[3] | 1 | MODULE trazdf_imp |
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[1438] | 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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[1438] | 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 | !! ! 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 | !! 3.2 ! 2009-03 (G. Madec) heat and salt content trends |
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[3] | 16 | !!---------------------------------------------------------------------- |
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[1438] | 17 | |
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| 18 | !!---------------------------------------------------------------------- |
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[457] | 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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[3] | 21 | !!---------------------------------------------------------------------- |
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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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[592] | 33 | USE domvvl ! variable volume |
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[915] | 34 | USE ldftra ! lateral mixing type |
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[3] | 35 | |
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| 36 | IMPLICIT NONE |
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| 37 | PRIVATE |
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| 38 | |
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[1438] | 39 | PUBLIC tra_zdf_imp ! routine called by step.F90 |
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[3] | 40 | |
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| 41 | !! * Substitutions |
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| 42 | # include "domzgr_substitute.h90" |
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[457] | 43 | # include "ldftra_substitute.h90" |
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[3] | 44 | # include "zdfddm_substitute.h90" |
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[457] | 45 | # include "vectopt_loop_substitute.h90" |
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[3] | 46 | !!---------------------------------------------------------------------- |
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[1438] | 47 | !! NEMO/OPA 3.2 , LOCEAN-IPSL (2009) |
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[1156] | 48 | !! $Id$ |
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| 49 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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[457] | 50 | !!---------------------------------------------------------------------- |
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[3] | 51 | CONTAINS |
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[457] | 52 | |
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| 53 | SUBROUTINE tra_zdf_imp( kt, p2dt ) |
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[3] | 54 | !!---------------------------------------------------------------------- |
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| 55 | !! *** ROUTINE tra_zdf_imp *** |
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| 56 | !! |
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[457] | 57 | !! ** Purpose : Compute the trend due to the vertical tracer diffusion |
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| 58 | !! including the vertical component of lateral mixing (only for 2nd |
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| 59 | !! order operator, for fourth order it is already computed and add |
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| 60 | !! to the general trend in traldf.F) and add it to the general trend |
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| 61 | !! of the tracer equations. |
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[3] | 62 | !! |
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[457] | 63 | !! ** Method : The vertical component of the lateral diffusive trends |
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[503] | 64 | !! is provided by a 2nd order operator rotated along neutral or geo- |
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[457] | 65 | !! potential surfaces to which an eddy induced advection can be |
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| 66 | !! added. It is computed using before fields (forward in time) and |
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| 67 | !! isopycnal or geopotential slopes computed in routine ldfslp. |
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| 68 | !! |
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| 69 | !! Second part: vertical trend associated with the vertical physics |
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| 70 | !! =========== (including the vertical flux proportional to dk[t] |
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| 71 | !! associated with the lateral mixing, through the |
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| 72 | !! update of avt) |
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| 73 | !! The vertical diffusion of tracers (t & s) is given by: |
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| 74 | !! difft = dz( avt dz(t) ) = 1/e3t dk+1( avt/e3w dk(t) ) |
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| 75 | !! It is computed using a backward time scheme (t=ta). |
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[3] | 76 | !! Surface and bottom boundary conditions: no diffusive flux on |
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| 77 | !! both tracers (bottom, applied through the masked field avt). |
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| 78 | !! Add this trend to the general trend ta,sa : |
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[457] | 79 | !! ta = ta + dz( avt dz(t) ) |
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| 80 | !! (sa = sa + dz( avs dz(t) ) if lk_zdfddm=T ) |
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[3] | 81 | !! |
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[457] | 82 | !! Third part: recover avt resulting from the vertical physics |
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| 83 | !! ========== alone, for further diagnostics (for example to |
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| 84 | !! compute the turbocline depth in zdfmxl.F90). |
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| 85 | !! avt = zavt |
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| 86 | !! (avs = zavs if lk_zdfddm=T ) |
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[3] | 87 | !! |
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[457] | 88 | !! ** Action : - Update (ta,sa) with before vertical diffusion trend |
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| 89 | !! |
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[3] | 90 | !!--------------------------------------------------------------------- |
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[1438] | 91 | USE oce , ONLY : zwd => ua ! ua used as workspace |
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| 92 | USE oce , ONLY : zws => va ! va - - |
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| 93 | !! |
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| 94 | INTEGER , INTENT(in) :: kt ! ocean time-step index |
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| 95 | REAL(wp), DIMENSION(jpk), INTENT(in) :: p2dt ! vertical profile of tracer time-step |
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| 96 | !! |
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| 97 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 98 | REAL(wp) :: zavi, zrhs, znvvl ! temporary scalars |
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| 99 | REAL(wp) :: ze3tb, ze3tn, ze3ta ! variable vertical scale factors |
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| 100 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwt, zavsi ! workspace arrays |
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[3] | 101 | !!--------------------------------------------------------------------- |
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| 102 | |
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[457] | 103 | IF( kt == nit000 ) THEN |
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| 104 | IF(lwp)WRITE(numout,*) |
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[789] | 105 | IF(lwp)WRITE(numout,*) 'tra_zdf_imp : implicit vertical mixing' |
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[457] | 106 | IF(lwp)WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 107 | zavi = 0.e0 ! avoid warning at compilation phase when lk_ldfslp=F |
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| 108 | ENDIF |
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[3] | 109 | |
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[457] | 110 | ! I. Local initialization |
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| 111 | ! ----------------------- |
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| 112 | zwd (1,:, : ) = 0.e0 ; zwd (jpi,:,:) = 0.e0 |
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| 113 | zws (1,:, : ) = 0.e0 ; zws (jpi,:,:) = 0.e0 |
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| 114 | zwi (1,:, : ) = 0.e0 ; zwi (jpi,:,:) = 0.e0 |
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| 115 | zwt (1,:, : ) = 0.e0 ; zwt (jpi,:,:) = 0.e0 |
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| 116 | zavsi(1,:, : ) = 0.e0 ; zavsi(jpi,:,:) = 0.e0 |
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| 117 | zwt (:,:,jpk) = 0.e0 ; zwt ( : ,:,1) = 0.e0 |
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| 118 | zavsi(:,:,jpk) = 0.e0 ; zavsi( : ,:,1) = 0.e0 |
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[3] | 119 | |
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[592] | 120 | ! I.1 Variable volume : to take into account vertical variable vertical scale factors |
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| 121 | ! ------------------- |
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| 122 | IF( lk_vvl ) THEN ; znvvl = 1. |
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| 123 | ELSE ; znvvl = 0.e0 |
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| 124 | ENDIF |
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| 125 | |
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[457] | 126 | ! II. Vertical trend associated with the vertical physics |
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| 127 | ! ======================================================= |
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| 128 | ! (including the vertical flux proportional to dk[t] associated |
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| 129 | ! with the lateral mixing, through the avt update) |
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| 130 | ! dk[ avt dk[ (t,s) ] ] diffusive trends |
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[3] | 131 | |
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[216] | 132 | |
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[457] | 133 | ! II.0 Matrix construction |
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| 134 | ! ------------------------ |
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[3] | 135 | |
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[457] | 136 | #if defined key_ldfslp |
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| 137 | ! update and save of avt (and avs if double diffusive mixing) |
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[915] | 138 | IF( l_traldf_rot ) THEN |
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[902] | 139 | DO jk = 2, jpkm1 |
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| 140 | DO jj = 2, jpjm1 |
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| 141 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 142 | zavi = fsahtw(ji,jj,jk) & ! vertical mixing coef. due to lateral mixing |
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| 143 | & * ( wslpi(ji,jj,jk) * wslpi(ji,jj,jk) & |
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| 144 | & + wslpj(ji,jj,jk) * wslpj(ji,jj,jk) ) |
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| 145 | zwt(ji,jj,jk) = avt(ji,jj,jk) + zavi ! zwt=avt+zavi (total vertical mixing coef. on temperature) |
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[457] | 146 | # if defined key_zdfddm |
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[902] | 147 | zavsi(ji,jj,jk) = fsavs(ji,jj,jk) + zavi ! dd mixing: zavsi = total vertical mixing coef. on salinity |
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[457] | 148 | # endif |
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[902] | 149 | END DO |
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[3] | 150 | END DO |
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| 151 | END DO |
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[1517] | 152 | ELSE ! no rotation but key_ldfslp defined |
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| 153 | zwt (:,:,:) = avt(:,:,:) |
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| 154 | # if defined key_zdfddm |
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| 155 | zavsi(:,:,:) = avs(:,:,:) ! avs /= avt (double diffusion mixing) |
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| 156 | # endif |
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[902] | 157 | ENDIF |
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[255] | 158 | #else |
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[592] | 159 | ! No isopycnal diffusion |
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| 160 | zwt(:,:,:) = avt(:,:,:) |
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| 161 | # if defined key_zdfddm |
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| 162 | zavsi(:,:,:) = avs(:,:,:) |
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| 163 | # endif |
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| 164 | |
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| 165 | #endif |
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| 166 | |
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[457] | 167 | ! Diagonal, inferior, superior (including the bottom boundary condition via avt masked) |
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| 168 | DO jk = 1, jpkm1 |
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| 169 | DO jj = 2, jpjm1 |
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| 170 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[1438] | 171 | ze3ta = ( 1. - znvvl ) & ! after scale factor at T-point |
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| 172 | & + znvvl * fse3t_a(ji,jj,jk) |
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| 173 | ze3tn = znvvl & ! now scale factor at T-point |
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| 174 | & + ( 1. - znvvl ) * fse3t_n(ji,jj,jk) |
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[592] | 175 | zwi(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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| 176 | zws(ji,jj,jk) = - p2dt(jk) * zwt(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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| 177 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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[3] | 178 | END DO |
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| 179 | END DO |
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[457] | 180 | END DO |
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[3] | 181 | |
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[457] | 182 | ! Surface boudary conditions |
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| 183 | DO jj = 2, jpjm1 |
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| 184 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[1438] | 185 | ze3ta = ( 1. - znvvl ) & ! after scale factor at T-point |
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| 186 | & + znvvl * fse3t_a(ji,jj,1) |
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[457] | 187 | zwi(ji,jj,1) = 0.e0 |
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[592] | 188 | zwd(ji,jj,1) = ze3ta - zws(ji,jj,1) |
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[457] | 189 | END DO |
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| 190 | END DO |
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[3] | 191 | |
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| 192 | |
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[457] | 193 | ! II.1. Vertical diffusion on t |
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| 194 | ! --------------------------- |
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| 195 | |
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| 196 | !! Matrix inversion from the first level |
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| 197 | !!---------------------------------------------------------------------- |
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| 198 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 199 | ! |
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| 200 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 201 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 202 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 203 | ! ( ... )( ... ) ( ... ) |
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| 204 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 205 | ! |
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| 206 | ! m is decomposed in the product of an upper and lower triangular matrix |
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| 207 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 208 | ! The second member is in 2d array zwy |
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| 209 | ! The solution is in 2d array zwx |
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| 210 | ! The 3d arry zwt is a work space array |
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| 211 | ! zwy is used and then used as a work space array : its value is modified! |
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| 212 | |
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| 213 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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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 | zwt(ji,jj,1) = zwd(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 | 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] | 223 | END DO |
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| 224 | END DO |
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[457] | 225 | END DO |
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[3] | 226 | |
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[457] | 227 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 228 | DO jj = 2, jpjm1 |
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| 229 | DO ji = fs_2, fs_jpim1 |
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[1438] | 230 | ze3tb = ( 1. - znvvl ) + znvvl * fse3t_b(ji,jj,1) |
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| 231 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t(ji,jj,1) |
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[592] | 232 | ta(ji,jj,1) = ze3tb * tb(ji,jj,1) + p2dt(1) * ze3tn * ta(ji,jj,1) |
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[457] | 233 | END DO |
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| 234 | END DO |
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| 235 | DO jk = 2, jpkm1 |
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| 236 | DO jj = 2, jpjm1 |
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| 237 | DO ji = fs_2, fs_jpim1 |
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[1438] | 238 | ze3tb = ( 1. - znvvl ) + znvvl * fse3t_b(ji,jj,jk) |
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| 239 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t (ji,jj,jk) |
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[592] | 240 | zrhs = ze3tb * tb(ji,jj,jk) + p2dt(jk) * ze3tn * ta(ji,jj,jk) ! zrhs=right hand side |
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[1438] | 241 | ta(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) * ta(ji,jj,jk-1) |
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[457] | 242 | END DO |
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| 243 | END DO |
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| 244 | END DO |
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[3] | 245 | |
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[457] | 246 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 247 | ! Save the masked temperature after in ta |
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| 248 | ! (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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| 249 | DO jj = 2, jpjm1 |
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| 250 | DO ji = fs_2, fs_jpim1 |
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| 251 | ta(ji,jj,jpkm1) = ta(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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| 252 | END DO |
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| 253 | END DO |
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| 254 | DO jk = jpk-2, 1, -1 |
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| 255 | DO jj = 2, jpjm1 |
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| 256 | DO ji = fs_2, fs_jpim1 |
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| 257 | 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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| 258 | END DO |
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| 259 | END DO |
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| 260 | END DO |
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[3] | 261 | |
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[457] | 262 | ! II.2 Vertical diffusion on salinity |
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| 263 | ! ----------------------------------- |
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| 264 | |
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[3] | 265 | #if defined key_zdfddm |
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[457] | 266 | ! Rebuild the Matrix as avt /= avs |
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[3] | 267 | |
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[457] | 268 | ! Diagonal, inferior, superior (including the bottom boundary condition via avs masked) |
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| 269 | DO jk = 1, jpkm1 |
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| 270 | DO jj = 2, jpjm1 |
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| 271 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[1438] | 272 | ze3ta = ( 1. - znvvl ) & ! after scale factor at T-point |
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| 273 | & + znvvl * fse3t_a(ji,jj,jk) |
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| 274 | ze3tn = znvvl & ! now scale factor at T-point |
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| 275 | & + ( 1. - znvvl ) * fse3t_n(ji,jj,jk) |
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[592] | 276 | zwi(ji,jj,jk) = - p2dt(jk) * zavsi(ji,jj,jk ) / ( ze3tn * fse3w(ji,jj,jk ) ) |
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| 277 | zws(ji,jj,jk) = - p2dt(jk) * zavsi(ji,jj,jk+1) / ( ze3tn * fse3w(ji,jj,jk+1) ) |
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| 278 | zwd(ji,jj,jk) = ze3ta - zwi(ji,jj,jk) - zws(ji,jj,jk) |
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[3] | 279 | END DO |
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| 280 | END DO |
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[457] | 281 | END DO |
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| 282 | |
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| 283 | ! Surface boudary conditions |
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| 284 | DO jj = 2, jpjm1 |
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| 285 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[1438] | 286 | ze3ta = ( 1. - znvvl ) + znvvl * fse3t_a(ji,jj,1) |
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[457] | 287 | zwi(ji,jj,1) = 0.e0 |
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[592] | 288 | zwd(ji,jj,1) = ze3ta - zws(ji,jj,1) |
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[3] | 289 | END DO |
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[457] | 290 | END DO |
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[255] | 291 | #endif |
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[3] | 292 | |
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| 293 | |
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[457] | 294 | !! Matrix inversion from the first level |
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| 295 | !!---------------------------------------------------------------------- |
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| 296 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 297 | ! |
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| 298 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 299 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 300 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 301 | ! ( ... )( ... ) ( ... ) |
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| 302 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 303 | ! |
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| 304 | ! m is decomposed in the product of an upper and lower triangular |
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| 305 | ! matrix |
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| 306 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 307 | ! The second member is in 2d array zwy |
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| 308 | ! The solution is in 2d array zwx |
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| 309 | ! The 3d arry zwt is a work space array |
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| 310 | ! zwy is used and then used as a work space array : its value is modified! |
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[3] | 311 | |
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[457] | 312 | ! first recurrence: Tk = Dk - Ik Sk-1 / Tk-1 (increasing k) |
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| 313 | DO jj = 2, jpjm1 |
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| 314 | DO ji = fs_2, fs_jpim1 |
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| 315 | zwt(ji,jj,1) = zwd(ji,jj,1) |
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| 316 | END DO |
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| 317 | END DO |
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| 318 | DO jk = 2, jpkm1 |
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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 | 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] | 322 | END DO |
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| 323 | END DO |
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[457] | 324 | END DO |
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[3] | 325 | |
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[457] | 326 | ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1 |
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| 327 | DO jj = 2, jpjm1 |
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| 328 | DO ji = fs_2, fs_jpim1 |
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[1438] | 329 | ze3tb = ( 1. - znvvl ) & ! before scale factor at T-point |
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| 330 | & + znvvl * fse3t_b(ji,jj,1) |
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| 331 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t (ji,jj,1) ! now scale factor at T-point |
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[592] | 332 | sa(ji,jj,1) = ze3tb * sb(ji,jj,1) + p2dt(1) * ze3tn * sa(ji,jj,1) |
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[457] | 333 | END DO |
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| 334 | END DO |
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| 335 | DO jk = 2, jpkm1 |
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| 336 | DO jj = 2, jpjm1 |
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| 337 | DO ji = fs_2, fs_jpim1 |
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[1438] | 338 | ze3tb = ( 1. - znvvl ) & ! before scale factor at T-point |
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| 339 | & + znvvl * fse3t_b(ji,jj,jk) |
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| 340 | ze3tn = ( 1. - znvvl ) + znvvl * fse3t (ji,jj,jk) ! now scale factor at T-point |
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[592] | 341 | zrhs = ze3tb * sb(ji,jj,jk) + p2dt(jk) * ze3tn * sa(ji,jj,jk) ! zrhs=right hand side |
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[457] | 342 | sa(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *sa(ji,jj,jk-1) |
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| 343 | END DO |
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| 344 | END DO |
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| 345 | END DO |
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[3] | 346 | |
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[457] | 347 | ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk |
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| 348 | ! Save the masked temperature after in ta |
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| 349 | ! (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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| 350 | DO jj = 2, jpjm1 |
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| 351 | DO ji = fs_2, fs_jpim1 |
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| 352 | sa(ji,jj,jpkm1) = sa(ji,jj,jpkm1) / zwt(ji,jj,jpkm1) * tmask(ji,jj,jpkm1) |
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[216] | 353 | END DO |
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[457] | 354 | END DO |
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| 355 | DO jk = jpk-2, 1, -1 |
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| 356 | DO jj = 2, jpjm1 |
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| 357 | DO ji = fs_2, fs_jpim1 |
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| 358 | 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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| 359 | END DO |
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| 360 | END DO |
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| 361 | END DO |
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[1438] | 362 | ! |
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[3] | 363 | END SUBROUTINE tra_zdf_imp |
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| 364 | |
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| 365 | !!============================================================================== |
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| 366 | END MODULE trazdf_imp |
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