[3] | 1 | MODULE dynzdf_iso |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE dynzdf_iso *** |
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| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
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| 5 | !!============================================================================== |
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| 6 | #if defined key_ldfslp || defined key_esopa |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | !! 'key_ldfslp' rotation of the mixing tensor |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! dyn_zdf_iso : update the momentum trend with the vertical diffusion |
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| 11 | !! (vertical mixing + vertical component of lateral |
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| 12 | !! mixing) (rotated lateral operator case) |
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| 13 | !!---------------------------------------------------------------------- |
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| 14 | !! * Modules used |
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| 15 | USE oce ! ocean dynamics and tracers |
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| 16 | USE dom_oce ! ocean space and time domain |
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| 17 | USE phycst ! physical constants |
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| 18 | USE zdf_oce ! ocean vertical physics |
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| 19 | USE in_out_manager ! I/O manager |
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| 20 | USE taumod ! surface ocean stress |
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| 21 | USE trddyn_oce ! dynamics trends diagnostics variables |
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| 22 | |
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| 23 | IMPLICIT NONE |
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| 24 | PRIVATE |
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| 25 | |
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| 26 | !! * Routine accessibility |
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| 27 | PUBLIC dyn_zdf_iso ! called by step.F90 |
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| 28 | |
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| 29 | !! * Substitutions |
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| 30 | # include "domzgr_substitute.h90" |
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| 31 | # include "vectopt_loop_substitute.h90" |
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| 32 | !!---------------------------------------------------------------------- |
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| 33 | !! OPA 9.0 , LODYC-IPSL (2003) |
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| 34 | !!---------------------------------------------------------------------- |
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| 35 | |
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| 36 | CONTAINS |
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| 37 | |
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| 38 | SUBROUTINE dyn_zdf_iso( kt ) |
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| 39 | !!---------------------------------------------------------------------- |
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| 40 | !! *** ROUTINE dyn_zdf_iso *** |
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| 41 | !! |
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| 42 | !! ** Purpose : |
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| 43 | !! Compute the vertical momentum trend due to both vertical and |
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| 44 | !! lateral mixing (only for second order lateral operator, for |
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| 45 | !! fourth order it is already computed and add to the general trend |
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| 46 | !! in dynldf.F) and the surface forcing, and add it to the general |
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| 47 | !! trend of the momentum equations. |
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| 48 | !! |
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| 49 | !! ** Method : |
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| 50 | !! The vertical component of the lateral diffusive trends is |
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| 51 | !! provided by a 2nd order operator rotated along neural or geopo- |
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| 52 | !! tential surfaces to which an eddy induced advection can be added |
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| 53 | !! It is computed using before fields (forward in time) and isopyc- |
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| 54 | !! nal or geopotential slopes computed in routine ldfslp. |
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| 55 | !! |
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| 56 | !! First part: vertical trends associated with the lateral mixing |
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| 57 | !! ========== (excluding the vertical flux proportional to dk[U] ) |
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| 58 | !! vertical fluxes associated with the rotated lateral mixing: |
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| 59 | !! zfuw =-ahm { e2t*mi(wslpi) di[ mi(mk(ub)) ] |
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| 60 | !! + e1t*mj(wslpj) dj[ mj(mk(ub)) ] } |
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| 61 | !! update and save in zavt the vertical eddy viscosity coefficient: |
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| 62 | !! avmu = avmu + mi(wslpi)^2 + mj(wslj)^2 |
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| 63 | !! take the horizontal divergence of the fluxes: |
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| 64 | !! diffu = 1/(e1u*e2u*e3u) dk[ zfuw ] |
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| 65 | !! Add this trend to the general trend (ta,sa): |
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| 66 | !! ua = ua + difft |
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| 67 | !! |
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| 68 | !! Second part: vertical trend associated with the vertical physics |
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| 69 | !! =========== (including the vertical flux proportional to dk[U] |
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| 70 | !! associated with the lateral mixing, through the |
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| 71 | !! update of avmu) |
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| 72 | !! The vertical diffusion of momentum is given by: |
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| 73 | !! diffu = dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
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| 74 | !! using a backward (implicit) time stepping. |
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| 75 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
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| 76 | !! Add this trend to the general trend ua : |
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| 77 | !! ua = ua + dz( avmu dz(u) ) |
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| 78 | !! |
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| 79 | !! 'key_trddyn' defined: trend saved for futher diagnostics. |
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| 80 | !! |
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| 81 | !! macro-tasked on vertical slab (jj-loop) |
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| 82 | !! |
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| 83 | !! ** Action : |
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| 84 | !! /comaft/ ua, va : general momentum trend increased |
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| 85 | !! by the after vertical diffusive trend |
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| 86 | !! /comtra/ utrd,vtrd: after vertical momentum diffusive |
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| 87 | !! trend ('key_trddyn' defined) |
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| 88 | !! |
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| 89 | !! History : |
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| 90 | !! original : 90-10 (B. Blanke) |
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| 91 | !! addition : 97-05 (G. Madec) vertical component of isopycnal |
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| 92 | !!--------------------------------------------------------------------- |
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| 93 | !! * Modules used |
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| 94 | USE ldfslp , ONLY : wslpi, wslpj |
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| 95 | USE ldftra_oce, ONLY : aht0 |
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| 96 | |
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| 97 | !! * Arguments |
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| 98 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 99 | |
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| 100 | !! * Local declarations |
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| 101 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 102 | INTEGER :: & |
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| 103 | ikst, ikenm2, ikstp1 ! temporary integers |
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| 104 | REAL(wp) :: & |
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| 105 | zrau0r, z2dt, & ! temporary scalars |
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| 106 | z2dtf, zua, zva, zcoef, zzws |
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| 107 | REAL(wp) :: & |
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| 108 | zcoef0, zcoef3, zcoef4, zbu, zbv, zmkt, zmkf, & |
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| 109 | zuav, zvav, zuwslpi, zuwslpj, zvwslpi, zvwslpj |
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| 110 | REAL(wp), DIMENSION(jpi,jpk) :: & |
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| 111 | zwx, zwy, zwz & ! workspace |
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| 112 | , zwd, zws, zwi, zwt |
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| 113 | REAL(wp), DIMENSION(jpi,jpk) :: & |
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| 114 | zfuw, zdiu, zdju, zdj1u, & ! workspace |
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| 115 | zfvw, zdiv, zdjv, zdj1v |
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| 116 | #if defined key_trddyn |
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| 117 | INTEGER :: & |
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| 118 | ikbu, ikbum1 , ikbv, ikbvm1 ! temporary integers |
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| 119 | #endif |
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| 120 | !!---------------------------------------------------------------------- |
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| 121 | |
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| 122 | IF( kt == nit000 ) THEN |
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| 123 | IF(lwp) WRITE(numout,*) |
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| 124 | IF(lwp) WRITE(numout,*) 'dyn_zdf_iso : vertical momentum diffusion isopycnal operator' |
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| 125 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 126 | ENDIF |
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| 127 | |
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| 128 | ! 0. Local constant initialization |
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| 129 | ! -------------------------------- |
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| 130 | |
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| 131 | ! inverse of the reference density |
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| 132 | zrau0r = 1. / rau0 |
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| 133 | ! Leap-frog environnement |
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| 134 | z2dt = 2. * rdt |
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| 135 | ! Euler time stepping when starting from rest |
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| 136 | IF ( neuler == 0 .AND. kt == nit000 ) z2dt = rdt |
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| 137 | |
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| 138 | ! ! =============== |
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| 139 | DO jj = 2, jpjm1 ! Vertical slab |
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| 140 | ! ! =============== |
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| 141 | |
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| 142 | |
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| 143 | ! I. vertical trends associated with the lateral mixing |
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| 144 | ! ===================================================== |
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| 145 | ! (excluding the vertical flux proportional to dk[t] |
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| 146 | |
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| 147 | |
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| 148 | ! I.1 horizontal momentum gradient |
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| 149 | ! -------------------------------- |
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| 150 | |
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| 151 | DO jk = 1, jpk |
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| 152 | DO ji = 2, jpi |
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| 153 | ! i-gradient of u at jj |
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| 154 | zdiu (ji,jk) = tmask(ji,jj ,jk) * ( ub(ji,jj ,jk) - ub(ji-1,jj ,jk) ) |
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| 155 | ! j-gradient of u and v at jj |
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| 156 | zdju (ji,jk) = fmask(ji,jj ,jk) * ( ub(ji,jj+1,jk) - ub(ji ,jj ,jk) ) |
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| 157 | zdjv (ji,jk) = tmask(ji,jj ,jk) * ( vb(ji,jj ,jk) - vb(ji ,jj-1,jk) ) |
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| 158 | ! j-gradient of u and v at jj+1 |
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| 159 | zdj1u(ji,jk) = fmask(ji,jj-1,jk) * ( ub(ji,jj ,jk) - ub(ji ,jj-1,jk) ) |
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| 160 | zdj1v(ji,jk) = tmask(ji,jj+1,jk) * ( vb(ji,jj+1,jk) - vb(ji ,jj ,jk) ) |
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| 161 | END DO |
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| 162 | END DO |
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| 163 | DO jk = 1, jpk |
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| 164 | DO ji = 1, jpim1 |
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| 165 | ! i-gradient of v at jj |
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| 166 | zdiv (ji,jk) = fmask(ji,jj ,jk) * ( vb(ji+1,jj,jk) - vb(ji ,jj ,jk) ) |
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| 167 | END DO |
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| 168 | END DO |
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| 169 | |
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| 170 | |
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| 171 | ! I.2 Vertical fluxes |
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| 172 | ! ------------------- |
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| 173 | |
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| 174 | ! Surface and bottom vertical fluxes set to zero |
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| 175 | DO ji = 1, jpi |
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| 176 | zfuw(ji, 1 ) = 0.e0 |
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| 177 | zfvw(ji, 1 ) = 0.e0 |
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| 178 | zfuw(ji,jpk) = 0.e0 |
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| 179 | zfvw(ji,jpk) = 0.e0 |
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| 180 | END DO |
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| 181 | |
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| 182 | ! interior (2=<jk=<jpk-1) on U field |
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| 183 | DO jk = 2, jpkm1 |
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| 184 | DO ji = 2, jpim1 |
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| 185 | zcoef0= 0.5 * aht0 * umask(ji,jj,jk) |
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| 186 | |
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| 187 | zuwslpi = zcoef0 * ( wslpi(ji+1,jj,jk) + wslpi(ji,jj,jk) ) |
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| 188 | zuwslpj = zcoef0 * ( wslpj(ji+1,jj,jk) + wslpj(ji,jj,jk) ) |
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| 189 | |
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| 190 | zmkt = 1./MAX( tmask(ji,jj,jk-1)+tmask(ji+1,jj,jk-1) & |
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| 191 | + tmask(ji,jj,jk )+tmask(ji+1,jj,jk ), 1. ) |
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| 192 | zmkf = 1./MAX( fmask(ji,jj-1,jk-1)+fmask(ji,jj,jk-1) & |
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| 193 | + fmask(ji,jj-1,jk )+fmask(ji,jj,jk ), 1. ) |
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| 194 | |
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| 195 | zcoef3 = - e2u(ji,jj) * zmkt * zuwslpi |
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| 196 | zcoef4 = - e1u(ji,jj) * zmkf * zuwslpj |
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| 197 | ! vertical flux on u field |
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| 198 | zfuw(ji,jk) = zcoef3 * ( zdiu (ji,jk-1) + zdiu (ji+1,jk-1) & |
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| 199 | +zdiu (ji,jk ) + zdiu (ji+1,jk ) ) & |
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| 200 | + zcoef4 * ( zdj1u(ji,jk-1) + zdju (ji ,jk-1) & |
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| 201 | +zdj1u(ji,jk ) + zdju (ji ,jk ) ) |
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| 202 | ! update avmu (add isopycnal vertical coefficient to avmu) |
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| 203 | avmu(ji,jj,jk) = avmu(ji,jj,jk) + ( zuwslpi * zuwslpi & |
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| 204 | + zuwslpj * zuwslpj ) / aht0 |
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| 205 | END DO |
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| 206 | END DO |
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| 207 | |
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| 208 | ! interior (2=<jk=<jpk-1) on V field |
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| 209 | DO jk = 2, jpkm1 |
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| 210 | DO ji = 2, jpim1 |
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| 211 | zcoef0= 0.5 * aht0 * vmask(ji,jj,jk) |
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| 212 | |
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| 213 | zvwslpi = zcoef0 * ( wslpi(ji,jj+1,jk) + wslpi(ji,jj,jk) ) |
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| 214 | zvwslpj = zcoef0 * ( wslpj(ji,jj+1,jk) + wslpj(ji,jj,jk) ) |
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| 215 | |
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| 216 | zmkf = 1./MAX( fmask(ji-1,jj,jk-1)+fmask(ji,jj,jk-1) & |
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| 217 | + fmask(ji-1,jj,jk )+fmask(ji,jj,jk ), 1. ) |
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| 218 | zmkt = 1./MAX( tmask(ji,jj,jk-1)+tmask(ji,jj+1,jk-1) & |
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| 219 | + tmask(ji,jj,jk )+tmask(ji,jj+1,jk ), 1. ) |
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| 220 | |
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| 221 | zcoef3 = - e2v(ji,jj) * zmkf * zvwslpi |
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| 222 | zcoef4 = - e1v(ji,jj) * zmkt * zvwslpj |
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| 223 | ! vertical flux on v field |
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| 224 | zfvw(ji,jk) = zcoef3 * ( zdiv (ji,jk-1) + zdiv (ji-1,jk-1) & |
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| 225 | +zdiv (ji,jk ) + zdiv (ji-1,jk ) ) & |
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| 226 | + zcoef4 * ( zdjv (ji,jk-1) + zdj1v(ji ,jk-1) & |
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| 227 | +zdjv (ji,jk ) + zdj1v(ji ,jk ) ) |
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| 228 | ! update avmv (add isopycnal vertical coefficient to avmv) |
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| 229 | avmv(ji,jj,jk) = avmv(ji,jj,jk) + ( zvwslpi * zvwslpi & |
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| 230 | + zvwslpj * zvwslpj ) / aht0 |
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| 231 | END DO |
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| 232 | END DO |
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| 233 | |
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| 234 | |
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| 235 | ! I.3 Divergence of vertical fluxes added to the general tracer trend |
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| 236 | ! ------------------------------------------------------------------- |
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| 237 | |
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| 238 | DO jk = 1, jpkm1 |
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| 239 | DO ji = 2, jpim1 |
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| 240 | ! volume elements |
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| 241 | zbu = e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) |
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| 242 | zbv = e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) |
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| 243 | ! part of the k-component of isopycnal momentum diffusive trends |
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| 244 | zuav = ( zfuw(ji,jk) - zfuw(ji,jk+1) ) / zbu |
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| 245 | zvav = ( zfvw(ji,jk) - zfvw(ji,jk+1) ) / zbv |
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| 246 | ! add the trends to the general trends |
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| 247 | ua(ji,jj,jk) = ua(ji,jj,jk) + zuav |
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| 248 | va(ji,jj,jk) = va(ji,jj,jk) + zvav |
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| 249 | #if defined key_trddyn |
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| 250 | ! save the trends for diagnostics |
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| 251 | utrd(ji,jj,jk,5) = utrd(ji,jj,jk,5) + zuav |
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| 252 | vtrd(ji,jj,jk,5) = vtrd(ji,jj,jk,5) + zvav |
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| 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 | |
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| 258 | ! 1. Vertical diffusion on u |
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| 259 | ! --------------------------- |
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| 260 | |
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| 261 | ! 1.0 Matrix and second member construction |
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| 262 | ! bottom boundary condition: only zws must be masked as avmu can take |
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| 263 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 264 | ! used (see zdfmix.F) |
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| 265 | DO jk = 1, jpkm1 |
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| 266 | DO ji = 2, jpim1 |
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| 267 | zcoef = - z2dt / fse3u(ji,jj,jk) |
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| 268 | zwi(ji,jk) = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) |
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| 269 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 270 | zws(ji,jk) = zzws * umask(ji,jj,jk+1) |
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| 271 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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| 272 | zwy(ji,jk) = ub(ji,jj,jk) + z2dt * ua(ji,jj,jk) |
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| 273 | END DO |
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| 274 | END DO |
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| 275 | |
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| 276 | ! 1.1 Surface boudary conditions |
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| 277 | DO ji = 2, jpim1 |
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| 278 | z2dtf = z2dt / ( fse3u(ji,jj,1)*rau0 ) |
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| 279 | zwi(ji,1) = 0. |
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| 280 | zwd(ji,1) = 1. - zws(ji,1) |
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| 281 | zwy(ji,1) = zwy(ji,1) + z2dtf * taux(ji,jj) |
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| 282 | END DO |
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| 283 | |
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| 284 | ! 1.2 Matrix inversion starting from the first level |
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| 285 | ikst = 1 |
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| 286 | #include "zdf.matrixsolver.h90" |
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| 287 | |
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| 288 | ! 1.3 Normalization to obtain the general momentum trend ua |
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| 289 | DO jk = 1, jpkm1 |
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| 290 | DO ji = 2, jpim1 |
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| 291 | zua = ( zwx(ji,jk) - ub(ji,jj,jk) ) / z2dt |
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| 292 | #if defined key_trddyn |
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| 293 | ! save the vertical diffusive momentum trend |
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| 294 | utrd(ji,jj,jk,7) = zua - ua(ji,jj,jk) |
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| 295 | #endif |
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| 296 | ua(ji,jj,jk) = zua |
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| 297 | END DO |
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| 298 | END DO |
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| 299 | |
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| 300 | #if defined key_trddyn |
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| 301 | |
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| 302 | ! 1.4 diagnose surface and bottom momentum fluxes |
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| 303 | DO ji = 2, jpim1 |
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| 304 | ! save the surface forcing momentum fluxes |
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| 305 | tautrd(ji,jj,1) = taux(ji,jj) / ( fse3u(ji,jj,1)*rau0 ) |
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| 306 | ! save bottom friction momentum fluxes |
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| 307 | ikbu = min( mbathy(ji+1,jj), mbathy(ji,jj) ) |
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| 308 | ikbum1 = max( ikbu-1, 1 ) |
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| 309 | tautrd(ji,jj,3) = - avmu(ji,jj,ikbu) * zwx(ji,ikbum1) & |
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| 310 | / ( fse3u(ji,jj,ikbum1)*fse3uw(ji,jj,ikbu) ) |
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| 311 | ! subtract surface forcing and bottom friction trend from vertical |
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| 312 | ! diffusive momentum trend |
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| 313 | utrd(ji,jj,1 ,7) = utrd(ji,jj,1 ,7) - tautrd(ji,jj,1) |
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| 314 | utrd(ji,jj,ikbum1,7) = utrd(ji,jj,ikbum1,7) - tautrd(ji,jj,3) |
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| 315 | END DO |
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| 316 | |
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| 317 | #endif |
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| 318 | |
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| 319 | ! 2. Vertical diffusion on v |
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| 320 | ! --------------------------- |
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| 321 | |
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| 322 | ! 2.0 Matrix and second member construction |
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| 323 | ! bottom boundary condition: only zws must be masked as avmv can take |
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| 324 | ! non zero value at the ocean bottom depending on the bottom friction |
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| 325 | ! used (see zdfmix.F) |
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| 326 | DO jk = 1, jpkm1 |
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| 327 | DO ji = 2, jpim1 |
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| 328 | zcoef = -z2dt/fse3v(ji,jj,jk) |
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| 329 | zwi(ji,jk) = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
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| 330 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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| 331 | zws(ji,jk) = zzws * vmask(ji,jj,jk+1) |
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| 332 | zwd(ji,jk) = 1. - zwi(ji,jk) - zzws |
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| 333 | zwy(ji,jk) = vb(ji,jj,jk) + z2dt * va(ji,jj,jk) |
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| 334 | END DO |
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| 335 | END DO |
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| 336 | |
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| 337 | ! 2.1 Surface boudary conditions |
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| 338 | DO ji = 2, jpim1 |
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| 339 | z2dtf = z2dt / ( fse3v(ji,jj,1)*rau0 ) |
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| 340 | zwi(ji,1) = 0.e0 |
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| 341 | zwd(ji,1) = 1. - zws(ji,1) |
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| 342 | zwy(ji,1) = zwy(ji,1) + z2dtf * tauy(ji,jj) |
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| 343 | END DO |
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| 344 | |
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| 345 | ! 2.2 Matrix inversion starting from the first level |
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| 346 | ikst = 1 |
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| 347 | #include "zdf.matrixsolver.h90" |
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| 348 | |
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| 349 | ! 2.3 Normalization to obtain the general momentum trend va |
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| 350 | DO jk = 1, jpkm1 |
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| 351 | DO ji = 2, jpim1 |
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| 352 | zva = ( zwx(ji,jk) - vb(ji,jj,jk) ) / z2dt |
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| 353 | #if defined key_trddyn |
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| 354 | ! save the vertical diffusive momentum fluxes |
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| 355 | vtrd(ji,jj,jk,7) = zva - va(ji,jj,jk) |
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| 356 | #endif |
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| 357 | va(ji,jj,jk) = zva |
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| 358 | END DO |
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| 359 | END DO |
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| 360 | |
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| 361 | #if defined key_trddyn |
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| 362 | ! 2.4 diagnose surface and bottom momentum fluxes |
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| 363 | DO ji = 2, jpim1 |
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| 364 | ! save the surface forcing momentum fluxes |
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| 365 | tautrd(ji,jj,2) = tauy(ji,jj) / ( fse3v(ji,jj,1)*rau0 ) |
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| 366 | ! save bottom friction momentum fluxes |
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| 367 | ikbv = min( mbathy(ji,jj+1), mbathy(ji,jj) ) |
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| 368 | ikbvm1 = max( ikbv-1, 1 ) |
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| 369 | tautrd(ji,jj,4) = - avmv(ji,jj,ikbv) * zwx(ji,ikbvm1) & |
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| 370 | / ( fse3v(ji,jj,ikbvm1)*fse3vw(ji,jj,ikbv) ) |
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| 371 | ! subtract surface forcing and bottom friction trend from vertical |
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| 372 | ! diffusive momentum trend |
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| 373 | vtrd(ji,jj,1 ,7) = vtrd(ji,jj,1 ,7) - tautrd(ji,jj,2) |
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| 374 | vtrd(ji,jj,ikbvm1,7) = vtrd(ji,jj,ikbvm1,7) - tautrd(ji,jj,4) |
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| 375 | END DO |
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| 376 | |
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| 377 | #endif |
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| 378 | ! ! =============== |
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| 379 | END DO ! End of slab |
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| 380 | ! ! =============== |
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| 381 | END SUBROUTINE dyn_zdf_iso |
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| 382 | |
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| 383 | #else |
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| 384 | !!---------------------------------------------------------------------- |
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| 385 | !! Dummy module NO rotation of the mixing tensor |
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| 386 | !!---------------------------------------------------------------------- |
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| 387 | CONTAINS |
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| 388 | SUBROUTINE dyn_zdf_iso( kt ) ! Dummy routine |
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| 389 | WRITE(*,*) kt |
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| 390 | END SUBROUTINE dyn_zdf_iso |
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| 391 | #endif |
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| 392 | |
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| 393 | !!============================================================================== |
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| 394 | END MODULE dynzdf_iso |
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