Index: TOOLS/CPLRESTART/nemo.py
===================================================================
--- TOOLS/CPLRESTART/nemo.py	(revision 3741)
+++ TOOLS/CPLRESTART/nemo.py	(revision 6669)
@@ -1,7 +1,10 @@
-### ===========================================================================
-###
-### Periodicity of ORCA fields
-###
-### ===========================================================================
+# -*- coding: utf-8 -*-
+## ===========================================================================
+##
+##  This software is governed by the CeCILL  license under French law and
+##  abiding by the rules of distribution of free software.  You can  use,
+##  modify and/ or redistribute the software under the terms of the CeCILL
+##  license as circulated by CEA, CNRS and INRIA at the following URL
+##  "http://www.cecill.info".
 ##
 ##  Warning, to install, configure, run, use any of Olivier Marti's
@@ -14,81 +17,2536 @@
 ##  personal.
 ##
+## ===========================================================================
+'''Utilities to plot NEMO ORCA fields,
+
+Handles periodicity and other stuff
+
+- Lots of tests for xarray object
+- Not much tested for numpy objects
+
+Author: olivier.marti@lsce.ipsl.fr
+
 ## SVN information
-__Author__   = "$Author$"
-__Date__     = "$Date$"
-__Revision__ = "$Revision$"
-__Id__       = "$Id$"
-__HeadURL    = "$HeadURL$"
-
-def lbc (ptab, nperio=6, cd_type='T', psgn=1.0) :
-      """
-      ptab      : Input array
-      rank 2 at least : patb[...., lat, lon]
-      nperio    : Type of periodicity
-         1, 4, 6   : Cyclic on i dimension (generaly longitudes)
-         2         : Obsolete (was symmetric condition at southern boundary ?)
-         3, 4      : North fold T-point pivot (legacy ORCA2)
-         5, 6      : North fold F-point pivot (ORCA1, ORCA025, ORCA2 with new grid for paleo)
-      cd_type   : Grid specification : T, U, V or F
-      psgn      : For change of sign for vector components
-      
-      See NEMO documentation for further details
-      """
-      jpi = ptab.shape[-1]
+Author   = "$Author$"
+Date     = "$Date$"
+Revision = "$Revision$"
+Id       = "$Id$"
+HeadURL  = "$HeadURL$"
+'''
+
+import numpy as np
+import xarray as xr
+
+# Tries to import some moldules that are available in all Python installations
+#  and used in only a few specific functions
+try :
+    from sklearn.impute import SimpleImputer
+except ImportError as err :
+    print ( f'===> Warning : Module nemo : Import error of sklearn.impute.SimpleImputer : {err}' )
+    SimpleImputer = None
+
+try :
+    import f90nml
+except ImportError as err :
+    print ( f'===> Warning : Module nemo : Import error of f90nml : {err}' )
+    f90nml = None
+
+# SVN information
+__SVN__ = ({
+    'Author'   : '$Author$',
+    'Date'     : '$Date$',
+    'Revision' : '$Revision$',
+    'Id'       : '$Id$',
+    'HeadURL'  : '$HeadURL$',
+    'SVN_Date' : '$SVN_Date: $',
+    })
+##
     
-      #
-      #> East-West boundary conditions
-      # --------------------------------
-      
-      if nperio in [1, 4, 6] :
+RPI   = np.pi
+RAD   = np.deg2rad (1.0)
+DAR   = np.rad2deg (1.0)
+REPSI = np.finfo (1.0).eps
+
+NPERIO_VALID_RANGE = [0, 1, 4, 4.2, 5, 6, 6.2]
+
+RAAMO    =      12          # Number of months in one year
+RJJHH    =      24          # Number of hours in one day
+RHHMM    =      60          # Number of minutes in one hour
+RMMSS    =      60          # Number of seconds in one minute
+RA       = 6371229.0        # Earth radius                                  [m]
+GRAV     =       9.80665    # Gravity                                       [m/s2]
+RT0      =     273.15       # Freezing point of fresh water                 [Kelvin]
+RAU0     =    1026.0        # Volumic mass of sea water                     [kg/m3]
+SICE     =       6.0        # Salinity of ice (for pisces)                  [psu]
+SOCE     =      34.7        # Salinity of sea (for pisces and isf)          [psu]
+RLEVAP   =       2.5e+6     # Latent heat of evaporation (water)            [J/K]
+VKARMN   =       0.4        # Von Karman constant
+STEFAN   =       5.67e-8    # Stefan-Boltzmann constant                     [W/m2/K4]
+RHOS     =     330.         # Volumic mass of snow                          [kg/m3]
+RHOI     =     917.         # Volumic mass of sea ice                       [kg/m3]
+RHOW     =    1000.         # Volumic mass of freshwater in melt ponds      [kg/m3]
+RCND_I   =       2.034396   # Thermal conductivity of fresh ice             [W/m/K]
+RCPI     =    2067.0        # Specific heat of fresh ice                    [J/kg/K]
+RLSUB    =       2.834e+6   # Pure ice latent heat of sublimation           [J/kg]
+RLFUS    =       0.334e+6   # Latent heat of fusion of fresh ice            [J/kg]
+RTMLT    =       0.054      # Decrease of seawater meltpoint with salinity
+
+RDAY     = RJJHH * RHHMM * RMMSS                # Day length               [s]
+RSIYEA   = 365.25 * RDAY * 2. * RPI / 6.283076  # Sideral year length      [s]
+RSIDAY   = RDAY / (1. + RDAY / RSIYEA)          # Sideral day length       [s]
+OMEGA    = 2. * RPI / RSIDAY                    # Earth rotation parameter [s-1]
+
+## Default names of dimensions
+UDIMS = {'x':'x', 'y':'y', 'z':'olevel', 't':'time_counter'}
+
+## All possibles name of dimensions in Nemo files
+XNAME = [ 'x', 'X', 'X1', 'xx', 'XX',
+              'x_grid_T', 'x_grid_U', 'x_grid_V', 'x_grid_F', 'x_grid_W',
+              'lon', 'nav_lon', 'longitude', 'X1', 'x_c', 'x_f', ]
+YNAME = [ 'y', 'Y', 'Y1', 'yy', 'YY',
+              'y_grid_T', 'y_grid_U', 'y_grid_V', 'y_grid_F', 'y_grid_W',
+              'lat', 'nav_lat', 'latitude' , 'Y1', 'y_c', 'y_f', ]
+ZNAME = [ 'z', 'Z', 'Z1', 'zz', 'ZZ', 'depth', 'tdepth', 'udepth',
+              'vdepth', 'wdepth', 'fdepth', 'deptht', 'depthu',
+              'depthv', 'depthw', 'depthf', 'olevel', 'z_c', 'z_f', ]
+TNAME = [ 't', 'T', 'tt', 'TT', 'time', 'time_counter', 'time_centered', ]
+
+## All possibles name of units of dimensions in Nemo files
+XUNIT = [ 'degrees_east', ]
+YUNIT = [ 'degrees_north', ]
+ZUNIT = [ 'm', 'meter', ]
+TUNIT = [ 'second', 'minute', 'hour', 'day', 'month', 'year', ]
+
+## All possibles size of dimensions in Orca files
+XLENGTH = [ 180, 182, 360, 362, 1440 ]
+YLENGTH = [ 148, 149, 331, 332 ]
+ZLENGTH = [ 31, 75]
+
+## ===========================================================================
+def __mmath__ (ptab, default=None) :
+    '''Determines the type of tab : xarray, numpy or numpy.ma object ?
+
+    Returns type
+    '''
+    mmath = default
+    if isinstance (ptab, xr.core.dataarray.DataArray) :
+        mmath = xr
+    if isinstance (ptab, np.ndarray) :
+        mmath = np
+    if isinstance (ptab, np.ma.MaskType) :
+        mmath = np.ma
+
+    return mmath
+
+def __guess_nperio__ (jpj, jpi, nperio=None, out='nperio') :
+    '''Tries to guess the value of nperio (periodicity parameter.
+
+    See NEMO documentation for details)
+    Inputs
+    jpj    : number of latitudes
+    jpi    : number of longitudes
+    nperio : periodicity parameter
+    '''
+    if nperio is None :
+        nperio = __guess_config__ (jpj, jpi, nperio=None, out=out)
+    return nperio
+
+def __guess_config__ (jpj, jpi, nperio=None, config=None, out='nperio') :
+    '''Tries to guess the value of nperio (periodicity parameter).
+
+    See NEMO documentation for details)
+    Inputs
+    jpj    : number of latitudes
+    jpi    : number of longitudes
+    nperio : periodicity parameter
+    '''
+    print ( jpi, jpj)
+    if nperio is None :
+        ## Values for NEMO version < 4.2
+        if ( (jpj == 149 and jpi == 182) or (jpj is None and jpi == 182) or
+             (jpj == 149 or jpi is None) ) :
+            # ORCA2. We choose legacy orca2.
+            config, nperio, iperio, jperio, nfold, nftype = 'ORCA2.3' , 4, 1, 0, 1, 'T'
+        if ((jpj == 332 and jpi == 362) or (jpj is None and jpi == 362) or
+            (jpj ==  332 and jpi is None) ) : # eORCA1.
+            config, nperio, iperio, jperio, nfold, nftype = 'eORCA1.2', 6, 1, 0, 1, 'F'
+        if jpi == 1442 :  # ORCA025.
+            config, nperio, iperio, jperio, nfold, nftype = 'ORCA025' , 6, 1, 0, 1, 'F'
+        if jpj ==  294 : # ORCA1
+            config, nperio, iperio, jperio, nfold, nftype = 'ORCA1'   , 6, 1, 0, 1, 'F'
+
+        ## Values for NEMO version >= 4.2. No more halo points
+        if  (jpj == 148 and jpi == 180) or (jpj is None and jpi == 180) or \
+            (jpj == 148 and jpi is None) :  # ORCA2. We choose legacy orca2.
+            config, nperio, iperio, jperio, nfold, nftype = 'ORCA2.4' , 4.2, 1, 0, 1, 'F'
+        if  (jpj == 331 and jpi == 360) or (jpj is None and jpi == 360) or \
+            (jpj == 331 and jpi is None) : # eORCA1.
+            config, nperio, iperio, jperio, nfold, nftype = 'eORCA1.4', 6.2, 1, 0, 1, 'F'
+        if jpi == 1440 : # ORCA025.
+            config, nperio, iperio, jperio, nfold, nftype = 'ORCA025' , 6.2, 1, 0, 1, 'F'
+
+        if nperio is None :
+            raise ValueError ('in nemo module : nperio not found, and cannot by guessed')
+
+        if nperio in NPERIO_VALID_RANGE :
+            print ( f'nperio set as {nperio} (deduced from {jpj=} and {jpi=})' )
+        else :
+            raise ValueError ( f'nperio set as {nperio} (deduced from {jpi=} and {jpj=}) : \n'+
+                                'nemo.py is not ready for this value' )
+
+    if out == 'nperio' :
+        return nperio
+    if out == 'config' :
+        return config
+    if out == 'perio'  :
+        return iperio, jperio, nfold, nftype
+    if out in ['full', 'all'] :
+        return {'nperio':nperio, 'iperio':iperio, 'jperio':jperio, 'nfold':nfold, 'nftype':nftype}
+
+def __guess_point__ (ptab) :
+    '''Tries to guess the grid point (periodicity parameter.
+
+    See NEMO documentation for details)
+    For array conforments with xgcm requirements
+
+    Inputs
+         ptab : xarray array
+
+    Credits : who is the original author ?
+    '''
+
+    gp = None
+    mmath = __mmath__ (ptab)
+    if mmath == xr :
+        if ('x_c' in ptab.dims and 'y_c' in ptab.dims ) :
+            gp = 'T'
+        if ('x_f' in ptab.dims and 'y_c' in ptab.dims ) :
+            gp = 'U'
+        if ('x_c' in ptab.dims and 'y_f' in ptab.dims ) :
+            gp = 'V'
+        if ('x_f' in ptab.dims and 'y_f' in ptab.dims ) :
+            gp = 'F'
+        if ('x_c' in ptab.dims and 'y_c' in ptab.dims
+              and 'z_c' in ptab.dims )                :
+            gp = 'T'
+        if ('x_c' in ptab.dims and 'y_c' in ptab.dims
+                and 'z_f' in ptab.dims )                :
+            gp = 'W'
+        if ('x_f' in ptab.dims and 'y_c' in ptab.dims
+                and 'z_f' in ptab.dims )                :
+            gp = 'U'
+        if ('x_c' in ptab.dims and 'y_f' in ptab.dims
+                and 'z_f' in ptab.dims ) :
+            gp = 'V'
+        if ('x_f' in ptab.dims and 'y_f' in ptab.dims
+                and 'z_f' in ptab.dims ) :
+            gp = 'F'
+
+        if gp is None :
+            raise AttributeError ('in nemo module : cd_type not found, and cannot by guessed')
+        print ( f'Grid set as {gp} deduced from dims {ptab.dims}' )
+        return gp
+    else :
+        raise AttributeError  ('in nemo module : cd_type not found, input is not an xarray data')
+
+def get_shape ( ptab ) :
+    '''Get shape of ptab return a string with axes names
+
+    shape may contain X, Y, Z or T
+    Y is missing for a latitudinal slice
+    X is missing for on longitudinal slice
+    etc ...
+    '''
+
+    g_shape = ''
+    if __find_axis__ (ptab, 'x')[0] :
+        g_shape = 'X'
+    if __find_axis__ (ptab, 'y')[0] :
+        g_shape = 'Y' + g_shape
+    if __find_axis__ (ptab, 'z')[0] :
+        g_shape = 'Z' + g_shape
+    if __find_axis__ (ptab, 't')[0] :
+        g_shape = 'T' + g_shape
+    return g_shape
+
+def lbc_diag (nperio) :
+    '''Useful to switch between field with and without halo'''
+    lperio, aperio = nperio, False
+    if nperio == 4.2 :
+        lperio, aperio = 4, True
+    if nperio == 6.2 :
+        lperio, aperio = 6, True
+    return lperio, aperio
+
+def __find_axis__ (ptab, axis='z', back=True) :
+    '''Returns name and name of the requested axis'''
+    mmath = __mmath__ (ptab)
+    ax, ix = None, None
+
+    if axis in XNAME :
+        ax_name, unit_list, length = XNAME, XUNIT, XLENGTH
+    if axis in YNAME :
+        ax_name, unit_list, length = YNAME, YUNIT, YLENGTH
+    if axis in ZNAME :
+        ax_name, unit_list, length = ZNAME, ZUNIT, ZLENGTH
+    if axis in TNAME :
+        ax_name, unit_list, length = TNAME, TUNIT, None
+
+    if mmath == xr :
+        # Try by name
+        for dim in ax_name :
+            if dim in ptab.dims :
+                ix, ax = ptab.dims.index (dim), dim
+
+        # If not found, try by axis attributes
+        if not ix :
+            for i, dim in enumerate (ptab.dims) :
+                if 'axis' in ptab.coords[dim].attrs.keys() :
+                    l_axis = ptab.coords[dim].attrs['axis']
+                    if axis in ax_name and l_axis == 'X' :
+                        ix, ax = (i, dim)
+                    if axis in ax_name and l_axis == 'Y' :
+                        ix, ax = (i, dim)
+                    if axis in ax_name and l_axis == 'Z' :
+                        ix, ax = (i, dim)
+                    if axis in ax_name and l_axis == 'T' :
+                        ix, ax = (i, dim)
+
+        # If not found, try by units
+        if not ix :
+            for i, dim in enumerate (ptab.dims) :
+                if 'units' in ptab.coords[dim].attrs.keys() :
+                    for name in unit_list :
+                        if name in ptab.coords[dim].attrs['units'] :
+                            ix, ax = i, dim
+
+    # If numpy array or dimension not found, try by length
+    if mmath != xr or not ix :
+        if length :
+            l_shape = ptab.shape
+            for nn in np.arange ( len(l_shape) ) :
+                if l_shape[nn] in length :
+                    ix = nn
+
+    if ix and back :
+        ix -= len(ptab.shape)
+
+    return ax, ix
+
+def find_axis ( ptab, axis='z', back=True ) :
+    '''Version of find_axis with no __'''
+    ix, xx = __find_axis__ (ptab, axis, back)
+    return xx, ix
+
+def fixed_lon (plon, center_lon=0.0) :
+    '''Returns corrected longitudes for nicer plots
+
+    lon        : longitudes of the grid. At least 2D.
+    center_lon : center longitude. Default=0.
+
+    Designed by Phil Pelson.
+    See https://gist.github.com/pelson/79cf31ef324774c97ae7
+    '''
+    mmath = __mmath__ (plon)
+
+    f_lon = plon.copy ()
+
+    f_lon = mmath.where (f_lon > center_lon+180., f_lon-360.0, f_lon)
+    f_lon = mmath.where (f_lon < center_lon-180., f_lon+360.0, f_lon)
+
+    for i, start in enumerate (np.argmax (np.abs (np.diff (f_lon, axis=-1)) > 180., axis=-1)) :
+        f_lon [..., i, start+1:] += 360.
+
+    # Special case for eORCA025
+    if f_lon.shape [-1] == 1442 :
+        f_lon [..., -2, :] = f_lon [..., -3, :]
+    if f_lon.shape [-1] == 1440 :
+        f_lon [..., -1, :] = f_lon [..., -2, :]
+
+    if f_lon.min () > center_lon :
+        f_lon += -360.0
+    if f_lon.max () < center_lon :
+        f_lon +=  360.0
+
+    if f_lon.min () < center_lon-360.0 :
+        f_lon +=  360.0
+    if f_lon.max () > center_lon+360.0 :
+        f_lon += -360.0
+
+    return f_lon
+
+def bounds_clolon ( pbounds_lon, plon, rad=False, deg=True) :
+    '''Choose closest to lon0 longitude, adding/substacting 360Â° if needed
+    '''
+
+    if rad :
+        lon_range = 2.0*np.pi
+    if deg :
+        lon_range = 360.0
+    b_clolon = pbounds_lon.copy ()
+
+    b_clolon = xr.where ( b_clolon < plon-lon_range/2.,
+                          b_clolon+lon_range,
+                          b_clolon )
+    b_clolon = xr.where ( b_clolon > plon+lon_range/2.,
+                          b_clolon-lon_range,
+                          b_clolon )
+    return b_clolon
+
+def unify_dims ( dd, x='x', y='y', z='olevel', t='time_counter', verbose=False ) :
+    '''Rename dimensions to unify them between NEMO versions
+    '''
+    for xx in XNAME :
+        if xx in dd.dims and xx != x :
+            if verbose :
+                print ( f"{xx} renamed to {x}" )
+            dd = dd.rename ( {xx:x})
+
+    for yy in YNAME :
+        if yy in dd.dims and yy != y  :
+            if verbose :
+                print ( f"{yy} renamed to {y}" )
+            dd = dd.rename ( {yy:y} )
+
+    for zz in ZNAME :
+        if zz in dd.dims and zz != z :
+            if verbose :
+                print ( f"{zz} renamed to {z}" )
+            dd = dd.rename ( {zz:z} )
+
+    for tt in TNAME  :
+        if tt in dd.dims and tt != t :
+            if verbose :
+                print ( f"{tt} renamed to {t}" )
+            dd = dd.rename ( {tt:t} )
+
+    return dd
+
+
+if SimpleImputer : 
+  def fill_empty (ptab, sval=np.nan, transpose=False) :
+        '''Fill empty values
+
+        Useful when NEMO has run with no wet points options :
+        some parts of the domain, with no ocean points, have no
+        values
+        '''
+        mmath = __mmath__ (ptab)
+
+        imp = SimpleImputer (missing_values=sval, strategy='mean')
+        if transpose :
+            imp.fit (ptab.T)
+            ztab = imp.transform (ptab.T).T
+        else :
+            imp.fit (ptab)
+            ztab = imp.transform (ptab)
+
+        if mmath == xr :
+            ztab = xr.DataArray (ztab, dims=ztab.dims, coords=ztab.coords)
+            ztab.attrs.update (ptab.attrs)
+
+        return ztab
+
+    
+else : 
+    print ("Import error of sklearn.impute.SimpleImputer")
+    def fill_empty (ptab, sval=np.nan, transpose=False) :
+        '''Void version of fill_empy, because module sklearn.impute.SimpleImputer is not available
+
+        fill_empty : 
+          Fill values
+
+          Useful when NEMO has run with no wet points options :
+          some parts of the domain, with no ocean points, have no
+          values
+        '''
+        print ( 'Error : module sklearn.impute.SimpleImputer not found' )
+        print ( 'Can not call fill_empty' )
+        print ( 'Call arguments where : ' )
+        print ( f'{ptab.shape=} {sval=} {transpose=}' )
+  
+def fill_lonlat (plon, plat, sval=-1) :
+    '''Fill longitude/latitude values
+
+    Useful when NEMO has run with no wet points options :
+    some parts of the domain, with no ocean points, have no
+    lon/lat values
+    '''
+    from sklearn.impute import SimpleImputer
+    mmath = __mmath__ (plon)
+
+    imp = SimpleImputer (missing_values=sval, strategy='mean')
+    imp.fit (plon)
+    zlon = imp.transform (plon)
+    imp.fit (plat.T)
+    zlat = imp.transform (plat.T).T
+
+    if mmath == xr :
+        zlon = xr.DataArray (zlon, dims=plon.dims, coords=plon.coords)
+        zlat = xr.DataArray (zlat, dims=plat.dims, coords=plat.coords)
+        zlon.attrs.update (plon.attrs)
+        zlat.attrs.update (plat.attrs)
+
+    zlon = fixed_lon (zlon)
+
+    return zlon, zlat
+
+def fill_bounds_lonlat (pbounds_lon, pbounds_lat, sval=-1) :
+    '''Fill longitude/latitude bounds values
+
+    Useful when NEMO has run with no wet points options :
+    some parts of the domain, with no ocean points, as no
+    lon/lat values
+    '''
+    mmath = __mmath__ (pbounds_lon)
+
+    z_bounds_lon = np.empty ( pbounds_lon.shape )
+    z_bounds_lat = np.empty ( pbounds_lat.shape )
+
+    imp = SimpleImputer (missing_values=sval, strategy='mean')
+
+    for n in np.arange (4) :
+        imp.fit (pbounds_lon[:,:,n])
+        z_bounds_lon[:,:,n] = imp.transform (pbounds_lon[:,:,n])
+        imp.fit (pbounds_lat[:,:,n].T)
+        z_bounds_lat[:,:,n] = imp.transform (pbounds_lat[:,:,n].T).T
+
+    if mmath == xr :
+        z_bounds_lon = xr.DataArray (pbounds_lon, dims=pbounds_lon.dims,
+                                         coords=pbounds_lon.coords)
+        z_bounds_lat = xr.DataArray (pbounds_lat, dims=pbounds_lat.dims,
+                                         coords=pbounds_lat.coords)
+        z_bounds_lon.attrs.update (pbounds_lat.attrs)
+        z_bounds_lat.attrs.update (pbounds_lat.attrs)
+
+    return z_bounds_lon, z_bounds_lat
+
+def jeq (plat) :
+    '''Returns j index of equator in the grid
+
+    lat : latitudes of the grid. At least 2D.
+    '''
+    mmath = __mmath__ (plat)
+    jy = __find_axis__ (plat, 'y')[-1]
+
+    if mmath == xr :
+        jj = int ( np.mean ( np.argmin (np.abs (np.float64 (plat)),
+                                                axis=jy) ) )
+    else :
+        jj = np.argmin (np.abs (np.float64 (plat[...,:, 0])))
+
+    return jj
+
+def lon1d (plon, plat=None) :
+    '''Returns 1D longitude for simple plots.
+
+    plon : longitudes of the grid
+    plat (optionnal) : latitudes of the grid
+    '''
+    mmath = __mmath__ (plon)
+    jpj, jpi  = plon.shape [-2:]
+    if np.max (plat) :
+        je    = jeq (plat)
+        lon0 = plon [..., je, 0].copy()
+        dlon = plon [..., je, 1].copy() - plon [..., je, 0].copy()
+        lon_1d = np.linspace ( start=lon0, stop=lon0+360.+2*dlon, num=jpi )
+    else :
+        lon0 = plon [..., jpj//3, 0].copy()
+        dlon = plon [..., jpj//3, 1].copy() - plon [..., jpj//3, 0].copy()
+        lon_1d = np.linspace ( start=lon0, stop=lon0+360.+2*dlon, num=jpi )
+
+    #start = np.argmax (np.abs (np.diff (lon1D, axis=-1)) > 180.0, axis=-1)
+    #lon1D [..., start+1:] += 360
+
+    if mmath == xr :
+        lon_1d = xr.DataArray( lon_1d, dims=('lon',), coords=(lon_1d,))
+        lon_1d.attrs.update (plon.attrs)
+        lon_1d.attrs['units']         = 'degrees_east'
+        lon_1d.attrs['standard_name'] = 'longitude'
+        lon_1d.attrs['long_name :']   = 'Longitude'
+
+    return lon_1d
+
+def latreg (plat, diff=0.1) :
+    '''Returns maximum j index where gridlines are along latitudes
+    in the northern hemisphere
+
+    lat : latitudes of the grid (2D)
+    diff [optional] : tolerance
+    '''
+    #mmath = __mmath__ (plat)
+    if diff is None :
+        dy = np.float64 (np.mean (np.abs (plat -
+                        np.roll (plat,shift=1,axis=-2, roll_coords=False))))
+        print ( f'{dy=}' )
+        diff = dy/100.
+
+    je     = jeq (plat)
+    jreg   = np.where (plat[...,je:,:].max(axis=-1) -
+                       plat[...,je:,:].min(axis=-1)< diff)[-1][-1] + je
+    lareg  = np.float64 (plat[...,jreg,:].mean(axis=-1))
+
+    return jreg, lareg
+
+def lat1d (plat) :
+    '''Returns 1D latitudes for zonal means and simple plots.
+
+    plat : latitudes of the grid (2D)
+    '''
+    mmath = __mmath__ (plat)
+    iy = __find_axis__ (plat, 'y')[-1]
+    jpj = plat.shape[iy]
+
+    dy     = np.float64 (np.mean (np.abs (plat - np.roll (plat, shift=1,axis=-2))))
+    je     = jeq (plat)
+    lat_eq = np.float64 (plat[...,je,:].mean(axis=-1))
+
+    jreg, lat_reg = latreg (plat)
+    lat_ave = np.mean (plat, axis=-1)
+
+    if np.abs (lat_eq) < dy/100. : # T, U or W grid
+        if jpj-1 > jreg :
+            dys = (90.-lat_reg) / (jpj-jreg-1)*0.5
+        else            :
+            dys = (90.-lat_reg) / 2.0
+        yrange = 90.-dys-lat_reg
+    else                           :  # V or F grid
+        yrange = 90.-lat_reg
+
+    if jpj-1 > jreg :
+        lat_1d = mmath.where (lat_ave<lat_reg,
+                 lat_ave,
+                 lat_reg + yrange * (np.arange(jpj)-jreg)/(jpj-jreg-1) )
+    else :
+        lat_1d = lat_ave
+    lat_1d[-1] = 90.0
+
+    if mmath == xr :
+        lat_1d = xr.DataArray( lat_1d.values, dims=('lat',), coords=(lat_1d,))
+        lat_1d.attrs.update (plat.attrs)
+        lat_1d.attrs ['units']         = 'degrees_north'
+        lat_1d.attrs ['standard_name'] = 'latitude'
+        lat_1d.attrs ['long_name :']   = 'Latitude'
+
+    return lat_1d
+
+def latlon1d (plat, plon) :
+    '''Returns simple latitude and longitude (1D) for simple plots.
+
+    plat, plon : latitudes and longitudes of the grid (2D)
+    '''
+    return lat1d (plat),  lon1d (plon, plat)
+
+def ff (plat) :
+    '''Returns Coriolis factor
+    '''
+    zff   = np.sin (RAD * plat) * OMEGA
+    return zff
+
+def beta (plat) :
+    '''Return Beta factor (derivative of Coriolis factor)
+    '''
+    zbeta = np.cos (RAD * plat) * OMEGA / RA
+    return zbeta
+
+def mask_lonlat (ptab, x0, x1, y0, y1, lon, lat, sval=np.nan) :
+    '''Returns masked values outside a lat/lon box
+    '''
+    mmath = __mmath__ (ptab)
+    if mmath == xr :
+        lon = lon.copy().to_masked_array()
+        lat = lat.copy().to_masked_array()
+
+    mask = np.logical_and (np.logical_and(lat>y0, lat<y1),
+            np.logical_or (np.logical_or (
+                np.logical_and(lon>x0, lon<x1),
+                np.logical_and(lon+360>x0, lon+360<x1)),
+                np.logical_and(lon-360>x0, lon-360<x1)))
+    tab = mmath.where (mask, ptab, sval)
+
+    return tab
+
+def extend (ptab, blon=False, jplus=25, jpi=None, nperio=4) :
+    '''Returns extended field eastward to have better plots,
+    and box average crossing the boundary
+
+    Works only for xarray and numpy data (?)
+    Useful for plotting vertical sections in OCE and ATM.
+
+    ptab : field to extend.
+    blon  : (optional, default=False) : if True, add 360 in the extended
+          parts of the field
+    jpi   : normal longitude dimension of the field. extend does nothing
+          if the actual size of the field != jpi
+          (avoid to extend several times in notebooks)
+    jplus (optional, default=25) : number of points added on
+          the east side of the field
+
+    '''
+    mmath = __mmath__ (ptab)
+
+    if ptab.shape[-1] == 1 :
+        tabex = ptab
+
+    else :
+        if jpi is None :
+            jpi = ptab.shape[-1]
+
+        if blon :
+            xplus = -360.0
+        else   :
+            xplus =    0.0
+
+        if ptab.shape[-1] > jpi :
+            tabex = ptab
+        else :
+            if nperio in [ 0, 4.2 ] :
+                istart, le, la = 0, jpi+1, 0
+            if nperio == 1 :
+                istart, le, la = 0, jpi+1, 0
+            if nperio in [4, 6] : # OPA case with two halo points for periodicity
+                # Perfect, except at the pole that should be masked by lbc_plot
+                istart, le, la = 1, jpi-2, 1
+            if mmath == xr :
+                tabex = np.concatenate (
+                     (ptab.values[..., istart   :istart+le+1    ] + xplus,
+                      ptab.values[..., istart+la:istart+la+jplus]         ),
+                      axis=-1)
+                lon    = ptab.dims[-1]
+                new_coords = []
+                for coord in ptab.dims :
+                    if coord == lon :
+                        new_coords.append ( np.arange( tabex.shape[-1]))
+                    else            :
+                        new_coords.append ( ptab.coords[coord].values)
+                tabex = xr.DataArray ( tabex, dims=ptab.dims,
+                                           coords=new_coords )
+            else :
+                tabex = np.concatenate (
+                    (ptab [..., istart   :istart+le+1    ] + xplus,
+                     ptab [..., istart+la:istart+la+jplus]          ),
+                     axis=-1)
+    return tabex
+
+def orca2reg (dd, lat_name='nav_lat', lon_name='nav_lon',
+                  y_name='y', x_name='x') :
+    '''Assign an ORCA dataset on a regular grid.
+
+    For use in the tropical region.
+    Inputs :
+      ff : xarray dataset
+      lat_name, lon_name : name of latitude and longitude 2D field in ff
+      y_name, x_name     : namex of dimensions in ff
+
+      Returns : xarray dataset with rectangular grid. Incorrect above 20Â°N
+    '''
+    # Compute 1D longitude and latitude
+    (zlat, zlon) = latlon1d ( dd[lat_name], dd[lon_name])
+
+    zdd = dd
+    # Assign lon and lat as dimensions of the dataset
+    if y_name in zdd.dims :
+        zlat = xr.DataArray (zlat, coords=[zlat,], dims=['lat',])
+        zdd  = zdd.rename_dims ({y_name: "lat",}).assign_coords (lat=zlat)
+    if x_name in zdd.dims :
+        zlon = xr.DataArray (zlon, coords=[zlon,], dims=['lon',])
+        zdd  = zdd.rename_dims ({x_name: "lon",}).assign_coords (lon=zlon)
+    # Force dimensions to be in the right order
+    coord_order = ['lat', 'lon']
+    for dim in [ 'depthw', 'depthv', 'depthu', 'deptht', 'depth', 'z',
+                 'time_counter', 'time', 'tbnds',
+                 'bnds', 'axis_nbounds', 'two2', 'two1', 'two', 'four',] :
+        if dim in zdd.dims :
+            coord_order.insert (0, dim)
+
+    zdd = zdd.transpose (*coord_order)
+    return zdd
+
+def lbc_init (ptab, nperio=None) :
+    '''Prepare for all lbc calls
+
+    Set periodicity on input field
+    nperio    : Type of periodicity
+      0       : No periodicity
+      1, 4, 6 : Cyclic on i dimension (generaly longitudes) with 2 points halo
+      2       : Obsolete (was symmetric condition at southern boundary ?)
+      3, 4    : North fold T-point pivot (legacy ORCA2)
+      5, 6    : North fold F-point pivot (ORCA1, ORCA025, ORCA2 with new grid for paleo)
+    cd_type   : Grid specification : T, U, V or F
+
+    See NEMO documentation for further details
+    '''
+    jpi, jpj = None, None
+    ax, ix = __find_axis__ (ptab, 'x')
+    ay, jy = __find_axis__ (ptab, 'y')
+    if ax :
+        jpi = ptab.shape[ix]
+    if ay :
+        jpj = ptab.shape[jy]
+
+    if nperio is None :
+        nperio = __guess_nperio__ (jpj, jpi, nperio)
+
+    if nperio not in NPERIO_VALID_RANGE :
+        raise AttributeError ( f'{nperio=} is not in the valid range {NPERIO_VALID_RANGE}' )
+
+    return jpj, jpi, nperio
+
+def lbc (ptab, nperio=None, cd_type='T', psgn=1.0, nemo_4u_bug=False) :
+    '''Set periodicity on input field
+
+    ptab      : Input array (works for rank 2 at least : ptab[...., lat, lon])
+    nperio    : Type of periodicity
+    cd_type   : Grid specification : T, U, V or F
+    psgn      : For change of sign for vector components (1 for scalars, -1 for vector components)
+
+    See NEMO documentation for further details
+    '''
+    jpi, nperio = lbc_init (ptab, nperio)[1:]
+    ax = __find_axis__ (ptab, 'x')[0]
+    ay = __find_axis__ (ptab, 'y')[0]
+    psgn   = ptab.dtype.type (psgn)
+    mmath  = __mmath__ (ptab)
+
+    if mmath == xr :
+        ztab = ptab.values.copy ()
+    else           :
+        ztab = ptab.copy ()
+
+    if ax :
+        #
+        #> East-West boundary conditions
+        # ------------------------------
+        if nperio in [1, 4, 6] :
+        # ... cyclic
+            ztab [...,  0] = ztab [..., -2]
+            ztab [..., -1] = ztab [...,  1]
+
+        if ay :
+            #
+            #> North-South boundary conditions
+            # --------------------------------
+            if nperio in [3, 4] :  # North fold T-point pivot
+                if cd_type in [ 'T', 'W' ] : # T-, W-point
+                    ztab [..., -1, 1:       ] = psgn * ztab [..., -3, -1:0:-1      ]
+                    ztab [..., -1, 0        ] = psgn * ztab [..., -3, 2            ]
+                    ztab [..., -2, jpi//2:  ] = psgn * ztab [..., -2, jpi//2:0:-1  ]
+
+                if cd_type == 'U' :
+                    ztab [..., -1, 0:-1     ] = psgn * ztab [..., -3, -1:0:-1      ]
+                    ztab [..., -1,  0       ] = psgn * ztab [..., -3,  1           ]
+                    ztab [..., -1, -1       ] = psgn * ztab [..., -3, -2           ]
+
+                    if nemo_4u_bug :
+                        ztab [..., -2, jpi//2+1:-1] = psgn * ztab [..., -2, jpi//2-2:0:-1]
+                        ztab [..., -2, jpi//2-1   ] = psgn * ztab [..., -2, jpi//2       ]
+                    else :
+                        ztab [..., -2, jpi//2-1:-1] = psgn * ztab [..., -2, jpi//2:0:-1]
+
+                if cd_type == 'V' :
+                    ztab [..., -2, 1:       ] = psgn * ztab [..., -3, jpi-1:0:-1   ]
+                    ztab [..., -1, 1:       ] = psgn * ztab [..., -4, -1:0:-1      ]
+                    ztab [..., -1, 0        ] = psgn * ztab [..., -4, 2            ]
+
+                if cd_type == 'F' :
+                    ztab [..., -2, 0:-1     ] = psgn * ztab [..., -3, -1:0:-1      ]
+                    ztab [..., -1, 0:-1     ] = psgn * ztab [..., -4, -1:0:-1      ]
+                    ztab [..., -1,  0       ] = psgn * ztab [..., -4,  1           ]
+                    ztab [..., -1, -1       ] = psgn * ztab [..., -4, -2           ]
+
+            if nperio in [4.2] :  # North fold T-point pivot
+                if cd_type in [ 'T', 'W' ] : # T-, W-point
+                    ztab [..., -1, jpi//2:  ] = psgn * ztab [..., -1, jpi//2:0:-1  ]
+
+                if cd_type == 'U' :
+                    ztab [..., -1, jpi//2-1:-1] = psgn * ztab [..., -1, jpi//2:0:-1]
+
+                if cd_type == 'V' :
+                    ztab [..., -1, 1:       ] = psgn * ztab [..., -2, jpi-1:0:-1   ]
+
+                if cd_type == 'F' :
+                    ztab [..., -1, 0:-1     ] = psgn * ztab [..., -2, -1:0:-1      ]
+
+            if nperio in [5, 6] :            #  North fold F-point pivot
+                if cd_type in ['T', 'W']  :
+                    ztab [..., -1, 0:       ] = psgn * ztab [..., -2, -1::-1       ]
+
+                if cd_type == 'U' :
+                    ztab [..., -1, 0:-1     ] = psgn * ztab [..., -2, -2::-1       ]
+                    ztab [..., -1, -1       ] = psgn * ztab [..., -2, 0            ] # Bug ?
+
+                if cd_type == 'V' :
+                    ztab [..., -1, 0:       ] = psgn * ztab [..., -3, -1::-1       ]
+                    ztab [..., -2, jpi//2:  ] = psgn * ztab [..., -2, jpi//2-1::-1 ]
+
+                if cd_type == 'F' :
+                    ztab [..., -1, 0:-1     ] = psgn * ztab [..., -3, -2::-1       ]
+                    ztab [..., -1, -1       ] = psgn * ztab [..., -3, 0            ]
+                    ztab [..., -2, jpi//2:-1] = psgn * ztab [..., -2, jpi//2-2::-1 ]
+
+            #
+            #> East-West boundary conditions
+            # ------------------------------
+            if nperio in [1, 4, 6] :
+                # ... cyclic
+                ztab [...,  0] = ztab [..., -2]
+                ztab [..., -1] = ztab [...,  1]
+
+    if mmath == xr :
+        ztab = xr.DataArray ( ztab, dims=ptab.dims, coords=ptab.coords )
+        ztab.attrs = ptab.attrs
+
+    return ztab
+
+def lbc_mask (ptab, nperio=None, cd_type='T', sval=np.nan) :
+    '''Mask fields on duplicated points
+
+    ptab      : Input array. Rank 2 at least : ptab [...., lat, lon]
+    nperio    : Type of periodicity
+    cd_type   : Grid specification : T, U, V or F
+
+    See NEMO documentation for further details
+    '''
+    jpi, nperio = lbc_init (ptab, nperio)[1:]
+    ax = __find_axis__ (ptab, 'x')[0]
+    ay = __find_axis__ (ptab, 'y')[0]
+    ztab = ptab.copy ()
+
+    if ax :
+        #
+        #> East-West boundary conditions
+        # ------------------------------
+        if nperio in [1, 4, 6] :
+        # ... cyclic
+            ztab [...,  0] = sval
+            ztab [..., -1] = sval
+
+        if ay :
+            #
+            #> South (in which nperio cases ?)
+            # --------------------------------
+            if nperio in [1, 3, 4, 5, 6] :
+                ztab [..., 0, :] = sval
+
+            #
+            #> North-South boundary conditions
+            # --------------------------------
+            if nperio in [3, 4] :  # North fold T-point pivot
+                if cd_type in [ 'T', 'W' ] : # T-, W-point
+                    ztab [..., -1,  :         ] = sval
+                    ztab [..., -2, :jpi//2  ] = sval
+
+                if cd_type == 'U' :
+                    ztab [..., -1,  :         ] = sval
+                    ztab [..., -2, jpi//2+1:  ] = sval
+
+                if cd_type == 'V' :
+                    ztab [..., -2, :       ] = sval
+                    ztab [..., -1, :       ] = sval
+
+                if cd_type == 'F' :
+                    ztab [..., -2, :       ] = sval
+                    ztab [..., -1, :       ] = sval
+
+            if nperio in [4.2] :  # North fold T-point pivot
+                if cd_type in [ 'T', 'W' ] : # T-, W-point
+                    ztab [..., -1, jpi//2  :  ] = sval
+
+                if cd_type == 'U' :
+                    ztab [..., -1, jpi//2-1:-1] = sval
+
+                if cd_type == 'V' :
+                    ztab [..., -1, 1:       ] = sval
+
+                if cd_type == 'F' :
+                    ztab [..., -1, 0:-1     ] = sval
+
+            if nperio in [5, 6] :            #  North fold F-point pivot
+                if cd_type in ['T', 'W']  :
+                    ztab [..., -1, 0:       ] = sval
+
+                if cd_type == 'U' :
+                    ztab [..., -1, 0:-1     ] = sval
+                    ztab [..., -1, -1       ] = sval
+
+                if cd_type == 'V' :
+                    ztab [..., -1, 0:       ] = sval
+                    ztab [..., -2, jpi//2:  ] = sval
+
+                if cd_type == 'F' :
+                    ztab [..., -1, 0:-1       ] = sval
+                    ztab [..., -1, -1         ] = sval
+                    ztab [..., -2, jpi//2+1:-1] = sval
+
+    return ztab
+
+def lbc_plot (ptab, nperio=None, cd_type='T', psgn=1.0, sval=np.nan) :
+    '''Set periodicity on input field, for plotting for any cartopy projection
+
+      Points at the north fold are masked
+      Points for zonal periodicity are kept
+    ptab      : Input array. Rank 2 at least : ptab[...., lat, lon]
+    nperio    : Type of periodicity
+    cd_type   : Grid specification : T, U, V or F
+    psgn      : For change of sign for vector components
+           (1 for scalars, -1 for vector components)
+
+    See NEMO documentation for further details
+    '''
+    jpi, nperio = lbc_init (ptab, nperio)[1:]
+    ax = __find_axis__ (ptab, 'x')[0]
+    ay = __find_axis__ (ptab, 'y')[0]
+    psgn   = ptab.dtype.type (psgn)
+    ztab   = ptab.copy ()
+
+    if ax :
+        #
+        #> East-West boundary conditions
+        # ------------------------------
+        if nperio in [1, 4, 6] :
             # ... cyclic
-            ptab [...,:,  0] = ptab [...,:,-2]
-            ptab [...,:, -1] = ptab [...,:, 1]
-      
-      #
-      #> North-South boundary conditions
-      # ----------------------------------
-      if nperio in [3, 4] :  # North fold T-point pivot     
-            if cd_type in [ 'T', 'W' ] : # T-, W-point
-                  ptab[..., -1, 1:       ] = psgn * ptab[..., -3, -1:0:-1      ]      
-                  ptab[..., -1, 0        ] = psgn * ptab[..., -3, 2            ]
-                  ptab[..., -2, jpi//2:  ] = psgn * ptab[..., -2, jpi//2:0:-1  ]
-                  
-            if cd_type == 'U' :
-                  ptab[..., -1, 0:-1     ] = psgn * ptab[..., -3, -1:0:-1      ]       
-                  ptab[..., -1,  0       ] = psgn * ptab[..., -3,  1           ]
-                  ptab[..., -1, -1       ] = psgn * ptab[..., -3, -2           ] 
-                  ptab[..., -2, jpi//2-1:] = psgn * ptab[..., -2, jpi//2+1:0:-1]
-                  
-            if cd_type == 'V' : 
-                  ptab[..., -2, 1:       ] = psgn * ptab[..., -3, jpi-1:0:-1   ]
-                  ptab[..., -1, 1:       ] = psgn * ptab[..., -4, -1:0:-1      ]   
-                  ptab[..., -1, 0        ] = psgn * ptab[..., -4, 2            ]
-              
-            if cd_type == 'F' :
-                  ptab[..., -2, 0:-1     ] = psgn * ptab[..., -3, -1:0:-1      ]
-                  ptab[..., -1, 0:-1     ] = psgn * ptab[..., -4, -1:0:-1      ]
-                  ptab[..., -1,  0       ] = psgn * ptab[..., -4,  1           ]
-                  ptab[..., -1, -1       ] = psgn * ptab[..., -4, -2           ] 
-                  
-      if nperio in [5, 6] :            #  North fold F-point pivot  
-            if cd_type in ['T', 'W']  :
-                  ptab[..., -1, 0:       ] = psgn * ptab[..., -2, -1::-1       ]
-            
-            if cd_type == 'U' :
-                  ptab[..., -1, 0:-1     ] = psgn * ptab[..., -2, -2::-1       ]       
-                  ptab[..., -1, -1       ] = psgn * ptab[..., -2, 0            ]
-              
-            if cd_type == 'V' :
-                  ptab[..., -1, 0:       ] = psgn * ptab[..., -3, -1::-1       ]
-                  ptab[..., -2, jpi/2:   ] = psgn * ptab[..., -2, jpi/2-1::-1  ]
-              
-            if cd_type == 'F' :
-                  ptab[..., -1, 0:-1     ] = psgn * ptab[..., -3, -2::-1       ]
-                  ptab[..., -1, -1       ] = psgn * ptab[..., -3, 0            ]
-                  ptab[..., -2, jpi//2:-1] = psgn * ptab[..., -2, jpi//2-2::-1 ]
-              
-      return ptab
-  
+            ztab [..., :,  0] = ztab [..., :, -2]
+            ztab [..., :, -1] = ztab [..., :,  1]
+
+        if ay :
+            #> Masks south
+            # ------------
+            if nperio in [4, 6] :
+                ztab [..., 0, : ] = sval
+
+            #
+            #> North-South boundary conditions
+            # --------------------------------
+            if nperio in [3, 4] :  # North fold T-point pivot
+                if cd_type in [ 'T', 'W' ] : # T-, W-point
+                    ztab [..., -1,  :      ] = sval
+                    #ztab [..., -2, jpi//2: ] = sval
+                    ztab [..., -2, :jpi//2 ] = sval # Give better plots than above
+                if cd_type == 'U' :
+                    ztab [..., -1, : ] = sval
+
+                if cd_type == 'V' :
+                    ztab [..., -2, : ] = sval
+                    ztab [..., -1, : ] = sval
+
+                if cd_type == 'F' :
+                    ztab [..., -2, : ] = sval
+                    ztab [..., -1, : ] = sval
+
+            if nperio in [4.2] :  # North fold T-point pivot
+                if cd_type in [ 'T', 'W' ] : # T-, W-point
+                    ztab [..., -1, jpi//2:  ] = sval
+
+                if cd_type == 'U' :
+                    ztab [..., -1, jpi//2-1:-1] = sval
+
+                if cd_type == 'V' :
+                    ztab [..., -1, 1:       ] = sval
+
+                if cd_type == 'F' :
+                    ztab [..., -1, 0:-1     ] = sval
+
+            if nperio in [5, 6] :            #  North fold F-point pivot
+                if cd_type in ['T', 'W']  :
+                    ztab [..., -1, : ] = sval
+
+                if cd_type == 'U' :
+                    ztab [..., -1, : ] = sval
+
+                if cd_type == 'V' :
+                    ztab [..., -1, :        ] = sval
+                    ztab [..., -2, jpi//2:  ] = sval
+
+                if cd_type == 'F' :
+                    ztab [..., -1, :          ] = sval
+                    ztab [..., -2, jpi//2+1:-1] = sval
+
+    return ztab
+
+def lbc_add (ptab, nperio=None, cd_type=None, psgn=1) :
+    '''Handles NEMO domain changes between NEMO 4.0 to NEMO 4.2
+
+    Periodicity and north fold halos has been removed in NEMO 4.2
+    This routine adds the halos if needed
+
+    ptab      : Input array (works
+      rank 2 at least : ptab[...., lat, lon]
+    nperio    : Type of periodicity
+
+    See NEMO documentation for further details
+    '''
+    mmath = __mmath__ (ptab)
+    nperio = lbc_init (ptab, nperio)[-1]
+    lshape = get_shape (ptab)
+    ix = __find_axis__ (ptab, 'x')[-1]
+    jy = __find_axis__ (ptab, 'y')[-1]
+
+    t_shape = np.array (ptab.shape)
+
+    if nperio in [4.2, 6.2] :
+
+        ext_shape = t_shape.copy()
+        if 'X' in lshape :
+            ext_shape[ix] = ext_shape[ix] + 2
+        if 'Y' in lshape :
+            ext_shape[jy] = ext_shape[jy] + 1
+
+        if mmath == xr :
+            ptab_ext = xr.DataArray (np.zeros (ext_shape), dims=ptab.dims)
+            if 'X' in lshape and 'Y' in lshape :
+                ptab_ext.values[..., :-1, 1:-1] = ptab.values.copy ()
+            else :
+                if 'X' in lshape     :
+                    ptab_ext.values[...,      1:-1] = ptab.values.copy ()
+                if 'Y' in lshape     :
+                    ptab_ext.values[..., :-1      ] = ptab.values.copy ()
+        else           :
+            ptab_ext =               np.zeros (ext_shape)
+            if 'X' in lshape and 'Y' in lshape :
+                ptab_ext       [..., :-1, 1:-1] = ptab.copy ()
+            else :
+                if 'X' in lshape     :
+                    ptab_ext       [...,      1:-1] = ptab.copy ()
+                if 'Y' in lshape     :
+                    ptab_ext       [..., :-1      ] = ptab.copy ()
+
+        if nperio == 4.2 :
+            ptab_ext = lbc (ptab_ext, nperio=4, cd_type=cd_type, psgn=psgn)
+        if nperio == 6.2 :
+            ptab_ext = lbc (ptab_ext, nperio=6, cd_type=cd_type, psgn=psgn)
+
+        if mmath == xr :
+            ptab_ext.attrs = ptab.attrs
+            az = __find_axis__ (ptab, 'z')[0]
+            at = __find_axis__ (ptab, 't')[0]
+            if az :
+                ptab_ext = ptab_ext.assign_coords ( {az:ptab.coords[az]} )
+            if at :
+                ptab_ext = ptab_ext.assign_coords ( {at:ptab.coords[at]} )
+
+    else : ptab_ext = lbc (ptab, nperio=nperio, cd_type=cd_type, psgn=psgn)
+
+    return ptab_ext
+
+def lbc_del (ptab, nperio=None, cd_type='T', psgn=1) :
+    '''Handles NEMO domain changes between NEMO 4.0 to NEMO 4.2
+
+    Periodicity and north fold halos has been removed in NEMO 4.2
+    This routine removes the halos if needed
+
+    ptab      : Input array (works
+      rank 2 at least : ptab[...., lat, lon]
+    nperio    : Type of periodicity
+
+    See NEMO documentation for further details
+    '''
+    nperio = lbc_init (ptab, nperio)[-1]
+    #lshape = get_shape (ptab)
+    ax = __find_axis__ (ptab, 'x')[0]
+    ay = __find_axis__ (ptab, 'y')[0]
+
+    if nperio in [4.2, 6.2] :
+        if ax or ay :
+            if ax and ay :
+                ztab = lbc (ptab[..., :-1, 1:-1],
+                            nperio=nperio, cd_type=cd_type, psgn=psgn)
+            else :
+                if ax :
+                    ztab = lbc (ptab[...,      1:-1],
+                                nperio=nperio, cd_type=cd_type, psgn=psgn)
+                if ay :
+                    ztab = lbc (ptab[..., -1],
+                                nperio=nperio, cd_type=cd_type, psgn=psgn)
+        else :
+            ztab = ptab
+    else :
+        ztab = ptab
+
+    return ztab
+
+def lbc_index (jj, ii, jpj, jpi, nperio=None, cd_type='T') :
+    '''For indexes of a NEMO point, give the corresponding point
+        inside the domain (i.e. not in the halo)
+
+    jj, ii    : indexes
+    jpi, jpi  : size of domain
+    nperio    : type of periodicity
+    cd_type   : grid specification : T, U, V or F
+
+    See NEMO documentation for further details
+    '''
+
+    if nperio is None :
+        nperio = __guess_nperio__ (jpj, jpi, nperio)
+
+    ## For the sake of simplicity, switch to the convention of original
+    ## lbc Fortran routine from NEMO : starts indexes at 1
+    jy = jj + 1
+    ix = ii + 1
+
+    mmath = __mmath__ (jj)
+    if mmath is None :
+        mmath=np
+
+    #
+    #> East-West boundary conditions
+    # ------------------------------
+    if nperio in [1, 4, 6] :
+        #... cyclic
+        ix = mmath.where (ix==jpi, 2   , ix)
+        ix = mmath.where (ix== 1 ,jpi-1, ix)
+
+    #
+    def mod_ij (cond, jy_new, ix_new) :
+        jy_r = mmath.where (cond, jy_new, jy)
+        ix_r = mmath.where (cond, ix_new, ix)
+        return jy_r, ix_r
+    #
+    #> North-South boundary conditions
+    # --------------------------------
+    if nperio in [ 3 , 4 ]  :
+        if cd_type in  [ 'T' , 'W' ] :
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix>=2       ), jpj-2, jpi-ix+2)
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix==1       ), jpj-1, 3       )
+            jy, ix = mod_ij (np.logical_and (jy==jpj-1, ix>=jpi//2+1),
+                                  jy , jpi-ix+2)
+
+        if cd_type in [ 'U' ] :
+            jy, ix = mod_ij (np.logical_and (
+                      jy==jpj  ,
+                      np.logical_and (ix>=1, ix <= jpi-1)   ),
+                                         jy   , jpi-ix+1)
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix==1  ) , jpj-2, 2       )
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix==jpi) , jpj-2, jpi-1   )
+            jy, ix = mod_ij (np.logical_and (jy==jpj-1,
+                            np.logical_and (ix>=jpi//2, ix<=jpi-1)), jy   , jpi-ix+1)
+
+        if cd_type in [ 'V' ] :
+            jy, ix = mod_ij (np.logical_and (jy==jpj-1, ix>=2  ), jpj-2, jpi-ix+2)
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix>=2  ), jpj-3, jpi-ix+2)
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix==1  ), jpj-3,  3      )
+
+        if cd_type in [ 'F' ] :
+            jy, ix = mod_ij (np.logical_and (jy==jpj-1, ix<=jpi-1), jpj-2, jpi-ix+1)
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix<=jpi-1), jpj-3, jpi-ix+1)
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix==1    ), jpj-3, 2       )
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix==jpi  ), jpj-3, jpi-1   )
+
+    if nperio in [ 5 , 6 ] :
+        if cd_type in [ 'T' , 'W' ] :                        # T-, W-point
+            jy, ix = mod_ij (jy==jpj, jpj-1, jpi-ix+1)
+
+        if cd_type in [ 'U' ] :                              # U-point
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix<=jpi-1   ), jpj-1, jpi-ix  )
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix==jpi     ), jpi-1, 1       )
+
+        if cd_type in [ 'V' ] :    # V-point
+            jy, ix = mod_ij (jy==jpj                                 , jy   , jpi-ix+1)
+            jy, ix = mod_ij (np.logical_and (jy==jpj-1, ix>=jpi//2+1), jy   , jpi-ix+1)
+
+        if cd_type in [ 'F' ] :                              # F-point
+            jy, ix = mod_ij (np.logical_and (jy==jpj  , ix<=jpi-1   ), jpj-2, jpi-ix  )
+            jy, ix = mod_ij (np.logical_and (ix==jpj  , ix==jpi     ), jpj-2, 1       )
+            jy, ix = mod_ij (np.logical_and (jy==jpj-1, ix>=jpi//2+1), jy   , jpi-ix  )
+
+    ## Restore convention to Python/C : indexes start at 0
+    jy += -1
+    ix += -1
+
+    if isinstance (jj, int) :
+        jy = jy.item ()
+    if isinstance (ii, int) :
+        ix = ix.item ()
+
+    return jy, ix
+
+def find_ji (lat_data, lon_data, lat_grid, lon_grid, mask=1.0, verbose=False, out=None) :
+    '''
+    Description: seeks J,I indices of the grid point which is the closest
+       of a given point
+
+    Usage: go FindJI  <data latitude> <data longitude> <grid latitudes> <grid longitudes> [mask]
+    <grid latitudes><grid longitudes> are 2D fields on J/I (Y/X) dimensions
+    mask : if given, seek only non masked grid points (i.e with mask=1)
+
+    Example : findIJ (40, -20, nav_lat, nav_lon, mask=1.0)
+
+    Note : all longitudes and latitudes in degrees
+
+    Note : may work with 1D lon/lat (?)
+    '''
+    # Get grid dimensions
+    if len (lon_grid.shape) == 2 :
+        jpi = lon_grid.shape[-1]
+    else                         :
+        jpi = len(lon_grid)
+
+    #mmath = __mmath__ (lat_grid)
+
+    # Compute distance from the point to all grid points (in RADian)
+    arg      = ( np.sin (RAD*lat_data) * np.sin (RAD*lat_grid)
+               + np.cos (RAD*lat_data) * np.cos (RAD*lat_grid) *
+                 np.cos(RAD*(lon_data-lon_grid)) )
+    # Send masked points to 'infinite'
+    distance = np.arccos (arg) + 4.0*RPI*(1.0-mask)
+
+    # Truncates to alleviate some precision problem with some grids
+    prec = int (1E7)
+    distance = (distance*prec).astype(int) / prec
+
+    # Compute minimum of distance, and index of minimum
+    #
+    #distance_min = distance.min    ()
+    jimin        = int (distance.argmin ())
+
+    # Compute 2D indices (Python/C flavor : starting at 0)
+    jmin = jimin // jpi
+    imin = jimin - jmin*jpi
+
+    # Result
+    if verbose :
+        # Compute distance achieved
+        #mindist = distance [jmin, imin]
+
+        # Compute azimuth
+        dlon = lon_data-lon_grid[jmin,imin]
+        arg  = np.sin (RAD*dlon) / (
+                  np.cos(RAD*lat_data)*np.tan(RAD*lat_grid[jmin,imin])
+                - np.sin(RAD*lat_data)*np.cos(RAD*dlon))
+        azimuth = DAR*np.arctan (arg)
+        print ( f'I={imin:d} J={jmin:d} - Data:{lat_data:5.1f}Â°N {lon_data:5.1f}Â°E' \
+            +   f'- Grid:{lat_grid[jmin,imin]:4.1f}Â°N '   \
+            +   f'{lon_grid[jmin,imin]:4.1f}Â°E - Dist: {RA*distance[jmin,imin]:6.1f}km' \
+            +   f' {DAR*distance[jmin,imin]:5.2f}Â° ' \
+            +   f'- Azimuth: {RAD*azimuth:3.2f}RAD - {azimuth:5.1f}Â°' )
+
+    if   out=='dict'                     :
+        return {'x':imin, 'y':jmin}
+    elif out in ['array', 'numpy', 'np'] :
+        return np.array ( [jmin, imin] )
+    elif out in ['xarray', 'xr']         :
+        return xr.DataArray ( [jmin, imin] )
+    elif out=='list'                     :
+        return [jmin, imin]
+    elif out=='tuple'                    :
+        return jmin, imin
+    else                                 :
+        return jmin, imin
+
+def curl (tx, ty, e1f, e2f, nperio=None) :
+    '''Returns curl of a vector field
+    '''
+    ax = __find_axis__ (tx, 'x')[0]
+    ay = __find_axis__ (ty, 'y')[0]
+
+    tx_0  = lbc_add (tx , nperio=nperio, cd_type='U', psgn=-1)
+    ty_0  = lbc_add (ty , nperio=nperio, cd_type='V', psgn=-1)
+    e1f_0 = lbc_add (e1f, nperio=nperio, cd_type='U', psgn=-1)
+    e2f_0 = lbc_add (e2f, nperio=nperio, cd_type='V', psgn=-1)
+
+    tx_1  = tx_0.roll ( {ay:-1} )
+    ty_1  = ty_0.roll ( {ax:-1} )
+    tx_1  = lbc (tx_1, nperio=nperio, cd_type='U', psgn=-1)
+    ty_1  = lbc (ty_1, nperio=nperio, cd_type='V', psgn=-1)
+
+    zcurl = (ty_1 - ty_0)/e1f_0 - (tx_1 - tx_0)/e2f_0
+
+    mask = np.logical_or (
+             np.logical_or ( np.isnan(tx_0), np.isnan(tx_1)),
+             np.logical_or ( np.isnan(ty_0), np.isnan(ty_1)) )
+
+    zcurl = zcurl.where (np.logical_not (mask), np.nan)
+
+    zcurl = lbc_del (zcurl, nperio=nperio, cd_type='F', psgn=1)
+    zcurl = lbc (zcurl, nperio=nperio, cd_type='F', psgn=1)
+
+    return zcurl
+
+def div (ux, uy, e1t, e2t, nperio=None) :
+    '''Returns divergence of a vector field
+    '''
+    ax = __find_axis__ (ux, 'x')[0]
+    ay = __find_axis__ (ux, 'y')[0]
+
+    ux_0  = lbc_add (ux , nperio=nperio, cd_type='U', psgn=-1)
+    uy_0  = lbc_add (uy , nperio=nperio, cd_type='V', psgn=-1)
+    e1t_0 = lbc_add (e1t, nperio=nperio, cd_type='U', psgn=-1)
+    e2t_0 = lbc_add (e2t, nperio=nperio, cd_type='V', psgn=-1)
+
+    ux_1 = ux_0.roll ( {ay:1} )
+    uy_1 = uy_0.roll ( {ax:1} )
+    ux_1 = lbc (ux_1, nperio=nperio, cd_type='U', psgn=-1)
+    uy_1 = lbc (uy_1, nperio=nperio, cd_type='V', psgn=-1)
+
+    zdiv = (ux_0 - ux_1)/e2t_0 + (uy_0 - uy_1)/e1t_0
+
+    mask = np.logical_or (
+             np.logical_or ( np.isnan(ux_0), np.isnan(ux_1)),
+             np.logical_or ( np.isnan(uy_0), np.isnan(uy_1)) )
+
+    zdiv = zdiv.where (np.logical_not (mask), np.nan)
+
+    zdiv = lbc_del (zdiv, nperio=nperio, cd_type='T', psgn=1)
+    zdiv = lbc (zdiv, nperio=nperio, cd_type='T', psgn=1)
+
+    return zdiv
+
+def geo2en (pxx, pyy, pzz, glam, gphi) :
+    '''Change vector from geocentric to east/north
+
+    Inputs :
+        pxx, pyy, pzz : components on the geocentric system
+        glam, gphi : longitude and latitude of the points
+    '''
+
+    gsinlon = np.sin (RAD * glam)
+    gcoslon = np.cos (RAD * glam)
+    gsinlat = np.sin (RAD * gphi)
+    gcoslat = np.cos (RAD * gphi)
+
+    pte = - pxx * gsinlon            + pyy * gcoslon
+    ptn = - pxx * gcoslon * gsinlat  - pyy * gsinlon * gsinlat + pzz * gcoslat
+
+    return pte, ptn
+
+def en2geo (pte, ptn, glam, gphi) :
+    '''Change vector from east/north to geocentric
+
+    Inputs :
+        pte, ptn   : eastward/northward components
+        glam, gphi : longitude and latitude of the points
+    '''
+
+    gsinlon = np.sin (RAD * glam)
+    gcoslon = np.cos (RAD * glam)
+    gsinlat = np.sin (RAD * gphi)
+    gcoslat = np.cos (RAD * gphi)
+
+    pxx = - pte * gsinlon - ptn * gcoslon * gsinlat
+    pyy =   pte * gcoslon - ptn * gsinlon * gsinlat
+    pzz =   ptn * gcoslat
+
+    return pxx, pyy, pzz
+
+
+def clo_lon (lon, lon0=0., rad=False, deg=True) :
+    '''Choose closest to lon0 longitude, adding/substacting 360Â°
+    if needed
+    '''
+    mmath = __mmath__ (lon, np)
+    if rad :
+        lon_range = 2.*np.pi
+    if deg :
+        lon_range = 360.
+    c_lon = lon
+    c_lon = mmath.where (c_lon > lon0 + lon_range*0.5,
+                             c_lon-lon_range, clo_lon)
+    c_lon = mmath.where (c_lon < lon0 - lon_range*0.5,
+                             c_lon+lon_range, clo_lon)
+    c_lon = mmath.where (c_lon > lon0 + lon_range*0.5,
+                             c_lon-lon_range, clo_lon)
+    c_lon = mmath.where (c_lon < lon0 - lon_range*0.5,
+                             c_lon+lon_range, clo_lon)
+    if c_lon.shape == () :
+        c_lon = c_lon.item ()
+    if mmath == xr :
+        if lon.attrs :
+            c_lon.attrs.update ( lon.attrs )
+    return c_lon
+
+def index2depth (pk, gdept_0) :
+    '''From index (real, continuous), get depth
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpk = gdept_0.shape[0]
+    kk = xr.DataArray(pk)
+    k  = np.maximum (0, np.minimum (jpk-1, kk    ))
+    k0 = np.floor (k).astype (int)
+    k1 = np.maximum (0, np.minimum (jpk-1,  k0+1))
+    zz = k - k0
+    gz = (1.0-zz)*gdept_0[k0]+ zz*gdept_0[k1]
+    return gz.values
+
+def depth2index (pz, gdept_0) :
+    '''From depth, get index (real, continuous)
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpk  = gdept_0.shape[0]
+    if   isinstance (pz, xr.core.dataarray.DataArray ) :
+        zz   = xr.DataArray (pz.values, dims=('zz',))
+    elif isinstance (pz,  np.ndarray) :
+        zz   = xr.DataArray (pz.ravel(), dims=('zz',))
+    else :
+        zz   = xr.DataArray (np.array([pz]).ravel(), dims=('zz',))
+    zz   = np.minimum (gdept_0[-1], np.maximum (0, zz))
+
+    idk1 = np.minimum ( (gdept_0-zz), 0.).argmax (axis=0).astype(int)
+    idk1 = np.maximum (0, np.minimum (jpk-1,  idk1  ))
+    idk2 = np.maximum (0, np.minimum (jpk-1,  idk1-1))
+
+    zff = (zz - gdept_0[idk2])/(gdept_0[idk1]-gdept_0[idk2])
+    idk = zff*idk1 + (1.0-zff)*idk2
+    idk = xr.where ( np.isnan(idk), idk1, idk)
+    return idk.values
+
+def index2depth_panels (pk, gdept_0, depth0, fact) :
+    '''From  index (real, continuous), get depth, with bottom part compressed
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpk = gdept_0.shape[0]
+    kk = xr.DataArray (pk)
+    k  = np.maximum (0, np.minimum (jpk-1, kk    ))
+    k0 = np.floor (k).astype (int)
+    k1 = np.maximum (0, np.minimum (jpk-1,  k0+1))
+    zz = k - k0
+    gz = (1.0-zz)*gdept_0[k0]+ zz*gdept_0[k1]
+    gz = xr.where ( gz<depth0, gz, depth0 + (gz-depth0)*fact)
+    return gz.values
+
+def depth2index_panels (pz, gdept_0, depth0, fact) :
+    '''From  index (real, continuous), get depth, with bottom part compressed
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpk = gdept_0.shape[0]
+    if isinstance (pz, xr.core.dataarray.DataArray) :
+        zz   = xr.DataArray (pz.values , dims=('zz',))
+    elif isinstance (pz, np.ndarray) :
+        zz   = xr.DataArray (pz.ravel(), dims=('zz',))
+    else :
+        zz   = xr.DataArray (np.array([pz]).ravel(), dims=('zz',))
+    zz         = np.minimum (gdept_0[-1], np.maximum (0, zz))
+    gdept_comp = xr.where ( gdept_0>depth0,
+                                (gdept_0-depth0)*fact+depth0, gdept_0)
+    zz_comp    = xr.where ( zz     >depth0, (zz     -depth0)*fact+depth0,
+                                zz     )
+    zz_comp    = np.minimum (gdept_comp[-1], np.maximum (0, zz_comp))
+
+    idk1 = np.minimum ( (gdept_0-zz_comp), 0.).argmax (axis=0).astype(int)
+    idk1 = np.maximum (0, np.minimum (jpk-1,  idk1  ))
+    idk2 = np.maximum (0, np.minimum (jpk-1,  idk1-1))
+
+    zff = (zz_comp - gdept_0[idk2])/(gdept_0[idk1]-gdept_0[idk2])
+    idk = zff*idk1 + (1.0-zff)*idk2
+    idk = xr.where ( np.isnan(idk), idk1, idk)
+    return idk.values
+
+def depth2comp (pz, depth0, fact ) :
+    '''Form depth, get compressed depth, with bottom part compressed
+
+    Needed to use transforms in Matplotlib
+    '''
+    #print ('start depth2comp')
+    if isinstance (pz, xr.core.dataarray.DataArray) :
+        zz   = pz.values
+    elif isinstance(pz, list) :
+        zz = np.array (pz)
+    else :
+        zz   = pz
+    gz = np.where ( zz>depth0, (zz-depth0)*fact+depth0, zz)
+    #print ( f'depth2comp : {gz=}' )
+    if type (pz) in [int, float] :
+        return gz.item()
+    else :
+        return gz
+
+def comp2depth (pz, depth0, fact ) :
+    '''Form compressed depth, get depth, with bottom part compressed
+
+    Needed to use transforms in Matplotlib
+    '''
+    if isinstance (pz, xr.core.dataarray.DataArray) :
+        zz   = pz.values
+    elif isinstance (pz, list) :
+        zz = np.array (pz)
+    else :
+        zz   = pz
+    gz = np.where ( zz>depth0, (zz-depth0)/fact+depth0, zz)
+    if type (pz) in [int, float] :
+        gz = gz.item()
+
+    return gz
+
+def index2lon (pi, plon_1d) :
+    '''From index (real, continuous), get longitude
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpi = plon_1d.shape[0]
+    ii = xr.DataArray (pi)
+    i =  np.maximum (0, np.minimum (jpi-1, ii    ))
+    i0 = np.floor (i).astype (int)
+    i1 = np.maximum (0, np.minimum (jpi-1,  i0+1))
+    xx = i - i0
+    gx = (1.0-xx)*plon_1d[i0]+ xx*plon_1d[i1]
+    return gx.values
+
+def lon2index (px, plon_1d) :
+    '''From longitude, get index (real, continuous)
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpi  = plon_1d.shape[0]
+    if isinstance (px, xr.core.dataarray.DataArray) :
+        xx   = xr.DataArray (px.values , dims=('xx',))
+    elif isinstance (px, np.ndarray) :
+        xx   = xr.DataArray (px.ravel(), dims=('xx',))
+    else :
+        xx   = xr.DataArray (np.array([px]).ravel(), dims=('xx',))
+    xx   = xr.where ( xx>plon_1d.max(), xx-360.0, xx)
+    xx   = xr.where ( xx<plon_1d.min(), xx+360.0, xx)
+    xx   = np.minimum (plon_1d.max(), np.maximum(xx, plon_1d.min() ))
+    idi1 = np.minimum ( (plon_1d-xx), 0.).argmax (axis=0).astype(int)
+    idi1 = np.maximum (0, np.minimum (jpi-1,  idi1  ))
+    idi2 = np.maximum (0, np.minimum (jpi-1,  idi1-1))
+
+    zff = (xx - plon_1d[idi2])/(plon_1d[idi1]-plon_1d[idi2])
+    idi = zff*idi1 + (1.0-zff)*idi2
+    idi = xr.where ( np.isnan(idi), idi1, idi)
+    return idi.values
+
+def index2lat (pj, plat_1d) :
+    '''From index (real, continuous), get latitude
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpj = plat_1d.shape[0]
+    jj  = xr.DataArray (pj)
+    j   = np.maximum (0, np.minimum (jpj-1, jj    ))
+    j0  = np.floor (j).astype (int)
+    j1  = np.maximum (0, np.minimum (jpj-1,  j0+1))
+    yy  = j - j0
+    gy  = (1.0-yy)*plat_1d[j0]+ yy*plat_1d[j1]
+    return gy.values
+
+def lat2index (py, plat_1d) :
+    '''From latitude, get index (real, continuous)
+
+    Needed to use transforms in Matplotlib
+    '''
+    jpj = plat_1d.shape[0]
+    if isinstance (py, xr.core.dataarray.DataArray) :
+        yy   = xr.DataArray (py.values , dims=('yy',))
+    elif isinstance (py, np.ndarray) :
+        yy   = xr.DataArray (py.ravel(), dims=('yy',))
+    else :
+        yy   = xr.DataArray (np.array([py]).ravel(), dims=('yy',))
+    yy   = np.minimum (plat_1d.max(), np.minimum(yy, plat_1d.max() ))
+    idj1 = np.minimum ( (plat_1d-yy), 0.).argmax (axis=0).astype(int)
+    idj1 = np.maximum (0, np.minimum (jpj-1,  idj1  ))
+    idj2 = np.maximum (0, np.minimum (jpj-1,  idj1-1))
+
+    zff = (yy - plat_1d[idj2])/(plat_1d[idj1]-plat_1d[idj2])
+    idj = zff*idj1 + (1.0-zff)*idj2
+    idj = xr.where ( np.isnan(idj), idj1, idj)
+    return idj.values
+
+def angle_full (glamt, gphit, glamu, gphiu, glamv, gphiv,
+                glamf, gphif, nperio=None) :
+    '''Computes sinus and cosinus of model line direction with
+    respect to east
+    '''
+    mmath = __mmath__ (glamt)
+
+    zlamt = lbc_add (glamt, nperio, 'T', 1.)
+    zphit = lbc_add (gphit, nperio, 'T', 1.)
+    zlamu = lbc_add (glamu, nperio, 'U', 1.)
+    zphiu = lbc_add (gphiu, nperio, 'U', 1.)
+    zlamv = lbc_add (glamv, nperio, 'V', 1.)
+    zphiv = lbc_add (gphiv, nperio, 'V', 1.)
+    zlamf = lbc_add (glamf, nperio, 'F', 1.)
+    zphif = lbc_add (gphif, nperio, 'F', 1.)
+
+    # north pole direction & modulous (at T-point)
+    zxnpt = 0. - 2.0 * np.cos (RAD*zlamt) * np.tan (RPI/4.0 - RAD*zphit/2.0)
+    zynpt = 0. - 2.0 * np.sin (RAD*zlamt) * np.tan (RPI/4.0 - RAD*zphit/2.0)
+    znnpt = zxnpt*zxnpt + zynpt*zynpt
+
+    # north pole direction & modulous (at U-point)
+    zxnpu = 0. - 2.0 * np.cos (RAD*zlamu) * np.tan (RPI/4.0 - RAD*zphiu/2.0)
+    zynpu = 0. - 2.0 * np.sin (RAD*zlamu) * np.tan (RPI/4.0 - RAD*zphiu/2.0)
+    znnpu = zxnpu*zxnpu + zynpu*zynpu
+
+    # north pole direction & modulous (at V-point)
+    zxnpv = 0. - 2.0 * np.cos (RAD*zlamv) * np.tan (RPI/4.0 - RAD*zphiv/2.0)
+    zynpv = 0. - 2.0 * np.sin (RAD*zlamv) * np.tan (RPI/4.0 - RAD*zphiv/2.0)
+    znnpv = zxnpv*zxnpv + zynpv*zynpv
+
+    # north pole direction & modulous (at F-point)
+    zxnpf = 0. - 2.0 * np.cos( RAD*zlamf ) * np.tan ( RPI/4. - RAD*zphif/2. )
+    zynpf = 0. - 2.0 * np.sin( RAD*zlamf ) * np.tan ( RPI/4. - RAD*zphif/2. )
+    znnpf = zxnpf*zxnpf + zynpf*zynpf
+
+    # j-direction: v-point segment direction (around T-point)
+    zlam = zlamv
+    zphi = zphiv
+    zlan = np.roll ( zlamv, axis=-2, shift=1)  # glamv (ji,jj-1)
+    zphh = np.roll ( zphiv, axis=-2, shift=1)  # gphiv (ji,jj-1)
+    zxvvt =  2.0 * np.cos ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2.0 * np.cos ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    zyvvt =  2.0 * np.sin ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2.0 * np.sin ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    znvvt = np.sqrt ( znnpt * ( zxvvt*zxvvt + zyvvt*zyvvt )  )
+
+    # j-direction: f-point segment direction (around u-point)
+    zlam = zlamf
+    zphi = zphif
+    zlan = np.roll (zlamf, axis=-2, shift=1) # glamf (ji,jj-1)
+    zphh = np.roll (zphif, axis=-2, shift=1) # gphif (ji,jj-1)
+    zxffu =  2.0 * np.cos ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2.0 * np.cos ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    zyffu =  2.0 * np.sin ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2.0 * np.sin ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    znffu = np.sqrt ( znnpu * ( zxffu*zxffu + zyffu*zyffu )  )
+
+    # i-direction: f-point segment direction (around v-point)
+    zlam = zlamf
+    zphi = zphif
+    zlan = np.roll (zlamf, axis=-1, shift=1) # glamf (ji-1,jj)
+    zphh = np.roll (zphif, axis=-1, shift=1) # gphif (ji-1,jj)
+    zxffv =  2.0 * np.cos ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2.0 * np.cos ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    zyffv =  2.0 * np.sin ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2.0 * np.sin ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    znffv = np.sqrt ( znnpv * ( zxffv*zxffv + zyffv*zyffv )  )
+
+    # j-direction: u-point segment direction (around f-point)
+    zlam = np.roll (zlamu, axis=-2, shift=-1) # glamu (ji,jj+1)
+    zphi = np.roll (zphiu, axis=-2, shift=-1) # gphiu (ji,jj+1)
+    zlan = zlamu
+    zphh = zphiu
+    zxuuf =  2. * np.cos ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2. * np.cos ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    zyuuf =  2. * np.sin ( RAD*zlam ) * np.tan ( RPI/4. - RAD*zphi/2. ) \
+          -  2. * np.sin ( RAD*zlan ) * np.tan ( RPI/4. - RAD*zphh/2. )
+    znuuf = np.sqrt ( znnpf * ( zxuuf*zxuuf + zyuuf*zyuuf )  )
+
+
+    # cosinus and sinus using scalar and vectorial products
+    gsint = ( zxnpt*zyvvt - zynpt*zxvvt ) / znvvt
+    gcost = ( zxnpt*zxvvt + zynpt*zyvvt ) / znvvt
+
+    gsinu = ( zxnpu*zyffu - zynpu*zxffu ) / znffu
+    gcosu = ( zxnpu*zxffu + zynpu*zyffu ) / znffu
+
+    gsinf = ( zxnpf*zyuuf - zynpf*zxuuf ) / znuuf
+    gcosf = ( zxnpf*zxuuf + zynpf*zyuuf ) / znuuf
+
+    gsinv = ( zxnpv*zxffv + zynpv*zyffv ) / znffv
+    # (caution, rotation of 90 degres)
+    gcosv =-( zxnpv*zyffv - zynpv*zxffv ) / znffv
+
+    gsint = lbc_del (gsint, cd_type='T', nperio=nperio, psgn=-1.)
+    gcost = lbc_del (gcost, cd_type='T', nperio=nperio, psgn=-1.)
+    gsinu = lbc_del (gsinu, cd_type='U', nperio=nperio, psgn=-1.)
+    gcosu = lbc_del (gcosu, cd_type='U', nperio=nperio, psgn=-1.)
+    gsinv = lbc_del (gsinv, cd_type='V', nperio=nperio, psgn=-1.)
+    gcosv = lbc_del (gcosv, cd_type='V', nperio=nperio, psgn=-1.)
+    gsinf = lbc_del (gsinf, cd_type='F', nperio=nperio, psgn=-1.)
+    gcosf = lbc_del (gcosf, cd_type='F', nperio=nperio, psgn=-1.)
+
+    if mmath == xr :
+        gsint = gsint.assign_coords ( glamt.coords )
+        gcost = gcost.assign_coords ( glamt.coords )
+        gsinu = gsinu.assign_coords ( glamu.coords )
+        gcosu = gcosu.assign_coords ( glamu.coords )
+        gsinv = gsinv.assign_coords ( glamv.coords )
+        gcosv = gcosv.assign_coords ( glamv.coords )
+        gsinf = gsinf.assign_coords ( glamf.coords )
+        gcosf = gcosf.assign_coords ( glamf.coords )
+
+    return gsint, gcost, gsinu, gcosu, gsinv, gcosv, gsinf, gcosf
+
+def angle (glam, gphi, nperio, cd_type='T') :
+    '''Computes sinus and cosinus of model line direction with
+    respect to east
+    '''
+    mmath = __mmath__ (glam)
+
+    zlam = lbc_add (glam, nperio, cd_type, 1.)
+    zphi = lbc_add (gphi, nperio, cd_type, 1.)
+
+    # north pole direction & modulous
+    zxnp = 0. - 2.0 * np.cos (RAD*zlam) * np.tan (RPI/4.0 - RAD*zphi/2.0)
+    zynp = 0. - 2.0 * np.sin (RAD*zlam) * np.tan (RPI/4.0 - RAD*zphi/2.0)
+    znnp = zxnp*zxnp + zynp*zynp
+
+    # j-direction: segment direction (around point)
+    zlan_n = np.roll (zlam, axis=-2, shift=-1) # glam [jj+1, ji]
+    zphh_n = np.roll (zphi, axis=-2, shift=-1) # gphi [jj+1, ji]
+    zlan_s = np.roll (zlam, axis=-2, shift= 1) # glam [jj-1, ji]
+    zphh_s = np.roll (zphi, axis=-2, shift= 1) # gphi [jj-1, ji]
+
+    zxff = 2.0 * np.cos (RAD*zlan_n) * np.tan (RPI/4.0 - RAD*zphh_n/2.0) \
+        -  2.0 * np.cos (RAD*zlan_s) * np.tan (RPI/4.0 - RAD*zphh_s/2.0)
+    zyff = 2.0 * np.sin (RAD*zlan_n) * np.tan (RPI/4.0 - RAD*zphh_n/2.0) \
+        -  2.0 * np.sin (RAD*zlan_s) * np.tan (RPI/4.0 - RAD*zphh_s/2.0)
+    znff = np.sqrt (znnp * (zxff*zxff + zyff*zyff) )
+
+    gsin = (zxnp*zyff - zynp*zxff) / znff
+    gcos = (zxnp*zxff + zynp*zyff) / znff
+
+    gsin = lbc_del (gsin, cd_type=cd_type, nperio=nperio, psgn=-1.)
+    gcos = lbc_del (gcos, cd_type=cd_type, nperio=nperio, psgn=-1.)
+
+    if mmath == xr :
+        gsin = gsin.assign_coords ( glam.coords )
+        gcos = gcos.assign_coords ( glam.coords )
+
+    return gsin, gcos
+
+def rot_en2ij ( u_e, v_n, gsin, gcos, nperio, cd_type ) :
+    '''Rotates the Repere: Change vector componantes between
+    geographic grid --> stretched coordinates grid.
+
+    All components are on the same grid (T, U, V or F)
+    '''
+
+    u_i = + u_e * gcos + v_n * gsin
+    v_j = - u_e * gsin + v_n * gcos
+
+    u_i = lbc (u_i, nperio=nperio, cd_type=cd_type, psgn=-1.0)
+    v_j = lbc (v_j, nperio=nperio, cd_type=cd_type, psgn=-1.0)
+
+    return u_i, v_j
+
+def rot_ij2en ( u_i, v_j, gsin, gcos, nperio, cd_type='T' ) :
+    '''Rotates the Repere: Change vector componantes from
+    stretched coordinates grid --> geographic grid
+
+    All components are on the same grid (T, U, V or F)
+    '''
+    u_e = + u_i * gcos - v_j * gsin
+    v_n = + u_i * gsin + v_j * gcos
+
+    u_e = lbc (u_e, nperio=nperio, cd_type=cd_type, psgn=1.0)
+    v_n = lbc (v_n, nperio=nperio, cd_type=cd_type, psgn=1.0)
+
+    return u_e, v_n
+
+def rot_uv2en ( uo, vo, gsint, gcost, nperio, zdim=None ) :
+    '''Rotate the Repere: Change vector componantes from
+    stretched coordinates grid --> geographic grid
+
+    uo : velocity along i at the U grid point
+    vo : valocity along j at the V grid point
+    
+    Returns east-north components on the T grid point
+    '''
+    ut = u2t (uo, nperio=nperio, psgn=-1.0, zdim=zdim)
+    vt = v2t (vo, nperio=nperio, psgn=-1.0, zdim=zdim)
+
+    u_e = + ut * gcost - vt * gsint
+    v_n = + ut * gsint + vt * gcost
+
+    u_e = lbc (u_e, nperio=nperio, cd_type='T', psgn=1.0)
+    v_n = lbc (v_n, nperio=nperio, cd_type='T', psgn=1.0)
+
+    return u_e, v_n
+
+def rot_uv2enf ( uo, vo, gsinf, gcosf, nperio, zdim=None ) :
+    '''Rotates the Repere: Change vector componantes from
+    stretched coordinates grid --> geographic grid
+
+    uo : velocity along i at the U grid point
+    vo : valocity along j at the V grid point
+    
+    Returns east-north components on the F grid point
+    '''
+    uf = u2f (uo, nperio=nperio, psgn=-1.0, zdim=zdim)
+    vf = v2f (vo, nperio=nperio, psgn=-1.0, zdim=zdim)
+
+    u_e = + uf * gcosf - vf * gsinf
+    v_n = + uf * gsinf + vf * gcosf
+
+    u_e = lbc (u_e, nperio=nperio, cd_type='F', psgn= 1.0)
+    v_n = lbc (v_n, nperio=nperio, cd_type='F', psgn= 1.0)
+
+    return u_e, v_n
+
+def u2t (utab, nperio=None, psgn=-1.0, zdim=None, action='ave') :
+    '''Interpolates an array from U grid to T grid (i-mean)
+    '''
+    mmath = __mmath__ (utab)
+    utab_0 = mmath.where ( np.isnan(utab), 0., utab)
+    #lperio, aperio = lbc_diag (nperio)
+    utab_0 = lbc_add (utab_0, nperio=nperio, cd_type='U', psgn=psgn)
+    ax, ix = __find_axis__ (utab_0, 'x')
+    az     = __find_axis__ (utab_0, 'z')[0]
+
+    if ax :
+        if action == 'ave' :
+            ttab = 0.5 *      (utab_0 + np.roll (utab_0, axis=ix, shift=1))
+        if action == 'min' :
+            ttab = np.minimum (utab_0 , np.roll (utab_0, axis=ix, shift=1))
+        if action == 'max' :
+            ttab = np.maximum (utab_0 , np.roll (utab_0, axis=ix, shift=1))
+        if action == 'mult':
+            ttab =             utab_0 * np.roll (utab_0, axis=ix, shift=1)
+        ttab = lbc_del (ttab  , nperio=nperio, cd_type='T', psgn=psgn)
+    else :
+        ttab = lbc_del (utab_0, nperio=nperio, cd_type='T', psgn=psgn)
+
+    if mmath == xr :
+        if ax :
+            ttab = ttab.assign_coords({ax:np.arange (ttab.shape[ix])+1.})
+        if zdim and az :
+            if az != zdim :
+                ttab = ttab.rename( {az:zdim})
+    return ttab
+
+def v2t (vtab, nperio=None, psgn=-1.0, zdim=None, action='ave') :
+    '''Interpolates an array from V grid to T grid (j-mean)
+    '''
+    mmath = __mmath__ (vtab)
+    #lperio, aperio = lbc_diag (nperio)
+    vtab_0 = mmath.where ( np.isnan(vtab), 0., vtab)
+    vtab_0 = lbc_add (vtab_0, nperio=nperio, cd_type='V', psgn=psgn)
+    ay, jy = __find_axis__ (vtab_0, 'y')
+    az     = __find_axis__ (vtab_0, 'z')[0]
+    if ay :
+        if action == 'ave'  :
+            ttab = 0.5 *      (vtab_0 + np.roll (vtab_0, axis=jy, shift=1))
+        if action == 'min'  :
+            ttab = np.minimum (vtab_0 , np.roll (vtab_0, axis=jy, shift=1))
+        if action == 'max'  :
+            ttab = np.maximum (vtab_0 , np.roll (vtab_0, axis=jy, shift=1))
+        if action == 'mult' :
+            ttab =             vtab_0 * np.roll (vtab_0, axis=jy, shift=1)
+        ttab = lbc_del (ttab  , nperio=nperio, cd_type='T', psgn=psgn)
+    else :
+        ttab = lbc_del (vtab_0, nperio=nperio, cd_type='T', psgn=psgn)
+
+    if mmath == xr :
+        if ay :
+            ttab = ttab.assign_coords({ay:np.arange(ttab.shape[jy])+1.})
+        if zdim and az :
+            if az != zdim :
+                ttab = ttab.rename( {az:zdim})
+    return ttab
+
+def f2t (ftab, nperio=None, psgn=1.0, zdim=None, action='ave') :
+    '''Interpolates an array from F grid to T grid (i- and j- means)
+    '''
+    mmath = __mmath__ (ftab)
+    ftab_0 = mmath.where ( np.isnan(ftab), 0., ftab)
+    ftab_0 = lbc_add (ftab_0 , nperio=nperio, cd_type='F', psgn=psgn)
+    ttab = v2t (f2v (ftab_0, nperio=nperio, psgn=psgn, zdim=zdim, action=action),
+                     nperio=nperio, psgn=psgn, zdim=zdim, action=action)
+    return lbc_del (ttab, nperio=nperio, cd_type='T', psgn=psgn)
+
+def t2u (ttab, nperio=None, psgn=1.0, zdim=None, action='ave') :
+    '''Interpolates an array from T grid to U grid (i-mean)
+    '''
+    mmath = __mmath__ (ttab)
+    ttab_0 = mmath.where ( np.isnan(ttab), 0., ttab)
+    ttab_0 = lbc_add (ttab_0 , nperio=nperio, cd_type='T', psgn=psgn)
+    ax, ix = __find_axis__ (ttab_0, 'x')[0]
+    az     = __find_axis__ (ttab_0, 'z')
+    if ix :
+        if action == 'ave'  :
+            utab = 0.5 *      (ttab_0 + np.roll (ttab_0, axis=ix, shift=-1))
+        if action == 'min'  :
+            utab = np.minimum (ttab_0 , np.roll (ttab_0, axis=ix, shift=-1))
+        if action == 'max'  :
+            utab = np.maximum (ttab_0 , np.roll (ttab_0, axis=ix, shift=-1))
+        if action == 'mult' :
+            utab =             ttab_0 * np.roll (ttab_0, axis=ix, shift=-1)
+        utab = lbc_del (utab  , nperio=nperio, cd_type='U', psgn=psgn)
+    else :
+        utab = lbc_del (ttab_0, nperio=nperio, cd_type='U', psgn=psgn)
+
+    if mmath == xr :
+        if ax :
+            utab = ttab.assign_coords({ax:np.arange(utab.shape[ix])+1.})
+        if zdim and az :
+            if az != zdim :
+                utab = utab.rename( {az:zdim})
+    return utab
+
+def t2v (ttab, nperio=None, psgn=1.0, zdim=None, action='ave') :
+    '''Interpolates an array from T grid to V grid (j-mean)
+    '''
+    mmath = __mmath__ (ttab)
+    ttab_0 = mmath.where ( np.isnan(ttab), 0., ttab)
+    ttab_0 = lbc_add (ttab_0 , nperio=nperio, cd_type='T', psgn=psgn)
+    ay, jy = __find_axis__ (ttab_0, 'y')
+    az     = __find_axis__ (ttab_0, 'z')[0]
+    if jy :
+        if action == 'ave'  :
+            vtab = 0.5 *      (ttab_0 + np.roll (ttab_0, axis=jy, shift=-1))
+        if action == 'min'  :
+            vtab = np.minimum (ttab_0 , np.roll (ttab_0, axis=jy, shift=-1))
+        if action == 'max'  :
+            vtab = np.maximum (ttab_0 , np.roll (ttab_0, axis=jy, shift=-1))
+        if action == 'mult' :
+            vtab =             ttab_0 * np.roll (ttab_0, axis=jy, shift=-1)
+        vtab = lbc_del (vtab  , nperio=nperio, cd_type='V', psgn=psgn)
+    else :
+        vtab = lbc_del (ttab_0, nperio=nperio, cd_type='V', psgn=psgn)
+
+    if mmath == xr :
+        if ay :
+            vtab = vtab.assign_coords({ay:np.arange(vtab.shape[jy])+1.})
+        if zdim and az :
+            if az != zdim :
+                vtab = vtab.rename( {az:zdim})
+    return vtab
+
+def v2f (vtab, nperio=None, psgn=-1.0, zdim=None, action='ave') :
+    '''Interpolates an array from V grid to F grid (i-mean)
+    '''
+    mmath = __mmath__ (vtab)
+    vtab_0 = mmath.where ( np.isnan(vtab), 0., vtab)
+    vtab_0 = lbc_add (vtab_0 , nperio=nperio, cd_type='V', psgn=psgn)
+    ax, ix = __find_axis__ (vtab_0, 'x')
+    az     = __find_axis__ (vtab_0, 'z')[0]
+    if ix :
+        if action == 'ave'  :
+            ftab = 0.5 *      (vtab_0 + np.roll (vtab_0, axis=ix, shift=-1))
+        if action == 'min'  :
+            ftab = np.minimum (vtab_0 , np.roll (vtab_0, axis=ix, shift=-1))
+        if action == 'max'  :
+            ftab = np.maximum (vtab_0 , np.roll (vtab_0, axis=ix, shift=-1))
+        if action == 'mult' :
+            ftab =             vtab_0 * np.roll (vtab_0, axis=ix, shift=-1)
+        ftab = lbc_del (ftab  , nperio=nperio, cd_type='F', psgn=psgn)
+    else :
+        ftab = lbc_del (vtab_0, nperio=nperio, cd_type='F', psgn=psgn)
+
+    if mmath == xr :
+        if ax :
+            ftab = ftab.assign_coords({ax:np.arange(ftab.shape[ix])+1.})
+        if zdim and az :
+            if az != zdim :
+                ftab = ftab.rename( {az:zdim})
+    return lbc_del (ftab, nperio=nperio, cd_type='F', psgn=psgn)
+
+def u2f (utab, nperio=None, psgn=-1.0, zdim=None, action='ave') :
+    '''Interpolates an array from U grid to F grid i-mean)
+    '''
+    mmath = __mmath__ (utab)
+    utab_0 = mmath.where ( np.isnan(utab), 0., utab)
+    utab_0 = lbc_add (utab_0 , nperio=nperio, cd_type='U', psgn=psgn)
+    ay, jy = __find_axis__ (utab_0, 'y')
+    az     = __find_axis__ (utab_0, 'z')[0]
+    if jy :
+        if action == 'ave'  :
+            ftab = 0.5 *      (utab_0 + np.roll (utab_0, axis=jy, shift=-1))
+        if action == 'min'  :
+            ftab = np.minimum (utab_0 , np.roll (utab_0, axis=jy, shift=-1))
+        if action == 'max'  :
+            ftab = np.maximum (utab_0 , np.roll (utab_0, axis=jy, shift=-1))
+        if action == 'mult' :
+            ftab =             utab_0 * np.roll (utab_0, axis=jy, shift=-1)
+        ftab = lbc_del (ftab, nperio=nperio, cd_type='F', psgn=psgn)
+    else :
+        ftab = lbc_del (utab_0, nperio=nperio, cd_type='F', psgn=psgn)
+
+    if mmath == xr :
+        if ay :
+            ftab = ftab.assign_coords({'y':np.arange(ftab.shape[jy])+1.})
+        if zdim and az :
+            if az != zdim :
+                ftab = ftab.rename( {az:zdim})
+    return ftab
+
+def t2f (ttab, nperio=None, psgn=1.0, zdim=None, action='mean') :
+    '''Interpolates an array on T grid to F grid (i- and j- means)
+    '''
+    mmath = __mmath__ (ttab)
+    ttab_0 = mmath.where ( np.isnan(ttab), 0., ttab)
+    ttab_0 = lbc_add (ttab_0 , nperio=nperio, cd_type='T', psgn=psgn)
+    ftab = t2u (u2f (ttab, nperio=nperio, psgn=psgn, zdim=zdim, action=action),
+                     nperio=nperio, psgn=psgn, zdim=zdim, action=action)
+
+    return lbc_del (ftab, nperio=nperio, cd_type='F', psgn=psgn)
+
+def f2u (ftab, nperio=None, psgn=1.0, zdim=None, action='ave') :
+    '''Interpolates an array on F grid to U grid (j-mean)
+    '''
+    mmath = __mmath__ (ftab)
+    ftab_0 = mmath.where ( np.isnan(ftab), 0., ftab)
+    ftab_0 = lbc_add (ftab_0 , nperio=nperio, cd_type='F', psgn=psgn)
+    ay, jy = __find_axis__ (ftab_0, 'y')
+    az     = __find_axis__ (ftab_0, 'z')[0]
+    if jy :
+        if action == 'ave'  :
+            utab = 0.5 *      (ftab_0 + np.roll (ftab_0, axis=jy, shift=-1))
+        if action == 'min'  :
+            utab = np.minimum (ftab_0 , np.roll (ftab_0, axis=jy, shift=-1))
+        if action == 'max'  :
+            utab = np.maximum (ftab_0 , np.roll (ftab_0, axis=jy, shift=-1))
+        if action == 'mult' :
+            utab =             ftab_0 * np.roll (ftab_0, axis=jy, shift=-1)
+        utab = lbc_del (utab  , nperio=nperio, cd_type='U', psgn=psgn)
+    else :
+        utab = lbc_del (ftab_0, nperio=nperio, cd_type='U', psgn=psgn)
+
+    if mmath == xr :
+        utab = utab.assign_coords({ay:np.arange(ftab.shape[jy])+1.})
+        if zdim and az and az != zdim :
+            utab = utab.rename( {az:zdim})
+    return utab
+
+def f2v (ftab, nperio=None, psgn=1.0, zdim=None, action='ave') :
+    '''Interpolates an array from F grid to V grid (i-mean)
+    '''
+    mmath = __mmath__ (ftab)
+    ftab_0 = mmath.where ( np.isnan(ftab), 0., ftab)
+    ftab_0 = lbc_add (ftab_0 , nperio=nperio, cd_type='F', psgn=psgn)
+    ax, ix = __find_axis__ (ftab_0, 'x')
+    az     = __find_axis__ (ftab_0, 'z')[0]
+    if ix :
+        if action == 'ave'  :
+            vtab = 0.5 *      (ftab_0 + np.roll (ftab_0, axis=ix, shift=-1))
+        if action == 'min'  :
+            vtab = np.minimum (ftab_0 , np.roll (ftab_0, axis=ix, shift=-1))
+        if action == 'max'  :
+            vtab = np.maximum (ftab_0 , np.roll (ftab_0, axis=ix, shift=-1))
+        if action == 'mult' :
+            vtab =             ftab_0 * np.roll (ftab_0, axis=ix, shift=-1)
+        vtab = lbc_del (vtab  , nperio=nperio, cd_type='V', psgn=psgn)
+    else :
+        vtab = lbc_del (ftab_0, nperio=nperio, cd_type='V', psgn=psgn)
+
+    if mmath == xr :
+        vtab = vtab.assign_coords({ax:np.arange(ftab.shape[ix])+1.})
+        if zdim and az :
+            if az != zdim :
+                vtab = vtab.rename( {az:zdim})
+    return vtab
+
+def w2t (wtab, zcoord=None, zdim=None, sval=np.nan) :
+    '''Interpolates an array on W grid to T grid (k-mean)
+
+    sval is the bottom value
+    '''
+    mmath = __mmath__ (wtab)
+    wtab_0 = mmath.where ( np.isnan(wtab), 0., wtab)
+
+    az, kz = __find_axis__ (wtab_0, 'z')
+
+    if kz :
+        ttab = 0.5 * ( wtab_0 + np.roll (wtab_0, axis=kz, shift=-1) )
+    else :
+        ttab = wtab_0
+
+    if mmath == xr :
+        ttab[{az:kz}] = sval
+        if zdim and az :
+            if az != zdim :
+                ttab = ttab.rename ( {az:zdim} )
+        if zcoord is not None :
+            ttab = ttab.assign_coords ( {zdim:zcoord} )
+    else :
+        ttab[..., -1, :, :] = sval
+
+    return ttab
+
+def t2w (ttab, zcoord=None, zdim=None, sval=np.nan, extrap_surf=False) :
+    '''Interpolates an array from T grid to W grid (k-mean)
+
+    sval is the surface value
+    if extrap_surf==True, surface value is taken from 1st level value.
+    '''
+    mmath = __mmath__ (ttab)
+    ttab_0 = mmath.where ( np.isnan(ttab), 0., ttab)
+    az, kz = __find_axis__ (ttab_0, 'z')
+    wtab = 0.5 * ( ttab_0 + np.roll (ttab_0, axis=kz, shift=1) )
+
+    if mmath == xr :
+        if extrap_surf :
+            wtab[{az:0}] = ttab[{az:0}]
+        else           :
+            wtab[{az:0}] = sval
+    else :
+        if extrap_surf :
+            wtab[..., 0, :, :] = ttab[..., 0, :, :]
+        else           :
+            wtab[..., 0, :, :] = sval
+
+    if mmath == xr :
+        if zdim and az and az != zdim :
+            wtab = wtab.rename ( {az:zdim})
+        if zcoord is not None :
+            wtab = wtab.assign_coords ( {zdim:zcoord})
+        else :
+            wtab = wtab.assign_coords ( {zdim:np.arange(ttab.shape[kz])+1.} )
+    return wtab
+
+def fill (ptab, nperio, cd_type='T', npass=1, sval=np.nan) :
+    '''Fills np.nan values with mean of neighbours
+
+    Inputs :
+       ptab : input field to fill
+       nperio, cd_type : periodicity characteristics
+    '''
+
+    mmath = __mmath__ (ptab)
+
+    do_perio  = False
+    lperio    = nperio
+    if nperio == 4.2 :
+        do_perio, lperio = True, 4
+    if nperio == 6.2 :
+        do_perio, lperio = True, 6
+
+    if do_perio :
+        ztab = lbc_add (ptab, nperio=nperio)
+    else :
+        ztab = ptab
+
+    if np.isnan (sval) :
+        ztab   = mmath.where (np.isnan(ztab), np.nan, ztab)
+    else :
+        ztab   = mmath.where (ztab==sval    , np.nan, ztab)
+
+    for _ in np.arange (npass) :
+        zmask = mmath.where ( np.isnan(ztab), 0., 1.   )
+        ztab0 = mmath.where ( np.isnan(ztab), 0., ztab )
+        # Compte du nombre de voisins
+        zcount = 1./6. * ( zmask \
+          + np.roll(zmask, shift=1, axis=-1) + np.roll(zmask, shift=-1, axis=-1) \
+          + np.roll(zmask, shift=1, axis=-2) + np.roll(zmask, shift=-1, axis=-2) \
+          + 0.5 * ( \
+                + np.roll(np.roll(zmask, shift= 1, axis=-2), shift= 1, axis=-1) \
+                + np.roll(np.roll(zmask, shift=-1, axis=-2), shift= 1, axis=-1) \
+                + np.roll(np.roll(zmask, shift= 1, axis=-2), shift=-1, axis=-1) \
+                + np.roll(np.roll(zmask, shift=-1, axis=-2), shift=-1, axis=-1) ) )
+
+        znew =1./6. * ( ztab0 \
+           + np.roll(ztab0, shift=1, axis=-1) + np.roll(ztab0, shift=-1, axis=-1) \
+           + np.roll(ztab0, shift=1, axis=-2) + np.roll(ztab0, shift=-1, axis=-2) \
+           + 0.5 * ( \
+                + np.roll(np.roll(ztab0 , shift= 1, axis=-2), shift= 1, axis=-1) \
+                + np.roll(np.roll(ztab0 , shift=-1, axis=-2), shift= 1, axis=-1) \
+                + np.roll(np.roll(ztab0 , shift= 1, axis=-2), shift=-1, axis=-1) \
+                + np.roll(np.roll(ztab0 , shift=-1, axis=-2), shift=-1, axis=-1) ) )
+
+        zcount = lbc (zcount, nperio=lperio, cd_type=cd_type)
+        znew   = lbc (znew  , nperio=lperio, cd_type=cd_type)
+
+        ztab = mmath.where (np.logical_and (zmask==0., zcount>0), znew/zcount, ztab)
+
+    ztab = mmath.where (zcount==0, sval, ztab)
+    if do_perio :
+        ztab = lbc_del (ztab, nperio=lperio)
+
+    return ztab
+
+def correct_uv (u, v, lat) :
+    '''
+    Corrects a Cartopy bug in orthographic projection
+
+    See https://github.com/SciTools/cartopy/issues/1179
+
+    The correction is needed with cartopy <= 0.20
+    It seems that version 0.21 will correct the bug (https://github.com/SciTools/cartopy/pull/1926)
+    Later note : the bug is still present in Cartopy 0.22
+
+    Inputs :
+       u, v : eastward/northward components
+       lat  : latitude of the point (degrees north)
+
+    Outputs :
+       modified eastward/nothward components to have correct polar projections in cartopy
+    '''
+    uv = np.sqrt (u*u + v*v)           # Original modulus
+    zu = u
+    zv = v * np.cos (RAD*lat)
+    zz = np.sqrt ( zu*zu + zv*zv )     # Corrected modulus
+    uc = zu*uv/zz
+    vc = zv*uv/zz      # Final corrected values
+    return uc, vc
+
+def norm_uv (u, v) :
+    '''Returns norm of a 2 components vector
+    '''
+    return np.sqrt (u*u + v*v)
+
+def normalize_uv (u, v) :
+    '''Normalizes 2 components vector
+    '''
+    uv = norm_uv (u, v)
+    return u/uv, v/uv
+
+def msf (vv, e1v_e3v, plat1d, depthw) :
+    '''Computes the meridonal stream function
+
+    vv : meridional_velocity
+    e1v_e3v : prodcut of scale factors e1v*e3v
+    '''
+
+    v_e1v_e3v = vv * e1v_e3v
+    v_e1v_e3v.attrs = vv.attrs
+
+    ax = __find_axis__ (v_e1v_e3v, 'x')[0]
+    az = __find_axis__ (v_e1v_e3v, 'z')[0]
+    if az == 'olevel' :
+        new_az = 'olevel'
+    else :
+        new_az = 'depthw'
+
+    zomsf = -v_e1v_e3v.cumsum ( dim=az, keep_attrs=True).sum (dim=ax, keep_attrs=True)*1.E-6
+    zomsf = zomsf - zomsf.isel ( { az:-1} )
+
+    ay = __find_axis__ (zomsf, 'y' )[0]
+    zomsf = zomsf.assign_coords ( {az:depthw.values, ay:plat1d.values})
+
+    zomsf = zomsf.rename ( {ay:'lat'})
+    if az != new_az :
+        zomsf = zomsf.rename ( {az:new_az} )
+    zomsf.attrs['standard_name'] = 'Meridional stream function'
+    zomsf.attrs['long_name'] = 'Meridional stream function'
+    zomsf.attrs['units'] = 'Sv'
+    zomsf[new_az].attrs  = depthw.attrs
+    zomsf.lat.attrs=plat1d.attrs
+
+    return zomsf
+
+def bsf (uu, e2u_e3u, mask, nperio=None, bsf0=None ) :
+    '''Computes the barotropic stream function
+
+    uu      : zonal_velocity
+    e2u_e3u : product of scales factor e2u*e3u
+    bsf0    : the point with bsf=0
+    (ex: bsf0={'x':3, 'y':120} for orca2,
+         bsf0={'x':5, 'y':300} for eORCA1
+    '''
+    u_e2u_e3u       = uu * e2u_e3u
+    u_e2u_e3u.attrs = uu.attrs
+
+    ay = __find_axis__ (u_e2u_e3u, 'y')[0]
+    az = __find_axis__ (u_e2u_e3u, 'z')[0]
+
+    zbsf = -u_e2u_e3u.cumsum ( dim=ay, keep_attrs=True )
+    zbsf = zbsf.sum (dim=az, keep_attrs=True)*1.E-6
+
+    if bsf0 :
+        zbsf = zbsf - zbsf.isel (bsf0)
+
+    zbsf = zbsf.where (mask !=0, np.nan)
+    zbsf.attrs.update (uu.attrs)
+    zbsf.attrs['standard_name'] = 'barotropic_stream_function'
+    zbsf.attrs['long_name']     = 'Barotropic stream function'
+    zbsf.attrs['units']         = 'Sv'
+    zbsf = lbc (zbsf, nperio=nperio, cd_type='F')
+
+    return zbsf
+
+if f90nml :
+    def namelist_read (ref=None, cfg=None, out='dict', flat=False, verbose=False) :
+        '''Read NEMO namelist(s) and return either a dictionnary or an xarray dataset
+
+        ref : file with reference namelist, or a f90nml.namelist.Namelist object
+        cfg : file with config namelist, or a f90nml.namelist.Namelist object
+        At least one namelist neaded
+
+        out:
+        'dict' to return a dictonnary
+        'xr'   to return an xarray dataset
+        flat : only for dict output. Output a flat dictionary with all values.
+
+        '''
+        if ref :
+            if isinstance (ref, str) :
+                nml_ref = f90nml.read (ref)
+            if isinstance (ref, f90nml.namelist.Namelist) :
+                nml_ref = ref
+
+        if cfg :
+            if isinstance (cfg, str) :
+                nml_cfg = f90nml.read (cfg)
+            if isinstance (cfg, f90nml.namelist.Namelist) :
+                nml_cfg = cfg
+
+        if out == 'dict' :
+            dict_namelist = {}
+        if out == 'xr'   :
+            xr_namelist = xr.Dataset ()
+
+        list_nml     = []
+        list_comment = []
+
+        if ref :
+            list_nml.append (nml_ref)
+            list_comment.append ('ref')
+        if cfg :
+            list_nml.append (nml_cfg)
+            list_comment.append ('cfg')
+
+        for nml, comment in zip (list_nml, list_comment) :
+            if verbose :
+                print (comment)
+            if flat and out =='dict' :
+                for nam in nml.keys () :
+                    if verbose :
+                        print (nam)
+                    for value in nml[nam] :
+                        if out == 'dict' :
+                            dict_namelist[value] = nml[nam][value]
+                        if verbose :
+                            print (nam, ':', value, ':', nml[nam][value])
+            else :
+                for nam in nml.keys () :
+                    if verbose :
+                        print (nam)
+                    if out == 'dict' :
+                        if nam not in dict_namelist.keys () :
+                            dict_namelist[nam] = {}
+                    for value in nml[nam] :
+                        if out == 'dict' :
+                            dict_namelist[nam][value] = nml[nam][value]
+                        if out == 'xr'   :
+                            xr_namelist[value] = nml[nam][value]
+                        if verbose :
+                            print (nam, ':', value, ':', nml[nam][value])
+
+        if out == 'dict' :
+            return dict_namelist
+        if out == 'xr'   :
+            return xr_namelist
+else :
+     def namelist_read (ref=None, cfg=None, out='dict', flat=False, verbose=False) :
+        '''Shadow version of namelist read, when f90nm module was not found
+
+        namelist_read : 
+        Read NEMO namelist(s) and return either a dictionnary or an xarray dataset
+        '''
+        print ( 'Error : module f90nml not found' )
+        print ( 'Cannot call namelist_read' )
+        print ( 'Call parameters where : ')
+        print ( f'{err=} {ref=} {cfg=} {out=} {flat=} {verbose=}' )
+
+def fill_closed_seas (imask, nperio=None,  cd_type='T') :
+    '''Fill closed seas with image processing library
+
+    imask : mask, 1 on ocean, 0 on land
+    '''
+    from scipy import ndimage
+
+    imask_filled = ndimage.binary_fill_holes ( lbc (imask, nperio=nperio, cd_type=cd_type))
+    imask_filled = lbc ( imask_filled, nperio=nperio, cd_type=cd_type)
+
+    return imask_filled
+
+# ======================================================
+# Sea water state function parameters from NEMO code
+
+RDELTAS = 32.
+R1_S0   = 0.875/35.16504
+R1_T0   = 1./40.
+R1_Z0   = 1.e-4
+
+EOS000 =  8.0189615746e+02
+EOS100 =  8.6672408165e+02
+EOS200 = -1.7864682637e+03
+EOS300 =  2.0375295546e+03
+EOS400 = -1.2849161071e+03
+EOS500 =  4.3227585684e+02
+EOS600 = -6.0579916612e+01
+EOS010 =  2.6010145068e+01
+EOS110 = -6.5281885265e+01
+EOS210 =  8.1770425108e+01
+EOS310 = -5.6888046321e+01
+EOS410 =  1.7681814114e+01
+EOS510 = -1.9193502195
+EOS020 = -3.7074170417e+01
+EOS120 =  6.1548258127e+01
+EOS220 = -6.0362551501e+01
+EOS320 =  2.9130021253e+01
+EOS420 = -5.4723692739
+EOS030 =  2.1661789529e+01
+EOS130 = -3.3449108469e+01
+EOS230 =  1.9717078466e+01
+EOS330 = -3.1742946532
+EOS040 = -8.3627885467
+EOS140 =  1.1311538584e+01
+EOS240 = -5.3563304045
+EOS050 =  5.4048723791e-01
+EOS150 =  4.8169980163e-01
+EOS060 = -1.9083568888e-01
+EOS001 =  1.9681925209e+01
+EOS101 = -4.2549998214e+01
+EOS201 =  5.0774768218e+01
+EOS301 = -3.0938076334e+01
+EOS401 =  6.6051753097
+EOS011 = -1.3336301113e+01
+EOS111 = -4.4870114575
+EOS211 =  5.0042598061
+EOS311 = -6.5399043664e-01
+EOS021 =  6.7080479603
+EOS121 =  3.5063081279
+EOS221 = -1.8795372996
+EOS031 = -2.4649669534
+EOS131 = -5.5077101279e-01
+EOS041 =  5.5927935970e-01
+EOS002 =  2.0660924175
+EOS102 = -4.9527603989
+EOS202 =  2.5019633244
+EOS012 =  2.0564311499
+EOS112 = -2.1311365518e-01
+EOS022 = -1.2419983026
+EOS003 = -2.3342758797e-02
+EOS103 = -1.8507636718e-02
+EOS013 =  3.7969820455e-01
+
+def rhop ( ptemp, psal ) :
+    '''Returns potential density referenced to surface
+
+    Computation from NEMO code
+    '''
+    zt      = ptemp * R1_T0                                  # Temperature (Â°C)
+    zs      = np.sqrt ( np.abs( psal + RDELTAS ) * R1_S0 )   # Square root of salinity (PSS)
+    #
+    prhop = (
+      (((((EOS060*zt
+         + EOS150*zs     + EOS050)*zt
+         + (EOS240*zs    + EOS140)*zs + EOS040)*zt
+         + ((EOS330*zs   + EOS230)*zs + EOS130)*zs + EOS030)*zt
+         + (((EOS420*zs  + EOS320)*zs + EOS220)*zs + EOS120)*zs + EOS020)*zt
+         + ((((EOS510*zs + EOS410)*zs + EOS310)*zs + EOS210)*zs + EOS110)*zs + EOS010)*zt
+         + (((((EOS600*zs+ EOS500)*zs + EOS400)*zs + EOS300)*zs + EOS200)*zs + EOS100)*zs + EOS000 )
+    #
+    return prhop
+
+def rho ( pdep, ptemp, psal ) :
+    '''Returns in situ density
+
+    Computation from NEMO code
+    '''
+    zh      = pdep  * R1_Z0                                  # Depth (m)
+    zt      = ptemp * R1_T0                                  # Temperature (Â°C)
+    zs      = np.sqrt ( np.abs( psal + RDELTAS ) * R1_S0 )   # Square root salinity (PSS)
+    #
+    zn3 = EOS013*zt + EOS103*zs+EOS003
+    #
+    zn2 = (EOS022*zt + EOS112*zs+EOS012)*zt + (EOS202*zs+EOS102)*zs+EOS002
+    #
+    zn1 = (
+      (((EOS041*zt
+       + EOS131*zs   + EOS031)*zt
+       + (EOS221*zs  + EOS121)*zs + EOS021)*zt
+       + ((EOS311*zs  + EOS211)*zs + EOS111)*zs + EOS011)*zt
+       + (((EOS401*zs + EOS301)*zs + EOS201)*zs + EOS101)*zs + EOS001 )
+    #
+    zn0 = (
+      (((((EOS060*zt
+         + EOS150*zs      + EOS050)*zt
+         + (EOS240*zs     + EOS140)*zs + EOS040)*zt
+         + ((EOS330*zs    + EOS230)*zs + EOS130)*zs + EOS030)*zt
+         + (((EOS420*zs   + EOS320)*zs + EOS220)*zs + EOS120)*zs + EOS020)*zt
+         + ((((EOS510*zs  + EOS410)*zs + EOS310)*zs + EOS210)*zs + EOS110)*zs + EOS010)*zt
+         + (((((EOS600*zs + EOS500)*zs + EOS400)*zs + EOS300)*zs +
+                                       EOS200)*zs + EOS100)*zs + EOS000 )
+    #
+    prho  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+    #
+    return prho
+
 ## ===========================================================================
 ##
@@ -96,2 +2554,45 @@
 ##
 ## ===========================================================================
+
+# def __is_orca_north_fold__ ( Xtest, cname_long='T' ) :
+#     '''
+#     Ported (pirated !!?) from Sosie
+
+#     Tell if there is a 2/point band overlaping folding at the north pole typical of the ORCA grid
+
+#     0 => not an orca grid (or unknown one)
+#     4 => North fold T-point pivot (ex: ORCA2)
+#     6 => North fold F-point pivot (ex: ORCA1)
+
+#     We need all this 'cname_long' stuff because with our method, there is a
+#     confusion between "Grid_U with T-fold" and "Grid_V with F-fold"
+#     => so knowing the name of the longitude array (as in namelist, and hence as
+#     in netcdf file) might help taking the righ decision !!! UGLY!!!
+#     => not implemented yet
+#     '''
+
+#     ifld_nord =  0 ; cgrd_type = 'X'
+#     ny, nx = Xtest.shape[-2:]
+
+#     if ny > 3 : # (case if called with a 1D array, ignoring...)
+#         if ( Xtest [ny-1, 1:nx//2-1] - Xtest [ny-3, nx-1:nx-nx//2+1:-1] ).sum() == 0. :
+#           ifld_nord = 4 ; cgrd_type = 'T' # T-pivot, grid_T
+
+#         if ( Xtest [ny-1, 1:nx//2-1] - Xtest [ny-3, nx-2:nx-nx//2  :-1] ).sum() == 0. :
+#             if cnlon == 'U' : ifld_nord = 4 ;  cgrd_type = 'U' # T-pivot, grid_T
+#                 ## LOLO: PROBLEM == 6, V !!!
+
+#         if ( Xtest [ny-1, 1:nx//2-1] - Xtest [ny-3, nx-1:nx-nx//2+1:-1] ).sum() == 0. :
+#             ifld_nord = 4 ; cgrd_type = 'V' # T-pivot, grid_V
+
+#         if ( Xtest [ny-1, 1:nx//2-1] - Xtest [ny-2, nx-1-1:nx-nx//2:-1] ).sum() == 0. :
+#             ifld_nord = 6 ; cgrd_type = 'T'# F-pivot, grid_T
+
+#         if ( Xtest [ny-1, 1:nx//2-1] - Xtest [ny-1, nx-1:nx-nx//2-1:-1] ).sum() == 0. :
+#             ifld_nord = 6 ;  cgrd_type = 'U' # F-pivot, grid_U
+
+#         if ( Xtest [ny-1, 1:nx//2-1] - Xtest [ny-3, nx-2:nx-nx//2  :-1] ).sum() == 0. :
+#             if cnlon == 'V' : ifld_nord = 6 ; cgrd_type = 'V' # F-pivot, grid_V
+#                 ## LOLO: PROBLEM == 4, U !!!
+
+#     return ifld_nord, cgrd_type
