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