| 1 | SUBROUTINE spline_z( vad_in_out, ad_v, dz_spline, spline_tri, var_char ) |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Current revisions: |
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| 5 | ! ----------------- |
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| 6 | ! |
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| 7 | ! |
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| 8 | ! Former revisions: |
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| 9 | ! ----------------- |
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| 10 | ! $Id: spline_z.f90 484 2010-02-05 07:36:54Z helmke $ |
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| 11 | ! |
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| 12 | ! 19 2007-02-23 04:53:48Z raasch |
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| 13 | ! Boundary condition for pt at top adjusted |
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| 14 | ! |
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| 15 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 16 | ! |
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| 17 | ! Revision 1.9 2005/06/29 08:22:56 steinfeld |
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| 18 | ! Dependency of ug and vg on height considered in the determination of the |
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| 19 | ! upper boundary condition for vad |
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| 20 | ! |
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| 21 | ! Revision 1.1 1999/02/05 09:17:16 raasch |
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| 22 | ! Initial revision |
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| 23 | ! |
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| 24 | ! |
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| 25 | ! Description: |
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| 26 | ! ------------ |
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| 27 | ! Upstream-spline advection along x |
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| 28 | ! |
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| 29 | ! Input/output parameters: |
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| 30 | ! ad_v = advecting wind speed component |
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| 31 | ! dz_spline = vertical grid spacing (dzu or dzw, depending on quantity to be |
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| 32 | ! advected) |
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| 33 | ! spline_tri = grid spacing factors (spl_tri_zu or spl_tri_zw, depending on |
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| 34 | ! quantity to be advected) |
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| 35 | ! vad_in_out = quantity to be advected, excluding ghost- or cyclic boundaries |
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| 36 | ! result is given to the calling routine in this array |
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| 37 | ! var_char = string which defines the quantity to be advected |
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| 38 | ! |
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| 39 | ! Internal arrays: |
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| 40 | ! r = 2D-working array (right hand side of linear equation, buffer for |
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| 41 | ! Long filter) |
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| 42 | ! tf = tendency field (2D), used for long filter |
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| 43 | ! vad = quantity to be advected (2D), including ghost- or cyclic |
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| 44 | ! boundarys along the direction of advection |
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| 45 | ! wrk_long = working array (long coefficients) |
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| 46 | ! wrk_spline = working array (spline coefficients) |
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| 47 | !------------------------------------------------------------------------------! |
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| 48 | |
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| 49 | USE arrays_3d |
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| 50 | USE grid_variables |
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| 51 | USE indices |
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| 52 | USE statistics |
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| 53 | USE control_parameters |
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| 54 | USE transpose_indices |
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| 55 | |
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| 56 | IMPLICIT NONE |
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| 57 | |
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| 58 | CHARACTER (LEN=*) :: var_char |
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| 59 | |
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| 60 | INTEGER :: component, i, j, k, sr |
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| 61 | REAL :: dzwd, dzwu, overshoot_limit, t1, t2, t3, ups_limit |
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| 62 | REAL :: dz_spline(1:nzt+1) |
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| 63 | REAL :: spline_tri(5,nzb:nzt+1) |
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| 64 | REAL :: ad_v(nzb+1:nzta,nys:nyna,nxl:nxra) |
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| 65 | |
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| 66 | REAL, DIMENSION(:,:), ALLOCATABLE :: r, tf, vad, wrk_spline |
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| 67 | REAL, DIMENSION(:,:,:), ALLOCATABLE :: wrk_long |
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| 68 | |
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| 69 | #if defined( __parallel ) |
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| 70 | REAL :: vad_in_out(nzb+1:nzta,nys:nyna,nxl:nxra) |
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| 71 | #else |
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| 72 | REAL :: vad_in_out(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
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| 73 | #endif |
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| 74 | |
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| 75 | ! |
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| 76 | !-- Set criteria for switching between upstream- and upstream-spline-method |
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| 77 | IF ( var_char == 'u' ) THEN |
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| 78 | overshoot_limit = overshoot_limit_u |
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| 79 | ups_limit = ups_limit_u |
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| 80 | component = 1 |
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| 81 | ELSEIF ( var_char == 'v' ) THEN |
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| 82 | overshoot_limit = overshoot_limit_v |
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| 83 | ups_limit = ups_limit_v |
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| 84 | component = 2 |
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| 85 | ELSEIF ( var_char == 'w' ) THEN |
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| 86 | overshoot_limit = overshoot_limit_w |
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| 87 | ups_limit = ups_limit_w |
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| 88 | component = 3 |
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| 89 | ELSEIF ( var_char == 'pt' ) THEN |
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| 90 | overshoot_limit = overshoot_limit_pt |
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| 91 | ups_limit = ups_limit_pt |
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| 92 | component = 4 |
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| 93 | ELSEIF ( var_char == 'e' ) THEN |
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| 94 | overshoot_limit = overshoot_limit_e |
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| 95 | ups_limit = ups_limit_e |
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| 96 | component = 5 |
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| 97 | ENDIF |
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| 98 | |
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| 99 | ! |
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| 100 | !-- Allocate working arrays |
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| 101 | ALLOCATE( r(nzb:nzt+1,nys:nyn), vad(nzb:nzt+1,nys:nyn), & |
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| 102 | wrk_spline(nzb:nzt+1,nys:nyn) ) |
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| 103 | IF ( long_filter_factor /= 0.0 ) THEN |
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| 104 | ALLOCATE( tf(nzb:nzt+1,nys:nyn), wrk_long(nzb+1:nzt,nys:nyn,1:3) ) |
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| 105 | ENDIF |
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| 106 | |
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| 107 | ! |
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| 108 | !-- Initialize calculation of relative upstream fraction |
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| 109 | sums_up_fraction_l(component,3,:) = 0.0 |
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| 110 | |
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| 111 | ! |
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| 112 | !-- Loop over all gridpoints along x |
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| 113 | DO i = nxl, nxr |
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| 114 | |
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| 115 | ! |
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| 116 | !-- Store array to be advected on work array |
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| 117 | vad(nzb+1:nzt,:) = vad_in_out(nzb+1:nzt,nys:nyn,i) |
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| 118 | ! |
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| 119 | !-- Add boundary conditions along z |
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| 120 | IF ( var_char == 'u' .OR. var_char == 'v' ) THEN |
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| 121 | ! |
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| 122 | !-- Bottom boundary |
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| 123 | !-- u- and v-component |
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| 124 | IF ( ibc_uv_b == 0 ) THEN |
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| 125 | vad(nzb,:) = -vad(nzb+1,:) |
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| 126 | ELSE |
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| 127 | vad(nzb,:) = vad(nzb+1,:) |
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| 128 | ENDIF |
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| 129 | ! |
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| 130 | !-- Top boundary |
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| 131 | !-- Dirichlet condition |
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| 132 | IF ( ibc_uv_t == 0 .AND. var_char == 'u' ) THEN |
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| 133 | ! |
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| 134 | !-- u-component |
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| 135 | vad(nzt+1,:) = ug(nzt+1) |
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| 136 | ELSEIF ( ibc_uv_t == 0 .AND. var_char == 'v' ) THEN |
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| 137 | ! |
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| 138 | !-- v-component |
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| 139 | vad(nzt+1,:) = vg(nzt+1) |
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| 140 | ELSE |
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| 141 | ! |
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| 142 | !-- Neumann condition |
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| 143 | vad(nzt+1,:) = vad(nzt,:) |
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| 144 | ENDIF |
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| 145 | |
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| 146 | ELSEIF ( var_char == 'w' ) THEN |
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| 147 | ! |
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| 148 | !-- Bottom and top boundary for w-component |
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| 149 | vad(nzb,:) = 0.0 |
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| 150 | vad(nzt+1,:) = 0.0 |
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| 151 | |
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| 152 | ELSEIF ( var_char == 'pt' ) THEN |
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| 153 | ! |
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| 154 | !-- Bottom boundary for temperature |
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| 155 | IF ( ibc_pt_b == 1 ) THEN |
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| 156 | vad(nzb,:) = vad(nzb+1,:) |
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| 157 | ELSE |
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| 158 | vad(nzb,:) = pt(nzb,:,i) |
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| 159 | ENDIF |
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| 160 | ! |
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| 161 | !-- Top boundary for temperature |
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| 162 | IF ( ibc_pt_t == 0 ) THEN |
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| 163 | vad(nzt+1,:) = pt(nzt+1,nys:nyn,i) |
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| 164 | ELSEIF ( ibc_pt_t == 1 ) THEN |
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| 165 | vad(nzt+1,:) = vad(nzt,:) |
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| 166 | ELSEIF ( ibc_pt_t == 2 ) THEN |
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| 167 | vad(nzt+1,:) = vad(nzt,:) + bc_pt_t_val * dz_spline(nzt+1) |
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| 168 | ENDIF |
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| 169 | |
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| 170 | ELSEIF ( var_char == 'e' ) THEN |
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| 171 | ! |
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| 172 | !-- Boundary conditions for TKE (Neumann in any case) |
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| 173 | vad(nzb,:) = vad(nzb+1,:) |
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| 174 | vad(nzt,:) = vad(nzt-1,:) |
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| 175 | vad(nzt+1,:) = vad(nzt,:) |
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| 176 | |
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| 177 | ENDIF |
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| 178 | |
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| 179 | ! |
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| 180 | !-- Calculate right hand side |
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| 181 | DO j = nys, nyn |
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| 182 | r(nzb,j) = 3.0 * ( vad(nzb+1,j)-vad(nzb,j) ) / dz_spline(1) |
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| 183 | r(nzt+1,j) = 3.0 * ( vad(nzt+1,j)-vad(nzt,j) ) / dz_spline(nzt+1) |
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| 184 | DO k = nzb+1, nzt |
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| 185 | r(k,j) = 3.0 * ( & |
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| 186 | spline_tri(2,k) * ( vad(k,j)-vad(k-1,j) ) / dz_spline(k) & |
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| 187 | + spline_tri(3,k) * ( vad(k+1,j)-vad(k,j) ) / dz_spline(k+1) & |
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| 188 | ) |
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| 189 | ENDDO |
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| 190 | ENDDO |
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| 191 | |
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| 192 | ! |
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| 193 | !-- Forward substitution |
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| 194 | DO j = nys, nyn |
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| 195 | wrk_spline(nzb,j) = r(nzb,j) |
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| 196 | DO k = nzb+1, nzt+1 |
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| 197 | wrk_spline(k,j) = r(k,j) - spline_tri(5,k) * r(k-1,j) |
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| 198 | ENDDO |
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| 199 | ENDDO |
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| 200 | |
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| 201 | ! |
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| 202 | !-- Backward substitution |
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| 203 | DO j = nys, nyn |
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| 204 | r(nzt+1,j) = wrk_spline(nzt+1,j) / spline_tri(4,nzt+1) |
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| 205 | DO k = nzt, nzb, -1 |
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| 206 | r(k,j) = ( wrk_spline(k,j) - spline_tri(3,k) * r(k+1,j) ) / & |
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| 207 | spline_tri(4,k) |
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| 208 | ENDDO |
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| 209 | ENDDO |
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| 210 | |
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| 211 | ! |
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| 212 | !-- Calculate advection along z |
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| 213 | DO j = nys, nyn |
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| 214 | DO k = nzb+1, nzt |
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| 215 | |
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| 216 | IF ( ad_v(k,j,i) == 0.0 ) THEN |
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| 217 | |
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| 218 | vad_in_out(k,j,i) = vad(k,j) |
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| 219 | |
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| 220 | ELSEIF ( ad_v(k,j,i) > 0.0 ) THEN |
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| 221 | |
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| 222 | IF ( ABS( vad(k,j) - vad(k-1,j) ) <= ups_limit ) THEN |
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| 223 | vad_in_out(k,j,i) = vad(k,j) - dt_3d * ad_v(k,j,i) * & |
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| 224 | ( vad(k,j) - vad(k-1,j) ) * ddzu(k) |
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| 225 | ! |
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| 226 | !-- Calculate upstream fraction in % (s. flow_statistics) |
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| 227 | DO sr = 0, statistic_regions |
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| 228 | sums_up_fraction_l(component,3,sr) = & |
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| 229 | sums_up_fraction_l(component,3,sr) + 1.0 |
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| 230 | ENDDO |
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| 231 | ELSE |
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| 232 | t1 = ad_v(k,j,i) * dt_3d / dz_spline(k) |
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| 233 | t2 = 3.0 * ( vad(k-1,j) - vad(k,j) ) + & |
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| 234 | ( 2.0 * r(k,j) + r(k-1,j) ) * dz_spline(k) |
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| 235 | t3 = 2.0 * ( vad(k-1,j) - vad(k,j) ) + & |
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| 236 | ( r(k,j) + r(k-1,j) ) * dz_spline(k) |
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| 237 | vad_in_out(k,j,i) = vad(k,j) - r(k,j) * t1* dz_spline(k) + & |
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| 238 | t2 * t1**2 - t3 * t1**3 |
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| 239 | IF ( vad(k-1,j) == vad(k,j) ) THEN |
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| 240 | vad_in_out(k,j,i) = vad(k,j) |
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| 241 | ENDIF |
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| 242 | ENDIF |
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| 243 | |
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| 244 | ELSE |
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| 245 | |
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| 246 | IF( ABS( vad(k,j) - vad(k+1,j) ) <= ups_limit ) THEN |
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| 247 | vad_in_out(k,j,i) = vad(k,j) - dt_3d * ad_v(k,j,i) * & |
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| 248 | ( vad(k+1,j) - vad(k,j) ) * ddzu(k+1) |
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| 249 | ! |
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| 250 | !-- Calculate upstream fraction in % (s. flow_statistics) |
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| 251 | DO sr = 0, statistic_regions |
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| 252 | sums_up_fraction_l(component,3,sr) = & |
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| 253 | sums_up_fraction_l(component,3,sr) + 1.0 |
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| 254 | ENDDO |
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| 255 | ELSE |
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| 256 | t1 = -ad_v(k,j,i) * dt_3d / dz_spline(k+1) |
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| 257 | t2 = 3.0 * ( vad(k,j) - vad(k+1,j) ) + & |
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| 258 | ( 2.0 * r(k,j) + r(k+1,j) ) * dz_spline(k+1) |
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| 259 | t3 = 2.0 * ( vad(k,j) - vad(k+1,j) ) + & |
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| 260 | ( r(k,j) + r(k+1,j) ) * dz_spline(k+1) |
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| 261 | vad_in_out(k,j,i) = vad(k,j) + r(k,j)*t1*dz_spline(k+1) - & |
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| 262 | t2 * t1**2 + t3 * t1**3 |
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| 263 | IF ( vad(k+1,j) == vad(k,j) ) THEN |
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| 264 | vad_in_out(k,j,i) = vad(k,j) |
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| 265 | ENDIF |
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| 266 | ENDIF |
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| 267 | |
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| 268 | ENDIF |
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| 269 | ENDDO |
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| 270 | ENDDO |
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| 271 | |
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| 272 | ! |
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| 273 | !-- Limit values in order to prevent overshooting |
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| 274 | IF ( cut_spline_overshoot ) THEN |
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| 275 | |
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| 276 | DO j = nys, nyn |
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| 277 | DO k = nzb+1, nzt |
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| 278 | IF ( ad_v(k,j,i) > 0.0 ) THEN |
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| 279 | IF ( vad(k,j) > vad(k-1,j) ) THEN |
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| 280 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 281 | vad(k,j) + overshoot_limit ) |
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| 282 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 283 | vad(k-1,j) - overshoot_limit ) |
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| 284 | ELSE |
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| 285 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 286 | vad(k,j) - overshoot_limit ) |
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| 287 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 288 | vad(k-1,j) + overshoot_limit ) |
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| 289 | ENDIF |
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| 290 | ELSE |
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| 291 | IF ( vad(k,j) > vad(k+1,j) ) THEN |
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| 292 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 293 | vad(k,j) + overshoot_limit ) |
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| 294 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 295 | vad(k+1,j) - overshoot_limit ) |
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| 296 | ELSE |
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| 297 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 298 | vad(k,j) - overshoot_limit ) |
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| 299 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 300 | vad(k+1,j) + overshoot_limit ) |
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| 301 | ENDIF |
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| 302 | ENDIF |
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| 303 | ENDDO |
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| 304 | ENDDO |
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| 305 | |
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| 306 | ENDIF |
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| 307 | |
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| 308 | ! |
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| 309 | !-- Long-filter (acting on tendency only) |
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| 310 | IF ( long_filter_factor /= 0.0 ) THEN |
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| 311 | |
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| 312 | ! |
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| 313 | !-- Compute tendency |
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| 314 | DO j = nys, nyn |
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| 315 | |
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| 316 | ! |
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| 317 | !-- Depending on the quantity to be advected, the respective vertical |
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| 318 | !-- boundary conditions must be applied. |
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| 319 | IF ( var_char == 'u' .OR. var_char == 'v' ) THEN |
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| 320 | |
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| 321 | IF ( ibc_uv_b == 0 ) THEN |
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| 322 | tf(nzb,j) = - ( vad_in_out(nzb+1,j,i) - vad(nzb+1,j) ) |
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| 323 | ELSE |
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| 324 | tf(nzb,j) = vad_in_out(nzb+1,j,i) - vad(nzb+1,j) |
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| 325 | ENDIF |
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| 326 | |
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| 327 | IF ( ibc_uv_t == 0 ) THEN |
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| 328 | tf(nzt+1,j) = 0.0 |
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| 329 | ELSE |
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| 330 | tf(nzt+1,j) = vad_in_out(nzt,j,i) - vad(nzt,j) |
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| 331 | ENDIF |
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| 332 | |
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| 333 | ELSEIF ( var_char == 'w' ) THEN |
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| 334 | |
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| 335 | tf(nzb,j) = 0.0 |
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| 336 | tf(nzt+1,j) = 0.0 |
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| 337 | |
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| 338 | ELSEIF ( var_char == 'pt' ) THEN |
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| 339 | |
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| 340 | IF ( ibc_pt_b == 1 ) THEN |
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| 341 | tf(nzb,j) = vad_in_out(nzb+1,j,i) - vad(nzb+1,j) |
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| 342 | ELSE |
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| 343 | tf(nzb,j) = 0.0 |
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| 344 | ENDIF |
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| 345 | |
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| 346 | IF ( ibc_pt_t == 1 ) THEN |
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| 347 | vad_in_out(nzt,j,i) = vad_in_out(nzt-1,j,i) + bc_pt_t_val * & |
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| 348 | dz_spline(nzt) |
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| 349 | tf(nzt+1,j) = vad_in_out(nzt,j,i) + bc_pt_t_val * & |
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| 350 | dz_spline(nzt+1) - vad(nzt+1,j) |
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| 351 | ELSE |
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| 352 | vad_in_out(nzt,j,i) = pt(nzt,j,i) |
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| 353 | tf(nzt+1,j) = 0.0 |
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| 354 | ENDIF |
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| 355 | |
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| 356 | ENDIF |
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| 357 | |
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| 358 | DO k = nzb+1, nzt |
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| 359 | tf(k,j) = vad_in_out(k,j,i) - vad(k,j) |
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| 360 | ENDDO |
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| 361 | |
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| 362 | ENDDO |
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| 363 | |
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| 364 | ! |
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| 365 | !-- Apply the filter. |
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| 366 | DO j = nys, nyn |
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| 367 | |
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| 368 | dzwd = dz_spline(1) / ( dz_spline(1) + dz_spline(2) ) |
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| 369 | dzwu = dz_spline(2) / ( dz_spline(1) + dz_spline(2) ) |
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| 370 | |
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| 371 | wrk_long(nzb+1,j,1) = 2.0 * ( 1.0 + long_filter_factor ) |
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| 372 | wrk_long(nzb+1,j,2) = ( 1.0 - long_filter_factor ) * dzwd / & |
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| 373 | wrk_long(nzb+1,j,1) |
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| 374 | wrk_long(nzb+1,j,3) = ( long_filter_factor * dzwu * tf(nzb,j) + & |
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| 375 | 2.0 * tf(nzb+1,j) + dzwd * tf(nzb+2,j) & |
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| 376 | ) / wrk_long(nzb+1,j,1) |
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| 377 | |
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| 378 | DO k = nzb+2, nzt-1 |
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| 379 | |
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| 380 | dzwd = dz_spline(k) / ( dz_spline(k) + dz_spline(k+1) ) |
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| 381 | dzwu = dz_spline(k+1) / ( dz_spline(k) + dz_spline(k+1) ) |
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| 382 | |
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| 383 | wrk_long(k,j,1) = 2.0 * ( 1.0 + long_filter_factor ) - & |
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| 384 | ( 1.0 - long_filter_factor ) * dzwu * & |
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| 385 | wrk_long(k-1,j,2) |
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| 386 | wrk_long(k,j,2) = ( 1.0 - long_filter_factor ) * dzwd / & |
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| 387 | wrk_long(k,j,1) |
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| 388 | wrk_long(k,j,3) = ( dzwu * tf(k-1,j) + 2.0 * tf(k,j) + & |
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| 389 | dzwd * tf(k+1,j) - & |
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| 390 | ( 1.0 - long_filter_factor ) * dzwu * & |
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| 391 | wrk_long(k-1,j,3) & |
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| 392 | ) / wrk_long(k,j,1) |
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| 393 | ENDDO |
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| 394 | |
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| 395 | dzwd = dz_spline(nzt) / ( dz_spline(nzt) + dz_spline(nzt+1) ) |
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| 396 | dzwu = dz_spline(nzt+1) / ( dz_spline(nzt) + dz_spline(nzt+1) ) |
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| 397 | |
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| 398 | wrk_long(nzt,j,1) = 2.0 * ( 1.0 + long_filter_factor ) - & |
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| 399 | ( 1.0 - long_filter_factor ) * dzwu * & |
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| 400 | wrk_long(nzt-1,j,2) |
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| 401 | wrk_long(nzt,j,2) = ( 1.0 - long_filter_factor ) * dzwd / & |
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| 402 | wrk_long(nzt,j,1) |
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| 403 | wrk_long(nzt,j,3) = ( dzwu * tf(nzt-1,j) + 2.0 * tf(nzt,j) + & |
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| 404 | dzwd * long_filter_factor * tf(nzt+1,j) - & |
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| 405 | ( 1.0 - long_filter_factor ) * dzwu * & |
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| 406 | wrk_long(nzt-1,j,3) & |
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| 407 | ) / wrk_long(nzt,j,1) |
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| 408 | r(nzt,j) = wrk_long(nzt,j,3) |
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| 409 | |
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| 410 | ENDDO |
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| 411 | |
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| 412 | DO j = nys, nyn |
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| 413 | DO k = nzt-1, nzb+1, -1 |
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| 414 | r(k,j) = wrk_long(k,j,3) - wrk_long(k,j,2) * r(k+1,j) |
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| 415 | ENDDO |
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| 416 | ENDDO |
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| 417 | |
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| 418 | DO j = nys, nyn |
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| 419 | DO k = nzb+1, nzt |
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| 420 | vad_in_out(k,j,i) = vad(k,j) + r(k,j) |
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| 421 | ENDDO |
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| 422 | ENDDO |
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| 423 | |
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| 424 | ENDIF ! Long filter |
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| 425 | |
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| 426 | ENDDO |
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| 427 | |
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| 428 | DEALLOCATE( r, vad, wrk_spline ) |
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| 429 | IF ( long_filter_factor /= 0.0 ) DEALLOCATE( tf, wrk_long ) |
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| 430 | |
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| 431 | END SUBROUTINE spline_z |
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