| 1 | MODULE production_e_mod |
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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: production_e.f90 226 2009-02-02 07:39:34Z heinze $ |
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| 11 | ! |
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| 12 | ! 208 2008-10-20 06:02:59Z raasch |
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| 13 | ! Bugfix concerning the calculation of velocity gradients at vertical walls |
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| 14 | ! in case of diabatic conditions |
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| 15 | ! |
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| 16 | ! 187 2008-08-06 16:25:09Z letzel |
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| 17 | ! Change: add 'minus' sign to fluxes obtained from subroutine wall_fluxes_e for |
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| 18 | ! consistency with subroutine wall_fluxes |
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| 19 | ! |
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| 20 | ! 124 2007-10-19 15:47:46Z raasch |
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| 21 | ! Bugfix: calculation of density flux in the ocean now starts from nzb+1 |
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| 22 | ! |
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| 23 | ! 108 2007-08-24 15:10:38Z letzel |
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| 24 | ! Bugfix: wrong sign removed from the buoyancy production term in the case |
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| 25 | ! use_reference = .T., |
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| 26 | ! u_0 and v_0 are calculated for nxr+1, nyn+1 also (otherwise these values are |
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| 27 | ! not available in case of non-cyclic boundary conditions) |
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| 28 | ! Bugfix for ocean density flux at bottom |
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| 29 | ! |
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| 30 | ! 97 2007-06-21 08:23:15Z raasch |
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| 31 | ! Energy production by density flux (in ocean) added |
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| 32 | ! use_pt_reference renamed use_reference |
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| 33 | ! |
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| 34 | ! 75 2007-03-22 09:54:05Z raasch |
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| 35 | ! Wall functions now include diabatic conditions, call of routine wall_fluxes_e, |
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| 36 | ! reference temperature pt_reference can be used in buoyancy term, |
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| 37 | ! moisture renamed humidity |
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| 38 | ! |
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| 39 | ! 37 2007-03-01 08:33:54Z raasch |
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| 40 | ! Calculation extended for gridpoint nzt, extended for given temperature / |
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| 41 | ! humidity fluxes at the top, wall-part is now executed in case that a |
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| 42 | ! Prandtl-layer is switched on (instead of surfaces fluxes switched on) |
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| 43 | ! |
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| 44 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 45 | ! |
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| 46 | ! Revision 1.21 2006/04/26 12:45:35 raasch |
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| 47 | ! OpenMP parallelization of production_e_init |
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| 48 | ! |
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| 49 | ! Revision 1.1 1997/09/19 07:45:35 raasch |
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| 50 | ! Initial revision |
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| 51 | ! |
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| 52 | ! |
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| 53 | ! Description: |
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| 54 | ! ------------ |
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| 55 | ! Production terms (shear + buoyancy) of the TKE |
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| 56 | ! WARNING: the case with prandtl_layer = F and use_surface_fluxes = T is |
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| 57 | ! not considered well! |
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| 58 | !------------------------------------------------------------------------------! |
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| 59 | |
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| 60 | USE wall_fluxes_mod |
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| 61 | |
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| 62 | PRIVATE |
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| 63 | PUBLIC production_e, production_e_init |
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| 64 | |
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| 65 | LOGICAL, SAVE :: first_call = .TRUE. |
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| 66 | |
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| 67 | REAL, DIMENSION(:,:), ALLOCATABLE, SAVE :: u_0, v_0 |
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| 68 | |
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| 69 | INTERFACE production_e |
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| 70 | MODULE PROCEDURE production_e |
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| 71 | MODULE PROCEDURE production_e_ij |
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| 72 | END INTERFACE production_e |
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| 73 | |
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| 74 | INTERFACE production_e_init |
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| 75 | MODULE PROCEDURE production_e_init |
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| 76 | END INTERFACE production_e_init |
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| 77 | |
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| 78 | CONTAINS |
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| 79 | |
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| 80 | |
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| 81 | !------------------------------------------------------------------------------! |
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| 82 | ! Call for all grid points |
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| 83 | !------------------------------------------------------------------------------! |
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| 84 | SUBROUTINE production_e |
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| 85 | |
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| 86 | USE arrays_3d |
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| 87 | USE cloud_parameters |
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| 88 | USE control_parameters |
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| 89 | USE grid_variables |
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| 90 | USE indices |
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| 91 | USE statistics |
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| 92 | |
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| 93 | IMPLICIT NONE |
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| 94 | |
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| 95 | INTEGER :: i, j, k |
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| 96 | |
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| 97 | REAL :: def, dudx, dudy, dudz, dvdx, dvdy, dvdz, dwdx, dwdy, dwdz, & |
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| 98 | k1, k2, km_neutral, theta, temp |
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| 99 | |
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| 100 | ! REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs, vsus, wsus, wsvs |
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| 101 | REAL, DIMENSION(nzb:nzt+1) :: usvs, vsus, wsus, wsvs |
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| 102 | |
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| 103 | ! |
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| 104 | !-- First calculate horizontal momentum flux u'v', w'v', v'u', w'u' at |
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| 105 | !-- vertical walls, if neccessary |
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| 106 | !-- So far, results are slightly different from the ij-Version. |
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| 107 | !-- Therefore, ij-Version is called further below within the ij-loops. |
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| 108 | ! IF ( topography /= 'flat' ) THEN |
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| 109 | ! CALL wall_fluxes_e( usvs, 1.0, 0.0, 0.0, 0.0, wall_e_y ) |
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| 110 | ! CALL wall_fluxes_e( wsvs, 0.0, 0.0, 1.0, 0.0, wall_e_y ) |
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| 111 | ! CALL wall_fluxes_e( vsus, 0.0, 1.0, 0.0, 0.0, wall_e_x ) |
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| 112 | ! CALL wall_fluxes_e( wsus, 0.0, 0.0, 0.0, 1.0, wall_e_x ) |
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| 113 | ! ENDIF |
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| 114 | |
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| 115 | ! |
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| 116 | !-- Calculate TKE production by shear |
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| 117 | DO i = nxl, nxr |
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| 118 | |
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| 119 | DO j = nys, nyn |
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| 120 | DO k = nzb_diff_s_outer(j,i), nzt |
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| 121 | |
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| 122 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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| 123 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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| 124 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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| 125 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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| 126 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
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| 127 | |
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| 128 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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| 129 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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| 130 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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| 131 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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| 132 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
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| 133 | |
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| 134 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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| 135 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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| 136 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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| 137 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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| 138 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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| 139 | |
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| 140 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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| 141 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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| 142 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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| 143 | |
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| 144 | IF ( def < 0.0 ) def = 0.0 |
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| 145 | |
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| 146 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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| 147 | |
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| 148 | ENDDO |
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| 149 | ENDDO |
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| 150 | |
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| 151 | IF ( prandtl_layer ) THEN |
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| 152 | |
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| 153 | ! |
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| 154 | !-- Position beneath wall |
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| 155 | !-- (2) - Will allways be executed. |
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| 156 | !-- 'bottom and wall: use u_0,v_0 and wall functions' |
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| 157 | DO j = nys, nyn |
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| 158 | |
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| 159 | IF ( ( wall_e_x(j,i) /= 0.0 ) .OR. ( wall_e_y(j,i) /= 0.0 ) ) & |
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| 160 | THEN |
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| 161 | |
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| 162 | k = nzb_diff_s_inner(j,i) - 1 |
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| 163 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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| 164 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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| 165 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
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| 166 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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| 167 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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| 168 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
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| 169 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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| 170 | |
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| 171 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
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| 172 | ! |
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| 173 | !-- Inconsistency removed: as the thermal stratification is |
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| 174 | !-- not taken into account for the evaluation of the wall |
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| 175 | !-- fluxes at vertical walls, the eddy viscosity km must not |
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| 176 | !-- be used for the evaluation of the velocity gradients dudy |
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| 177 | !-- and dwdy |
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| 178 | !-- Note: The validity of the new method has not yet been |
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| 179 | !-- shown, as so far no suitable data for a validation |
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| 180 | !-- has been available |
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| 181 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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| 182 | usvs, 1.0, 0.0, 0.0, 0.0 ) |
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| 183 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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| 184 | wsvs, 0.0, 0.0, 1.0, 0.0 ) |
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| 185 | km_neutral = kappa * ( usvs(k)**2 + wsvs(k)**2 )**0.25 * & |
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| 186 | 0.5 * dy |
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| 187 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
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| 188 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
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| 189 | ELSE |
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| 190 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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| 191 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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| 192 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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| 193 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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| 194 | ENDIF |
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| 195 | |
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| 196 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
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| 197 | ! |
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| 198 | !-- Inconsistency removed: as the thermal stratification is |
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| 199 | !-- not taken into account for the evaluation of the wall |
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| 200 | !-- fluxes at vertical walls, the eddy viscosity km must not |
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| 201 | !-- be used for the evaluation of the velocity gradients dvdx |
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| 202 | !-- and dwdx |
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| 203 | !-- Note: The validity of the new method has not yet been |
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| 204 | !-- shown, as so far no suitable data for a validation |
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| 205 | !-- has been available |
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| 206 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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| 207 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
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| 208 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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| 209 | wsus, 0.0, 0.0, 0.0, 1.0 ) |
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| 210 | km_neutral = kappa * ( vsus(k)**2 + wsus(k)**2 )**0.25 * & |
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| 211 | 0.5 * dx |
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| 212 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
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| 213 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
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| 214 | ELSE |
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| 215 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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| 216 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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| 217 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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| 218 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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| 219 | ENDIF |
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| 220 | |
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| 221 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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| 222 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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| 223 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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| 224 | |
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| 225 | IF ( def < 0.0 ) def = 0.0 |
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| 226 | |
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| 227 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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| 228 | |
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| 229 | |
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| 230 | ! |
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| 231 | !-- (3) - will be executed only, if there is at least one level |
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| 232 | !-- between (2) and (4), i.e. the topography must have a |
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| 233 | !-- minimum height of 2 dz. Wall fluxes for this case have |
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| 234 | !-- already been calculated for (2). |
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| 235 | !-- 'wall only: use wall functions' |
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| 236 | |
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| 237 | DO k = nzb_diff_s_inner(j,i), nzb_diff_s_outer(j,i)-2 |
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| 238 | |
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| 239 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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| 240 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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| 241 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
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| 242 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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| 243 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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| 244 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
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| 245 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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| 246 | |
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| 247 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
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| 248 | ! |
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| 249 | !-- Inconsistency removed: as the thermal stratification |
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| 250 | !-- is not taken into account for the evaluation of the |
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| 251 | !-- wall fluxes at vertical walls, the eddy viscosity km |
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| 252 | !-- must not be used for the evaluation of the velocity |
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| 253 | !-- gradients dudy and dwdy |
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| 254 | !-- Note: The validity of the new method has not yet |
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| 255 | !-- been shown, as so far no suitable data for a |
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| 256 | !-- validation has been available |
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| 257 | km_neutral = kappa * ( usvs(k)**2 + & |
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| 258 | wsvs(k)**2 )**0.25 * 0.5 * dy |
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| 259 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
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| 260 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
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| 261 | ELSE |
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| 262 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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| 263 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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| 264 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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| 265 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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| 266 | ENDIF |
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| 267 | |
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| 268 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
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| 269 | ! |
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| 270 | !-- Inconsistency removed: as the thermal stratification |
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| 271 | !-- is not taken into account for the evaluation of the |
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| 272 | !-- wall fluxes at vertical walls, the eddy viscosity km |
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| 273 | !-- must not be used for the evaluation of the velocity |
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| 274 | !-- gradients dvdx and dwdx |
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| 275 | !-- Note: The validity of the new method has not yet |
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| 276 | !-- been shown, as so far no suitable data for a |
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| 277 | !-- validation has been available |
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| 278 | km_neutral = kappa * ( vsus(k)**2 + & |
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| 279 | wsus(k)**2 )**0.25 * 0.5 * dx |
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| 280 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
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| 281 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
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| 282 | ELSE |
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| 283 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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| 284 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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| 285 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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| 286 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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| 287 | ENDIF |
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| 288 | |
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| 289 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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| 290 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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| 291 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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| 292 | |
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| 293 | IF ( def < 0.0 ) def = 0.0 |
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| 294 | |
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| 295 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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| 296 | |
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| 297 | ENDDO |
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| 298 | |
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| 299 | ENDIF |
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| 300 | |
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| 301 | ENDDO |
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| 302 | |
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| 303 | ! |
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| 304 | !-- (4) - will allways be executed. |
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| 305 | !-- 'special case: free atmosphere' (as for case (0)) |
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| 306 | DO j = nys, nyn |
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| 307 | |
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| 308 | IF ( ( wall_e_x(j,i) /= 0.0 ) .OR. ( wall_e_y(j,i) /= 0.0 ) ) & |
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| 309 | THEN |
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| 310 | |
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| 311 | k = nzb_diff_s_outer(j,i)-1 |
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| 312 | |
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| 313 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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| 314 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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| 315 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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| 316 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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| 317 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
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| 318 | |
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| 319 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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| 320 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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| 321 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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| 322 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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| 323 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
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| 324 | |
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| 325 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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| 326 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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| 327 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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| 328 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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| 329 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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| 330 | |
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| 331 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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| 332 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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| 333 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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| 334 | |
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| 335 | IF ( def < 0.0 ) def = 0.0 |
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| 336 | |
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| 337 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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| 338 | |
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| 339 | ENDIF |
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| 340 | |
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| 341 | ENDDO |
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| 342 | |
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| 343 | ! |
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| 344 | !-- Position without adjacent wall |
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| 345 | !-- (1) - will allways be executed. |
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| 346 | !-- 'bottom only: use u_0,v_0' |
|---|
| 347 | DO j = nys, nyn |
|---|
| 348 | |
|---|
| 349 | IF ( ( wall_e_x(j,i) == 0.0 ) .AND. ( wall_e_y(j,i) == 0.0 ) ) & |
|---|
| 350 | THEN |
|---|
| 351 | |
|---|
| 352 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 353 | |
|---|
| 354 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 355 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 356 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 357 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 358 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
|---|
| 359 | |
|---|
| 360 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 361 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 362 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 363 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 364 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
|---|
| 365 | |
|---|
| 366 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 367 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 368 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 369 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 370 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 371 | |
|---|
| 372 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
|---|
| 373 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
|---|
| 374 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 375 | |
|---|
| 376 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 377 | |
|---|
| 378 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 379 | |
|---|
| 380 | ENDIF |
|---|
| 381 | |
|---|
| 382 | ENDDO |
|---|
| 383 | |
|---|
| 384 | ELSEIF ( use_surface_fluxes ) THEN |
|---|
| 385 | |
|---|
| 386 | DO j = nys, nyn |
|---|
| 387 | |
|---|
| 388 | k = nzb_diff_s_outer(j,i)-1 |
|---|
| 389 | |
|---|
| 390 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 391 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 392 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 393 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 394 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
|---|
| 395 | |
|---|
| 396 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 397 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 398 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 399 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 400 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
|---|
| 401 | |
|---|
| 402 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 403 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 404 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 405 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 406 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 407 | |
|---|
| 408 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
|---|
| 409 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
|---|
| 410 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 411 | |
|---|
| 412 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 413 | |
|---|
| 414 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 415 | |
|---|
| 416 | ENDDO |
|---|
| 417 | |
|---|
| 418 | ENDIF |
|---|
| 419 | |
|---|
| 420 | ! |
|---|
| 421 | !-- Calculate TKE production by buoyancy |
|---|
| 422 | IF ( .NOT. humidity ) THEN |
|---|
| 423 | |
|---|
| 424 | IF ( use_reference ) THEN |
|---|
| 425 | |
|---|
| 426 | IF ( ocean ) THEN |
|---|
| 427 | ! |
|---|
| 428 | !-- So far in the ocean no special treatment of density flux in |
|---|
| 429 | !-- the bottom and top surface layer |
|---|
| 430 | DO j = nys, nyn |
|---|
| 431 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 432 | tend(k,j,i) = tend(k,j,i) + & |
|---|
| 433 | kh(k,j,i) * g / prho_reference * & |
|---|
| 434 | ( rho(k+1,j,i)-rho(k-1,j,i) ) * dd2zu(k) |
|---|
| 435 | ENDDO |
|---|
| 436 | ENDDO |
|---|
| 437 | |
|---|
| 438 | ELSE |
|---|
| 439 | |
|---|
| 440 | DO j = nys, nyn |
|---|
| 441 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
|---|
| 442 | tend(k,j,i) = tend(k,j,i) - & |
|---|
| 443 | kh(k,j,i) * g / pt_reference * & |
|---|
| 444 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
|---|
| 445 | ENDDO |
|---|
| 446 | |
|---|
| 447 | IF ( use_surface_fluxes ) THEN |
|---|
| 448 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 449 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * shf(j,i) |
|---|
| 450 | ENDIF |
|---|
| 451 | |
|---|
| 452 | IF ( use_top_fluxes ) THEN |
|---|
| 453 | k = nzt |
|---|
| 454 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * & |
|---|
| 455 | tswst(j,i) |
|---|
| 456 | ENDIF |
|---|
| 457 | ENDDO |
|---|
| 458 | |
|---|
| 459 | ENDIF |
|---|
| 460 | |
|---|
| 461 | ELSE |
|---|
| 462 | |
|---|
| 463 | IF ( ocean ) THEN |
|---|
| 464 | ! |
|---|
| 465 | !-- So far in the ocean no special treatment of density flux in |
|---|
| 466 | !-- the bottom and top surface layer |
|---|
| 467 | DO j = nys, nyn |
|---|
| 468 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 469 | tend(k,j,i) = tend(k,j,i) - & |
|---|
| 470 | kh(k,j,i) * g / rho(k,j,i) * & |
|---|
| 471 | ( rho(k+1,j,i)-rho(k-1,j,i) ) * dd2zu(k) |
|---|
| 472 | ENDDO |
|---|
| 473 | ENDDO |
|---|
| 474 | |
|---|
| 475 | ELSE |
|---|
| 476 | |
|---|
| 477 | DO j = nys, nyn |
|---|
| 478 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
|---|
| 479 | tend(k,j,i) = tend(k,j,i) - & |
|---|
| 480 | kh(k,j,i) * g / pt(k,j,i) * & |
|---|
| 481 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
|---|
| 482 | ENDDO |
|---|
| 483 | |
|---|
| 484 | IF ( use_surface_fluxes ) THEN |
|---|
| 485 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 486 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * shf(j,i) |
|---|
| 487 | ENDIF |
|---|
| 488 | |
|---|
| 489 | IF ( use_top_fluxes ) THEN |
|---|
| 490 | k = nzt |
|---|
| 491 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * tswst(j,i) |
|---|
| 492 | ENDIF |
|---|
| 493 | ENDDO |
|---|
| 494 | |
|---|
| 495 | ENDIF |
|---|
| 496 | |
|---|
| 497 | ENDIF |
|---|
| 498 | |
|---|
| 499 | ELSE |
|---|
| 500 | |
|---|
| 501 | DO j = nys, nyn |
|---|
| 502 | |
|---|
| 503 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
|---|
| 504 | |
|---|
| 505 | IF ( .NOT. cloud_physics ) THEN |
|---|
| 506 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 507 | k2 = 0.61 * pt(k,j,i) |
|---|
| 508 | ELSE |
|---|
| 509 | IF ( ql(k,j,i) == 0.0 ) THEN |
|---|
| 510 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 511 | k2 = 0.61 * pt(k,j,i) |
|---|
| 512 | ELSE |
|---|
| 513 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
|---|
| 514 | temp = theta * t_d_pt(k) |
|---|
| 515 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
|---|
| 516 | ( q(k,j,i) - ql(k,j,i) ) * & |
|---|
| 517 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
|---|
| 518 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
|---|
| 519 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
|---|
| 520 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
|---|
| 521 | ENDIF |
|---|
| 522 | ENDIF |
|---|
| 523 | |
|---|
| 524 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / vpt(k,j,i) * & |
|---|
| 525 | ( k1 * ( pt(k+1,j,i)-pt(k-1,j,i) ) + & |
|---|
| 526 | k2 * ( q(k+1,j,i) - q(k-1,j,i) ) & |
|---|
| 527 | ) * dd2zu(k) |
|---|
| 528 | ENDDO |
|---|
| 529 | |
|---|
| 530 | ENDDO |
|---|
| 531 | |
|---|
| 532 | IF ( use_surface_fluxes ) THEN |
|---|
| 533 | |
|---|
| 534 | DO j = nys, nyn |
|---|
| 535 | |
|---|
| 536 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 537 | |
|---|
| 538 | IF ( .NOT. cloud_physics ) THEN |
|---|
| 539 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 540 | k2 = 0.61 * pt(k,j,i) |
|---|
| 541 | ELSE |
|---|
| 542 | IF ( ql(k,j,i) == 0.0 ) THEN |
|---|
| 543 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 544 | k2 = 0.61 * pt(k,j,i) |
|---|
| 545 | ELSE |
|---|
| 546 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
|---|
| 547 | temp = theta * t_d_pt(k) |
|---|
| 548 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
|---|
| 549 | ( q(k,j,i) - ql(k,j,i) ) * & |
|---|
| 550 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
|---|
| 551 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
|---|
| 552 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
|---|
| 553 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
|---|
| 554 | ENDIF |
|---|
| 555 | ENDIF |
|---|
| 556 | |
|---|
| 557 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
|---|
| 558 | ( k1* shf(j,i) + k2 * qsws(j,i) ) |
|---|
| 559 | ENDDO |
|---|
| 560 | |
|---|
| 561 | ENDIF |
|---|
| 562 | |
|---|
| 563 | IF ( use_top_fluxes ) THEN |
|---|
| 564 | |
|---|
| 565 | DO j = nys, nyn |
|---|
| 566 | |
|---|
| 567 | k = nzt |
|---|
| 568 | |
|---|
| 569 | IF ( .NOT. cloud_physics ) THEN |
|---|
| 570 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 571 | k2 = 0.61 * pt(k,j,i) |
|---|
| 572 | ELSE |
|---|
| 573 | IF ( ql(k,j,i) == 0.0 ) THEN |
|---|
| 574 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 575 | k2 = 0.61 * pt(k,j,i) |
|---|
| 576 | ELSE |
|---|
| 577 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
|---|
| 578 | temp = theta * t_d_pt(k) |
|---|
| 579 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
|---|
| 580 | ( q(k,j,i) - ql(k,j,i) ) * & |
|---|
| 581 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
|---|
| 582 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
|---|
| 583 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
|---|
| 584 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
|---|
| 585 | ENDIF |
|---|
| 586 | ENDIF |
|---|
| 587 | |
|---|
| 588 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
|---|
| 589 | ( k1* tswst(j,i) + k2 * qswst(j,i) ) |
|---|
| 590 | ENDDO |
|---|
| 591 | |
|---|
| 592 | ENDIF |
|---|
| 593 | |
|---|
| 594 | ENDIF |
|---|
| 595 | |
|---|
| 596 | ENDDO |
|---|
| 597 | |
|---|
| 598 | END SUBROUTINE production_e |
|---|
| 599 | |
|---|
| 600 | |
|---|
| 601 | !------------------------------------------------------------------------------! |
|---|
| 602 | ! Call for grid point i,j |
|---|
| 603 | !------------------------------------------------------------------------------! |
|---|
| 604 | SUBROUTINE production_e_ij( i, j ) |
|---|
| 605 | |
|---|
| 606 | USE arrays_3d |
|---|
| 607 | USE cloud_parameters |
|---|
| 608 | USE control_parameters |
|---|
| 609 | USE grid_variables |
|---|
| 610 | USE indices |
|---|
| 611 | USE statistics |
|---|
| 612 | |
|---|
| 613 | IMPLICIT NONE |
|---|
| 614 | |
|---|
| 615 | INTEGER :: i, j, k |
|---|
| 616 | |
|---|
| 617 | REAL :: def, dudx, dudy, dudz, dvdx, dvdy, dvdz, dwdx, dwdy, dwdz, & |
|---|
| 618 | k1, k2, km_neutral, theta, temp |
|---|
| 619 | |
|---|
| 620 | REAL, DIMENSION(nzb:nzt+1) :: usvs, vsus, wsus, wsvs |
|---|
| 621 | |
|---|
| 622 | ! |
|---|
| 623 | !-- Calculate TKE production by shear |
|---|
| 624 | DO k = nzb_diff_s_outer(j,i), nzt |
|---|
| 625 | |
|---|
| 626 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 627 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 628 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 629 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 630 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
|---|
| 631 | |
|---|
| 632 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 633 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 634 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 635 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 636 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
|---|
| 637 | |
|---|
| 638 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 639 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 640 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 641 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 642 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 643 | |
|---|
| 644 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) & |
|---|
| 645 | + dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + dvdz**2 & |
|---|
| 646 | + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 647 | |
|---|
| 648 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 649 | |
|---|
| 650 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 651 | |
|---|
| 652 | ENDDO |
|---|
| 653 | |
|---|
| 654 | IF ( prandtl_layer ) THEN |
|---|
| 655 | |
|---|
| 656 | IF ( ( wall_e_x(j,i) /= 0.0 ) .OR. ( wall_e_y(j,i) /= 0.0 ) ) THEN |
|---|
| 657 | |
|---|
| 658 | ! |
|---|
| 659 | !-- Position beneath wall |
|---|
| 660 | !-- (2) - Will allways be executed. |
|---|
| 661 | !-- 'bottom and wall: use u_0,v_0 and wall functions' |
|---|
| 662 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 663 | |
|---|
| 664 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 665 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 666 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
|---|
| 667 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 668 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 669 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
|---|
| 670 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 671 | |
|---|
| 672 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
|---|
| 673 | ! |
|---|
| 674 | !-- Inconsistency removed: as the thermal stratification |
|---|
| 675 | !-- is not taken into account for the evaluation of the |
|---|
| 676 | !-- wall fluxes at vertical walls, the eddy viscosity km |
|---|
| 677 | !-- must not be used for the evaluation of the velocity |
|---|
| 678 | !-- gradients dudy and dwdy |
|---|
| 679 | !-- Note: The validity of the new method has not yet |
|---|
| 680 | !-- been shown, as so far no suitable data for a |
|---|
| 681 | !-- validation has been available |
|---|
| 682 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
|---|
| 683 | usvs, 1.0, 0.0, 0.0, 0.0 ) |
|---|
| 684 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
|---|
| 685 | wsvs, 0.0, 0.0, 1.0, 0.0 ) |
|---|
| 686 | km_neutral = kappa * ( usvs(k)**2 + wsvs(k)**2 )**0.25 * & |
|---|
| 687 | 0.5 * dy |
|---|
| 688 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
|---|
| 689 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
|---|
| 690 | ELSE |
|---|
| 691 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 692 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 693 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 694 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 695 | ENDIF |
|---|
| 696 | |
|---|
| 697 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
|---|
| 698 | ! |
|---|
| 699 | !-- Inconsistency removed: as the thermal stratification |
|---|
| 700 | !-- is not taken into account for the evaluation of the |
|---|
| 701 | !-- wall fluxes at vertical walls, the eddy viscosity km |
|---|
| 702 | !-- must not be used for the evaluation of the velocity |
|---|
| 703 | !-- gradients dvdx and dwdx |
|---|
| 704 | !-- Note: The validity of the new method has not yet |
|---|
| 705 | !-- been shown, as so far no suitable data for a |
|---|
| 706 | !-- validation has been available |
|---|
| 707 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
|---|
| 708 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
|---|
| 709 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
|---|
| 710 | wsus, 0.0, 0.0, 0.0, 1.0 ) |
|---|
| 711 | km_neutral = kappa * ( vsus(k)**2 + wsus(k)**2 )**0.25 * & |
|---|
| 712 | 0.5 * dx |
|---|
| 713 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
|---|
| 714 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
|---|
| 715 | ELSE |
|---|
| 716 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 717 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 718 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 719 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 720 | ENDIF |
|---|
| 721 | |
|---|
| 722 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
|---|
| 723 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
|---|
| 724 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 725 | |
|---|
| 726 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 727 | |
|---|
| 728 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 729 | |
|---|
| 730 | ! |
|---|
| 731 | !-- (3) - will be executed only, if there is at least one level |
|---|
| 732 | !-- between (2) and (4), i.e. the topography must have a |
|---|
| 733 | !-- minimum height of 2 dz. Wall fluxes for this case have |
|---|
| 734 | !-- already been calculated for (2). |
|---|
| 735 | !-- 'wall only: use wall functions' |
|---|
| 736 | DO k = nzb_diff_s_inner(j,i), nzb_diff_s_outer(j,i)-2 |
|---|
| 737 | |
|---|
| 738 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 739 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 740 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
|---|
| 741 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 742 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 743 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
|---|
| 744 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 745 | |
|---|
| 746 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
|---|
| 747 | ! |
|---|
| 748 | !-- Inconsistency removed: as the thermal stratification |
|---|
| 749 | !-- is not taken into account for the evaluation of the |
|---|
| 750 | !-- wall fluxes at vertical walls, the eddy viscosity km |
|---|
| 751 | !-- must not be used for the evaluation of the velocity |
|---|
| 752 | !-- gradients dudy and dwdy |
|---|
| 753 | !-- Note: The validity of the new method has not yet |
|---|
| 754 | !-- been shown, as so far no suitable data for a |
|---|
| 755 | !-- validation has been available |
|---|
| 756 | km_neutral = kappa * ( usvs(k)**2 + & |
|---|
| 757 | wsvs(k)**2 )**0.25 * 0.5 * dy |
|---|
| 758 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
|---|
| 759 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
|---|
| 760 | ELSE |
|---|
| 761 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 762 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 763 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 764 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 765 | ENDIF |
|---|
| 766 | |
|---|
| 767 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
|---|
| 768 | ! |
|---|
| 769 | !-- Inconsistency removed: as the thermal stratification |
|---|
| 770 | !-- is not taken into account for the evaluation of the |
|---|
| 771 | !-- wall fluxes at vertical walls, the eddy viscosity km |
|---|
| 772 | !-- must not be used for the evaluation of the velocity |
|---|
| 773 | !-- gradients dvdx and dwdx |
|---|
| 774 | !-- Note: The validity of the new method has not yet |
|---|
| 775 | !-- been shown, as so far no suitable data for a |
|---|
| 776 | !-- validation has been available |
|---|
| 777 | km_neutral = kappa * ( vsus(k)**2 + & |
|---|
| 778 | wsus(k)**2 )**0.25 * 0.5 * dx |
|---|
| 779 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
|---|
| 780 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
|---|
| 781 | ELSE |
|---|
| 782 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 783 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 784 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 785 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 786 | ENDIF |
|---|
| 787 | |
|---|
| 788 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
|---|
| 789 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
|---|
| 790 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 791 | |
|---|
| 792 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 793 | |
|---|
| 794 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 795 | |
|---|
| 796 | ENDDO |
|---|
| 797 | |
|---|
| 798 | ! |
|---|
| 799 | !-- (4) - will allways be executed. |
|---|
| 800 | !-- 'special case: free atmosphere' (as for case (0)) |
|---|
| 801 | k = nzb_diff_s_outer(j,i)-1 |
|---|
| 802 | |
|---|
| 803 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 804 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 805 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 806 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 807 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
|---|
| 808 | |
|---|
| 809 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 810 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 811 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 812 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 813 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
|---|
| 814 | |
|---|
| 815 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 816 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 817 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 818 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 819 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 820 | |
|---|
| 821 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
|---|
| 822 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
|---|
| 823 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 824 | |
|---|
| 825 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 826 | |
|---|
| 827 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 828 | |
|---|
| 829 | ELSE |
|---|
| 830 | |
|---|
| 831 | ! |
|---|
| 832 | !-- Position without adjacent wall |
|---|
| 833 | !-- (1) - will allways be executed. |
|---|
| 834 | !-- 'bottom only: use u_0,v_0' |
|---|
| 835 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 836 | |
|---|
| 837 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 838 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 839 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 840 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 841 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
|---|
| 842 | |
|---|
| 843 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 844 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 845 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 846 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 847 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
|---|
| 848 | |
|---|
| 849 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 850 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 851 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 852 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 853 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 854 | |
|---|
| 855 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) & |
|---|
| 856 | + dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + dvdz**2 & |
|---|
| 857 | + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 858 | |
|---|
| 859 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 860 | |
|---|
| 861 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 862 | |
|---|
| 863 | ENDIF |
|---|
| 864 | |
|---|
| 865 | ELSEIF ( use_surface_fluxes ) THEN |
|---|
| 866 | |
|---|
| 867 | k = nzb_diff_s_outer(j,i)-1 |
|---|
| 868 | |
|---|
| 869 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
|---|
| 870 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
|---|
| 871 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
|---|
| 872 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
|---|
| 873 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
|---|
| 874 | |
|---|
| 875 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
|---|
| 876 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
|---|
| 877 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
|---|
| 878 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
|---|
| 879 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
|---|
| 880 | |
|---|
| 881 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
|---|
| 882 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
|---|
| 883 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
|---|
| 884 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
|---|
| 885 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
|---|
| 886 | |
|---|
| 887 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
|---|
| 888 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
|---|
| 889 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
|---|
| 890 | |
|---|
| 891 | IF ( def < 0.0 ) def = 0.0 |
|---|
| 892 | |
|---|
| 893 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
|---|
| 894 | |
|---|
| 895 | ENDIF |
|---|
| 896 | |
|---|
| 897 | ! |
|---|
| 898 | !-- Calculate TKE production by buoyancy |
|---|
| 899 | IF ( .NOT. humidity ) THEN |
|---|
| 900 | |
|---|
| 901 | IF ( use_reference ) THEN |
|---|
| 902 | |
|---|
| 903 | IF ( ocean ) THEN |
|---|
| 904 | ! |
|---|
| 905 | !-- So far in the ocean no special treatment of density flux in the |
|---|
| 906 | !-- bottom and top surface layer |
|---|
| 907 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 908 | tend(k,j,i) = tend(k,j,i) + kh(k,j,i) * g / prho_reference * & |
|---|
| 909 | ( rho(k+1,j,i) - rho(k-1,j,i) ) * dd2zu(k) |
|---|
| 910 | ENDDO |
|---|
| 911 | |
|---|
| 912 | ELSE |
|---|
| 913 | |
|---|
| 914 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
|---|
| 915 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / pt_reference * & |
|---|
| 916 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
|---|
| 917 | ENDDO |
|---|
| 918 | |
|---|
| 919 | IF ( use_surface_fluxes ) THEN |
|---|
| 920 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 921 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * shf(j,i) |
|---|
| 922 | ENDIF |
|---|
| 923 | |
|---|
| 924 | IF ( use_top_fluxes ) THEN |
|---|
| 925 | k = nzt |
|---|
| 926 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * tswst(j,i) |
|---|
| 927 | ENDIF |
|---|
| 928 | |
|---|
| 929 | ENDIF |
|---|
| 930 | |
|---|
| 931 | ELSE |
|---|
| 932 | |
|---|
| 933 | IF ( ocean ) THEN |
|---|
| 934 | ! |
|---|
| 935 | !-- So far in the ocean no special treatment of density flux in the |
|---|
| 936 | !-- bottom and top surface layer |
|---|
| 937 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 938 | tend(k,j,i) = tend(k,j,i) + kh(k,j,i) * g / rho(k,j,i) * & |
|---|
| 939 | ( rho(k+1,j,i) - rho(k-1,j,i) ) * dd2zu(k) |
|---|
| 940 | ENDDO |
|---|
| 941 | |
|---|
| 942 | ELSE |
|---|
| 943 | |
|---|
| 944 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
|---|
| 945 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / pt(k,j,i) * & |
|---|
| 946 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
|---|
| 947 | ENDDO |
|---|
| 948 | |
|---|
| 949 | IF ( use_surface_fluxes ) THEN |
|---|
| 950 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 951 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * shf(j,i) |
|---|
| 952 | ENDIF |
|---|
| 953 | |
|---|
| 954 | IF ( use_top_fluxes ) THEN |
|---|
| 955 | k = nzt |
|---|
| 956 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * tswst(j,i) |
|---|
| 957 | ENDIF |
|---|
| 958 | |
|---|
| 959 | ENDIF |
|---|
| 960 | |
|---|
| 961 | ENDIF |
|---|
| 962 | |
|---|
| 963 | ELSE |
|---|
| 964 | |
|---|
| 965 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
|---|
| 966 | |
|---|
| 967 | IF ( .NOT. cloud_physics ) THEN |
|---|
| 968 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 969 | k2 = 0.61 * pt(k,j,i) |
|---|
| 970 | ELSE |
|---|
| 971 | IF ( ql(k,j,i) == 0.0 ) THEN |
|---|
| 972 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 973 | k2 = 0.61 * pt(k,j,i) |
|---|
| 974 | ELSE |
|---|
| 975 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
|---|
| 976 | temp = theta * t_d_pt(k) |
|---|
| 977 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
|---|
| 978 | ( q(k,j,i) - ql(k,j,i) ) * & |
|---|
| 979 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
|---|
| 980 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
|---|
| 981 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
|---|
| 982 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
|---|
| 983 | ENDIF |
|---|
| 984 | ENDIF |
|---|
| 985 | |
|---|
| 986 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / vpt(k,j,i) * & |
|---|
| 987 | ( k1 * ( pt(k+1,j,i)-pt(k-1,j,i) ) + & |
|---|
| 988 | k2 * ( q(k+1,j,i) - q(k-1,j,i) ) & |
|---|
| 989 | ) * dd2zu(k) |
|---|
| 990 | ENDDO |
|---|
| 991 | |
|---|
| 992 | IF ( use_surface_fluxes ) THEN |
|---|
| 993 | k = nzb_diff_s_inner(j,i)-1 |
|---|
| 994 | |
|---|
| 995 | IF ( .NOT. cloud_physics ) THEN |
|---|
| 996 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 997 | k2 = 0.61 * pt(k,j,i) |
|---|
| 998 | ELSE |
|---|
| 999 | IF ( ql(k,j,i) == 0.0 ) THEN |
|---|
| 1000 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 1001 | k2 = 0.61 * pt(k,j,i) |
|---|
| 1002 | ELSE |
|---|
| 1003 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
|---|
| 1004 | temp = theta * t_d_pt(k) |
|---|
| 1005 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
|---|
| 1006 | ( q(k,j,i) - ql(k,j,i) ) * & |
|---|
| 1007 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
|---|
| 1008 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
|---|
| 1009 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
|---|
| 1010 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
|---|
| 1011 | ENDIF |
|---|
| 1012 | ENDIF |
|---|
| 1013 | |
|---|
| 1014 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
|---|
| 1015 | ( k1* shf(j,i) + k2 * qsws(j,i) ) |
|---|
| 1016 | ENDIF |
|---|
| 1017 | |
|---|
| 1018 | IF ( use_top_fluxes ) THEN |
|---|
| 1019 | k = nzt |
|---|
| 1020 | |
|---|
| 1021 | IF ( .NOT. cloud_physics ) THEN |
|---|
| 1022 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 1023 | k2 = 0.61 * pt(k,j,i) |
|---|
| 1024 | ELSE |
|---|
| 1025 | IF ( ql(k,j,i) == 0.0 ) THEN |
|---|
| 1026 | k1 = 1.0 + 0.61 * q(k,j,i) |
|---|
| 1027 | k2 = 0.61 * pt(k,j,i) |
|---|
| 1028 | ELSE |
|---|
| 1029 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
|---|
| 1030 | temp = theta * t_d_pt(k) |
|---|
| 1031 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
|---|
| 1032 | ( q(k,j,i) - ql(k,j,i) ) * & |
|---|
| 1033 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
|---|
| 1034 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
|---|
| 1035 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
|---|
| 1036 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
|---|
| 1037 | ENDIF |
|---|
| 1038 | ENDIF |
|---|
| 1039 | |
|---|
| 1040 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
|---|
| 1041 | ( k1* tswst(j,i) + k2 * qswst(j,i) ) |
|---|
| 1042 | ENDIF |
|---|
| 1043 | |
|---|
| 1044 | ENDIF |
|---|
| 1045 | |
|---|
| 1046 | END SUBROUTINE production_e_ij |
|---|
| 1047 | |
|---|
| 1048 | |
|---|
| 1049 | SUBROUTINE production_e_init |
|---|
| 1050 | |
|---|
| 1051 | USE arrays_3d |
|---|
| 1052 | USE control_parameters |
|---|
| 1053 | USE grid_variables |
|---|
| 1054 | USE indices |
|---|
| 1055 | |
|---|
| 1056 | IMPLICIT NONE |
|---|
| 1057 | |
|---|
| 1058 | INTEGER :: i, j, ku, kv |
|---|
| 1059 | |
|---|
| 1060 | IF ( prandtl_layer ) THEN |
|---|
| 1061 | |
|---|
| 1062 | IF ( first_call ) THEN |
|---|
| 1063 | ALLOCATE( u_0(nys-1:nyn+1,nxl-1:nxr+1), & |
|---|
| 1064 | v_0(nys-1:nyn+1,nxl-1:nxr+1) ) |
|---|
| 1065 | first_call = .FALSE. |
|---|
| 1066 | ENDIF |
|---|
| 1067 | |
|---|
| 1068 | ! |
|---|
| 1069 | !-- Calculate a virtual velocity at the surface in a way that the |
|---|
| 1070 | !-- vertical velocity gradient at k = 1 (u(k+1)-u_0) matches the |
|---|
| 1071 | !-- Prandtl law (-w'u'/km). This gradient is used in the TKE shear |
|---|
| 1072 | !-- production term at k=1 (see production_e_ij). |
|---|
| 1073 | !-- The velocity gradient has to be limited in case of too small km |
|---|
| 1074 | !-- (otherwise the timestep may be significantly reduced by large |
|---|
| 1075 | !-- surface winds). |
|---|
| 1076 | !-- Upper bounds are nxr+1 and nyn+1 because otherwise these values are |
|---|
| 1077 | !-- not available in case of non-cyclic boundary conditions. |
|---|
| 1078 | !-- WARNING: the exact analytical solution would require the determination |
|---|
| 1079 | !-- of the eddy diffusivity by km = u* * kappa * zp / phi_m. |
|---|
| 1080 | !$OMP PARALLEL DO PRIVATE( ku, kv ) |
|---|
| 1081 | DO i = nxl, nxr+1 |
|---|
| 1082 | DO j = nys, nyn+1 |
|---|
| 1083 | |
|---|
| 1084 | ku = nzb_u_inner(j,i)+1 |
|---|
| 1085 | kv = nzb_v_inner(j,i)+1 |
|---|
| 1086 | |
|---|
| 1087 | u_0(j,i) = u(ku+1,j,i) + usws(j,i) * ( zu(ku+1) - zu(ku-1) ) / & |
|---|
| 1088 | ( 0.5 * ( km(ku,j,i) + km(ku,j,i-1) ) + & |
|---|
| 1089 | 1.0E-20 ) |
|---|
| 1090 | ! ( us(j,i) * kappa * zu(1) ) |
|---|
| 1091 | v_0(j,i) = v(kv+1,j,i) + vsws(j,i) * ( zu(kv+1) - zu(kv-1) ) / & |
|---|
| 1092 | ( 0.5 * ( km(kv,j,i) + km(kv,j-1,i) ) + & |
|---|
| 1093 | 1.0E-20 ) |
|---|
| 1094 | ! ( us(j,i) * kappa * zu(1) ) |
|---|
| 1095 | |
|---|
| 1096 | IF ( ABS( u(ku+1,j,i) - u_0(j,i) ) > & |
|---|
| 1097 | ABS( u(ku+1,j,i) - u(ku-1,j,i) ) ) u_0(j,i) = u(ku-1,j,i) |
|---|
| 1098 | IF ( ABS( v(kv+1,j,i) - v_0(j,i) ) > & |
|---|
| 1099 | ABS( v(kv+1,j,i) - v(kv-1,j,i) ) ) v_0(j,i) = v(kv-1,j,i) |
|---|
| 1100 | |
|---|
| 1101 | ENDDO |
|---|
| 1102 | ENDDO |
|---|
| 1103 | |
|---|
| 1104 | CALL exchange_horiz_2d( u_0 ) |
|---|
| 1105 | CALL exchange_horiz_2d( v_0 ) |
|---|
| 1106 | |
|---|
| 1107 | ENDIF |
|---|
| 1108 | |
|---|
| 1109 | END SUBROUTINE production_e_init |
|---|
| 1110 | |
|---|
| 1111 | END MODULE production_e_mod |
|---|
