[3611] | 1 | MODULE eosbn2_tam |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE eosbn2_tam *** |
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| 4 | !! Ocean diagnostic variable : equation of state - in situ and potential density |
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| 5 | !! - Brunt-Vaisala frequency |
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| 6 | !! Tangent and Adjoint module |
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| 7 | !!============================================================================== |
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| 8 | !! History : OPA ! 1989-03 (O. Marti) Original code |
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| 9 | !! 6.0 ! 1994-07 (G. Madec, M. Imbard) add bn2 |
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| 10 | !! 6.0 ! 1994-08 (G. Madec) Add Jackett & McDougall eos |
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| 11 | !! 7.0 ! 1996-01 (G. Madec) statement function for e3 |
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| 12 | !! 8.1 ! 1997-07 (G. Madec) density instead of volumic mass |
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| 13 | !! - ! 1999-02 (G. Madec, N. Grima) semi-implicit pressure gradient |
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| 14 | !! 8.2 ! 2001-09 (M. Ben Jelloul) bugfix on linear eos |
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| 15 | !! NEMO 1.0 ! 2002-10 (G. Madec) add eos_init |
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| 16 | !! - ! 2002-11 (G. Madec, A. Bozec) partial step, eos_insitu_2d |
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| 17 | !! - ! 2003-08 (G. Madec) F90, free form |
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| 18 | !! 3.0 ! 2006-08 (G. Madec) add tfreez function |
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| 19 | !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA |
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| 20 | !! - ! 2010-10 (G. Nurser, G. Madec) add eos_alpbet used in ldfslp |
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| 21 | !! History of the TAM Module : |
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| 22 | !! 8.2 ! 2005-03 (F. Van den Berghe, A. Weaver, N. Daget) |
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| 23 | !! - eostan.F |
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| 24 | !! 9.0 ! 2007-07 (K. Mogensen) Initial version based on eostan.F |
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| 25 | !! ! 2008-07 (A. Vidard) bug fix in computation of prd_tl if neos=1 |
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| 26 | !! ! 2008-11 (A. Vidard) TAM of the 06-08 version |
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| 27 | !! NEMO 3.2 ! 2010-04 (F. Vigilant) version 3.2 |
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| 28 | !! 3.4 ! 2012-04 (P.-A. Bouttier) version 3.4 |
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| 29 | !!---------------------------------------------------------------------- |
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| 30 | |
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| 31 | !!---------------------------------------------------------------------- |
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| 32 | !! Direct subroutines |
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| 33 | !! eos : generic interface of the equation of state |
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| 34 | !! eos_insitu : Compute the in situ density |
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| 35 | !! eos_insitu_pot : Compute the insitu and surface referenced potential |
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| 36 | !! volumic mass |
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| 37 | !! eos_insitu_2d : Compute the in situ density for 2d fields |
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| 38 | !! eos_bn2 : Compute the Brunt-Vaisala frequency |
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| 39 | !! eos_alpbet : calculates the in situ thermal/haline expansion ratio |
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| 40 | !! tfreez : Compute the surface freezing temperature |
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| 41 | !! eos_init : set eos parameters (namelist) |
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| 42 | !!---------------------------------------------------------------------- |
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| 43 | !! * Modules used |
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| 44 | #if defined key_zdfddm |
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| 45 | USE oce_tam |
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| 46 | #endif |
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| 47 | USE dom_oce |
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| 48 | USE par_kind |
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| 49 | USE par_oce |
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| 50 | USE oce |
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| 51 | USE phycst |
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| 52 | USE in_out_manager |
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| 53 | #if defined key_zdfddm |
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| 54 | USE zdfddm ! vertical physics: double diffusion |
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| 55 | #endif |
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| 56 | USE eosbn2 |
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| 57 | USE gridrandom |
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| 58 | USE dotprodfld |
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| 59 | USE tstool_tam |
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| 60 | USE wrk_nemo |
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| 61 | USE timing |
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| 62 | USE lib_mpp |
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| 63 | IMPLICIT NONE |
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| 64 | PRIVATE |
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| 65 | ! |
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| 66 | !! * Interface |
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| 67 | INTERFACE eos_tan |
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| 68 | MODULE PROCEDURE eos_insitu_tan, eos_insitu_pot_tan, eos_insitu_2d_tan, & |
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| 69 | eos_alpbet_tan |
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| 70 | END INTERFACE |
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| 71 | INTERFACE eos_adj |
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| 72 | MODULE PROCEDURE eos_insitu_adj, eos_insitu_pot_adj, eos_insitu_2d_adj, & |
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| 73 | eos_alpbet_adj |
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| 74 | END INTERFACE |
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| 75 | INTERFACE bn2_tan |
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| 76 | MODULE PROCEDURE eos_bn2_tan |
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| 77 | END INTERFACE |
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| 78 | INTERFACE bn2_adj |
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| 79 | MODULE PROCEDURE eos_bn2_adj |
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| 80 | END INTERFACE |
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| 81 | ! |
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| 82 | !! * Routine accessibility |
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| 83 | PUBLIC eos_tan ! called by step.F90, inidtr.F90, tranpc.F90 and intgrd.F90 |
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| 84 | PUBLIC bn2_tan ! called by step.F90 |
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| 85 | PUBLIC eos_adj ! called by step.F90, inidtr.F90, tranpc.F90 and intgrd.F90 |
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| 86 | PUBLIC bn2_adj ! called by step.F90 |
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| 87 | #if defined key_tam |
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| 88 | PUBLIC eos_adj_tst |
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| 89 | PUBLIC bn2_adj_tst |
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| 90 | #endif |
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| 91 | !! * Substitutions |
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| 92 | # include "domzgr_substitute.h90" |
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| 93 | # include "vectopt_loop_substitute.h90" |
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| 94 | !!---------------------------------------------------------------------- |
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| 95 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 96 | !! $Id$ |
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| 97 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 98 | !!---------------------------------------------------------------------- |
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| 99 | CONTAINS |
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| 100 | SUBROUTINE eos_insitu_tan( pts, pts_tl, prd_tl ) |
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| 101 | !!----------------------------------------------------------------------- |
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| 102 | !! |
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| 103 | !! *** ROUTINE eos_insitu_tan : TL OF ROUTINE eos_insitu *** |
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| 104 | !! |
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| 105 | !! ** Purpose of direct routine : Compute the in situ density |
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| 106 | !! (ratio rho/rau0) from potential temperature and salinity |
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| 107 | !! using an equation of state defined through the namelist |
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| 108 | !! parameter nn_eos. |
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| 109 | !! |
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| 110 | !! ** Method of direct routine : 3 cases: |
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| 111 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
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| 112 | !! the in situ density is computed directly as a function of |
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| 113 | !! potential temperature relative to the surface (the opa t |
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| 114 | !! variable), salt and pressure (assuming no pressure variation |
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| 115 | !! along geopotential surfaces, i.e. the pressure p in decibars |
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| 116 | !! is approximated by the depth in meters. |
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| 117 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
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| 118 | !! with pressure p decibars |
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| 119 | !! potential temperature t deg celsius |
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| 120 | !! salinity s psu |
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| 121 | !! reference volumic mass rau0 kg/m**3 |
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| 122 | !! in situ volumic mass rho kg/m**3 |
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| 123 | !! in situ density anomalie prd no units |
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| 124 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
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| 125 | !! t = 40 deg celcius, s=40 psu |
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| 126 | !! nn_eos = 1 : linear equation of state function of temperature only |
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| 127 | !! prd(t) = 0.0285 - rn_alpha * t |
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| 128 | !! nn_eos = 2 : linear equation of state function of temperature and |
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| 129 | !! salinity |
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| 130 | !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. |
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| 131 | !! Note that no boundary condition problem occurs in this routine |
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| 132 | !! as (ptem,psal) are defined over the whole domain. |
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| 133 | !! |
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| 134 | !! ** Comments on Adjoint Routine : |
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| 135 | !! Care has been taken to avoid division by zero when computing |
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| 136 | !! the inverse of the square root of salinity at masked salinity |
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| 137 | !! points. |
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| 138 | !! |
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| 139 | !! * Arguments |
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| 140 | REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts, & ! 1 : potential temperature [Celcius] |
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| 141 | ! ! 2 : salinity [psu] |
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| 142 | & pts_tl ! 1 : TL of potential temperature [Celsius] |
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| 143 | ! 2 : TL of salinity [psu] |
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| 144 | REAL(wp), DIMENSION(:,:,:), INTENT( out ) :: & |
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| 145 | & prd_tl ! TL of potential density (surface referenced) |
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| 146 | !! * Local declarations |
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| 147 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 148 | REAL(wp) :: & ! temporary scalars |
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| 149 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
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| 150 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
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| 151 | zttl, zstl, zhtl, zsrtl, zr1tl, zr2tl, zr3tl, & |
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| 152 | zr4tl, zrhoptl, zetl, zbwtl, & |
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| 153 | zbtl, zdtl, zctl, zawtl, zatl, zb1tl, za1tl, & |
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| 154 | zkwtl, zk0tl, zpes, zrdc1, zrdc2, zeps, & |
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| 155 | zmask, zrau0r |
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| 156 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zws |
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| 157 | !!---------------------------------------------------------------------- |
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| 158 | ! |
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| 159 | IF( nn_timing == 1 ) CALL timing_start('eos_tan') |
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| 160 | ! |
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| 161 | CALL wrk_alloc( jpi, jpj, jpk, zws ) |
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| 162 | ! |
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| 163 | SELECT CASE ( nn_eos ) |
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| 164 | |
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| 165 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
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| 166 | zrau0r = 1._wp / rau0 |
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| 167 | #ifdef key_sp |
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| 168 | zeps = 1.e-7_wp |
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| 169 | #else |
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| 170 | zeps = 1.e-14_wp |
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| 171 | #endif |
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| 172 | !CDIR NOVERRCHK |
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| 173 | zws(:,:,:) = SQRT( ABS( pts(:,:,:, jp_sal) ) ) |
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| 174 | ! |
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| 175 | DO jk = 1, jpkm1 |
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| 176 | DO jj = 1, jpj |
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| 177 | DO ji = 1, jpi |
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| 178 | zt = pts(ji,jj,jk,jp_tem) |
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| 179 | zs = pts(ji,jj,jk,jp_sal) |
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| 180 | zh = fsdept(ji,jj,jk) ! depth |
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| 181 | zsr= zws(ji,jj,jk) ! square root salinity |
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| 182 | ! compute volumic mass pure water at atm pressure |
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| 183 | zr1= ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp)*zt & |
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| 184 | -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp |
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| 185 | ! seawater volumic mass atm pressure |
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| 186 | zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & |
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| 187 | -4.0899e-3_wp ) *zt+0.824493_wp |
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| 188 | zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp |
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| 189 | zr4= 4.8314e-4_wp |
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| 190 | ! |
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| 191 | ! potential volumic mass (reference to the surface) |
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| 192 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
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| 193 | ! |
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| 194 | ! add the compression terms |
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| 195 | ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp |
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| 196 | zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp |
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| 197 | zb = zbw + ze * zs |
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| 198 | |
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| 199 | zd = -2.042967e-2_wp |
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| 200 | zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp |
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| 201 | zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp |
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| 202 | za = ( zd*zsr + zc ) *zs + zaw |
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| 203 | |
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| 204 | zb1= (-0.1909078_wp*zt+7.390729_wp ) *zt-55.87545_wp |
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| 205 | za1= ( ( 2.326469e-3_wp*zt+1.553190_wp)*zt-65.00517_wp ) *zt+1044.077_wp |
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| 206 | zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp |
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| 207 | zk0= ( zb1*zsr + za1 )*zs + zkw |
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| 208 | |
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| 209 | ! Tangent linear part |
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| 210 | |
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| 211 | zttl = pts_tl(ji,jj,jk, jp_tem) |
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| 212 | zstl = pts_tl(ji,jj,jk, jp_sal) |
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| 213 | |
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| 214 | zsrtl= ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
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| 215 | & * tmask(ji,jj,jk) * zstl |
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| 216 | |
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| 217 | zr1tl= ( ( ( ( 5.*6.536332e-9_wp * zt & |
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| 218 | & -4.*1.120083e-6_wp ) * zt & |
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| 219 | & +3.*1.001685e-4_wp ) * zt & |
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| 220 | & -2.*9.095290e-3_wp ) * zt & |
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| 221 | & + 6.793952e-2_wp ) * zttl |
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| 222 | |
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| 223 | zr2tl= ( ( ( 4.*5.3875e-9_wp * zt & |
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| 224 | & -3.*8.2467e-7_wp ) * zt & |
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| 225 | & +2.*7.6438e-5_wp ) * zt & |
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| 226 | & - 4.0899e-3_wp ) * zttl |
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| 227 | |
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| 228 | zr3tl= ( -2.*1.6546e-6_wp * zt & |
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| 229 | & + 1.0227e-4_wp ) * zttl |
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| 230 | |
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| 231 | zrhoptl= zr1tl & |
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| 232 | & + zs * zr2tl & |
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| 233 | & + zsr * zs * zr3tl & |
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| 234 | & + zr3 * zs * zsrtl & |
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| 235 | & + ( 2. * zr4 * zs + zr2 & |
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| 236 | & + zr3 * zsr ) * zstl |
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| 237 | |
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| 238 | zetl = ( -2.*3.508914e-8_wp * zt & |
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| 239 | & - 1.248266e-8_wp ) * zttl |
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| 240 | |
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| 241 | zbwtl= ( 2.*1.296821e-6_wp * zt & |
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| 242 | & - 5.782165e-9_wp ) * zttl |
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| 243 | |
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| 244 | zbtl = zbwtl & |
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| 245 | & + zs * zetl & |
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| 246 | & + ze * zstl |
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| 247 | |
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| 248 | zctl = ( -2.*7.267926e-5_wp * zt & |
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| 249 | & + 2.598241e-3_wp ) * zttl |
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| 250 | |
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| 251 | zawtl= ( ( 3.*5.939910e-6_wp * zt & |
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| 252 | & +2.*2.512549e-3_wp ) * zt & |
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| 253 | & - 0.1028859_wp ) * zttl |
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| 254 | |
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| 255 | zatl = zawtl & |
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| 256 | & + zd * zs * zsrtl & |
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| 257 | & + zs * zctl & |
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| 258 | & + ( zd * zsr + zc ) * zstl |
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| 259 | |
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| 260 | zb1tl= ( -2.*0.1909078_wp * zt & |
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| 261 | & + 7.390729_wp ) * zttl |
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| 262 | |
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| 263 | za1tl= ( ( 3.*2.326469e-3_wp * zt & |
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| 264 | & +2.*1.553190_wp ) * zt & |
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| 265 | & - 65.00517_wp ) * zttl |
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| 266 | |
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| 267 | zkwtl= ( ( ( -4.*1.361629e-4_wp * zt & |
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| 268 | & -3.*1.852732e-2_wp ) * zt & |
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| 269 | & -2.*30.41638_wp ) * zt & |
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| 270 | & + 2098.925_wp ) * zttl |
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| 271 | |
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| 272 | zk0tl= zkwtl & |
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| 273 | & + zb1 * zs * zsrtl & |
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| 274 | & + zs * zsr * zb1tl & |
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| 275 | & + zs * za1tl & |
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| 276 | & + ( zb1 * zsr + za1 ) * zstl |
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| 277 | |
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| 278 | ! Masked in situ density anomaly |
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| 279 | |
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| 280 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
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| 281 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
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| 282 | |
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| 283 | prd_tl(ji,jj,jk) = tmask(ji,jj,jk) * zrdc2 * & |
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| 284 | & ( zrhoptl & |
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| 285 | & - zrdc2 * zh * zrdc1**2 * zrhop & |
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| 286 | & * ( zk0tl & |
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| 287 | & - zh * ( zatl & |
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| 288 | & - zh * zbtl ) ) )& |
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| 289 | & * zrau0r |
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| 290 | END DO |
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| 291 | END DO |
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| 292 | END DO |
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| 293 | ! |
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| 294 | CASE ( 1 ) !== Linear formulation function of temperature only ==! |
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| 295 | DO jk = 1, jpkm1 |
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| 296 | prd_tl(:,:,jk) = ( - rn_alpha * pts_tl(:,:,jk,jp_tem) ) * tmask(:,:,jk) |
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| 297 | END DO |
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| 298 | ! |
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| 299 | CASE ( 2 ) !== Linear formulation function of temperature and salinity ==! |
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| 300 | |
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| 301 | ! ! =============== |
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| 302 | DO jk = 1, jpkm1 |
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| 303 | prd_tl(:,:,jk) = ( rn_beta * pts_tl(:,:,jk,jp_sal) - rn_alpha * pts_tl(:,:,jk,jp_tem ) ) * tmask(:,:,jk) |
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| 304 | END DO |
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| 305 | ! |
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| 306 | END SELECT |
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| 307 | ! |
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| 308 | CALL wrk_dealloc( jpi, jpj, jpk, zws ) |
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| 309 | ! |
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| 310 | IF( nn_timing == 1 ) CALL timing_stop('eos_tan') |
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| 311 | ! |
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| 312 | END SUBROUTINE eos_insitu_tan |
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| 313 | |
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| 314 | SUBROUTINE eos_insitu_pot_tan( pts, pts_tl, prd_tl, prhop_tl) |
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| 315 | !!---------------------------------------------------------------------- |
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| 316 | !! *** ROUTINE eos_insitu_pot_tan *** |
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| 317 | !! |
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| 318 | !! ** Purpose or the direct routine: |
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| 319 | !! Compute the in situ density (ratio rho/rau0) and the |
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| 320 | !! potential volumic mass (Kg/m3) from potential temperature and |
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| 321 | !! salinity fields using an equation of state defined through the |
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| 322 | !! namelist parameter nn_eos. |
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| 323 | !! |
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| 324 | !! ** Method : |
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| 325 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
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| 326 | !! the in situ density is computed directly as a function of |
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| 327 | !! potential temperature relative to the surface (the opa t |
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| 328 | !! variable), salt and pressure (assuming no pressure variation |
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| 329 | !! along geopotential surfaces, i.e. the pressure p in decibars |
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| 330 | !! is approximated by the depth in meters. |
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| 331 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
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| 332 | !! rhop(t,s) = rho(t,s,0) |
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| 333 | !! with pressure p decibars |
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| 334 | !! potential temperature t deg celsius |
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| 335 | !! salinity s psu |
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| 336 | !! reference volumic mass rau0 kg/m**3 |
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| 337 | !! in situ volumic mass rho kg/m**3 |
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| 338 | !! in situ density anomalie prd no units |
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| 339 | !! |
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| 340 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
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| 341 | !! t = 40 deg celcius, s=40 psu |
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| 342 | !! |
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| 343 | !! nn_eos = 1 : linear equation of state function of temperature only |
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| 344 | !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - rn_alpha * t |
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| 345 | !! rhop(t,s) = rho(t,s) |
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| 346 | !! |
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| 347 | !! nn_eos = 2 : linear equation of state function of temperature and |
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| 348 | !! salinity |
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| 349 | !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 |
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| 350 | !! = rn_beta * s - rn_alpha * tn - 1. |
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| 351 | !! rhop(t,s) = rho(t,s) |
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| 352 | !! Note that no boundary condition problem occurs in this routine |
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| 353 | !! as (tn,sn) or (ta,sa) are defined over the whole domain. |
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| 354 | !! |
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| 355 | !! ** Action : - prd , the in situ density (no units) |
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| 356 | !! - prhop, the potential volumic mass (Kg/m3) |
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| 357 | !! |
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| 358 | !! References : |
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| 359 | !! Jackett, D.R., and T.J. McDougall. J. Atmos. Ocean. Tech., 1994 |
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| 360 | !! Brown, J. A. and K. A. Campana. Mon. Weather Rev., 1978 |
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| 361 | !! |
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| 362 | !!---------------------------------------------------------------------- |
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| 363 | !! * Arguments |
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| 364 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts, & ! 1 : potential temperature [Celcius] |
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| 365 | ! ! 2 : salinity [psu] |
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| 366 | & pts_tl ! 1 : TL of potential temperature [Celcius] |
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| 367 | ! ! 2 : TL of salinity [psu] |
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| 368 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: prd_tl ! TL of in_situ density [-] |
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| 369 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT( out) :: prhop_tl ! TL of potential density (surface referenced) |
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| 370 | !! * Local declarations |
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| 371 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 372 | REAL(wp) :: & ! temporary scalars |
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| 373 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
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| 374 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
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| 375 | zttl, zstl, zhtl, zsrtl, zr1tl, zr2tl, zr3tl, & |
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| 376 | zr4tl, zrhoptl, zetl, zbwtl, & |
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| 377 | zbtl, zdtl, zctl, zawtl, zatl, zb1tl, za1tl, & |
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| 378 | zkwtl, zk0tl, zpes, zrdc1, zrdc2, zeps, & |
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| 379 | zmask, zrau0r |
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| 380 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zws |
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| 381 | !!---------------------------------------------------------------------- |
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| 382 | ! |
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| 383 | IF( nn_timing == 1 ) CALL timing_start('eos-p_tan') |
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| 384 | ! |
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| 385 | CALL wrk_alloc( jpi, jpj, jpk, zws ) |
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| 386 | ! |
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| 387 | SELECT CASE ( nn_eos ) |
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| 388 | ! |
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| 389 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
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| 390 | zrau0r = 1.e0 / rau0 |
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| 391 | #ifdef key_sp |
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| 392 | zeps = 1.e-7 |
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| 393 | #else |
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| 394 | zeps = 1.e-14 |
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| 395 | #endif |
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| 396 | !CDIR NOVERRCHK |
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| 397 | zws(:,:,:) = SQRT( ABS( pts(:,:,:, jp_sal) ) ) |
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| 398 | ! |
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| 399 | DO jk = 1, jpkm1 |
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| 400 | DO jj = 1, jpj |
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| 401 | DO ji = 1, jpi |
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| 402 | zt = pts(ji,jj,jk, jp_tem) |
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| 403 | zs = pts(ji,jj,jk, jp_sal) |
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| 404 | zh = fsdept(ji,jj,jk) ! depth |
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| 405 | zsr = zws(ji,jj,jk) ! square root salinity |
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| 406 | ! compute volumic mass pure water at atm pressure |
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| 407 | zr1 = ( ( ( ( 6.536332e-9_wp * zt - 1.120083e-6_wp ) * zt & |
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| 408 | & + 1.001685e-4_wp ) * zt - 9.095290e-3_wp ) * zt & |
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| 409 | & + 6.793952e-2_wp ) * zt + 999.842594_wp |
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| 410 | ! seawater volumic mass atm pressure |
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| 411 | zr2 = ( ( ( 5.3875e-9_wp * zt - 8.2467e-7_wp ) * zt & |
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| 412 | & + 7.6438e-5_wp ) * zt - 4.0899e-3_wp ) * zt & |
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| 413 | & + 0.824493_wp |
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| 414 | zr3 = ( -1.6546e-6_wp * zt + 1.0227e-4_wp ) * zt - 5.72466e-3_wp |
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| 415 | zr4 = 4.8314e-4_wp |
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| 416 | |
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| 417 | ! potential volumic mass (reference to the surface) |
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| 418 | zrhop= ( zr4 * zs + zr3 * zsr + zr2 ) * zs + zr1 |
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| 419 | |
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| 420 | ! add the compression terms |
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| 421 | ze = ( -3.508914e-8_wp * zt - 1.248266e-8_wp ) * zt - 2.595994e-6_wp |
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| 422 | zbw = ( 1.296821e-6_wp * zt - 5.782165e-9_wp ) * zt + 1.045941e-4_wp |
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| 423 | zb = zbw + ze * zs |
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| 424 | |
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| 425 | zd = -2.042967e-2_wp |
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| 426 | zc = (-7.267926e-5_wp * zt + 2.598241e-3_wp ) * zt + 0.1571896_wp |
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| 427 | zaw= ( ( 5.939910e-6_wp * zt + 2.512549e-3_wp ) * zt - 0.1028859_wp ) * zt - 4.721788_wp |
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| 428 | za = ( zd * zsr + zc ) * zs + zaw |
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| 429 | |
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| 430 | zb1 = (-0.1909078_wp * zt + 7.390729_wp ) * zt - 55.87545_wp |
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| 431 | za1 = ( ( 2.326469e-3_wp * zt + 1.553190_wp ) * zt - 65.00517_wp & |
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| 432 | & ) * zt + 1044.077_wp |
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| 433 | zkw = ( ( (-1.361629e-4_wp * zt - 1.852732e-2_wp ) * zt - 30.41638_wp & |
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| 434 | & ) * zt + 2098.925_wp ) * zt + 190925.6_wp |
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| 435 | zk0 = ( zb1 * zsr + za1 ) * zs + zkw |
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| 436 | |
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| 437 | |
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| 438 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
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| 439 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
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| 440 | |
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| 441 | ! Tangent linear part |
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| 442 | |
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| 443 | zttl = pts_tl(ji,jj,jk, jp_tem) |
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| 444 | zstl = pts_tl(ji,jj,jk, jp_sal) |
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| 445 | |
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| 446 | zsrtl= ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
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| 447 | & * tmask(ji,jj,jk) * zstl |
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| 448 | |
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| 449 | zr1tl= ( ( ( ( 5.*6.536332e-9_wp * zt & |
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| 450 | & -4.*1.120083e-6_wp ) * zt & |
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| 451 | & +3.*1.001685e-4_wp ) * zt & |
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| 452 | & -2.*9.095290e-3_wp ) * zt & |
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| 453 | & + 6.793952e-2_wp ) * zttl |
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| 454 | |
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| 455 | zr2tl= ( ( ( 4.*5.3875e-9_wp * zt & |
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| 456 | & -3.*8.2467e-7_wp ) * zt & |
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| 457 | & +2.*7.6438e-5_wp ) * zt & |
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| 458 | & - 4.0899e-3_wp ) * zttl |
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| 459 | |
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| 460 | zr3tl= ( -2.*1.6546e-6_wp * zt & |
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| 461 | & + 1.0227e-4_wp ) * zttl |
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| 462 | |
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| 463 | zrhoptl= zr1tl & |
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| 464 | & + zs * zr2tl & |
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| 465 | & + zsr * zs * zr3tl & |
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| 466 | & + zr3 * zs * zsrtl & |
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| 467 | & + ( 2. * zr4 * zs + zr2 & |
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| 468 | & + zr3 * zsr ) * zstl |
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| 469 | |
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| 470 | prhop_tl(ji,jj,jk) = zrhoptl * tmask(ji,jj,jk) |
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| 471 | |
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| 472 | zetl = ( -2.*3.508914e-8_wp * zt & |
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| 473 | & - 1.248266e-8_wp ) * zttl |
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| 474 | |
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| 475 | zbwtl= ( 2.*1.296821e-6_wp * zt & |
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| 476 | & - 5.782165e-9_wp ) * zttl |
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| 477 | |
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| 478 | zbtl = zbwtl & |
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| 479 | & + zs * zetl & |
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| 480 | & + ze * zstl |
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| 481 | |
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| 482 | zctl = ( -2.*7.267926e-5_wp * zt & |
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| 483 | & + 2.598241e-3_wp ) * zttl |
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| 484 | |
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| 485 | zawtl= ( ( 3.*5.939910e-6_wp * zt & |
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| 486 | & +2.*2.512549e-3_wp ) * zt & |
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| 487 | & - 0.1028859_wp ) * zttl |
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| 488 | |
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| 489 | zatl = zawtl & |
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| 490 | & + zd * zs * zsrtl & |
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| 491 | & + zs * zctl & |
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| 492 | & + ( zd * zsr + zc ) * zstl |
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| 493 | |
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| 494 | zb1tl= ( -2.*0.1909078_wp * zt & |
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| 495 | & + 7.390729_wp ) * zttl |
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| 496 | |
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| 497 | za1tl= ( ( 3.*2.326469e-3_wp * zt & |
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| 498 | & +2.*1.553190_wp ) * zt & |
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| 499 | & - 65.00517_wp ) * zttl |
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| 500 | |
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| 501 | zkwtl= ( ( ( -4.*1.361629e-4_wp * zt & |
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| 502 | & -3.*1.852732e-2_wp ) * zt & |
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| 503 | & -2.*30.41638_wp ) * zt & |
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| 504 | & + 2098.925_wp ) * zttl |
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| 505 | |
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| 506 | zk0tl= zkwtl & |
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| 507 | & + zb1 * zs * zsrtl & |
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| 508 | & + zs * zsr * zb1tl & |
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| 509 | & + zs * za1tl & |
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| 510 | & + ( zb1 * zsr + za1 ) * zstl |
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| 511 | |
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| 512 | ! Masked in situ density anomaly |
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| 513 | |
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| 514 | prd_tl(ji,jj,jk) = tmask(ji,jj,jk) * zrdc2 * & |
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| 515 | & ( zrhoptl & |
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| 516 | & - zrdc2 * zh * zrdc1**2 * zrhop & |
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| 517 | & * ( zk0tl & |
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| 518 | & - zh * ( zatl & |
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| 519 | & - zh * zbtl ) ) )& |
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| 520 | & * zrau0r |
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| 521 | END DO |
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| 522 | END DO |
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| 523 | END DO |
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| 524 | ! |
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| 525 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
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| 526 | DO jk = 1, jpkm1 |
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| 527 | prd_tl (:,:,jk) = ( - rn_alpha * pts_tl(:,:,jk, jp_tem) ) * tmask(:,:,jk) |
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| 528 | prhop_tl(:,:,jk) = ( rau0 * prd_tl(:,:,jk) ) * tmask(:,:,jk) |
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| 529 | END DO |
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| 530 | ! |
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| 531 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
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| 532 | DO jk = 1, jpkm1 |
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| 533 | prd_tl(:,:,jk) = ( rn_beta * pts_tl(:,:,jk, jp_sal) - rn_alpha * pts_tl(:,:,jk, jp_tem) ) * tmask(:,:,jk) |
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| 534 | prhop_tl(:,:,jk) = ( rau0 * prd_tl(:,:,jk) ) * tmask(:,:,jk) |
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| 535 | END DO |
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| 536 | ! |
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| 537 | END SELECT |
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| 538 | ! |
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| 539 | CALL wrk_dealloc( jpi, jpj, jpk, zws ) |
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| 540 | ! |
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| 541 | IF( nn_timing == 1 ) CALL timing_stop('eos-p_tan') |
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| 542 | ! |
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| 543 | END SUBROUTINE eos_insitu_pot_tan |
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| 544 | SUBROUTINE eos_insitu_2d_tan( pts, pdep, pts_tl, prd_tl ) |
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| 545 | !!----------------------------------------------------------------------- |
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| 546 | !! |
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| 547 | !! *** ROUTINE eos_insitu_2d_tan : TL OF ROUTINE eos_insitu_2d *** |
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| 548 | !! |
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| 549 | !! ** Purpose of direct routine : Compute the in situ density |
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| 550 | !! (ratio rho/rau0) from potential temperature and salinity |
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| 551 | !! using an equation of state defined through the namelist |
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| 552 | !! parameter nn_eos. * 2D field case |
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| 553 | !! |
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| 554 | !! ** Method of direct routine : 3 cases: |
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| 555 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
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| 556 | !! the in situ density is computed directly as a function of |
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| 557 | !! potential temperature relative to the surface (the opa t |
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| 558 | !! variable), salt and pressure (assuming no pressure variation |
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| 559 | !! along geopotential surfaces, i.e. the pressure p in decibars |
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| 560 | !! is approximated by the depth in meters. |
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| 561 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
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| 562 | !! with pressure p decibars |
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| 563 | !! potential temperature t deg celsius |
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| 564 | !! salinity s psu |
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| 565 | !! reference volumic mass rau0 kg/m**3 |
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| 566 | !! in situ volumic mass rho kg/m**3 |
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| 567 | !! in situ density anomalie prd no units |
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| 568 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
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| 569 | !! t = 40 deg celcius, s=40 psu |
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| 570 | !! nn_eos = 1 : linear equation of state function of temperature only |
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| 571 | !! prd(t) = 0.0285 - ralpha * t |
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| 572 | !! nn_eos = 2 : linear equation of state function of temperature and |
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| 573 | !! salinity |
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| 574 | !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. |
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| 575 | !! Note that no boundary condition problem occurs in this routine |
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| 576 | !! as (ptem,psal) are defined over the whole domain. |
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| 577 | !! |
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| 578 | !! ** Comments on Adjoint Routine : |
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| 579 | !! Care has been taken to avoid division by zero when computing |
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| 580 | !! the inverse of the square root of salinity at masked salinity |
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| 581 | !! points. |
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| 582 | !! |
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| 583 | !! ** Action : |
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| 584 | !! |
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| 585 | !! References : |
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| 586 | !! |
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| 587 | !! History : |
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| 588 | !! 8.2 ! 05-03 ((F. Van den Berghe, A. Weaver, N. Daget) - eostan.F |
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| 589 | !! 9.0 ! 07-07 (K. Mogensen) Initial version based on eostan.F |
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| 590 | !! ! 08-07 (A. Vidard) bug fix in computation of prd_tl if neos=1 |
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| 591 | !!----------------------------------------------------------------------- |
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| 592 | !! * Modules used |
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| 593 | !! * Arguments |
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| 594 | REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(in ) :: pts, & ! 1 : potential temperature [Celcius] |
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| 595 | ! ! 2 : salinity [psu] |
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| 596 | & pts_tl ! 1 : TL of potential temperature [Celcius] |
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| 597 | ! ! 2 : TL of salinity [psu] |
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| 598 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out) :: prd_tl ! TL of in_situ density [-] |
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| 599 | REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: pdep ! depth [m] |
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| 600 | ! |
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| 601 | !! * Local declarations |
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| 602 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 603 | REAL(wp) :: & ! temporary scalars |
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| 604 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
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| 605 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
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| 606 | zttl, zstl, zhtl, zsrtl, zr1tl, zr2tl, zr3tl, & |
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| 607 | zr4tl, zrhoptl, zetl, zbwtl, & |
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| 608 | zbtl, zdtl, zctl, zawtl, zatl, zb1tl, za1tl, & |
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| 609 | zkwtl, zk0tl, zpes, zrdc1, zrdc2, zeps, & |
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| 610 | zmask |
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| 611 | REAL(wp), POINTER, DIMENSION(:,:) :: zws |
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| 612 | !!---------------------------------------------------------------------- |
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| 613 | ! |
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| 614 | IF( nn_timing == 1 ) CALL timing_start('eos2d') |
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| 615 | ! |
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| 616 | CALL wrk_alloc( jpi, jpj, zws ) |
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| 617 | ! |
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| 618 | SELECT CASE ( nn_eos ) |
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| 619 | ! |
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| 620 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
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| 621 | ! |
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| 622 | #ifdef key_sp |
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| 623 | zeps = 1.e-7 |
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| 624 | #else |
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| 625 | zeps = 1.e-14 |
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| 626 | #endif |
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| 627 | !CDIR NOVERRCHK |
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| 628 | DO jj = 1, jpjm1 |
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| 629 | !CDIR NOVERRCHK |
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| 630 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 631 | zws(ji,jj) = SQRT( ABS( pts(ji,jj, jp_sal) ) ) |
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| 632 | END DO |
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| 633 | END DO |
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| 634 | DO jj = 1, jpjm1 |
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| 635 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 636 | |
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| 637 | zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask |
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| 638 | |
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| 639 | zt = pts (ji,jj, jp_tem) ! interpolated T |
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| 640 | zs = pts (ji,jj, jp_sal) ! interpolated S |
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| 641 | zsr= zws(ji,jj) ! square root of interpolated S |
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| 642 | zh = pdep(ji,jj) ! depth at the partial step level |
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| 643 | ! compute volumic mass pure water at atm pressure |
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| 644 | zr1= ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp)*zt & |
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| 645 | & -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp |
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| 646 | ! seawater volumic mass atm pressure |
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| 647 | zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & |
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| 648 | & -4.0899e-3_wp ) *zt+0.824493_wp |
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| 649 | zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp |
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| 650 | zr4= 4.8314e-4_wp |
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| 651 | |
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| 652 | ! potential volumic mass (reference to the surface) |
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| 653 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
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| 654 | |
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| 655 | ! add the compression terms |
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| 656 | ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp |
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| 657 | zbw= ( 1.296821e-6*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp |
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| 658 | zb = zbw + ze * zs |
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| 659 | |
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| 660 | zd = -2.042967e-2_wp |
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| 661 | zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp |
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| 662 | zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp |
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| 663 | za = ( zd*zsr + zc ) *zs + zaw |
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| 664 | |
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| 665 | zb1= (-0.1909078_wp*zt+7.390729_wp ) *zt-55.87545_wp |
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| 666 | za1= ( ( 2.326469e-3_wp*zt+1.553190_wp)*zt-65.00517_wp ) *zt+1044.077_wp |
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| 667 | zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp |
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| 668 | zk0= ( zb1*zsr + za1 )*zs + zkw |
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| 669 | |
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| 670 | ! Tangent linear part |
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| 671 | |
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| 672 | zttl = pts_tl(ji,jj, jp_tem) |
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| 673 | zstl = pts_tl(ji,jj, jp_sal) |
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| 674 | |
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| 675 | zsrtl= ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
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| 676 | & * tmask(ji,jj,1) * zstl |
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| 677 | |
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| 678 | zr1tl= ( ( ( ( 5.*6.536332e-9_wp * zt & |
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| 679 | & -4.*1.120083e-6_wp ) * zt & |
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| 680 | & +3.*1.001685e-4_wp ) * zt & |
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| 681 | & -2.*9.095290e-3_wp ) * zt & |
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| 682 | & + 6.793952e-2_wp ) * zttl |
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| 683 | |
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| 684 | zr2tl= ( ( ( 4.*5.3875e-9_wp * zt & |
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| 685 | & -3.*8.2467e-7_wp ) * zt & |
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| 686 | & +2.*7.6438e-5_wp ) * zt & |
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| 687 | & - 4.0899e-3_wp ) * zttl |
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| 688 | |
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| 689 | zr3tl= ( -2.*1.6546e-6_wp * zt & |
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| 690 | & + 1.0227e-4_wp ) * zttl |
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| 691 | |
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| 692 | zrhoptl= zr1tl & |
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| 693 | & + zs * zr2tl & |
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| 694 | & + zsr * zs * zr3tl & |
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| 695 | & + zr3 * zs * zsrtl & |
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| 696 | & + ( 2. * zr4 * zs + zr2 & |
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| 697 | & + zr3 * zsr ) * zstl |
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| 698 | |
---|
| 699 | zetl = ( -2.*3.508914e-8_wp * zt & |
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| 700 | & - 1.248266e-8_wp ) * zttl |
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| 701 | |
---|
| 702 | zbwtl= ( 2.*1.296821e-6_wp * zt & |
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| 703 | & - 5.782165e-9_wp ) * zttl |
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| 704 | |
---|
| 705 | zbtl = zbwtl & |
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| 706 | & + zs * zetl & |
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| 707 | & + ze * zstl |
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| 708 | |
---|
| 709 | zctl = ( -2.*7.267926e-5_wp * zt & |
---|
| 710 | & + 2.598241e-3_wp ) * zttl |
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| 711 | |
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| 712 | zawtl= ( ( 3.*5.939910e-6_wp * zt & |
---|
| 713 | & +2.*2.512549e-3_wp ) * zt & |
---|
| 714 | & - 0.1028859_wp ) * zttl |
---|
| 715 | |
---|
| 716 | zatl = zawtl & |
---|
| 717 | & + zd * zs * zsrtl & |
---|
| 718 | & + zs * zctl & |
---|
| 719 | & + ( zd * zsr + zc ) * zstl |
---|
| 720 | |
---|
| 721 | zb1tl= ( -2.*0.1909078_wp * zt & |
---|
| 722 | & + 7.390729_wp ) * zttl |
---|
| 723 | |
---|
| 724 | za1tl= ( ( 3.*2.326469e-3_wp * zt & |
---|
| 725 | & +2.*1.553190_wp ) * zt & |
---|
| 726 | & - 65.00517_wp ) * zttl |
---|
| 727 | |
---|
| 728 | zkwtl= ( ( ( -4.*1.361629e-4_wp * zt & |
---|
| 729 | & -3.*1.852732e-2_wp ) * zt & |
---|
| 730 | & -2.*30.41638_wp ) * zt & |
---|
| 731 | & + 2098.925_wp ) * zttl |
---|
| 732 | |
---|
| 733 | zk0tl= zkwtl & |
---|
| 734 | & + zb1 * zs * zsrtl & |
---|
| 735 | & + zs * zsr * zb1tl & |
---|
| 736 | & + zs * za1tl & |
---|
| 737 | & + ( zb1 * zsr + za1 ) * zstl |
---|
| 738 | |
---|
| 739 | ! Masked in situ density anomaly |
---|
| 740 | |
---|
| 741 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
| 742 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
| 743 | |
---|
| 744 | prd_tl(ji,jj) = tmask(ji,jj,1) * zrdc2 * & |
---|
| 745 | & ( zrhoptl & |
---|
| 746 | & - zrdc2 * zh * zrdc1**2 * zrhop & |
---|
| 747 | & * ( zk0tl & |
---|
| 748 | & - zh * ( zatl & |
---|
| 749 | & - zh * zbtl ) ) )& |
---|
| 750 | & / rau0 |
---|
| 751 | |
---|
| 752 | |
---|
| 753 | END DO |
---|
| 754 | END DO |
---|
| 755 | ! |
---|
| 756 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
---|
| 757 | DO jj = 1, jpjm1 |
---|
| 758 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 759 | prd_tl(ji,jj) = ( - rn_alpha * pts_tl(ji,jj,jp_tem) ) * tmask(ji,jj,1) |
---|
| 760 | END DO |
---|
| 761 | END DO |
---|
| 762 | ! |
---|
| 763 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
---|
| 764 | DO jj = 1, jpjm1 |
---|
| 765 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 766 | prd_tl (ji,jj) = ( rn_beta * pts_tl(ji,jj, jp_sal) - rn_alpha * pts_tl(ji,jj, jp_tem) ) * tmask(ji,jj,1) |
---|
| 767 | END DO |
---|
| 768 | END DO |
---|
| 769 | ! |
---|
| 770 | END SELECT |
---|
[3640] | 771 | CALL wrk_dealloc( jpi, jpj, zws ) |
---|
[3611] | 772 | ! |
---|
| 773 | END SUBROUTINE eos_insitu_2d_tan |
---|
| 774 | |
---|
| 775 | SUBROUTINE eos_insitu_adj(pts, pts_ad, prd_ad) |
---|
| 776 | !!----------------------------------------------------------------------- |
---|
| 777 | !! |
---|
| 778 | !! *** ROUTINE eos_insitu_tan : Adjoint OF ROUTINE eos_insitu *** |
---|
| 779 | !! |
---|
| 780 | !! ** Purpose of direct routine : Compute the in situ density |
---|
| 781 | !! (ratio rho/rau0) from potential temperature and salinity |
---|
| 782 | !! using an equation of state defined through the namelist |
---|
| 783 | !! parameter nneos. |
---|
| 784 | !! |
---|
| 785 | !! ** Method of direct routine : 3 cases: |
---|
| 786 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
---|
| 787 | !! the in situ density is computed directly as a function of |
---|
| 788 | !! potential temperature relative to the surface (the opa t |
---|
| 789 | !! variable), salt and pressure (assuming no pressure variation |
---|
| 790 | !! along geopotential surfaces, i.e. the pressure p in decibars |
---|
| 791 | !! is approximated by the depth in meters. |
---|
| 792 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
---|
| 793 | !! with pressure p decibars |
---|
| 794 | !! potential temperature t deg celsius |
---|
| 795 | !! salinity s psu |
---|
| 796 | !! reference volumic mass rau0 kg/m**3 |
---|
| 797 | !! in situ volumic mass rho kg/m**3 |
---|
| 798 | !! in situ density anomalie prd no units |
---|
| 799 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
---|
| 800 | !! t = 40 deg celcius, s=40 psu |
---|
| 801 | !! nn_eos = 1 : linear equation of state function of temperature only |
---|
| 802 | !! prd(t) = 0.0285 - rn_alpha * t |
---|
| 803 | !! nn_eos = 2 : linear equation of state function of temperature and |
---|
| 804 | !! salinity |
---|
| 805 | !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. |
---|
| 806 | !! Note that no boundary condition problem occurs in this routine |
---|
| 807 | !! as (ptem,psal) are defined over the whole domain. |
---|
| 808 | !! |
---|
| 809 | !! ** Comments on Adjoint Routine : |
---|
| 810 | !! Care has been taken to avoid division by zero when computing |
---|
| 811 | !! the inverse of the square root of salinity at masked salinity |
---|
| 812 | !! points. |
---|
| 813 | !! |
---|
| 814 | !! ** Action : |
---|
| 815 | !! |
---|
| 816 | !! References : |
---|
| 817 | !! |
---|
| 818 | !! History : |
---|
| 819 | !! 8.2 ! 05-03 ((F. Van den Berghe, A. Weaver, N. Daget) - eostan.F |
---|
| 820 | !! 9.0 ! 08-08 (A. Vidard) 9.0 version |
---|
| 821 | !!----------------------------------------------------------------------- |
---|
| 822 | !! * Modules used |
---|
| 823 | !! * Arguments |
---|
| 824 | REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] |
---|
| 825 | ! ! 2 : salinity [psu] |
---|
| 826 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pts_ad ! 1 : TL of potential temperature [Celsius] |
---|
| 827 | ! 2 : TL of salinity [psu] |
---|
| 828 | REAL(wp), DIMENSION(:,:,:), INTENT( inout ) :: & |
---|
| 829 | & prd_ad ! TL of potential density (surface referenced) |
---|
| 830 | |
---|
| 831 | !! * Local declarations |
---|
| 832 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 833 | REAL(wp) :: & ! temporary scalars |
---|
| 834 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
| 835 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
| 836 | ztad, zsad, zhad, zsrad, zr1ad, zr2ad, zr3ad, & |
---|
| 837 | zr4ad, zrhopad, zead, zbwad, & |
---|
| 838 | zbad, zdad, zcad, zawad, zaad, zb1ad, za1ad, & |
---|
| 839 | zkwad, zk0ad, zpes, zrdc1, zrdc2, zeps, & |
---|
| 840 | zmask, zrau0r |
---|
| 841 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zws |
---|
| 842 | !!---------------------------------------------------------------------- |
---|
| 843 | IF( nn_timing == 1 ) CALL timing_start('eos_adj') |
---|
| 844 | ! |
---|
| 845 | CALL wrk_alloc( jpi, jpj, jpk, zws ) |
---|
| 846 | ! |
---|
| 847 | ! initialization of adjoint variables |
---|
| 848 | ztad = 0.0_wp |
---|
| 849 | zsad = 0.0_wp |
---|
| 850 | zhad = 0.0_wp |
---|
| 851 | zsrad = 0.0_wp |
---|
| 852 | zr1ad = 0.0_wp |
---|
| 853 | zr2ad = 0.0_wp |
---|
| 854 | zr3ad = 0.0_wp |
---|
| 855 | zr4ad = 0.0_wp |
---|
| 856 | zrhopad = 0.0_wp |
---|
| 857 | zead = 0.0_wp |
---|
| 858 | zbwad = 0.0_wp |
---|
| 859 | zbad = 0.0_wp |
---|
| 860 | zdad = 0.0_wp |
---|
| 861 | zcad = 0.0_wp |
---|
| 862 | zawad = 0.0_wp |
---|
| 863 | zaad = 0.0_wp |
---|
| 864 | zb1ad = 0.0_wp |
---|
| 865 | za1ad = 0.0_wp |
---|
| 866 | zkwad = 0.0_wp |
---|
| 867 | zk0ad = 0.0_wp |
---|
| 868 | SELECT CASE ( nn_eos ) |
---|
| 869 | |
---|
| 870 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
---|
| 871 | zrau0r = 1.e0 / rau0 |
---|
| 872 | #ifdef key_sp |
---|
| 873 | zeps = 1.e-7 |
---|
| 874 | #else |
---|
| 875 | zeps = 1.e-14 |
---|
| 876 | #endif |
---|
| 877 | !CDIR NOVERRCHK |
---|
| 878 | zws(:,:,:) = SQRT( ABS( pts(:,:,:, jp_sal) ) ) |
---|
| 879 | DO jk = jpkm1, 1, -1 |
---|
| 880 | DO jj = jpj, 1, -1 |
---|
| 881 | DO ji = jpi, 1, -1 |
---|
| 882 | zt = pts(ji,jj,jk, jp_tem) |
---|
| 883 | zs = pts(ji,jj,jk, jp_sal) |
---|
| 884 | zh = fsdept(ji,jj,jk) ! depth |
---|
| 885 | zsr= zws(ji,jj,jk) ! square root salinity |
---|
| 886 | ! compute volumic mass pure water at atm pressure |
---|
| 887 | zr1= ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp)*zt & |
---|
| 888 | -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp |
---|
| 889 | ! seawater volumic mass atm pressure |
---|
| 890 | zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & |
---|
| 891 | -4.0899e-3_wp ) *zt+0.824493_wp |
---|
| 892 | zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp |
---|
| 893 | zr4= 4.8314e-4_wp |
---|
| 894 | |
---|
| 895 | ! potential volumic mass (reference to the surface) |
---|
| 896 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
---|
| 897 | |
---|
| 898 | ! add the compression terms |
---|
| 899 | ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp |
---|
| 900 | zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp |
---|
| 901 | zb = zbw + ze * zs |
---|
| 902 | |
---|
| 903 | zd = -2.042967e-2_wp |
---|
| 904 | zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp |
---|
| 905 | zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp |
---|
| 906 | za = ( zd*zsr + zc ) *zs + zaw |
---|
| 907 | |
---|
| 908 | zb1= (-0.1909078_wp*zt+7.390729_wp ) *zt-55.87545_wp |
---|
| 909 | za1= ( ( 2.326469e-3_wp*zt+1.553190_wp)*zt-65.00517_wp ) *zt+1044.077_wp |
---|
| 910 | zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp |
---|
| 911 | zk0= ( zb1*zsr + za1 )*zs + zkw |
---|
| 912 | |
---|
| 913 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
| 914 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
| 915 | ! ============ |
---|
| 916 | ! Adjoint part |
---|
| 917 | ! ============ |
---|
| 918 | |
---|
| 919 | ! Masked in situ density anomaly |
---|
| 920 | |
---|
| 921 | zrhopad = zrhopad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 922 | & * zrdc2 * zrau0r |
---|
| 923 | zk0ad = zk0ad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 924 | & * zrdc2 * zrdc2 * zh & |
---|
| 925 | & * zrdc1**2 * zrhop & |
---|
| 926 | & * zrau0r |
---|
| 927 | zaad = zaad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 928 | & * zrdc2 * zrdc2 * zh & |
---|
| 929 | & * zrdc1**2 * zrhop & |
---|
| 930 | & * zh * zrau0r |
---|
| 931 | zbad = zbad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 932 | & * zrdc2 * zrdc2 * zh & |
---|
| 933 | & * zrdc1**2 * zrhop & |
---|
| 934 | & * zh * zh * zrau0r |
---|
| 935 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
| 936 | |
---|
| 937 | zkwad = zkwad + zk0ad |
---|
| 938 | zsrad = zsrad + zk0ad * zb1 * zs |
---|
| 939 | zb1ad = zb1ad + zk0ad * zs * zsr |
---|
| 940 | za1ad = za1ad + zk0ad * zs |
---|
| 941 | zsad = zsad + zk0ad * ( zb1 * zsr + za1 ) |
---|
| 942 | zk0ad = 0.0_wp |
---|
| 943 | |
---|
| 944 | ztad = ztad + zkwad * ( ( (-4.*1.361629e-4_wp * zt & |
---|
| 945 | & -3.*1.852732e-2_wp ) * zt & |
---|
| 946 | & -2.*30.41638_wp ) * zt & |
---|
| 947 | & + 2098.925_wp ) |
---|
| 948 | zkwad = 0.0_wp |
---|
| 949 | |
---|
| 950 | ztad = ztad + za1ad * ( ( 3.*2.326469e-3_wp * zt & |
---|
| 951 | & +2.*1.553190_wp ) * zt & |
---|
| 952 | & - 65.00517_wp ) |
---|
| 953 | za1ad = 0.0_wp |
---|
| 954 | |
---|
| 955 | ztad = ztad + zb1ad * (-2.*0.1909078_wp * zt & |
---|
| 956 | & + 7.390729_wp ) |
---|
| 957 | zb1ad = 0.0_wp |
---|
| 958 | |
---|
| 959 | zawad = zawad + zaad |
---|
| 960 | zsrad = zsrad + zaad * zd * zs |
---|
| 961 | zcad = zcad + zaad * zs |
---|
| 962 | zsad = zsad + zaad * ( zd * zsr + zc ) |
---|
| 963 | zaad = 0.0_wp |
---|
| 964 | |
---|
| 965 | ztad = ztad + zawad * ( ( 3.*5.939910e-6_wp * zt & |
---|
| 966 | & +2.*2.512549e-3_wp ) * zt & |
---|
| 967 | & - 0.1028859_wp ) |
---|
| 968 | zawad = 0.0_wp |
---|
| 969 | |
---|
| 970 | ztad = ztad + zcad * (-2.*7.267926e-5_wp * zt & |
---|
| 971 | & + 2.598241e-3_wp ) |
---|
| 972 | zcad = 0.0_wp |
---|
| 973 | |
---|
| 974 | zbwad = zbwad + zbad |
---|
| 975 | zead = zead + zbad * zs |
---|
| 976 | zsad = zsad + zbad * ze |
---|
| 977 | zbad = 0.0_wp |
---|
| 978 | |
---|
| 979 | ztad = ztad + zbwad * ( 2.*1.296821e-6_wp * zt & |
---|
| 980 | & - 5.782165e-9_wp ) |
---|
| 981 | zbwad = 0.0_wp |
---|
| 982 | |
---|
| 983 | ztad = ztad + zead * (-2.*3.508914e-8_wp * zt & |
---|
| 984 | & - 1.248266e-8_wp ) |
---|
| 985 | zead = 0.0_wp |
---|
| 986 | |
---|
| 987 | zr1ad = zr1ad + zrhopad |
---|
| 988 | zr2ad = zr2ad + zrhopad * zs |
---|
| 989 | zr3ad = zr3ad + zrhopad * zsr * zs |
---|
| 990 | zsrad = zsrad + zrhopad * zr3 * zs |
---|
| 991 | zsad = zsad + zrhopad * ( 2. * zr4 * zs + zr2 & |
---|
| 992 | & + zr3 * zsr ) |
---|
| 993 | zrhopad = 0.0_wp |
---|
| 994 | |
---|
| 995 | ztad = ztad + zr3ad * (-2.*1.6546e-6_wp * zt & |
---|
| 996 | & + 1.0227e-4_wp ) |
---|
| 997 | zr3ad = 0.0_wp |
---|
| 998 | |
---|
| 999 | ztad = ztad + zr2ad * ( ( ( 4.*5.3875e-9_wp * zt & |
---|
| 1000 | & -3.*8.2467e-7_wp ) * zt & |
---|
| 1001 | & +2.*7.6438e-5_wp ) * zt & |
---|
| 1002 | & - 4.0899e-3_wp ) |
---|
| 1003 | zr2ad = 0.0_wp |
---|
| 1004 | |
---|
| 1005 | ztad = ztad + zr1ad * ( ( ( ( 5.*6.536332e-9_wp * zt & |
---|
| 1006 | & -4.*1.120083e-6_wp ) * zt & |
---|
| 1007 | & +3.*1.001685e-4_wp ) * zt & |
---|
| 1008 | & -2.*9.095290e-3_wp ) * zt & |
---|
| 1009 | & + 6.793952e-2_wp ) |
---|
| 1010 | zr1ad = 0.0_wp |
---|
| 1011 | |
---|
| 1012 | zsad = zsad + zsrad * ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
| 1013 | & * tmask(ji,jj,jk) |
---|
| 1014 | zsrad = 0.0_wp |
---|
| 1015 | |
---|
| 1016 | pts_ad(ji,jj,jk, jp_sal) = pts_ad(ji,jj,jk, jp_sal) + zsad |
---|
| 1017 | pts_ad(ji,jj,jk,jp_tem) = pts_ad(ji,jj,jk, jp_tem) + ztad |
---|
| 1018 | ztad = 0.0_wp |
---|
| 1019 | zsad = 0.0_wp |
---|
| 1020 | END DO |
---|
| 1021 | END DO |
---|
| 1022 | END DO |
---|
| 1023 | ! |
---|
| 1024 | CASE ( 1 ) !== Linear formulation function of temperature only ==! |
---|
| 1025 | DO jk = jpkm1, 1, -1 |
---|
| 1026 | pts_ad(:,:,jk,jp_tem) = pts_ad(:,:,jk,jp_tem) - rn_alpha * prd_ad(:,:,jk) * tmask(:,:,jk) |
---|
| 1027 | prd_ad(:,:,jk) = 0.0_wp |
---|
| 1028 | END DO |
---|
| 1029 | ! |
---|
| 1030 | CASE ( 2 ) !== Linear formulation function of temperature and salinity ==! |
---|
| 1031 | DO jk = jpkm1, 1, -1 |
---|
| 1032 | pts_ad(:,:,jk,jp_tem) = pts_ad(:,:,jk,jp_tem) - rn_alpha * prd_ad(:,:,jk) * tmask(:,:,jk) |
---|
| 1033 | pts_ad(:,:,jk,jp_sal) = pts_ad(:,:,jk,jp_sal) + rn_beta * prd_ad( :,:,jk) * tmask(:,:,jk) |
---|
| 1034 | prd_ad( :,:,jk) = 0.0_wp |
---|
| 1035 | END DO |
---|
| 1036 | ! |
---|
| 1037 | END SELECT |
---|
| 1038 | ! |
---|
| 1039 | CALL wrk_dealloc( jpi, jpj, jpk, zws ) |
---|
| 1040 | ! |
---|
| 1041 | IF( nn_timing == 1 ) CALL timing_stop('eos_adj') |
---|
| 1042 | ! |
---|
| 1043 | END SUBROUTINE eos_insitu_adj |
---|
| 1044 | |
---|
| 1045 | SUBROUTINE eos_insitu_pot_adj ( pts, pts_ad, prd_ad, prhop_ad ) |
---|
| 1046 | !!---------------------------------------------------------------------- |
---|
| 1047 | !! *** ROUTINE eos_insitu_pot_adj *** |
---|
| 1048 | !! |
---|
| 1049 | !! ** Purpose or the direct routine: |
---|
| 1050 | !! Compute the in situ density (ratio rho/rau0) and the |
---|
| 1051 | !! potential volumic mass (Kg/m3) from potential temperature and |
---|
| 1052 | !! salinity fields using an equation of state defined through the |
---|
| 1053 | !! namelist parameter nn_eos. |
---|
| 1054 | !! |
---|
| 1055 | !! ** Method : |
---|
| 1056 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
---|
| 1057 | !! the in situ density is computed directly as a function of |
---|
| 1058 | !! potential temperature relative to the surface (the opa t |
---|
| 1059 | !! variable), salt and pressure (assuming no pressure variation |
---|
| 1060 | !! along geopotential surfaces, i.e. the pressure p in decibars |
---|
| 1061 | !! is approximated by the depth in meters. |
---|
| 1062 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
---|
| 1063 | !! rhop(t,s) = rho(t,s,0) |
---|
| 1064 | !! with pressure p decibars |
---|
| 1065 | !! potential temperature t deg celsius |
---|
| 1066 | !! salinity s psu |
---|
| 1067 | !! reference volumic mass rau0 kg/m**3 |
---|
| 1068 | !! in situ volumic mass rho kg/m**3 |
---|
| 1069 | !! in situ density anomalie prd no units |
---|
| 1070 | !! |
---|
| 1071 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
---|
| 1072 | !! t = 40 deg celcius, s=40 psu |
---|
| 1073 | !! |
---|
| 1074 | !! neos = 1 : linear equation of state function of temperature only |
---|
| 1075 | !! prd(t) = ( rho(t) - rau0 ) / rau0 = 0.028 - ralpha * t |
---|
| 1076 | !! rhop(t,s) = rho(t,s) |
---|
| 1077 | !! |
---|
| 1078 | !! nn_eos = 2 : linear equation of state function of temperature and |
---|
| 1079 | !! salinity |
---|
| 1080 | !! prd(t,s) = ( rho(t,s) - rau0 ) / rau0 |
---|
| 1081 | !! = rn_beta * s - rn_alpha * tn - 1. |
---|
| 1082 | !! rhop(t,s) = rho(t,s) |
---|
| 1083 | !! Note that no boundary condition problem occurs in this routine |
---|
| 1084 | !! as (tn,sn) or (ta,sa) are defined over the whole domain. |
---|
| 1085 | !! |
---|
| 1086 | !! ** Action : - prd , the in situ density (no units) |
---|
| 1087 | !! - prhop, the potential volumic mass (Kg/m3) |
---|
| 1088 | !! |
---|
| 1089 | !! References : |
---|
| 1090 | !! Jackett, D.R., and T.J. McDougall. J. Atmos. Ocean. Tech., 1994 |
---|
| 1091 | !! Brown, J. A. and K. A. Campana. Mon. Weather Rev., 1978 |
---|
| 1092 | !! |
---|
| 1093 | !! History of the adjoint routine: |
---|
| 1094 | !! 9.0 ! 08-06 (A. Vidard) Initial version |
---|
| 1095 | !!---------------------------------------------------------------------- |
---|
| 1096 | !! * Arguments |
---|
| 1097 | |
---|
| 1098 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature/salinity [Celcius/psu] |
---|
| 1099 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(inout) :: pts_ad ! 1 : potential temperature/salinity [Celcius/psu] |
---|
| 1100 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(inout) :: prd_ad ! TL of in_situ density [-] |
---|
| 1101 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(inout) :: prhop_ad ! TL of potential density (surface referenced) |
---|
| 1102 | !! * Local declarations |
---|
| 1103 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1104 | REAL(wp) :: & ! temporary scalars |
---|
| 1105 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
| 1106 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
| 1107 | ztad, zsad, zhad, zsrad, zr1ad, zr2ad, zr3ad, & |
---|
| 1108 | zr4ad, zrhopad, zead, zbwad, & |
---|
| 1109 | zbad, zdad, zcad, zawad, zaad, zb1ad, za1ad, & |
---|
| 1110 | zkwad, zk0ad, zpes, zrdc1, zrdc2, zeps, & |
---|
| 1111 | zmask, zrau0r |
---|
| 1112 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zws |
---|
| 1113 | !!---------------------------------------------------------------------- |
---|
| 1114 | ! |
---|
| 1115 | IF( nn_timing == 1 ) CALL timing_start('eos-p_adj') |
---|
| 1116 | ! |
---|
| 1117 | CALL wrk_alloc( jpi, jpj, jpk, zws ) |
---|
| 1118 | ! |
---|
| 1119 | ! initialization of adjoint variables |
---|
| 1120 | ztad = 0.0_wp |
---|
| 1121 | zsad = 0.0_wp |
---|
| 1122 | zhad = 0.0_wp |
---|
| 1123 | zsrad = 0.0_wp |
---|
| 1124 | zr1ad = 0.0_wp |
---|
| 1125 | zr2ad = 0.0_wp |
---|
| 1126 | zr3ad = 0.0_wp |
---|
| 1127 | zr4ad = 0.0_wp |
---|
| 1128 | zrhopad = 0.0_wp |
---|
| 1129 | zead = 0.0_wp |
---|
| 1130 | zbwad = 0.0_wp |
---|
| 1131 | zbad = 0.0_wp |
---|
| 1132 | zdad = 0.0_wp |
---|
| 1133 | zcad = 0.0_wp |
---|
| 1134 | zawad = 0.0_wp |
---|
| 1135 | zaad = 0.0_wp |
---|
| 1136 | zb1ad = 0.0_wp |
---|
| 1137 | za1ad = 0.0_wp |
---|
| 1138 | zkwad = 0.0_wp |
---|
| 1139 | zk0ad = 0.0_wp |
---|
| 1140 | |
---|
| 1141 | SELECT CASE ( nn_eos ) |
---|
| 1142 | |
---|
| 1143 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
---|
| 1144 | zrau0r = 1.e0 / rau0 |
---|
| 1145 | #ifdef key_sp |
---|
| 1146 | zeps = 1.e-7 |
---|
| 1147 | #else |
---|
| 1148 | zeps = 1.e-14 |
---|
| 1149 | #endif |
---|
| 1150 | !CDIR NOVERRCHK |
---|
| 1151 | zws(:,:,:) = SQRT( ABS( pts(:,:,:,jp_sal) ) ) |
---|
| 1152 | ! |
---|
| 1153 | DO jk = jpkm1, 1, -1 |
---|
| 1154 | DO jj = jpj, 1, -1 |
---|
| 1155 | DO ji = jpi, 1, -1 |
---|
| 1156 | ! direct recomputing |
---|
| 1157 | zt = pts(ji,jj,jk,jp_tem) |
---|
| 1158 | zs = pts(ji,jj,jk,jp_sal) |
---|
| 1159 | zh = fsdept(ji,jj,jk) ! depth |
---|
| 1160 | zsr = zws(ji,jj,jk) ! square root salinity |
---|
| 1161 | ! compute volumic mass pure water at atm pressure |
---|
| 1162 | zr1 = ( ( ( ( 6.536332e-9_wp * zt - 1.120083e-6_wp ) * zt & |
---|
| 1163 | & + 1.001685e-4_wp ) * zt - 9.095290e-3_wp ) * zt & |
---|
| 1164 | & + 6.793952e-2_wp ) * zt + 999.842594_wp |
---|
| 1165 | ! seawater volumic mass atm pressure |
---|
| 1166 | zr2 = ( ( ( 5.3875e-9_wp * zt - 8.2467e-7_wp ) * zt & |
---|
| 1167 | & + 7.6438e-5_wp ) * zt - 4.0899e-3_wp ) * zt + 0.824493_wp |
---|
| 1168 | zr3 = ( -1.6546e-6_wp * zt + 1.0227e-4_wp ) * zt - 5.72466e-3_wp |
---|
| 1169 | zr4 = 4.8314e-4_wp |
---|
| 1170 | ! potential volumic mass (reference to the surface) |
---|
| 1171 | zrhop = ( zr4 * zs + zr3*zsr + zr2 ) * zs + zr1 |
---|
| 1172 | ! add the compression terms |
---|
| 1173 | ze = ( -3.508914e-8_wp * zt - 1.248266e-8_wp ) * zt - 2.595994e-6_wp |
---|
| 1174 | zbw = ( 1.296821e-6_wp * zt - 5.782165e-9_wp ) * zt + 1.045941e-4_wp |
---|
| 1175 | zb = zbw + ze * zs |
---|
| 1176 | |
---|
| 1177 | zd = -2.042967e-2_wp |
---|
| 1178 | zc = (-7.267926e-5_wp * zt + 2.598241e-3_wp ) * zt + 0.1571896_wp |
---|
| 1179 | zaw= ( ( 5.939910e-6_wp * zt + 2.512549e-3_wp ) * zt - 0.1028859_wp & |
---|
| 1180 | & ) * zt - 4.721788 |
---|
| 1181 | za = ( zd * zsr + zc ) * zs + zaw |
---|
| 1182 | |
---|
| 1183 | zb1= (-0.1909078_wp * zt + 7.390729_wp ) * zt - 55.87545_wp |
---|
| 1184 | za1= ( ( 2.326469e-3_wp * zt + 1.553190_wp ) * zt - 65.00517_wp & |
---|
| 1185 | & ) * zt + 1044.077_wp |
---|
| 1186 | zkw= ( ( (-1.361629e-4_wp * zt - 1.852732e-2_wp ) * zt - 30.41638_wp & |
---|
| 1187 | & ) * zt + 2098.925_wp ) * zt + 190925.6_wp |
---|
| 1188 | zk0= ( zb1 * zsr + za1 ) * zs + zkw |
---|
| 1189 | |
---|
| 1190 | |
---|
| 1191 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
| 1192 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
| 1193 | |
---|
| 1194 | ! ============ |
---|
| 1195 | ! Adjoint part |
---|
| 1196 | ! ============ |
---|
| 1197 | |
---|
| 1198 | ! Masked in situ density anomaly |
---|
| 1199 | |
---|
| 1200 | zrhopad = zrhopad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 1201 | & * zrdc2 * zrau0r |
---|
| 1202 | zk0ad = zk0ad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 1203 | & * zrdc2 * zrdc2 * zh & |
---|
| 1204 | & * zrdc1**2 * zrhop & |
---|
| 1205 | & * zrau0r |
---|
| 1206 | zaad = zaad + prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 1207 | & * zrdc2 * zrdc2 * zh & |
---|
| 1208 | & * zrdc1**2 * zrhop & |
---|
| 1209 | & * zh * zrau0r |
---|
| 1210 | zbad = zbad - prd_ad(ji,jj,jk) * tmask(ji,jj,jk) & |
---|
| 1211 | & * zrdc2 * zrdc2 * zh & |
---|
| 1212 | & * zrdc1**2 * zrhop & |
---|
| 1213 | & * zh * zh * zrau0r |
---|
| 1214 | prd_ad(ji,jj,jk) = 0.0_wp |
---|
| 1215 | |
---|
| 1216 | zkwad = zkwad + zk0ad |
---|
| 1217 | zsrad = zsrad + zk0ad * zb1 * zs |
---|
| 1218 | zb1ad = zb1ad + zk0ad * zs * zsr |
---|
| 1219 | za1ad = za1ad + zk0ad * zs |
---|
| 1220 | zsad = zsad + zk0ad * ( zb1 * zsr + za1 ) |
---|
| 1221 | zk0ad = 0.0_wp |
---|
| 1222 | |
---|
| 1223 | ztad = ztad + zkwad * ( ( (-4.*1.361629e-4_wp * zt & |
---|
| 1224 | & -3.*1.852732e-2_wp ) * zt & |
---|
| 1225 | & -2.*30.41638_wp ) * zt & |
---|
| 1226 | & + 2098.925_wp ) |
---|
| 1227 | zkwad = 0.0_wp |
---|
| 1228 | |
---|
| 1229 | ztad = ztad + za1ad * ( ( 3.*2.326469e-3_wp * zt & |
---|
| 1230 | & +2.*1.553190_wp ) * zt & |
---|
| 1231 | & - 65.00517_wp ) |
---|
| 1232 | za1ad = 0.0_wp |
---|
| 1233 | |
---|
| 1234 | ztad = ztad + zb1ad * (-2.*0.1909078_wp * zt & |
---|
| 1235 | & + 7.390729_wp ) |
---|
| 1236 | zb1ad = 0.0_wp |
---|
| 1237 | |
---|
| 1238 | zawad = zawad + zaad |
---|
| 1239 | zsrad = zsrad + zaad * zd * zs |
---|
| 1240 | zcad = zcad + zaad * zs |
---|
| 1241 | zsad = zsad + zaad * ( zd * zsr + zc ) |
---|
| 1242 | zaad = 0.0_wp |
---|
| 1243 | |
---|
| 1244 | ztad = ztad + zawad * ( ( 3.*5.939910e-6_wp * zt & |
---|
| 1245 | & +2.*2.512549e-3_wp ) * zt & |
---|
| 1246 | & - 0.1028859_wp ) |
---|
| 1247 | zawad = 0.0_wp |
---|
| 1248 | |
---|
| 1249 | ztad = ztad + zcad * (-2.*7.267926e-5_wp * zt & |
---|
| 1250 | & + 2.598241e-3_wp ) |
---|
| 1251 | zcad = 0.0_wp |
---|
| 1252 | |
---|
| 1253 | |
---|
| 1254 | zsad = zsad + zbad * ze |
---|
| 1255 | zead = zead + zbad * zs |
---|
| 1256 | zbwad = zbwad + zbad |
---|
| 1257 | zbad = 0.0_wp |
---|
| 1258 | |
---|
| 1259 | ztad = ztad + zbwad * ( 2.*1.296821e-6_wp * zt & |
---|
| 1260 | & - 5.782165e-9_wp ) |
---|
| 1261 | zbwad = 0.0_wp |
---|
| 1262 | |
---|
| 1263 | ztad = ztad + zead * (-2.*3.508914e-8_wp * zt & |
---|
| 1264 | & - 1.248266e-8_wp ) |
---|
| 1265 | zead = 0.0_wp |
---|
| 1266 | |
---|
| 1267 | zrhopad = zrhopad + prhop_ad(ji,jj,jk) * tmask(ji,jj,jk) |
---|
| 1268 | prhop_ad(ji,jj,jk) = 0.0_wp |
---|
| 1269 | |
---|
| 1270 | zr1ad = zr1ad + zrhopad |
---|
| 1271 | zr2ad = zr2ad + zrhopad * zs |
---|
| 1272 | zr3ad = zr3ad + zrhopad * zsr * zs |
---|
| 1273 | zsrad = zsrad + zrhopad * zr3 * zs |
---|
| 1274 | zsad = zsad + zrhopad * ( 2. * zr4 * zs + zr2 & |
---|
| 1275 | & + zr3 * zsr ) |
---|
| 1276 | zrhopad = 0.0_wp |
---|
| 1277 | |
---|
| 1278 | ztad = ztad + zr3ad * (-2.*1.6546e-6_wp * zt & |
---|
| 1279 | & + 1.0227e-4_wp ) |
---|
| 1280 | zr3ad = 0.0_wp |
---|
| 1281 | |
---|
| 1282 | ztad = ztad + zr2ad * ( ( ( 4.*5.3875e-9_wp * zt & |
---|
| 1283 | & -3.*8.2467e-7_wp ) * zt & |
---|
| 1284 | & +2.*7.6438e-5_wp ) * zt & |
---|
| 1285 | & - 4.0899e-3_wp ) |
---|
| 1286 | zr2ad = 0.0_wp |
---|
| 1287 | |
---|
| 1288 | ztad = ztad + zr1ad * ( ( ( ( 5.*6.536332e-9_wp * zt & |
---|
| 1289 | & -4.*1.120083e-6_wp ) * zt & |
---|
| 1290 | & +3.*1.001685e-4_wp ) * zt & |
---|
| 1291 | & -2.*9.095290e-3_wp ) * zt & |
---|
| 1292 | & + 6.793952e-2_wp ) |
---|
| 1293 | zr1ad = 0.0_wp |
---|
| 1294 | |
---|
| 1295 | zsad = zsad + zsrad * ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
| 1296 | & * tmask(ji,jj,jk) |
---|
| 1297 | zsrad = 0.0_wp |
---|
| 1298 | |
---|
| 1299 | pts_ad(ji,jj,jk,jp_sal) = pts_ad(ji,jj,jk,jp_sal) + zsad |
---|
| 1300 | pts_ad(ji,jj,jk,jp_tem) = pts_ad(ji,jj,jk,jp_tem) + ztad |
---|
| 1301 | ztad = 0.0_wp |
---|
| 1302 | zsad = 0.0_wp |
---|
| 1303 | END DO |
---|
| 1304 | END DO |
---|
| 1305 | END DO |
---|
| 1306 | ! |
---|
| 1307 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
---|
| 1308 | DO jk = jpkm1, 1, -1 |
---|
| 1309 | prd_ad(:,:,jk) = prd_ad(:,:,jk) + rau0 * prhop_ad(:,:,jk) * tmask(:,:,jk) |
---|
| 1310 | prhop_ad(:,:,jk) = 0.0_wp |
---|
| 1311 | pts_ad(:,:,jk,jp_tem) = pts_ad(:,:,jk,jp_tem) - rn_alpha * prd_ad(:,:,jk) * tmask(:,:,jk) |
---|
| 1312 | prd_ad(:,:,jk) = 0.0_wp |
---|
| 1313 | END DO |
---|
| 1314 | ! |
---|
| 1315 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
---|
| 1316 | DO jk = jpkm1, 1, -1 |
---|
| 1317 | prd_ad( :,:,jk) = prd_ad(:,:,jk) + rau0 * prhop_ad(:,:,jk) * tmask(:,:,jk) |
---|
| 1318 | prhop_ad(:,:,jk) = 0.0_wp |
---|
| 1319 | pts_ad( :,:,jk,jp_tem) = pts_ad(:,:,jk,jp_tem) - rn_alpha * prd_ad(:,:,jk) * tmask(:,:,jk) |
---|
| 1320 | pts_ad( :,:,jk,jp_sal) = pts_ad(:,:,jk,jp_sal) + rn_beta * prd_ad(:,:,jk) * tmask(:,:,jk) |
---|
| 1321 | prd_ad( :,:,jk) = 0.0_wp |
---|
| 1322 | END DO |
---|
| 1323 | ! |
---|
| 1324 | END SELECT |
---|
| 1325 | CALL wrk_dealloc( jpi, jpj, jpk, zws ) |
---|
| 1326 | ! |
---|
| 1327 | IF( nn_timing == 1 ) CALL timing_stop('eos-p_adj') |
---|
| 1328 | ! |
---|
| 1329 | END SUBROUTINE eos_insitu_pot_adj |
---|
| 1330 | |
---|
| 1331 | SUBROUTINE eos_insitu_2d_adj( pts, pdep, pts_ad, prd_ad ) |
---|
| 1332 | !!----------------------------------------------------------------------- |
---|
| 1333 | !! |
---|
| 1334 | !! *** ROUTINE eos_insitu_2d_adj : adj OF ROUTINE eos_insitu_2d *** |
---|
| 1335 | !! |
---|
| 1336 | !! ** Purpose of direct routine : Compute the in situ density |
---|
| 1337 | !! (ratio rho/rau0) from potential temperature and salinity |
---|
| 1338 | !! using an equation of state defined through the namelist |
---|
| 1339 | !! parameter nn_eos. * 2D field case |
---|
| 1340 | !! |
---|
| 1341 | !! ** Method of direct routine : 3 cases: |
---|
| 1342 | !! nn_eos = 0 : Jackett and McDougall (1994) equation of state. |
---|
| 1343 | !! the in situ density is computed directly as a function of |
---|
| 1344 | !! potential temperature relative to the surface (the opa t |
---|
| 1345 | !! variable), salt and pressure (assuming no pressure variation |
---|
| 1346 | !! along geopotential surfaces, i.e. the pressure p in decibars |
---|
| 1347 | !! is approximated by the depth in meters. |
---|
| 1348 | !! prd(t,s,p) = ( rho(t,s,p) - rau0 ) / rau0 |
---|
| 1349 | !! with pressure p decibars |
---|
| 1350 | !! potential temperature t deg celsius |
---|
| 1351 | !! salinity s psu |
---|
| 1352 | !! reference volumic mass rau0 kg/m**3 |
---|
| 1353 | !! in situ volumic mass rho kg/m**3 |
---|
| 1354 | !! in situ density anomalie prd no units |
---|
| 1355 | !! Check value: rho = 1060.93298 kg/m**3 for p=10000 dbar, |
---|
| 1356 | !! t = 40 deg celcius, s=40 psu |
---|
| 1357 | !! nn_eos = 1 : linear equation of state function of temperature only |
---|
| 1358 | !! prd(t) = 0.0285 - rn_alpha * t |
---|
| 1359 | !! nn_eos = 2 : linear equation of state function of temperature and |
---|
| 1360 | !! salinity |
---|
| 1361 | !! prd(t,s) = rn_beta * s - rn_alpha * tn - 1. |
---|
| 1362 | !! Note that no boundary condition problem occurs in this routine |
---|
| 1363 | !! as (ptem,psal) are defined over the whole domain. |
---|
| 1364 | !! |
---|
| 1365 | !! ** Comments on Adjoint Routine : |
---|
| 1366 | !! Care has been taken to avoid division by zero when computing |
---|
| 1367 | !! the inverse of the square root of salinity at masked salinity |
---|
| 1368 | !! points. |
---|
| 1369 | !! |
---|
| 1370 | !! ** Action : |
---|
| 1371 | !! |
---|
| 1372 | !! References : |
---|
| 1373 | !! |
---|
| 1374 | !! History : |
---|
| 1375 | !! 8.2 ! 05-03 ((F. Van den Berghe, A. Weaver, N. Daget) - eosadj.F |
---|
| 1376 | !! 9.0 ! 08-07 (A. Vidard) first version based on eosadj |
---|
| 1377 | !!----------------------------------------------------------------------- |
---|
| 1378 | !! * Modules used |
---|
| 1379 | !! * Arguments |
---|
| 1380 | REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] |
---|
| 1381 | ! ! 2 : salinity [psu] |
---|
| 1382 | REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(inout) :: pts_ad ! 1 : TL of potential temperature [Celcius] |
---|
| 1383 | ! ! 2 : TL of salinity [psu] |
---|
| 1384 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( inout) :: prd_ad ! TL of in_situ density [-] |
---|
| 1385 | REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: pdep ! depth [m] |
---|
| 1386 | ! |
---|
| 1387 | |
---|
| 1388 | INTEGER :: ji, jj ! dummy loop indices |
---|
| 1389 | REAL(wp) :: & ! temporary scalars |
---|
| 1390 | zt, zs, zh, zsr, zr1, zr2, zr3, zr4, zrhop, ze, zbw, & |
---|
| 1391 | zb, zd, zc, zaw, za, zb1, za1, zkw, zk0, & |
---|
| 1392 | ztad, zsad, zhad, zsrad, zr1ad, zr2ad, zr3ad, & |
---|
| 1393 | zr4ad, zrhopad, zead, zbwad, & |
---|
| 1394 | zbad, zdad, zcad, zawad, zaad, zb1ad, za1ad, & |
---|
| 1395 | zkwad, zk0ad, zpes, zrdc1, zrdc2, zeps, & |
---|
| 1396 | zmask |
---|
| 1397 | REAL(wp), POINTER, DIMENSION(:,:) :: zws |
---|
| 1398 | !!---------------------------------------------------------------------- |
---|
| 1399 | ! |
---|
| 1400 | IF( nn_timing == 1 ) CALL timing_start('eos2d_adj') |
---|
| 1401 | ! |
---|
| 1402 | CALL wrk_alloc( jpi, jpj, zws ) |
---|
| 1403 | ! |
---|
| 1404 | ! initialization of adjoint variables |
---|
| 1405 | ztad = 0.0_wp |
---|
| 1406 | zsad = 0.0_wp |
---|
| 1407 | zhad = 0.0_wp |
---|
| 1408 | zsrad = 0.0_wp |
---|
| 1409 | zr1ad = 0.0_wp |
---|
| 1410 | zr2ad = 0.0_wp |
---|
| 1411 | zr3ad = 0.0_wp |
---|
| 1412 | zr4ad = 0.0_wp |
---|
| 1413 | zrhopad = 0.0_wp |
---|
| 1414 | zead = 0.0_wp |
---|
| 1415 | zbwad = 0.0_wp |
---|
| 1416 | zbad = 0.0_wp |
---|
| 1417 | zdad = 0.0_wp |
---|
| 1418 | zcad = 0.0_wp |
---|
| 1419 | zawad = 0.0_wp |
---|
| 1420 | zaad = 0.0_wp |
---|
| 1421 | zb1ad = 0.0_wp |
---|
| 1422 | za1ad = 0.0_wp |
---|
| 1423 | zkwad = 0.0_wp |
---|
| 1424 | zk0ad = 0.0_wp |
---|
| 1425 | SELECT CASE ( nn_eos ) |
---|
| 1426 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
---|
| 1427 | |
---|
| 1428 | #ifdef key_sp |
---|
| 1429 | zeps = 1.e-7 |
---|
| 1430 | #else |
---|
| 1431 | zeps = 1.e-14 |
---|
| 1432 | #endif |
---|
| 1433 | !CDIR NOVERRCHK |
---|
| 1434 | DO jj = jpjm1, 1, -1 |
---|
| 1435 | !CDIR NOVERRCHK |
---|
| 1436 | DO ji = fs_jpim1, 1, -1 ! vector opt. |
---|
| 1437 | zws(ji,jj) = SQRT( ABS( pts(ji,jj,jp_sal) ) ) |
---|
| 1438 | END DO |
---|
| 1439 | END DO |
---|
| 1440 | ! |
---|
| 1441 | DO jj = jpjm1, 1, -1 |
---|
| 1442 | DO ji = fs_jpim1, 1, -1 ! vector opt. |
---|
| 1443 | zmask = tmask(ji,jj,1) ! land/sea bottom mask = surf. mask |
---|
| 1444 | zt = pts (ji,jj,jp_tem) ! interpolated T |
---|
| 1445 | zs = pts (ji,jj,jp_sal) ! interpolated S |
---|
| 1446 | zsr= zws(ji,jj) ! square root of interpolated S |
---|
| 1447 | zh = pdep(ji,jj) ! depth at the partial step level |
---|
| 1448 | ! compute volumic mass pure water at atm pressure |
---|
| 1449 | zr1= ( ( ( ( 6.536332e-9_wp*zt-1.120083e-6_wp )*zt+1.001685e-4_wp)*zt & |
---|
| 1450 | & -9.095290e-3_wp )*zt+6.793952e-2_wp )*zt+999.842594_wp |
---|
| 1451 | ! seawater volumic mass atm pressure |
---|
| 1452 | zr2= ( ( ( 5.3875e-9_wp*zt-8.2467e-7_wp ) *zt+7.6438e-5_wp ) *zt & |
---|
| 1453 | & -4.0899e-3_wp ) *zt+0.824493_wp |
---|
| 1454 | zr3= ( -1.6546e-6_wp*zt+1.0227e-4_wp ) *zt-5.72466e-3_wp |
---|
| 1455 | zr4= 4.8314e-4_wp |
---|
| 1456 | |
---|
| 1457 | ! potential volumic mass (reference to the surface) |
---|
| 1458 | zrhop= ( zr4*zs + zr3*zsr + zr2 ) *zs + zr1 |
---|
| 1459 | |
---|
| 1460 | ! add the compression terms |
---|
| 1461 | ze = ( -3.508914e-8_wp*zt-1.248266e-8_wp ) *zt-2.595994e-6_wp |
---|
| 1462 | zbw= ( 1.296821e-6_wp*zt-5.782165e-9_wp ) *zt+1.045941e-4_wp |
---|
| 1463 | zb = zbw + ze * zs |
---|
| 1464 | |
---|
| 1465 | zd = -2.042967e-2_wp |
---|
| 1466 | zc = (-7.267926e-5_wp*zt+2.598241e-3_wp ) *zt+0.1571896_wp |
---|
| 1467 | zaw= ( ( 5.939910e-6_wp*zt+2.512549e-3_wp ) *zt-0.1028859_wp ) *zt - 4.721788_wp |
---|
| 1468 | za = ( zd*zsr + zc ) *zs + zaw |
---|
| 1469 | |
---|
| 1470 | zb1= (-0.1909078_wp*zt+7.390729_wp ) *zt-55.87545_wp |
---|
| 1471 | za1= ( ( 2.326469e-3_wp*zt+1.553190_wp)*zt-65.00517_wp ) *zt+1044.077_wp |
---|
| 1472 | zkw= ( ( (-1.361629e-4_wp*zt-1.852732e-2_wp ) *zt-30.41638_wp ) *zt + 2098.925_wp ) *zt+190925.6_wp |
---|
| 1473 | zk0= ( zb1*zsr + za1 )*zs + zkw |
---|
| 1474 | |
---|
| 1475 | zrdc1 = 1.0 / ( zk0 - zh * ( za - zh * zb ) ) |
---|
| 1476 | zrdc2 = 1.0 / ( 1.0 - zh * zrdc1 ) |
---|
| 1477 | ! ============ |
---|
| 1478 | ! Adjoint part |
---|
| 1479 | ! ============ |
---|
| 1480 | |
---|
| 1481 | ! Masked in situ density anomaly |
---|
| 1482 | |
---|
| 1483 | zrhopad = zrhopad + prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
| 1484 | & * zrdc2 / rau0 |
---|
| 1485 | zk0ad = zk0ad - prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
| 1486 | & * zrdc2 * zrdc2 * zh & |
---|
| 1487 | & * zrdc1**2 * zrhop & |
---|
| 1488 | & / rau0 |
---|
| 1489 | zaad = zaad + prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
| 1490 | & * zrdc2 * zrdc2 * zh & |
---|
| 1491 | & * zrdc1**2 * zrhop & |
---|
| 1492 | & * zh / rau0 |
---|
| 1493 | zbad = zbad - prd_ad(ji,jj) * tmask(ji,jj,1) & |
---|
| 1494 | & * zrdc2 * zrdc2 * zh & |
---|
| 1495 | & * zrdc1**2 * zrhop & |
---|
| 1496 | & * zh * zh / rau0 |
---|
| 1497 | prd_ad(ji,jj) = 0.0_wp |
---|
| 1498 | |
---|
| 1499 | zkwad = zkwad + zk0ad |
---|
| 1500 | zsrad = zsrad + zk0ad * zb1 * zs |
---|
| 1501 | zb1ad = zb1ad + zk0ad * zs * zsr |
---|
| 1502 | za1ad = za1ad + zk0ad * zs |
---|
| 1503 | zsad = zsad + zk0ad * ( zb1 * zsr + za1 ) |
---|
| 1504 | zk0ad = 0.0_wp |
---|
| 1505 | |
---|
| 1506 | ztad = ztad + zkwad * ( ( (-4.*1.361629e-4_wp * zt & |
---|
| 1507 | & -3.*1.852732e-2_wp ) * zt & |
---|
| 1508 | & -2.*30.41638_wp ) * zt & |
---|
| 1509 | & + 2098.925_wp ) |
---|
| 1510 | zkwad = 0.0_wp |
---|
| 1511 | |
---|
| 1512 | ztad = ztad + za1ad * ( ( 3.*2.326469e-3_wp * zt & |
---|
| 1513 | & +2.*1.553190_wp ) * zt & |
---|
| 1514 | & - 65.00517_wp ) |
---|
| 1515 | za1ad = 0.0_wp |
---|
| 1516 | |
---|
| 1517 | ztad = ztad + zb1ad * (-2.*0.1909078_wp * zt & |
---|
| 1518 | & + 7.390729_wp ) |
---|
| 1519 | zb1ad = 0.0_wp |
---|
| 1520 | |
---|
| 1521 | zawad = zawad + zaad |
---|
| 1522 | zsrad = zsrad + zaad * zd * zs |
---|
| 1523 | zcad = zcad + zaad * zs |
---|
| 1524 | zsad = zsad + zaad * ( zd * zsr + zc ) |
---|
| 1525 | zaad = 0.0_wp |
---|
| 1526 | |
---|
| 1527 | ztad = ztad + zawad * ( ( 3.*5.939910e-6_wp * zt & |
---|
| 1528 | & +2.*2.512549e-3_wp ) * zt & |
---|
| 1529 | & - 0.1028859_wp ) |
---|
| 1530 | zawad = 0.0_wp |
---|
| 1531 | |
---|
| 1532 | ztad = ztad + zcad * (-2.*7.267926e-5_wp * zt & |
---|
| 1533 | & + 2.598241e-3_wp ) |
---|
| 1534 | zcad = 0.0_wp |
---|
| 1535 | |
---|
| 1536 | zbwad = zbwad + zbad |
---|
| 1537 | zead = zead + zbad * zs |
---|
| 1538 | zsad = zsad + zbad * ze |
---|
| 1539 | zbad = 0.0_wp |
---|
| 1540 | |
---|
| 1541 | ztad = ztad + zbwad * ( 2.*1.296821e-6_wp * zt & |
---|
| 1542 | & - 5.782165e-9_wp ) |
---|
| 1543 | zbwad = 0.0_wp |
---|
| 1544 | |
---|
| 1545 | ztad = ztad + zead * (-2.*3.508914e-8_wp * zt & |
---|
| 1546 | & - 1.248266e-8_wp ) |
---|
| 1547 | zead = 0.0_wp |
---|
| 1548 | |
---|
| 1549 | zr1ad = zr1ad + zrhopad |
---|
| 1550 | zr2ad = zr2ad + zrhopad * zs |
---|
| 1551 | zr3ad = zr3ad + zrhopad * zsr * zs |
---|
| 1552 | zsrad = zsrad + zrhopad * zr3 * zs |
---|
| 1553 | zsad = zsad + zrhopad * ( 2. * zr4 * zs + zr2 & |
---|
| 1554 | & + zr3 * zsr ) |
---|
| 1555 | zrhopad = 0.0_wp |
---|
| 1556 | |
---|
| 1557 | ztad = ztad + zr3ad * (-2.*1.6546e-6_wp * zt & |
---|
| 1558 | & + 1.0227e-4_wp ) |
---|
| 1559 | zr3ad = 0.0_wp |
---|
| 1560 | |
---|
| 1561 | ztad = ztad + zr2ad * ( ( ( 4.*5.3875e-9_wp * zt & |
---|
| 1562 | & -3.*8.2467e-7_wp ) * zt & |
---|
| 1563 | & +2.*7.6438e-5_wp ) * zt & |
---|
| 1564 | & - 4.0899e-3_wp ) |
---|
| 1565 | zr2ad = 0.0_wp |
---|
| 1566 | |
---|
| 1567 | ztad = ztad + zr1ad * ( ( ( ( 5.*6.536332e-9_wp * zt & |
---|
| 1568 | & -4.*1.120083e-6_wp ) * zt & |
---|
| 1569 | & +3.*1.001685e-4_wp ) * zt & |
---|
| 1570 | & -2.*9.095290e-3_wp ) * zt & |
---|
| 1571 | & + 6.793952e-2_wp ) |
---|
| 1572 | zr1ad = 0.0_wp |
---|
| 1573 | |
---|
| 1574 | zsad = zsad + zsrad * ( 1.0 / MAX( 2.*zsr, zeps ) ) & |
---|
| 1575 | & * tmask(ji,jj, 1) |
---|
| 1576 | zsrad = 0.0_wp |
---|
| 1577 | |
---|
| 1578 | pts_ad(ji,jj,jp_sal) = pts_ad(ji,jj,jp_sal) + zsad |
---|
| 1579 | pts_ad(ji,jj,jp_tem) = pts_ad(ji,jj,jp_tem) + ztad |
---|
| 1580 | ztad = 0.0_wp |
---|
| 1581 | zsad = 0.0_wp |
---|
| 1582 | END DO |
---|
| 1583 | END DO |
---|
| 1584 | ! |
---|
| 1585 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
---|
| 1586 | DO jj = jpjm1, 1, -1 |
---|
| 1587 | DO ji = fs_jpim1, 1, -1 ! vector opt. |
---|
| 1588 | pts_ad(ji,jj,jp_tem) = pts_ad(ji,jj,jp_tem) - prd_ad(ji,jj) * rn_alpha * tmask(ji,jj,1) |
---|
| 1589 | prd_ad(ji,jj) = 0.0_wp |
---|
| 1590 | END DO |
---|
| 1591 | END DO |
---|
| 1592 | ! |
---|
| 1593 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
---|
| 1594 | DO jj = jpjm1, 1, -1 |
---|
| 1595 | DO ji = fs_jpim1, 1, -1 ! vector opt. |
---|
| 1596 | pts_ad(ji,jj,jp_tem) = pts_ad(ji,jj,jp_tem) - prd_ad(ji,jj) * rn_alpha * tmask(ji,jj,1) |
---|
| 1597 | pts_ad(ji,jj,jp_sal) = pts_ad(ji,jj,jp_sal) + prd_ad(ji,jj) * rn_beta * tmask(ji,jj,1) |
---|
| 1598 | prd_ad (ji,jj) = 0.0_wp |
---|
| 1599 | END DO |
---|
| 1600 | END DO |
---|
| 1601 | ! |
---|
| 1602 | END SELECT |
---|
| 1603 | ! |
---|
| 1604 | CALL wrk_dealloc( jpi, jpj, zws ) |
---|
| 1605 | ! |
---|
| 1606 | IF( nn_timing == 1 ) CALL timing_stop('eos2d_adj') |
---|
| 1607 | ! |
---|
| 1608 | END SUBROUTINE eos_insitu_2d_adj |
---|
| 1609 | |
---|
| 1610 | SUBROUTINE eos_bn2_tan ( pts, pts_tl, pn2_tl ) |
---|
| 1611 | !!---------------------------------------------------------------------- |
---|
| 1612 | !! *** ROUTINE eos_bn2_tan *** |
---|
| 1613 | !! |
---|
| 1614 | !! ** Purpose of the direct routine: Compute the local |
---|
| 1615 | !! Brunt-Vaisala frequency at the time-step of the input arguments |
---|
| 1616 | !! |
---|
| 1617 | !! ** Method of the direct routine: |
---|
| 1618 | !! * nn_eos = 0 : UNESCO sea water properties |
---|
| 1619 | !! The brunt-vaisala frequency is computed using the polynomial |
---|
| 1620 | !! polynomial expression of McDougall (1987): |
---|
| 1621 | !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w |
---|
| 1622 | !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is |
---|
| 1623 | !! computed and used in zdfddm module : |
---|
| 1624 | !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) |
---|
| 1625 | !! * nn_eos = 1 : linear equation of state (temperature only) |
---|
| 1626 | !! N^2 = grav * rn_alpha * dk[ t ]/e3w |
---|
| 1627 | !! * nn_eos = 2 : linear equation of state (temperature & salinity) |
---|
| 1628 | !! N^2 = grav * (rn_alpha * dk[ t ] - rn_beta * dk[ s ] ) / e3w |
---|
| 1629 | !! The use of potential density to compute N^2 introduces e r r o r |
---|
| 1630 | !! in the sign of N^2 at great depths. We recommand the use of |
---|
| 1631 | !! nn_eos = 0, except for academical studies. |
---|
| 1632 | !! Macro-tasked on horizontal slab (jk-loop) |
---|
| 1633 | !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr |
---|
| 1634 | !! and is never used at this level. |
---|
| 1635 | !! |
---|
| 1636 | !! ** Action : - pn2 : the brunt-vaisala frequency |
---|
| 1637 | !! |
---|
| 1638 | !! References : |
---|
| 1639 | !! McDougall, T. J., J. Phys. Oceanogr., 17, 1950-1964, 1987. |
---|
| 1640 | !! |
---|
| 1641 | !! History: |
---|
| 1642 | !! ! 08-07 (A. Vidard) First version |
---|
| 1643 | !!---------------------------------------------------------------------- |
---|
| 1644 | !! * Arguments |
---|
| 1645 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts, & ! 1 : potential temperature [Celcius] |
---|
| 1646 | ! ! 2 : salinity [psu] |
---|
| 1647 | & pts_tl ! 1 : TL of potential temperature [Celsius] |
---|
| 1648 | ! 2 : TL of salinity [psu] |
---|
| 1649 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( out ) :: & |
---|
| 1650 | & pn2_tl ! TL of potential density (surface referenced) |
---|
| 1651 | !! * Local declarations |
---|
| 1652 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1653 | REAL(wp) :: & |
---|
| 1654 | zgde3w, zt, zs, zh, & ! temporary scalars |
---|
| 1655 | zalbet, zbeta ! " " |
---|
| 1656 | REAL(wp) :: & |
---|
| 1657 | zttl, zstl, & ! temporary scalars |
---|
| 1658 | zalbettl, zbetatl ! " " |
---|
| 1659 | #if defined key_zdfddm |
---|
| 1660 | REAL(wp) :: zds, zdstl ! temporary scalars |
---|
| 1661 | #endif |
---|
| 1662 | |
---|
| 1663 | ! pn2_tl : interior points only (2=< jk =< jpkm1 ) |
---|
| 1664 | ! -------------------------- |
---|
| 1665 | SELECT CASE ( nn_eos ) |
---|
| 1666 | |
---|
| 1667 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
---|
| 1668 | DO jk = 2, jpkm1 |
---|
| 1669 | DO jj = 1, jpj |
---|
| 1670 | DO ji = 1, jpi |
---|
| 1671 | zgde3w = grav / fse3w(ji,jj,jk) |
---|
| 1672 | zt = 0.5 * ( pts(ji,jj,jk,jp_tem) + pts(ji,jj,jk-1,jp_tem) ) ! potential temperature at w-point |
---|
| 1673 | zs = 0.5 * ( pts(ji,jj,jk,jp_sal) + pts(ji,jj,jk-1,jp_sal) ) - 35.0 ! salinity anomaly (s-35) at w-point |
---|
| 1674 | zh = fsdepw(ji,jj,jk) ! depth in meters at w-point |
---|
| 1675 | |
---|
| 1676 | zalbet = ( ( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt & ! ratio alpha/beta |
---|
| 1677 | & - 0.203814e-03_wp ) * zt & |
---|
| 1678 | & + 0.170907e-01_wp ) * zt & |
---|
| 1679 | & + 0.665157e-01_wp & |
---|
| 1680 | & + ( - 0.678662e-05_wp * zs & |
---|
| 1681 | & - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs & |
---|
| 1682 | & + ( ( - 0.302285e-13_wp * zh & |
---|
| 1683 | & - 0.251520e-11_wp * zs & |
---|
| 1684 | & + 0.512857e-12_wp * zt * zt ) * zh & |
---|
| 1685 | & - 0.164759e-06_wp * zs & |
---|
| 1686 | & +( 0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt & |
---|
| 1687 | & + 0.380374e-04_wp ) * zh |
---|
| 1688 | |
---|
| 1689 | zbeta = ( ( -0.415613e-09_wp * zt + 0.555579e-07_wp ) * zt & ! beta |
---|
| 1690 | & - 0.301985e-05_wp ) * zt & |
---|
| 1691 | & + 0.785567e-03_wp & |
---|
| 1692 | & + ( 0.515032e-08_wp * zs & |
---|
| 1693 | & + 0.788212e-08_wp * zt - 0.356603e-06_wp ) * zs & |
---|
| 1694 | & +( ( 0.121551e-17_wp * zh & |
---|
| 1695 | & - 0.602281e-15_wp * zs & |
---|
| 1696 | & - 0.175379e-14_wp * zt + 0.176621e-12_wp ) * zh & |
---|
| 1697 | & + 0.408195e-10_wp * zs & |
---|
| 1698 | & + ( - 0.213127e-11_wp * zt + 0.192867e-09_wp ) * zt & |
---|
| 1699 | & - 0.121555e-07_wp ) * zh |
---|
| 1700 | |
---|
| 1701 | !! tangent part |
---|
| 1702 | zttl = 0.5 * ( pts_tl(ji,jj,jk,jp_tem) + pts_tl(ji,jj,jk-1,jp_tem) ) ! potential temperature at w-point |
---|
| 1703 | zstl = 0.5 * ( pts_tl(ji,jj,jk,jp_sal) + pts_tl(ji,jj,jk-1,jp_sal) ) ! salinity anomaly at w-point |
---|
| 1704 | zalbettl = ( ( ( -4.*0.255019e-07_wp * zt & ! ratio alpha/beta |
---|
| 1705 | & +3.*0.298357e-05_wp ) * zt & |
---|
| 1706 | & -2.*0.203814e-03_wp ) * zt & |
---|
| 1707 | & + 0.170907e-01_wp & |
---|
| 1708 | & - 0.846960e-04_wp * zs & |
---|
| 1709 | & - ( 0.933746e-06_wp & |
---|
| 1710 | & - ( 2.*0.791325e-08_wp & |
---|
| 1711 | & +2.*0.512857e-12_wp * zh ) * zt ) * zh ) * zttl & |
---|
| 1712 | & + ( - 2.*0.678662e-05_wp * zs & |
---|
| 1713 | & - 0.846960e-04_wp * zt & |
---|
| 1714 | & + 0.378110e-02_wp & |
---|
| 1715 | & + ( - 0.164759e-06_wp & |
---|
| 1716 | & - 0.251520e-11_wp * zh ) * zh ) * zstl |
---|
| 1717 | |
---|
| 1718 | zbetatl = ( ( -3.*0.415613e-09_wp * zt & |
---|
| 1719 | & +2.*0.555579e-07_wp ) * zt & |
---|
| 1720 | & - 0.301985e-05_wp & |
---|
| 1721 | & + 0.788212e-08_wp * zs & |
---|
| 1722 | & + ( -2.*0.213127e-11_wp * zt & |
---|
| 1723 | & - 0.175379e-14_wp * zh & |
---|
| 1724 | & + 0.192867e-09_wp ) * zh ) * zttl & |
---|
| 1725 | & + ( 2.*0.515032e-08_wp * zs & |
---|
| 1726 | & + 0.788212e-08_wp * zt & |
---|
| 1727 | & - 0.356603e-06_wp & |
---|
| 1728 | & + ( - 0.602281e-15_wp * zh & |
---|
| 1729 | & + 0.408195e-10_wp ) * zh ) * zstl |
---|
| 1730 | |
---|
| 1731 | pn2_tl(ji,jj,jk) = zgde3w * tmask(ji,jj,jk) * ( & |
---|
| 1732 | & zbeta * ( zalbet & |
---|
| 1733 | & * ( pts_tl(ji,jj,jk-1,jp_tem) - pts_tl(ji,jj,jk,jp_tem) ) & |
---|
| 1734 | & + zalbettl & |
---|
| 1735 | & * ( pts (ji,jj,jk-1,jp_tem) - pts (ji,jj,jk,jp_tem) ) & |
---|
| 1736 | & - ( pts_tl(ji,jj,jk-1,jp_sal) - pts_tl(ji,jj,jk,jp_sal) ) ) & |
---|
| 1737 | & + zbetatl * ( zalbet & |
---|
| 1738 | & * ( pts (ji,jj,jk-1,jp_tem) - pts (ji,jj,jk,jp_tem) ) & |
---|
| 1739 | & - ( pts (ji,jj,jk-1,jp_sal) - pts (ji,jj,jk,jp_sal) ) ) ) |
---|
| 1740 | #if defined key_zdfddm |
---|
| 1741 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) |
---|
| 1742 | zdstl = ( pts_tl(ji,jj,jk-1,jp_sal) - pts_tl(ji,jj,jk,jp_sal) ) |
---|
| 1743 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
| 1744 | zds = 1.e-20 |
---|
| 1745 | rrau_tl(ji,jj,jk) = zalbettl * & |
---|
| 1746 | & ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds & |
---|
| 1747 | & + zalbet * & |
---|
| 1748 | & ( ( pts_tl(ji,jj,jk-1,jp_tem) - pts_tl(ji,jj,jk,jp_tem) ) / zds ) |
---|
| 1749 | ELSE |
---|
| 1750 | rrau_tl(ji,jj,jk) = zalbettl * & |
---|
| 1751 | & ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds & |
---|
| 1752 | & + zalbet * & |
---|
| 1753 | & ( ( pts_tl(ji,jj,jk-1,jp_tem) - pts_tl(ji,jj,jk,jp_tem) ) / zds & |
---|
| 1754 | & - ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) * zdstl/ zds**2 ) |
---|
| 1755 | ENDIF |
---|
| 1756 | #endif |
---|
| 1757 | END DO |
---|
| 1758 | END DO |
---|
| 1759 | END DO |
---|
| 1760 | ! |
---|
| 1761 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
---|
| 1762 | DO jk = 2, jpkm1 |
---|
| 1763 | pn2_tl(:,:,jk) = rn_alpha * ( pts_tl(:,:,jk-1,jp_tem) - pts_tl(:,:,jk,jp_tem) ) * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 1764 | END DO |
---|
| 1765 | ! |
---|
| 1766 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
---|
| 1767 | DO jk = 2, jpkm1 |
---|
| 1768 | pn2_tl(:,:,jk) = ( rn_alpha * ( pts_tl(:,:,jk-1,jp_tem) - pts_tl(:,:,jk,jp_tem) ) & |
---|
| 1769 | & - rn_beta * ( pts_tl(:,:,jk-1,jp_sal) - pts_tl(:,:,jk,jp_sal) ) ) & |
---|
| 1770 | & * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 1771 | END DO |
---|
| 1772 | #if defined key_zdfddm |
---|
| 1773 | DO jk = 2, jpkm1 |
---|
| 1774 | DO jj = 1, jpj |
---|
| 1775 | DO ji = 1, jpi |
---|
| 1776 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) |
---|
| 1777 | zdstl = pts_tl(ji,jj,jk-1,jp_sal) - pts_tl(ji,jj,jk,jp_sal) |
---|
| 1778 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
| 1779 | zds = 1.e-20 |
---|
| 1780 | rrau_tl(ji,jj,jk) = ralpbet * & |
---|
| 1781 | & ( ( pts_tl(ji,jj,jk-1,jp_tem) - pts_tl(ji,jj,jk,jp_tem) ) / zds ) |
---|
| 1782 | ELSE |
---|
| 1783 | rrau_tl(ji,jj,jk) = ralpbet * & |
---|
| 1784 | & ( ( pts_tl(ji,jj,jk-1,jp_tem) - pts_tl(ji,jj,jk,jp_tem) ) / zds & |
---|
| 1785 | & - ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) * zdstl / zds**2 ) |
---|
| 1786 | ENDIF |
---|
| 1787 | rrau(ji,jj,jk) = ralpbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds |
---|
| 1788 | END DO |
---|
| 1789 | END DO |
---|
| 1790 | END DO |
---|
| 1791 | #endif |
---|
| 1792 | END SELECT |
---|
| 1793 | END SUBROUTINE eos_bn2_tan |
---|
| 1794 | |
---|
| 1795 | SUBROUTINE eos_bn2_adj ( pts, pts_ad, pn2_ad ) |
---|
| 1796 | !!---------------------------------------------------------------------- |
---|
| 1797 | !! *** ROUTINE eos_bn2_adj *** |
---|
| 1798 | !! |
---|
| 1799 | !! ** Purpose of the direct routine: Compute the local |
---|
| 1800 | !! Brunt-Vaisala frequency at the time-step of the input arguments |
---|
| 1801 | !! |
---|
| 1802 | !! ** Method of the direct routine: |
---|
| 1803 | !! * nn_eos = 0 : UNESCO sea water properties |
---|
| 1804 | !! The brunt-vaisala frequency is computed using the polynomial |
---|
| 1805 | !! polynomial expression of McDougall (1987): |
---|
| 1806 | !! N^2 = grav * beta * ( alpha/beta*dk[ t ] - dk[ s ] )/e3w |
---|
| 1807 | !! If lk_zdfddm=T, the heat/salt buoyancy flux ratio Rrau is |
---|
| 1808 | !! computed and used in zdfddm module : |
---|
| 1809 | !! Rrau = alpha/beta * ( dk[ t ] / dk[ s ] ) |
---|
| 1810 | !! * nn_eos = 1 : linear equation of state (temperature only) |
---|
| 1811 | !! N^2 = grav * rn_alpha * dk[ t ]/e3w |
---|
| 1812 | !! * nn_eos = 2 : linear equation of state (temperature & salinity) |
---|
| 1813 | !! N^2 = grav * (rn_alpha * dk[ t ] - rn_beta * dk[ s ] ) / e3w |
---|
| 1814 | !! The use of potential density to compute N^2 introduces e r r o r |
---|
| 1815 | !! in the sign of N^2 at great depths. We recommand the use of |
---|
| 1816 | !! nn_eos = 0, except for academical studies. |
---|
| 1817 | !! Macro-tasked on horizontal slab (jk-loop) |
---|
| 1818 | !! N.B. N^2 is set to zero at the first level (JK=1) in inidtr |
---|
| 1819 | !! and is never used at this level. |
---|
| 1820 | !! |
---|
| 1821 | !! ** Action : - pn2 : the brunt-vaisala frequency |
---|
| 1822 | !! |
---|
| 1823 | !! References : |
---|
| 1824 | !! McDougall, T. J., J. Phys. Oceanogr., 17, 1950-1964, 1987. |
---|
| 1825 | !! |
---|
| 1826 | !! History: |
---|
| 1827 | !! ! 08-07 (A. Vidard) First version |
---|
| 1828 | !!---------------------------------------------------------------------- |
---|
| 1829 | !! * Arguments |
---|
| 1830 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celcius] |
---|
| 1831 | ! ! 2 : salinity [psu] |
---|
| 1832 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(inout ) :: pts_ad ! 1 : Adjoint of potential temperature [Celsius] |
---|
| 1833 | ! 2 : Adjoint of salinity [psu] |
---|
| 1834 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( inout ) :: & |
---|
| 1835 | & pn2_ad ! Adjoint of potential density (surface referenced) |
---|
| 1836 | ! |
---|
| 1837 | !! * Local declarations |
---|
| 1838 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1839 | REAL(wp) :: & |
---|
| 1840 | zgde3w, zt, zs, zh, & ! temporary scalars |
---|
| 1841 | zalbet, zbeta ! " " |
---|
| 1842 | REAL(wp) :: & |
---|
| 1843 | ztad, zsad, & ! temporary scalars |
---|
| 1844 | zalbetad, zbetaad ! " " |
---|
| 1845 | #if defined key_zdfddm |
---|
| 1846 | REAL(wp) :: zds, zdsad ! temporary scalars |
---|
| 1847 | #endif |
---|
| 1848 | |
---|
| 1849 | ! pn2_tl : interior points only (2=< jk =< jpkm1 ) |
---|
| 1850 | ! -------------------------- |
---|
| 1851 | zalbetad = 0.0_wp |
---|
| 1852 | zbetaad = 0.0_wp |
---|
| 1853 | ztad = 0.0_wp |
---|
| 1854 | zsad = 0.0_wp |
---|
| 1855 | #if defined key_zdfddm |
---|
| 1856 | zdsad = 0.0_wp |
---|
| 1857 | #endif |
---|
| 1858 | |
---|
| 1859 | SELECT CASE ( nn_eos ) |
---|
| 1860 | |
---|
| 1861 | CASE ( 0 ) !== Jackett and McDougall (1994) formulation ==! |
---|
| 1862 | DO jk = jpkm1, 2, -1 |
---|
| 1863 | DO jj = jpj, 1, -1 |
---|
| 1864 | DO ji = jpi, 1, -1 |
---|
| 1865 | zgde3w = grav / fse3w(ji,jj,jk) |
---|
| 1866 | zt = 0.5 * ( pts(ji,jj,jk,jp_tem) + pts(ji,jj,jk-1,jp_tem) ) ! potential temperature at w-point |
---|
| 1867 | zs = 0.5 * ( pts(ji,jj,jk,jp_sal) + pts(ji,jj,jk-1,jp_sal) ) - 35.0 ! salinity anomaly (s-35) at w-point |
---|
| 1868 | zh = fsdepw(ji,jj,jk) ! depth in meters at w-point |
---|
| 1869 | |
---|
| 1870 | zalbet = ( ( ( - 0.255019e-07_wp * zt + 0.298357e-05_wp ) * zt & ! ratio alpha/beta |
---|
| 1871 | & - 0.203814e-03_wp ) * zt & |
---|
| 1872 | & + 0.170907e-01_wp ) * zt & |
---|
| 1873 | & + 0.665157e-01_wp & |
---|
| 1874 | & + ( - 0.678662e-05_wp * zs & |
---|
| 1875 | & - 0.846960e-04_wp * zt + 0.378110e-02_wp ) * zs & |
---|
| 1876 | & + ( ( - 0.302285e-13_wp * zh & |
---|
| 1877 | & - 0.251520e-11_wp * zs & |
---|
| 1878 | & + 0.512857e-12_wp * zt * zt ) * zh & |
---|
| 1879 | & - 0.164759e-06_wp * zs & |
---|
| 1880 | & +( 0.791325e-08_wp * zt - 0.933746e-06_wp ) * zt & |
---|
| 1881 | & + 0.380374e-04_wp ) * zh |
---|
| 1882 | |
---|
| 1883 | zbeta = ( ( -0.415613e-09_wp * zt + 0.555579e-07_wp ) * zt & ! beta |
---|
| 1884 | & - 0.301985e-05_wp ) * zt & |
---|
| 1885 | & + 0.785567e-03_wp & |
---|
| 1886 | & + ( 0.515032e-08_wp * zs & |
---|
| 1887 | & + 0.788212e-08_wp * zt - 0.356603e-06_wp ) * zs & |
---|
| 1888 | & +( ( 0.121551e-17_wp * zh & |
---|
| 1889 | & - 0.602281e-15_wp * zs & |
---|
| 1890 | & - 0.175379e-14_wp * zt + 0.176621e-12_wp ) * zh & |
---|
| 1891 | & + 0.408195e-10_wp * zs & |
---|
| 1892 | & + ( - 0.213127e-11_wp * zt + 0.192867e-09_wp ) * zt & |
---|
| 1893 | & - 0.121555e-07_wp ) * zh |
---|
| 1894 | |
---|
| 1895 | #if defined key_zdfddm |
---|
| 1896 | |
---|
| 1897 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) |
---|
| 1898 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
| 1899 | zds = 1.e-20 |
---|
| 1900 | zdsad = 0.0_wp |
---|
| 1901 | ELSE |
---|
| 1902 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) |
---|
| 1903 | zdsad = rrau_ad(ji,jj,jk) * zalbet *( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds**2 |
---|
| 1904 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) |
---|
| 1905 | ENDIF |
---|
| 1906 | pts_ad(ji,jj,jk-1,jp_tem) = pts_ad(ji,jj,jk-1,jp_tem) + rrau_ad(ji,jj,jk) * zalbet / zds |
---|
| 1907 | pts_ad(ji,jj,jk,jp_tem ) = pts_ad(ji,jj,jk,jp_tem ) - rrau_ad(ji,jj,jk) * zalbet / zds |
---|
| 1908 | zalbetad = zalbetad + rrau_ad(ji,jj,jk) * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds |
---|
| 1909 | rrau_ad(ji,jj,jk) = 0._wp |
---|
| 1910 | pts_ad(ji,jj,jk-1,jp_sal) = pts_ad(ji,jj,jk-1,jp_sal) + zdsad |
---|
| 1911 | pts_ad(ji,jj,jk,jp_sal ) = pts_ad(ji,jj,jk,jp_sal ) - zdsad |
---|
| 1912 | zdsad = 0._wp |
---|
| 1913 | #endif |
---|
| 1914 | pts_ad(ji,jj,jk-1,jp_tem) = pts_ad(ji,jj,jk-1,jp_tem) + zalbet*zbeta*zgde3w*tmask(ji,jj,jk)*pn2_ad(ji,jj,jk) |
---|
| 1915 | pts_ad(ji,jj,jk,jp_tem ) = pts_ad(ji,jj,jk,jp_tem ) - zalbet*zbeta*zgde3w*tmask(ji,jj,jk)*pn2_ad(ji,jj,jk) |
---|
[3627] | 1916 | zalbetad = zalbetad + zbeta*zgde3w*tmask(ji,jj,jk) & |
---|
| 1917 | & *( pts (ji,jj,jk-1,jp_tem) - pts (ji,jj,jk,jp_tem) ) * pn2_ad(ji,jj,jk) |
---|
[3611] | 1918 | pts_ad(ji,jj,jk-1,jp_sal) = pts_ad(ji,jj,jk-1,jp_sal) - zbeta*tmask(ji,jj,jk)*zgde3w*pn2_ad(ji,jj,jk) |
---|
| 1919 | pts_ad(ji,jj,jk,jp_sal ) = pts_ad(ji,jj,jk,jp_sal ) + zbeta*tmask(ji,jj,jk)*zgde3w*pn2_ad(ji,jj,jk) |
---|
| 1920 | zbetaad = zbetaad & |
---|
| 1921 | & + zgde3w *tmask(ji,jj,jk)* ( zalbet * ( pts (ji,jj,jk-1,jp_tem) - pts (ji,jj,jk,jp_tem) ) & |
---|
| 1922 | & - ( pts (ji,jj,jk-1,jp_sal) - pts (ji,jj,jk,jp_sal) ) )*pn2_ad(ji,jj,jk) |
---|
| 1923 | |
---|
| 1924 | pn2_ad(ji,jj,jk) = 0.0_wp |
---|
| 1925 | |
---|
| 1926 | ztad = ztad + ( ( -3.*0.415613e-09_wp * zt & |
---|
| 1927 | & +2.*0.555579e-07_wp ) * zt & |
---|
| 1928 | & - 0.301985e-05_wp & |
---|
| 1929 | & + 0.788212e-08_wp * zs & |
---|
| 1930 | & + ( -2.*0.213127e-11_wp * zt & |
---|
| 1931 | & - 0.175379e-14_wp * zh & |
---|
| 1932 | & + 0.192867e-09_wp ) * zh ) *zbetaad |
---|
| 1933 | |
---|
| 1934 | zsad = zsad + ( 2.*0.515032e-08_wp * zs & |
---|
| 1935 | & + 0.788212e-08_wp * zt & |
---|
| 1936 | & - 0.356603e-06_wp & |
---|
| 1937 | & + ( - 0.602281e-15_wp * zh & |
---|
| 1938 | & + 0.408195e-10_wp ) * zh ) * zbetaad |
---|
| 1939 | |
---|
| 1940 | zbetaad = 0.0_wp |
---|
| 1941 | |
---|
| 1942 | ztad = ztad + ( ( ( -4.*0.255019e-07_wp * zt &! ratio alpha/beta |
---|
| 1943 | & +3.*0.298357e-05_wp ) * zt & |
---|
| 1944 | & -2.*0.203814e-03_wp ) * zt & |
---|
| 1945 | & + 0.170907e-01_wp & |
---|
| 1946 | & - 0.846960e-04_wp * zs & |
---|
| 1947 | & - ( 0.933746e-06_wp & |
---|
| 1948 | & - ( 2.*0.791325e-08_wp & |
---|
| 1949 | & +2.*0.512857e-12_wp * zh ) * zt ) * zh & |
---|
| 1950 | & ) *zalbetad |
---|
| 1951 | |
---|
| 1952 | zsad = zsad + ( - 2.*0.678662e-05_wp * zs & |
---|
| 1953 | & - 0.846960e-04_wp * zt & |
---|
| 1954 | & + 0.378110e-02_wp & |
---|
| 1955 | & + ( - 0.164759e-06_wp & |
---|
| 1956 | & - 0.251520e-11_wp * zh ) * zh & |
---|
| 1957 | & ) *zalbetad |
---|
| 1958 | |
---|
| 1959 | zalbetad = 0.0_wp |
---|
| 1960 | |
---|
| 1961 | |
---|
| 1962 | pts_ad(ji,jj,jk,jp_sal) = pts_ad(ji,jj,jk,jp_sal) + 0.5 * zsad |
---|
| 1963 | pts_ad(ji,jj,jk-1,jp_sal) = pts_ad(ji,jj,jk-1,jp_sal) + 0.5 * zsad |
---|
| 1964 | zsad = 0.0_wp |
---|
| 1965 | |
---|
| 1966 | pts_ad(ji,jj,jk,jp_tem) = pts_ad(ji,jj,jk,jp_tem) + 0.5 * ztad |
---|
| 1967 | pts_ad(ji,jj,jk-1,jp_tem) = pts_ad(ji,jj,jk-1,jp_tem) + 0.5 * ztad |
---|
| 1968 | ztad = 0.0_wp |
---|
| 1969 | |
---|
| 1970 | END DO |
---|
| 1971 | END DO |
---|
| 1972 | END DO |
---|
| 1973 | ! |
---|
| 1974 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
---|
| 1975 | DO jk = jpkm1, 2, -1 |
---|
| 1976 | pts_ad(:,:,jk-1,jp_tem) = pts_ad(:,:,jk-1,jp_tem) + rn_alpha * pn2_ad(:,:,jk) & |
---|
| 1977 | & * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 1978 | pts_ad(:,:,jk,jp_tem ) = pts_ad(:,:,jk,jp_tem ) - rn_alpha * pn2_ad(:,:,jk) & |
---|
| 1979 | & * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 1980 | pn2_ad(:,:,jk) = 0.0_wp |
---|
| 1981 | END DO |
---|
| 1982 | ! |
---|
| 1983 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
---|
| 1984 | #if defined key_zdfddm |
---|
| 1985 | DO jk = jpkm1, 2, -1 |
---|
| 1986 | DO jj = jpj, 1, -1 |
---|
| 1987 | DO ji = jpi, 1, -1 |
---|
| 1988 | zds = ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) |
---|
| 1989 | IF ( ABS( zds) <= 1.e-20 ) THEN |
---|
| 1990 | zds = 1.e-20 |
---|
| 1991 | zdsad = 0.0_wp |
---|
| 1992 | ELSE |
---|
| 1993 | zdsad = zdsad - rrau_ad(ji,jj,jk) * ralpbet & |
---|
| 1994 | & * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds**2 |
---|
| 1995 | ENDIF |
---|
| 1996 | rrau(ji,jj,jk) = ralpbet * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) / zds |
---|
| 1997 | pts_ad(ji,jj,jk-1,jp_tem) = pts_ad(ji,jj,jk-1,jp_tem) & |
---|
| 1998 | & + rrau_ad(ji,jj,jk) * ralpbet / zds |
---|
| 1999 | pts_ad(ji,jj,jk,jp_tem ) = pts_ad(ji,jj,jk,jp_tem ) & |
---|
| 2000 | & - rrau_ad(ji,jj,jk) * ralpbet / zds |
---|
| 2001 | rrau_ad(ji,jj,jk) = 0._wp |
---|
| 2002 | |
---|
| 2003 | pts_ad(ji,jj,jk-1,jp_sal) = pts_ad(ji,jj,jk-1,jp_sal) + zdsad |
---|
| 2004 | pts_ad(ji,jj,jk,jp_sal ) = pts_ad(ji,jj,jk,jp_sal ) - zdsad |
---|
| 2005 | zdsad = 0._wp |
---|
| 2006 | END DO |
---|
| 2007 | END DO |
---|
| 2008 | END DO |
---|
| 2009 | #endif |
---|
| 2010 | DO jk = jpkm1, 2, -1 |
---|
| 2011 | pts_ad(:,:,jk-1,jp_tem) = pts_ad(:,:,jk-1,jp_tem) + rn_alpha * pn2_ad(:,:,jk) & |
---|
| 2012 | & * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 2013 | pts_ad(:,:,jk,jp_tem ) = pts_ad(:,:,jk,jp_tem ) - rn_alpha * pn2_ad(:,:,jk) & |
---|
| 2014 | & * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 2015 | pts_ad(:,:,jk-1,jp_sal) = pts_ad(:,:,jk-1,jp_sal) - rn_beta * pn2_ad(:,:,jk) & |
---|
| 2016 | & * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 2017 | pts_ad(:,:,jk,jp_sal ) = pts_ad(:,:,jk,jp_sal ) + rn_beta * pn2_ad(:,:,jk) & |
---|
| 2018 | & * grav / fse3w(:,:,jk) * tmask(:,:,jk) |
---|
| 2019 | pn2_ad(:,:,jk) = 0.0_wp |
---|
| 2020 | END DO |
---|
| 2021 | END SELECT |
---|
| 2022 | END SUBROUTINE eos_bn2_adj |
---|
| 2023 | |
---|
| 2024 | SUBROUTINE eos_alpbet_tan( pts, pts_tl, palpbet_tl, beta0_tl ) |
---|
| 2025 | !!---------------------------------------------------------------------- |
---|
| 2026 | !! *** ROUTINE eos_alpbet_tan *** |
---|
| 2027 | !! |
---|
| 2028 | !! ** Purpose of the direct routine : |
---|
| 2029 | !! Calculates the in situ thermal/haline expansion ratio at T-points |
---|
| 2030 | !! |
---|
| 2031 | !! ** Method of the direct routine : |
---|
| 2032 | !! calculates alpha / beta ratio at T-points |
---|
| 2033 | !! * nn_eos = 0 : UNESCO sea water properties |
---|
| 2034 | !! The alpha/beta ratio is returned as 3-D array palpbet using the polynomial |
---|
| 2035 | !! polynomial expression of McDougall (1987). |
---|
| 2036 | !! Scalar beta0 is returned = 1. |
---|
| 2037 | !! * nn_eos = 1 : linear equation of state (temperature only) |
---|
| 2038 | !! The ratio is undefined, so we return alpha as palpbet |
---|
| 2039 | !! Scalar beta0 is returned = 0. |
---|
| 2040 | !! * nn_eos = 2 : linear equation of state (temperature & salinity) |
---|
| 2041 | !! The alpha/beta ratio is returned as ralpbet |
---|
| 2042 | !! Scalar beta0 is returned = 1. |
---|
| 2043 | !! |
---|
| 2044 | !! ** Action : - palpbet : thermal/haline expansion ratio at T-points |
---|
| 2045 | !! : beta0 : 1. or 0. |
---|
| 2046 | !!---------------------------------------------------------------------- |
---|
| 2047 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts_tl, & ! linear tangent of pot. temperature & salinity |
---|
| 2048 | & pts ! pot. temperature & salinity |
---|
| 2049 | REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: palpbet_tl ! thermal/haline expansion ratio |
---|
| 2050 | REAL(wp), INTENT( out) :: beta0_tl ! set = 1 except with case 1 eos, rho=rho(T) |
---|
| 2051 | !! |
---|
| 2052 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 2053 | REAL(wp) :: zt, zs, zh, & ! local scalars |
---|
| 2054 | & zttl, zstl |
---|
| 2055 | !!---------------------------------------------------------------------- |
---|
| 2056 | ! |
---|
| 2057 | IF( nn_timing == 1 ) CALL timing_start('eos_alpbet_tan') |
---|
| 2058 | ! |
---|
| 2059 | SELECT CASE ( nn_eos ) |
---|
| 2060 | ! |
---|
| 2061 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
| 2062 | DO jk = 1, jpk |
---|
| 2063 | DO jj = 1, jpj |
---|
| 2064 | DO ji = 1, jpi |
---|
| 2065 | zt = pts(ji,jj,jk,jp_tem) ! potential temperature |
---|
| 2066 | zs = pts(ji,jj,jk,jp_sal) - 35._wp ! salinity anomaly (s-35) |
---|
| 2067 | zh = fsdept(ji,jj,jk) ! depth in meters |
---|
| 2068 | !! Tangent part |
---|
| 2069 | zttl = pts_tl(ji,jj,jk,jp_tem) ! potential temperature |
---|
| 2070 | zstl = pts_tl(ji,jj,jk,jp_sal) ! salinity anomaly (s-35) |
---|
| 2071 | palpbet_tl(ji,jj,jk) = & |
---|
| 2072 | & ( ( ( ( - 4. * 0.255019e-07_wp * zt & |
---|
| 2073 | & + 3. * 0.298357e-05_wp ) * zt & |
---|
| 2074 | & - 2. * 0.203814e-03_wp ) * zt & |
---|
| 2075 | & + 0.170907e-01_wp * zt ) & |
---|
| 2076 | & - 0.846960e-04_wp * zs & |
---|
| 2077 | & + ( ( 2. * 0.512857e-12_wp * zt ) * zh & |
---|
| 2078 | & + ( 2. * 0.791325e-08_wp * zt & |
---|
| 2079 | & - 0.933746e-06_wp ) ) * zh ) * zttl & |
---|
| 2080 | & + ( ( - 2. * 0.678662e-05_wp * zs & |
---|
| 2081 | & - 0.846960e-04_wp * zt & |
---|
| 2082 | & + 0.378110e-02_wp ) & |
---|
| 2083 | & + ( - 0.251520e-11_wp * zh & |
---|
| 2084 | & - 0.164759e-06_wp ) * zh ) * zstl |
---|
| 2085 | END DO |
---|
| 2086 | END DO |
---|
| 2087 | END DO |
---|
| 2088 | beta0_tl = 0._wp |
---|
| 2089 | ! |
---|
| 2090 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
---|
| 2091 | palpbet_tl(:,:,:) = 0._wp |
---|
| 2092 | beta0_tl = 0._wp |
---|
| 2093 | ! |
---|
| 2094 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
---|
| 2095 | palpbet_tl(:,:,:) = 0._wp |
---|
| 2096 | beta0_tl = 0._wp |
---|
| 2097 | ! |
---|
| 2098 | CASE DEFAULT |
---|
| 2099 | IF(lwp) WRITE(numout,cform_err) |
---|
| 2100 | IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos |
---|
| 2101 | nstop = nstop + 1 |
---|
| 2102 | ! |
---|
| 2103 | END SELECT |
---|
| 2104 | ! |
---|
| 2105 | IF( nn_timing == 1 ) CALL timing_stop('eos_alpbet_tan') |
---|
| 2106 | ! |
---|
| 2107 | END SUBROUTINE eos_alpbet_tan |
---|
| 2108 | |
---|
| 2109 | SUBROUTINE eos_alpbet_adj( pts, pts_ad, palpbet_ad, beta0_ad ) |
---|
| 2110 | !!---------------------------------------------------------------------- |
---|
| 2111 | !! *** ROUTINE eos_alpbet_adj *** |
---|
| 2112 | !! |
---|
| 2113 | !! ** Purpose of the direct routine : |
---|
| 2114 | !! Calculates the in situ thermal/haline expansion ratio at T-points |
---|
| 2115 | !! |
---|
| 2116 | !! ** Method of the direct routine : |
---|
| 2117 | !! calculates alpha / beta ratio at T-points |
---|
| 2118 | !! * nn_eos = 0 : UNESCO sea water properties |
---|
| 2119 | !! The alpha/beta ratio is returned as 3-D array palpbet using the polynomial |
---|
| 2120 | !! polynomial expression of McDougall (1987). |
---|
| 2121 | !! Scalar beta0 is returned = 1. |
---|
| 2122 | !! * nn_eos = 1 : linear equation of state (temperature only) |
---|
| 2123 | !! The ratio is undefined, so we return alpha as palpbet |
---|
| 2124 | !! Scalar beta0 is returned = 0. |
---|
| 2125 | !! * nn_eos = 2 : linear equation of state (temperature & salinity) |
---|
| 2126 | !! The alpha/beta ratio is returned as ralpbet |
---|
| 2127 | !! Scalar beta0 is returned = 1. |
---|
| 2128 | !! |
---|
| 2129 | !! ** Action : - palpbet : thermal/haline expansion ratio at T-points |
---|
| 2130 | !! : beta0 : 1. or 0. |
---|
| 2131 | !!---------------------------------------------------------------------- |
---|
| 2132 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(inout) :: pts_ad ! linear tangent of pot. temperature & salinity |
---|
| 2133 | REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in) :: pts ! pot. temperature & salinity |
---|
| 2134 | REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT(inout) :: palpbet_ad ! thermal/haline expansion ratio |
---|
| 2135 | REAL(wp), INTENT(inout) :: beta0_ad ! set = 1 except with case 1 eos, rho=rho(T) |
---|
| 2136 | !! |
---|
| 2137 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 2138 | REAL(wp) :: zt, zs, zh, & ! local scalars |
---|
| 2139 | & ztad, zsad |
---|
| 2140 | !!---------------------------------------------------------------------- |
---|
| 2141 | ! |
---|
| 2142 | ztad = 0.0_wp |
---|
| 2143 | zsad = 0.0_wp |
---|
| 2144 | IF( nn_timing == 1 ) CALL timing_start('eos_alpbet_adj') |
---|
| 2145 | ! |
---|
| 2146 | SELECT CASE ( nn_eos ) |
---|
| 2147 | ! |
---|
| 2148 | CASE ( 0 ) ! Jackett and McDougall (1994) formulation |
---|
| 2149 | DO jk = jpk, 1, -1 |
---|
| 2150 | DO jj = jpj, 1, -1 |
---|
| 2151 | DO ji = jpi, 1, -1 |
---|
| 2152 | zt = pts(ji,jj,jk,jp_tem) ! potential temperature |
---|
| 2153 | zs = pts(ji,jj,jk,jp_sal) - 35._wp ! salinity anomaly (s-35) |
---|
| 2154 | zh = fsdept(ji,jj,jk) ! depth in meters |
---|
| 2155 | !! Adjoint part |
---|
| 2156 | ztad = ztad + ( ( ( ( - 4. * 0.255019e-07_wp * zt & |
---|
| 2157 | & + 3. * 0.298357e-05_wp ) * zt & |
---|
| 2158 | & - 2. * 0.203814e-03_wp ) * zt & |
---|
| 2159 | & + 0.170907e-01_wp * zt ) & |
---|
| 2160 | & - 0.846960e-04_wp * zs & |
---|
| 2161 | & + ( ( 2. * 0.512857e-12_wp * zt ) * zh & |
---|
| 2162 | & + ( 2. * 0.791325e-08_wp * zt & |
---|
| 2163 | & - 0.933746e-06_wp ) ) * zh ) * palpbet_ad(ji,jj,jk) |
---|
| 2164 | zsad = zsad + ( ( - 2. * 0.678662e-05_wp * zs & |
---|
| 2165 | & - 0.846960e-04_wp * zt & |
---|
| 2166 | & + 0.378110e-02_wp ) & |
---|
| 2167 | & + ( - 0.251520e-11_wp * zh & |
---|
| 2168 | & - 0.164759e-06_wp ) * zh ) * palpbet_ad(ji,jj,jk) |
---|
| 2169 | palpbet_ad(ji,jj,jk) = 0.0_wp |
---|
| 2170 | pts_ad(ji,jj,jk,jp_tem) = pts_ad(ji,jj,jk,jp_tem) + ztad |
---|
| 2171 | pts_ad(ji,jj,jk,jp_sal) = pts_ad(ji,jj,jk,jp_sal) + zsad |
---|
| 2172 | ztad = 0.0_wp |
---|
| 2173 | zsad = 0.0_wp |
---|
| 2174 | END DO |
---|
| 2175 | END DO |
---|
| 2176 | END DO |
---|
| 2177 | beta0_ad = 0._wp |
---|
| 2178 | ! |
---|
| 2179 | CASE ( 1 ) !== Linear formulation = F( temperature ) ==! |
---|
| 2180 | palpbet_ad(:,:,:) = 0._wp |
---|
| 2181 | beta0_ad = 0._wp |
---|
| 2182 | ! |
---|
| 2183 | CASE ( 2 ) !== Linear formulation = F( temperature , salinity ) ==! |
---|
| 2184 | palpbet_ad(:,:,:) = 0._wp |
---|
| 2185 | beta0_ad = 0._wp |
---|
| 2186 | ! |
---|
| 2187 | CASE DEFAULT |
---|
| 2188 | IF(lwp) WRITE(numout,cform_err) |
---|
| 2189 | IF(lwp) WRITE(numout,*) ' bad flag value for nn_eos = ', nn_eos |
---|
| 2190 | nstop = nstop + 1 |
---|
| 2191 | ! |
---|
| 2192 | END SELECT |
---|
| 2193 | ! |
---|
| 2194 | IF( nn_timing == 1 ) CALL timing_stop('eos_alpbet_adj') |
---|
| 2195 | ! |
---|
| 2196 | END SUBROUTINE eos_alpbet_adj |
---|
| 2197 | |
---|
| 2198 | #if defined key_tam |
---|
| 2199 | SUBROUTINE eos_insitu_adj_tst( kumadt ) |
---|
| 2200 | !!----------------------------------------------------------------------- |
---|
| 2201 | !! |
---|
| 2202 | !! *** ROUTINE eos_adj_tst *** |
---|
| 2203 | !! |
---|
| 2204 | !! ** Purpose : Test the adjoint routine. |
---|
| 2205 | !! |
---|
| 2206 | !! ** Method : Verify the scalar product |
---|
| 2207 | !! |
---|
| 2208 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
| 2209 | !! |
---|
| 2210 | !! where L = tangent routine |
---|
| 2211 | !! L^T = adjoint routine |
---|
| 2212 | !! W = diagonal matrix of scale factors |
---|
| 2213 | !! dx = input perturbation (random field) |
---|
| 2214 | !! dy = L dx |
---|
| 2215 | !! |
---|
| 2216 | !! |
---|
| 2217 | !! History : |
---|
| 2218 | !! ! 08-07 (A. Vidard) |
---|
| 2219 | !!----------------------------------------------------------------------- |
---|
| 2220 | !! * Modules used |
---|
| 2221 | |
---|
| 2222 | !! * Arguments |
---|
| 2223 | INTEGER, INTENT(IN) :: & |
---|
| 2224 | & kumadt ! Output unit |
---|
| 2225 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2226 | zts ! potential temperature |
---|
| 2227 | ! salinity |
---|
| 2228 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2229 | & zts_adout ! potential temperature |
---|
| 2230 | ! salinity |
---|
| 2231 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2232 | & zrd_adin ! anomaly density |
---|
| 2233 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2234 | & zts_tlin ! potential temperature |
---|
| 2235 | ! salinity |
---|
| 2236 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2237 | & znts ! potential temperature |
---|
| 2238 | ! salinity |
---|
| 2239 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2240 | & zrd_tlout ! anomaly density |
---|
| 2241 | REAL(KIND=wp) :: & |
---|
| 2242 | & zsp1, & ! scalar product involving the tangent routine |
---|
| 2243 | & zsp2 ! scalar product involving the adjoint routine |
---|
| 2244 | INTEGER :: & |
---|
| 2245 | & ji, & |
---|
| 2246 | & jj, & |
---|
| 2247 | & jk, & |
---|
| 2248 | & jn, & |
---|
| 2249 | & jeos |
---|
| 2250 | CHARACTER(LEN=14) :: cl_name |
---|
| 2251 | ALLOCATE( & |
---|
| 2252 | & zts( jpi, jpj, jpk, jpts ), & |
---|
| 2253 | & znts( jpi, jpj, jpk, jpts ), & |
---|
| 2254 | & zts_adout( jpi, jpj, jpk,jpts ), & |
---|
| 2255 | & zrd_adin( jpi, jpj, jpk ), & |
---|
| 2256 | & zts_tlin( jpi, jpj, jpk,jpts ), & |
---|
| 2257 | & zrd_tlout(jpi, jpj, jpk ) ) |
---|
| 2258 | ! Initialize the reference state |
---|
| 2259 | zts = tsn |
---|
| 2260 | ! store initial nn_eos |
---|
| 2261 | jeos = nn_eos |
---|
| 2262 | DO jn = 0, 2 |
---|
| 2263 | nn_eos = jn |
---|
| 2264 | !============================================================= |
---|
| 2265 | ! 1) dx = ( T ) and dy = ( T ) |
---|
| 2266 | !============================================================= |
---|
| 2267 | |
---|
| 2268 | !-------------------------------------------------------------------- |
---|
| 2269 | ! Reset the tangent and adjoint variables |
---|
| 2270 | !-------------------------------------------------------------------- |
---|
| 2271 | zts_tlin(:,:,:,:) = 0.0_wp |
---|
| 2272 | zrd_tlout(:,:,:) = 0.0_wp |
---|
| 2273 | zts_adout(:,:,:,:) = 0.0_wp |
---|
| 2274 | zrd_adin(:,:,:) = 0.0_wp |
---|
| 2275 | |
---|
| 2276 | !-------------------------------------------------------------------- |
---|
| 2277 | ! Initialize the tangent input with random noise: dx |
---|
| 2278 | !-------------------------------------------------------------------- |
---|
| 2279 | CALL grid_random( znts(:,:,:,jp_tem), 'T', 0.0_wp, stdt ) |
---|
| 2280 | CALL grid_random( znts(:,:,:,jp_sal), 'T', 0.0_wp, stds ) |
---|
| 2281 | |
---|
| 2282 | DO jk = 1, jpk |
---|
| 2283 | DO jj = nldj, nlej |
---|
| 2284 | DO ji = nldi, nlei |
---|
| 2285 | zts_tlin(ji,jj,jk,jp_tem) = znts(ji,jj,jk,jp_tem) |
---|
| 2286 | zts_tlin(ji,jj,jk,jp_sal) = znts(ji,jj,jk,jp_sal) |
---|
| 2287 | END DO |
---|
| 2288 | END DO |
---|
| 2289 | END DO |
---|
| 2290 | CALL eos_insitu_tan(zts, zts_tlin, zrd_tlout) |
---|
| 2291 | |
---|
| 2292 | DO jk = 1, jpk |
---|
| 2293 | DO jj = nldj, nlej |
---|
| 2294 | DO ji = nldi, nlei |
---|
| 2295 | zrd_adin(ji,jj,jk) = zrd_tlout(ji,jj,jk) & |
---|
| 2296 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk)& |
---|
| 2297 | & * tmask(ji,jj,jk) |
---|
| 2298 | END DO |
---|
| 2299 | END DO |
---|
| 2300 | END DO |
---|
| 2301 | |
---|
| 2302 | !-------------------------------------------------------------------- |
---|
| 2303 | ! Compute the scalar product: ( L dx )^T W dy |
---|
| 2304 | !-------------------------------------------------------------------- |
---|
| 2305 | |
---|
| 2306 | zsp1 = DOT_PRODUCT( zrd_tlout, zrd_adin ) |
---|
| 2307 | |
---|
| 2308 | !-------------------------------------------------------------------- |
---|
| 2309 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
| 2310 | !-------------------------------------------------------------------- |
---|
| 2311 | CALL eos_insitu_adj(zts, zts_adout, zrd_adin) |
---|
| 2312 | zsp2 = DOT_PRODUCT( zts_tlin(:,:,:,jp_tem), zts_adout(:,:,:,jp_tem) ) + & |
---|
| 2313 | & DOT_PRODUCT( zts_tlin(:,:,:,jp_sal), zts_adout(:,:,:,jp_sal) ) |
---|
| 2314 | |
---|
| 2315 | ! Compare the scalar products |
---|
| 2316 | |
---|
| 2317 | ! Compare the scalar products |
---|
| 2318 | ! 14 char:'12345678901234' |
---|
| 2319 | SELECT CASE( jn ) |
---|
| 2320 | CASE (0) ; cl_name = 'eos_adj ins T1' |
---|
| 2321 | CASE (1) ; cl_name = 'eos_adj ins T2' |
---|
| 2322 | CASE (2) ; cl_name = 'eos_adj ins T3' |
---|
| 2323 | END SELECT |
---|
| 2324 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
| 2325 | ENDDO |
---|
| 2326 | ! restore initial nn_eos |
---|
| 2327 | nn_eos = jeos |
---|
| 2328 | |
---|
| 2329 | ! Deallocate memory |
---|
| 2330 | |
---|
| 2331 | DEALLOCATE( & |
---|
| 2332 | & zts, & |
---|
| 2333 | & zts_adout, & |
---|
| 2334 | & zrd_adin, & |
---|
| 2335 | & zts_tlin, & |
---|
| 2336 | & zrd_tlout, & |
---|
| 2337 | & znts & |
---|
| 2338 | & ) |
---|
| 2339 | END SUBROUTINE eos_insitu_adj_tst |
---|
| 2340 | |
---|
| 2341 | SUBROUTINE eos_insitu_pot_adj_tst( kumadt ) |
---|
| 2342 | !!----------------------------------------------------------------------- |
---|
| 2343 | !! |
---|
| 2344 | !! *** ROUTINE eos_adj_tst *** |
---|
| 2345 | !! |
---|
| 2346 | !! ** Purpose : Test the adjoint routine. |
---|
| 2347 | !! |
---|
| 2348 | !! ** Method : Verify the scalar product |
---|
| 2349 | !! |
---|
| 2350 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
| 2351 | !! |
---|
| 2352 | !! where L = tangent routine |
---|
| 2353 | !! L^T = adjoint routine |
---|
| 2354 | !! W = diagonal matrix of scale factors |
---|
| 2355 | !! dx = input perturbation (random field) |
---|
| 2356 | !! dy = L dx |
---|
| 2357 | !! |
---|
| 2358 | !! ** Action : Separate tests are applied for the following dx and dy: |
---|
| 2359 | !! |
---|
| 2360 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
---|
| 2361 | !! |
---|
| 2362 | !! History : |
---|
| 2363 | !! ! 08-07 (A. Vidard) |
---|
| 2364 | !!----------------------------------------------------------------------- |
---|
| 2365 | !! * Modules used |
---|
| 2366 | |
---|
| 2367 | !! * Arguments |
---|
| 2368 | INTEGER, INTENT(IN) :: & |
---|
| 2369 | & kumadt ! Output unit |
---|
| 2370 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2371 | zts ! potential temperature |
---|
| 2372 | ! salinity |
---|
| 2373 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2374 | & zts_adout ! potential temperature |
---|
| 2375 | ! salinity |
---|
| 2376 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2377 | & zrd_adin ! anomaly density |
---|
| 2378 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2379 | & zrhop_adin ! volume mass |
---|
| 2380 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2381 | & zts_tlin ! potential temperature |
---|
| 2382 | ! salinity |
---|
| 2383 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2384 | & znts ! potential temperature |
---|
| 2385 | ! salinity |
---|
| 2386 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2387 | & zrd_tlout ! anomaly density |
---|
| 2388 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2389 | & zrhop_tlout ! volume mass |
---|
| 2390 | REAL(KIND=wp) :: & |
---|
| 2391 | & zsp1, & ! scalar product involving the tangent routine |
---|
| 2392 | & zsp2 ! scalar product involving the adjoint routine |
---|
| 2393 | INTEGER :: & |
---|
| 2394 | & ji, & |
---|
| 2395 | & jj, & |
---|
| 2396 | & jk, & |
---|
| 2397 | & jn, & |
---|
| 2398 | & jeos |
---|
| 2399 | CHARACTER(LEN=14) :: cl_name |
---|
| 2400 | |
---|
| 2401 | ! Allocate memory |
---|
| 2402 | ALLOCATE( & |
---|
| 2403 | & zts( jpi, jpj, jpk, jpts ), & |
---|
| 2404 | & zts_adout( jpi, jpj, jpk, jpts ), & |
---|
| 2405 | & zrhop_adin( jpi, jpj, jpk ), & |
---|
| 2406 | & zrd_adin( jpi, jpj, jpk ), & |
---|
| 2407 | & zts_tlin( jpi, jpj, jpk, jpts ), & |
---|
| 2408 | & znts( jpi, jpj, jpk, jpts ), & |
---|
| 2409 | & zrd_tlout(jpi, jpj, jpk ), & |
---|
| 2410 | & zrhop_tlout(jpi, jpj, jpk ) ) |
---|
| 2411 | |
---|
| 2412 | ! Initialize random field standard deviationsthe reference state |
---|
| 2413 | zts = tsn |
---|
| 2414 | |
---|
| 2415 | ! store initial nn_eos |
---|
| 2416 | jeos = nn_eos |
---|
| 2417 | DO jn = 0, 2 |
---|
| 2418 | nn_eos = jn |
---|
| 2419 | !============================================= |
---|
| 2420 | ! testing of eos_insitu_pot |
---|
| 2421 | !============================================= |
---|
| 2422 | |
---|
| 2423 | !============================================================= |
---|
| 2424 | ! 1) dx = ( T ) and dy = ( T ) |
---|
| 2425 | !============================================================= |
---|
| 2426 | |
---|
| 2427 | !-------------------------------------------------------------------- |
---|
| 2428 | ! Reset the tangent and adjoint variables |
---|
| 2429 | !-------------------------------------------------------------------- |
---|
| 2430 | zts_tlin(:,:,:,:) = 0.0_wp |
---|
| 2431 | zrd_tlout(:,:,:) = 0.0_wp |
---|
| 2432 | zrhop_tlout(:,:,:) = 0.0_wp |
---|
| 2433 | zts_adout(:,:,:,:) = 0.0_wp |
---|
| 2434 | zrhop_adin(:,:,:) = 0.0_wp |
---|
| 2435 | zrd_adin(:,:,:) = 0.0_wp |
---|
| 2436 | |
---|
| 2437 | !-------------------------------------------------------------------- |
---|
| 2438 | ! Initialize the tangent input with random noise: dx |
---|
| 2439 | !-------------------------------------------------------------------- |
---|
| 2440 | CALL grid_random( znts(:,:,:,jp_tem), 'T', 0.0_wp, stdt ) |
---|
| 2441 | CALL grid_random( znts(:,:,:,jp_sal), 'T', 0.0_wp, stds ) |
---|
| 2442 | DO jk = 1, jpk |
---|
| 2443 | DO jj = nldj, nlej |
---|
| 2444 | DO ji = nldi, nlei |
---|
| 2445 | zts_tlin(ji,jj,jk,:) = znts(ji,jj,jk,:) |
---|
| 2446 | END DO |
---|
| 2447 | END DO |
---|
| 2448 | END DO |
---|
| 2449 | !-------------------------------------------------------------------- |
---|
| 2450 | ! Call the tangent routine: dy = L dx |
---|
| 2451 | !-------------------------------------------------------------------- |
---|
| 2452 | |
---|
| 2453 | call eos_insitu_pot_tan ( zts, zts_tlin, zrd_tlout, zrhop_tlout ) |
---|
| 2454 | |
---|
| 2455 | !-------------------------------------------------------------------- |
---|
| 2456 | ! Initialize the adjoint variables: dy^* = W dy |
---|
| 2457 | !-------------------------------------------------------------------- |
---|
| 2458 | DO jk = 1, jpk |
---|
| 2459 | DO jj = nldj, nlej |
---|
| 2460 | DO ji = nldi, nlei |
---|
| 2461 | zrd_adin(ji,jj,jk) = zrd_tlout(ji,jj,jk) & |
---|
| 2462 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk)& |
---|
| 2463 | & * tmask(ji,jj,jk) |
---|
| 2464 | zrhop_adin(ji,jj,jk) = zrhop_tlout(ji,jj,jk) & |
---|
| 2465 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk)& |
---|
| 2466 | & * tmask(ji,jj,jk) |
---|
| 2467 | END DO |
---|
| 2468 | END DO |
---|
| 2469 | END DO |
---|
| 2470 | |
---|
| 2471 | !-------------------------------------------------------------------- |
---|
| 2472 | ! Compute the scalar product: ( L dx )^T W dy |
---|
| 2473 | !-------------------------------------------------------------------- |
---|
| 2474 | |
---|
| 2475 | zsp1 = DOT_PRODUCT( zrd_tlout , zrd_adin ) & |
---|
| 2476 | & + DOT_PRODUCT( zrhop_tlout, zrhop_adin ) |
---|
| 2477 | !-------------------------------------------------------------------- |
---|
| 2478 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
| 2479 | !-------------------------------------------------------------------- |
---|
| 2480 | |
---|
| 2481 | CALL eos_insitu_pot_adj( zts, zts_adout, zrd_adin, zrhop_adin ) |
---|
| 2482 | !-------------------------------------------------------------------- |
---|
| 2483 | ! Compute the scalar product: dx^T L^T W dy |
---|
| 2484 | !-------------------------------------------------------------------- |
---|
| 2485 | |
---|
| 2486 | zsp2 = DOT_PRODUCT( zts_tlin(:,:,:,jp_tem), zts_adout(:,:,:,jp_tem) ) + & |
---|
| 2487 | & DOT_PRODUCT( zts_tlin(:,:,:,jp_sal), zts_adout(:,:,:,jp_sal) ) |
---|
| 2488 | ! Compare the scalar products |
---|
| 2489 | |
---|
| 2490 | ! 14 char:'12345678901234' |
---|
| 2491 | SELECT CASE( jn ) |
---|
| 2492 | CASE (0) ; cl_name = 'eos_adj pot T1' |
---|
| 2493 | CASE (1) ; cl_name = 'eos_adj pot T2' |
---|
| 2494 | CASE (2) ; cl_name = 'eos_adj pot T3' |
---|
| 2495 | END SELECT |
---|
| 2496 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
| 2497 | |
---|
| 2498 | ENDDO |
---|
| 2499 | |
---|
| 2500 | ! restore initial nn_eos |
---|
| 2501 | nn_eos = jeos |
---|
| 2502 | |
---|
| 2503 | ! Deallocate memory |
---|
| 2504 | DEALLOCATE( & |
---|
| 2505 | & zts, & |
---|
| 2506 | & zts_adout, & |
---|
| 2507 | & zrd_adin, & |
---|
| 2508 | & zrhop_adin, & |
---|
| 2509 | & zts_tlin, & |
---|
| 2510 | & zrd_tlout, & |
---|
| 2511 | & zrhop_tlout,& |
---|
| 2512 | & znts ) |
---|
| 2513 | END SUBROUTINE eos_insitu_pot_adj_tst |
---|
| 2514 | |
---|
| 2515 | SUBROUTINE eos_alpbet_adj_tst(kumadt) |
---|
| 2516 | !!----------------------------------------------------------------------- |
---|
| 2517 | !! |
---|
| 2518 | !! *** ROUTINE eos_adj_tst *** |
---|
| 2519 | !! |
---|
| 2520 | !! ** Purpose : Test the adjoint routine. |
---|
| 2521 | !! |
---|
| 2522 | !! ** Method : Verify the scalar product |
---|
| 2523 | !! |
---|
| 2524 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
| 2525 | !! |
---|
| 2526 | !! where L = tangent routine |
---|
| 2527 | !! L^T = adjoint routine |
---|
| 2528 | !! W = diagonal matrix of scale factors |
---|
| 2529 | !! dx = input perturbation (random field) |
---|
| 2530 | !! dy = L dx |
---|
| 2531 | !! |
---|
| 2532 | !! ** Action : Separate tests are applied for the following dx and dy: |
---|
| 2533 | !! |
---|
| 2534 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
---|
| 2535 | !! |
---|
| 2536 | !! History : |
---|
| 2537 | !! ! 05-12 (P.-A. Bouttier) |
---|
| 2538 | !!----------------------------------------------------------------------- |
---|
| 2539 | !! * Modules used |
---|
| 2540 | |
---|
| 2541 | !! * Arguments |
---|
| 2542 | INTEGER, INTENT(IN) :: & |
---|
| 2543 | & kumadt ! Output unit |
---|
| 2544 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2545 | & zts ! potential temperature |
---|
| 2546 | ! salinity |
---|
| 2547 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2548 | & zts_adout ! potential temperature |
---|
| 2549 | ! salinity |
---|
| 2550 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2551 | & zpalpbet_adin |
---|
| 2552 | REAL(wp) :: & |
---|
| 2553 | & zbeta0_adin |
---|
| 2554 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2555 | & zts_tlin ! potential temperature |
---|
| 2556 | ! salinity |
---|
| 2557 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
---|
| 2558 | & znts ! potential temperature |
---|
| 2559 | ! salinity |
---|
| 2560 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2561 | & zpalpbet_tlout |
---|
| 2562 | REAL(wp) :: & |
---|
| 2563 | & zbeta0_tlout |
---|
| 2564 | REAL(KIND=wp) :: & |
---|
| 2565 | & zsp1, & ! scalar product involving the tangent routine |
---|
| 2566 | & zsp2 ! scalar product involving the adjoint routine |
---|
| 2567 | INTEGER :: & |
---|
| 2568 | & ji, & |
---|
| 2569 | & jj, & |
---|
| 2570 | & jk, & |
---|
| 2571 | & jn, & |
---|
| 2572 | & jeos |
---|
| 2573 | CHARACTER(LEN=14) :: cl_name |
---|
| 2574 | |
---|
| 2575 | ! Allocate memory |
---|
| 2576 | ALLOCATE( & |
---|
| 2577 | & zts( jpi, jpj, jpk, jpts ), & |
---|
| 2578 | & zts_adout( jpi, jpj, jpk, jpts ), & |
---|
| 2579 | & zpalpbet_adin( jpi, jpj, jpk ), & |
---|
| 2580 | & zts_tlin( jpi, jpj, jpk, jpts ), & |
---|
| 2581 | & znts( jpi, jpj, jpk, jpts ), & |
---|
| 2582 | & zpalpbet_tlout(jpi, jpj, jpk ) ) |
---|
| 2583 | |
---|
| 2584 | |
---|
| 2585 | ! Initialize random field standard deviationsthe reference state |
---|
| 2586 | zts = tsn |
---|
| 2587 | |
---|
| 2588 | ! store initial nn_eos |
---|
| 2589 | jeos = nn_eos |
---|
| 2590 | DO jn = 0, 2 |
---|
| 2591 | nn_eos = jn |
---|
| 2592 | !============================================= |
---|
| 2593 | ! testing of eos_insitu_pot |
---|
| 2594 | !============================================= |
---|
| 2595 | |
---|
| 2596 | !============================================================= |
---|
| 2597 | ! 1) dx = ( T ) and dy = ( T ) |
---|
| 2598 | !============================================================= |
---|
| 2599 | |
---|
| 2600 | !-------------------------------------------------------------------- |
---|
| 2601 | ! Reset the tangent and adjoint variables |
---|
| 2602 | !-------------------------------------------------------------------- |
---|
| 2603 | zts_tlin(:,:,:,:) = 0.0_wp |
---|
| 2604 | zpalpbet_tlout(:,:,:) = 0.0_wp |
---|
| 2605 | zbeta0_tlout = 0.0_wp |
---|
| 2606 | zts_adout(:,:,:,:) = 0.0_wp |
---|
| 2607 | zbeta0_adin = 0.0_wp |
---|
| 2608 | zpalpbet_adin(:,:,:) = 0.0_wp |
---|
| 2609 | |
---|
| 2610 | !-------------------------------------------------------------------- |
---|
| 2611 | ! Initialize the tangent input with random noise: dx |
---|
| 2612 | !-------------------------------------------------------------------- |
---|
| 2613 | CALL grid_random( znts(:,:,:,jp_tem), 'T', 0.0_wp, stdt ) |
---|
| 2614 | CALL grid_random( znts(:,:,:,jp_sal), 'T', 0.0_wp, stds ) |
---|
| 2615 | DO jk = 1, jpk |
---|
| 2616 | DO jj = nldj, nlej |
---|
| 2617 | DO ji = nldi, nlei |
---|
| 2618 | zts_tlin(ji,jj,jk,:) = znts(ji,jj,jk,:) |
---|
| 2619 | END DO |
---|
| 2620 | END DO |
---|
| 2621 | END DO |
---|
| 2622 | !-------------------------------------------------------------------- |
---|
| 2623 | ! Call the tangent routine: dy = L dx |
---|
| 2624 | !-------------------------------------------------------------------- |
---|
| 2625 | |
---|
| 2626 | call eos_alpbet_tan ( zts, zts_tlin, zpalpbet_tlout, zbeta0_tlout ) |
---|
| 2627 | |
---|
| 2628 | !-------------------------------------------------------------------- |
---|
| 2629 | ! Initialize the adjoint variables: dy^* = W dy |
---|
| 2630 | !-------------------------------------------------------------------- |
---|
| 2631 | DO jk = 1, jpk |
---|
| 2632 | DO jj = nldj, nlej |
---|
| 2633 | DO ji = nldi, nlei |
---|
| 2634 | zpalpbet_adin(ji,jj,jk) = zpalpbet_tlout(ji,jj,jk) & |
---|
| 2635 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk)& |
---|
| 2636 | & * tmask(ji,jj,jk) |
---|
| 2637 | END DO |
---|
| 2638 | END DO |
---|
| 2639 | END DO |
---|
| 2640 | zbeta0_adin = zbeta0_tlout |
---|
| 2641 | |
---|
| 2642 | !-------------------------------------------------------------------- |
---|
| 2643 | ! Compute the scalar product: ( L dx )^T W dy |
---|
| 2644 | !-------------------------------------------------------------------- |
---|
| 2645 | |
---|
| 2646 | zsp1 = DOT_PRODUCT( zpalpbet_tlout , zpalpbet_adin ) & |
---|
| 2647 | & + zbeta0_tlout * zbeta0_adin |
---|
| 2648 | !-------------------------------------------------------------------- |
---|
| 2649 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
| 2650 | !-------------------------------------------------------------------- |
---|
| 2651 | |
---|
| 2652 | CALL eos_alpbet_adj( zts, zts_adout, zpalpbet_adin, zbeta0_adin ) |
---|
| 2653 | |
---|
| 2654 | !-------------------------------------------------------------------- |
---|
| 2655 | ! Compute the scalar product: dx^T L^T W dy |
---|
| 2656 | !-------------------------------------------------------------------- |
---|
| 2657 | |
---|
| 2658 | zsp2 = DOT_PRODUCT( zts_tlin(:,:,:,jp_tem), zts_adout(:,:,:,jp_tem) ) + & |
---|
| 2659 | & DOT_PRODUCT( zts_tlin(:,:,:,jp_sal), zts_adout(:,:,:,jp_sal) ) |
---|
| 2660 | ! Compare the scalar products |
---|
| 2661 | |
---|
| 2662 | ! 14 char:'12345678901234' |
---|
| 2663 | SELECT CASE( jn ) |
---|
| 2664 | CASE (0) ; cl_name = 'eos_adj ab T1' |
---|
| 2665 | CASE (1) ; cl_name = 'eos_adj ab T2' |
---|
| 2666 | CASE (2) ; cl_name = 'eos_adj ab T3' |
---|
| 2667 | END SELECT |
---|
| 2668 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
| 2669 | |
---|
| 2670 | ENDDO |
---|
| 2671 | |
---|
| 2672 | ! restore initial nn_eos |
---|
| 2673 | nn_eos = jeos |
---|
| 2674 | |
---|
| 2675 | ! Deallocate memory |
---|
| 2676 | DEALLOCATE( & |
---|
| 2677 | & zts, & |
---|
| 2678 | & zts_adout, & |
---|
| 2679 | & zpalpbet_adin, & |
---|
| 2680 | & zts_tlin, & |
---|
| 2681 | & zpalpbet_tlout, & |
---|
| 2682 | & znts ) |
---|
| 2683 | |
---|
| 2684 | END SUBROUTINE eos_alpbet_adj_tst |
---|
| 2685 | |
---|
| 2686 | SUBROUTINE eos_insitu_2d_adj_tst( kumadt ) |
---|
| 2687 | !!----------------------------------------------------------------------- |
---|
| 2688 | !! |
---|
| 2689 | !! *** ROUTINE eos_adj_tst *** |
---|
| 2690 | !! |
---|
| 2691 | !! ** Purpose : Test the adjoint routine. |
---|
| 2692 | !! |
---|
| 2693 | !! ** Method : Verify the scalar product |
---|
| 2694 | !! |
---|
| 2695 | !! ( L dx )^T W dy = dx^T L^T W dy |
---|
| 2696 | !! |
---|
| 2697 | !! where L = tangent routine |
---|
| 2698 | !! L^T = adjoint routine |
---|
| 2699 | !! W = diagonal matrix of scale factors |
---|
| 2700 | !! dx = input perturbation (random field) |
---|
| 2701 | !! dy = L dx |
---|
| 2702 | !! |
---|
| 2703 | !! ** Action : Separate tests are applied for the following dx and dy: |
---|
| 2704 | !! |
---|
| 2705 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
---|
| 2706 | !! |
---|
| 2707 | !! History : |
---|
| 2708 | !! ! 08-07 (A. Vidard) |
---|
| 2709 | !!----------------------------------------------------------------------- |
---|
| 2710 | !! * Modules used |
---|
| 2711 | |
---|
| 2712 | !! * Arguments |
---|
| 2713 | INTEGER, INTENT(IN) :: & |
---|
| 2714 | & kumadt ! Output unit |
---|
| 2715 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
| 2716 | zdep ! depth |
---|
| 2717 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2718 | zts ! potential temperature |
---|
| 2719 | ! salinity |
---|
| 2720 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2721 | & zts_adout ! potential temperature |
---|
| 2722 | ! salinity |
---|
| 2723 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
| 2724 | & zrd_adin ! anomaly density |
---|
| 2725 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2726 | & zts_tlin ! potential temperature |
---|
| 2727 | ! salinity |
---|
| 2728 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
---|
| 2729 | & znts ! potential temperature |
---|
| 2730 | ! salinity |
---|
| 2731 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: & |
---|
| 2732 | & zrd_tlout ! anomaly density |
---|
| 2733 | REAL(KIND=wp) :: & |
---|
| 2734 | & zsp1, & ! scalar product involving the tangent routine |
---|
| 2735 | & zsp2 ! scalar product involving the adjoint routine |
---|
| 2736 | INTEGER :: & |
---|
| 2737 | & ji, & |
---|
| 2738 | & jj, & |
---|
| 2739 | & jn, & |
---|
| 2740 | & jeos |
---|
| 2741 | CHARACTER(LEN=14) :: cl_name |
---|
| 2742 | ! Allocate memory |
---|
| 2743 | |
---|
| 2744 | ALLOCATE( & |
---|
| 2745 | & zdep( jpi, jpj), & |
---|
| 2746 | & zts( jpi, jpj, jpts ), & |
---|
| 2747 | & znts( jpi, jpj, jpts ), & |
---|
| 2748 | & zts_adout( jpi, jpj, jpts ), & |
---|
| 2749 | & zrd_adin( jpi, jpj ), & |
---|
| 2750 | & zts_tlin( jpi, jpj, jpts ), & |
---|
| 2751 | & zrd_tlout(jpi, jpj ) ) |
---|
| 2752 | |
---|
| 2753 | ! Initialize the reference state |
---|
| 2754 | zts(:,:,:) = tsn(:,:,2,:) |
---|
| 2755 | zdep(:,:) = fsdept(:,:,2) |
---|
| 2756 | |
---|
| 2757 | ! store initial nn_eos |
---|
| 2758 | jeos = nn_eos |
---|
| 2759 | DO jn = 0, 2 |
---|
| 2760 | nn_eos = jn |
---|
| 2761 | !============================================================= |
---|
| 2762 | ! 1) dx = ( T ) and dy = ( T ) |
---|
| 2763 | !============================================================= |
---|
| 2764 | |
---|
| 2765 | !-------------------------------------------------------------------- |
---|
| 2766 | ! Reset the tangent and adjoint variables |
---|
| 2767 | !-------------------------------------------------------------------- |
---|
| 2768 | zts_tlin(:,:,:) = 0.0_wp |
---|
| 2769 | zrd_tlout(:,:) = 0.0_wp |
---|
| 2770 | zts_adout(:,:,:) = 0.0_wp |
---|
| 2771 | zrd_adin(:,:) = 0.0_wp |
---|
| 2772 | |
---|
| 2773 | !-------------------------------------------------------------------- |
---|
| 2774 | ! Initialize the tangent input with random noise: dx |
---|
| 2775 | !-------------------------------------------------------------------- |
---|
| 2776 | CALL grid_random( znts(:,:,jp_tem), 'T', 0.0_wp, stdt ) |
---|
| 2777 | CALL grid_random( znts(:,:,jp_sal), 'T', 0.0_wp, stds ) |
---|
| 2778 | DO jj = nldj, nlej |
---|
| 2779 | DO ji = nldi, nlei |
---|
| 2780 | zts_tlin(ji,jj,:) = znts(ji,jj,:) |
---|
| 2781 | END DO |
---|
| 2782 | END DO |
---|
| 2783 | |
---|
| 2784 | CALL eos_insitu_2d_tan(zts, zdep, zts_tlin, zrd_tlout) |
---|
| 2785 | |
---|
| 2786 | DO jj = nldj, nlej |
---|
| 2787 | DO ji = nldi, nlei |
---|
| 2788 | zrd_adin(ji,jj) = zrd_tlout(ji,jj) & |
---|
| 2789 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,2)& |
---|
| 2790 | & * tmask(ji,jj,2) |
---|
| 2791 | END DO |
---|
| 2792 | END DO |
---|
| 2793 | |
---|
| 2794 | !-------------------------------------------------------------------- |
---|
| 2795 | ! Compute the scalar product: ( L dx )^T W dy |
---|
| 2796 | !-------------------------------------------------------------------- |
---|
| 2797 | |
---|
| 2798 | zsp1 = DOT_PRODUCT( zrd_tlout, zrd_adin ) |
---|
| 2799 | |
---|
| 2800 | !-------------------------------------------------------------------- |
---|
| 2801 | ! Call the adjoint routine: dx^* = L^T dy^* |
---|
| 2802 | !-------------------------------------------------------------------- |
---|
| 2803 | CALL eos_insitu_2d_adj(zts, zdep, zts_adout, zrd_adin) |
---|
| 2804 | zsp2 = DOT_PRODUCT( zts_tlin(:,:,jp_tem), zts_adout(:,:,jp_tem) ) + & |
---|
| 2805 | & DOT_PRODUCT( zts_tlin(:,:,jp_sal), zts_adout(:,:,jp_sal) ) |
---|
| 2806 | |
---|
| 2807 | ! Compare the scalar products |
---|
| 2808 | |
---|
| 2809 | ! 14 char:'12345678901234' |
---|
| 2810 | SELECT CASE( jn ) |
---|
| 2811 | CASE (0) ; cl_name = 'eos_adj 2d T1' |
---|
| 2812 | CASE (1) ; cl_name = 'eos_adj 2d T2' |
---|
| 2813 | CASE (2) ; cl_name = 'eos_adj 2d T3' |
---|
| 2814 | END SELECT |
---|
| 2815 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
---|
| 2816 | |
---|
| 2817 | ENDDO |
---|
| 2818 | |
---|
| 2819 | ! restore initial nn_eos |
---|
| 2820 | nn_eos = jeos |
---|
| 2821 | |
---|
| 2822 | ! Deallocate memory |
---|
| 2823 | |
---|
| 2824 | DEALLOCATE( & |
---|
| 2825 | & zdep, & |
---|
| 2826 | & zts, & |
---|
| 2827 | & zts_adout, & |
---|
| 2828 | & zrd_adin, & |
---|
| 2829 | & zts_tlin, & |
---|
| 2830 | & zrd_tlout, & |
---|
| 2831 | & znts ) |
---|
| 2832 | END SUBROUTINE eos_insitu_2d_adj_tst |
---|
| 2833 | |
---|
| 2834 | SUBROUTINE eos_adj_tst( kumadt ) |
---|
| 2835 | !!----------------------------------------------------------------------- |
---|
| 2836 | !! |
---|
| 2837 | !! *** ROUTINE eos_adj_tst *** |
---|
| 2838 | !! |
---|
| 2839 | !! ** Purpose : Test the adjoint routine. |
---|
| 2840 | !! |
---|
| 2841 | !! History : |
---|
| 2842 | !! ! 08-07 (A. Vidard) |
---|
| 2843 | !!----------------------------------------------------------------------- |
---|
| 2844 | !! * Arguments |
---|
| 2845 | INTEGER, INTENT(IN) :: & |
---|
| 2846 | & kumadt ! Output unit |
---|
| 2847 | |
---|
| 2848 | CALL eos_insitu_adj_tst( kumadt ) |
---|
| 2849 | CALL eos_insitu_pot_adj_tst( kumadt ) |
---|
| 2850 | CALL eos_insitu_2d_adj_tst( kumadt ) |
---|
| 2851 | CALL eos_alpbet_adj_tst( kumadt ) |
---|
| 2852 | |
---|
| 2853 | END SUBROUTINE eos_adj_tst |
---|
| 2854 | |
---|
| 2855 | SUBROUTINE bn2_adj_tst( kumadt ) |
---|
| 2856 | !!----------------------------------------------------------------------- |
---|
| 2857 | !! |
---|
| 2858 | !! *** ROUTINE bn2_adj_tst *** |
---|
| 2859 | !! |
---|
| 2860 | !! ** Purpose : Test the adjoint routine. |
---|
| 2861 | !! |
---|
| 2862 | !! ** Method : Verify the scalar product |
---|
| 2863 | !! |
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| 2864 | !! ( L dx )^T W dy = dx^T L^T W dy |
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| 2865 | !! |
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| 2866 | !! where L = tangent routine |
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| 2867 | !! L^T = adjoint routine |
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| 2868 | !! W = diagonal matrix of scale factors |
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| 2869 | !! dx = input perturbation (random field) |
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| 2870 | !! dy = L dx |
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| 2871 | !! |
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| 2872 | !! ** Action : Separate tests are applied for the following dx and dy: |
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| 2873 | !! |
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| 2874 | !! 1) dx = ( SSH ) and dy = ( SSH ) |
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| 2875 | !! |
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| 2876 | !! History : |
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| 2877 | !! ! 08-07 (A. Vidard) |
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| 2878 | !!----------------------------------------------------------------------- |
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| 2879 | !! * Modules used |
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| 2880 | |
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| 2881 | !! * Arguments |
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| 2882 | INTEGER, INTENT(IN) :: & |
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| 2883 | & kumadt ! Output unit |
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| 2884 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
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| 2885 | zts ! potential temperature |
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| 2886 | ! salinity |
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| 2887 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
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| 2888 | & zts_adout ! potential temperature |
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| 2889 | ! salinity |
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| 2890 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
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| 2891 | & zrd_adin, & ! potential density (surface referenced) |
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| 2892 | & zrd_adout ! potential density (surface referenced) |
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| 2893 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
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| 2894 | & zts_tlin, & ! potential temperature |
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| 2895 | ! salinity |
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| 2896 | & zts_tlout ! potential temperature |
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| 2897 | ! salinity |
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| 2898 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
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| 2899 | & zrd_tlout ! potential density (surface referenced) |
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| 2900 | REAL(KIND=wp) :: & |
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| 2901 | & zsp1, & ! scalar product involving the tangent routine |
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| 2902 | & zsp2 ! scalar product involving the adjoint routine |
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| 2903 | REAL(wp), DIMENSION(:,:,:,:), ALLOCATABLE :: & |
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| 2904 | & znts ! potential temperature |
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| 2905 | ! salinity |
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| 2906 | INTEGER :: & |
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| 2907 | & ji, & |
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| 2908 | & jj, & |
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| 2909 | & jk, & |
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| 2910 | & jn, & |
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| 2911 | & jeos |
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| 2912 | CHARACTER(LEN=14) :: cl_name |
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| 2913 | |
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| 2914 | ! Allocate memory |
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| 2915 | ALLOCATE( & |
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| 2916 | & zts( jpi, jpj, jpk, jpts ), & |
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| 2917 | & zts_adout( jpi, jpj, jpk, jpts ), & |
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| 2918 | & zrd_adin( jpi, jpj, jpk ), & |
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| 2919 | & zrd_adout(jpi, jpj, jpk ), & |
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| 2920 | & zts_tlin( jpi, jpj, jpk, jpts ), & |
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| 2921 | & znts( jpi, jpj, jpk, jpts ), & |
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| 2922 | & zts_tlout( jpi, jpj, jpk, jpts ), & |
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| 2923 | & zrd_tlout(jpi, jpj, jpk ) ) |
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| 2924 | |
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| 2925 | ! Initialize random field standard deviationsthe reference state |
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| 2926 | zts = tsn |
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| 2927 | ! store initial nn_eos |
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| 2928 | jeos = nn_eos |
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| 2929 | DO jn = 0, 2 |
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| 2930 | nn_eos = jn |
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| 2931 | !============================================================= |
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| 2932 | ! 1) dx = ( T ) and dy = ( T ) |
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| 2933 | !============================================================= |
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| 2934 | |
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| 2935 | !-------------------------------------------------------------------- |
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| 2936 | ! Reset the tangent and adjoint variables |
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| 2937 | !-------------------------------------------------------------------- |
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| 2938 | zts_tlin(:,:,:,:) = 0.0_wp |
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| 2939 | zts_tlout(:,:,:,:) = 0.0_wp |
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| 2940 | zrd_tlout(:,:,:) = 0.0_wp |
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| 2941 | zts_adout(:,:,:,:) = 0.0_wp |
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| 2942 | zrd_adin(:,:,:) = 0.0_wp |
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| 2943 | zrd_adout(:,:,:) = 0.0_wp |
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| 2944 | |
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| 2945 | !-------------------------------------------------------------------- |
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| 2946 | ! Initialize the tangent input with random noise: dx |
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| 2947 | !-------------------------------------------------------------------- |
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| 2948 | CALL grid_random( znts(:,:,:,jp_tem), 'T', 0.0_wp, stdt ) |
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| 2949 | CALL grid_random( znts(:,:,:,jp_sal), 'T', 0.0_wp, stds ) |
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| 2950 | DO jk = 1, jpk |
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| 2951 | DO jj = nldj, nlej |
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| 2952 | DO ji = nldi, nlei |
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| 2953 | zts_tlin(ji,jj,jk,:) = znts(ji,jj,jk,:) |
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| 2954 | END DO |
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| 2955 | END DO |
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| 2956 | END DO |
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| 2957 | !-------------------------------------------------------------------- |
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| 2958 | ! Call the tangent routine: dy = L dx |
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| 2959 | !-------------------------------------------------------------------- |
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| 2960 | zts_tlout(:,:,:,:) = zts_tlin |
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| 2961 | CALL eos_bn2_tan( zts, zts_tlout, zrd_tlout ) |
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| 2962 | !-------------------------------------------------------------------- |
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| 2963 | ! Initialize the adjoint variables: dy^* = W dy |
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| 2964 | !-------------------------------------------------------------------- |
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| 2965 | DO jk = 1, jpk |
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| 2966 | DO jj = nldj, nlej |
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| 2967 | DO ji = nldi, nlei |
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| 2968 | zrd_adin(ji,jj,jk) = zrd_tlout(ji,jj,jk) & |
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| 2969 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) & |
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| 2970 | & * tmask(ji,jj,jk) |
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| 2971 | END DO |
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| 2972 | END DO |
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| 2973 | END DO |
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| 2974 | |
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| 2975 | !-------------------------------------------------------------------- |
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| 2976 | ! Compute the scalar product: ( L dx )^T W dy |
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| 2977 | !-------------------------------------------------------------------- |
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| 2978 | |
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| 2979 | zsp1 = DOT_PRODUCT( zrd_tlout, zrd_adin ) |
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| 2980 | |
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| 2981 | !-------------------------------------------------------------------- |
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| 2982 | ! Call the adjoint routine: dx^* = L^T dy^* |
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| 2983 | !-------------------------------------------------------------------- |
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| 2984 | |
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| 2985 | zrd_adout(:,:,:) = zrd_adin(:,:,:) |
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| 2986 | CALL eos_bn2_adj( zts, zts_adout, zrd_adout ) |
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| 2987 | |
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| 2988 | !-------------------------------------------------------------------- |
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| 2989 | ! Compute the scalar product: dx^T L^T W dy |
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| 2990 | !-------------------------------------------------------------------- |
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| 2991 | zsp2 = DOT_PRODUCT( zts_tlin(:,:,:,jp_tem), zts_adout(:,:,:,jp_tem )) + & |
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| 2992 | & DOT_PRODUCT( zts_tlin(:,:,:,jp_sal), zts_adout(:,:,:,jp_sal )) |
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| 2993 | |
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| 2994 | ! Compare the scalar products |
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| 2995 | ! 14 char:'12345678901234' |
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| 2996 | SELECT CASE( jn ) |
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| 2997 | CASE (0) ; cl_name = 'bn2_adj T1' |
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| 2998 | CASE (1) ; cl_name = 'bn2_adj T2' |
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| 2999 | CASE (2) ; cl_name = 'bn2_adj T3' |
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| 3000 | END SELECT |
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| 3001 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
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| 3002 | ENDDO |
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| 3003 | ! restore initial nn_eos |
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| 3004 | nn_eos = jeos |
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| 3005 | |
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| 3006 | ! Deallocate memory |
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| 3007 | DEALLOCATE( & |
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| 3008 | & zts, & |
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| 3009 | & zts_adout, & |
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| 3010 | & zrd_adin, & |
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| 3011 | & zrd_adout, & |
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| 3012 | & zts_tlin, & |
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| 3013 | & zts_tlout, & |
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| 3014 | & zrd_tlout, & |
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| 3015 | & znts ) |
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| 3016 | END SUBROUTINE bn2_adj_tst |
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| 3017 | #endif |
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| 3018 | !!====================================================================== |
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| 3019 | END MODULE eosbn2_tam |
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