[3] | 1 | MODULE trazdf_imp |
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| 2 | !!============================================================================== |
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[457] | 3 | !! *** MODULE trazdf_imp *** |
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[3] | 4 | !! Ocean active tracers: vertical component of the tracer mixing trend |
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| 5 | !!============================================================================== |
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[457] | 6 | !! History : |
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| 7 | !! 6.0 ! 90-10 (B. Blanke) Original code |
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| 8 | !! 7.0 ! 91-11 (G. Madec) |
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| 9 | !! ! 92-06 (M. Imbard) correction on tracer trend loops |
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| 10 | !! ! 96-01 (G. Madec) statement function for e3 |
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| 11 | !! ! 97-05 (G. Madec) vertical component of isopycnal |
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| 12 | !! ! 97-07 (G. Madec) geopotential diffusion in s-coord |
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| 13 | !! ! 00-08 (G. Madec) double diffusive mixing |
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| 14 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
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[503] | 15 | !! 9.0 ! 06-11 (G. Madec) New step reorganisation |
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[3] | 16 | !!---------------------------------------------------------------------- |
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[457] | 17 | !! tra_zdf_imp : Update the tracer trend with the diagonal vertical |
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| 18 | !! part of the mixing tensor. |
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| 19 | !! Vector optimization, use k-j-i loops. |
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[3] | 20 | !!---------------------------------------------------------------------- |
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| 21 | !! * Modules used |
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[457] | 22 | USE oce ! ocean dynamics and tracers variables |
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| 23 | USE dom_oce ! ocean space and time domain variables |
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| 24 | USE zdf_oce ! ocean vertical physics variables |
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[216] | 25 | USE ldftra_oce ! ocean active tracers: lateral physics |
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[457] | 26 | USE ldfslp ! lateral physics: slope of diffusion |
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[216] | 27 | USE trdmod ! ocean active tracers trends |
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| 28 | USE trdmod_oce ! ocean variables trends |
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[457] | 29 | USE zdfddm ! ocean vertical physics: double diffusion |
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[3] | 30 | USE in_out_manager ! I/O manager |
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[457] | 31 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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[258] | 32 | USE prtctl ! Print control |
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[3] | 33 | |
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| 34 | IMPLICIT NONE |
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| 35 | PRIVATE |
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| 36 | |
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| 37 | !! * Routine accessibility |
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[457] | 38 | PUBLIC tra_zdf_imp ! routine called by step.F90 |
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[3] | 39 | |
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| 40 | !! * Substitutions |
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| 41 | # include "domzgr_substitute.h90" |
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[457] | 42 | # include "ldftra_substitute.h90" |
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[3] | 43 | # include "zdfddm_substitute.h90" |
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[457] | 44 | # include "vectopt_loop_substitute.h90" |
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[3] | 45 | !!---------------------------------------------------------------------- |
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| 46 | !!---------------------------------------------------------------------- |
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[457] | 47 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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| 48 | !!---------------------------------------------------------------------- |
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[3] | 49 | CONTAINS |
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[457] | 50 | |
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| 51 | SUBROUTINE tra_zdf_imp( kt, p2dt ) |
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[3] | 52 | !!---------------------------------------------------------------------- |
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| 53 | !! *** ROUTINE tra_zdf_imp *** |
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| 54 | !! |
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[457] | 55 | !! ** Purpose : Compute the trend due to the vertical tracer diffusion |
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| 56 | !! including the vertical component of lateral mixing (only for 2nd |
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| 57 | !! order operator, for fourth order it is already computed and add |
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| 58 | !! to the general trend in traldf.F) and add it to the general trend |
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| 59 | !! of the tracer equations. |
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[3] | 60 | !! |
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[457] | 61 | !! ** Method : The vertical component of the lateral diffusive trends |
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[503] | 62 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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[457] | 63 | !! potential surfaces to which an eddy induced advection can be |
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| 64 | !! added. It is computed using before fields (forward in time) and |
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| 65 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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| 66 | !! |
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| 67 | !! Second part: vertical trend associated with the vertical physics |
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| 68 | !! =========== (including the vertical flux proportional to dk[t] |
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| 69 | !! associated with the lateral mixing, through the |
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| 70 | !! update of avt) |
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| 71 | !! The vertical diffusion of tracers (t & s) is given by: |
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| 72 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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| 73 | !! It is computed using a backward time scheme (t=ta). |
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[3] | 74 | !! Surface and bottom boundary conditions: no diffusive flux on |
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| 75 | !! both tracers (bottom, applied through the masked field avt). |
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| 76 | !! Add this trend to the general trend ta,sa : |
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[457] | 77 | !! ta = ta + dz( avt dz(t) ) |
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| 78 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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[3] | 79 | !! |
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[457] | 80 | !! Third part: recover avt resulting from the vertical physics |
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| 81 | !! ========== alone, for further diagnostics (for example to |
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| 82 | !! compute the turbocline depth in zdfmxl.F90). |
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| 83 | !! avt = zavt |
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| 84 | !! (avs = zavs if lk_zdfddm=T ) |
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[3] | 85 | !! |
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[457] | 86 | !! ** Action : - Update (ta,sa) with before vertical diffusion trend |
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| 87 | !! |
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[3] | 88 | !!--------------------------------------------------------------------- |
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[457] | 89 | !! * Modules used |
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| 90 | USE oce , ONLY : zwd => ua, & ! ua used as workspace |
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| 91 | zws => va ! va " " |
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[3] | 92 | !! * Arguments |
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[457] | 93 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 94 | REAL(wp), DIMENSION(jpk), INTENT( in ) :: & |
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| 95 | p2dt ! vertical profile of tracer time-step |
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[3] | 96 | |
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| 97 | !! * Local declarations |
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[457] | 98 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 99 | REAL(wp) :: zavi, zrhs ! temporary scalars |
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| 100 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & |
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| 101 | zwi, zwt, zavsi ! workspace arrays |
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[3] | 102 | !!--------------------------------------------------------------------- |
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| 103 | |
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[457] | 104 | IF( kt == nit000 ) THEN |
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| 105 | IF(lwp)WRITE(numout,*) |
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| 106 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp : implicit vertical mixing (k-j-i loops)' |
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| 107 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 108 | zavi = 0.e0 ! avoid warning at compilation phase when lk_ldfslp=F |
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| 109 | ENDIF |
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[3] | 110 | |
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[457] | 111 | ! I. Local initialization |
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| 112 | ! ----------------------- |
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| 113 | zwd (1,:, : ) = 0.e0 ; zwd (jpi,:,:) = 0.e0 |
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| 114 | zws (1,:, : ) = 0.e0 ; zws (jpi,:,:) = 0.e0 |
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| 115 | zwi (1,:, : ) = 0.e0 ; zwi (jpi,:,:) = 0.e0 |
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| 116 | zwt (1,:, : ) = 0.e0 ; zwt (jpi,:,:) = 0.e0 |
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| 117 | zavsi(1,:, : ) = 0.e0 ; zavsi(jpi,:,:) = 0.e0 |
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| 118 | zwt (:,:,jpk) = 0.e0 ; zwt ( : ,:,1) = 0.e0 |
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| 119 | zavsi(:,:,jpk) = 0.e0 ; zavsi( : ,:,1) = 0.e0 |
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[3] | 120 | |
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[457] | 121 | ! II. Vertical trend associated with the vertical physics |
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| 122 | ! ======================================================= |
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| 123 | ! (including the vertical flux proportional to dk[t] associated |
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| 124 | ! with the lateral mixing, through the avt update) |
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| 125 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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[3] | 126 | |
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[216] | 127 | |
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[457] | 128 | ! II.0 Matrix construction |
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| 129 | ! ------------------------ |
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[3] | 130 | |
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[457] | 131 | #if defined key_ldfslp |
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| 132 | ! update and save of avt (and avs if double diffusive mixing) |
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| 133 | DO jk = 2, jpkm1 |
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| 134 | DO jj = 2, jpjm1 |
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| 135 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 136 | zavi = fsahtw(ji,jj,jk) & ! vertical mixing coef. due to lateral mixing |
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| 137 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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| 138 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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| 139 | zwt(ji,jj,jk) = avt(ji,jj,jk) + zavi ! zwt=avt+zavi (total vertical mixing coef. on temperature) |
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| 140 | # if defined key_zdfddm |
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| 141 | zavsi(ji,jj,jk) = fsavs(ji,jj,jk) + zavi ! dd mixing: zavsi = total vertical mixing coef. on salinity |
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| 142 | # endif |
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[3] | 143 | END DO |
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| 144 | END DO |
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[457] | 145 | END DO |
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[3] | 146 | |
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[457] | 147 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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| 148 | DO jk = 1, jpkm1 |
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| 149 | DO jj = 2, jpjm1 |
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| 150 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 151 | zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk ) ) |
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| 152 | zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk+1) ) |
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| 153 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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[255] | 154 | END DO |
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| 155 | END DO |
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[457] | 156 | END DO |
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[255] | 157 | #else |
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[457] | 158 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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| 159 | DO jk = 1, jpkm1 |
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| 160 | DO jj = 2, jpjm1 |
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| 161 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 162 | zwi(ji,jj,jk) = - p2dt(jk) * avt(ji,jj,jk ) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk ) ) |
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| 163 | zws(ji,jj,jk) = - p2dt(jk) * avt(ji,jj,jk+1) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk+1) ) |
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| 164 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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[3] | 165 | END DO |
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| 166 | END DO |
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[457] | 167 | END DO |
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[255] | 168 | #endif |
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[3] | 169 | |
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[457] | 170 | ! Surface boudary conditions |
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| 171 | DO jj = 2, jpjm1 |
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| 172 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 173 | zwi(ji,jj,1) = 0.e0 |
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| 174 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
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| 175 | END DO |
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| 176 | END DO |
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[3] | 177 | |
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| 178 | |
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[457] | 179 | ! II.1. Vertical diffusion on t |
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| 180 | ! --------------------------- |
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| 181 | |
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| 182 | !! Matrix inversion from the first level |
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| 183 | !!---------------------------------------------------------------------- |
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| 184 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 185 | ! |
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| 186 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 187 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 188 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 189 | ! ( ... )( ... ) ( ... ) |
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| 190 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 191 | ! |
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| 192 | ! m is decomposed in the product of an upper and lower triangular matrix |
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| 193 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 194 | ! The second member is in 2d array zwy |
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| 195 | ! The solution is in 2d array zwx |
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| 196 | ! The 3d arry zwt is a work space array |
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| 197 | ! zwy is used and then used as a work space array : its value is modified! |
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| 198 | |
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| 199 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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| 200 | DO jj = 2, jpjm1 |
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| 201 | DO ji = fs_2, fs_jpim1 |
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| 202 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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| 203 | END DO |
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| 204 | END DO |
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| 205 | DO jk = 2, jpkm1 |
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| 206 | DO jj = 2, jpjm1 |
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| 207 | DO ji = fs_2, fs_jpim1 |
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| 208 | 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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[3] | 209 | END DO |
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| 210 | END DO |
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[457] | 211 | END DO |
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[3] | 212 | |
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[457] | 213 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 214 | DO jj = 2, jpjm1 |
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| 215 | DO ji = fs_2, fs_jpim1 |
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| 216 | ta(ji,jj,1) = tb(ji,jj,1) + p2dt(1) * ta(ji,jj,1) |
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| 217 | END DO |
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| 218 | END DO |
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| 219 | DO jk = 2, jpkm1 |
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| 220 | DO jj = 2, jpjm1 |
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| 221 | DO ji = fs_2, fs_jpim1 |
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| 222 | zrhs = tb(ji,jj,jk) + p2dt(jk) * ta(ji,jj,jk) ! zrhs=right hand side |
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| 223 | ta(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *ta(ji,jj,jk-1) |
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| 224 | END DO |
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| 225 | END DO |
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| 226 | END DO |
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[3] | 227 | |
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[457] | 228 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 229 | ! Save the masked temperature after in ta |
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| 230 | ! (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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| 231 | DO jj = 2, jpjm1 |
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| 232 | DO ji = fs_2, fs_jpim1 |
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| 233 | ta(ji,jj,jpkm1) = ta(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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| 234 | END DO |
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| 235 | END DO |
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| 236 | DO jk = jpk-2, 1, -1 |
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| 237 | DO jj = 2, jpjm1 |
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| 238 | DO ji = fs_2, fs_jpim1 |
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| 239 | ta(ji,jj,jk) = ( ta(ji,jj,jk) - zws(ji,jj,jk) * ta(ji,jj,jk+1) ) / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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| 240 | END DO |
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| 241 | END DO |
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| 242 | END DO |
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[3] | 243 | |
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[457] | 244 | ! II.2 Vertical diffusion on salinity |
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| 245 | ! ----------------------------------- |
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| 246 | |
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[3] | 247 | #if defined key_zdfddm |
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[457] | 248 | ! Rebuild the Matrix as avt /= avs |
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[3] | 249 | |
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[457] | 250 | ! Diagonal, inferior, superior (including the bottom boundary condition via avs masked) |
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| 251 | # if defined key_ldfslp |
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| 252 | DO jk = 1, jpkm1 |
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| 253 | DO jj = 2, jpjm1 |
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| 254 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 255 | zwi(ji,jj,jk) = - p2dt(jk) * zavsi(ji,jj,jk ) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk ) ) |
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| 256 | zws(ji,jj,jk) = - p2dt(jk) * zavsi(ji,jj,jk+1) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk+1) ) |
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| 257 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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[3] | 258 | END DO |
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| 259 | END DO |
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[457] | 260 | END DO |
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| 261 | # else |
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| 262 | DO jk = 1, jpkm1 |
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| 263 | DO jj = 2, jpjm1 |
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| 264 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 265 | zwi(ji,jj,jk) = - p2dt(jk) * avs(ji,jj,jk ) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk ) ) |
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| 266 | zws(ji,jj,jk) = - p2dt(jk) * avs(ji,jj,jk+1) / ( fse3t(ji,jj,jk) * fse3w(ji,jj,jk+1) ) |
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| 267 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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[255] | 268 | END DO |
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| 269 | END DO |
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[457] | 270 | END DO |
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| 271 | # endif |
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| 272 | |
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| 273 | ! Surface boudary conditions |
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| 274 | DO jj = 2, jpjm1 |
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| 275 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 276 | zwi(ji,jj,1) = 0.e0 |
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| 277 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
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[3] | 278 | END DO |
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[457] | 279 | END DO |
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[255] | 280 | #endif |
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[3] | 281 | |
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| 282 | |
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[457] | 283 | !! Matrix inversion from the first level |
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| 284 | !!---------------------------------------------------------------------- |
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| 285 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 286 | ! |
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| 287 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 288 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 289 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 290 | ! ( ... )( ... ) ( ... ) |
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| 291 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 292 | ! |
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| 293 | ! m is decomposed in the product of an upper and lower triangular |
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| 294 | ! matrix |
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| 295 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 296 | ! The second member is in 2d array zwy |
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| 297 | ! The solution is in 2d array zwx |
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| 298 | ! The 3d arry zwt is a work space array |
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| 299 | ! zwy is used and then used as a work space array : its value is modified! |
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[3] | 300 | |
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[457] | 301 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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| 302 | DO jj = 2, jpjm1 |
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| 303 | DO ji = fs_2, fs_jpim1 |
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| 304 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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| 305 | END DO |
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| 306 | END DO |
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| 307 | DO jk = 2, jpkm1 |
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| 308 | DO jj = 2, jpjm1 |
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| 309 | DO ji = fs_2, fs_jpim1 |
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| 310 | 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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[3] | 311 | END DO |
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| 312 | END DO |
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[457] | 313 | END DO |
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[3] | 314 | |
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[457] | 315 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 316 | DO jj = 2, jpjm1 |
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| 317 | DO ji = fs_2, fs_jpim1 |
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| 318 | sa(ji,jj,1) = sb(ji,jj,1) + p2dt(1) * sa(ji,jj,1) |
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| 319 | END DO |
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| 320 | END DO |
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| 321 | DO jk = 2, jpkm1 |
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| 322 | DO jj = 2, jpjm1 |
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| 323 | DO ji = fs_2, fs_jpim1 |
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| 324 | zrhs = sb(ji,jj,jk) + p2dt(jk) * sa(ji,jj,jk) ! zrhs=right hand side |
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| 325 | sa(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *sa(ji,jj,jk-1) |
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| 326 | END DO |
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| 327 | END DO |
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| 328 | END DO |
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[3] | 329 | |
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[457] | 330 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 331 | ! Save the masked temperature after in ta |
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| 332 | ! (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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| 333 | DO jj = 2, jpjm1 |
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| 334 | DO ji = fs_2, fs_jpim1 |
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| 335 | sa(ji,jj,jpkm1) = sa(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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[216] | 336 | END DO |
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[457] | 337 | END DO |
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| 338 | DO jk = jpk-2, 1, -1 |
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| 339 | DO jj = 2, jpjm1 |
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| 340 | DO ji = fs_2, fs_jpim1 |
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| 341 | sa(ji,jj,jk) = ( sa(ji,jj,jk) - zws(ji,jj,jk) * sa(ji,jj,jk+1) ) / zwt(ji,jj,jk) * tmask(ji,jj,jk) |
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| 342 | END DO |
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| 343 | END DO |
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| 344 | END DO |
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[216] | 345 | |
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[3] | 346 | END SUBROUTINE tra_zdf_imp |
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| 347 | |
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| 348 | !!============================================================================== |
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| 349 | END MODULE trazdf_imp |
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