfg tool
19                                              when setting up new domains                            }
20  \end{tabularx}
21}
22
23\clearpage
24
25This appendix briefly describes some of the options available in the
26\forcode{DOMAINcfg} tool mentioned in \autoref{chap:DOM}.
27
28This tool will evolve into an independent utility with its own documentation but its
29current manifestation is mostly a wrapper for \NEMO\ \forcode{DOM} modules more aligned to
30those in the previous versions of \NEMO. These versions allowed the user to define some
31horizontal and vertical grids through additional namelist parameters. Explanations of
32these parameters are retained here for reference pending better documentation for
33\forcode{DOMAINcfg}. Please note that the namelist blocks named in this appendix refer to
34those read by \forcode{DOMAINcfg} via its own \forcode{namelist_ref} and
35\forcode{namelist_cfg} files. Although, due to their origins, these namelists share names
36with those used by \NEMO, they are not interchangeable and should be considered independent
37of those described elsewhere in this manual.
38
39%% =================================================================================================
40\section{Choice of horizontal grid}
41\label{sec:DOMCFG_hor}
42
43\begin{listing}
44%  \nlst{namdom_domcfg}
45  \begin{forlines}
46!-----------------------------------------------------------------------
47&namdom        !   space and time domain (bathymetry, mesh, timestep)
48!-----------------------------------------------------------------------
49   nn_bathy    =    1      !  compute analyticaly (=0) or read (=1) the bathymetry file
50                           !  or compute (2) from external bathymetry
51   nn_interp   =    1                          ! type of interpolation (nn_bathy =2)                       
52   cn_topo     =  'bathymetry_ORCA12_V3.3.nc'  ! external topo file (nn_bathy =2)
53   cn_bath     =  'Bathymetry'                 ! topo name in file  (nn_bathy =2)
54   cn_lon      =  'nav_lon'                    ! lon  name in file  (nn_bathy =2)
55   cn_lat      =  'nav_lat'                    ! lat  name in file  (nn_bathy =2)
56   rn_scale    = 1
57   rn_bathy    =    0.     !  value of the bathymetry. if (=0) bottom flat at jpkm1
58   jphgr_msh   =       0               !  type of horizontal mesh
59   ppglam0     =  999999.0             !  longitude of first raw and column T-point (jphgr_msh = 1)
60   ppgphi0     =  999999.0             ! latitude  of first raw and column T-point (jphgr_msh = 1)
61   ppe1_deg    =  999999.0             !  zonal      grid-spacing (degrees)
62   ppe2_deg    =  999999.0             !  meridional grid-spacing (degrees)
63   ppe1_m      =  999999.0             !  zonal      grid-spacing (degrees)
64   ppe2_m      =  999999.0             !  meridional grid-spacing (degrees)
65   ppsur       =   -4762.96143546300   !  ORCA r4, r2 and r05 coefficients
66   ppa0        =     255.58049070440   ! (default coefficients)
67   ppa1        =     245.58132232490   !
68   ppkth       =      21.43336197938   !
69   ppacr       =       3.0             !
70   ppdzmin     =  999999.              !  Minimum vertical spacing
71   pphmax      =  999999.              !  Maximum depth
72   ldbletanh   =  .FALSE.              !  Use/do not use double tanf function for vertical coordinates
73   ppa2        =  999999.              !  Double tanh function parameters
74   ppkth2      =  999999.              !
75   ppacr2      =  999999.              !
76/
77  \end{forlines}
78  \caption{\forcode{&namdom_domcfg}}
79  \label{lst:namdom_domcfg}
80\end{listing}
81
82The user has three options available in defining a horizontal grid, which involve the
83namelist variable \np{jphgr_mesh}{jphgr\_mesh} of the \nam{dom}{dom} (\texttt{DOMAINcfg} variant only)
84namelist.
85
86\begin{description}
87 \item [{\np{jphgr_mesh}{jphgr\_mesh}=0}]  The most general curvilinear orthogonal grids.
88  The coordinates and their first derivatives with respect to $i$ and $j$ are provided
89  in a input file (\textit{coordinates.nc}), read in \rou{hgr\_read} subroutine of the domhgr module.
90  This is now the only option available within \NEMO\ itself from v4.0 onwards.
91\item [{\np{jphgr_mesh}{jphgr\_mesh}=1 to 5}] A few simple analytical grids are provided (see below).
92  For other analytical grids, the \mdl{domhgr} module (\texttt{DOMAINcfg} variant) must be
93  modified by the user. In most cases, modifying the \mdl{usrdef\_hgr} module of \NEMO\ is
94  a better alternative since this is designed to allow simple analytical domains to be
95  configured and used without the need for external data files.
96\end{description}
97
98There are two simple cases of geographical grids on the sphere. With
99\np{jphgr_mesh}{jphgr\_mesh}=1, the grid (expressed in degrees) is regular in space,
100with grid sizes specified by parameters \np{ppe1_deg}{ppe1\_deg} and \np{ppe2_deg}{ppe2\_deg},
101respectively. Such a geographical grid can be very anisotropic at high latitudes
102because of the convergence of meridians (the zonal scale factors $e_1$
103become much smaller than the meridional scale factors $e_2$). The Mercator
104grid (\np{jphgr_mesh}{jphgr\_mesh}=4) avoids this anisotropy by refining the meridional scale
105factors in the same way as the zonal ones. In this case, meridional scale factors
106and latitudes are calculated analytically using the formulae appropriate for
107a Mercator projection, based on \np{ppe1_deg}{ppe1\_deg} which is a reference grid spacing
108at the equator (this applies even when the geographical equator is situated outside
109the model domain).
110
111In these two cases (\np{jphgr_mesh}{jphgr\_mesh}=1 or 4), the grid position is defined by the
112longitude and latitude of the south-westernmost point (\np{ppglamt0}
113and \np{ppgphi0}{ppgphi0}). Note that for the Mercator grid the user need only provide
114an approximate starting latitude: the real latitude will be recalculated analytically,
115in order to ensure that the equator corresponds to line passing through $t$-
116and $u$-points.
117
118Rectangular grids ignoring the spherical geometry are defined with
119\np{jphgr_mesh}{jphgr\_mesh} = 2, 3, 5. The domain is either an $f$-plane (\np{jphgr_mesh}{jphgr\_mesh} = 2,
120Coriolis factor is constant) or a beta-plane (\np{jphgr_mesh}{jphgr\_mesh} = 3, the Coriolis factor
121is linear in the $j$-direction). The grid size is uniform in meter in each direction,
122and given by the parameters \np{ppe1_m}{ppe1\_m} and \np{ppe2_m}{ppe2\_m} respectively.
123The zonal grid coordinate (\textit{glam} arrays) is in kilometers, starting at zero
124with the first $t$-point. The meridional coordinate (gphi. arrays) is in kilometers,
125and the second $t$-point corresponds to coordinate $gphit=0$. The input
126variable \np{ppglam0}{ppglam0} is ignored. \np{ppgphi0}{ppgphi0} is used to set the reference
127latitude for computation of the Coriolis parameter. In the case of the beta plane,
128\np{ppgphi0}{ppgphi0} corresponds to the center of the domain. Finally, the special case
129\np{jphgr_mesh}{jphgr\_mesh}=5 corresponds to a beta plane in a rotated domain for the
130GYRE configuration, representing a classical mid-latitude double gyre system.
131The rotation allows us to maximize the jet length relative to the gyre areas
132(and the number of grid points).
133
134%% =================================================================================================
135\section{Vertical grid}
136\label{sec:DOMCFG_vert}
137
138%% =================================================================================================
139\subsection{Vertical reference coordinate}
140\label{sec:DOMCFG_zref}
141
142\begin{figure}[!tb]
143  \centering
144  \includegraphics[width=0.66\textwidth]{DOMCFG_zgr}
145  \caption[DOMAINcfg: default vertical mesh for ORCA2]{
146    Default vertical mesh for ORCA2: 30 ocean levels (L30).
147    Vertical level functions for (a) T-point depth and (b) the associated scale factor for
148    the $z$-coordinate case.}
149  \label{fig:DOMCFG_zgr}
150\end{figure}
151
152The reference coordinate transformation $z_0(k)$ defines the arrays $gdept_0$ and
153$gdepw_0$ for $t$- and $w$-points, respectively. See \autoref{sec:DOMCFG_sco} for the
154S-coordinate options.  As indicated on \autoref{fig:DOM_index_vert} \texttt{jpk} is the number of
155$w$-levels.  $gdepw_0(1)$ is the ocean surface.  There are at most \texttt{jpk}-1 $t$-points
156inside the ocean, the additional $t$-point at $jk = jpk$ is below the sea floor and is not
157used.  The vertical location of $w$- and $t$-levels is defined from the analytic
158expression of the depth $z_0(k)$ whose analytical derivative with respect to $k$ provides
159the vertical scale factors.  The user must provide the analytical expression of both $z_0$
160and its first derivative with respect to $k$.  This is done in routine \mdl{domzgr}
161through statement functions, using parameters provided in the \nam{dom}{dom} namelist
162(\texttt{DOMAINcfg} variant).
163
164It is possible to define a simple regular vertical grid by giving zero stretching
165(\np[=0]{ppacr}{ppacr}).  In that case, the parameters \texttt{jpk} (number of $w$-levels)
166and \np{pphmax}{pphmax} (total ocean depth in meters) fully define the grid.
167
168For climate-related studies it is often desirable to concentrate the vertical resolution
169near the ocean surface.  The following function is proposed as a standard for a
170$z$-coordinate (with either full or partial steps):
171\begin{gather}
172  \label{eq:DOMCFG_zgr_ana_1}
173    z_0  (k) = h_{sur} - h_0 \; k - \; h_1 \; \log  \big[ \cosh ((k - h_{th}) / h_{cr}) \big] \\
174    e_3^0(k) = \lt|    - h_0      -    h_1 \; \tanh \big[        (k - h_{th}) / h_{cr}  \big] \rt|
175\end{gather}
176
177where $k = 1$ to \texttt{jpk} for $w$-levels and $k = 1$ to $k = 1$ for $t-$levels.  Such an
178expression allows us to define a nearly uniform vertical location of levels at the ocean
179top and bottom with a smooth hyperbolic tangent transition in between (\autoref{fig:DOMCFG_zgr}).
180
181A double hyperbolic tangent version (\np[=.true.]{ldbletanh}{ldbletanh}) is also available
182which permits finer control and is used, typically, to obtain a well resolved upper ocean
183without compromising on resolution at depth using a moderate number of levels.
184
185\begin{gather}
186  \label{eq:DOMCFG_zgr_ana_1b}
187    \begin{split}
188    z_0  (k) = h_{sur} - h_0 \; k &- \; h_1 \; \log  \big[ \cosh ((k - h_{th}) / h_{cr}) \big] \\
189                             \;   &- \; h2_1 \; \log  \big[ \cosh ((k - h2_{th}) / h2_{cr}) \big]
190    \end{split}
191\end{gather}
192\begin{gather}
193    \begin{split}
194    e_3^0(k) = \big|    - h_0    &-   h_1 \; \tanh \big[       (k - h_{th})  / h_{cr}   \big]  \\
195                                 &-  h2_1 \; \tanh \big[       (k - h2_{th}) / h2_{cr}  \big] \big|
196    \end{split}
197\end{gather}
198
199If the ice shelf cavities are opened (\np[=.true.]{ln_isfcav}{ln\_isfcav}), the definition
200of $z_0$ is the same.  However, definition of $e_3^0$ at $t$- and $w$-points is
201respectively changed to:
202\begin{equation}
203  \label{eq:DOMCFG_zgr_ana_2}
204  \begin{split}
205    e_3^T(k) &= z_W (k + 1) - z_W (k    ) \\
206    e_3^W(k) &= z_T (k    ) - z_T (k - 1)
207  \end{split}
208\end{equation}
209
210This formulation decreases the self-generated circulation into the ice shelf cavity
211(which can, in extreme case, leads to numerical instability). This is now the recommended formulation for all configurations using v4.0 onwards. The analytical derivation of thicknesses is maintained for backwards compatibility.
212
213The most used vertical grid for ORCA2 has $10~m$ ($500~m$) resolution in the surface
214(bottom) layers and a depth which varies from 0 at the sea surface to a minimum of
215$-5000~m$.  This leads to the following conditions:
216
217\begin{equation}
218  \label{eq:DOMCFG_zgr_coef}
219  \begin{array}{ll}
220    e_3 (1   + 1/2) =  10. & z(1  ) =     0. \\
221    e_3 (jpk - 1/2) = 500. & z(jpk) = -5000.
222  \end{array}
223\end{equation}
224
225With the choice of the stretching $h_{cr} = 3$ and the number of levels \texttt{jpk}~$= 31$,
226the four coefficients $h_{sur}$, $h_0$, $h_1$, and $h_{th}$ in
227\autoref{eq:DOMCFG_zgr_ana_2} have been determined such that \autoref{eq:DOMCFG_zgr_coef}
228is satisfied, through an optimisation procedure using a bisection method.
229For the first standard ORCA2 vertical grid this led to the following values:
230$h_{sur} = 4762.96$, $h_0 = 255.58, h_1 = 245.5813$, and $h_{th} = 21.43336$.
231The resulting depths and scale factors as a function of the model levels are shown in
232\autoref{fig:DOMCFG_zgr} and given in \autoref{tab:DOMCFG_orca_zgr}.
233Those values correspond to the parameters \np{ppsur}{ppsur}, \np{ppa0}{ppa0}, \np{ppa1}{ppa1}, \np{ppkth}{ppkth} in \nam{cfg}{cfg} namelist.
234
235Rather than entering parameters $h_{sur}$, $h_0$, and $h_1$ directly, it is possible to
236recalculate them.  In that case the user sets \np{ppsur}{ppsur}~$=$~\np{ppa0}{ppa0}~$=$~\np{ppa1}{ppa1}~$=
237999999$., in \nam{cfg}{cfg} namelist, and specifies instead the four following parameters:
238\begin{itemize}
239\item \np{ppacr}{ppacr}~$= h_{cr}$: stretching factor (nondimensional).
240  The larger \np{ppacr}{ppacr}, the smaller the stretching.
241  Values from $3$ to $10$ are usual.
242\item \np{ppkth}{ppkth}~$= h_{th}$: is approximately the model level at which maximum stretching occurs
243  (nondimensional, usually of order 1/2 or 2/3 of \texttt{jpk})
244\item \np{ppdzmin}{ppdzmin}: minimum thickness for the top layer (in meters).
245\item \np{pphmax}{pphmax}: total depth of the ocean (meters).
246\end{itemize}
247
248As an example, for the $45$ layers used in the DRAKKAR configuration those parameters are:
249\texttt{jpk}~$= 46$, \np{ppacr}{ppacr}~$= 9$, \np{ppkth}{ppkth}~$= 23.563$, \np{ppdzmin}{ppdzmin}~$= 6~m$,
250\np{pphmax}{pphmax}~$= 5750~m$.
251
252\begin{table}
253  \centering
254  \begin{tabular}{c||r|r|r|r}
255    \hline
256    \textbf{LEVEL} & \textbf{gdept\_1d} & \textbf{gdepw\_1d} & \textbf{e3t\_1d } & \textbf{e3w\_1d} \\
257    \hline
258    1              & \textbf{     5.00} &               0.00 & \textbf{   10.00} &            10.00 \\
259    \hline
260    2              & \textbf{    15.00} &              10.00 & \textbf{   10.00} &            10.00 \\
261    \hline
262    3              & \textbf{    25.00} &              20.00 & \textbf{   10.00} &            10.00 \\
263    \hline
264    4              & \textbf{    35.01} &              30.00 & \textbf{   10.01} &            10.00 \\
265    \hline
266    5              & \textbf{    45.01} &              40.01 & \textbf{   10.01} &            10.01 \\
267    \hline
268    6              & \textbf{    55.03} &              50.02 & \textbf{   10.02} &            10.02 \\
269    \hline
270    7              & \textbf{    65.06} &              60.04 & \textbf{   10.04} &            10.03 \\
271    \hline
272    8              & \textbf{    75.13} &              70.09 & \textbf{   10.09} &            10.06 \\
273    \hline
274    9              & \textbf{    85.25} &              80.18 & \textbf{   10.17} &            10.12 \\
275    \hline
276    10             & \textbf{    95.49} &              90.35 & \textbf{   10.33} &            10.24 \\
277    \hline
278    11             & \textbf{   105.97} &             100.69 & \textbf{   10.65} &            10.47 \\
279    \hline
280    12             & \textbf{   116.90} &             111.36 & \textbf{   11.27} &            10.91 \\
281    \hline
282    13             & \textbf{   128.70} &             122.65 & \textbf{   12.47} &            11.77 \\
283    \hline
284    14             & \textbf{   142.20} &             135.16 & \textbf{   14.78} &            13.43 \\
285    \hline
286    15             & \textbf{   158.96} &             150.03 & \textbf{   19.23} &            16.65 \\
287    \hline
288    16             & \textbf{   181.96} &             169.42 & \textbf{   27.66} &            22.78 \\
289    \hline
290    17             & \textbf{   216.65} &             197.37 & \textbf{   43.26} &            34.30 \\
291    \hline
292    18             & \textbf{   272.48} &             241.13 & \textbf{   70.88} &            55.21 \\
293    \hline
294    19             & \textbf{   364.30} &             312.74 & \textbf{  116.11} &            90.99 \\
295    \hline
296    20             & \textbf{   511.53} &             429.72 & \textbf{  181.55} &           146.43 \\
297    \hline
298    21             & \textbf{   732.20} &             611.89 & \textbf{  261.03} &           220.35 \\
299    \hline
300    22             & \textbf{  1033.22} &             872.87 & \textbf{  339.39} &           301.42 \\
301    \hline
302    23             & \textbf{  1405.70} &            1211.59 & \textbf{  402.26} &           373.31 \\
303    \hline
304    24             & \textbf{  1830.89} &            1612.98 & \textbf{  444.87} &           426.00 \\
305    \hline
306    25             & \textbf{  2289.77} &            2057.13 & \textbf{  470.55} &           459.47 \\
307    \hline
308    26             & \textbf{  2768.24} &            2527.22 & \textbf{  484.95} &           478.83 \\
309    \hline
310    27             & \textbf{  3257.48} &            3011.90 & \textbf{  492.70} &           489.44 \\
311    \hline
312    28             & \textbf{  3752.44} &            3504.46 & \textbf{  496.78} &           495.07 \\
313    \hline
314    29             & \textbf{  4250.40} &            4001.16 & \textbf{  498.90} &           498.02 \\
315    \hline
316    30             & \textbf{  4749.91} &            4500.02 & \textbf{  500.00} &           499.54 \\
317    \hline
318    31             & \textbf{  5250.23} &            5000.00 & \textbf{  500.56} &           500.33 \\
319    \hline
320  \end{tabular}
321  \caption[Default vertical mesh in $z$-coordinate for 30 layers ORCA2 configuration]{
322    Default vertical mesh in $z$-coordinate for 30 layers ORCA2 configuration as
323    computed from \autoref{eq:DOMCFG_zgr_ana_2} using
324    the coefficients given in \autoref{eq:DOMCFG_zgr_coef}}
325  \label{tab:DOMCFG_orca_zgr}
326\end{table}
327%%%YY
328%% % -------------------------------------------------------------------------------------------------------------
329%% %        Meter Bathymetry
330%% % -------------------------------------------------------------------------------------------------------------
331%% =================================================================================================
332\subsection{Model bathymetry}
333\label{subsec:DOMCFG_bathy}
334
335Three options are possible for defining the bathymetry, according to the namelist variable
336\np{nn_bathy}{nn\_bathy} (found in \nam{dom}{dom} namelist (\texttt{DOMAINCFG} variant) ):
337\begin{description}
338\item [{\np[=0]{nn_bathy}{nn\_bathy}}]: a flat-bottom domain is defined.
339  The total depth $z_w (jpk)$ is given by the coordinate transformation.
340  The domain can either be a closed basin or a periodic channel depending on the parameter \np{jperio}{jperio}.
341\item [{\np[=-1]{nn_bathy}{nn\_bathy}}]: a domain with a bump of topography one third of the domain width at the central latitude.
342  This is meant for the "EEL-R5" configuration, a periodic or open boundary channel with a seamount.
343\item [{\np[=1]{nn_bathy}{nn\_bathy}}]: read a bathymetry and ice shelf draft (if needed).
344  The \textit{bathy\_meter.nc} file (Netcdf format) provides the ocean depth (positive, in meters) at
345  each grid point of the model grid.
346  The bathymetry is usually built by interpolating a standard bathymetry product (\eg\ ETOPO2) onto
347  the horizontal ocean mesh.
348  Defining the bathymetry also defines the coastline: where the bathymetry is zero,
349  no wet levels are defined (all levels are masked).
350\end{description}
351
352%% =================================================================================================
353\subsection{Choice of vertical grid}
354\label{sec:DOMCFG_vgrd}
355
356After reading the bathymetry, the algorithm for vertical grid definition differs between the different options:
357\begin{description}
358\item [\forcode{ln_zco = .true.}] set a reference coordinate transformation $z_0(k)$, and set $z(i,j,k,t) = z_0(k)$ where $z_0(k)$ is the closest match to the depth at $(i,j)$.
359\item [\forcode{ln_zps = .true.}] set a reference coordinate transformation $z_0(k)$, and calculate the thickness of the deepest level at
360  each $(i,j)$ point using the bathymetry, to obtain the final three-dimensional depth and scale factor arrays.
361\item [\forcode{ln_sco = .true.}] smooth the bathymetry to fulfill the hydrostatic consistency criteria and
362  set the three-dimensional transformation.
363\item [\forcode{s-z and s-zps}] smooth the bathymetry to fulfill the hydrostatic consistency criteria and
364  set the three-dimensional transformation $z(i,j,k)$,
365  and possibly introduce masking of extra land points to better fit the original bathymetry file.
366\end{description}
367
368%% =================================================================================================
369\subsubsection[$Z$-coordinate with uniform thickness levels (\forcode{ln_zco})]{$Z$-coordinate with uniform thickness levels (\protect\np{ln_zco}{ln\_zco})}
370\label{subsec:DOMCFG_zco}
371
372With this option the model topography can be fully described by the reference vertical
373coordinate and a 2D integer field giving the number of wet levels at each location
374(\forcode{bathy_level}). The resulting match to the real topography is likely to be poor
375though (especially with thick, deep levels) and slopes poorly represented. This option is
376rarely used in modern simulations but it can be useful for testing purposes.
377
378%% =================================================================================================
379\subsubsection[$Z$-coordinate with partial step (\forcode{ln_zps})]{$Z$-coordinate with partial step (\protect\np{ln_zps}{ln\_zps})}
380\label{subsec:DOMCFG_zps}
381
382In $z$-coordinate partial step, the depths of the model levels are defined by the
383reference analytical function $z_0(k)$ as described in \autoref{sec:DOMCFG_zref},
384\textit{except} in the bottom layer.  The thickness of the bottom layer is allowed to vary
385as a function of geographical location $(\lambda,\varphi)$ to allow a better
386representation of the bathymetry, especially in the case of small slopes (where the
387bathymetry varies by less than one level thickness from one grid point to the next).  The
388reference layer thicknesses $e_{3t}^0$ have been defined in the absence of bathymetry.
389With partial steps, layers from 1 to \texttt{jpk-2} can have a thickness smaller than
390$e_{3t}(jk)$.
391
392The model deepest layer (\texttt{jpk-1}) is allowed to have either a smaller or larger
393thickness than $e_{3t}(jpk)$: the maximum thickness allowed is $2*e_{3t}(jpk - 1)$.
394
395This has to be kept in mind when specifying values in \nam{dom}{dom} namelist
396(\texttt{DOMAINCFG} variant), such as the maximum depth \np{pphmax}{pphmax} in partial steps.
397
398For example, with \np{pphmax}{pphmax}~$= 5750~m$ for the DRAKKAR 45 layer grid, the maximum ocean
399depth allowed is actually $6000~m$ (the default thickness $e_{3t}(jpk - 1)$ being
400$250~m$).  Two variables in the namdom namelist are used to define the partial step
401vertical grid.  The mimimum water thickness (in meters) allowed for a cell partially
402filled with bathymetry at level jk is the minimum of \np{rn_e3zps_min}{rn\_e3zps\_min} (thickness in
403meters, usually $20~m$) or $e_{3t}(jk)*$\np{rn_e3zps_rat}{rn\_e3zps\_rat} (a fraction, usually 10\%, of
404the default thickness $e_{3t}(jk)$).
405
406%% =================================================================================================
407\subsubsection[$S$-coordinate (\forcode{ln_sco})]{$S$-coordinate (\protect\np{ln_sco}{ln\_sco})}
408\label{sec:DOMCFG_sco}
409
410\begin{listing}
411%  \nlst{namzgr_sco_domcfg}
412  \caption{\forcode{&namzgr_sco_domcfg}}
413  \label{lst:namzgr_sco_domcfg}
414  \begin{forlines}
415!-----------------------------------------------------------------------
416&namzgr_sco    !   s-coordinate or hybrid z-s-coordinate                (default: OFF)
417!-----------------------------------------------------------------------
418   ln_s_sh94   = .false.    !  Song & Haidvogel 1994 hybrid S-sigma   (T)|
419   ln_s_sf12   = .false.   !  Siddorn & Furner 2012 hybrid S-z-sigma (T)| if both are false the NEMO tanh stretching is applied
420   ln_sigcrit  = .false.   !  use sigma coordinates below critical depth (T) or Z coordinates (F) for Siddorn & Furner stretch
421                           !  stretching coefficients for all functions
422   rn_sbot_min =   10.0    !  minimum depth of s-bottom surface (>0) (m)
423   rn_sbot_max = 7000.0    !  maximum depth of s-bottom surface (= ocean depth) (>0) (m)
424   rn_hc       =  150.0    !  critical depth for transition to stretched coordinates
425                        !!!!!!!  Envelop bathymetry
426   rn_rmax     =    0.3    !  maximum cut-off r-value allowed (0<r_max<1)
427                        !!!!!!!  SH94 stretching coefficients  (ln_s_sh94 = .true.)
428   rn_theta    =    6.0    !  surface control parameter (0<=theta<=20)
429   rn_bb       =    0.8    !  stretching with SH94 s-sigma
430                        !!!!!!!  SF12 stretching coefficient  (ln_s_sf12 = .true.)
431   rn_alpha    =    4.4    !  stretching with SF12 s-sigma
432   rn_efold    =    0.0    !  efold length scale for transition to stretched coord
433   rn_zs       =    1.0    !  depth of surface grid box
434                           !  bottom cell depth (Zb) is a linear function of water depth Zb = H*a + b
435   rn_zb_a     =    0.024  !  bathymetry scaling factor for calculating Zb
436   rn_zb_b     =   -0.2    !  offset for calculating Zb
437                        !!!!!!!! Other stretching (not SH94 or SF12) [also uses rn_theta above]
438   rn_thetb    =    1.0    !  bottom control parameter  (0<=thetb<= 1)
439/
440  \end{forlines}
441\end{listing}
442
443Options are defined in \forcode{&zgr_sco} (\texttt{DOMAINcfg} only).
444In $s$-coordinate (\np[=.true.]{ln_sco}{ln\_sco}), the depth and thickness of the model levels are defined from
445the product of a depth field and either a stretching function or its derivative, respectively:
446
447\begin{align*}
448  % \label{eq:DOMCFG_sco_ana}
449  z(k)   &= h(i,j) \; z_0 (k) \\
450  e_3(k) &= h(i,j) \; z_0'(k)
451\end{align*}
452
453where $h$ is the depth of the last $w$-level ($z_0(k)$) defined at the $t$-point location in the horizontal and
454$z_0(k)$ is a function which varies from $0$ at the sea surface to $1$ at the ocean bottom.
455The depth field $h$ is not necessary the ocean depth,
456since a mixed step-like and bottom-following representation of the topography can be used
457(\autoref{fig:DOM_z_zps_s_sps}) or an envelop bathymetry can be defined (\autoref{fig:DOM_z_zps_s_sps}).
458The namelist parameter \np{rn_rmax}{rn\_rmax} determines the slope at which
459the terrain-following coordinate intersects the sea bed and becomes a pseudo z-coordinate.
460The coordinate can also be hybridised by specifying \np{rn_sbot_min}{rn\_sbot\_min} and \np{rn_sbot_max}{rn\_sbot\_max} as
461the minimum and maximum depths at which the terrain-following vertical coordinate is calculated.
462
463Options for stretching the coordinate are provided as examples,
464but care must be taken to ensure that the vertical stretch used is appropriate for the application.
465
466The original default \NEMO\ s-coordinate stretching is available if neither of the other options are specified as true
467(\np[=.false.]{ln_s_SH94}{ln\_s\_SH94} and \np[=.false.]{ln_s_SF12}{ln\_s\_SF12}).
468This uses a depth independent $\tanh$ function for the stretching \citep{madec.delecluse.ea_JPO96}:
469
470\[
471  z = s_{min} + C (s) (H - s_{min})
472  % \label{eq:DOMCFG_SH94_1}
473\]
474
475where $s_{min}$ is the depth at which the $s$-coordinate stretching starts and
476allows a $z$-coordinate to placed on top of the stretched coordinate,
477and $z$ is the depth (negative down from the asea surface).
478\begin{gather*}
479  s = - \frac{k}{n - 1} \quad \text{and} \quad 0 \leq k \leq n - 1
480  % \label{eq:DOMCFG_s}
481 \\
482 \label{eq:DOMCFG_sco_function}
483  C(s) = \frac{[\tanh(\theta \, (s + b)) - \tanh(\theta \, b)]}{2 \; \sinh(\theta)}
484\end{gather*}
485
486A stretching function,
487modified from the commonly used \citet{song.haidvogel_JCP94} stretching (\np[=.true.]{ln_s_SH94}{ln\_s\_SH94}),
488is also available and is more commonly used for shelf seas modelling:
489
490\[
491  C(s) =   (1 - b) \frac{\sinh(\theta s)}{\sinh(\theta)}
492         + b       \frac{\tanh \lt[ \theta \lt(s + \frac{1}{2} \rt) \rt] -   \tanh \lt( \frac{\theta}{2} \rt)}
493                        {                                                  2 \tanh \lt( \frac{\theta}{2} \rt)}
494 \label{eq:DOMCFG_SH94_2}
495\]
496
497\begin{figure}[!ht]
498  \centering
499  \includegraphics[width=0.66\textwidth]{DOMCFG_sco_function}
500  \caption[DOMAINcfg: examples of the stretching function applied to a seamount]{
501    Examples of the stretching function applied to a seamount;
502    from left to right: surface, surface and bottom, and bottom intensified resolutions}
503  \label{fig:DOMCFG_sco_function}
504\end{figure}
505
506where $H_c$ is the critical depth (\np{rn_hc}{rn\_hc}) at which the coordinate transitions from pure $\sigma$ to
507the stretched coordinate, and $\theta$ (\np{rn_theta}{rn\_theta}) and $b$ (\np{rn_bb}{rn\_bb}) are the surface and
508bottom control parameters such that $0 \leqslant \theta \leqslant 20$, and $0 \leqslant b \leqslant 1$.
509$b$ has been designed to allow surface and/or bottom increase of the vertical resolution
510(\autoref{fig:DOMCFG_sco_function}).
511
512Another example has been provided at version 3.5 (\np{ln_s_SF12}{ln\_s\_SF12}) that allows a fixed surface resolution in
513an analytical terrain-following stretching \citet{siddorn.furner_OM13}.
514In this case the a stretching function $\gamma$ is defined such that:
515
516\begin{equation}
517  z = - \gamma h \quad \text{with} \quad 0 \leq \gamma \leq 1
518  % \label{eq:DOMCFG_z}
519\end{equation}
520
521The function is defined with respect to $\sigma$, the unstretched terrain-following coordinate:
522
523\begin{gather*}
524  % \label{eq:DOMCFG_gamma_deriv}
525  \gamma =   A \lt( \sigma   - \frac{1}{2} (\sigma^2     + f (\sigma)) \rt)
526           + B \lt( \sigma^3 - f           (\sigma) \rt) + f (\sigma)       \\
527  \intertext{Where:}
528 \label{eq:DOMCFG_gamma}
529  f(\sigma) = (\alpha + 2) \sigma^{\alpha + 1} - (\alpha + 1) \sigma^{\alpha + 2}
530  \quad \text{and} \quad \sigma = \frac{k}{n - 1}
531\end{gather*}
532
533This gives an analytical stretching of $\sigma$ that is solvable in $A$ and $B$ as a function of
534the user prescribed stretching parameter $\alpha$ (\np{rn_alpha}{rn\_alpha}) that stretches towards
535the surface ($\alpha > 1.0$) or the bottom ($\alpha < 1.0$) and
536user prescribed surface (\np{rn_zs}{rn\_zs}) and bottom depths.
537The bottom cell depth in this example is given as a function of water depth:
538
539\[
540  % \label{eq:DOMCFG_zb}
541  Z_b = h a + b
542\]
543
544where the namelist parameters \np{rn_zb_a}{rn\_zb\_a} and \np{rn_zb_b}{rn\_zb\_b} are $a$ and $b$ respectively.
545
546\begin{figure}[!ht]
547  \centering
548  \includegraphics[width=0.66\textwidth]{DOMCFG_compare_coordinates_surface}
549  \caption[DOMAINcfg: comparison of $s$- and $z$-coordinate]{
550    A comparison of the \citet{song.haidvogel_JCP94} $S$-coordinate (solid lines),
551    a 50 level $Z$-coordinate (contoured surfaces) and
552    the \citet{siddorn.furner_OM13} $S$-coordinate (dashed lines) in the surface $100~m$ for
553    a idealised bathymetry that goes from $50~m$ to $5500~m$ depth.
554    For clarity every third coordinate surface is shown.}
555  \label{fig:DOMCFG_fig_compare_coordinates_surface}
556\end{figure}
557 % >>>>>>>>>>>>>>>>>>>>>>>>>>>>
558
559This gives a smooth analytical stretching in computational space that is constrained to
560given specified surface and bottom grid cell thicknesses in real space.
561This is not to be confused with the hybrid schemes that
562superimpose geopotential coordinates on terrain following coordinates thus
563creating a non-analytical vertical coordinate that
564therefore may suffer from large gradients in the vertical resolutions.
565This stretching is less straightforward to implement than the \citet{song.haidvogel_JCP94} stretching,
566but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes.
567
568As with the \citet{song.haidvogel_JCP94} stretching the stretch is only applied at depths greater than
569the critical depth $h_c$.
570In this example two options are available in depths shallower than $h_c$,
571with pure sigma being applied if the \np{ln_sigcrit}{ln\_sigcrit} is true and pure z-coordinates if it is false
572(the z-coordinate being equal to the depths of the stretched coordinate at $h_c$).
573
574Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as
575large slopes lead to hydrostatic consistency.
576A hydrostatic consistency parameter diagnostic following \citet{haney_JPO91} has been implemented,
577and is output as part of the model mesh file at the start of the run.
578
579%% =================================================================================================
580\subsubsection[\zstar- or \sstar-coordinate (\forcode{ln_linssh})]{\zstar- or \sstar-coordinate (\protect\np{ln_linssh}{ln\_linssh})}
581\label{subsec:DOMCFG_zgr_star}
582
583This option is described in the Report by Levier \textit{et al.} (2007), available on the \NEMO\ web site.
584
585\section{Ice shelf cavity definition}
586\label{subsec:zgrisf}
587
588  If the under ice shelf seas are opened (\np{ln_isfcav}{ln\_isfcav}), the depth of the ice shelf/ocean interface has to be include in
589  the \textit{isfdraft\_meter} file (Netcdf format). This file need to include the \textit{isf\_draft} variable.
590  A positive value will mean ice shelf/ocean or ice shelf bedrock interface below the reference 0m ssh.
591  The exact shape of the ice shelf cavity (grounding line position and minimum thickness of the water column under an ice shelf, ...) can be specify in \nam{zgr_isf}{zgr\_isf}.
592
593\begin{listing}
594  \caption{\forcode{&namzgr_isf}}
595  \label{lst:namzgr_isf}
596  \begin{forlines}
597!-----------------------------------------------------------------------
598&namzgr_isf    !   isf cavity geometry definition                       (default: OFF)
599!-----------------------------------------------------------------------
600   rn_isfdep_min    = 10.         ! minimum isf draft tickness (if lower, isf draft set to this value)
601   rn_glhw_min      = 1.e-3       ! minimum water column thickness to define the grounding line
602   rn_isfhw_min     = 10          ! minimum water column thickness in the cavity once the grounding line defined.
603   ln_isfchannel    = .false.     ! remove channel (based on 2d mask build from isfdraft-bathy)
604   ln_isfconnect    = .false.     ! force connection under the ice shelf (based on 2d mask build from isfdraft-bathy)
605      nn_kisfmax       = 999         ! limiter in level on the previous condition. (if change larger than this number, get back to value before we enforce the connection)
606      rn_zisfmax       = 7000.       ! limiter in m     on the previous condition. (if change larger than this number, get back to value before we enforce the connection)
607   ln_isfcheminey   = .false.     ! close cheminey
608   ln_isfsubgl      = .false.     ! remove subglacial lake created by the remapping process
609      rn_isfsubgllon   =    0.0      !  longitude of the seed to determine the open ocean
610      rn_isfsubgllat   =    0.0      !  latitude  of the seed to determine the open ocean
611/
612  \end{forlines}
613\end{listing}
614
615   The options available to define the shape of the under ice shelf cavities are listed in \nam{zgr_isf}{zgr\_isf} (\texttt{DOMAINcfg} only, \autoref{lst:namzgr_isf}).
616
617\subsection{Model ice shelf draft definition}
618\label{subsec:zgrisf_isfd}
619
620First of all, the tool make sure, the ice shelf draft ($h_{isf}$) is sensible and compatible with the bathymetry.
621There are 3 compulsory steps to achieve this:
622
623\begin{description}
624\item{\np{rn_isfdep_min}{rn\_isfdep\_min}:} this is the minimum ice shelf draft. This is to make sure there is no ridiculous thin ice shelf. If \np{rn_isfdep_min}{rn\_isfdep\_min} is smaller than the surface level, \np{rn_isfdep_min}{rn\_isfdep\_min} is set to $e3t\_1d(1)$.
625  Where $h_{isf} < MAX(e3t\_1d(1),rn\_isfdep\_min)$, $h_{isf}$ is set to \np{rn_isfdep_min}{rn\_isfdep\_min}.
626
627\item{\np{rn_glhw_min}{rn\_glhw\_min}:} This parameter is used to define the grounding line position.
628  Where the difference between the bathymetry and the ice shelf draft is smaller than \np{rn_glhw_min}{rn\_glhw\_min}, the cell are grounded (ie masked).
629  This step is needed to take into account possible small mismatch between ice shelf draft value and bathymetry value (sources are coming from different grid, different data processes, rounding error, ...).
630
631\item{\np{rn_isfhw_min}{rn\_isfhw\_min}:} This parameter is the minimum water column thickness in the cavity.
632  Where the water column thickness is lower than \np{rn_isfhw_min}{rn\_isfhw\_min}, the ice shelf draft is adjusted to match this criterion.
633  If for any reason, this adjustement break the minimum ice shelf draft allowed (\np{rn_isfdep_min}{rn\_isfdep\_min}), the cell is masked.
634\end{description}
635
636Once all these adjustements are made, if the water column thickness contains one cell wide channels, these channels can be closed using \np{ln_isfchannel}{ln\_isfchannel}
637 
638\subsection{Model top level definition}
639After the definition of the ice shelf draft, the tool defines the top level.
640The compulsory criterion is that the water column needs at least 2 wet cells in the water column at U- and V-points.
641To do so, if there one cell wide water column, the tools adjust the ice shelf draft to fillful the requierement.\\
642
643The process is the following:
644\begin{description}
645\item{step 1:} The top level is defined in the same way as the bottom level is defined.
646\item{step 2:} The isolated grid point in the bathymetry are filled (as it is done in a domain without ice shelf)
647\item{step 3:} The tools make sure, the top level is above or equal to the bottom level
648\item{step 4:} If the water column at a U- or V- point is one wet cell wide, the ice shelf draft is adjusted. So the actual top cell become fully open and the new
649  top cell thickness is set to the minimum cell thickness allowed (following the same logic as for the bottom partial cell). This step is iterated 4 times to ensure the condition is fullfill along the 4 sides of the cell.
650\end{description}
651
652In case of steep slope and shallow water column, it likely that 2 cells are disconnected (bathymetry above its neigbourging ice shelf draft).
653The option \np{ln_isfconnect}{ln\_isfconnect} allow the tool to force the connection between these 2 cells.
654Some limiters in meter or levels on the digging allowed by the tool are available (respectively, \np{rn_zisfmax}{rn\_zisfmax} or \np{rn_kisfmax}{rn\_kisfmax}).
655This will prevent the formation of subglacial lakes at the expense of long vertical pipe to connect cells at very different levels.
656
657\subsection{Subglacial lakes}
658Despite careful setting of your ice shelf draft and bathymetry input file as well as setting described in \autoref{subsec:zgrisf_isfd}, some situation are unavoidable.
659For exemple if you setup your ice shelf draft and bathymetry to do ocean/ice sheet coupling,
660you may decide to fill the whole antarctic with a bathymetry and an ice shelf draft value (ice/bedrock interface depth when grounded).
661If you do so, the subglacial lakes will show up (Vostock for example). An other possibility is with coarse vertical resolution, some ice shelves could be cut in 2 parts:
662one connected to the main ocean and an other one closed which can be considered as a subglacial sea be the model.\\
663
664The namelist option \np{ln_isfsubgl}{ln\_isfsubgl} allow you to remove theses subglacial lakes.
665This may be useful for esthetical reason or for stability reasons:
666
667\begin{description}
668\item $\bullet$ In a subglacial lakes, in case of very weak circulation (often the case), the only heat flux is the conductive heat flux through the ice sheet.
669  This will lead to constant freezing until water reaches -20C.
670  This is one of the defitiency of the 3 equation melt formulation (for details on this formulation, see: \autoref{sec:isf}).
671\item $\bullet$ In case of coupling with an ice sheet model,
672  the ssh in the subglacial lakes and the main ocean could be very different (ssh initial adjustement for example),
673  and so if for any reason both a connected at some point, the model is likely to fall over.\\
674\end{description}
675
676\section{Closed sea definition}
677\label{sec:clocfg}
678
679\begin{listing}
680  \caption{\forcode{&namclo}}
681  \label{lst:namdom_clo}
682  \begin{forlines}
683!-----------------------------------------------------------------------
684&namclo ! (closed sea : need ln_domclo = .true. in namcfg)
685!-----------------------------------------------------------------------
686   rn_lon_opnsea = -2.0     ! longitude seed of open ocean
687   rn_lat_opnsea = -2.0     ! latitude  seed of open ocean
688   nn_closea = 8           ! number of closed seas ( = 0; only the open_sea mask will be computed)
689   !                name   ! lon_src ! lat_src ! lon_trg ! lat_trg ! river mouth area   ! net evap/precip correction scheme ! radius tgt   ! id trg
690   !                       ! (degree)! (degree)! (degree)! (degree)! local/coast/global ! (glo/rnf/emp)                     !     (m)      !
691   ! North American lakes
692   sn_lake(1) = 'superior' ,  -86.57 ,  47.30  , -66.49  , 50.45   , 'local'            , 'rnf'                             ,   550000.0 , 2   
693   sn_lake(2) = 'michigan' ,  -87.06 ,  42.74  , -66.49  , 50.45   , 'local'            , 'rnf'                             ,   550000.0 , 2   
694   sn_lake(3) = 'huron'    ,  -82.51 ,  44.74  , -66.49  , 50.45   , 'local'            , 'rnf'                             ,   550000.0 , 2   
695   sn_lake(4) = 'erie'     ,  -81.13 ,  42.25  , -66.49  , 50.45   , 'local'            , 'rnf'                             ,   550000.0 , 2   
696   sn_lake(5) = 'ontario'  ,  -77.72 ,  43.62  , -66.49  , 50.45   , 'local'            , 'rnf'                             ,   550000.0 , 2   
697   ! African Lake
698   sn_lake(6) = 'victoria' ,   32.93 ,  -1.08  ,  30.44  , 31.37   , 'coast'            , 'emp'                             ,   100000.0 , 3   
699   ! Asian Lakes
700   sn_lake(7) = 'caspian'  ,   50.0  ,  44.0   ,   0.0   ,  0.0    , 'global'           , 'glo'                             ,        0.0 , 1     
701   sn_lake(8) = 'aral'     ,   60.0  ,  45.0   ,   0.0   ,  0.0    , 'global'           , 'glo'                             ,        0.0 , 1   
702/
703   \end{forlines}
704\end{listing}
705
706The options available to define the closed seas and how closed sea net fresh water input will be redistributed by NEMO are listed in \nam{dom_clo}{dom\_clo} (\texttt{DOMAINcfg} only).
707The individual definition of each closed sea is managed by \np{sn_lake}{sn\_lake}. In this fields the user needs to define:\\
708   \begin{description}
709   \item $\bullet$    the name of the closed sea (print output purposes).
710   \item $\bullet$    the seed location to define the area of the closed sea (if seed on land because not present in this configuration, this closed sea will be ignored).\\
711   \item $\bullet$    the seed location for the target area.
712   \item $\bullet$    the type of target area ('local','coast' or 'global'). See point 6 for definition of these cases.
713   \item $\bullet$    the type of redistribution scheme for the net fresh water flux over the closed sea (as a runoff in a target area, as emp in a target area, as emp globally). For the runoff case, if the net fwf is negative, it will be redistribut globally.
714   \item $\bullet$    the radius of the target area (not used for the 'global' case). So the target defined by a 'local' target area of a radius of 100km, for example, correspond to all the wet points within this radius. The coastal case will return only the coastal point within the specifid radius.
715   \item $\bullet$    the target id. This target id is used to group multiple lakes into the same river ouflow (Great Lakes for example).
716   \end{description}
717
718The closed sea module defines a number of masks in the \textit{domain\_cfg} output:
719   \begin{description}
720   \item[\textit{mask\_opensea}:] a mask of the main ocean without all the closed seas closed. This mask is defined by a flood filling algorithm with an initial seed (localisation defined by \np{rn_lon_opnsea}{rn\_lon\_opnsea} and \np{rn_lat_opnsea}{rn\_lat\_opnsea}).
721   \item[\textit{mask\_csglo}, \textit{mask\_csrnf}, \textit{mask\_csemp}:] a mask of all the closed seas defined in the namelist by \np{sn_lake}{sn\_lake} for each redistribution scheme. The total number of defined closed seas has to be defined in \np{nn_closea}{nn\_closea}.
722   \item[\textit{mask\_csgrpglo}, \textit{mask\_csgrprnf}, \textit{mask\_csgrpemp}:] a mask of all the closed seas and targets grouped by target id for each type of redistribution scheme.
723   \item[\textit{mask\_csundef}:] a mask of all the closed sea not defined in \np{sn_lake}{sn\_lake}. This will allows NEMO to mask them if needed or to inform the user of potential minor issues in its bathymetry.
724   \end{description}
725   
726\subinc{\input{../../global/epilogue}}
727
728\end{document}
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