| 1 | MODULE trazdf_imp |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE trazdf_imp *** |
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| 4 | !! Ocean active tracers: vertical component of the tracer mixing trend |
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| 5 | !!============================================================================== |
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| 6 | !! History : OPA ! 1990-10 (B. Blanke) Original code |
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| 7 | !! 7.0 ! 1991-11 (G. Madec) |
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| 8 | !! - ! 1992-06 (M. Imbard) correction on tracer trend loops |
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| 9 | !! 8.0 ! 1996-01 (G. Madec) statement function for e3 |
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| 10 | !! - ! 1997-05 (G. Madec) vertical component of isopycnal |
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| 11 | !! - ! 1997-07 (G. Madec) geopotential diffusion in s-coord |
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| 12 | !! - ! 2000-08 (G. Madec) double diffusive mixing |
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| 13 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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| 14 | !! 2.0 ! 2006-11 (G. Madec) New step reorganisation |
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| 15 | !! 2.4 ! 2008-01 (G. Madec) Merge TRA-TRC |
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| 16 | !!---------------------------------------------------------------------- |
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| 17 | |
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| 18 | !!---------------------------------------------------------------------- |
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| 19 | !! tra_zdf_imp : Update the tracer trend with the diagonal vertical |
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| 20 | !! part of the mixing tensor. |
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| 21 | !! Vector optimization, use k-j-i loops. |
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| 22 | !!---------------------------------------------------------------------- |
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| 23 | USE oce ! ocean dynamics and tracers variables |
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| 24 | USE dom_oce ! ocean space and time domain variables |
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| 25 | USE zdf_oce ! ocean vertical physics variables |
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| 26 | USE ldftra_oce ! ocean active tracers: lateral physics |
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| 27 | USE ldfslp ! lateral physics: slope of diffusion |
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| 28 | USE trdmod ! ocean active tracers trends |
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| 29 | USE trdmod_oce ! ocean variables trends |
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| 30 | USE zdfddm ! ocean vertical physics: double diffusion |
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| 31 | USE in_out_manager ! I/O manager |
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| 32 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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| 33 | USE prtctl ! Print control |
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| 34 | USE domvvl ! variable volume |
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| 35 | |
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| 36 | IMPLICIT NONE |
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| 37 | PRIVATE |
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| 38 | |
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| 39 | PUBLIC tra_zdf_imp ! routine called by step.F90 |
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| 40 | |
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| 41 | !! * Substitutions |
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| 42 | # include "domzgr_substitute.h90" |
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| 43 | # include "ldftra_substitute.h90" |
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| 44 | # include "zdfddm_substitute.h90" |
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| 45 | # include "vectopt_loop_substitute.h90" |
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| 46 | !!---------------------------------------------------------------------- |
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| 47 | !!---------------------------------------------------------------------- |
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| 48 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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| 49 | !!---------------------------------------------------------------------- |
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| 50 | CONTAINS |
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| 51 | |
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| 52 | SUBROUTINE tra_zdf_imp( kt, p2dt, cdtype ) |
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| 53 | !!---------------------------------------------------------------------- |
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| 54 | !! *** ROUTINE tra_zdf_imp *** |
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| 55 | !! |
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| 56 | !! ** Purpose : Compute the trend due to the vertical tracer diffusion |
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| 57 | !! including the vertical component of lateral mixing (only for 2nd |
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| 58 | !! order operator, for fourth order it is already computed and add |
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| 59 | !! to the general trend in traldf.F) and add it to the general trend |
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| 60 | !! of the tracer equations. |
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| 61 | !! |
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| 62 | !! ** Method : The vertical component of the lateral diffusive trends |
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| 63 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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| 64 | !! potential surfaces to which an eddy induced advection can be |
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| 65 | !! added. It is computed using before fields (forward in time) and |
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| 66 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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| 67 | !! |
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| 68 | !! Second part: vertical trend associated with the vertical physics |
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| 69 | !! =========== (including the vertical flux proportional to dk[t] |
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| 70 | !! associated with the lateral mixing, through the |
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| 71 | !! update of avt) |
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| 72 | !! The vertical diffusion of tracers (t & s) is given by: |
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| 73 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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| 74 | !! It is computed using a backward time scheme (t=ta). |
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| 75 | !! Surface and bottom boundary conditions: no diffusive flux on |
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| 76 | !! both tracers (bottom, applied through the masked field avt). |
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| 77 | !! Add this trend to the general trend ta,sa : |
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| 78 | !! ta = ta + dz( avt dz(t) ) |
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| 79 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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| 80 | !! |
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| 81 | !! Third part: recover avt resulting from the vertical physics |
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| 82 | !! ========== alone, for further diagnostics (for example to |
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| 83 | !! compute the turbocline depth in zdfmxl.F90). |
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| 84 | !! avt = zavt |
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| 85 | !! (avs = zavs if lk_zdfddm=T ) |
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| 86 | !! |
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| 87 | !! ** Action : - Update (ta,sa) with before vertical diffusion trend |
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| 88 | !! |
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| 89 | !!--------------------------------------------------------------------- |
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| 90 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 91 | CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) |
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| 92 | REAL(wp) , INTENT(in ), DIMENSION(jpk) :: p2dt ! vertical profile of tracer time-step |
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| 93 | !! |
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| 94 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 95 | REAL(wp) :: znvvl ! temporary scalars |
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| 96 | REAL(wp) :: ze3tn, ze3ta, zvsfvvl ! variable vertical scale factors |
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| 97 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwd, zws, zwi, zav ! workspace arrays |
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| 98 | !!--------------------------------------------------------------------- |
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| 99 | |
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| 100 | IF( kt == nit000 ) THEN |
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| 101 | IF(lwp)WRITE(numout,*) |
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| 102 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp : implicit vertical mixing (k-j-i loops)' |
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| 103 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 104 | IF( cdtype /= 'TRA' ) THEN |
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| 105 | IF(lwp)WRITE(numout,*) 'CAUTION TRC casei still not coded ' |
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| 106 | ENDIF |
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| 107 | ENDIF |
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| 108 | |
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| 109 | ! I. Local initialization |
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| 110 | ! ----------------------- |
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| 111 | zwd (1,:, : ) = 0.e0 ; zwd (jpi,:,:) = 0.e0 |
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| 112 | zws (1,:, : ) = 0.e0 ; zws (jpi,:,:) = 0.e0 |
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| 113 | zwi (1,:, : ) = 0.e0 ; zwi (jpi,:,:) = 0.e0 |
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| 114 | zav (1,:, : ) = 0.e0 ; zav (jpi,:,:) = 0.e0 |
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| 115 | zav (:,:,jpk) = 0.e0 ; zav ( : ,:,1) = 0.e0 |
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| 116 | |
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| 117 | ! I.1 Variable volume : to take into account vertical variable vertical scale factors |
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| 118 | ! ------------------- |
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| 119 | IF( lk_vvl ) THEN ; znvvl = 1. |
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| 120 | ELSE ; znvvl = 0.e0 |
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| 121 | ENDIF |
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| 122 | |
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| 123 | ! II. Vertical trend associated with the vertical physics |
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| 124 | ! ======================================================= |
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| 125 | ! (including the vertical flux proportional to dk[t] associated |
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| 126 | ! with the lateral mixing, through the avt update) |
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| 127 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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| 128 | |
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| 129 | |
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| 130 | ! II.0 Matrix construction |
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| 131 | ! ------------------------ |
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| 132 | |
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| 133 | ! vertical mixing coef. put in zav |
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| 134 | IF( ln_traldf_iso ) THEN ! zav = avt + lateral mixing contribution |
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| 135 | #if defined key_ldfslp |
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| 136 | DO jk = 2, jpkm1 |
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| 137 | DO jj = 2, jpjm1 |
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| 138 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 139 | zav(ji,jj,jk) = avt(ji,jj,jk) + fsahtw(ji,jj,jk) * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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| 140 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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| 141 | END DO |
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| 142 | END DO |
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| 143 | END DO |
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| 144 | #endif |
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| 145 | ELSE |
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| 146 | zav(:,:,:) = avt(:,:,:) ! zav = avt |
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| 147 | ENDIF |
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| 148 | |
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| 149 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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| 150 | DO jk = 1, jpkm1 |
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| 151 | DO jj = 2, jpjm1 |
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| 152 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 153 | zvsfvvl = fsve3t(ji,jj,jk) * ( 1 + ssha(ji,jj) * mut(ji,jj,jk) ) |
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| 154 | ze3ta = ( 1. - znvvl ) + znvvl*zvsfvvl ! after scale factor at T-point |
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| 155 | ze3tn = ( 1. - znvvl )*fse3t(ji,jj,jk) + znvvl ! now scale factor at T-point |
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| 156 | zwi(ji,jj,jk) = - p2dt(jk) * zav(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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| 157 | zws(ji,jj,jk) = - p2dt(jk) * zav(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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| 158 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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| 159 | END DO |
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| 160 | END DO |
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| 161 | END DO |
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| 162 | |
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| 163 | ! Surface boudary conditions |
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| 164 | DO jj = 2, jpjm1 |
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| 165 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 166 | zvsfvvl = fsve3t(ji,jj,1) * ( 1 + ssha(ji,jj) * mut(ji,jj,1) ) |
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| 167 | ze3ta = ( 1. - znvvl ) + znvvl*zvsfvvl ! after scale factor at T-point |
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| 168 | zwi(ji,jj,1) = 0.e0 |
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| 169 | zwd(ji,jj,1) = ze3ta - zws(ji,jj,1) |
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| 170 | END DO |
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| 171 | END DO |
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| 172 | |
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| 173 | |
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| 174 | ! II.1. Vertical diffusion on t |
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| 175 | ! --------------------------- |
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| 176 | CALL zdf_imp( p2dt, zwd, zws, zwi, tb, ta ) |
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| 177 | |
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| 178 | |
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| 179 | ! II.2 Vertical diffusion on salinity |
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| 180 | ! ----------------------------------- |
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| 181 | |
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| 182 | !!gm question: why surface value of zav is zero???? to be checked |
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| 183 | IF( lk_zdfddm ) THEN |
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| 184 | ! vertical mixing coef. on salintity including isopycnal slope (if necessary) put in zav |
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| 185 | IF( ln_traldf_iso ) THEN ! zav = avt + lateral mixing contribution |
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| 186 | #if defined key_ldfslp |
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| 187 | DO jk = 2, jpkm1 |
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| 188 | DO jj = 2, jpjm1 |
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| 189 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 190 | zav(ji,jj,jk) = zav(ji,jj,jk) - avt(ji,jj,jk) + fsavs(ji,jj,jk) |
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| 191 | END DO |
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| 192 | END DO |
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| 193 | END DO |
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| 194 | #endif |
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| 195 | ELSE ! zav = avs |
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| 196 | zav(:,:,:) = avs(:,:,:) |
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| 197 | ENDIF |
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| 198 | |
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| 199 | ! Rebuild the Matrix as avt /= avs |
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| 200 | |
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| 201 | ! Diagonal, inferior, superior (including the bottom boundary condition via avs masked) |
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| 202 | DO jk = 1, jpkm1 |
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| 203 | DO jj = 2, jpjm1 |
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| 204 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 205 | zvsfvvl = fsve3t(ji,jj,jk) * ( 1 + ssha(ji,jj) * mut(ji,jj,jk) ) |
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| 206 | ze3ta = ( 1. - znvvl ) + znvvl*zvsfvvl ! after scale factor at T-point |
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| 207 | ze3tn = ( 1. - znvvl )*fse3t(ji,jj,jk) + znvvl ! now scale factor at T-point |
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| 208 | zwi(ji,jj,jk) = - p2dt(jk) * zav(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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| 209 | zws(ji,jj,jk) = - p2dt(jk) * zav(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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| 210 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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| 211 | END DO |
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| 212 | END DO |
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| 213 | END DO |
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| 214 | |
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| 215 | ! Surface boudary conditions |
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| 216 | DO jj = 2, jpjm1 |
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| 217 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 218 | zvsfvvl = fsve3t(ji,jj,1) * ( 1 + ssha(ji,jj) * mut(ji,jj,1) ) |
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| 219 | ze3ta = ( 1. - znvvl ) + znvvl*zvsfvvl ! after scale factor at T-point |
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| 220 | zwi(ji,jj,1) = 0.e0 |
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| 221 | zwd(ji,jj,1) = ze3ta - zws(ji,jj,1) |
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| 222 | END DO |
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| 223 | END DO |
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| 224 | ! |
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| 225 | ENDIF |
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| 226 | |
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| 227 | CALL zdf_imp( p2dt, zwd, zws, zwi, tb, ta ) |
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| 228 | ! |
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| 229 | END SUBROUTINE tra_zdf_imp |
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| 230 | |
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| 231 | |
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| 232 | SUBROUTINE zdf_imp( p2dt, pwd, pws, pwi, ptb, pta ) |
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| 233 | !!---------------------------------------------------------------------- |
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| 234 | !! *** ROUTINE tra_zdf_imp *** |
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| 235 | !! |
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| 236 | !! ** Purpose : Compute the trend due to the vertical tracer diffusion |
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| 237 | !! including the vertical component of lateral mixing (only for 2nd |
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| 238 | !! order operator, for fourth order it is already computed and add |
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| 239 | !! to the general trend in traldf.F) and add it to the general trend |
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| 240 | !! of the tracer equations. |
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| 241 | !! |
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| 242 | !! ** Method : The vertical component of the lateral diffusive trends |
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| 243 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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| 244 | !! potential surfaces to which an eddy induced advection can be |
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| 245 | !! added. It is computed using before fields (forward in time) and |
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| 246 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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| 247 | !! |
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| 248 | !! Second part: vertical trend associated with the vertical physics |
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| 249 | !! =========== (including the vertical flux proportional to dk[t] |
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| 250 | !! associated with the lateral mixing, through the |
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| 251 | !! update of avt) |
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| 252 | !! The vertical diffusion of tracers (t & s) is given by: |
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| 253 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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| 254 | !! It is computed using a backward time scheme (t=ta). |
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| 255 | !! Surface and bottom boundary conditions: no diffusive flux on |
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| 256 | !! both tracers (bottom, applied through the masked field avt). |
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| 257 | !! Add this trend to the general trend ta,sa : |
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| 258 | !! ta = ta + dz( avt dz(t) ) |
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| 259 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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| 260 | !! |
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| 261 | !! Third part: recover avt resulting from the vertical physics |
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| 262 | !! ========== alone, for further diagnostics (for example to |
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| 263 | !! compute the turbocline depth in zdfmxl.F90). |
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| 264 | !! avt = zavt |
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| 265 | !! (avs = zavs if lk_zdfddm=T ) |
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| 266 | !! |
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| 267 | !! ** Action : - Update (ta,sa) with before vertical diffusion trend |
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| 268 | !! |
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| 269 | !!--------------------------------------------------------------------- |
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| 270 | REAL(wp), INTENT(in ), DIMENSION(jpk) :: p2dt ! vertical profile of tracer time-step |
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| 271 | REAL(wp), INTENT(in ), DIMENSION(jpi,jpj,jpk) :: pwd ! matrix: diagnal terms |
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| 272 | REAL(wp), INTENT(in ), DIMENSION(jpi,jpj,jpk) :: pws ! matrix: upper terms |
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| 273 | REAL(wp), INTENT(in ), DIMENSION(jpi,jpj,jpk) :: pwi ! matrix: lower terms |
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| 274 | REAL(wp), INTENT(in ), DIMENSION(jpi,jpj,jpk) :: ptb ! before tracer field |
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| 275 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pta ! in : tracer trend |
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| 276 | ! ! out: after tracer |
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| 277 | !! |
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| 278 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 279 | REAL(wp) :: zrhs, znvvl ! temporary scalars |
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| 280 | REAL(wp) :: ze3tb, ze3tn, zvsfvvl ! variable vertical scale factors |
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| 281 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwt ! workspace arrays |
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| 282 | !!--------------------------------------------------------------------- |
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| 283 | |
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| 284 | ! Variable volume : to take into account vertical variable vertical scale factors |
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| 285 | IF( lk_vvl ) THEN ; znvvl = 1. |
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| 286 | ELSE ; znvvl = 0.e0 |
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| 287 | ENDIF |
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| 288 | |
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| 289 | !! Matrix inversion from the first level |
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| 290 | !!---------------------------------------------------------------------- |
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| 291 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 292 | ! |
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| 293 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 294 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 295 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 296 | ! ( ... )( ... ) ( ... ) |
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| 297 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 298 | ! |
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| 299 | ! m is decomposed in the product of an upper and lower triangular matrix |
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| 300 | ! The 3 diagonal terms are the input 3d arrays: zwd, zws, zwi |
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| 301 | ! The second member and solution are put in pta array |
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| 302 | ! The zwt array is a work space array |
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| 303 | |
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| 304 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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| 305 | DO jj = 2, jpjm1 |
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| 306 | DO ji = fs_2, fs_jpim1 |
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| 307 | zwt(ji,jj,1) = pwd(ji,jj,1) |
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| 308 | END DO |
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| 309 | END DO |
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| 310 | DO jk = 2, jpkm1 |
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| 311 | DO jj = 2, jpjm1 |
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| 312 | DO ji = fs_2, fs_jpim1 |
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| 313 | zwt(ji,jj,jk) = pwd(ji,jj,jk) - pwi(ji,jj,jk) * pws(ji,jj,jk-1) /zwt(ji,jj,jk-1) |
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| 314 | END DO |
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| 315 | END DO |
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| 316 | END DO |
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| 317 | |
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| 318 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 319 | DO jj = 2, jpjm1 |
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| 320 | DO ji = fs_2, fs_jpim1 |
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| 321 | zvsfvvl = fsve3t(ji,jj,1) * ( 1 + sshb(ji,jj) * mut(ji,jj,1) ) |
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| 322 | ze3tb = ( 1. - znvvl ) + znvvl*zvsfvvl |
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| 323 | ze3tn = ( 1. - znvvl ) + znvvl*fse3t (ji,jj,1) |
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| 324 | pta(ji,jj,1) = ze3tb * ptb(ji,jj,1) + p2dt(1) * ze3tn * pta(ji,jj,1) |
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| 325 | END DO |
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| 326 | END DO |
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| 327 | DO jk = 2, jpkm1 |
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| 328 | DO jj = 2, jpjm1 |
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| 329 | DO ji = fs_2, fs_jpim1 |
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| 330 | zvsfvvl = fsve3t(ji,jj,jk) * ( 1 + sshb(ji,jj) * mut(ji,jj,jk) ) |
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| 331 | ze3tb = ( 1. - znvvl ) + znvvl*zvsfvvl |
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| 332 | ze3tn = ( 1. - znvvl ) + znvvl*fse3t (ji,jj,jk) |
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| 333 | zrhs = ze3tb * tb(ji,jj,jk) + p2dt(jk) * ze3tn * ta(ji,jj,jk) ! zrhs=right hand side |
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| 334 | pta(ji,jj,jk) = zrhs - pwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pta(ji,jj,jk-1) |
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| 335 | END DO |
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| 336 | END DO |
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| 337 | END DO |
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| 338 | |
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| 339 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 340 | ! Save the masked temperature after in ta |
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| 341 | ! (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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| 342 | DO jj = 2, jpjm1 |
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| 343 | DO ji = fs_2, fs_jpim1 |
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| 344 | pta(ji,jj,jpkm1) = pta(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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| 345 | END DO |
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| 346 | END DO |
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| 347 | DO jk = jpk-2, 1, -1 |
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| 348 | DO jj = 2, jpjm1 |
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| 349 | DO ji = fs_2, fs_jpim1 |
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| 350 | pta(ji,jj,jk) = ( pta(ji,jj,jk) - pws(ji,jj,jk) * ta(ji,jj,jk+1) ) & |
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| 351 | & / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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| 352 | END DO |
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| 353 | END DO |
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| 354 | END DO |
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| 355 | ! |
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| 356 | END SUBROUTINE zdf_imp |
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| 357 | |
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| 358 | !!============================================================================== |
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| 359 | END MODULE trazdf_imp |
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