| 1 | MODULE trazdf_imp_tam |
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| 2 | #ifdef key_tam |
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| 3 | !!============================================================================== |
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| 4 | !! *** MODULE trazdf_imp_tam *** |
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| 5 | !! Ocean active tracers: vertical component of the tracer mixing trend |
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| 6 | !! Tangent and Adjoint Module |
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| 7 | !!============================================================================== |
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| 8 | !! History of the direct module: |
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| 9 | !! OPA ! 1990-10 (B. Blanke) Original code |
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| 10 | !! 7.0 ! 1991-11 (G. Madec) |
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| 11 | !! ! 1992-06 (M. Imbard) correction on tracer trend loops |
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| 12 | !! ! 1996-01 (G. Madec) statement function for e3 |
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| 13 | !! ! 1997-05 (G. Madec) vertical component of isopycnal |
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| 14 | !! ! 1997-07 (G. Madec) geopotential diffusion in s-coord |
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| 15 | !! ! 2000-08 (G. Madec) double diffusive mixing |
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| 16 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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| 17 | !! 2.0 ! 2006-11 (G. Madec) New step reorganisation |
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| 18 | !! 3.2 ! 2009-03 (G. Madec) heat and salt content trends |
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| 19 | |
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| 20 | !! History of the T&A module: |
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| 21 | !! ! 09-01 (A. Vidard) tam of the 06-11 version |
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| 22 | !!---------------------------------------------------------------------- |
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| 23 | !! tra_zdf_imp_tan : Update the tracer trend with the diagonal vertical |
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| 24 | !! part of the mixing tensor (tangent). |
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| 25 | !! tra_zdf_imp_adj : Update the tracer trend with the diagonal vertical |
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| 26 | !! part of the mixing tensor (adjoint). |
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| 27 | !!---------------------------------------------------------------------- |
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| 28 | !! * Modules used |
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| 29 | USE par_kind |
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| 30 | USE par_oce |
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| 31 | USE oce_tam |
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| 32 | USE dom_oce |
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| 33 | USE oce |
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| 34 | USE zdf_oce |
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| 35 | USE ldftra_oce |
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| 36 | USE zdfddm |
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| 37 | USE traldf_tam |
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| 38 | USE in_out_manager |
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| 39 | USE gridrandom |
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| 40 | USE dotprodfld |
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| 41 | USE tstool_tam |
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| 42 | USE trc_oce |
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| 43 | USE trc_oce_tam |
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| 44 | USE ldftra |
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| 45 | USE lib_mpp |
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| 46 | USE wrk_nemo |
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| 47 | USE timing |
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| 48 | USE ldfslp |
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| 49 | USE paresp |
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| 50 | |
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| 51 | IMPLICIT NONE |
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| 52 | PRIVATE |
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| 53 | |
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| 54 | !! * Routine accessibility |
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| 55 | PUBLIC tra_zdf_imp_tan ! routine called by tra_zdf_tan.F90 |
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| 56 | PUBLIC tra_zdf_imp_adj ! routine called by tra_zdf_adj.F90 |
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| 57 | PUBLIC tra_zdf_imp_adj_tst ! routine called by tst.F90 |
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| 58 | #if defined key_tst_tlm |
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| 59 | PUBLIC tra_zdf_imp_tlm_tst ! routine called by tamtst.F90 |
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| 60 | #endif |
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| 61 | |
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| 62 | !! * Substitutions |
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| 63 | # include "domzgr_substitute.h90" |
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| 64 | # include "ldftra_substitute.h90" |
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| 65 | # include "zdfddm_substitute.h90" |
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| 66 | # include "vectopt_loop_substitute.h90" |
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| 67 | !!---------------------------------------------------------------------- |
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| 68 | !!---------------------------------------------------------------------- |
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| 69 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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| 70 | !! $Id: trazdf_imp.F90 1156 2008-06-26 16:06:45Z rblod $ |
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| 71 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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| 72 | !!---------------------------------------------------------------------- |
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| 73 | CONTAINS |
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| 74 | |
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| 75 | SUBROUTINE tra_zdf_imp_tan( kt, kit000, cdtype, p2dt, ptb_tl, pta_tl, kjpt ) |
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| 76 | !!---------------------------------------------------------------------- |
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| 77 | !! *** ROUTINE tra_zdf_imp_tan *** |
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| 78 | !! |
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| 79 | !! ** Purpose of the direct routine: |
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| 80 | !! Compute the trend due to the vertical tracer diffusion |
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| 81 | !! including the vertical component of lateral mixing (only for 2nd |
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| 82 | !! order operator, for fourth order it is already computed and add |
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| 83 | !! to the general trend in traldf.F) and add it to the general trend |
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| 84 | !! of the tracer equations. |
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| 85 | !! |
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| 86 | !! ** Method of the direct routine : |
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| 87 | !! The vertical component of the lateral diffusive trends |
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| 88 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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| 89 | !! potential surfaces to which an eddy induced advection can be |
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| 90 | !! added. It is computed using before fields (forward in time) and |
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| 91 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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| 92 | !! |
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| 93 | !! Second part: vertical trend associated with the vertical physics |
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| 94 | !! =========== (including the vertical flux proportional to dk[t] |
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| 95 | !! associated with the lateral mixing, through the |
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| 96 | !! update of avt) |
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| 97 | !! The vertical diffusion of tracers (t & s) is given by: |
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| 98 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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| 99 | !! It is computed using a backward time scheme (t=ta). |
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| 100 | !! Surface and bottom boundary conditions: no diffusive flux on |
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| 101 | !! both tracers (bottom, applied through the masked field avt). |
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| 102 | !! Add this trend to the general trend ta,sa : |
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| 103 | !! ta = ta + dz( avt dz(t) ) |
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| 104 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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| 105 | !! |
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| 106 | !! Third part: recover avt resulting from the vertical physics |
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| 107 | !! ========== alone, for further diagnostics (for example to |
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| 108 | !! compute the turbocline depth in zdfmxl.F90). |
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| 109 | !! avt = zavt |
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| 110 | !! (avs = zavs if lk_zdfddm=T ) |
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| 111 | !! |
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| 112 | !! ** Remarks on the tangent routine : - key_vvl is not available in tangent yet. |
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| 113 | !! Once it will be this routine wil need to be rewritten |
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| 114 | !! - simplified version, slopes (wslp[ij]) |
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| 115 | !! assumed to be constant (read from the trajectory). same for av[ts] |
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| 116 | !! |
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| 117 | !!--------------------------------------------------------------------- |
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| 118 | !! |
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| 119 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 120 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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| 121 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 122 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 123 | REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
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| 124 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb_tl ! before and now tracer fields |
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| 125 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta_tl ! tracer trend |
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| 126 | !! * Local declarations |
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| 127 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 128 | REAL(wp) :: zavi, zrhstl, znvvl, & ! temporary scalars |
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| 129 | ze3tb, ze3tn, ze3ta, zvsfvvl ! variable vertical scale factors |
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| 130 | REAL(wp), POINTER, DIMENSION(:,:,:) :: & |
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| 131 | zwi, zwt, zwd, zws ! workspace arrays |
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| 132 | !!--------------------------------------------------------------------- |
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| 133 | ! |
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| 134 | IF( nn_timing == 1 ) CALL timing_start('tra_zdf_imp_tan') |
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| 135 | ! |
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| 136 | CALL wrk_alloc( jpi, jpj, jpk, zwi, zwt, zwd, zws ) |
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| 137 | ! |
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| 138 | IF( kt == kit000 ) THEN |
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| 139 | IF(lwp)WRITE(numout,*) |
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| 140 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp_tan : implicit vertical mixing on ', cdtype |
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| 141 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 142 | ENDIF |
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| 143 | |
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| 144 | ! I.1 Variable volume : to take into account vertical variable vertical scale factors |
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| 145 | ! ------------------- |
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| 146 | ! ... not available in tangent yet |
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| 147 | ! II. Vertical trend associated with the vertical physics |
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| 148 | ! ======================================================= |
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| 149 | ! (including the vertical flux proportional to dk[t] associated |
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| 150 | ! with the lateral mixing, through the avt update) |
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| 151 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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| 152 | DO jn = 1, kjpt ! tracer loop ! |
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| 153 | ! ! ============= ! |
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| 154 | ! |
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| 155 | ! Matrix construction |
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| 156 | ! -------------------- |
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| 157 | ! Build matrix if temperature or salinity (only in double diffusion case) or first passive tracer |
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| 158 | ! |
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| 159 | IF( ( cdtype == 'TRA' .AND. ( jn == jp_tem .OR. ( jn == jp_sal .AND. lk_zdfddm ) ) ) .OR. & |
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| 160 | & ( cdtype == 'TRC' .AND. jn == 1 ) ) THEN |
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| 161 | ! |
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| 162 | ! vertical mixing coef.: avt for temperature, avs for salinity and passive tracers |
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| 163 | IF( cdtype == 'TRA' .AND. jn == jp_tem ) THEN ; zwt(:,:,2:jpk) = avt (:,:,2:jpk) |
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| 164 | ELSE ; zwt(:,:,2:jpk) = fsavs(:,:,2:jpk) |
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| 165 | ENDIF |
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| 166 | zwt(:,:,1) = 0._wp |
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| 167 | ! |
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| 168 | ! II.0 Matrix construction |
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| 169 | ! ------------------------ |
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| 170 | #if defined key_ldfslp |
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| 171 | ! update and save of avt (and avs if double diffusive mixing) |
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| 172 | IF ( ln_traldf_grif ) THEN |
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| 173 | IF ( lwp ) WRITE(numout, *) 'Griffies operator for lateral tracer diffusion not avaible in TAM yet' |
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| 174 | CALL abort |
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| 175 | ELSE IF( l_traldf_rot ) THEN |
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| 176 | DO jk = 2, jpkm1 |
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| 177 | DO jj = 2, jpjm1 |
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| 178 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 179 | zwt(ji,jj,jk) = zwt(ji,jj,jk) + fsahtw(ji,jj,jk) & ! vertical mixing coef. due to lateral mixing |
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| 180 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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| 181 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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| 182 | END DO |
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| 183 | END DO |
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| 184 | END DO |
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| 185 | ENDIF |
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| 186 | #endif |
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| 187 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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| 188 | DO jk = 1, jpkm1 |
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| 189 | DO jj = 2, jpjm1 |
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| 190 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 191 | ze3ta = 1._wp ! after scale factor at T-point |
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| 192 | ze3tn = fse3t(ji,jj,jk) ! now scale factor at T-point |
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| 193 | zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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| 194 | zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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| 195 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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| 196 | END DO |
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| 197 | END DO |
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| 198 | END DO |
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| 199 | ! |
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| 200 | ! II.1. Vertical diffusion on t |
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| 201 | ! --------------------------- |
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| 202 | ! |
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| 203 | !! Matrix inversion from the first level |
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| 204 | !!---------------------------------------------------------------------- |
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| 205 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 206 | ! |
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| 207 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 208 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 209 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 210 | ! ( ... )( ... ) ( ... ) |
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| 211 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 212 | ! |
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| 213 | ! m is decomposed in the product of an upper and lower triangular matrix |
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| 214 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 215 | ! The second member is in 2d array zwy |
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| 216 | ! The solution is in 2d array zwx |
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| 217 | ! The 3d arry zwt is a work space array |
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| 218 | ! zwy is used and then used as a work space array : its value is modified! |
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| 219 | |
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| 220 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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| 221 | DO jj = 2, jpjm1 |
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| 222 | DO ji = fs_2, fs_jpim1 |
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| 223 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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| 224 | END DO |
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| 225 | END DO |
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| 226 | DO jk = 2, jpkm1 |
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| 227 | DO jj = 2, jpjm1 |
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| 228 | DO ji = fs_2, fs_jpim1 |
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| 229 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
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| 230 | END DO |
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| 231 | END DO |
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| 232 | END DO |
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| 233 | END IF |
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| 234 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 235 | DO jj = 2, jpjm1 |
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| 236 | DO ji = fs_2, fs_jpim1 |
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| 237 | ze3tb = 1._wp |
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| 238 | ze3tn = 1._wp |
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| 239 | pta_tl(ji,jj,1,jn) = ze3tb * ptb_tl(ji,jj,1,jn) + p2dt(1) * ze3tn * pta_tl(ji,jj,1,jn) |
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| 240 | END DO |
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| 241 | END DO |
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| 242 | |
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| 243 | DO jk = 2, jpkm1 |
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| 244 | DO jj = 2, jpjm1 |
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| 245 | DO ji = fs_2, fs_jpim1 |
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| 246 | ze3tb = 1._wp |
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| 247 | ze3tn = 1._wp |
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| 248 | zrhstl = ze3tb * ptb_tl(ji,jj,jk,jn) + p2dt(jk) * ze3tn * pta_tl(ji,jj,jk,jn) ! zrhs=right hand side |
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| 249 | pta_tl(ji,jj,jk,jn) = zrhstl - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * pta_tl(ji,jj,jk-1,jn) |
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| 250 | END DO |
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| 251 | END DO |
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| 252 | END DO |
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| 253 | |
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| 254 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 255 | ! Save the masked temperature after in ta |
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| 256 | ! (c a u t i o n: temperature not its trend, Leap-frog scheme done it will not be done in tranxt) |
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| 257 | DO jj = 2, jpjm1 |
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| 258 | DO ji = fs_2, fs_jpim1 |
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| 259 | pta_tl(ji,jj,jpkm1,jn) = pta_tl(ji,jj,jpkm1,jn) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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| 260 | END DO |
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| 261 | END DO |
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| 262 | DO jk = jpk-2, 1, -1 |
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| 263 | DO jj = 2, jpjm1 |
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| 264 | DO ji = fs_2, fs_jpim1 |
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| 265 | pta_tl(ji,jj,jk,jn) = ( pta_tl(ji,jj,jk,jn) - zws(ji,jj,jk) * pta_tl(ji,jj,jk+1,jn) ) & |
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| 266 | & / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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| 267 | END DO |
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| 268 | END DO |
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| 269 | END DO |
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| 270 | ! ! ================= ! |
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| 271 | END DO ! end tracer loop ! |
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| 272 | ! ! ================= ! |
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| 273 | ! |
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| 274 | CALL wrk_dealloc( jpi, jpj, jpk, zwi, zwt, zwd, zws ) |
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| 275 | ! |
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| 276 | IF( nn_timing == 1 ) CALL timing_stop('tra_zdf_imp_tan') |
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| 277 | ! |
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| 278 | END SUBROUTINE tra_zdf_imp_tan |
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| 279 | SUBROUTINE tra_zdf_imp_adj( kt, kit000, cdtype, p2dt, ptb_ad, pta_ad, kjpt ) |
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| 280 | !!---------------------------------------------------------------------- |
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| 281 | !! *** ROUTINE tra_zdf_imp_adj *** |
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| 282 | !! |
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| 283 | !! ** Purpose of the direct routine: |
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| 284 | !! Compute the trend due to the vertical tracer diffusion |
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| 285 | !! including the vertical component of lateral mixing (only for 2nd |
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| 286 | !! order operator, for fourth order it is already computed and add |
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| 287 | !! to the general trend in traldf.F) and add it to the general trend |
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| 288 | !! of the tracer equations. |
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| 289 | !! |
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| 290 | !! ** Method of the direct routine : |
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| 291 | !! The vertical component of the lateral diffusive trends |
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| 292 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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| 293 | !! potential surfaces to which an eddy induced advection can be |
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| 294 | !! added. It is computed using before fields (forward in time) and |
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| 295 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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| 296 | !! |
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| 297 | !! Second part: vertical trend associated with the vertical physics |
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| 298 | !! =========== (including the vertical flux proportional to dk[t] |
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| 299 | !! associated with the lateral mixing, through the |
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| 300 | !! update of avt) |
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| 301 | !! The vertical diffusion of tracers (t & s) is given by: |
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| 302 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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| 303 | !! It is computed using a backward time scheme (t=ta). |
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| 304 | !! Surface and bottom boundary conditions: no diffusive flux on |
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| 305 | !! both tracers (bottom, applied through the masked field avt). |
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| 306 | !! Add this trend to the general trend ta,sa : |
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| 307 | !! ta = ta + dz( avt dz(t) ) |
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| 308 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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| 309 | !! |
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| 310 | !! Third part: recover avt resulting from the vertical physics |
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| 311 | !! ========== alone, for further diagnostics (for example to |
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| 312 | !! compute the turbocline depth in zdfmxl.F90). |
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| 313 | !! avt = zavt |
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| 314 | !! (avs = zavs if lk_zdfddm=T ) |
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| 315 | !! |
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| 316 | !! ** Remarks on the adjoint routine : - key_vvl is not available in adjoint yet. |
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| 317 | !! Once it will be this routine wil need to be rewritten |
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| 318 | !! - simplified version, slopes (wslp[ij]) |
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| 319 | !! assumed to be constant (read from the trajectory). same for av[ts] |
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| 320 | !! |
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| 321 | !!--------------------------------------------------------------------- |
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| 322 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 323 | INTEGER , INTENT(in ) :: kit000 ! first time step index |
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| 324 | CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 325 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
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| 326 | REAL(wp), DIMENSION( jpk ), INTENT(in ) :: p2dt ! vertical profile of tracer time-step |
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| 327 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: ptb_ad ! before and now tracer fields |
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| 328 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta_ad ! tracer trend |
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| 329 | !! * Local declarations |
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| 330 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 331 | REAL(wp) :: zavi, zrhsad, znvvl, & ! temporary scalars |
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| 332 | ze3tb, ze3tn, ze3ta, zvsfvvl ! variable vertical scale factors |
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| 333 | REAL(wp), POINTER, DIMENSION(:,:,:) :: & |
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| 334 | zwi, zwt, zws, zwd ! workspace arrays |
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| 335 | !!--------------------------------------------------------------------- |
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| 336 | ! |
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| 337 | IF( nn_timing == 1 ) CALL timing_start('tra_zdf_imp_adj') |
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| 338 | ! |
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| 339 | CALL wrk_alloc( jpi, jpj, jpk, zwi, zwt, zws, zwd ) |
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| 340 | ! |
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| 341 | IF( kt == nitend ) THEN |
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| 342 | IF(lwp)WRITE(numout,*) |
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| 343 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp_adj : implicit vertical mixing on', cdtype |
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| 344 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~~~~~ ' |
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| 345 | ENDIF |
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| 346 | |
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| 347 | ! I.1 Variable volume : to take into account vertical variable vertical scale factors |
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| 348 | ! ------------------- |
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| 349 | ! ... not available in tangent yet |
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| 350 | ! II. Vertical trend associated with the vertical physics |
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| 351 | ! ======================================================= |
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| 352 | ! (including the vertical flux proportional to dk[t] associated |
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| 353 | ! with the lateral mixing, through the avt update) |
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| 354 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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| 355 | DO jn = 1, kjpt ! tracer loop ! |
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| 356 | ! ! ============= ! |
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| 357 | ! |
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| 358 | ! Matrix construction |
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| 359 | ! -------------------- |
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| 360 | ! Build matrix if temperature or salinity (only in double diffusion case) or first passive tracer |
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| 361 | ! |
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| 362 | IF( ( cdtype == 'TRA' .AND. ( jn == jp_tem .OR. ( jn == jp_sal .AND. lk_zdfddm ) ) ) .OR. & |
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| 363 | & ( cdtype == 'TRC' .AND. jn == 1 ) ) THEN |
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| 364 | ! |
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| 365 | ! vertical mixing coef.: avt for temperature, avs for salinity and passive tracers |
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| 366 | IF( cdtype == 'TRA' .AND. jn == jp_tem ) THEN ; zwt(:,:,2:jpk) = avt (:,:,2:jpk) |
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| 367 | ELSE ; zwt(:,:,2:jpk) = fsavs(:,:,2:jpk) |
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| 368 | ENDIF |
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| 369 | zwt(:,:,1) = 0._wp |
|---|
| 370 | |
|---|
| 371 | #if defined key_ldfslp |
|---|
| 372 | ! update and save of avt (and avs if double diffusive mixing) |
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| 373 | IF ( ln_traldf_grif ) THEN |
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| 374 | IF ( lwp ) WRITE(numout, *) 'Griffies operator for lateral tracer diffusion not avaible in TAM yet' |
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| 375 | CALL abort |
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| 376 | ELSE IF( l_traldf_rot ) THEN |
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| 377 | DO jk = 2, jpkm1 |
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| 378 | DO jj = 2, jpjm1 |
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| 379 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 380 | zwt(ji,jj,jk) = zwt(ji,jj,jk) + fsahtw(ji,jj,jk) & ! vertical mixing coef. due to lateral mixing |
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| 381 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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| 382 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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| 383 | END DO |
|---|
| 384 | END DO |
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| 385 | END DO |
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| 386 | ENDIF |
|---|
| 387 | #endif |
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| 388 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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| 389 | DO jk = 1, jpkm1 |
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| 390 | DO jj = 2, jpjm1 |
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| 391 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 392 | ze3ta = 1._wp ! after scale factor at T-point |
|---|
| 393 | ze3tn = fse3t(ji,jj,jk) ! now scale factor at T-point |
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| 394 | zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
|---|
| 395 | zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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| 396 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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| 397 | END DO |
|---|
| 398 | END DO |
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| 399 | END DO |
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| 400 | |
|---|
| 401 | !! Matrix inversion from the first level |
|---|
| 402 | !!---------------------------------------------------------------------- |
|---|
| 403 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
|---|
| 404 | ! |
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| 405 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 406 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 407 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 408 | ! ( ... )( ... ) ( ... ) |
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| 409 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
|---|
| 410 | ! |
|---|
| 411 | ! m is decomposed in the product of an upper and lower triangular matrix |
|---|
| 412 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
|---|
| 413 | ! The second member is in 2d array zwy |
|---|
| 414 | ! The solution is in 2d array zwx |
|---|
| 415 | ! The 3d arry zwt is a work space array |
|---|
| 416 | ! zwy is used and then used as a work space array : its value is modified! |
|---|
| 417 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
|---|
| 418 | DO jj = 2, jpjm1 |
|---|
| 419 | DO ji = fs_2, fs_jpim1 |
|---|
| 420 | zwt(ji,jj,1) = zwd(ji,jj,1) |
|---|
| 421 | END DO |
|---|
| 422 | END DO |
|---|
| 423 | DO jk = 2, jpkm1 |
|---|
| 424 | DO jj = 2, jpjm1 |
|---|
| 425 | DO ji = fs_2, fs_jpim1 |
|---|
| 426 | zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
|---|
| 427 | END DO |
|---|
| 428 | END DO |
|---|
| 429 | END DO |
|---|
| 430 | END IF |
|---|
| 431 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
|---|
| 432 | ! Save the masked temperature after in ta |
|---|
| 433 | ! (c a u t i o n: temperature not its trend, Leap-frog scheme done it will not be done in tranxt) |
|---|
| 434 | DO jk = 1, jpk-2 |
|---|
| 435 | DO jj = 2, jpjm1 |
|---|
| 436 | DO ji = fs_2, fs_jpim1 |
|---|
| 437 | pta_ad(ji,jj,jk+1,jn) = pta_ad(ji,jj,jk+1,jn) - zws(ji,jj,jk) * pta_ad(ji,jj,jk,jn) & |
|---|
| 438 | & / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
|---|
| 439 | pta_ad(ji,jj,jk,jn) = pta_ad(ji,jj,jk,jn) / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
|---|
| 440 | END DO |
|---|
| 441 | END DO |
|---|
| 442 | END DO |
|---|
| 443 | DO jj = 2, jpjm1 |
|---|
| 444 | DO ji = fs_2, fs_jpim1 |
|---|
| 445 | pta_ad(ji,jj,jpkm1,jn) = pta_ad(ji,jj,jpkm1,jn) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
|---|
| 446 | END DO |
|---|
| 447 | END DO |
|---|
| 448 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
|---|
| 449 | DO jk = jpkm1, 2, -1 |
|---|
| 450 | DO jj = 2, jpjm1 |
|---|
| 451 | DO ji = fs_2, fs_jpim1 |
|---|
| 452 | ze3tb = 1._wp |
|---|
| 453 | ze3tn = 1._wp |
|---|
| 454 | zrhsad = zrhsad + pta_ad(ji,jj,jk,jn) |
|---|
| 455 | pta_ad(ji,jj,jk-1,jn) = pta_ad(ji,jj,jk-1,jn) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * pta_ad(ji,jj,jk,jn) |
|---|
| 456 | pta_ad(ji,jj,jk,jn) = 0.0_wp |
|---|
| 457 | ptb_ad(ji,jj,jk,jn) = ptb_ad(ji,jj,jk,jn) + ze3tb * zrhsad |
|---|
| 458 | pta_ad(ji,jj,jk,jn) = pta_ad(ji,jj,jk,jn) + p2dt(jk) * ze3tn * zrhsad |
|---|
| 459 | zrhsad = 0.0_wp |
|---|
| 460 | END DO |
|---|
| 461 | END DO |
|---|
| 462 | END DO |
|---|
| 463 | DO jj = 2, jpjm1 |
|---|
| 464 | DO ji = fs_2, fs_jpim1 |
|---|
| 465 | ze3tb = 1._wp |
|---|
| 466 | ze3tn = 1._wp |
|---|
| 467 | ptb_ad(ji,jj,1,jn) = ptb_ad(ji,jj,1,jn) + ze3tb * pta_ad(ji,jj,1,jn) |
|---|
| 468 | pta_ad(ji,jj,1,jn) = pta_ad(ji,jj,1,jn) * p2dt(1) * ze3tn |
|---|
| 469 | END DO |
|---|
| 470 | END DO |
|---|
| 471 | END DO |
|---|
| 472 | ! |
|---|
| 473 | CALL wrk_dealloc( jpi, jpj, jpk, zwi, zwt, zws, zwd ) |
|---|
| 474 | ! |
|---|
| 475 | IF( nn_timing == 1 ) CALL timing_stop('tra_zdf_imp_adj') |
|---|
| 476 | ! |
|---|
| 477 | END SUBROUTINE tra_zdf_imp_adj |
|---|
| 478 | SUBROUTINE tra_zdf_imp_adj_tst( kumadt ) |
|---|
| 479 | !!----------------------------------------------------------------------- |
|---|
| 480 | !! |
|---|
| 481 | !! *** ROUTINE tra_zdf_imp_adj_tst *** |
|---|
| 482 | !! |
|---|
| 483 | !! ** Purpose : Test the adjoint routine. |
|---|
| 484 | !! |
|---|
| 485 | !! ** Method : Verify the scalar product |
|---|
| 486 | !! |
|---|
| 487 | !! ( L dx )^T W dy = dx^T L^T W dy |
|---|
| 488 | !! |
|---|
| 489 | !! where L = tangent routine |
|---|
| 490 | !! L^T = adjoint routine |
|---|
| 491 | !! W = diagonal matrix of scale factors |
|---|
| 492 | !! dx = input perturbation (random field) |
|---|
| 493 | !! dy = L dx |
|---|
| 494 | !! |
|---|
| 495 | !! |
|---|
| 496 | !! History : |
|---|
| 497 | !! ! 08-08 (A. Vidard) |
|---|
| 498 | !!----------------------------------------------------------------------- |
|---|
| 499 | !! * Modules used |
|---|
| 500 | |
|---|
| 501 | !! * Arguments |
|---|
| 502 | INTEGER, INTENT(IN) :: & |
|---|
| 503 | & kumadt ! Output unit |
|---|
| 504 | |
|---|
| 505 | !! * Local declarations |
|---|
| 506 | INTEGER :: & |
|---|
| 507 | & istp, & |
|---|
| 508 | & jstp, & |
|---|
| 509 | & ji, & ! dummy loop indices |
|---|
| 510 | & jj, & |
|---|
| 511 | & jk |
|---|
| 512 | REAL(KIND=wp) :: & |
|---|
| 513 | & zsp1, & ! scalar product involving the tangent routine |
|---|
| 514 | & zsp2 ! scalar product involving the adjoint routine |
|---|
| 515 | REAL(KIND=wp), DIMENSION(:,:,:), ALLOCATABLE :: & |
|---|
| 516 | & zta_tlin , & ! Tangent input |
|---|
| 517 | & ztb_tlin , & ! Tangent input |
|---|
| 518 | & zsa_tlin , & ! Tangent input |
|---|
| 519 | & zsb_tlin , & ! Tangent input |
|---|
| 520 | & zta_tlout, & ! Tangent output |
|---|
| 521 | & zsa_tlout, & ! Tangent output |
|---|
| 522 | & zta_adin , & ! Adjoint input |
|---|
| 523 | & zsa_adin , & ! Adjoint input |
|---|
| 524 | & zta_adout, & ! Adjoint output |
|---|
| 525 | & ztb_adout, & ! Adjoint output |
|---|
| 526 | & zsa_adout, & ! Adjoint output |
|---|
| 527 | & zsb_adout, & ! Adjoint output |
|---|
| 528 | & zr ! 3D random field |
|---|
| 529 | CHARACTER(LEN=14) :: cl_name |
|---|
| 530 | ! Allocate memory |
|---|
| 531 | |
|---|
| 532 | ALLOCATE( & |
|---|
| 533 | & zta_tlin( jpi,jpj,jpk), & |
|---|
| 534 | & zsa_tlin( jpi,jpj,jpk), & |
|---|
| 535 | & ztb_tlin( jpi,jpj,jpk), & |
|---|
| 536 | & zsb_tlin( jpi,jpj,jpk), & |
|---|
| 537 | & zta_tlout(jpi,jpj,jpk), & |
|---|
| 538 | & zsa_tlout(jpi,jpj,jpk), & |
|---|
| 539 | & zta_adin( jpi,jpj,jpk), & |
|---|
| 540 | & zsa_adin( jpi,jpj,jpk), & |
|---|
| 541 | & zta_adout(jpi,jpj,jpk), & |
|---|
| 542 | & zsa_adout(jpi,jpj,jpk), & |
|---|
| 543 | & ztb_adout(jpi,jpj,jpk), & |
|---|
| 544 | & zsb_adout(jpi,jpj,jpk), & |
|---|
| 545 | & zr( jpi,jpj,jpk) & |
|---|
| 546 | & ) |
|---|
| 547 | !================================================================== |
|---|
| 548 | ! 1) dx = ( un_tl, vn_tl, hdivn_tl ) and |
|---|
| 549 | ! dy = ( hdivb_tl, hdivn_tl ) |
|---|
| 550 | !================================================================== |
|---|
| 551 | |
|---|
| 552 | ! initialization (normally done in traldf) |
|---|
| 553 | l_traldf_rot = .TRUE. |
|---|
| 554 | |
|---|
| 555 | ! Test for time steps nit000 and nit000 + 1 (the matrix changes) |
|---|
| 556 | |
|---|
| 557 | DO jstp = nit000, nit000 + 2 |
|---|
| 558 | istp = jstp |
|---|
| 559 | IF ( jstp == nit000+2 ) istp = nitend |
|---|
| 560 | |
|---|
| 561 | !-------------------------------------------------------------------- |
|---|
| 562 | ! Reset the tangent and adjoint variables |
|---|
| 563 | !-------------------------------------------------------------------- |
|---|
| 564 | zta_tlin( :,:,:) = 0.0_wp |
|---|
| 565 | ztb_tlin( :,:,:) = 0.0_wp |
|---|
| 566 | zsa_tlin( :,:,:) = 0.0_wp |
|---|
| 567 | zsb_tlin( :,:,:) = 0.0_wp |
|---|
| 568 | zta_tlout(:,:,:) = 0.0_wp |
|---|
| 569 | zsa_tlout(:,:,:) = 0.0_wp |
|---|
| 570 | zta_adin( :,:,:) = 0.0_wp |
|---|
| 571 | zsa_adin( :,:,:) = 0.0_wp |
|---|
| 572 | zta_adout(:,:,:) = 0.0_wp |
|---|
| 573 | zsa_adout(:,:,:) = 0.0_wp |
|---|
| 574 | ztb_adout(:,:,:) = 0.0_wp |
|---|
| 575 | zsb_adout(:,:,:) = 0.0_wp |
|---|
| 576 | zr( :,:,:) = 0.0_wp |
|---|
| 577 | tsb_ad(:,:,:,:) = 0.0_wp |
|---|
| 578 | tsb_ad(:,:,:,:) = 0.0_wp |
|---|
| 579 | !-------------------------------------------------------------------- |
|---|
| 580 | ! Initialize the tangent input with random noise: dx |
|---|
| 581 | !-------------------------------------------------------------------- |
|---|
| 582 | |
|---|
| 583 | CALL grid_random( zr, 'T', 0.0_wp, stdt ) |
|---|
| 584 | DO jk = 1, jpk |
|---|
| 585 | DO jj = nldj, nlej |
|---|
| 586 | DO ji = nldi, nlei |
|---|
| 587 | zta_tlin(ji,jj,jk) = zr(ji,jj,jk) |
|---|
| 588 | END DO |
|---|
| 589 | END DO |
|---|
| 590 | END DO |
|---|
| 591 | CALL grid_random( zr, 'T', 0.0_wp, stdt ) |
|---|
| 592 | DO jk = 1, jpk |
|---|
| 593 | DO jj = nldj, nlej |
|---|
| 594 | DO ji = nldi, nlei |
|---|
| 595 | ztb_tlin(ji,jj,jk) = zr(ji,jj,jk) |
|---|
| 596 | END DO |
|---|
| 597 | END DO |
|---|
| 598 | END DO |
|---|
| 599 | CALL grid_random( zr, 'T', 0.0_wp, stds ) |
|---|
| 600 | DO jk = 1, jpk |
|---|
| 601 | DO jj = nldj, nlej |
|---|
| 602 | DO ji = nldi, nlei |
|---|
| 603 | zsa_tlin(ji,jj,jk) = zr(ji,jj,jk) |
|---|
| 604 | END DO |
|---|
| 605 | END DO |
|---|
| 606 | END DO |
|---|
| 607 | CALL grid_random( zr, 'T', 0.0_wp, stds ) |
|---|
| 608 | DO jk = 1, jpk |
|---|
| 609 | DO jj = nldj, nlej |
|---|
| 610 | DO ji = nldi, nlei |
|---|
| 611 | zsb_tlin(ji,jj,jk) = zr(ji,jj,jk) |
|---|
| 612 | END DO |
|---|
| 613 | END DO |
|---|
| 614 | END DO |
|---|
| 615 | |
|---|
| 616 | |
|---|
| 617 | tsa_tl(:,:,:,jp_tem) = zta_tlin(:,:,:) |
|---|
| 618 | tsa_tl(:,:,:,jp_sal) = zsa_tlin(:,:,:) |
|---|
| 619 | tsb_tl(:,:,:,jp_tem) = ztb_tlin(:,:,:) |
|---|
| 620 | tsb_tl(:,:,:,jp_sal) = zsb_tlin(:,:,:) |
|---|
| 621 | CALL tra_zdf_imp_tan ( istp, nit000, 'TRA', r2dtra, tsb_tl, tsa_tl, jpts ) |
|---|
| 622 | zta_tlout(:,:,:) = tsa_tl(:,:,:,jp_tem) |
|---|
| 623 | zsa_tlout(:,:,:) = tsa_tl(:,:,:,jp_sal) |
|---|
| 624 | |
|---|
| 625 | !-------------------------------------------------------------------- |
|---|
| 626 | ! Initialize the adjoint variables: dy^* = W dy |
|---|
| 627 | !-------------------------------------------------------------------- |
|---|
| 628 | |
|---|
| 629 | DO jk = 1, jpk |
|---|
| 630 | DO jj = nldj, nlej |
|---|
| 631 | DO ji = nldi, nlei |
|---|
| 632 | zta_adin(ji,jj,jk) = zta_tlout(ji,jj,jk) & |
|---|
| 633 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) & |
|---|
| 634 | & * tmask(ji,jj,jk) * wesp_t(jk) |
|---|
| 635 | zsa_adin(ji,jj,jk) = zsa_tlout(ji,jj,jk) & |
|---|
| 636 | & * e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) & |
|---|
| 637 | & * tmask(ji,jj,jk) * wesp_s(jk) |
|---|
| 638 | END DO |
|---|
| 639 | END DO |
|---|
| 640 | END DO |
|---|
| 641 | !-------------------------------------------------------------------- |
|---|
| 642 | ! Compute the scalar product: ( L dx )^T W dy |
|---|
| 643 | !-------------------------------------------------------------------- |
|---|
| 644 | |
|---|
| 645 | zsp1 = DOT_PRODUCT( zta_tlout, zta_adin ) & |
|---|
| 646 | & + DOT_PRODUCT( zsa_tlout, zsa_adin ) |
|---|
| 647 | |
|---|
| 648 | !-------------------------------------------------------------------- |
|---|
| 649 | ! Call the adjoint routine: dx^* = L^T dy^* |
|---|
| 650 | !-------------------------------------------------------------------- |
|---|
| 651 | |
|---|
| 652 | tsa_ad(:,:,:,jp_tem) = zta_adin(:,:,:) |
|---|
| 653 | tsa_ad(:,:,:,jp_sal) = zsa_adin(:,:,:) |
|---|
| 654 | |
|---|
| 655 | CALL tra_zdf_imp_adj ( istp, nit000, 'TRA', r2dtra, tsb_ad, tsa_ad, jpts ) |
|---|
| 656 | |
|---|
| 657 | zta_adout(:,:,:) = tsa_ad(:,:,:,jp_tem) |
|---|
| 658 | zsa_adout(:,:,:) = tsa_ad(:,:,:,jp_sal) |
|---|
| 659 | ztb_adout(:,:,:) = tsb_ad(:,:,:,jp_tem) |
|---|
| 660 | zsb_adout(:,:,:) = tsb_ad(:,:,:,jp_sal) |
|---|
| 661 | zsp2 = DOT_PRODUCT( zta_tlin, zta_adout ) & |
|---|
| 662 | & + DOT_PRODUCT( zsa_tlin, zsa_adout ) & |
|---|
| 663 | & + DOT_PRODUCT( ztb_tlin, ztb_adout ) & |
|---|
| 664 | & + DOT_PRODUCT( zsb_tlin, zsb_adout ) |
|---|
| 665 | |
|---|
| 666 | ! 14 char:'12345678901234' |
|---|
| 667 | IF ( istp == nit000 ) THEN |
|---|
| 668 | cl_name = 'trazdfimpadjT1' |
|---|
| 669 | ELSEIF ( istp == nit000 +1 ) THEN |
|---|
| 670 | cl_name = 'trazdfimpadjT2' |
|---|
| 671 | ELSEIF ( istp == nitend ) THEN |
|---|
| 672 | cl_name = 'trazdfimpadjT3' |
|---|
| 673 | END IF |
|---|
| 674 | CALL prntst_adj( cl_name, kumadt, zsp1, zsp2 ) |
|---|
| 675 | |
|---|
| 676 | END DO |
|---|
| 677 | |
|---|
| 678 | DEALLOCATE( & |
|---|
| 679 | & zta_tlin, & |
|---|
| 680 | & ztb_tlin, & |
|---|
| 681 | & zsa_tlin, & |
|---|
| 682 | & zsb_tlin, & |
|---|
| 683 | & zta_tlout, & |
|---|
| 684 | & zsa_tlout, & |
|---|
| 685 | & zta_adin, & |
|---|
| 686 | & zsa_adin, & |
|---|
| 687 | & zta_adout, & |
|---|
| 688 | & ztb_adout, & |
|---|
| 689 | & zsa_adout, & |
|---|
| 690 | & zsb_adout, & |
|---|
| 691 | & zr & |
|---|
| 692 | & ) |
|---|
| 693 | |
|---|
| 694 | |
|---|
| 695 | |
|---|
| 696 | END SUBROUTINE tra_zdf_imp_adj_tst |
|---|
| 697 | #endif |
|---|
| 698 | END MODULE trazdf_imp_tam |
|---|
