Index: branches/2014/dev_r4650_UKMO12_CFL_diags_take2/NEMOGCM/NEMO/OPA_SRC/TRA/eosbn2.F90
===================================================================
--- branches/2014/dev_r4650_UKMO12_CFL_diags_take2/NEMOGCM/NEMO/OPA_SRC/TRA/eosbn2.F90	(revision 4712)
+++ branches/2014/dev_r4650_UKMO12_CFL_diags_take2/NEMOGCM/NEMO/OPA_SRC/TRA/eosbn2.F90	(revision 5832)
@@ -15,7 +15,11 @@
    !!             -   ! 2002-11  (G. Madec, A. Bozec)  partial step, eos_insitu_2d
    !!             -   ! 2003-08  (G. Madec)  F90, free form
-   !!            3.0  ! 2006-08  (G. Madec)  add tfreez function
+   !!            3.0  ! 2006-08  (G. Madec)  add tfreez function (now eos_fzp function)
    !!            3.3  ! 2010-05  (C. Ethe, G. Madec)  merge TRC-TRA
-   !!             -   ! 2010-10  (G. Nurser, G. Madec)  add eos_alpbet used in ldfslp
+   !!             -   ! 2010-10  (G. Nurser, G. Madec)  add alpha/beta used in ldfslp
+   !!            3.7  ! 2012-03  (F. Roquet, G. Madec)  add primitive of alpha and beta used in PE computation
+   !!             -   ! 2012-05  (F. Roquet)  add Vallis and original JM95 equation of state
+   !!             -   ! 2013-04  (F. Roquet, G. Madec)  add eos_rab, change bn2 computation and reorganize the module
+   !!             -   ! 2014-09  (F. Roquet)  add TEOS-10, S-EOS, and modify EOS-80
    !!----------------------------------------------------------------------
 
@@ -23,20 +27,26 @@
    !!   eos            : generic interface of the equation of state
    !!   eos_insitu     : Compute the in situ density
-   !!   eos_insitu_pot : Compute the insitu and surface referenced potential
-   !!                    volumic mass
+   !!   eos_insitu_pot : Compute the insitu and surface referenced potential volumic mass
    !!   eos_insitu_2d  : Compute the in situ density for 2d fields
-   !!   eos_bn2        : Compute the Brunt-Vaisala frequency
-   !!   eos_alpbet     : calculates the in situ thermal/haline expansion ratio
-   !!   tfreez         : Compute the surface freezing temperature
+   !!   bn2            : Compute the Brunt-Vaisala frequency
+   !!   eos_rab        : generic interface of in situ thermal/haline expansion ratio 
+   !!   eos_rab_3d     : compute in situ thermal/haline expansion ratio
+   !!   eos_rab_2d     : compute in situ thermal/haline expansion ratio for 2d fields
+   !!   eos_fzp_2d     : freezing temperature for 2d fields
+   !!   eos_fzp_0d     : freezing temperature for scalar
    !!   eos_init       : set eos parameters (namelist)
    !!----------------------------------------------------------------------
    USE dom_oce         ! ocean space and time domain
    USE phycst          ! physical constants
-   USE zdfddm          ! vertical physics: double diffusion
+   !
    USE in_out_manager  ! I/O manager
    USE lib_mpp         ! MPP library
+   USE lib_fortran     ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)  
    USE prtctl          ! Print control
    USE wrk_nemo        ! Memory Allocation
+   USE lbclnk         ! ocean lateral boundary conditions
    USE timing          ! Timing
+   USE stopar          ! Stochastic T/S fluctuations
+   USE stopts          ! Stochastic T/S fluctuations
 
    IMPLICIT NONE
@@ -47,20 +57,116 @@
       MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d
    END INTERFACE
-   INTERFACE bn2
-      MODULE PROCEDURE eos_bn2
+   !
+   INTERFACE eos_rab
+      MODULE PROCEDURE rab_3d, rab_2d, rab_0d
    END INTERFACE
-
-   PUBLIC   eos        ! called by step, istate, tranpc and zpsgrd modules
-   PUBLIC   eos_init   ! called by istate module
-   PUBLIC   bn2        ! called by step module
-   PUBLIC   eos_alpbet ! called by ldfslp module
-   PUBLIC   tfreez     ! called by sbcice_... modules
-
-   !                                  !!* Namelist (nameos) *
-   INTEGER , PUBLIC ::   nn_eos       !: = 0/1/2 type of eq. of state and Brunt-Vaisala frequ.
-   REAL(wp), PUBLIC ::   rn_alpha     !: thermal expension coeff. (linear equation of state)
-   REAL(wp), PUBLIC ::   rn_beta      !: saline  expension coeff. (linear equation of state)
-
-   REAL(wp), PUBLIC ::   ralpbet              !: alpha / beta ratio
+   !
+   INTERFACE eos_fzp 
+      MODULE PROCEDURE eos_fzp_2d, eos_fzp_0d
+   END INTERFACE
+   !
+   PUBLIC   eos            ! called by step, istate, tranpc and zpsgrd modules
+   PUBLIC   bn2            ! called by step module
+   PUBLIC   eos_rab        ! called by ldfslp, zdfddm, trabbl
+   PUBLIC   eos_pt_from_ct ! called by sbcssm
+   PUBLIC   eos_fzp        ! called by traadv_cen2 and sbcice_... modules
+   PUBLIC   eos_pen        ! used for pe diagnostics in trdpen module
+   PUBLIC   eos_init       ! called by istate module
+
+   !                                !!* Namelist (nameos) *
+   INTEGER , PUBLIC ::   nn_eos     ! = 0/1/2 type of eq. of state and Brunt-Vaisala frequ.
+   LOGICAL , PUBLIC ::   ln_useCT   ! determine if eos_pt_from_ct is used to compute sst_m
+
+   !                                   !!!  simplified eos coefficients
+   ! default value: Vallis 2006
+   REAL(wp) ::   rn_a0      = 1.6550e-1_wp     ! thermal expansion coeff. 
+   REAL(wp) ::   rn_b0      = 7.6554e-1_wp     ! saline  expansion coeff. 
+   REAL(wp) ::   rn_lambda1 = 5.9520e-2_wp     ! cabbeling coeff. in T^2        
+   REAL(wp) ::   rn_lambda2 = 5.4914e-4_wp     ! cabbeling coeff. in S^2        
+   REAL(wp) ::   rn_mu1     = 1.4970e-4_wp     ! thermobaric coeff. in T  
+   REAL(wp) ::   rn_mu2     = 1.1090e-5_wp     ! thermobaric coeff. in S  
+   REAL(wp) ::   rn_nu      = 2.4341e-3_wp     ! cabbeling coeff. in theta*salt  
+   
+   ! TEOS10/EOS80 parameters
+   REAL(wp) ::   r1_S0, r1_T0, r1_Z0, rdeltaS
+   
+   ! EOS parameters
+   REAL(wp) ::   EOS000 , EOS100 , EOS200 , EOS300 , EOS400 , EOS500 , EOS600
+   REAL(wp) ::   EOS010 , EOS110 , EOS210 , EOS310 , EOS410 , EOS510
+   REAL(wp) ::   EOS020 , EOS120 , EOS220 , EOS320 , EOS420
+   REAL(wp) ::   EOS030 , EOS130 , EOS230 , EOS330
+   REAL(wp) ::   EOS040 , EOS140 , EOS240
+   REAL(wp) ::   EOS050 , EOS150
+   REAL(wp) ::   EOS060
+   REAL(wp) ::   EOS001 , EOS101 , EOS201 , EOS301 , EOS401
+   REAL(wp) ::   EOS011 , EOS111 , EOS211 , EOS311
+   REAL(wp) ::   EOS021 , EOS121 , EOS221
+   REAL(wp) ::   EOS031 , EOS131
+   REAL(wp) ::   EOS041
+   REAL(wp) ::   EOS002 , EOS102 , EOS202
+   REAL(wp) ::   EOS012 , EOS112
+   REAL(wp) ::   EOS022
+   REAL(wp) ::   EOS003 , EOS103
+   REAL(wp) ::   EOS013 
+   
+   ! ALPHA parameters
+   REAL(wp) ::   ALP000 , ALP100 , ALP200 , ALP300 , ALP400 , ALP500
+   REAL(wp) ::   ALP010 , ALP110 , ALP210 , ALP310 , ALP410
+   REAL(wp) ::   ALP020 , ALP120 , ALP220 , ALP320
+   REAL(wp) ::   ALP030 , ALP130 , ALP230
+   REAL(wp) ::   ALP040 , ALP140
+   REAL(wp) ::   ALP050
+   REAL(wp) ::   ALP001 , ALP101 , ALP201 , ALP301
+   REAL(wp) ::   ALP011 , ALP111 , ALP211
+   REAL(wp) ::   ALP021 , ALP121
+   REAL(wp) ::   ALP031
+   REAL(wp) ::   ALP002 , ALP102
+   REAL(wp) ::   ALP012
+   REAL(wp) ::   ALP003
+   
+   ! BETA parameters
+   REAL(wp) ::   BET000 , BET100 , BET200 , BET300 , BET400 , BET500
+   REAL(wp) ::   BET010 , BET110 , BET210 , BET310 , BET410
+   REAL(wp) ::   BET020 , BET120 , BET220 , BET320
+   REAL(wp) ::   BET030 , BET130 , BET230
+   REAL(wp) ::   BET040 , BET140
+   REAL(wp) ::   BET050
+   REAL(wp) ::   BET001 , BET101 , BET201 , BET301
+   REAL(wp) ::   BET011 , BET111 , BET211
+   REAL(wp) ::   BET021 , BET121
+   REAL(wp) ::   BET031
+   REAL(wp) ::   BET002 , BET102
+   REAL(wp) ::   BET012
+   REAL(wp) ::   BET003
+
+   ! PEN parameters
+   REAL(wp) ::   PEN000 , PEN100 , PEN200 , PEN300 , PEN400
+   REAL(wp) ::   PEN010 , PEN110 , PEN210 , PEN310
+   REAL(wp) ::   PEN020 , PEN120 , PEN220
+   REAL(wp) ::   PEN030 , PEN130
+   REAL(wp) ::   PEN040
+   REAL(wp) ::   PEN001 , PEN101 , PEN201
+   REAL(wp) ::   PEN011 , PEN111
+   REAL(wp) ::   PEN021
+   REAL(wp) ::   PEN002 , PEN102
+   REAL(wp) ::   PEN012
+   
+   ! ALPHA_PEN parameters
+   REAL(wp) ::   APE000 , APE100 , APE200 , APE300
+   REAL(wp) ::   APE010 , APE110 , APE210
+   REAL(wp) ::   APE020 , APE120
+   REAL(wp) ::   APE030
+   REAL(wp) ::   APE001 , APE101
+   REAL(wp) ::   APE011
+   REAL(wp) ::   APE002
+
+   ! BETA_PEN parameters
+   REAL(wp) ::   BPE000 , BPE100 , BPE200 , BPE300
+   REAL(wp) ::   BPE010 , BPE110 , BPE210
+   REAL(wp) ::   BPE020 , BPE120
+   REAL(wp) ::   BPE030
+   REAL(wp) ::   BPE001 , BPE101
+   REAL(wp) ::   BPE011
+   REAL(wp) ::   BPE002
 
    !! * Substitutions
@@ -68,5 +174,5 @@
 #  include "vectopt_loop_substitute.h90"
    !!----------------------------------------------------------------------
-   !! NEMO/OPA 3.3 , NEMO Consortium (2010)
+   !! NEMO/OPA 3.7 , NEMO Consortium (2014)
    !! $Id$
    !! Software governed by the CeCILL licence     (NEMOGCM/NEMO_CeCILL.txt)
@@ -82,117 +188,108 @@
       !!       defined through the namelist parameter nn_eos.
       !!
-      !! ** Method  :   3 cases:
-      !!      nn_eos = 0 : Jackett and McDougall (1994) equation of state.
-      !!         the in situ density is computed directly as a function of
-      !!         potential temperature relative to the surface (the opa t
-      !!         variable), salt and pressure (assuming no pressure variation
-      !!         along geopotential surfaces, i.e. the pressure p in decibars
-      !!         is approximated by the depth in meters.
-      !!              prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0
-      !!         with pressure                      p        decibars
-      !!              potential temperature         t        deg celsius
-      !!              salinity                      s        psu
-      !!              reference volumic mass        rau0     kg/m**3
-      !!              in situ volumic mass          rho      kg/m**3
-      !!              in situ density anomalie      prd      no units
-      !!         Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar,
-      !!          t = 40 deg celcius, s=40 psu
-      !!      nn_eos = 1 : linear equation of state function of temperature only
-      !!              prd(t) = 0.0285 - rn_alpha * t
-      !!      nn_eos = 2 : linear equation of state function of temperature and
-      !!               salinity
-      !!              prd(t,s) = rn_beta * s - rn_alpha * tn - 1.
-      !!      Note that no boundary condition problem occurs in this routine
-      !!      as pts are defined over the whole domain.
+      !! ** Method  :   prd(t,s,z) = ( rho(t,s,z) - rau0 ) / rau0
+      !!         with   prd    in situ density anomaly      no units
+      !!                t      TEOS10: CT or EOS80: PT      Celsius
+      !!                s      TEOS10: SA or EOS80: SP      TEOS10: g/kg or EOS80: psu
+      !!                z      depth                        meters
+      !!                rho    in situ density              kg/m^3
+      !!                rau0   reference density            kg/m^3
+      !!
+      !!     nn_eos = -1 : polynomial TEOS-10 equation of state is used for rho(t,s,z).
+      !!         Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celcius, sa=35.5 g/kg
+      !!
+      !!     nn_eos =  0 : polynomial EOS-80 equation of state is used for rho(t,s,z).
+      !!         Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celcius, sp=35.5 psu
+      !!
+      !!     nn_eos =  1 : simplified equation of state
+      !!              prd(t,s,z) = ( -a0*(1+lambda/2*(T-T0)+mu*z+nu*(S-S0))*(T-T0) + b0*(S-S0) ) / rau0
+      !!              linear case function of T only: rn_alpha<>0, other coefficients = 0
+      !!              linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0
+      !!              Vallis like equation: use default values of coefficients
       !!
       !! ** Action  :   compute prd , the in situ density (no units)
       !!
-      !! References :   Jackett and McDougall, J. Atmos. Ocean. Tech., 1994
-      !!----------------------------------------------------------------------
-      !!
-      REAL(wp), DIMENSION(:,:,:,:), INTENT(in   ) ::   pts   ! 1 : potential temperature  [Celcius]
-      !                                                      ! 2 : salinity               [psu]
-      REAL(wp), DIMENSION(:,:,:)  , INTENT(  out) ::   prd   ! in situ density            [-]
-      REAL(wp), DIMENSION(:,:,:)  , INTENT(in   ) ::   pdep  ! depth                      [m]
-      !!
-      INTEGER  ::   ji, jj, jk           ! dummy loop indices
-      REAL(wp) ::   zt , zs , zh , zsr   ! local scalars
-      REAL(wp) ::   zr1, zr2, zr3, zr4   !   -      -
-      REAL(wp) ::   zrhop, ze, zbw, zb   !   -      -
-      REAL(wp) ::   zd , zc , zaw, za    !   -      -
-      REAL(wp) ::   zb1, za1, zkw, zk0   !   -      -
-      REAL(wp), POINTER, DIMENSION(:,:,:) :: zws
-      !!----------------------------------------------------------------------
-
-      !
-      IF( nn_timing == 1 ) CALL timing_start('eos')
-      !
-      CALL wrk_alloc( jpi, jpj, jpk, zws )
+      !! References :   Roquet et al, Ocean Modelling, in preparation (2014)
+      !!                Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006
+      !!                TEOS-10 Manual, 2010
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::   pts   ! 1 : potential temperature  [Celcius]
+      !                                                               ! 2 : salinity               [psu]
+      REAL(wp), DIMENSION(jpi,jpj,jpk     ), INTENT(  out) ::   prd   ! in situ density            [-]
+      REAL(wp), DIMENSION(jpi,jpj,jpk     ), INTENT(in   ) ::   pdep  ! depth                      [m]
+      !
+      INTEGER  ::   ji, jj, jk                ! dummy loop indices
+      REAL(wp) ::   zt , zh , zs , ztm        ! local scalars
+      REAL(wp) ::   zn , zn0, zn1, zn2, zn3   !   -      -
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 )   CALL timing_start('eos-insitu')
       !
       SELECT CASE( nn_eos )
       !
-      CASE( 0 )                !==  Jackett and McDougall (1994) formulation  ==!
-!CDIR NOVERRCHK
-         zws(:,:,:) = SQRT( ABS( pts(:,:,:,jp_sal) ) )
+      CASE( -1, 0 )                !==  polynomial TEOS-10 / EOS-80 ==!
          !
          DO jk = 1, jpkm1
             DO jj = 1, jpj
                DO ji = 1, jpi
-                  zt = pts   (ji,jj,jk,jp_tem)
-                  zs = pts   (ji,jj,jk,jp_sal)
-                  zh = pdep(ji,jj,jk)        ! depth
-                  zsr= zws   (ji,jj,jk)        ! square root salinity
-                  !
-                  ! compute volumic mass pure water at atm pressure
-                  zr1= ( ( ( ( 6.536332e-9_wp  *zt - 1.120083e-6_wp )*zt + 1.001685e-4_wp )*zt   &
-                     &        -9.095290e-3_wp )*zt + 6.793952e-2_wp )*zt +  999.842594_wp
-                  ! seawater volumic mass atm pressure
-                  zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt        &
-                     &                      -4.0899e-3_wp ) *zt+0.824493_wp
-                  zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp )    *zt-5.72466e-3_wp
-                  zr4= 4.8314e-4_wp
-                  !
-                  ! potential volumic mass (reference to the surface)
-                  zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1
-                  !
-                  ! add the compression terms
-                  ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp
-                  zbw= (  1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp
-                  zb = zbw + ze * zs
-                  !
-                  zd = -2.042967e-2_wp
-                  zc =   (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp
-                  zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp
-                  za = ( zd*zsr + zc ) *zs + zaw
-                  !
-                  zb1=   (-0.1909078_wp*zt+7.390729_wp )        *zt-55.87545_wp
-                  za1= ( ( 2.326469e-3_wp*zt+1.553190_wp)       *zt-65.00517_wp ) *zt+1044.077_wp
-                  zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp
-                  zk0= ( zb1*zsr + za1 )*zs + zkw
-                  !
-                  ! masked in situ density anomaly
-                  prd(ji,jj,jk) = (  zrhop / (  1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) )  )    &
-                     &             - rau0  ) * r1_rau0 * tmask(ji,jj,jk)
+                  !
+                  zh  = pdep(ji,jj,jk) * r1_Z0                                  ! depth
+                  zt  = pts (ji,jj,jk,jp_tem) * r1_T0                           ! temperature
+                  zs  = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 )   ! square root salinity
+                  ztm = tmask(ji,jj,jk)                                         ! tmask
+                  !
+                  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
+                     !
+                  zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+                  !
+                  prd(ji,jj,jk) = (  zn * r1_rau0 - 1._wp  ) * ztm  ! density anomaly (masked)
+                  !
                END DO
             END DO
          END DO
          !
-      CASE( 1 )                !==  Linear formulation function of temperature only  ==!
+      CASE( 1 )                !==  simplified EOS  ==!
+         !
          DO jk = 1, jpkm1
-            prd(:,:,jk) = ( 0.0285_wp - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk)
+            DO jj = 1, jpj
+               DO ji = 1, jpi
+                  zt  = pts  (ji,jj,jk,jp_tem) - 10._wp
+                  zs  = pts  (ji,jj,jk,jp_sal) - 35._wp
+                  zh  = pdep (ji,jj,jk)
+                  ztm = tmask(ji,jj,jk)
+                  !
+                  zn =  - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt + rn_mu1*zh ) * zt   &
+                     &  + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs - rn_mu2*zh ) * zs   &
+                     &  - rn_nu * zt * zs
+                     !                                 
+                  prd(ji,jj,jk) = zn * r1_rau0 * ztm                ! density anomaly (masked)
+               END DO
+            END DO
          END DO
          !
-      CASE( 2 )                !==  Linear formulation function of temperature and salinity  ==!
-         DO jk = 1, jpkm1
-            prd(:,:,jk) = ( rn_beta  * pts(:,:,jk,jp_sal) - rn_alpha * pts(:,:,jk,jp_tem) ) * tmask(:,:,jk)
-         END DO
-         !
       END SELECT
       !
-      IF(ln_ctl)   CALL prt_ctl( tab3d_1=prd, clinfo1=' eos  : ', ovlap=1, kdim=jpk )
-      !
-      CALL wrk_dealloc( jpi, jpj, jpk, zws )
-      !
-      IF( nn_timing == 1 ) CALL timing_stop('eos')
+      IF(ln_ctl)   CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-insitu  : ', ovlap=1, kdim=jpk )
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('eos-insitu')
       !
    END SUBROUTINE eos_insitu
@@ -208,42 +305,8 @@
       !!     namelist parameter nn_eos.
       !!
-      !! ** Method  :
-      !!      nn_eos = 0 : Jackett and McDougall (1994) equation of state.
-      !!         the in situ density is computed directly as a function of
-      !!         potential temperature relative to the surface (the opa t
-      !!         variable), salt and pressure (assuming no pressure variation
-      !!         along geopotential surfaces, i.e. the pressure p in decibars
-      !!         is approximated by the depth in meters.
-      !!              prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0
-      !!              rhop(t,s)  = rho(t,s,0)
-      !!         with pressure                      p        decibars
-      !!              potential temperature         t        deg celsius
-      !!              salinity                      s        psu
-      !!              reference volumic mass        rau0     kg/m**3
-      !!              in situ volumic mass          rho      kg/m**3
-      !!              in situ density anomalie      prd      no units
-      !!
-      !!         Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar,
-      !!          t = 40 deg celcius, s=40 psu
-      !!
-      !!      nn_eos = 1 : linear equation of state function of temperature only
-      !!              prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - rn_alpha * t
-      !!              rhop(t,s)  = rho(t,s)
-      !!
-      !!      nn_eos = 2 : linear equation of state function of temperature and
-      !!               salinity
-      !!              prd(t,s) = ( rho(t,s) - rau0 ) / rau0
-      !!                       = rn_beta * s - rn_alpha * tn - 1.
-      !!              rhop(t,s)  = rho(t,s)
-      !!      Note that no boundary condition problem occurs in this routine
-      !!      as (tn,sn) or (ta,sa) are defined over the whole domain.
-      !!
       !! ** Action  : - prd  , the in situ density (no units)
       !!              - prhop, the potential volumic mass (Kg/m3)
       !!
-      !! References :   Jackett and McDougall, J. Atmos. Ocean. Tech., 1994
-      !!                Brown and Campana, Mon. Weather Rev., 1978
-      !!----------------------------------------------------------------------
-      !!
+      !!----------------------------------------------------------------------
       REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::   pts    ! 1 : potential temperature  [Celcius]
       !                                                                ! 2 : salinity               [psu]
@@ -252,84 +315,148 @@
       REAL(wp), DIMENSION(jpi,jpj,jpk     ), INTENT(in   ) ::   pdep   ! depth                      [m]
       !
-      INTEGER  ::   ji, jj, jk   ! dummy loop indices
-      REAL(wp) ::   zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw   ! local scalars
-      REAL(wp) ::   zb, zd, zc, zaw, za, zb1, za1, zkw, zk0               !   -      -
-      REAL(wp), POINTER, DIMENSION(:,:,:) :: zws
-      !!----------------------------------------------------------------------
-      !
-      IF( nn_timing == 1 ) CALL timing_start('eos-p')
-      !
-      CALL wrk_alloc( jpi, jpj, jpk, zws )
+      INTEGER  ::   ji, jj, jk, jsmp             ! dummy loop indices
+      INTEGER  ::   jdof
+      REAL(wp) ::   zt , zh , zstemp, zs , ztm   ! local scalars
+      REAL(wp) ::   zn , zn0, zn1, zn2, zn3      !   -      -
+      REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign    ! local vectors
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 )   CALL timing_start('eos-pot')
       !
       SELECT CASE ( nn_eos )
       !
-      CASE( 0 )                !==  Jackett and McDougall (1994) formulation  ==!
-!CDIR NOVERRCHK
-         zws(:,:,:) = SQRT( ABS( pts(:,:,:,jp_sal) ) )
+      CASE( -1, 0 )                !==  polynomial TEOS-10 / EOS-80 ==!
+         !
+         ! Stochastic equation of state
+         IF ( ln_sto_eos ) THEN
+            ALLOCATE(zn0_sto(1:2*nn_sto_eos))
+            ALLOCATE(zn_sto(1:2*nn_sto_eos))
+            ALLOCATE(zsign(1:2*nn_sto_eos))
+            DO jsmp = 1, 2*nn_sto_eos, 2
+              zsign(jsmp)   = 1._wp
+              zsign(jsmp+1) = -1._wp
+            END DO
+            !
+            DO jk = 1, jpkm1
+               DO jj = 1, jpj
+                  DO ji = 1, jpi
+                     !
+                     ! compute density (2*nn_sto_eos) times:
+                     ! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts)
+                     ! (2) for t-dt, s-ds (with the opposite fluctuation)
+                     DO jsmp = 1, nn_sto_eos*2
+                        jdof   = (jsmp + 1) / 2
+                        zh     = pdep(ji,jj,jk) * r1_Z0                                  ! depth
+                        zt     = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0    ! temperature
+                        zstemp = pts  (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp)
+                        zs     = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 )   ! square root salinity
+                        ztm    = tmask(ji,jj,jk)                                         ! tmask
+                        !
+                        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_sto(jsmp) = (((((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
+                           !
+                        zn_sto(jsmp)  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp)
+                     END DO
+                     !
+                     ! compute stochastic density as the mean of the (2*nn_sto_eos) densities
+                     prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp
+                     DO jsmp = 1, nn_sto_eos*2
+                        prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp)                      ! potential density referenced at the surface
+                        !
+                        prd(ji,jj,jk) = prd(ji,jj,jk) + (  zn_sto(jsmp) * r1_rau0 - 1._wp  )   ! density anomaly (masked)
+                     END DO
+                     prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos
+                     prd  (ji,jj,jk) = 0.5_wp * prd  (ji,jj,jk) * ztm / nn_sto_eos
+                  END DO
+               END DO
+            END DO
+            DEALLOCATE(zn0_sto,zn_sto,zsign)
+         ! Non-stochastic equation of state
+         ELSE
+            DO jk = 1, jpkm1
+               DO jj = 1, jpj
+                  DO ji = 1, jpi
+                     !
+                     zh  = pdep(ji,jj,jk) * r1_Z0                                  ! depth
+                     zt  = pts (ji,jj,jk,jp_tem) * r1_T0                           ! temperature
+                     zs  = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 )   ! square root salinity
+                     ztm = tmask(ji,jj,jk)                                         ! tmask
+                     !
+                     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
+                        !
+                     zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+                     !
+                     prhop(ji,jj,jk) = zn0 * ztm                           ! potential density referenced at the surface
+                     !
+                     prd(ji,jj,jk) = (  zn * r1_rau0 - 1._wp  ) * ztm      ! density anomaly (masked)
+                  END DO
+               END DO
+            END DO
+         ENDIF
+         
+      CASE( 1 )                !==  simplified EOS  ==!
          !
          DO jk = 1, jpkm1
             DO jj = 1, jpj
                DO ji = 1, jpi
-                  zt = pts   (ji,jj,jk,jp_tem)
-                  zs = pts   (ji,jj,jk,jp_sal)
-                  zh = pdep(ji,jj,jk)        ! depth
-                  zsr= zws   (ji,jj,jk)        ! square root salinity
-                  !
-                  ! compute volumic mass pure water at atm pressure
-                  zr1= ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp )*zt   &
-                     &                          -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp
-                  ! seawater volumic mass atm pressure
-                  zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt   &
-                     &                                         -4.0899e-3_wp ) *zt+0.824493_wp
-                  zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp )    *zt-5.72466e-3_wp
-                  zr4= 4.8314e-4_wp
-                  !
-                  ! potential volumic mass (reference to the surface)
-                  zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1
-                  !
-                  ! save potential volumic mass
-                  prhop(ji,jj,jk) = zrhop * tmask(ji,jj,jk)
-                  !
-                  ! add the compression terms
-                  ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp
-                  zbw= (  1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp
-                  zb = zbw + ze * zs
-                  !
-                  zd = -2.042967e-2_wp
-                  zc =   (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp
-                  zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp
-                  za = ( zd*zsr + zc ) *zs + zaw
-                  !
-                  zb1=   (  -0.1909078_wp  *zt+7.390729_wp    ) *zt-55.87545_wp
-                  za1= ( (   2.326469e-3_wp*zt+1.553190_wp    ) *zt-65.00517_wp ) *zt + 1044.077_wp
-                  zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp
-                  zk0= ( zb1*zsr + za1 )*zs + zkw
-                  !
-                  ! masked in situ density anomaly
-                  prd(ji,jj,jk) = (  zrhop / (  1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) )  )    &
-                     &             - rau0  ) * r1_rau0 * tmask(ji,jj,jk)
+                  zt  = pts  (ji,jj,jk,jp_tem) - 10._wp
+                  zs  = pts  (ji,jj,jk,jp_sal) - 35._wp
+                  zh  = pdep (ji,jj,jk)
+                  ztm = tmask(ji,jj,jk)
+                  !                                                     ! potential density referenced at the surface
+                  zn =  - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt ) * zt   &
+                     &  + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs ) * zs   &
+                     &  - rn_nu * zt * zs
+                  prhop(ji,jj,jk) = ( rau0 + zn ) * ztm
+                  !                                                     ! density anomaly (masked)
+                  zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh
+                  prd(ji,jj,jk) = zn * r1_rau0 * ztm
+                  !
                END DO
             END DO
          END DO
          !
-      CASE( 1 )                !==  Linear formulation = F( temperature )  ==!
-         DO jk = 1, jpkm1
-            prd  (:,:,jk) = ( 0.0285_wp - rn_alpha * pts(:,:,jk,jp_tem) )        * tmask(:,:,jk)
-            prhop(:,:,jk) = ( 1.e0_wp   +            prd (:,:,jk)       ) * rau0 * tmask(:,:,jk)
-         END DO
-         !
-      CASE( 2 )                !==  Linear formulation = F( temperature , salinity )  ==!
-         DO jk = 1, jpkm1
-            prd  (:,:,jk) = ( rn_beta  * pts(:,:,jk,jp_sal) - rn_alpha * pts(:,:,jk,jp_tem) )        * tmask(:,:,jk)
-            prhop(:,:,jk) = ( 1.e0_wp  + prd (:,:,jk) )                                       * rau0 * tmask(:,:,jk)
-         END DO
-         !
       END SELECT
       !
-      IF(ln_ctl)   CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-p: ', tab3d_2=prhop, clinfo2=' pot : ', ovlap=1, kdim=jpk )
-      !
-      CALL wrk_dealloc( jpi, jpj, jpk, zws )
-      !
-      IF( nn_timing == 1 ) CALL timing_stop('eos-p')
+      IF(ln_ctl)   CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-pot: ', tab3d_2=prhop, clinfo2=' pot : ', ovlap=1, kdim=jpk )
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('eos-pot')
       !
    END SUBROUTINE eos_insitu_pot
@@ -344,324 +471,189 @@
       !!      defined through the namelist parameter nn_eos. * 2D field case
       !!
-      !! ** Method :
-      !!      nn_eos = 0 : Jackett and McDougall (1994) equation of state.
-      !!         the in situ density is computed directly as a function of
-      !!         potential temperature relative to the surface (the opa t
-      !!         variable), salt and pressure (assuming no pressure variation
-      !!         along geopotential surfaces, i.e. the pressure p in decibars
-      !!         is approximated by the depth in meters.
-      !!              prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0
-      !!         with pressure                      p        decibars
-      !!              potential temperature         t        deg celsius
-      !!              salinity                      s        psu
-      !!              reference volumic mass        rau0     kg/m**3
-      !!              in situ volumic mass          rho      kg/m**3
-      !!              in situ density anomalie      prd      no units
-      !!         Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar,
-      !!          t = 40 deg celcius, s=40 psu
-      !!      nn_eos = 1 : linear equation of state function of temperature only
-      !!              prd(t) = 0.0285 - rn_alpha * t
-      !!      nn_eos = 2 : linear equation of state function of temperature and
-      !!               salinity
-      !!              prd(t,s) = rn_beta * s - rn_alpha * tn - 1.
-      !!      Note that no boundary condition problem occurs in this routine
-      !!      as pts are defined over the whole domain.
-      !!
-      !! ** Action  : - prd , the in situ density (no units)
-      !!
-      !! References :   Jackett and McDougall, J. Atmos. Ocean. Tech., 1994
-      !!----------------------------------------------------------------------
-      !!
+      !! ** Action  : - prd , the in situ density (no units) (unmasked)
+      !!
+      !!----------------------------------------------------------------------
       REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(in   ) ::   pts   ! 1 : potential temperature  [Celcius]
       !                                                           ! 2 : salinity               [psu]
-      REAL(wp), DIMENSION(jpi,jpj)     , INTENT(in   ) ::   pdep  ! depth                  [m]
+      REAL(wp), DIMENSION(jpi,jpj)     , INTENT(in   ) ::   pdep  ! depth                      [m]
       REAL(wp), DIMENSION(jpi,jpj)     , INTENT(  out) ::   prd   ! in situ density
-      !!
-      INTEGER  ::   ji, jj                    ! dummy loop indices
-      REAL(wp) ::   zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw   ! temporary scalars
-      REAL(wp) ::   zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, zmask        !    -         -
-      REAL(wp), POINTER, DIMENSION(:,:) :: zws
-      !!----------------------------------------------------------------------
-      !
-      IF( nn_timing == 1 ) CALL timing_start('eos2d')
-      !
-      CALL wrk_alloc( jpi, jpj, zws )
-      !
-
+      !
+      INTEGER  ::   ji, jj, jk                ! dummy loop indices
+      REAL(wp) ::   zt , zh , zs              ! local scalars
+      REAL(wp) ::   zn , zn0, zn1, zn2, zn3   !   -      -
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 )   CALL timing_start('eos2d')
+      !
       prd(:,:) = 0._wp
-
+      !
       SELECT CASE( nn_eos )
       !
-      CASE( 0 )                !==  Jackett and McDougall (1994) formulation  ==!
-      !
-!CDIR NOVERRCHK
+      CASE( -1, 0 )                !==  polynomial TEOS-10 / EOS-80 ==!
+         !
          DO jj = 1, jpjm1
-!CDIR NOVERRCHK
             DO ji = 1, fs_jpim1   ! vector opt.
-               zws(ji,jj) = SQRT( ABS( pts(ji,jj,jp_sal) ) )
+               !
+               zh  = pdep(ji,jj) * r1_Z0                                  ! depth
+               zt  = pts (ji,jj,jp_tem) * r1_T0                           ! temperature
+               zs  = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 )   ! square root salinity
+               !
+               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
+                  !
+               zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+               !
+               prd(ji,jj) = zn * r1_rau0 - 1._wp               ! unmasked in situ density anomaly
+               !
             END DO
          END DO
+         !
+         CALL lbc_lnk( prd, 'T', 1. )                    ! Lateral boundary conditions
+         !
+      CASE( 1 )                !==  simplified EOS  ==!
+         !
          DO jj = 1, jpjm1
             DO ji = 1, fs_jpim1   ! vector opt.
-               zmask = tmask(ji,jj,1)          ! land/sea bottom mask = surf. mask
-               zt    = pts  (ji,jj,jp_tem)            ! interpolated T
-               zs    = pts  (ji,jj,jp_sal)            ! interpolated S
-               zsr   = zws  (ji,jj)            ! square root of interpolated S
-               zh    = pdep (ji,jj)            ! depth at the partial step level
-               !
-               ! compute volumic mass pure water at atm pressure
-               zr1 = ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp )*zt   &
-                  &                        -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp
-               ! seawater volumic mass atm pressure
-               zr2 = ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp )*zt+7.6438e-5_wp ) *zt   &
-                  &                                   -4.0899e-3_wp ) *zt+0.824493_wp
-               zr3 = ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp
-               zr4 = 4.8314e-4_wp
-               !
-               ! potential volumic mass (reference to the surface)
-               zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1
-               !
-               ! add the compression terms
-               ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp
-               zbw= (  1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp
-               zb = zbw + ze * zs
-               !
-               zd =    -2.042967e-2_wp
-               zc =   (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp
-               zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt -4.721788_wp
-               za = ( zd*zsr + zc ) *zs + zaw
-               !
-               zb1=     (-0.1909078_wp  *zt+7.390729_wp      ) *zt-55.87545_wp
-               za1=   ( ( 2.326469e-3_wp*zt+1.553190_wp      ) *zt-65.00517_wp ) *zt+1044.077_wp
-               zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp   ) *zt-30.41638_wp ) *zt   &
-                  &                             +2098.925_wp ) *zt+190925.6_wp
-               zk0= ( zb1*zsr + za1 )*zs + zkw
-               !
-               ! masked in situ density anomaly
-               prd(ji,jj) = ( zrhop / (  1.0_wp - zh / ( zk0 - zh * ( za - zh * zb ) )  ) - rau0 ) / rau0 * zmask
+               !
+               zt    = pts  (ji,jj,jp_tem)  - 10._wp
+               zs    = pts  (ji,jj,jp_sal)  - 35._wp
+               zh    = pdep (ji,jj)                         ! depth at the partial step level
+               !
+               zn =  - rn_a0 * ( 1._wp + 0.5_wp*rn_lambda1*zt + rn_mu1*zh ) * zt   &
+                  &  + rn_b0 * ( 1._wp - 0.5_wp*rn_lambda2*zs - rn_mu2*zh ) * zs   &
+                  &  - rn_nu * zt * zs
+                  !
+               prd(ji,jj) = zn * r1_rau0               ! unmasked in situ density anomaly
+               !
             END DO
          END DO
          !
-      CASE( 1 )                !==  Linear formulation = F( temperature )  ==!
-         DO jj = 1, jpjm1
-            DO ji = 1, fs_jpim1   ! vector opt.
-               prd(ji,jj) = ( 0.0285_wp - rn_alpha * pts(ji,jj,jp_tem) ) * tmask(ji,jj,1)
-            END DO
-         END DO
-         !
-      CASE( 2 )                !==  Linear formulation = F( temperature , salinity )  ==!
-         DO jj = 1, jpjm1
-            DO ji = 1, fs_jpim1   ! vector opt.
-               prd(ji,jj) = ( rn_beta * pts(ji,jj,jp_sal) - rn_alpha * pts(ji,jj,jp_tem) ) * tmask(ji,jj,1)
-            END DO
-         END DO
+         CALL lbc_lnk( prd, 'T', 1. )                    ! Lateral boundary conditions
          !
       END SELECT
-
+      !
       IF(ln_ctl)   CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' )
       !
-      CALL wrk_dealloc( jpi, jpj, zws )
-      !
-      IF( nn_timing == 1 ) CALL timing_stop('eos2d')
+      IF( nn_timing == 1 )   CALL timing_stop('eos2d')
       !
    END SUBROUTINE eos_insitu_2d
 
 
-   SUBROUTINE eos_bn2( pts, pn2 )
-      !!----------------------------------------------------------------------
-      !!                  ***  ROUTINE eos_bn2  ***
-      !!
-      !! ** Purpose :   Compute the local Brunt-Vaisala frequency at the time-
-      !!      step of the input arguments
-      !!
-      !! ** Method :
-      !!       * nn_eos = 0  : UNESCO sea water properties
-      !!         The brunt-vaisala frequency is computed using the polynomial
-      !!      polynomial expression of McDougall (1987):
-      !!            N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w
-      !!      If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is
-      !!      computed and used in zdfddm module :
-      !!              Rrau = alpha/beta * ( dk[ t ] / dk[ s ] )
-      !!       * nn_eos = 1  : linear equation of state (temperature only)
-      !!            N^2 = grav * rn_alpha * dk[ t ]/e3w
-      !!       * nn_eos = 2  : linear equation of state (temperature & salinity)
-      !!            N^2 = grav * (rn_alpha * dk[ t ] - rn_beta * dk[ s ] ) / e3w
-      !!      The use of potential density to compute N^2 introduces e r r o r
-      !!      in the sign of N^2 at great depths. We recommand the use of
-      !!      nn_eos = 0, except for academical studies.
-      !!        Macro-tasked on horizontal slab (jk-loop)
-      !!      N.B. N^2 is set to zero at the first level (JK=1) in inidtr
-      !!      and is never used at this level.
-      !!
-      !! ** Action  : - pn2 : the brunt-vaisala frequency
-      !!
-      !! References :   McDougall, J. Phys. Oceanogr., 17, 1950-1964, 1987.
-      !!----------------------------------------------------------------------
-      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::   pts   ! 1 : potential temperature  [Celcius]
-      !                                                               ! 2 : salinity               [psu]
-      REAL(wp), DIMENSION(jpi,jpj,jpk)     , INTENT(  out) ::   pn2   ! Brunt-Vaisala frequency    [s-1]
-      !!
-      INTEGER  ::   ji, jj, jk   ! dummy loop indices
-      REAL(wp) ::   zgde3w, zt, zs, zh, zalbet, zbeta   ! local scalars
-#if defined key_zdfddm
-      REAL(wp) ::   zds   ! local scalars
-#endif
-      !!----------------------------------------------------------------------
-
-      !
-      IF( nn_timing == 1 ) CALL timing_start('bn2')
-      !
-      ! pn2 : interior points only (2=< jk =< jpkm1 )
-      ! --------------------------
-      !
-      SELECT CASE( nn_eos )
-      !
-      CASE( 0 )                !==  Jackett and McDougall (1994) formulation  ==!
-         DO jk = 2, jpkm1
+   SUBROUTINE rab_3d( pts, pab )
+      !!----------------------------------------------------------------------
+      !!                 ***  ROUTINE rab_3d  ***
+      !!
+      !! ** Purpose :   Calculates thermal/haline expansion ratio at T-points
+      !!
+      !! ** Method  :   calculates alpha / beta at T-points
+      !!
+      !! ** Action  : - pab     : thermal/haline expansion ratio at T-points
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::   pts   ! pot. temperature & salinity
+      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(  out) ::   pab   ! thermal/haline expansion ratio
+      !
+      INTEGER  ::   ji, jj, jk                ! dummy loop indices
+      REAL(wp) ::   zt , zh , zs , ztm        ! local scalars
+      REAL(wp) ::   zn , zn0, zn1, zn2, zn3   !   -      -
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 )   CALL timing_start('rab_3d')
+      !
+      SELECT CASE ( nn_eos )
+      !
+      CASE( -1, 0 )                !==  polynomial TEOS-10 / EOS-80 ==!
+         !
+         DO jk = 1, jpkm1
             DO jj = 1, jpj
                DO ji = 1, jpi
-                  zgde3w = grav / fse3w(ji,jj,jk)
-                  zt = 0.5 * ( pts(ji,jj,jk,jp_tem) + pts(ji,jj,jk-1,jp_tem) )         ! potential temperature at w-pt
-                  zs = 0.5 * ( pts(ji,jj,jk,jp_sal) + pts(ji,jj,jk-1,jp_sal) ) - 35.0  ! salinity anomaly (s-35) at w-pt
-                  zh = fsdepw(ji,jj,jk)                                                ! depth in meters  at w-point
-                  !
-                  zalbet = ( ( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt   &   ! ratio alpha/beta
-                     &                                  - 0.203814e-03_wp ) * zt   &
-                     &                                  + 0.170907e-01_wp ) * zt   &
-                     &   +         0.665157e-01_wp                                 &
-                     &   +     ( - 0.678662e-05_wp * zs                            &
-                     &           - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs   &
-                     &   +   ( ( - 0.302285e-13_wp * zh                            &
-                     &           - 0.251520e-11_wp * zs                            &
-                     &           + 0.512857e-12_wp * zt * zt              ) * zh   &
-                     &           - 0.164759e-06_wp * zs                            &
-                     &        +(   0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt   &
-                     &                                  + 0.380374e-04_wp ) * zh
-                     !
-                  zbeta  = ( ( -0.415613e-09_wp * zt + 0.555579e-07_wp ) * zt      &   ! beta
-                     &                               - 0.301985e-05_wp ) * zt      &
-                     &   +       0.785567e-03_wp                                   &
-                     &   + (     0.515032e-08_wp * zs                              &
-                     &         + 0.788212e-08_wp * zt - 0.356603e-06_wp ) * zs     &
-                     &   + ( (   0.121551e-17_wp * zh                              &
-                     &         - 0.602281e-15_wp * zs                              &
-                     &         - 0.175379e-14_wp * zt + 0.176621e-12_wp ) * zh     &
-                     &                                + 0.408195e-10_wp   * zs     &
-                     &     + ( - 0.213127e-11_wp * zt + 0.192867e-09_wp ) * zt     &
-                     &                                - 0.121555e-07_wp ) * zh
-                     !
-                  pn2(ji,jj,jk) = zgde3w * zbeta * tmask(ji,jj,jk)           &   ! N^2
-                     &          * ( zalbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) )   &
-                     &                     - ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) )
-#if defined key_zdfddm
-                  !                                                         !!bug **** caution a traiter zds=dk[S]= 0 !!!!
-                  zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) )                    ! Rrau = (alpha / beta) (dk[t] / dk[s])
-                  IF ( ABS( zds) <= 1.e-20_wp ) zds = 1.e-20_wp
-                  rrau(ji,jj,jk) = zalbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds
-#endif
+                  !
+                  zh  = fsdept(ji,jj,jk) * r1_Z0                                ! depth
+                  zt  = pts (ji,jj,jk,jp_tem) * r1_T0                           ! temperature
+                  zs  = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 )   ! square root salinity
+                  ztm = tmask(ji,jj,jk)                                         ! tmask
+                  !
+                  ! alpha
+                  zn3 = ALP003
+                  !
+                  zn2 = ALP012*zt + ALP102*zs+ALP002
+                  !
+                  zn1 = ((ALP031*zt   &
+                     &   + ALP121*zs+ALP021)*zt   &
+                     &   + (ALP211*zs+ALP111)*zs+ALP011)*zt   &
+                     &   + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001
+                     !
+                  zn0 = ((((ALP050*zt   &
+                     &   + ALP140*zs+ALP040)*zt   &
+                     &   + (ALP230*zs+ALP130)*zs+ALP030)*zt   &
+                     &   + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt   &
+                     &   + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt   &
+                     &   + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000
+                     !
+                  zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+                  !
+                  pab(ji,jj,jk,jp_tem) = zn * r1_rau0 * ztm
+                  !
+                  ! beta
+                  zn3 = BET003
+                  !
+                  zn2 = BET012*zt + BET102*zs+BET002
+                  !
+                  zn1 = ((BET031*zt   &
+                     &   + BET121*zs+BET021)*zt   &
+                     &   + (BET211*zs+BET111)*zs+BET011)*zt   &
+                     &   + ((BET301*zs+BET201)*zs+BET101)*zs+BET001
+                     !
+                  zn0 = ((((BET050*zt   &
+                     &   + BET140*zs+BET040)*zt   &
+                     &   + (BET230*zs+BET130)*zs+BET030)*zt   &
+                     &   + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt   &
+                     &   + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt   &
+                     &   + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000
+                     !
+                  zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+                  !
+                  pab(ji,jj,jk,jp_sal) = zn / zs * r1_rau0 * ztm
+                  !
                END DO
             END DO
          END DO
          !
-      CASE( 1 )                !==  Linear formulation = F( temperature )  ==!
-         DO jk = 2, jpkm1
-            pn2(:,:,jk) = grav * rn_alpha * ( pts(:,:,jk-1,jp_tem) - pts(:,:,jk,jp_tem) ) / fse3w(:,:,jk) * tmask(:,:,jk)
-         END DO
-         !
-      CASE( 2 )                !==  Linear formulation = F( temperature , salinity )  ==!
-         DO jk = 2, jpkm1
-            pn2(:,:,jk) = grav * (  rn_alpha * ( pts(:,:,jk-1,jp_tem) - pts(:,:,jk,jp_tem) )      &
-               &                  - rn_beta  * ( pts(:,:,jk-1,jp_sal) - pts(:,:,jk,jp_sal) )  )   &
-               &               / fse3w(:,:,jk) * tmask(:,:,jk)
-         END DO
-#if defined key_zdfddm
-         DO jk = 2, jpkm1                                 ! Rrau = (alpha / beta) (dk[t] / dk[s])
+      CASE( 1 )                  !==  simplified EOS  ==!
+         !
+         DO jk = 1, jpkm1
             DO jj = 1, jpj
                DO ji = 1, jpi
-                  zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) )
-                  IF ( ABS( zds ) <= 1.e-20_wp ) zds = 1.e-20_wp
-                  rrau(ji,jj,jk) = ralpbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds
+                  zt  = pts (ji,jj,jk,jp_tem) - 10._wp   ! pot. temperature anomaly (t-T0)
+                  zs  = pts (ji,jj,jk,jp_sal) - 35._wp   ! abs. salinity anomaly (s-S0)
+                  zh  = fsdept(ji,jj,jk)                 ! depth in meters at t-point
+                  ztm = tmask(ji,jj,jk)                  ! land/sea bottom mask = surf. mask
+                  !
+                  zn  = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs
+                  pab(ji,jj,jk,jp_tem) = zn * r1_rau0 * ztm   ! alpha
+                  !
+                  zn  = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt
+                  pab(ji,jj,jk,jp_sal) = zn * r1_rau0 * ztm   ! beta
+                  !
                END DO
             END DO
          END DO
-#endif
-      END SELECT
-
-      IF(ln_ctl)   CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2  : ', ovlap=1, kdim=jpk )
-#if defined key_zdfddm
-      IF(ln_ctl)   CALL prt_ctl( tab3d_1=rrau, clinfo1=' rrau : ', ovlap=1, kdim=jpk )
-#endif
-      !
-      IF( nn_timing == 1 ) CALL timing_stop('bn2')
-      !
-   END SUBROUTINE eos_bn2
-
-
-   SUBROUTINE eos_alpbet( pts, palpbet, beta0 )
-      !!----------------------------------------------------------------------
-      !!                 ***  ROUTINE eos_alpbet  ***
-      !!
-      !! ** Purpose :   Calculates the in situ thermal/haline expansion ratio at T-points
-      !!
-      !! ** Method  :   calculates alpha / beta ratio at T-points
-      !!       * nn_eos = 0  : UNESCO sea water properties
-      !!                       The alpha/beta ratio is returned as 3-D array palpbet using the polynomial
-      !!                       polynomial expression of McDougall (1987).
-      !!                       Scalar beta0 is returned = 1.
-      !!       * nn_eos = 1  : linear equation of state (temperature only)
-      !!                       The ratio is undefined, so we return alpha as palpbet
-      !!                       Scalar beta0 is returned = 0.
-      !!       * nn_eos = 2  : linear equation of state (temperature & salinity)
-      !!                       The alpha/beta ratio is returned as ralpbet
-      !!                       Scalar beta0 is returned = 1.
-      !!
-      !! ** Action  : - palpbet : thermal/haline expansion ratio at T-points
-      !!            :   beta0   : 1. or 0.
-      !!----------------------------------------------------------------------
-      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::   pts       ! pot. temperature & salinity
-      REAL(wp), DIMENSION(jpi,jpj,jpk)     , INTENT(  out) ::   palpbet   ! thermal/haline expansion ratio
-      REAL(wp),                              INTENT(  out) ::   beta0     ! set = 1 except with case 1 eos, rho=rho(T)
-      !!
-      INTEGER  ::   ji, jj, jk   ! dummy loop indices
-      REAL(wp) ::   zt, zs, zh   ! local scalars
-      !!----------------------------------------------------------------------
-      !
-      IF( nn_timing == 1 ) CALL timing_start('eos_alpbet')
-      !
-      SELECT CASE ( nn_eos )
-      !
-      CASE ( 0 )               ! Jackett and McDougall (1994) formulation
-         DO jk = 1, jpk
-            DO jj = 1, jpj
-               DO ji = 1, jpi
-                  zt = pts(ji,jj,jk,jp_tem)           ! potential temperature
-                  zs = pts(ji,jj,jk,jp_sal) - 35._wp  ! salinity anomaly (s-35)
-                  zh = fsdept(ji,jj,jk)               ! depth in meters
-                  !
-                  palpbet(ji,jj,jk) =                                              &
-                     &     ( ( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt   &
-                     &                                  - 0.203814e-03_wp ) * zt   &
-                     &                                  + 0.170907e-01_wp ) * zt   &
-                     &   + 0.665157e-01_wp                                         &
-                     &   +     ( - 0.678662e-05_wp * zs                            &
-                     &           - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs   &
-                     &   +   ( ( - 0.302285e-13_wp * zh                            &
-                     &           - 0.251520e-11_wp * zs                            &
-                     &           + 0.512857e-12_wp * zt * zt              ) * zh   &
-                     &           - 0.164759e-06_wp * zs                            &
-                     &        +(   0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt   &
-                     &                                  + 0.380374e-04_wp ) * zh
-               END DO
-            END DO
-         END DO
-         beta0 = 1._wp
-         !
-      CASE ( 1 )              !==  Linear formulation = F( temperature )  ==!
-         palpbet(:,:,:) = rn_alpha
-         beta0 = 0._wp
-         !
-      CASE ( 2 )              !==  Linear formulation = F( temperature , salinity )  ==!
-         palpbet(:,:,:) = ralpbet
-         beta0 = 1._wp
          !
       CASE DEFAULT
@@ -672,56 +664,582 @@
       END SELECT
       !
-      IF( nn_timing == 1 ) CALL timing_stop('eos_alpbet')
-      !
-   END SUBROUTINE eos_alpbet
-
-
-   FUNCTION tfreez( psal, pdep ) RESULT( ptf )
+      IF(ln_ctl)   CALL prt_ctl( tab3d_1=pab(:,:,:,jp_tem), clinfo1=' rab_3d_t: ', &
+         &                       tab3d_2=pab(:,:,:,jp_sal), clinfo2=' rab_3d_s : ', ovlap=1, kdim=jpk )
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('rab_3d')
+      !
+   END SUBROUTINE rab_3d
+
+   SUBROUTINE rab_2d( pts, pdep, pab )
+      !!----------------------------------------------------------------------
+      !!                 ***  ROUTINE rab_2d  ***
+      !!
+      !! ** Purpose :   Calculates thermal/haline expansion ratio for a 2d field (unmasked)
+      !!
+      !! ** Action  : - pab     : thermal/haline expansion ratio at T-points
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpi,jpj,jpts)    , INTENT(in   ) ::   pts    ! pot. temperature & salinity
+      REAL(wp), DIMENSION(jpi,jpj)         , INTENT(in   ) ::   pdep   ! depth                  [m]
+      REAL(wp), DIMENSION(jpi,jpj,jpts)    , INTENT(  out) ::   pab    ! thermal/haline expansion ratio
+      !
+      INTEGER  ::   ji, jj, jk                ! dummy loop indices
+      REAL(wp) ::   zt , zh , zs              ! local scalars
+      REAL(wp) ::   zn , zn0, zn1, zn2, zn3   !   -      -
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 ) CALL timing_start('rab_2d')
+      !
+      pab(:,:,:) = 0._wp
+      !
+      SELECT CASE ( nn_eos )
+      !
+      CASE( -1, 0 )                !==  polynomial TEOS-10 / EOS-80 ==!
+         !
+         DO jj = 1, jpjm1
+            DO ji = 1, fs_jpim1   ! vector opt.
+               !
+               zh  = pdep(ji,jj) * r1_Z0                                  ! depth
+               zt  = pts (ji,jj,jp_tem) * r1_T0                           ! temperature
+               zs  = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 )   ! square root salinity
+               !
+               ! alpha
+               zn3 = ALP003
+               !
+               zn2 = ALP012*zt + ALP102*zs+ALP002
+               !
+               zn1 = ((ALP031*zt   &
+                  &   + ALP121*zs+ALP021)*zt   &
+                  &   + (ALP211*zs+ALP111)*zs+ALP011)*zt   &
+                  &   + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001
+                  !
+               zn0 = ((((ALP050*zt   &
+                  &   + ALP140*zs+ALP040)*zt   &
+                  &   + (ALP230*zs+ALP130)*zs+ALP030)*zt   &
+                  &   + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt   &
+                  &   + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt   &
+                  &   + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000
+                  !
+               zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+               !
+               pab(ji,jj,jp_tem) = zn * r1_rau0
+               !
+               ! beta
+               zn3 = BET003
+               !
+               zn2 = BET012*zt + BET102*zs+BET002
+               !
+               zn1 = ((BET031*zt   &
+                  &   + BET121*zs+BET021)*zt   &
+                  &   + (BET211*zs+BET111)*zs+BET011)*zt   &
+                  &   + ((BET301*zs+BET201)*zs+BET101)*zs+BET001
+                  !
+               zn0 = ((((BET050*zt   &
+                  &   + BET140*zs+BET040)*zt   &
+                  &   + (BET230*zs+BET130)*zs+BET030)*zt   &
+                  &   + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt   &
+                  &   + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt   &
+                  &   + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000
+                  !
+               zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+               !
+               pab(ji,jj,jp_sal) = zn / zs * r1_rau0
+               !
+               !
+            END DO
+         END DO
+         !
+         CALL lbc_lnk( pab(:,:,jp_tem), 'T', 1. )                    ! Lateral boundary conditions
+         CALL lbc_lnk( pab(:,:,jp_sal), 'T', 1. )                    
+         !
+      CASE( 1 )                  !==  simplified EOS  ==!
+         !
+         DO jj = 1, jpjm1
+            DO ji = 1, fs_jpim1   ! vector opt.
+               !
+               zt    = pts  (ji,jj,jp_tem) - 10._wp   ! pot. temperature anomaly (t-T0)
+               zs    = pts  (ji,jj,jp_sal) - 35._wp   ! abs. salinity anomaly (s-S0)
+               zh    = pdep (ji,jj)                   ! depth at the partial step level
+               !
+               zn  = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs
+               pab(ji,jj,jp_tem) = zn * r1_rau0   ! alpha
+               !
+               zn  = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt
+               pab(ji,jj,jp_sal) = zn * r1_rau0   ! beta
+               !
+            END DO
+         END DO
+         !
+         CALL lbc_lnk( pab(:,:,jp_tem), 'T', 1. )                    ! Lateral boundary conditions
+         CALL lbc_lnk( pab(:,:,jp_sal), 'T', 1. )                    
+         !
+      CASE DEFAULT
+         IF(lwp) WRITE(numout,cform_err)
+         IF(lwp) WRITE(numout,*) '          bad flag value for nn_eos = ', nn_eos
+         nstop = nstop + 1
+         !
+      END SELECT
+      !
+      IF(ln_ctl)   CALL prt_ctl( tab2d_1=pab(:,:,jp_tem), clinfo1=' rab_2d_t: ', &
+         &                       tab2d_2=pab(:,:,jp_sal), clinfo2=' rab_2d_s : ' )
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('rab_2d')
+      !
+   END SUBROUTINE rab_2d
+
+
+   SUBROUTINE rab_0d( pts, pdep, pab )
+      !!----------------------------------------------------------------------
+      !!                 ***  ROUTINE rab_0d  ***
+      !!
+      !! ** Purpose :   Calculates thermal/haline expansion ratio for a 2d field (unmasked)
+      !!
+      !! ** Action  : - pab     : thermal/haline expansion ratio at T-points
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpts)    , INTENT(in   ) ::   pts    ! pot. temperature & salinity
+      REAL(wp),                      INTENT(in   ) ::   pdep   ! depth                  [m]
+      REAL(wp), DIMENSION(jpts)    , INTENT(  out) ::   pab    ! thermal/haline expansion ratio
+      !
+      REAL(wp) ::   zt , zh , zs              ! local scalars
+      REAL(wp) ::   zn , zn0, zn1, zn2, zn3   !   -      -
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 ) CALL timing_start('rab_2d')
+      !
+      pab(:) = 0._wp
+      !
+      SELECT CASE ( nn_eos )
+      !
+      CASE( -1, 0 )                !==  polynomial TEOS-10 / EOS-80 ==!
+         !
+         !
+         zh  = pdep * r1_Z0                                  ! depth
+         zt  = pts (jp_tem) * r1_T0                           ! temperature
+         zs  = SQRT( ABS( pts(jp_sal) + rdeltaS ) * r1_S0 )   ! square root salinity
+         !
+         ! alpha
+         zn3 = ALP003
+         !
+         zn2 = ALP012*zt + ALP102*zs+ALP002
+         !
+         zn1 = ((ALP031*zt   &
+            &   + ALP121*zs+ALP021)*zt   &
+            &   + (ALP211*zs+ALP111)*zs+ALP011)*zt   &
+            &   + ((ALP301*zs+ALP201)*zs+ALP101)*zs+ALP001
+            !
+         zn0 = ((((ALP050*zt   &
+            &   + ALP140*zs+ALP040)*zt   &
+            &   + (ALP230*zs+ALP130)*zs+ALP030)*zt   &
+            &   + ((ALP320*zs+ALP220)*zs+ALP120)*zs+ALP020)*zt   &
+            &   + (((ALP410*zs+ALP310)*zs+ALP210)*zs+ALP110)*zs+ALP010)*zt   &
+            &   + ((((ALP500*zs+ALP400)*zs+ALP300)*zs+ALP200)*zs+ALP100)*zs+ALP000
+            !
+         zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+         !
+         pab(jp_tem) = zn * r1_rau0
+         !
+         ! beta
+         zn3 = BET003
+         !
+         zn2 = BET012*zt + BET102*zs+BET002
+         !
+         zn1 = ((BET031*zt   &
+            &   + BET121*zs+BET021)*zt   &
+            &   + (BET211*zs+BET111)*zs+BET011)*zt   &
+            &   + ((BET301*zs+BET201)*zs+BET101)*zs+BET001
+            !
+         zn0 = ((((BET050*zt   &
+            &   + BET140*zs+BET040)*zt   &
+            &   + (BET230*zs+BET130)*zs+BET030)*zt   &
+            &   + ((BET320*zs+BET220)*zs+BET120)*zs+BET020)*zt   &
+            &   + (((BET410*zs+BET310)*zs+BET210)*zs+BET110)*zs+BET010)*zt   &
+            &   + ((((BET500*zs+BET400)*zs+BET300)*zs+BET200)*zs+BET100)*zs+BET000
+            !
+         zn  = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
+         !
+         pab(jp_sal) = zn / zs * r1_rau0
+         !
+         !
+         !
+      CASE( 1 )                  !==  simplified EOS  ==!
+         !
+         zt    = pts(jp_tem) - 10._wp   ! pot. temperature anomaly (t-T0)
+         zs    = pts(jp_sal) - 35._wp   ! abs. salinity anomaly (s-S0)
+         zh    = pdep                    ! depth at the partial step level
+         !
+         zn  = rn_a0 * ( 1._wp + rn_lambda1*zt + rn_mu1*zh ) + rn_nu*zs
+         pab(jp_tem) = zn * r1_rau0   ! alpha
+         !
+         zn  = rn_b0 * ( 1._wp - rn_lambda2*zs - rn_mu2*zh ) - rn_nu*zt
+         pab(jp_sal) = zn * r1_rau0   ! beta
+         !
+      CASE DEFAULT
+         IF(lwp) WRITE(numout,cform_err)
+         IF(lwp) WRITE(numout,*) '          bad flag value for nn_eos = ', nn_eos
+         nstop = nstop + 1
+         !
+      END SELECT
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('rab_2d')
+      !
+   END SUBROUTINE rab_0d
+
+
+   SUBROUTINE bn2( pts, pab, pn2 )
+      !!----------------------------------------------------------------------
+      !!                  ***  ROUTINE bn2  ***
+      !!
+      !! ** Purpose :   Compute the local Brunt-Vaisala frequency at the 
+      !!                time-step of the input arguments
+      !!
+      !! ** Method  :   pn2 = grav * (alpha dk[T] + beta dk[S] ) / e3w
+      !!      where alpha and beta are given in pab, and computed on T-points.
+      !!      N.B. N^2 is set one for all to zero at jk=1 in istate module.
+      !!
+      !! ** Action  :   pn2 : square of the brunt-vaisala frequency at w-point 
+      !!
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::  pts   ! pot. temperature and salinity   [Celcius,psu]
+      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::  pab   ! thermal/haline expansion coef.  [Celcius-1,psu-1]
+      REAL(wp), DIMENSION(jpi,jpj,jpk     ), INTENT(  out) ::  pn2   ! Brunt-Vaisala frequency squared [1/s^2]
+      !
+      INTEGER  ::   ji, jj, jk      ! dummy loop indices
+      REAL(wp) ::   zaw, zbw, zrw   ! local scalars
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 ) CALL timing_start('bn2')
+      !
+      DO jk = 2, jpkm1           ! interior points only (2=< jk =< jpkm1 )
+         DO jj = 1, jpj          ! surface and bottom value set to zero one for all in istate.F90
+            DO ji = 1, jpi
+               zrw =   ( fsdepw(ji,jj,jk  ) - fsdept(ji,jj,jk) )   &
+                  &  / ( fsdept(ji,jj,jk-1) - fsdept(ji,jj,jk) ) 
+                  !
+               zaw = pab(ji,jj,jk,jp_tem) * (1. - zrw) + pab(ji,jj,jk-1,jp_tem) * zrw 
+               zbw = pab(ji,jj,jk,jp_sal) * (1. - zrw) + pab(ji,jj,jk-1,jp_sal) * zrw
+               !
+               pn2(ji,jj,jk) = grav * (  zaw * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) )     &
+                  &                    - zbw * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) )  )  &
+                  &            / fse3w(ji,jj,jk) * tmask(ji,jj,jk)
+            END DO
+         END DO
+      END DO
+      !
+      IF(ln_ctl)   CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2  : ', ovlap=1, kdim=jpk )
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('bn2')
+      !
+   END SUBROUTINE bn2
+
+
+   FUNCTION eos_pt_from_ct( ctmp, psal ) RESULT( ptmp )
+      !!----------------------------------------------------------------------
+      !!                 ***  ROUTINE eos_pt_from_ct  ***
+      !!
+      !! ** Purpose :   Compute pot.temp. from cons. temp. [Celcius]
+      !!
+      !! ** Method  :   rational approximation (5/3th order) of TEOS-10 algorithm
+      !!       checkvalue: pt=20.02391895 Celsius for sa=35.7g/kg, ct=20degC
+      !!
+      !! Reference  :   TEOS-10, UNESCO
+      !!                Rational approximation to TEOS10 algorithm (rms error on WOA13 values: 4.0e-5 degC)
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpi,jpj), INTENT(in   ) ::   ctmp   ! Cons. Temp [Celcius]
+      REAL(wp), DIMENSION(jpi,jpj), INTENT(in   ) ::   psal   ! salinity   [psu]
+      ! Leave result array automatic rather than making explicitly allocated
+      REAL(wp), DIMENSION(jpi,jpj) ::   ptmp   ! potential temperature [Celcius]
+      !
+      INTEGER  ::   ji, jj               ! dummy loop indices
+      REAL(wp) ::   zt , zs , ztm        ! local scalars
+      REAL(wp) ::   zn , zd              ! local scalars
+      REAL(wp) ::   zdeltaS , z1_S0 , z1_T0
+      !!----------------------------------------------------------------------
+      !
+      IF ( nn_timing == 1 )   CALL timing_start('eos_pt_from_ct')
+      !
+      zdeltaS = 5._wp
+      z1_S0   = 0.875_wp/35.16504_wp
+      z1_T0   = 1._wp/40._wp
+      !
+      DO jj = 1, jpj
+         DO ji = 1, jpi
+            !
+            zt  = ctmp   (ji,jj) * z1_T0
+            zs  = SQRT( ABS( psal(ji,jj) + zdeltaS ) * r1_S0 )
+            ztm = tmask(ji,jj,1)
+            !
+            zn = ((((-2.1385727895e-01_wp*zt   &
+               &   - 2.7674419971e-01_wp*zs+1.0728094330_wp)*zt   &
+               &   + (2.6366564313_wp*zs+3.3546960647_wp)*zs-7.8012209473_wp)*zt   &
+               &   + ((1.8835586562_wp*zs+7.3949191679_wp)*zs-3.3937395875_wp)*zs-5.6414948432_wp)*zt   &
+               &   + (((3.5737370589_wp*zs-1.5512427389e+01_wp)*zs+2.4625741105e+01_wp)*zs   &
+               &      +1.9912291000e+01_wp)*zs-3.2191146312e+01_wp)*zt   &
+               &   + ((((5.7153204649e-01_wp*zs-3.0943149543_wp)*zs+9.3052495181_wp)*zs   &
+               &      -9.4528934807_wp)*zs+3.1066408996_wp)*zs-4.3504021262e-01_wp
+               !
+            zd = (2.0035003456_wp*zt   &
+               &   -3.4570358592e-01_wp*zs+5.6471810638_wp)*zt   &
+               &   + (1.5393993508_wp*zs-6.9394762624_wp)*zs+1.2750522650e+01_wp
+               !
+            ptmp(ji,jj) = ( zt / z1_T0 + zn / zd ) * ztm
+               !
+         END DO
+      END DO
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('eos_pt_from_ct')
+      !
+   END FUNCTION eos_pt_from_ct
+
+
+   FUNCTION eos_fzp_2d( psal, pdep ) RESULT( ptf )
+      !!----------------------------------------------------------------------
+      !!                 ***  ROUTINE eos_fzp  ***
+      !!
+      !! ** Purpose :   Compute the freezing point temperature [Celcius]
+      !!
+      !! ** Method  :   UNESCO freezing point (ptf) in Celcius is given by
+      !!       ptf(t,z) = (-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s - 7.53e-4*z
+      !!       checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
+      !!
+      !! Reference  :   UNESCO tech. papers in the marine science no. 28. 1978
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpi,jpj), INTENT(in   )           ::   psal   ! salinity   [psu]
+      REAL(wp), DIMENSION(jpi,jpj), INTENT(in   ), OPTIONAL ::   pdep   ! depth      [m]
+      REAL(wp), DIMENSION(jpi,jpj)                          ::   ptf   ! freezing temperature [Celcius]
+      !
+      INTEGER  ::   ji, jj   ! dummy loop indices
+      REAL(wp) ::   zt, zs   ! local scalars
+      !!----------------------------------------------------------------------
+      !
+      SELECT CASE ( nn_eos )
+      !
+      CASE ( -1, 1 )                !==  CT,SA (TEOS-10 formulation) ==!
+         !
+         DO jj = 1, jpj
+            DO ji = 1, jpi
+               zs= SQRT( ABS( psal(ji,jj) ) * r1_S0 )           ! square root salinity
+               ptf(ji,jj) = ((((1.46873e-03_wp*zs-9.64972e-03_wp)*zs+2.28348e-02_wp)*zs &
+                  &          - 3.12775e-02_wp)*zs+2.07679e-02_wp)*zs-5.87701e-02_wp
+            END DO
+         END DO
+         ptf(:,:) = ptf(:,:) * psal(:,:)
+         !
+         IF( PRESENT( pdep ) )   ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
+         !
+      CASE ( 0 )                     !==  PT,SP (UNESCO formulation)  ==!
+         !
+         ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) )   &
+            &                     - 2.154996e-4_wp *       psal(:,:)   ) * psal(:,:)
+            !
+         IF( PRESENT( pdep ) )   ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
+         !
+      CASE DEFAULT
+         IF(lwp) WRITE(numout,cform_err)
+         IF(lwp) WRITE(numout,*) '          bad flag value for nn_eos = ', nn_eos
+         nstop = nstop + 1
+         !
+      END SELECT
+      !
+   END FUNCTION eos_fzp_2d
+
+  FUNCTION eos_fzp_0d( psal, pdep ) RESULT( ptf )
+      !!----------------------------------------------------------------------
+      !!                 ***  ROUTINE eos_fzp  ***
+      !!
+      !! ** Purpose :   Compute the freezing point temperature [Celcius]
+      !!
+      !! ** Method  :   UNESCO freezing point (ptf) in Celcius is given by
+      !!       ptf(t,z) = (-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s - 7.53e-4*z
+      !!       checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
+      !!
+      !! Reference  :   UNESCO tech. papers in the marine science no. 28. 1978
+      !!----------------------------------------------------------------------
+      REAL(wp), INTENT(in)           ::   psal   ! salinity   [psu]
+      REAL(wp), INTENT(in), OPTIONAL ::   pdep   ! depth      [m]
+      REAL(wp)                       ::   ptf   ! freezing temperature [Celcius]
+      !
+      REAL(wp) :: zs   ! local scalars
+      !!----------------------------------------------------------------------
+      !
+      SELECT CASE ( nn_eos )
+      !
+      CASE ( -1, 1 )                !==  CT,SA (TEOS-10 formulation) ==!
+         !
+         zs  = SQRT( ABS( psal ) * r1_S0 )           ! square root salinity
+         ptf = ((((1.46873e-03_wp*zs-9.64972e-03_wp)*zs+2.28348e-02_wp)*zs &
+                  &          - 3.12775e-02_wp)*zs+2.07679e-02_wp)*zs-5.87701e-02_wp
+         ptf = ptf * psal
+         !
+         IF( PRESENT( pdep ) )   ptf = ptf - 7.53e-4 * pdep
+         !
+      CASE ( 0 )                     !==  PT,SP (UNESCO formulation)  ==!
+         !
+         ptf = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal )   &
+            &                - 2.154996e-4_wp *       psal   ) * psal
+            !
+         IF( PRESENT( pdep ) )   ptf = ptf - 7.53e-4 * pdep
+         !
+      CASE DEFAULT
+         IF(lwp) WRITE(numout,cform_err)
+         IF(lwp) WRITE(numout,*) '          bad flag value for nn_eos = ', nn_eos
+         nstop = nstop + 1
+         !
+      END SELECT
+      !
+   END FUNCTION eos_fzp_0d
+
+
+   SUBROUTINE eos_pen( pts, pab_pe, ppen )
+      !!----------------------------------------------------------------------
+      !!                 ***  ROUTINE eos_pen  ***
+      !!
+      !! ** Purpose :   Calculates nonlinear anomalies of alpha_PE, beta_PE and PE at T-points
+      !!
+      !! ** Method  :   PE is defined analytically as the vertical 
+      !!                   primitive of EOS times -g integrated between 0 and z>0.
+      !!                pen is the nonlinear bsq-PE anomaly: pen = ( PE - rau0 gz ) / rau0 gz - rd
+      !!                                                      = 1/z * /int_0^z rd dz - rd 
+      !!                                where rd is the density anomaly (see eos_rhd function)
+      !!                ab_pe are partial derivatives of PE anomaly with respect to T and S:
+      !!                    ab_pe(1) = - 1/(rau0 gz) * dPE/dT + drd/dT = - d(pen)/dT
+      !!                    ab_pe(2) =   1/(rau0 gz) * dPE/dS + drd/dS =   d(pen)/dS
+      !!
+      !! ** Action  : - pen         : PE anomaly given at T-points
+      !!            : - pab_pe  : given at T-points
+      !!                    pab_pe(:,:,:,jp_tem) is alpha_pe
+      !!                    pab_pe(:,:,:,jp_sal) is beta_pe
+      !!----------------------------------------------------------------------
+      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in   ) ::   pts     ! pot. temperature & salinity
+      REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(  out) ::   pab_pe  ! alpha_pe and beta_pe
+      REAL(wp), DIMENSION(jpi,jpj,jpk)     , INTENT(  out) ::   ppen     ! potential energy anomaly
+      !
+      INTEGER  ::   ji, jj, jk                ! dummy loop indices
+      REAL(wp) ::   zt , zh , zs , ztm        ! local scalars
+      REAL(wp) ::   zn , zn0, zn1, zn2        !   -      -
+      !!----------------------------------------------------------------------
+      !
+      IF( nn_timing == 1 )   CALL timing_start('eos_pen')
+      !
+      SELECT CASE ( nn_eos )
+      !
+      CASE( -1, 0 )                !==  polynomial TEOS-10 / EOS-80 ==!
+         !
+         DO jk = 1, jpkm1
+            DO jj = 1, jpj
+               DO ji = 1, jpi
+                  !
+                  zh  = fsdept(ji,jj,jk) * r1_Z0                                ! depth
+                  zt  = pts (ji,jj,jk,jp_tem) * r1_T0                           ! temperature
+                  zs  = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 )   ! square root salinity
+                  ztm = tmask(ji,jj,jk)                                         ! tmask
+                  !
+                  ! potential energy non-linear anomaly
+                  zn2 = (PEN012)*zt   &
+                     &   + PEN102*zs+PEN002
+                     !
+                  zn1 = ((PEN021)*zt   &
+                     &   + PEN111*zs+PEN011)*zt   &
+                     &   + (PEN201*zs+PEN101)*zs+PEN001
+                     !
+                  zn0 = ((((PEN040)*zt   &
+                     &   + PEN130*zs+PEN030)*zt   &
+                     &   + (PEN220*zs+PEN120)*zs+PEN020)*zt   &
+                     &   + ((PEN310*zs+PEN210)*zs+PEN110)*zs+PEN010)*zt   &
+                     &   + (((PEN400*zs+PEN300)*zs+PEN200)*zs+PEN100)*zs+PEN000
+                     !
+                  zn  = ( zn2 * zh + zn1 ) * zh + zn0
+                  !
+                  ppen(ji,jj,jk)  = zn * zh * r1_rau0 * ztm
+                  !
+                  ! alphaPE non-linear anomaly
+                  zn2 = APE002
+                  !
+                  zn1 = (APE011)*zt   &
+                     &   + APE101*zs+APE001
+                     !
+                  zn0 = (((APE030)*zt   &
+                     &   + APE120*zs+APE020)*zt   &
+                     &   + (APE210*zs+APE110)*zs+APE010)*zt   &
+                     &   + ((APE300*zs+APE200)*zs+APE100)*zs+APE000
+                     !
+                  zn  = ( zn2 * zh + zn1 ) * zh + zn0
+                  !                              
+                  pab_pe(ji,jj,jk,jp_tem) = zn * zh * r1_rau0 * ztm
+                  !
+                  ! betaPE non-linear anomaly
+                  zn2 = BPE002
+                  !
+                  zn1 = (BPE011)*zt   &
+                     &   + BPE101*zs+BPE001
+                     !
+                  zn0 = (((BPE030)*zt   &
+                     &   + BPE120*zs+BPE020)*zt   &
+                     &   + (BPE210*zs+BPE110)*zs+BPE010)*zt   &
+                     &   + ((BPE300*zs+BPE200)*zs+BPE100)*zs+BPE000
+                     !
+                  zn  = ( zn2 * zh + zn1 ) * zh + zn0
+                  !                              
+                  pab_pe(ji,jj,jk,jp_sal) = zn / zs * zh * r1_rau0 * ztm
+                  !
+               END DO
+            END DO
+         END DO
+         !
+      CASE( 1 )                !==  Vallis (2006) simplified EOS  ==!
+         !
+         DO jk = 1, jpkm1
+            DO jj = 1, jpj
+               DO ji = 1, jpi
+                  zt  = pts(ji,jj,jk,jp_tem) - 10._wp  ! temperature anomaly (t-T0)
+                  zs = pts (ji,jj,jk,jp_sal) - 35._wp  ! abs. salinity anomaly (s-S0)
+                  zh  = fsdept(ji,jj,jk)               ! depth in meters  at t-point
+                  ztm = tmask(ji,jj,jk)                ! tmask
+                  zn  = 0.5_wp * zh * r1_rau0 * ztm
+                  !                                    ! Potential Energy
+                  ppen(ji,jj,jk) = ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zn
+                  !                                    ! alphaPE
+                  pab_pe(ji,jj,jk,jp_tem) = - rn_a0 * rn_mu1 * zn
+                  pab_pe(ji,jj,jk,jp_sal) =   rn_b0 * rn_mu2 * zn
+                  !
+               END DO
+            END DO
+         END DO
+         !
+      CASE DEFAULT
+         IF(lwp) WRITE(numout,cform_err)
+         IF(lwp) WRITE(numout,*) '          bad flag value for nn_eos = ', nn_eos
+         nstop = nstop + 1
+         !
+      END SELECT
+      !
+      IF( nn_timing == 1 )   CALL timing_stop('eos_pen')
+      !
+   END SUBROUTINE eos_pen
+
+
+   SUBROUTINE eos_init
       !!----------------------------------------------------------------------
       !!                 ***  ROUTINE eos_init  ***
       !!
-      !! ** Purpose :   Compute the sea surface freezing temperature [Celcius]
-      !!
-      !! ** Method  :   UNESCO freezing point at the surface (pressure = 0???)
-      !!       freezing point [Celcius]=(-.0575+1.710523e-3*sqrt(abs(s))-2.154996e-4*s)*s-7.53e-4*p
-      !!       checkvalue: tf= -2.588567 Celsius for s=40.0psu, p=500. decibars
-      !!
-      !! Reference  :   UNESCO tech. papers in the marine science no. 28. 1978
-      !!----------------------------------------------------------------------
-      REAL(wp), DIMENSION(jpi,jpj), INTENT(in   ) ::   psal   ! salinity             [psu]
-      REAL(wp), DIMENSION(jpi,jpj), INTENT(in   ), OPTIONAL ::   pdep   ! depth      [decibars]
-      ! Leave result array automatic rather than making explicitly allocated
-      REAL(wp), DIMENSION(jpi,jpj)                ::   ptf    ! freezing temperature [Celcius]
-      !!----------------------------------------------------------------------
-      !
-      ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) )   &
-         &                     - 2.154996e-4_wp *       psal(:,:)   ) * psal(:,:)
-      IF ( PRESENT( pdep ) ) THEN   
-         ptf(:,:) = ptf(:,:) - 7.53e-4_wp * pdep(:,:)
-      ENDIF
-      !
-   END FUNCTION tfreez
-
-
-   SUBROUTINE eos_init
-      !!----------------------------------------------------------------------
-      !!                 ***  ROUTINE eos_init  ***
-      !!
       !! ** Purpose :   initializations for the equation of state
       !!
       !! ** Method  :   Read the namelist nameos and control the parameters
       !!----------------------------------------------------------------------
-      NAMELIST/nameos/ nn_eos, rn_alpha, rn_beta
-      !!----------------------------------------------------------------------
-      INTEGER  ::   ios
+      INTEGER  ::   ios   ! local integer
+      !!
+      NAMELIST/nameos/ nn_eos, ln_useCT, rn_a0, rn_b0, rn_lambda1, rn_mu1,   &
+         &                                             rn_lambda2, rn_mu2, rn_nu
+      !!----------------------------------------------------------------------
       !
       REWIND( numnam_ref )              ! Namelist nameos in reference namelist : equation of state
       READ  ( numnam_ref, nameos, IOSTAT = ios, ERR = 901 )
 901   IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in reference namelist', lwp )
-
+      !
       REWIND( numnam_cfg )              ! Namelist nameos in configuration namelist : equation of state
       READ  ( numnam_cfg, nameos, IOSTAT = ios, ERR = 902 )
 902   IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in configuration namelist', lwp )
       IF(lwm) WRITE( numond, nameos )
+      !
+      rau0        = 1026._wp                 !: volumic mass of reference     [kg/m3]
+      rcp         = 3991.86795711963_wp      !: heat capacity     [J/K]
       !
       IF(lwp) THEN                ! Control print
@@ -731,25 +1249,408 @@
          WRITE(numout,*) '          Namelist nameos : set eos parameters'
          WRITE(numout,*) '             flag for eq. of state and N^2  nn_eos   = ', nn_eos
-         WRITE(numout,*) '             thermal exp. coef. (linear)    rn_alpha = ', rn_alpha
-         WRITE(numout,*) '             saline  exp. coef. (linear)    rn_beta  = ', rn_beta
+         IF( ln_useCT )   THEN
+            WRITE(numout,*) '             model uses Conservative Temperature'
+            WRITE(numout,*) '             Important: model must be initialized with CT and SA fields'
+         ELSE
+            WRITE(numout,*) '             model does not use Conservative Temperature'
+         ENDIF
       ENDIF
       !
       SELECT CASE( nn_eos )         ! check option
       !
-      CASE( 0 )                        !==  Jackett and McDougall (1994) formulation  ==!
+      CASE( -1 )                       !==  polynomial TEOS-10  ==!
          IF(lwp) WRITE(numout,*)
-         IF(lwp) WRITE(numout,*) '          use of Jackett & McDougall (1994) equation of state and'
-         IF(lwp) WRITE(numout,*) '                 McDougall (1987) Brunt-Vaisala frequency'
-         !
-      CASE( 1 )                        !==  Linear formulation = F( temperature )  ==!
+         IF(lwp) WRITE(numout,*) '          use of TEOS-10 equation of state (cons. temp. and abs. salinity)'
+         !
+         rdeltaS = 32._wp
+         r1_S0  = 0.875_wp/35.16504_wp
+         r1_T0  = 1._wp/40._wp
+         r1_Z0  = 1.e-4_wp
+         !
+         EOS000 = 8.0189615746e+02_wp
+         EOS100 = 8.6672408165e+02_wp
+         EOS200 = -1.7864682637e+03_wp
+         EOS300 = 2.0375295546e+03_wp
+         EOS400 = -1.2849161071e+03_wp
+         EOS500 = 4.3227585684e+02_wp
+         EOS600 = -6.0579916612e+01_wp
+         EOS010 = 2.6010145068e+01_wp
+         EOS110 = -6.5281885265e+01_wp
+         EOS210 = 8.1770425108e+01_wp
+         EOS310 = -5.6888046321e+01_wp
+         EOS410 = 1.7681814114e+01_wp
+         EOS510 = -1.9193502195_wp
+         EOS020 = -3.7074170417e+01_wp
+         EOS120 = 6.1548258127e+01_wp
+         EOS220 = -6.0362551501e+01_wp
+         EOS320 = 2.9130021253e+01_wp
+         EOS420 = -5.4723692739_wp
+         EOS030 = 2.1661789529e+01_wp
+         EOS130 = -3.3449108469e+01_wp
+         EOS230 = 1.9717078466e+01_wp
+         EOS330 = -3.1742946532_wp
+         EOS040 = -8.3627885467_wp
+         EOS140 = 1.1311538584e+01_wp
+         EOS240 = -5.3563304045_wp
+         EOS050 = 5.4048723791e-01_wp
+         EOS150 = 4.8169980163e-01_wp
+         EOS060 = -1.9083568888e-01_wp
+         EOS001 = 1.9681925209e+01_wp
+         EOS101 = -4.2549998214e+01_wp
+         EOS201 = 5.0774768218e+01_wp
+         EOS301 = -3.0938076334e+01_wp
+         EOS401 = 6.6051753097_wp
+         EOS011 = -1.3336301113e+01_wp
+         EOS111 = -4.4870114575_wp
+         EOS211 = 5.0042598061_wp
+         EOS311 = -6.5399043664e-01_wp
+         EOS021 = 6.7080479603_wp
+         EOS121 = 3.5063081279_wp
+         EOS221 = -1.8795372996_wp
+         EOS031 = -2.4649669534_wp
+         EOS131 = -5.5077101279e-01_wp
+         EOS041 = 5.5927935970e-01_wp
+         EOS002 = 2.0660924175_wp
+         EOS102 = -4.9527603989_wp
+         EOS202 = 2.5019633244_wp
+         EOS012 = 2.0564311499_wp
+         EOS112 = -2.1311365518e-01_wp
+         EOS022 = -1.2419983026_wp
+         EOS003 = -2.3342758797e-02_wp
+         EOS103 = -1.8507636718e-02_wp
+         EOS013 = 3.7969820455e-01_wp
+         !
+         ALP000 = -6.5025362670e-01_wp
+         ALP100 = 1.6320471316_wp
+         ALP200 = -2.0442606277_wp
+         ALP300 = 1.4222011580_wp
+         ALP400 = -4.4204535284e-01_wp
+         ALP500 = 4.7983755487e-02_wp
+         ALP010 = 1.8537085209_wp
+         ALP110 = -3.0774129064_wp
+         ALP210 = 3.0181275751_wp
+         ALP310 = -1.4565010626_wp
+         ALP410 = 2.7361846370e-01_wp
+         ALP020 = -1.6246342147_wp
+         ALP120 = 2.5086831352_wp
+         ALP220 = -1.4787808849_wp
+         ALP320 = 2.3807209899e-01_wp
+         ALP030 = 8.3627885467e-01_wp
+         ALP130 = -1.1311538584_wp
+         ALP230 = 5.3563304045e-01_wp
+         ALP040 = -6.7560904739e-02_wp
+         ALP140 = -6.0212475204e-02_wp
+         ALP050 = 2.8625353333e-02_wp
+         ALP001 = 3.3340752782e-01_wp
+         ALP101 = 1.1217528644e-01_wp
+         ALP201 = -1.2510649515e-01_wp
+         ALP301 = 1.6349760916e-02_wp
+         ALP011 = -3.3540239802e-01_wp
+         ALP111 = -1.7531540640e-01_wp
+         ALP211 = 9.3976864981e-02_wp
+         ALP021 = 1.8487252150e-01_wp
+         ALP121 = 4.1307825959e-02_wp
+         ALP031 = -5.5927935970e-02_wp
+         ALP002 = -5.1410778748e-02_wp
+         ALP102 = 5.3278413794e-03_wp
+         ALP012 = 6.2099915132e-02_wp
+         ALP003 = -9.4924551138e-03_wp
+         !
+         BET000 = 1.0783203594e+01_wp
+         BET100 = -4.4452095908e+01_wp
+         BET200 = 7.6048755820e+01_wp
+         BET300 = -6.3944280668e+01_wp
+         BET400 = 2.6890441098e+01_wp
+         BET500 = -4.5221697773_wp
+         BET010 = -8.1219372432e-01_wp
+         BET110 = 2.0346663041_wp
+         BET210 = -2.1232895170_wp
+         BET310 = 8.7994140485e-01_wp
+         BET410 = -1.1939638360e-01_wp
+         BET020 = 7.6574242289e-01_wp
+         BET120 = -1.5019813020_wp
+         BET220 = 1.0872489522_wp
+         BET320 = -2.7233429080e-01_wp
+         BET030 = -4.1615152308e-01_wp
+         BET130 = 4.9061350869e-01_wp
+         BET230 = -1.1847737788e-01_wp
+         BET040 = 1.4073062708e-01_wp
+         BET140 = -1.3327978879e-01_wp
+         BET050 = 5.9929880134e-03_wp
+         BET001 = -5.2937873009e-01_wp
+         BET101 = 1.2634116779_wp
+         BET201 = -1.1547328025_wp
+         BET301 = 3.2870876279e-01_wp
+         BET011 = -5.5824407214e-02_wp
+         BET111 = 1.2451933313e-01_wp
+         BET211 = -2.4409539932e-02_wp
+         BET021 = 4.3623149752e-02_wp
+         BET121 = -4.6767901790e-02_wp
+         BET031 = -6.8523260060e-03_wp
+         BET002 = -6.1618945251e-02_wp
+         BET102 = 6.2255521644e-02_wp
+         BET012 = -2.6514181169e-03_wp
+         BET003 = -2.3025968587e-04_wp
+         !
+         PEN000 = -9.8409626043_wp
+         PEN100 = 2.1274999107e+01_wp
+         PEN200 = -2.5387384109e+01_wp
+         PEN300 = 1.5469038167e+01_wp
+         PEN400 = -3.3025876549_wp
+         PEN010 = 6.6681505563_wp
+         PEN110 = 2.2435057288_wp
+         PEN210 = -2.5021299030_wp
+         PEN310 = 3.2699521832e-01_wp
+         PEN020 = -3.3540239802_wp
+         PEN120 = -1.7531540640_wp
+         PEN220 = 9.3976864981e-01_wp
+         PEN030 = 1.2324834767_wp
+         PEN130 = 2.7538550639e-01_wp
+         PEN040 = -2.7963967985e-01_wp
+         PEN001 = -1.3773949450_wp
+         PEN101 = 3.3018402659_wp
+         PEN201 = -1.6679755496_wp
+         PEN011 = -1.3709540999_wp
+         PEN111 = 1.4207577012e-01_wp
+         PEN021 = 8.2799886843e-01_wp
+         PEN002 = 1.7507069098e-02_wp
+         PEN102 = 1.3880727538e-02_wp
+         PEN012 = -2.8477365341e-01_wp
+         !
+         APE000 = -1.6670376391e-01_wp
+         APE100 = -5.6087643219e-02_wp
+         APE200 = 6.2553247576e-02_wp
+         APE300 = -8.1748804580e-03_wp
+         APE010 = 1.6770119901e-01_wp
+         APE110 = 8.7657703198e-02_wp
+         APE210 = -4.6988432490e-02_wp
+         APE020 = -9.2436260751e-02_wp
+         APE120 = -2.0653912979e-02_wp
+         APE030 = 2.7963967985e-02_wp
+         APE001 = 3.4273852498e-02_wp
+         APE101 = -3.5518942529e-03_wp
+         APE011 = -4.1399943421e-02_wp
+         APE002 = 7.1193413354e-03_wp
+         !
+         BPE000 = 2.6468936504e-01_wp
+         BPE100 = -6.3170583896e-01_wp
+         BPE200 = 5.7736640125e-01_wp
+         BPE300 = -1.6435438140e-01_wp
+         BPE010 = 2.7912203607e-02_wp
+         BPE110 = -6.2259666565e-02_wp
+         BPE210 = 1.2204769966e-02_wp
+         BPE020 = -2.1811574876e-02_wp
+         BPE120 = 2.3383950895e-02_wp
+         BPE030 = 3.4261630030e-03_wp
+         BPE001 = 4.1079296834e-02_wp
+         BPE101 = -4.1503681096e-02_wp
+         BPE011 = 1.7676120780e-03_wp
+         BPE002 = 1.7269476440e-04_wp
+         !
+      CASE( 0 )                        !==  polynomial EOS-80 formulation  ==!
+         !
          IF(lwp) WRITE(numout,*)
-         IF(lwp) WRITE(numout,*) '          use of linear eos rho(T) = rau0 * ( 1.0285 - rn_alpha * T )'
-         IF( lk_zdfddm ) CALL ctl_stop( '          double diffusive mixing parameterization requires',   &
-              &                         ' that T and S are used as state variables' )
-         !
-      CASE( 2 )                        !==  Linear formulation = F( temperature , salinity )  ==!
-         ralpbet = rn_alpha / rn_beta
-         IF(lwp) WRITE(numout,*)
-         IF(lwp) WRITE(numout,*) '          use of linear eos rho(T,S) = rau0 * ( rn_beta * S - rn_alpha * T )'
+         IF(lwp) WRITE(numout,*) '          use of EOS-80 equation of state (pot. temp. and pract. salinity)'
+         !
+         rdeltaS = 20._wp
+         r1_S0  = 1._wp/40._wp
+         r1_T0  = 1._wp/40._wp
+         r1_Z0  = 1.e-4_wp
+         !
+         EOS000 = 9.5356891948e+02_wp
+         EOS100 = 1.7136499189e+02_wp
+         EOS200 = -3.7501039454e+02_wp
+         EOS300 = 5.1856810420e+02_wp
+         EOS400 = -3.7264470465e+02_wp
+         EOS500 = 1.4302533998e+02_wp
+         EOS600 = -2.2856621162e+01_wp
+         EOS010 = 1.0087518651e+01_wp
+         EOS110 = -1.3647741861e+01_wp
+         EOS210 = 8.8478359933_wp
+         EOS310 = -7.2329388377_wp
+         EOS410 = 1.4774410611_wp
+         EOS510 = 2.0036720553e-01_wp
+         EOS020 = -2.5579830599e+01_wp
+         EOS120 = 2.4043512327e+01_wp
+         EOS220 = -1.6807503990e+01_wp
+         EOS320 = 8.3811577084_wp
+         EOS420 = -1.9771060192_wp
+         EOS030 = 1.6846451198e+01_wp
+         EOS130 = -2.1482926901e+01_wp
+         EOS230 = 1.0108954054e+01_wp
+         EOS330 = -6.2675951440e-01_wp
+         EOS040 = -8.0812310102_wp
+         EOS140 = 1.0102374985e+01_wp
+         EOS240 = -4.8340368631_wp
+         EOS050 = 1.2079167803_wp
+         EOS150 = 1.1515380987e-01_wp
+         EOS060 = -2.4520288837e-01_wp
+         EOS001 = 1.0748601068e+01_wp
+         EOS101 = -1.7817043500e+01_wp
+         EOS201 = 2.2181366768e+01_wp
+         EOS301 = -1.6750916338e+01_wp
+         EOS401 = 4.1202230403_wp
+         EOS011 = -1.5852644587e+01_wp
+         EOS111 = -7.6639383522e-01_wp
+         EOS211 = 4.1144627302_wp
+         EOS311 = -6.6955877448e-01_wp
+         EOS021 = 9.9994861860_wp
+         EOS121 = -1.9467067787e-01_wp
+         EOS221 = -1.2177554330_wp
+         EOS031 = -3.4866102017_wp
+         EOS131 = 2.2229155620e-01_wp
+         EOS041 = 5.9503008642e-01_wp
+         EOS002 = 1.0375676547_wp
+         EOS102 = -3.4249470629_wp
+         EOS202 = 2.0542026429_wp
+         EOS012 = 2.1836324814_wp
+         EOS112 = -3.4453674320e-01_wp
+         EOS022 = -1.2548163097_wp
+         EOS003 = 1.8729078427e-02_wp
+         EOS103 = -5.7238495240e-02_wp
+         EOS013 = 3.8306136687e-01_wp
+         !
+         ALP000 = -2.5218796628e-01_wp
+         ALP100 = 3.4119354654e-01_wp
+         ALP200 = -2.2119589983e-01_wp
+         ALP300 = 1.8082347094e-01_wp
+         ALP400 = -3.6936026529e-02_wp
+         ALP500 = -5.0091801383e-03_wp
+         ALP010 = 1.2789915300_wp
+         ALP110 = -1.2021756164_wp
+         ALP210 = 8.4037519952e-01_wp
+         ALP310 = -4.1905788542e-01_wp
+         ALP410 = 9.8855300959e-02_wp
+         ALP020 = -1.2634838399_wp
+         ALP120 = 1.6112195176_wp
+         ALP220 = -7.5817155402e-01_wp
+         ALP320 = 4.7006963580e-02_wp
+         ALP030 = 8.0812310102e-01_wp
+         ALP130 = -1.0102374985_wp
+         ALP230 = 4.8340368631e-01_wp
+         ALP040 = -1.5098959754e-01_wp
+         ALP140 = -1.4394226233e-02_wp
+         ALP050 = 3.6780433255e-02_wp
+         ALP001 = 3.9631611467e-01_wp
+         ALP101 = 1.9159845880e-02_wp
+         ALP201 = -1.0286156825e-01_wp
+         ALP301 = 1.6738969362e-02_wp
+         ALP011 = -4.9997430930e-01_wp
+         ALP111 = 9.7335338937e-03_wp
+         ALP211 = 6.0887771651e-02_wp
+         ALP021 = 2.6149576513e-01_wp
+         ALP121 = -1.6671866715e-02_wp
+         ALP031 = -5.9503008642e-02_wp
+         ALP002 = -5.4590812035e-02_wp
+         ALP102 = 8.6134185799e-03_wp
+         ALP012 = 6.2740815484e-02_wp
+         ALP003 = -9.5765341718e-03_wp
+         !
+         BET000 = 2.1420623987_wp
+         BET100 = -9.3752598635_wp
+         BET200 = 1.9446303907e+01_wp
+         BET300 = -1.8632235232e+01_wp
+         BET400 = 8.9390837485_wp
+         BET500 = -1.7142465871_wp
+         BET010 = -1.7059677327e-01_wp
+         BET110 = 2.2119589983e-01_wp
+         BET210 = -2.7123520642e-01_wp
+         BET310 = 7.3872053057e-02_wp
+         BET410 = 1.2522950346e-02_wp
+         BET020 = 3.0054390409e-01_wp
+         BET120 = -4.2018759976e-01_wp
+         BET220 = 3.1429341406e-01_wp
+         BET320 = -9.8855300959e-02_wp
+         BET030 = -2.6853658626e-01_wp
+         BET130 = 2.5272385134e-01_wp
+         BET230 = -2.3503481790e-02_wp
+         BET040 = 1.2627968731e-01_wp
+         BET140 = -1.2085092158e-01_wp
+         BET050 = 1.4394226233e-03_wp
+         BET001 = -2.2271304375e-01_wp
+         BET101 = 5.5453416919e-01_wp
+         BET201 = -6.2815936268e-01_wp
+         BET301 = 2.0601115202e-01_wp
+         BET011 = -9.5799229402e-03_wp
+         BET111 = 1.0286156825e-01_wp
+         BET211 = -2.5108454043e-02_wp
+         BET021 = -2.4333834734e-03_wp
+         BET121 = -3.0443885826e-02_wp
+         BET031 = 2.7786444526e-03_wp
+         BET002 = -4.2811838287e-02_wp
+         BET102 = 5.1355066072e-02_wp
+         BET012 = -4.3067092900e-03_wp
+         BET003 = -7.1548119050e-04_wp
+         !
+         PEN000 = -5.3743005340_wp
+         PEN100 = 8.9085217499_wp
+         PEN200 = -1.1090683384e+01_wp
+         PEN300 = 8.3754581690_wp
+         PEN400 = -2.0601115202_wp
+         PEN010 = 7.9263222935_wp
+         PEN110 = 3.8319691761e-01_wp
+         PEN210 = -2.0572313651_wp
+         PEN310 = 3.3477938724e-01_wp
+         PEN020 = -4.9997430930_wp
+         PEN120 = 9.7335338937e-02_wp
+         PEN220 = 6.0887771651e-01_wp
+         PEN030 = 1.7433051009_wp
+         PEN130 = -1.1114577810e-01_wp
+         PEN040 = -2.9751504321e-01_wp
+         PEN001 = -6.9171176978e-01_wp
+         PEN101 = 2.2832980419_wp
+         PEN201 = -1.3694684286_wp
+         PEN011 = -1.4557549876_wp
+         PEN111 = 2.2969116213e-01_wp
+         PEN021 = 8.3654420645e-01_wp
+         PEN002 = -1.4046808820e-02_wp
+         PEN102 = 4.2928871430e-02_wp
+         PEN012 = -2.8729602515e-01_wp
+         !
+         APE000 = -1.9815805734e-01_wp
+         APE100 = -9.5799229402e-03_wp
+         APE200 = 5.1430784127e-02_wp
+         APE300 = -8.3694846809e-03_wp
+         APE010 = 2.4998715465e-01_wp
+         APE110 = -4.8667669469e-03_wp
+         APE210 = -3.0443885826e-02_wp
+         APE020 = -1.3074788257e-01_wp
+         APE120 = 8.3359333577e-03_wp
+         APE030 = 2.9751504321e-02_wp
+         APE001 = 3.6393874690e-02_wp
+         APE101 = -5.7422790533e-03_wp
+         APE011 = -4.1827210323e-02_wp
+         APE002 = 7.1824006288e-03_wp
+         !
+         BPE000 = 1.1135652187e-01_wp
+         BPE100 = -2.7726708459e-01_wp
+         BPE200 = 3.1407968134e-01_wp
+         BPE300 = -1.0300557601e-01_wp
+         BPE010 = 4.7899614701e-03_wp
+         BPE110 = -5.1430784127e-02_wp
+         BPE210 = 1.2554227021e-02_wp
+         BPE020 = 1.2166917367e-03_wp
+         BPE120 = 1.5221942913e-02_wp
+         BPE030 = -1.3893222263e-03_wp
+         BPE001 = 2.8541225524e-02_wp
+         BPE101 = -3.4236710714e-02_wp
+         BPE011 = 2.8711395266e-03_wp
+         BPE002 = 5.3661089288e-04_wp
+         !
+      CASE( 1 )                        !==  Simplified EOS     ==!
+         IF(lwp) THEN
+            WRITE(numout,*)
+            WRITE(numout,*) '          use of simplified eos:    rhd(dT=T-10,dS=S-35,Z) = '
+            WRITE(numout,*) '             [-a0*(1+lambda1/2*dT+mu1*Z)*dT + b0*(1+lambda2/2*dT+mu2*Z)*dS - nu*dT*dS]/rau0'
+            WRITE(numout,*)
+            WRITE(numout,*) '             thermal exp. coef.    rn_a0      = ', rn_a0
+            WRITE(numout,*) '             saline  cont. coef.   rn_b0      = ', rn_b0
+            WRITE(numout,*) '             cabbeling coef.       rn_lambda1 = ', rn_lambda1
+            WRITE(numout,*) '             cabbeling coef.       rn_lambda2 = ', rn_lambda2
+            WRITE(numout,*) '             thermobar. coef.      rn_mu1     = ', rn_mu1
+            WRITE(numout,*) '             thermobar. coef.      rn_mu2     = ', rn_mu2
+            WRITE(numout,*) '             2nd cabbel. coef.     rn_nu      = ', rn_nu
+            WRITE(numout,*) '               Caution: rn_beta0=0 incompatible with ddm parameterization '
+         ENDIF
          !
       CASE DEFAULT                     !==  ERROR in nn_eos  ==!
@@ -759,4 +1660,16 @@
       END SELECT
       !
+      rau0_rcp    = rau0 * rcp 
+      r1_rau0     = 1._wp / rau0
+      r1_rcp      = 1._wp / rcp
+      r1_rau0_rcp = 1._wp / rau0_rcp 
+      !
+      IF(lwp) WRITE(numout,*)
+      IF(lwp) WRITE(numout,*) '          volumic mass of reference           rau0  = ', rau0   , ' kg/m^3'
+      IF(lwp) WRITE(numout,*) '          1. / rau0                        r1_rau0  = ', r1_rau0, ' m^3/kg'
+      IF(lwp) WRITE(numout,*) '          ocean specific heat                 rcp   = ', rcp    , ' J/Kelvin'
+      IF(lwp) WRITE(numout,*) '          rau0 * rcp                       rau0_rcp = ', rau0_rcp
+      IF(lwp) WRITE(numout,*) '          1. / ( rau0 * rcp )           r1_rau0_rcp = ', r1_rau0_rcp
+      !
    END SUBROUTINE eos_init
 
