[186] | 1 | MODULE trcadv_cen2 |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE trcadv_cen2 *** |
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| 4 | !! Ocean passive tracers: horizontal & vertical advective tracer trend |
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| 5 | !!============================================================================== |
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| 6 | #if defined key_passivetrc |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | !! trc_adv_cen2 : update the tracer trend with the horizontal |
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| 9 | !! and vertical advection trends using a 2nd order |
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| 10 | !! centered finite difference scheme |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! * Modules used |
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[202] | 13 | USE oce_trc ! ocean dynamics and active tracers variables |
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| 14 | USE trc ! ocean passive tracers variables |
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[204] | 15 | USE trcbbl ! advective passive tracers in the BBL |
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[334] | 16 | USE prtctl_trc |
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[186] | 17 | |
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| 18 | IMPLICIT NONE |
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| 19 | PRIVATE |
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| 20 | |
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| 21 | !! * Accessibility |
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| 22 | PUBLIC trc_adv_cen2 ! routine called by trcstp.F90 |
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| 23 | |
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| 24 | !! * Substitutions |
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| 25 | # include "passivetrc_substitute.h90" |
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| 26 | !!---------------------------------------------------------------------- |
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[349] | 27 | !! TOP 1.0 , LOCEAN-IPSL (2005) |
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[342] | 28 | !! $Header$ |
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| 29 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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[186] | 30 | !!---------------------------------------------------------------------- |
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| 31 | |
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| 32 | CONTAINS |
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| 33 | |
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| 34 | !!---------------------------------------------------------------------- |
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| 35 | !! Default option : 2nd order centered scheme (k-j-i loop) |
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| 36 | !!---------------------------------------------------------------------- |
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| 37 | |
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| 38 | SUBROUTINE trc_adv_cen2( kt ) |
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| 39 | !!---------------------------------------------------------------------- |
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| 40 | !! *** ROUTINE trc_adv_cen2 *** |
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| 41 | !! |
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| 42 | !! ** Purpose : Compute the now trend due to the advection of tracers |
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| 43 | !! and add it to the general trend of passive tracer equations. |
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| 44 | !! |
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| 45 | !! ** Method : The advection is evaluated by a second order centered |
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| 46 | !! scheme using now fields (leap-frog scheme). In specific areas |
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| 47 | !! (vicinity of major river mouths, some straits, or where tn is |
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| 48 | !! is approaching the freezing point) it is mixed with an upstream |
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| 49 | !! scheme for stability reasons. |
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| 50 | !! Part 0 : compute the upstream / centered flag |
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| 51 | !! (3D array, zind, defined at T-point (0<zind<1)) |
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| 52 | !! Part I : horizontal advection |
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| 53 | !! * centered flux: |
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[501] | 54 | !! * s-coordinate (ln_sco=T) or |
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| 55 | !! * z-coordinate with partial steps (ln_zps=T), |
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[186] | 56 | !! the vertical scale factors e3. are inside the derivatives: |
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| 57 | !! zcenu = e2u*e3u un mi(tn) |
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| 58 | !! zcenv = e1v*e3v vn mj(tn) |
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| 59 | !! * z-coordinate (default key), e3t=e3u=e3v: |
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| 60 | !! zcenu = e2u un mi(tn) |
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| 61 | !! zcenv = e1v vn mj(tn) |
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| 62 | !! * horizontal advective trend (divergence of the fluxes) |
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[501] | 63 | !! * s-coordinate (ln_sco=T) or |
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| 64 | !! * z-coordinate with partial steps (ln_zps=T) |
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[186] | 65 | !! ztra = 1/(e1t*e2t*e3t) { di-1[zwx] + dj-1[zwy] } |
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| 66 | !! * z-coordinate (default key), e3t=e3u=e3v: |
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| 67 | !! ztra = 1/(e1t*e2t) { di-1[zwx] + dj-1[zwy] } |
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| 68 | !! * Add this trend now to the general trend of tracer tra: |
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| 69 | !! tra = tra + ztra |
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| 70 | !! * trend diagnostic ('key_trc_diatrd'): the trend is saved |
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| 71 | !! for diagnostics. The trends saved is expressed as |
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| 72 | !! Uh.gradh(T) |
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| 73 | !! |
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| 74 | !! Part II : vertical advection |
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| 75 | !! For any tracer the advective trend is computed as follows : |
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| 76 | !! ztra = 1/e3t dk+1[ zwz ] |
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| 77 | !! where the vertical advective flux, zwz, is given by : |
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| 78 | !! zwz = zcofk * zupst + (1-zcofk) * zcent |
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| 79 | !! with |
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| 80 | !! zupsv = upstream flux = wn * (trb(k) or trb(k-1) ) [wn>0 or <0] |
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| 81 | !! zcenu = centered flux = wn * mk(trn) |
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| 82 | !! The surface boundary condition is : |
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| 83 | !! rigid-lid (default option) : zero advective flux |
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| 84 | !! free-surf ("key_fresurf_cstvol") : wn(:,:,1) * trn(:,:,1) |
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| 85 | !! Add this trend now to the general trend of tracer tra : |
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| 86 | !! tra = tra + ztra |
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| 87 | !! Trend diagnostic ('key_trc_diatrd'): the trend is saved for |
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| 88 | !! diagnostics. The trends saved is expressed as : |
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| 89 | !! save trend = w.gradz(T) = ztra - trn divn. |
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| 90 | !! |
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| 91 | !! ** Action : - update tra with the now advective tracer trends |
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| 92 | !! - save the trends in trtrd ('key_trc_diatrd') |
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| 93 | !! |
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| 94 | !! History : |
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| 95 | !! 8.2 ! 01-08 (M-A Filiberti, and M.Levy) trahad+trazad = traadv |
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| 96 | !! 8.5 ! 02-06 (G. Madec, C. Ethe) F90: Free form and module |
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| 97 | !!---------------------------------------------------------------------- |
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| 98 | !! * Modules used |
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| 99 | USE oce_trc , zwx => ua, & ! use ua as workspace |
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| 100 | & zwy => va ! use va as workspace |
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| 101 | #if defined key_trcbbl_adv |
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| 102 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & ! temporary arrays |
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| 103 | & zun, zvn, zwn |
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| 104 | #else |
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| 105 | USE oce_trc , zun => un, & ! When no bbl, zun == un |
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| 106 | & zvn => vn, & ! When no bbl, zvn == vn |
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| 107 | & zwn => wn ! When no bbl, zwn == wn |
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| 108 | #endif |
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| 109 | |
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| 110 | |
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| 111 | !! * Arguments |
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| 112 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 113 | |
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| 114 | !! * Local save |
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| 115 | REAL(wp), DIMENSION(jpi,jpj), SAVE :: & |
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| 116 | zbtr2 |
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| 117 | |
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| 118 | !! * Local declarations |
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| 119 | INTEGER :: ji, jj, jk, jn ! dummy loop indices |
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| 120 | REAL(wp) :: & |
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| 121 | zbtr, ztra, zfui, zfvj, & ! temporary scalars |
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| 122 | zhw, ze3tr, zcofi, zcofj, & ! " " |
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| 123 | zupsut, zupsvt, & ! " " |
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| 124 | zfp_ui, zfp_vj, zfm_ui, zfm_vj, & ! " " |
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| 125 | zcofk, zupst, zcent, & ! " " |
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| 126 | zfp_w, zfm_w, & ! " " |
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| 127 | zcenut, zcenvt ! |
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| 128 | |
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| 129 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: & |
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| 130 | zind ! temporary workspace arrays |
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| 131 | #if defined key_trc_diatrd |
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| 132 | REAL(wp) :: & |
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| 133 | ztai, ztaj, & ! temporary scalars |
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| 134 | zfui1, zfvj1 ! " " |
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| 135 | #endif |
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[334] | 136 | CHARACTER (len=22) :: charout |
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[186] | 137 | !!---------------------------------------------------------------------- |
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| 138 | |
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| 139 | IF( kt == nittrc000 ) THEN |
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| 140 | IF(lwp) WRITE(numout,*) |
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| 141 | IF(lwp) WRITE(numout,*) 'trc_adv_cen2 : 2nd order centered advection scheme' |
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| 142 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~ Vector optimization case' |
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| 143 | IF(lwp) WRITE(numout,*) |
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| 144 | |
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| 145 | zbtr2(:,:) = 1. / ( e1t(:,:) * e2t(:,:) ) |
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| 146 | ENDIF |
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| 147 | |
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| 148 | #if defined key_trcbbl_adv |
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| 149 | |
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| 150 | ! Advective bottom boundary layer |
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| 151 | ! ------------------------------- |
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| 152 | zun(:,:,:) = un(:,:,:) - u_trc_bbl(:,:,:) |
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| 153 | zvn(:,:,:) = vn(:,:,:) - v_trc_bbl(:,:,:) |
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| 154 | zwn(:,:,:) = wn(:,:,:) + w_trc_bbl(:,:,:) |
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| 155 | #endif |
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| 156 | |
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| 157 | |
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| 158 | ! Upstream / centered scheme indicator |
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| 159 | ! ------------------------------------ |
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| 160 | |
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[334] | 161 | DO jk = 1, jpk |
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| 162 | DO jj = 1, jpj |
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| 163 | DO ji = 1, jpi |
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| 164 | zind(ji,jj,jk) = MAX ( upsrnfh(ji,jj) * upsrnfz(jk), & ! changing advection scheme near runoff |
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| 165 | & upsadv(ji,jj) & ! in the vicinity of some straits |
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[186] | 166 | #if defined key_ice_lim |
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[334] | 167 | & , tmask(ji,jj,jk) & ! half upstream tracer fluxes |
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| 168 | & * MAX( 0., SIGN( 1., fzptn(ji,jj) & ! if tn < ("freezing"+0.1 ) |
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| 169 | & +0.1-tn(ji,jj,jk) ) ) & |
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[186] | 170 | #endif |
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[334] | 171 | & ) |
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[186] | 172 | END DO |
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| 173 | END DO |
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[334] | 174 | END DO |
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[186] | 175 | |
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| 176 | |
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[334] | 177 | DO jn = 1, jptra |
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[186] | 178 | ! I. Horizontal advective fluxes |
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| 179 | ! ------------------------------ |
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| 180 | |
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| 181 | ! Second order centered tracer flux at u and v-points |
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| 182 | |
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| 183 | ! ! =============== |
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| 184 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 185 | ! ! =============== |
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| 186 | DO jj = 1, jpjm1 |
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| 187 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 188 | ! upstream indicator |
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| 189 | zcofi = MAX( zind(ji+1,jj,jk), zind(ji,jj,jk) ) |
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| 190 | zcofj = MAX( zind(ji,jj+1,jk), zind(ji,jj,jk) ) |
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| 191 | ! volume fluxes * 1/2 |
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[501] | 192 | #if ! defined key_zco |
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[186] | 193 | zfui = 0.5 * e2u(ji,jj) * fse3u(ji,jj,jk) * zun(ji,jj,jk) |
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| 194 | zfvj = 0.5 * e1v(ji,jj) * fse3v(ji,jj,jk) * zvn(ji,jj,jk) |
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| 195 | #else |
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| 196 | zfui = 0.5 * e2u(ji,jj) * zun(ji,jj,jk) |
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| 197 | zfvj = 0.5 * e1v(ji,jj) * zvn(ji,jj,jk) |
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| 198 | #endif |
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| 199 | ! upstream scheme |
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| 200 | zfp_ui = zfui + ABS( zfui ) |
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| 201 | zfp_vj = zfvj + ABS( zfvj ) |
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| 202 | zfm_ui = zfui - ABS( zfui ) |
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| 203 | zfm_vj = zfvj - ABS( zfvj ) |
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| 204 | zupsut = zfp_ui * trb(ji,jj,jk,jn) + zfm_ui * trb(ji+1,jj ,jk,jn) |
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| 205 | zupsvt = zfp_vj * trb(ji,jj,jk,jn) + zfm_vj * trb(ji ,jj+1,jk,jn) |
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| 206 | ! centered scheme |
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| 207 | zcenut = zfui * ( trn(ji,jj,jk,jn) + trn(ji+1,jj ,jk,jn) ) |
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| 208 | zcenvt = zfvj * ( trn(ji,jj,jk,jn) + trn(ji ,jj+1,jk,jn) ) |
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| 209 | ! mixed centered / upstream scheme |
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| 210 | zwx(ji,jj,jk) = zcofi * zupsut + (1.-zcofi) * zcenut |
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| 211 | zwy(ji,jj,jk) = zcofj * zupsvt + (1.-zcofj) * zcenvt |
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| 212 | END DO |
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| 213 | END DO |
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| 214 | |
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| 215 | |
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| 216 | ! 2. Tracer flux divergence at t-point added to the general trend |
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| 217 | ! ------------------------- |
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| 218 | |
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| 219 | DO jj = 2, jpjm1 |
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| 220 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[501] | 221 | #if ! defined key_zco |
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[186] | 222 | zbtr = zbtr2(ji,jj) / fse3t(ji,jj,jk) |
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| 223 | #else |
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| 224 | zbtr = zbtr2(ji,jj) |
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| 225 | #endif |
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| 226 | ! horizontal advective trends |
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| 227 | ztra = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk) & |
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| 228 | & + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk) ) |
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| 229 | |
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| 230 | ! add it to the general tracer trends |
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| 231 | tra(ji,jj,jk,jn) = tra(ji,jj,jk,jn) + ztra |
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| 232 | |
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| 233 | #if defined key_trc_diatrd |
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| 234 | ! recompute the trends in i- and j-direction as Uh gradh(T) |
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[501] | 235 | #if ! defined key_zco |
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[186] | 236 | zfui = 0.5 * e2u(ji ,jj) * fse3u(ji, jj,jk) * zun(ji, jj,jk) |
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| 237 | zfui1= 0.5 * e2u(ji-1,jj) * fse3u(ji-1,jj,jk) * zun(ji-1,jj,jk) |
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| 238 | zfvj = 0.5 * e1v(ji,jj ) * fse3v(ji,jj ,jk) * zvn(ji,jj ,jk) |
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| 239 | zfvj1= 0.5 * e1v(ji,jj-1) * fse3v(ji,jj-1,jk) * zvn(ji,jj-1,jk) |
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| 240 | # else |
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| 241 | zfui = 0.5 * e2u(ji ,jj) * zun(ji, jj,jk) |
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| 242 | zfui1= 0.5 * e2u(ji-1,jj) * zun(ji-1,jj,jk) |
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| 243 | zfvj = 0.5 * e1v(ji,jj ) * zvn(ji,jj ,jk) |
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| 244 | zfvj1= 0.5 * e1v(ji,jj-1) * zvn(ji,jj-1,jk) |
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| 245 | # endif |
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| 246 | ztai = - zbtr * ( zfui * ( trn(ji+1,jj ,jk,jn) - trn(ji, jj,jk,jn) ) & |
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| 247 | & + zfui1 * ( trn(ji, jj, jk,jn) - trn(ji-1,jj,jk,jn) ) ) |
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| 248 | ztaj = - zbtr * ( zfvj * ( trn(ji ,jj+1,jk,jn) - trn(ji,jj ,jk,jn) ) & |
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| 249 | & + zfvj1 * ( trn(ji ,jj ,jk,jn) - trn(ji,jj-1,jk,jn) ) ) |
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| 250 | ! save i- and j- advective trends computed as Uh gradh(T) |
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[433] | 251 | IF (luttrd(jn)) trtrd(ji,jj,jk,ikeep(jn),1) = ztai |
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| 252 | IF (luttrd(jn)) trtrd(ji,jj,jk,ikeep(jn),2) = ztaj |
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[186] | 253 | #endif |
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| 254 | END DO |
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| 255 | END DO |
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| 256 | ! ! =============== |
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| 257 | END DO ! End of slab |
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| 258 | ! ! =============== |
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[334] | 259 | ENDDO |
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[186] | 260 | |
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[334] | 261 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
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| 262 | WRITE(charout, FMT="('centered2 - had')") |
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| 263 | CALL prt_ctl_trc_info(charout) |
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| 264 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm,clinfo2='trd') |
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| 265 | ENDIF |
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| 266 | |
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| 267 | ! II. Vertical advection |
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| 268 | ! ---------------------- |
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| 269 | DO jn = 1, jptra |
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[186] | 270 | |
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| 271 | ! Bottom value : flux set to zero |
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| 272 | zwx(:,:,jpk) = 0.e0 |
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| 273 | |
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| 274 | ! Surface value |
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[361] | 275 | IF ( lk_dynspg_rl ) THEN ! rigid lid : flux set to zero |
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| 276 | zwx(:,:, 1 ) = 0.e0 |
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| 277 | ELSE ! free surface-constant volume |
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[202] | 278 | zwx(:,:, 1 ) = zwn(:,:,1) * trn(:,:,1,jn) |
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| 279 | ENDIF |
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[186] | 280 | |
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| 281 | ! 1. Vertical advective fluxes |
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| 282 | ! ---------------------------- |
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| 283 | |
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| 284 | ! Second order centered tracer flux at w-point |
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| 285 | |
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| 286 | DO jk = 2, jpk |
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| 287 | DO jj = 2, jpjm1 |
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| 288 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 289 | ! upstream indicator |
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| 290 | zcofk = MAX( zind(ji,jj,jk-1), zind(ji,jj,jk) ) |
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| 291 | ! velocity * 1/2 |
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| 292 | zhw = 0.5 * zwn(ji,jj,jk) |
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| 293 | ! upstream scheme |
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| 294 | zfp_w = zhw + ABS( zhw ) |
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| 295 | zfm_w = zhw - ABS( zhw ) |
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| 296 | zupst = zfp_w * trb(ji,jj,jk,jn) + zfm_w * trb(ji,jj,jk-1,jn) |
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| 297 | ! centered scheme |
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| 298 | zcent = zhw * ( trn(ji,jj,jk,jn) + trn(ji,jj,jk-1,jn) ) |
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| 299 | ! centered scheme |
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| 300 | zwx(ji,jj,jk) = zcofk * zupst + (1.-zcofk) * zcent |
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| 301 | END DO |
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| 302 | END DO |
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| 303 | END DO |
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| 304 | |
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| 305 | |
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| 306 | ! 2. Tracer flux divergence at t-point added to the general trend |
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| 307 | ! ------------------------- |
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| 308 | |
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| 309 | DO jk = 1, jpkm1 |
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| 310 | DO jj = 2, jpjm1 |
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| 311 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 312 | ze3tr = 1. / fse3t(ji,jj,jk) |
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| 313 | ! vertical advective trends |
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| 314 | ztra = - ze3tr * ( zwx(ji,jj,jk) - zwx(ji,jj,jk+1) ) |
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| 315 | ! add it to the general tracer trends |
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| 316 | tra(ji,jj,jk,jn) = tra(ji,jj,jk,jn) + ztra |
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| 317 | #if defined key_trc_diatrd |
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| 318 | ! save the vertical advective trends computed as w gradz(T) |
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[433] | 319 | IF (luttrd(jn)) trtrd(ji,jj,jk,ikeep(jn),3) = ztra - trn(ji,jj,jk,jn) * hdivn(ji,jj,jk) |
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[186] | 320 | #endif |
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| 321 | END DO |
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| 322 | END DO |
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| 323 | END DO |
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| 324 | |
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| 325 | END DO |
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| 326 | |
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[334] | 327 | IF(ln_ctl) THEN ! print mean trends (used for debugging) |
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| 328 | WRITE(charout, FMT="('centered - zad')") |
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| 329 | CALL prt_ctl_trc_info(charout) |
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| 330 | CALL prt_ctl_trc(tab4d=tra, mask=tmask, clinfo=ctrcnm,clinfo2='trd') |
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| 331 | ENDIF |
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[186] | 332 | |
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| 333 | END SUBROUTINE trc_adv_cen2 |
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| 334 | #else |
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| 335 | |
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| 336 | !!---------------------------------------------------------------------- |
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| 337 | !! Default option Empty module |
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| 338 | !!---------------------------------------------------------------------- |
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| 339 | CONTAINS |
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| 340 | SUBROUTINE trc_adv_cen2( kt ) |
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| 341 | INTEGER, INTENT(in) :: kt |
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| 342 | WRITE(*,*) 'trc_adv_cen2: You should not have seen this print! error?', kt |
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| 343 | END SUBROUTINE trc_adv_cen2 |
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| 344 | #endif |
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| 345 | !!====================================================================== |
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| 346 | END MODULE trcadv_cen2 |
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