[1] | 1 | SUBROUTINE spline_x( vad_in_out, ad_v, var_char ) |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Actual 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 | ! $Log: spline_x.f90,v $ |
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| 11 | ! Revision 1.8 2004/04/30 12:54:20 raasch |
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| 12 | ! Names of transpose indices changed, enlarged transposition arrays introduced |
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| 13 | ! |
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| 14 | ! Revision 1.7 2003/03/16 09:47:17 raasch |
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| 15 | ! Two underscores (_) are placed in front of all define-strings |
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| 16 | ! |
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| 17 | ! Revision 1.6 2001/03/30 07:53:19 raasch |
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| 18 | ! Arrays r, vad and wrk_spline changed from 3D to 2D and removed from argument |
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| 19 | ! list. Several loops over k/j (parallel/non-parallel) combined to one loop. |
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| 20 | ! Application of long filter moved to this routine. All comments and identifiers |
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| 21 | ! translated into English. |
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| 22 | ! |
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| 23 | ! Revision 1.5 2001/01/22 08:07:41 raasch |
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| 24 | ! Module test_variables removed |
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| 25 | ! |
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| 26 | ! Revision 1.4 1999/03/25 07:32:31 raasch |
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| 27 | ! Filterung der Ueberschwinger geschieht optional, ups_limit_e eingefuehrt, |
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| 28 | ! Ueberschwinger werden in gewissen Grenzen erlaubt |
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| 29 | ! |
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| 30 | ! Revision 1.3 1999/02/26 17:53:26 schroeter |
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| 31 | ! - Gradientenkontrolle fuer den nicht-parallelen Teil |
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| 32 | ! - statistische Auswertung ueber den prozentualen Anteil des |
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| 33 | ! Upstream-Verfahrens an der Gesamtadvektion fuer nicht- |
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| 34 | ! parallelen Teil |
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| 35 | ! |
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| 36 | ! Revision 1.2 1999/02/17 09:30:19 raasch |
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| 37 | ! Wertebegrenzung zur Verhinderung von Ueberschwingern |
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| 38 | ! |
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| 39 | ! Revision 1.1 1999/02/05 09:15:59 raasch |
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| 40 | ! Initial revision |
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| 41 | ! |
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| 42 | ! |
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| 43 | ! Description: |
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| 44 | ! ------------ |
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| 45 | ! Upstream-spline advection along x |
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| 46 | ! |
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| 47 | ! Input/output parameters: |
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| 48 | ! ad_v = advecting wind speed component |
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| 49 | ! vad_in_out = quantity to be advected, excluding ghost- or cyclic boundaries |
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| 50 | ! result is given to the calling routine in this array |
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| 51 | ! var_char = string which defines the quantity to be advected |
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| 52 | ! |
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| 53 | ! Internal arrays: |
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| 54 | ! r = 2D-working array (right hand side of linear equation, buffer for |
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| 55 | ! Long filter) |
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| 56 | ! tf = tendency field (2D), used for long filter |
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| 57 | ! vad = quantity to be advected (2D), including ghost- or cyclic |
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| 58 | ! boundarys along the direction of advection |
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| 59 | ! wrk_long = working array (long coefficients) |
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| 60 | ! wrk_spline = working array (spline coefficients) |
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| 61 | !------------------------------------------------------------------------------! |
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| 62 | |
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| 63 | USE advection |
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| 64 | USE grid_variables |
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| 65 | USE indices |
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| 66 | USE statistics |
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| 67 | USE control_parameters |
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| 68 | USE transpose_indices |
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| 69 | |
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| 70 | IMPLICIT NONE |
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| 71 | |
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| 72 | CHARACTER (LEN=*) :: var_char |
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| 73 | |
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| 74 | INTEGER :: component, i, j, k, sr |
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| 75 | REAL :: overshoot_limit, sm_faktor, t1, t2, t3, ups_limit |
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| 76 | REAL, DIMENSION(:,:), ALLOCATABLE :: r, tf, vad, wrk_spline |
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| 77 | REAL, DIMENSION(:,:,:), ALLOCATABLE :: wrk_long |
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| 78 | |
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| 79 | #if defined( __parallel ) |
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| 80 | REAL :: ad_v(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa), & |
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| 81 | vad_in_out(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa) |
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| 82 | #else |
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| 83 | REAL :: ad_v(nzb+1:nzt,nys:nyn,nxl:nxr), & |
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| 84 | vad_in_out(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
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| 85 | #endif |
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| 86 | |
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| 87 | ! |
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| 88 | !-- Set criteria for switching between upstream- and upstream-spline-method |
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| 89 | IF ( var_char == 'u' ) THEN |
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| 90 | overshoot_limit = overshoot_limit_u |
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| 91 | ups_limit = ups_limit_u |
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| 92 | component = 1 |
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| 93 | ELSEIF ( var_char == 'v' ) THEN |
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| 94 | overshoot_limit = overshoot_limit_v |
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| 95 | ups_limit = ups_limit_v |
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| 96 | component = 2 |
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| 97 | ELSEIF ( var_char == 'w' ) THEN |
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| 98 | overshoot_limit = overshoot_limit_w |
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| 99 | ups_limit = ups_limit_w |
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| 100 | component = 3 |
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| 101 | ELSEIF ( var_char == 'pt' ) THEN |
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| 102 | overshoot_limit = overshoot_limit_pt |
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| 103 | ups_limit = ups_limit_pt |
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| 104 | component = 4 |
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| 105 | ELSEIF ( var_char == 'e' ) THEN |
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| 106 | overshoot_limit = overshoot_limit_e |
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| 107 | ups_limit = ups_limit_e |
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| 108 | component = 5 |
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| 109 | ENDIF |
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| 110 | |
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| 111 | ! |
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| 112 | !-- Initialize calculation of relative upstream fraction |
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| 113 | sums_up_fraction_l(component,1,:) = 0.0 |
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| 114 | |
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| 115 | #if defined( __parallel ) |
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| 116 | |
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| 117 | ! |
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| 118 | !-- Allocate working arrays |
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| 119 | ALLOCATE( r(-1:nx+1,nys_x:nyn_x), vad(-1:nx+1,nys_x:nyn_x), & |
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| 120 | wrk_spline(0:nx,nys_x:nyn_x) ) |
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| 121 | IF ( long_filter_factor /= 0.0 ) THEN |
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| 122 | ALLOCATE( tf(0:nx,nys_x:nyn_x), wrk_long(0:nx,nys_x:nyn_x,1:3) ) |
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| 123 | ENDIF |
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| 124 | |
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| 125 | ! |
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| 126 | !-- Loop over all gridpoints along z |
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| 127 | DO k = nzb_x, nzt_x |
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| 128 | |
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| 129 | ! |
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| 130 | !-- Store array to be advected on work array and add cyclic boundary along x |
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| 131 | vad(0:nx,nys_x:nyn_x) = vad_in_out(0:nx,nys_x:nyn_x,k) |
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| 132 | vad(-1,:) = vad(nx,:) |
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| 133 | vad(nx+1,:) = vad(0,:) |
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| 134 | |
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| 135 | ! |
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| 136 | !-- Calculate right hand side |
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| 137 | DO j = nys_x, nyn_x |
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| 138 | DO i = 0, nx |
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| 139 | r(i,j) = 3.0 * ( & |
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| 140 | spl_tri_x(2,i) * ( vad(i,j) - vad(i-1,j) ) * ddx + & |
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| 141 | spl_tri_x(3,i) * ( vad(i+1,j) - vad(i,j) ) * ddx & |
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| 142 | ) |
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| 143 | ENDDO |
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| 144 | ENDDO |
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| 145 | |
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| 146 | ! |
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| 147 | !-- Forward substitution |
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| 148 | DO j = nys_x, nyn_x |
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| 149 | wrk_spline(0,j) = r(0,j) |
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| 150 | DO i = 1, nx |
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| 151 | wrk_spline(i,j) = r(i,j) - spl_tri_x(5,i) * wrk_spline(i-1,j) |
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| 152 | ENDDO |
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| 153 | ENDDO |
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| 154 | |
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| 155 | ! |
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| 156 | !-- Backward substitution (Sherman-Morrison-formula) |
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| 157 | DO j = nys_x, nyn_x |
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| 158 | r(nx,j) = wrk_spline(nx,j) / spl_tri_x(4,nx) |
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| 159 | DO i = nx-1, 0, -1 |
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| 160 | r(i,j) = ( wrk_spline(i,j) - spl_tri_x(3,i) * r(i+1,j) ) / & |
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| 161 | spl_tri_x(4,i) |
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| 162 | ENDDO |
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| 163 | sm_faktor = ( r(0,j) + 0.5 * r(nx,j) / spl_gamma_x ) / & |
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| 164 | ( 1.0 + spl_z_x(0) + 0.5 * spl_z_x(nx) / spl_gamma_x ) |
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| 165 | DO i = 0, nx |
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| 166 | r(i,j) = r(i,j) - sm_faktor * spl_z_x(i) |
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| 167 | ENDDO |
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| 168 | ENDDO |
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| 169 | |
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| 170 | ! |
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| 171 | !-- Add cyclic boundary to right hand side |
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| 172 | r(-1,:) = r(nx,:) |
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| 173 | r(nx+1,:) = r(0,:) |
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| 174 | |
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| 175 | ! |
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| 176 | !-- Calculate advection along x |
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| 177 | DO j = nys_x, nyn_x |
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| 178 | DO i = 0, nx |
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| 179 | |
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| 180 | IF ( ad_v(i,j,k) == 0.0 ) THEN |
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| 181 | |
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| 182 | vad_in_out(i,j,k) = vad(i,j) |
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| 183 | |
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| 184 | ELSEIF ( ad_v(i,j,k) > 0.0 ) THEN |
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| 185 | |
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| 186 | IF ( ABS( vad(i,j) - vad(i-1,j) ) <= ups_limit ) THEN |
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| 187 | vad_in_out(i,j,k) = vad(i,j) - dt_3d * ad_v(i,j,k) * & |
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| 188 | ( vad(i,j) - vad(i-1,j) ) * ddx |
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| 189 | ! |
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| 190 | !-- Calculate upstream fraction in % (s. flow_statistics) |
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| 191 | DO sr = 0, statistic_regions |
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| 192 | sums_up_fraction_l(component,1,sr) = & |
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| 193 | sums_up_fraction_l(component,1,sr) + 1.0 |
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| 194 | ENDDO |
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| 195 | ELSE |
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| 196 | t1 = ad_v(i,j,k) * dt_3d * ddx |
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| 197 | t2 = 3.0 * ( vad(i-1,j) - vad(i,j) ) + & |
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| 198 | ( 2.0 * r(i,j) + r(i-1,j) ) * dx |
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| 199 | t3 = 2.0 * ( vad(i-1,j) - vad(i,j) ) + & |
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| 200 | ( r(i,j) + r(i-1,j) ) * dx |
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| 201 | vad_in_out(i,j,k) = vad(i,j) - r(i,j) * t1 * dx + & |
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| 202 | t2 * t1**2 - t3 * t1**3 |
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| 203 | IF ( vad(i-1,j) == vad(i,j) ) THEN |
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| 204 | vad_in_out(i,j,k) = vad(i,j) |
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| 205 | ENDIF |
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| 206 | ENDIF |
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| 207 | |
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| 208 | ELSE |
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| 209 | |
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| 210 | IF ( ABS( vad(i,j) - vad(i+1,j) ) <= ups_limit ) THEN |
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| 211 | vad_in_out(i,j,k) = vad(i,j) - dt_3d * ad_v(i,j,k) * & |
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| 212 | ( vad(i+1,j) - vad(i,j) ) * ddx |
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| 213 | ! |
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| 214 | !-- Calculate upstream fraction in % (s. flow_statistics) |
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| 215 | DO sr = 0, statistic_regions |
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| 216 | sums_up_fraction_l(component,1,sr) = & |
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| 217 | sums_up_fraction_l(component,1,sr) + 1.0 |
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| 218 | ENDDO |
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| 219 | ELSE |
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| 220 | t1 = -ad_v(i,j,k) * dt_3d * ddx |
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| 221 | t2 = 3.0 * ( vad(i,j) - vad(i+1,j) ) + & |
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| 222 | ( 2.0 * r(i,j) + r(i+1,j) ) * dx |
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| 223 | t3 = 2.0 * ( vad(i,j) - vad(i+1,j) ) + & |
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| 224 | ( r(i,j) + r(i+1,j) ) * dx |
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| 225 | vad_in_out(i,j,k) = vad(i,j) + r(i,j) * t1 * dx - & |
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| 226 | t2 * t1**2 + t3 * t1**3 |
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| 227 | IF ( vad(i+1,j) == vad(i,j) ) THEN |
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| 228 | vad_in_out(i,j,k) = vad(i,j) |
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| 229 | ENDIF |
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| 230 | ENDIF |
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| 231 | |
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| 232 | ENDIF |
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| 233 | ENDDO |
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| 234 | ENDDO |
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| 235 | |
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| 236 | ! |
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| 237 | !-- Limit values in order to prevent overshooting |
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| 238 | IF ( cut_spline_overshoot ) THEN |
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| 239 | |
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| 240 | DO j = nys_x, nyn_x |
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| 241 | DO i = 0, nx |
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| 242 | IF ( ad_v(i,j,k) > 0.0 ) THEN |
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| 243 | IF ( vad(i,j) > vad(i-1,j) ) THEN |
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| 244 | vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), & |
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| 245 | vad(i,j) + overshoot_limit ) |
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| 246 | vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), & |
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| 247 | vad(i-1,j) - overshoot_limit ) |
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| 248 | ELSE |
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| 249 | vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), & |
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| 250 | vad(i,j) - overshoot_limit ) |
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| 251 | vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), & |
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| 252 | vad(i-1,j) + overshoot_limit ) |
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| 253 | ENDIF |
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| 254 | ELSE |
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| 255 | IF ( vad(i,j) > vad(i+1,j) ) THEN |
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| 256 | vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), & |
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| 257 | vad(i,j) + overshoot_limit ) |
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| 258 | vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), & |
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| 259 | vad(i+1,j) - overshoot_limit ) |
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| 260 | ELSE |
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| 261 | vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), & |
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| 262 | vad(i,j) - overshoot_limit ) |
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| 263 | vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), & |
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| 264 | vad(i+1,j) + overshoot_limit ) |
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| 265 | ENDIF |
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| 266 | ENDIF |
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| 267 | ENDDO |
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| 268 | ENDDO |
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| 269 | |
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| 270 | ENDIF |
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| 271 | |
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| 272 | ! |
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| 273 | !-- Long-filter (acting on tendency only) |
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| 274 | IF ( long_filter_factor /= 0.0 ) THEN |
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| 275 | |
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| 276 | ! |
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| 277 | !-- Compute tendency |
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| 278 | DO j = nys_x, nyn_x |
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| 279 | DO i = 0, nx |
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| 280 | tf(i,j) = vad_in_out(i,j,k) - vad(i,j) |
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| 281 | ENDDO |
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| 282 | ENDDO |
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| 283 | |
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| 284 | ! |
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| 285 | !-- Apply the filter. |
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| 286 | DO j = nys_x, nyn_x |
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| 287 | wrk_long(0,j,1) = 2.0 * ( 1.0 + long_filter_factor ) |
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| 288 | wrk_long(0,j,2) = ( 1.0 - long_filter_factor ) / wrk_long(0,j,1) |
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| 289 | wrk_long(0,j,3) = ( long_filter_factor * tf(nx,j) + & |
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| 290 | 2.0 * tf(0,j) + tf(1,j) & |
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| 291 | ) / wrk_long(0,j,1) |
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| 292 | DO i = 1, nx-1 |
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| 293 | wrk_long(i,j,1) = 2.0 * ( 1.0 + long_filter_factor ) - & |
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| 294 | ( 1.0 - long_filter_factor ) * wrk_long(i-1,j,2) |
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| 295 | wrk_long(i,j,2) = ( 1.0 - long_filter_factor ) / wrk_long(i,j,1) |
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| 296 | wrk_long(i,j,3) = ( tf(i-1,j) + 2.0 * tf(i,j) + & |
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| 297 | tf(i+1,j) - ( 1.0 - long_filter_factor ) * & |
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| 298 | wrk_long(i-1,j,3) ) / wrk_long(i,j,1) |
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| 299 | ENDDO |
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| 300 | wrk_long(nx,j,1) = 2.0 * ( 1.0 + long_filter_factor ) - & |
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| 301 | ( 1.0 - long_filter_factor ) * wrk_long(nx-1,j,2) |
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| 302 | wrk_long(nx,j,2) = ( 1.0 - long_filter_factor ) / wrk_long(nx,j,1) |
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| 303 | wrk_long(nx,j,3) = ( tf(nx-1,j) + 2.0 * tf(nx,j) + & |
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| 304 | long_filter_factor * tf(0,j) - & |
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| 305 | ( 1.0 - long_filter_factor ) * & |
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| 306 | wrk_long(nx-1,j,3) & |
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| 307 | ) / wrk_long(nx,j,1) |
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| 308 | r(nx,j) = wrk_long(nx,j,3) |
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| 309 | ENDDO |
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| 310 | |
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| 311 | DO i = nx-1, 0, -1 |
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| 312 | DO j = nys_x, nyn_x |
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| 313 | r(i,j) = wrk_long(i,j,3) - wrk_long(i,j,2) * r(i+1,j) |
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| 314 | ENDDO |
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| 315 | ENDDO |
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| 316 | |
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| 317 | DO j = nys_x, nyn_x |
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| 318 | DO i = 0, nx |
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| 319 | vad_in_out(i,j,k) = vad(i,j) + r(i,j) |
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| 320 | ENDDO |
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| 321 | ENDDO |
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| 322 | |
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| 323 | ENDIF ! Long filter |
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| 324 | |
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| 325 | ENDDO |
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| 326 | |
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| 327 | #else |
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| 328 | |
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| 329 | ! |
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| 330 | !-- Allocate working arrays |
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| 331 | ALLOCATE( r(nzb+1:nzt,nxl-1:nxr+1), vad(nzb:nzt+1,nxl-1:nxr+1), & |
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| 332 | wrk_spline(nzb+1:nzt,nxl-1:nxr+1) ) |
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| 333 | IF ( long_filter_factor /= 0.0 ) THEN |
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| 334 | ALLOCATE( tf(nzb+1:nzt,nxl-1:nxr+1), wrk_long(nzb+1:nzt,0:nx,1:3) ) |
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| 335 | ENDIF |
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| 336 | |
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| 337 | ! |
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| 338 | !-- Loop over all gridpoints along y |
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| 339 | DO j = nys, nyn |
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| 340 | |
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| 341 | ! |
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| 342 | !-- Store array to be advected on work array and add cyclic boundary along x |
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| 343 | vad(:,:) = vad_in_out(:,j,:) |
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| 344 | vad(:,-1) = vad(:,nx) |
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| 345 | vad(:,nx+1) = vad(:,0) |
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| 346 | |
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| 347 | ! |
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| 348 | !-- Calculate right hand side |
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| 349 | DO i = 0, nx |
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| 350 | DO k = nzb+1, nzt |
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| 351 | r(k,i) = 3.0 * ( & |
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| 352 | spl_tri_x(2,i) * ( vad(k,i) - vad(k,i-1) ) * ddx + & |
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| 353 | spl_tri_x(3,i) * ( vad(k,i+1) - vad(k,i) ) * ddx & |
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| 354 | ) |
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| 355 | ENDDO |
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| 356 | ENDDO |
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| 357 | |
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| 358 | ! |
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| 359 | !-- Forward substitution |
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| 360 | DO k = nzb+1, nzt |
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| 361 | wrk_spline(k,0) = r(k,0) |
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| 362 | ENDDO |
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| 363 | |
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| 364 | DO i = 1, nx |
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| 365 | DO k = nzb+1, nzt |
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| 366 | wrk_spline(k,i) = r(k,i) - spl_tri_x(5,i) * wrk_spline(k,i-1) |
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| 367 | ENDDO |
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| 368 | ENDDO |
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| 369 | |
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| 370 | ! |
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| 371 | !-- Backward substitution (Sherman-Morrison-formula) |
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| 372 | DO k = nzb+1, nzt |
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| 373 | r(k,nx) = wrk_spline(k,nx) / spl_tri_x(4,nx) |
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| 374 | ENDDO |
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| 375 | |
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| 376 | DO k = nzb+1, nzt |
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| 377 | DO i = nx-1, 0, -1 |
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| 378 | r(k,i) = ( wrk_spline(k,i) - spl_tri_x(3,i) * r(k,i+1) ) / & |
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| 379 | spl_tri_x(4,i) |
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| 380 | ENDDO |
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| 381 | sm_faktor = ( r(k,0) + 0.5 * r(k,nx) / spl_gamma_x ) / & |
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| 382 | ( 1.0 + spl_z_x(0) + 0.5 * spl_z_x(nx) / spl_gamma_x ) |
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| 383 | DO i = 0, nx |
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| 384 | r(k,i) = r(k,i) - sm_faktor * spl_z_x(i) |
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| 385 | ENDDO |
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| 386 | ENDDO |
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| 387 | |
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| 388 | ! |
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| 389 | !-- Add cyclic boundary to the right hand side |
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| 390 | r(:,-1) = r(:,nx) |
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| 391 | r(:,nx+1) = r(:,0) |
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| 392 | |
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| 393 | ! |
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| 394 | !-- Calculate advection along x |
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| 395 | DO i = 0, nx |
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| 396 | DO k = nzb+1, nzt |
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| 397 | |
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| 398 | IF (ad_v(k,j,i) == 0.0) THEN |
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| 399 | |
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| 400 | vad_in_out(k,j,i) = vad(k,i) |
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| 401 | |
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| 402 | ELSEIF ( ad_v(k,j,i) > 0.0) THEN |
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| 403 | |
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| 404 | IF ( ABS( vad(k,i) - vad(k,i-1) ) <= ups_limit ) THEN |
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| 405 | vad_in_out(k,j,i) = vad(k,i) - dt_3d * ad_v(k,j,i) * & |
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| 406 | ( vad(k,i) - vad(k,i-1) ) * ddx |
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| 407 | ! |
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| 408 | !-- Calculate upstream fraction in % (s. flow_statistics) |
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| 409 | DO sr = 0, statistic_regions |
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| 410 | sums_up_fraction_l(component,1,sr) = & |
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| 411 | sums_up_fraction_l(component,1,sr) + 1.0 |
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| 412 | ENDDO |
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| 413 | ELSE |
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| 414 | t1 = ad_v(k,j,i) * dt_3d * ddx |
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| 415 | t2 = 3.0 * ( vad(k,i-1) - vad(k,i) ) + & |
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| 416 | ( 2.0 * r(k,i) + r(k,i-1) ) * dx |
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| 417 | t3 = 2.0 * ( vad(k,i-1) - vad(k,i) ) + & |
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| 418 | ( r(k,i) + r(k,i-1) ) * dx |
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| 419 | vad_in_out(k,j,i) = vad(k,i) - r(k,i) * t1 * dx + & |
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| 420 | t2 * t1**2 - t3 * t1**3 |
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| 421 | IF ( vad(k,i-1) == vad(k,i) ) THEN |
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| 422 | vad_in_out(k,j,i) = vad(k,i) |
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| 423 | ENDIF |
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| 424 | ENDIF |
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| 425 | |
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| 426 | ELSE |
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| 427 | |
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| 428 | IF ( ABS( vad(k,i) - vad(k,i+1) ) <= ups_limit ) THEN |
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| 429 | vad_in_out(k,j,i) = vad(k,i) - dt_3d * ad_v(k,j,i) * & |
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| 430 | ( vad(k,i+1) - vad(k,i) ) * ddx |
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| 431 | ! |
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| 432 | !-- Calculate upstream fraction in % (s. flow_statistics) |
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| 433 | DO sr = 0, statistic_regions |
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| 434 | sums_up_fraction_l(component,1,sr) = & |
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| 435 | sums_up_fraction_l(component,1,sr) + 1.0 |
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| 436 | ENDDO |
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| 437 | ELSE |
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| 438 | t1 = -ad_v(k,j,i) * dt_3d * ddx |
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| 439 | t2 = 3.0 * ( vad(k,i) - vad(k,i+1) ) + & |
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| 440 | ( 2.0 * r(k,i) + r(k,i+1)) * dx |
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| 441 | t3 = 2.0 * ( vad(k,i) - vad(k,i+1) ) + & |
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| 442 | ( r(k,i) + r(k,i+1) ) * dx |
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| 443 | vad_in_out(k,j,i) = vad(k,i) + r(k,i) * t1 * dx - & |
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| 444 | t2 * t1**2 + t3 * t1**3 |
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| 445 | IF ( vad(k,i+1) == vad(k,i) ) THEN |
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| 446 | vad_in_out(k,j,i) = vad(k,i) |
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| 447 | ENDIF |
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| 448 | ENDIF |
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| 449 | |
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| 450 | ENDIF |
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| 451 | ENDDO |
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| 452 | ENDDO |
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| 453 | |
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| 454 | ! |
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| 455 | !-- Limit values in order to prevent overshooting |
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| 456 | IF ( cut_spline_overshoot ) THEN |
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| 457 | |
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| 458 | DO i = 0, nx |
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| 459 | DO k = nzb+1, nzt |
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| 460 | IF ( ad_v(k,j,i) > 0.0 ) THEN |
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| 461 | IF ( vad(k,i) > vad(k,i-1) ) THEN |
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| 462 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 463 | vad(k,i) + overshoot_limit ) |
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| 464 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 465 | vad(k,i-1) - overshoot_limit ) |
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| 466 | ELSE |
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| 467 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 468 | vad(k,i) - overshoot_limit ) |
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| 469 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 470 | vad(k,i-1) + overshoot_limit ) |
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| 471 | ENDIF |
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| 472 | ELSE |
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| 473 | IF ( vad(k,i) > vad(k,i+1) ) THEN |
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| 474 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 475 | vad(k,i) + overshoot_limit ) |
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| 476 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 477 | vad(k,i+1) - overshoot_limit ) |
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| 478 | ELSE |
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| 479 | vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), & |
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| 480 | vad(k,i) - overshoot_limit ) |
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| 481 | vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), & |
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| 482 | vad(k,i+1) + overshoot_limit ) |
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| 483 | ENDIF |
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| 484 | ENDIF |
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| 485 | ENDDO |
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| 486 | ENDDO |
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| 487 | |
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| 488 | ENDIF |
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| 489 | |
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| 490 | ! |
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| 491 | !-- Long filter (acting on tendency only) |
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| 492 | IF ( long_filter_factor /= 0.0 ) THEN |
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| 493 | |
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| 494 | ! |
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| 495 | !-- Compute tendency |
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| 496 | DO i = nxl, nxr |
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| 497 | DO k = nzb+1, nzt |
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| 498 | tf(k,i) = vad_in_out(k,j,i) - vad(k,i) |
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| 499 | ENDDO |
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| 500 | ENDDO |
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| 501 | |
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| 502 | ! |
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| 503 | !-- Apply the filter |
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| 504 | wrk_long(:,0,1) = 2.0 * ( 1.0 + long_filter_factor ) |
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| 505 | wrk_long(:,0,2) = ( 1.0 - long_filter_factor ) / wrk_long(:,0,1) |
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| 506 | wrk_long(:,0,3) = ( long_filter_factor * tf(:,nx) + & |
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| 507 | 2.0 * tf(:,0) + tf(:,1) ) / wrk_long(:,0,1) |
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| 508 | |
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| 509 | DO i = 1, nx-1 |
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| 510 | DO k = nzb+1, nzt |
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| 511 | wrk_long(k,i,1) = 2.0 * ( 1.0 + long_filter_factor ) - & |
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| 512 | ( 1.0 - long_filter_factor ) * & |
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| 513 | wrk_long(k,i-1,2) |
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| 514 | wrk_long(k,i,2) = ( 1.0 - long_filter_factor ) / wrk_long(k,i,1) |
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| 515 | wrk_long(k,i,3) = ( tf(k,i-1) + 2.0 * tf(k,i) + & |
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| 516 | tf(k,i+1) - ( 1.0 - long_filter_factor ) * & |
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| 517 | wrk_long(k,i-1,3) ) / wrk_long(k,i,1) |
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| 518 | ENDDO |
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| 519 | wrk_long(:,nx,1) = 2.0 * ( 1.0 + long_filter_factor ) - & |
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| 520 | ( 1.0 - long_filter_factor ) * & |
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| 521 | wrk_long(:,nx-1,2) |
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| 522 | wrk_long(:,nx,2) = ( 1.0 - long_filter_factor ) / wrk_long(:,nx,1) |
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| 523 | wrk_long(:,nx,3) = ( tf(:,nx-1) + 2.0 * tf(:,nx) + & |
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| 524 | long_filter_factor * tf(:,0) - & |
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| 525 | ( 1.0 - long_filter_factor ) * & |
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| 526 | wrk_long(:,nx-1,3) ) / wrk_long(:,nx,1) |
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| 527 | r(:,nx) = wrk_long(:,nx,3) |
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| 528 | ENDDO |
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| 529 | DO i = nx-1, 0, -1 |
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| 530 | DO k = nzb+1, nzt |
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| 531 | r(k,i) = wrk_long(k,i,3) - wrk_long(k,i,2) * r(k,i+1) |
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| 532 | ENDDO |
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| 533 | ENDDO |
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| 534 | DO i = 0, nx |
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| 535 | DO k = nzb+1, nzt |
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| 536 | vad_in_out(k,j,i) = vad(k,i) + r(k,i) |
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| 537 | ENDDO |
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| 538 | ENDDO |
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| 539 | |
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| 540 | ENDIF ! Long filter |
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| 541 | |
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| 542 | ENDDO |
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| 543 | #endif |
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| 544 | |
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| 545 | IF ( long_filter_factor /= 0.0 ) DEALLOCATE( tf, wrk_long ) |
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| 546 | DEALLOCATE( r, vad, wrk_spline ) |
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| 547 | |
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| 548 | END SUBROUTINE spline_x |
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