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 | ! Bugfix: wrong sign in buoyancy production of ocean part in case of not using |
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7 | ! the reference density (only in 3D routine production_e) |
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8 | ! Bugfix to avoid zero division by km_neutral |
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9 | ! |
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10 | ! Former revisions: |
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11 | ! ----------------- |
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12 | ! $Id: production_e.f90 388 2009-09-23 09:40:33Z raasch $ |
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13 | ! |
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14 | ! 208 2008-10-20 06:02:59Z raasch |
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15 | ! Bugfix concerning the calculation of velocity gradients at vertical walls |
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16 | ! in case of diabatic conditions |
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17 | ! |
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18 | ! 187 2008-08-06 16:25:09Z letzel |
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19 | ! Change: add 'minus' sign to fluxes obtained from subroutine wall_fluxes_e for |
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20 | ! consistency with subroutine wall_fluxes |
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21 | ! |
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22 | ! 124 2007-10-19 15:47:46Z raasch |
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23 | ! Bugfix: calculation of density flux in the ocean now starts from nzb+1 |
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24 | ! |
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25 | ! 108 2007-08-24 15:10:38Z letzel |
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26 | ! Bugfix: wrong sign removed from the buoyancy production term in the case |
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27 | ! use_reference = .T., |
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28 | ! u_0 and v_0 are calculated for nxr+1, nyn+1 also (otherwise these values are |
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29 | ! not available in case of non-cyclic boundary conditions) |
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30 | ! Bugfix for ocean density flux at bottom |
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31 | ! |
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32 | ! 97 2007-06-21 08:23:15Z raasch |
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33 | ! Energy production by density flux (in ocean) added |
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34 | ! use_pt_reference renamed use_reference |
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35 | ! |
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36 | ! 75 2007-03-22 09:54:05Z raasch |
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37 | ! Wall functions now include diabatic conditions, call of routine wall_fluxes_e, |
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38 | ! reference temperature pt_reference can be used in buoyancy term, |
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39 | ! moisture renamed humidity |
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40 | ! |
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41 | ! 37 2007-03-01 08:33:54Z raasch |
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42 | ! Calculation extended for gridpoint nzt, extended for given temperature / |
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43 | ! humidity fluxes at the top, wall-part is now executed in case that a |
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44 | ! Prandtl-layer is switched on (instead of surfaces fluxes switched on) |
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45 | ! |
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46 | ! RCS Log replace by Id keyword, revision history cleaned up |
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47 | ! |
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48 | ! Revision 1.21 2006/04/26 12:45:35 raasch |
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49 | ! OpenMP parallelization of production_e_init |
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50 | ! |
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51 | ! Revision 1.1 1997/09/19 07:45:35 raasch |
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52 | ! Initial revision |
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53 | ! |
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54 | ! |
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55 | ! Description: |
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56 | ! ------------ |
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57 | ! Production terms (shear + buoyancy) of the TKE |
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58 | ! WARNING: the case with prandtl_layer = F and use_surface_fluxes = T is |
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59 | ! not considered well! |
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60 | !------------------------------------------------------------------------------! |
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61 | |
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62 | USE wall_fluxes_mod |
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63 | |
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64 | PRIVATE |
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65 | PUBLIC production_e, production_e_init |
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66 | |
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67 | LOGICAL, SAVE :: first_call = .TRUE. |
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68 | |
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69 | REAL, DIMENSION(:,:), ALLOCATABLE, SAVE :: u_0, v_0 |
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70 | |
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71 | INTERFACE production_e |
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72 | MODULE PROCEDURE production_e |
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73 | MODULE PROCEDURE production_e_ij |
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74 | END INTERFACE production_e |
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75 | |
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76 | INTERFACE production_e_init |
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77 | MODULE PROCEDURE production_e_init |
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78 | END INTERFACE production_e_init |
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79 | |
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80 | CONTAINS |
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81 | |
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82 | |
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83 | !------------------------------------------------------------------------------! |
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84 | ! Call for all grid points |
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85 | !------------------------------------------------------------------------------! |
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86 | SUBROUTINE production_e |
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87 | |
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88 | USE arrays_3d |
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89 | USE cloud_parameters |
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90 | USE control_parameters |
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91 | USE grid_variables |
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92 | USE indices |
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93 | USE statistics |
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94 | |
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95 | IMPLICIT NONE |
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96 | |
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97 | INTEGER :: i, j, k |
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98 | |
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99 | REAL :: def, dudx, dudy, dudz, dvdx, dvdy, dvdz, dwdx, dwdy, dwdz, & |
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100 | k1, k2, km_neutral, theta, temp |
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101 | |
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102 | ! REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs, vsus, wsus, wsvs |
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103 | REAL, DIMENSION(nzb:nzt+1) :: usvs, vsus, wsus, wsvs |
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104 | |
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105 | ! |
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106 | !-- First calculate horizontal momentum flux u'v', w'v', v'u', w'u' at |
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107 | !-- vertical walls, if neccessary |
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108 | !-- So far, results are slightly different from the ij-Version. |
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109 | !-- Therefore, ij-Version is called further below within the ij-loops. |
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110 | ! IF ( topography /= 'flat' ) THEN |
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111 | ! CALL wall_fluxes_e( usvs, 1.0, 0.0, 0.0, 0.0, wall_e_y ) |
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112 | ! CALL wall_fluxes_e( wsvs, 0.0, 0.0, 1.0, 0.0, wall_e_y ) |
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113 | ! CALL wall_fluxes_e( vsus, 0.0, 1.0, 0.0, 0.0, wall_e_x ) |
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114 | ! CALL wall_fluxes_e( wsus, 0.0, 0.0, 0.0, 1.0, wall_e_x ) |
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115 | ! ENDIF |
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116 | |
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117 | ! |
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118 | !-- Calculate TKE production by shear |
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119 | DO i = nxl, nxr |
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120 | |
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121 | DO j = nys, nyn |
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122 | DO k = nzb_diff_s_outer(j,i), nzt |
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123 | |
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124 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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125 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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126 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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127 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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128 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
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129 | |
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130 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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131 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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132 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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133 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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134 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
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135 | |
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136 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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137 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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138 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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139 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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140 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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141 | |
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142 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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143 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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144 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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145 | |
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146 | IF ( def < 0.0 ) def = 0.0 |
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147 | |
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148 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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149 | |
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150 | ENDDO |
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151 | ENDDO |
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152 | |
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153 | IF ( prandtl_layer ) THEN |
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154 | |
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155 | ! |
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156 | !-- Position beneath wall |
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157 | !-- (2) - Will allways be executed. |
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158 | !-- 'bottom and wall: use u_0,v_0 and wall functions' |
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159 | DO j = nys, nyn |
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160 | |
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161 | IF ( ( wall_e_x(j,i) /= 0.0 ) .OR. ( wall_e_y(j,i) /= 0.0 ) ) & |
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162 | THEN |
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163 | |
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164 | k = nzb_diff_s_inner(j,i) - 1 |
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165 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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166 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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167 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
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168 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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169 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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170 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
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171 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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172 | |
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173 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
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174 | ! |
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175 | !-- Inconsistency removed: as the thermal stratification is |
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176 | !-- not taken into account for the evaluation of the wall |
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177 | !-- fluxes at vertical walls, the eddy viscosity km must not |
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178 | !-- be used for the evaluation of the velocity gradients dudy |
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179 | !-- and dwdy |
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180 | !-- Note: The validity of the new method has not yet been |
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181 | !-- shown, as so far no suitable data for a validation |
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182 | !-- has been available |
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183 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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184 | usvs, 1.0, 0.0, 0.0, 0.0 ) |
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185 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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186 | wsvs, 0.0, 0.0, 1.0, 0.0 ) |
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187 | km_neutral = kappa * ( usvs(k)**2 + wsvs(k)**2 )**0.25 * & |
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188 | 0.5 * dy |
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189 | IF ( km_neutral > 0.0 ) THEN |
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190 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
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191 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
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192 | ELSE |
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193 | dudy = 0.0 |
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194 | dwdy = 0.0 |
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195 | ENDIF |
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196 | ELSE |
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197 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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198 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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199 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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200 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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201 | ENDIF |
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202 | |
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203 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
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204 | ! |
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205 | !-- Inconsistency removed: as the thermal stratification is |
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206 | !-- not taken into account for the evaluation of the wall |
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207 | !-- fluxes at vertical walls, the eddy viscosity km must not |
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208 | !-- be used for the evaluation of the velocity gradients dvdx |
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209 | !-- and dwdx |
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210 | !-- Note: The validity of the new method has not yet been |
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211 | !-- shown, as so far no suitable data for a validation |
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212 | !-- has been available |
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213 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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214 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
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215 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
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216 | wsus, 0.0, 0.0, 0.0, 1.0 ) |
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217 | km_neutral = kappa * ( vsus(k)**2 + wsus(k)**2 )**0.25 * & |
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218 | 0.5 * dx |
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219 | IF ( km_neutral > 0.0 ) THEN |
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220 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
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221 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
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222 | ELSE |
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223 | dvdx = 0.0 |
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224 | dwdx = 0.0 |
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225 | ENDIF |
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226 | ELSE |
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227 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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228 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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229 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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230 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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231 | ENDIF |
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232 | |
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233 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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234 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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235 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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236 | |
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237 | IF ( def < 0.0 ) def = 0.0 |
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238 | |
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239 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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240 | |
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241 | |
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242 | ! |
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243 | !-- (3) - will be executed only, if there is at least one level |
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244 | !-- between (2) and (4), i.e. the topography must have a |
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245 | !-- minimum height of 2 dz. Wall fluxes for this case have |
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246 | !-- already been calculated for (2). |
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247 | !-- 'wall only: use wall functions' |
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248 | |
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249 | DO k = nzb_diff_s_inner(j,i), nzb_diff_s_outer(j,i)-2 |
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250 | |
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251 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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252 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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253 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
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254 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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255 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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256 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
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257 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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258 | |
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259 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
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260 | ! |
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261 | !-- Inconsistency removed: as the thermal stratification |
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262 | !-- is not taken into account for the evaluation of the |
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263 | !-- wall fluxes at vertical walls, the eddy viscosity km |
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264 | !-- must not be used for the evaluation of the velocity |
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265 | !-- gradients dudy and dwdy |
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266 | !-- Note: The validity of the new method has not yet |
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267 | !-- been shown, as so far no suitable data for a |
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268 | !-- validation has been available |
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269 | km_neutral = kappa * ( usvs(k)**2 + & |
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270 | wsvs(k)**2 )**0.25 * 0.5 * dy |
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271 | IF ( km_neutral > 0.0 ) THEN |
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272 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
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273 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
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274 | ELSE |
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275 | dudy = 0.0 |
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276 | dwdy = 0.0 |
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277 | ENDIF |
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278 | ELSE |
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279 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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280 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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281 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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282 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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283 | ENDIF |
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284 | |
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285 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
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286 | ! |
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287 | !-- Inconsistency removed: as the thermal stratification |
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288 | !-- is not taken into account for the evaluation of the |
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289 | !-- wall fluxes at vertical walls, the eddy viscosity km |
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290 | !-- must not be used for the evaluation of the velocity |
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291 | !-- gradients dvdx and dwdx |
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292 | !-- Note: The validity of the new method has not yet |
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293 | !-- been shown, as so far no suitable data for a |
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294 | !-- validation has been available |
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295 | km_neutral = kappa * ( vsus(k)**2 + & |
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296 | wsus(k)**2 )**0.25 * 0.5 * dx |
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297 | IF ( km_neutral > 0.0 ) THEN |
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298 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
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299 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
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300 | ELSE |
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301 | dvdx = 0.0 |
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302 | dwdx = 0.0 |
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303 | ENDIF |
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304 | ELSE |
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305 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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306 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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307 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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308 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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309 | ENDIF |
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310 | |
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311 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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312 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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313 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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314 | |
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315 | IF ( def < 0.0 ) def = 0.0 |
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316 | |
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317 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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318 | |
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319 | ENDDO |
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320 | |
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321 | ENDIF |
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322 | |
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323 | ENDDO |
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324 | |
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325 | ! |
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326 | !-- (4) - will allways be executed. |
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327 | !-- 'special case: free atmosphere' (as for case (0)) |
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328 | DO j = nys, nyn |
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329 | |
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330 | IF ( ( wall_e_x(j,i) /= 0.0 ) .OR. ( wall_e_y(j,i) /= 0.0 ) ) & |
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331 | THEN |
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332 | |
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333 | k = nzb_diff_s_outer(j,i)-1 |
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334 | |
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335 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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336 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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337 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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338 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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339 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
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340 | |
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341 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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342 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
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343 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
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344 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
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345 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
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346 | |
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347 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
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348 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
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349 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
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350 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
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351 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
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352 | |
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353 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
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354 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
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355 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
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356 | |
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357 | IF ( def < 0.0 ) def = 0.0 |
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358 | |
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359 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
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360 | |
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361 | ENDIF |
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362 | |
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363 | ENDDO |
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364 | |
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365 | ! |
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366 | !-- Position without adjacent wall |
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367 | !-- (1) - will allways be executed. |
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368 | !-- 'bottom only: use u_0,v_0' |
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369 | DO j = nys, nyn |
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370 | |
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371 | IF ( ( wall_e_x(j,i) == 0.0 ) .AND. ( wall_e_y(j,i) == 0.0 ) ) & |
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372 | THEN |
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373 | |
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374 | k = nzb_diff_s_inner(j,i)-1 |
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375 | |
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376 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
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377 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
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378 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
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379 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
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380 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
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381 | |
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382 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
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383 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
384 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
385 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
386 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
---|
387 | |
---|
388 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
389 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
390 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
391 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
392 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
393 | |
---|
394 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
---|
395 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
---|
396 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
397 | |
---|
398 | IF ( def < 0.0 ) def = 0.0 |
---|
399 | |
---|
400 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
401 | |
---|
402 | ENDIF |
---|
403 | |
---|
404 | ENDDO |
---|
405 | |
---|
406 | ELSEIF ( use_surface_fluxes ) THEN |
---|
407 | |
---|
408 | DO j = nys, nyn |
---|
409 | |
---|
410 | k = nzb_diff_s_outer(j,i)-1 |
---|
411 | |
---|
412 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
---|
413 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
---|
414 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
---|
415 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
---|
416 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
---|
417 | |
---|
418 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
---|
419 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
420 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
421 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
422 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
---|
423 | |
---|
424 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
425 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
426 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
427 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
428 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
429 | |
---|
430 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
---|
431 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
---|
432 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
433 | |
---|
434 | IF ( def < 0.0 ) def = 0.0 |
---|
435 | |
---|
436 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
437 | |
---|
438 | ENDDO |
---|
439 | |
---|
440 | ENDIF |
---|
441 | |
---|
442 | ! |
---|
443 | !-- Calculate TKE production by buoyancy |
---|
444 | IF ( .NOT. humidity ) THEN |
---|
445 | |
---|
446 | IF ( use_reference ) THEN |
---|
447 | |
---|
448 | IF ( ocean ) THEN |
---|
449 | ! |
---|
450 | !-- So far in the ocean no special treatment of density flux in |
---|
451 | !-- the bottom and top surface layer |
---|
452 | DO j = nys, nyn |
---|
453 | DO k = nzb_s_inner(j,i)+1, nzt |
---|
454 | tend(k,j,i) = tend(k,j,i) + & |
---|
455 | kh(k,j,i) * g / rho_reference * & |
---|
456 | ( rho(k+1,j,i)-rho(k-1,j,i) ) * dd2zu(k) |
---|
457 | ENDDO |
---|
458 | ENDDO |
---|
459 | |
---|
460 | ELSE |
---|
461 | |
---|
462 | DO j = nys, nyn |
---|
463 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
---|
464 | tend(k,j,i) = tend(k,j,i) - & |
---|
465 | kh(k,j,i) * g / pt_reference * & |
---|
466 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
---|
467 | ENDDO |
---|
468 | |
---|
469 | IF ( use_surface_fluxes ) THEN |
---|
470 | k = nzb_diff_s_inner(j,i)-1 |
---|
471 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * shf(j,i) |
---|
472 | ENDIF |
---|
473 | |
---|
474 | IF ( use_top_fluxes ) THEN |
---|
475 | k = nzt |
---|
476 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * & |
---|
477 | tswst(j,i) |
---|
478 | ENDIF |
---|
479 | ENDDO |
---|
480 | |
---|
481 | ENDIF |
---|
482 | |
---|
483 | ELSE |
---|
484 | |
---|
485 | IF ( ocean ) THEN |
---|
486 | ! |
---|
487 | !-- So far in the ocean no special treatment of density flux in |
---|
488 | !-- the bottom and top surface layer |
---|
489 | DO j = nys, nyn |
---|
490 | DO k = nzb_s_inner(j,i)+1, nzt |
---|
491 | tend(k,j,i) = tend(k,j,i) + & |
---|
492 | kh(k,j,i) * g / rho(k,j,i) * & |
---|
493 | ( rho(k+1,j,i)-rho(k-1,j,i) ) * dd2zu(k) |
---|
494 | ENDDO |
---|
495 | ENDDO |
---|
496 | |
---|
497 | ELSE |
---|
498 | |
---|
499 | DO j = nys, nyn |
---|
500 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
---|
501 | tend(k,j,i) = tend(k,j,i) - & |
---|
502 | kh(k,j,i) * g / pt(k,j,i) * & |
---|
503 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
---|
504 | ENDDO |
---|
505 | |
---|
506 | IF ( use_surface_fluxes ) THEN |
---|
507 | k = nzb_diff_s_inner(j,i)-1 |
---|
508 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * shf(j,i) |
---|
509 | ENDIF |
---|
510 | |
---|
511 | IF ( use_top_fluxes ) THEN |
---|
512 | k = nzt |
---|
513 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * tswst(j,i) |
---|
514 | ENDIF |
---|
515 | ENDDO |
---|
516 | |
---|
517 | ENDIF |
---|
518 | |
---|
519 | ENDIF |
---|
520 | |
---|
521 | ELSE |
---|
522 | |
---|
523 | DO j = nys, nyn |
---|
524 | |
---|
525 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
---|
526 | |
---|
527 | IF ( .NOT. cloud_physics ) THEN |
---|
528 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
529 | k2 = 0.61 * pt(k,j,i) |
---|
530 | ELSE |
---|
531 | IF ( ql(k,j,i) == 0.0 ) THEN |
---|
532 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
533 | k2 = 0.61 * pt(k,j,i) |
---|
534 | ELSE |
---|
535 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
---|
536 | temp = theta * t_d_pt(k) |
---|
537 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
---|
538 | ( q(k,j,i) - ql(k,j,i) ) * & |
---|
539 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
---|
540 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
---|
541 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
---|
542 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
---|
543 | ENDIF |
---|
544 | ENDIF |
---|
545 | |
---|
546 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / vpt(k,j,i) * & |
---|
547 | ( k1 * ( pt(k+1,j,i)-pt(k-1,j,i) ) + & |
---|
548 | k2 * ( q(k+1,j,i) - q(k-1,j,i) ) & |
---|
549 | ) * dd2zu(k) |
---|
550 | ENDDO |
---|
551 | |
---|
552 | ENDDO |
---|
553 | |
---|
554 | IF ( use_surface_fluxes ) THEN |
---|
555 | |
---|
556 | DO j = nys, nyn |
---|
557 | |
---|
558 | k = nzb_diff_s_inner(j,i)-1 |
---|
559 | |
---|
560 | IF ( .NOT. cloud_physics ) THEN |
---|
561 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
562 | k2 = 0.61 * pt(k,j,i) |
---|
563 | ELSE |
---|
564 | IF ( ql(k,j,i) == 0.0 ) THEN |
---|
565 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
566 | k2 = 0.61 * pt(k,j,i) |
---|
567 | ELSE |
---|
568 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
---|
569 | temp = theta * t_d_pt(k) |
---|
570 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
---|
571 | ( q(k,j,i) - ql(k,j,i) ) * & |
---|
572 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
---|
573 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
---|
574 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
---|
575 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
---|
576 | ENDIF |
---|
577 | ENDIF |
---|
578 | |
---|
579 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
---|
580 | ( k1* shf(j,i) + k2 * qsws(j,i) ) |
---|
581 | ENDDO |
---|
582 | |
---|
583 | ENDIF |
---|
584 | |
---|
585 | IF ( use_top_fluxes ) THEN |
---|
586 | |
---|
587 | DO j = nys, nyn |
---|
588 | |
---|
589 | k = nzt |
---|
590 | |
---|
591 | IF ( .NOT. cloud_physics ) THEN |
---|
592 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
593 | k2 = 0.61 * pt(k,j,i) |
---|
594 | ELSE |
---|
595 | IF ( ql(k,j,i) == 0.0 ) THEN |
---|
596 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
597 | k2 = 0.61 * pt(k,j,i) |
---|
598 | ELSE |
---|
599 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
---|
600 | temp = theta * t_d_pt(k) |
---|
601 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
---|
602 | ( q(k,j,i) - ql(k,j,i) ) * & |
---|
603 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
---|
604 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
---|
605 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
---|
606 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
---|
607 | ENDIF |
---|
608 | ENDIF |
---|
609 | |
---|
610 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
---|
611 | ( k1* tswst(j,i) + k2 * qswst(j,i) ) |
---|
612 | ENDDO |
---|
613 | |
---|
614 | ENDIF |
---|
615 | |
---|
616 | ENDIF |
---|
617 | |
---|
618 | ENDDO |
---|
619 | |
---|
620 | END SUBROUTINE production_e |
---|
621 | |
---|
622 | |
---|
623 | !------------------------------------------------------------------------------! |
---|
624 | ! Call for grid point i,j |
---|
625 | !------------------------------------------------------------------------------! |
---|
626 | SUBROUTINE production_e_ij( i, j ) |
---|
627 | |
---|
628 | USE arrays_3d |
---|
629 | USE cloud_parameters |
---|
630 | USE control_parameters |
---|
631 | USE grid_variables |
---|
632 | USE indices |
---|
633 | USE statistics |
---|
634 | |
---|
635 | IMPLICIT NONE |
---|
636 | |
---|
637 | INTEGER :: i, j, k |
---|
638 | |
---|
639 | REAL :: def, dudx, dudy, dudz, dvdx, dvdy, dvdz, dwdx, dwdy, dwdz, & |
---|
640 | k1, k2, km_neutral, theta, temp |
---|
641 | |
---|
642 | REAL, DIMENSION(nzb:nzt+1) :: usvs, vsus, wsus, wsvs |
---|
643 | |
---|
644 | ! |
---|
645 | !-- Calculate TKE production by shear |
---|
646 | DO k = nzb_diff_s_outer(j,i), nzt |
---|
647 | |
---|
648 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
---|
649 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
---|
650 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
---|
651 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
---|
652 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
---|
653 | |
---|
654 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
---|
655 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
656 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
657 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
658 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
---|
659 | |
---|
660 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
661 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
662 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
663 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
664 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
665 | |
---|
666 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) & |
---|
667 | + dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + dvdz**2 & |
---|
668 | + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
669 | |
---|
670 | IF ( def < 0.0 ) def = 0.0 |
---|
671 | |
---|
672 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
673 | |
---|
674 | ENDDO |
---|
675 | |
---|
676 | IF ( prandtl_layer ) THEN |
---|
677 | |
---|
678 | IF ( ( wall_e_x(j,i) /= 0.0 ) .OR. ( wall_e_y(j,i) /= 0.0 ) ) THEN |
---|
679 | |
---|
680 | ! |
---|
681 | !-- Position beneath wall |
---|
682 | !-- (2) - Will allways be executed. |
---|
683 | !-- 'bottom and wall: use u_0,v_0 and wall functions' |
---|
684 | k = nzb_diff_s_inner(j,i)-1 |
---|
685 | |
---|
686 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
---|
687 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
---|
688 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
---|
689 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
690 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
691 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
---|
692 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
693 | |
---|
694 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
---|
695 | ! |
---|
696 | !-- Inconsistency removed: as the thermal stratification |
---|
697 | !-- is not taken into account for the evaluation of the |
---|
698 | !-- wall fluxes at vertical walls, the eddy viscosity km |
---|
699 | !-- must not be used for the evaluation of the velocity |
---|
700 | !-- gradients dudy and dwdy |
---|
701 | !-- Note: The validity of the new method has not yet |
---|
702 | !-- been shown, as so far no suitable data for a |
---|
703 | !-- validation has been available |
---|
704 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
---|
705 | usvs, 1.0, 0.0, 0.0, 0.0 ) |
---|
706 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
---|
707 | wsvs, 0.0, 0.0, 1.0, 0.0 ) |
---|
708 | km_neutral = kappa * ( usvs(k)**2 + wsvs(k)**2 )**0.25 * & |
---|
709 | 0.5 * dy |
---|
710 | IF ( km_neutral > 0.0 ) THEN |
---|
711 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
---|
712 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
---|
713 | ELSE |
---|
714 | dudy = 0.0 |
---|
715 | dwdy = 0.0 |
---|
716 | ENDIF |
---|
717 | ELSE |
---|
718 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
---|
719 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
---|
720 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
721 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
722 | ENDIF |
---|
723 | |
---|
724 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
---|
725 | ! |
---|
726 | !-- Inconsistency removed: as the thermal stratification |
---|
727 | !-- is not taken into account for the evaluation of the |
---|
728 | !-- wall fluxes at vertical walls, the eddy viscosity km |
---|
729 | !-- must not be used for the evaluation of the velocity |
---|
730 | !-- gradients dvdx and dwdx |
---|
731 | !-- Note: The validity of the new method has not yet |
---|
732 | !-- been shown, as so far no suitable data for a |
---|
733 | !-- validation has been available |
---|
734 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
---|
735 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
---|
736 | CALL wall_fluxes_e( i, j, k, nzb_diff_s_outer(j,i)-2, & |
---|
737 | wsus, 0.0, 0.0, 0.0, 1.0 ) |
---|
738 | km_neutral = kappa * ( vsus(k)**2 + wsus(k)**2 )**0.25 * & |
---|
739 | 0.5 * dx |
---|
740 | IF ( km_neutral > 0.0 ) THEN |
---|
741 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
---|
742 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
---|
743 | ELSE |
---|
744 | dvdx = 0.0 |
---|
745 | dwdx = 0.0 |
---|
746 | ENDIF |
---|
747 | ELSE |
---|
748 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
---|
749 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
750 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
751 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
752 | ENDIF |
---|
753 | |
---|
754 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
---|
755 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
---|
756 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
757 | |
---|
758 | IF ( def < 0.0 ) def = 0.0 |
---|
759 | |
---|
760 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
761 | |
---|
762 | ! |
---|
763 | !-- (3) - will be executed only, if there is at least one level |
---|
764 | !-- between (2) and (4), i.e. the topography must have a |
---|
765 | !-- minimum height of 2 dz. Wall fluxes for this case have |
---|
766 | !-- already been calculated for (2). |
---|
767 | !-- 'wall only: use wall functions' |
---|
768 | DO k = nzb_diff_s_inner(j,i), nzb_diff_s_outer(j,i)-2 |
---|
769 | |
---|
770 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
---|
771 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
---|
772 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
---|
773 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
774 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
775 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
---|
776 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
777 | |
---|
778 | IF ( wall_e_y(j,i) /= 0.0 ) THEN |
---|
779 | ! |
---|
780 | !-- Inconsistency removed: as the thermal stratification |
---|
781 | !-- is not taken into account for the evaluation of the |
---|
782 | !-- wall fluxes at vertical walls, the eddy viscosity km |
---|
783 | !-- must not be used for the evaluation of the velocity |
---|
784 | !-- gradients dudy and dwdy |
---|
785 | !-- Note: The validity of the new method has not yet |
---|
786 | !-- been shown, as so far no suitable data for a |
---|
787 | !-- validation has been available |
---|
788 | km_neutral = kappa * ( usvs(k)**2 + & |
---|
789 | wsvs(k)**2 )**0.25 * 0.5 * dy |
---|
790 | IF ( km_neutral > 0.0 ) THEN |
---|
791 | dudy = - wall_e_y(j,i) * usvs(k) / km_neutral |
---|
792 | dwdy = - wall_e_y(j,i) * wsvs(k) / km_neutral |
---|
793 | ELSE |
---|
794 | dudy = 0.0 |
---|
795 | dwdy = 0.0 |
---|
796 | ENDIF |
---|
797 | ELSE |
---|
798 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
---|
799 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
---|
800 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
801 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
802 | ENDIF |
---|
803 | |
---|
804 | IF ( wall_e_x(j,i) /= 0.0 ) THEN |
---|
805 | ! |
---|
806 | !-- Inconsistency removed: as the thermal stratification |
---|
807 | !-- is not taken into account for the evaluation of the |
---|
808 | !-- wall fluxes at vertical walls, the eddy viscosity km |
---|
809 | !-- must not be used for the evaluation of the velocity |
---|
810 | !-- gradients dvdx and dwdx |
---|
811 | !-- Note: The validity of the new method has not yet |
---|
812 | !-- been shown, as so far no suitable data for a |
---|
813 | !-- validation has been available |
---|
814 | km_neutral = kappa * ( vsus(k)**2 + & |
---|
815 | wsus(k)**2 )**0.25 * 0.5 * dx |
---|
816 | IF ( km_neutral > 0.0 ) THEN |
---|
817 | dvdx = - wall_e_x(j,i) * vsus(k) / km_neutral |
---|
818 | dwdx = - wall_e_x(j,i) * wsus(k) / km_neutral |
---|
819 | ELSE |
---|
820 | dvdx = 0.0 |
---|
821 | dwdx = 0.0 |
---|
822 | ENDIF |
---|
823 | ELSE |
---|
824 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
---|
825 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
826 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
827 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
828 | ENDIF |
---|
829 | |
---|
830 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
---|
831 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
---|
832 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
833 | |
---|
834 | IF ( def < 0.0 ) def = 0.0 |
---|
835 | |
---|
836 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
837 | |
---|
838 | ENDDO |
---|
839 | |
---|
840 | ! |
---|
841 | !-- (4) - will allways be executed. |
---|
842 | !-- 'special case: free atmosphere' (as for case (0)) |
---|
843 | k = nzb_diff_s_outer(j,i)-1 |
---|
844 | |
---|
845 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
---|
846 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
---|
847 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
---|
848 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
---|
849 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
---|
850 | |
---|
851 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
---|
852 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
853 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
854 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
855 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
---|
856 | |
---|
857 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
858 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
859 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
860 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
861 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
862 | |
---|
863 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
---|
864 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
---|
865 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
866 | |
---|
867 | IF ( def < 0.0 ) def = 0.0 |
---|
868 | |
---|
869 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
870 | |
---|
871 | ELSE |
---|
872 | |
---|
873 | ! |
---|
874 | !-- Position without adjacent wall |
---|
875 | !-- (1) - will allways be executed. |
---|
876 | !-- 'bottom only: use u_0,v_0' |
---|
877 | k = nzb_diff_s_inner(j,i)-1 |
---|
878 | |
---|
879 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
---|
880 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
---|
881 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
---|
882 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
---|
883 | u_0(j,i) - u_0(j,i+1) ) * dd2zu(k) |
---|
884 | |
---|
885 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
---|
886 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
887 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
888 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
889 | v_0(j,i) - v_0(j+1,i) ) * dd2zu(k) |
---|
890 | |
---|
891 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
892 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
893 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
894 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
895 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
896 | |
---|
897 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) & |
---|
898 | + dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + dvdz**2 & |
---|
899 | + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
900 | |
---|
901 | IF ( def < 0.0 ) def = 0.0 |
---|
902 | |
---|
903 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
904 | |
---|
905 | ENDIF |
---|
906 | |
---|
907 | ELSEIF ( use_surface_fluxes ) THEN |
---|
908 | |
---|
909 | k = nzb_diff_s_outer(j,i)-1 |
---|
910 | |
---|
911 | dudx = ( u(k,j,i+1) - u(k,j,i) ) * ddx |
---|
912 | dudy = 0.25 * ( u(k,j+1,i) + u(k,j+1,i+1) - & |
---|
913 | u(k,j-1,i) - u(k,j-1,i+1) ) * ddy |
---|
914 | dudz = 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) - & |
---|
915 | u(k-1,j,i) - u(k-1,j,i+1) ) * dd2zu(k) |
---|
916 | |
---|
917 | dvdx = 0.25 * ( v(k,j,i+1) + v(k,j+1,i+1) - & |
---|
918 | v(k,j,i-1) - v(k,j+1,i-1) ) * ddx |
---|
919 | dvdy = ( v(k,j+1,i) - v(k,j,i) ) * ddy |
---|
920 | dvdz = 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) - & |
---|
921 | v(k-1,j,i) - v(k-1,j+1,i) ) * dd2zu(k) |
---|
922 | |
---|
923 | dwdx = 0.25 * ( w(k,j,i+1) + w(k-1,j,i+1) - & |
---|
924 | w(k,j,i-1) - w(k-1,j,i-1) ) * ddx |
---|
925 | dwdy = 0.25 * ( w(k,j+1,i) + w(k-1,j+1,i) - & |
---|
926 | w(k,j-1,i) - w(k-1,j-1,i) ) * ddy |
---|
927 | dwdz = ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) |
---|
928 | |
---|
929 | def = 2.0 * ( dudx**2 + dvdy**2 + dwdz**2 ) + & |
---|
930 | dudy**2 + dvdx**2 + dwdx**2 + dwdy**2 + dudz**2 + & |
---|
931 | dvdz**2 + 2.0 * ( dvdx*dudy + dwdx*dudz + dwdy*dvdz ) |
---|
932 | |
---|
933 | IF ( def < 0.0 ) def = 0.0 |
---|
934 | |
---|
935 | tend(k,j,i) = tend(k,j,i) + km(k,j,i) * def |
---|
936 | |
---|
937 | ENDIF |
---|
938 | |
---|
939 | ! |
---|
940 | !-- Calculate TKE production by buoyancy |
---|
941 | IF ( .NOT. humidity ) THEN |
---|
942 | |
---|
943 | IF ( use_reference ) THEN |
---|
944 | |
---|
945 | IF ( ocean ) THEN |
---|
946 | ! |
---|
947 | !-- So far in the ocean no special treatment of density flux in the |
---|
948 | !-- bottom and top surface layer |
---|
949 | DO k = nzb_s_inner(j,i)+1, nzt |
---|
950 | tend(k,j,i) = tend(k,j,i) + kh(k,j,i) * g / rho_reference * & |
---|
951 | ( rho(k+1,j,i) - rho(k-1,j,i) ) * dd2zu(k) |
---|
952 | ENDDO |
---|
953 | |
---|
954 | ELSE |
---|
955 | |
---|
956 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
---|
957 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / pt_reference * & |
---|
958 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
---|
959 | ENDDO |
---|
960 | |
---|
961 | IF ( use_surface_fluxes ) THEN |
---|
962 | k = nzb_diff_s_inner(j,i)-1 |
---|
963 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * shf(j,i) |
---|
964 | ENDIF |
---|
965 | |
---|
966 | IF ( use_top_fluxes ) THEN |
---|
967 | k = nzt |
---|
968 | tend(k,j,i) = tend(k,j,i) + g / pt_reference * tswst(j,i) |
---|
969 | ENDIF |
---|
970 | |
---|
971 | ENDIF |
---|
972 | |
---|
973 | ELSE |
---|
974 | |
---|
975 | IF ( ocean ) THEN |
---|
976 | ! |
---|
977 | !-- So far in the ocean no special treatment of density flux in the |
---|
978 | !-- bottom and top surface layer |
---|
979 | DO k = nzb_s_inner(j,i)+1, nzt |
---|
980 | tend(k,j,i) = tend(k,j,i) + kh(k,j,i) * g / rho(k,j,i) * & |
---|
981 | ( rho(k+1,j,i) - rho(k-1,j,i) ) * dd2zu(k) |
---|
982 | ENDDO |
---|
983 | |
---|
984 | ELSE |
---|
985 | |
---|
986 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
---|
987 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / pt(k,j,i) * & |
---|
988 | ( pt(k+1,j,i) - pt(k-1,j,i) ) * dd2zu(k) |
---|
989 | ENDDO |
---|
990 | |
---|
991 | IF ( use_surface_fluxes ) THEN |
---|
992 | k = nzb_diff_s_inner(j,i)-1 |
---|
993 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * shf(j,i) |
---|
994 | ENDIF |
---|
995 | |
---|
996 | IF ( use_top_fluxes ) THEN |
---|
997 | k = nzt |
---|
998 | tend(k,j,i) = tend(k,j,i) + g / pt(k,j,i) * tswst(j,i) |
---|
999 | ENDIF |
---|
1000 | |
---|
1001 | ENDIF |
---|
1002 | |
---|
1003 | ENDIF |
---|
1004 | |
---|
1005 | ELSE |
---|
1006 | |
---|
1007 | DO k = nzb_diff_s_inner(j,i), nzt_diff |
---|
1008 | |
---|
1009 | IF ( .NOT. cloud_physics ) THEN |
---|
1010 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
1011 | k2 = 0.61 * pt(k,j,i) |
---|
1012 | ELSE |
---|
1013 | IF ( ql(k,j,i) == 0.0 ) THEN |
---|
1014 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
1015 | k2 = 0.61 * pt(k,j,i) |
---|
1016 | ELSE |
---|
1017 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
---|
1018 | temp = theta * t_d_pt(k) |
---|
1019 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
---|
1020 | ( q(k,j,i) - ql(k,j,i) ) * & |
---|
1021 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
---|
1022 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
---|
1023 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
---|
1024 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
---|
1025 | ENDIF |
---|
1026 | ENDIF |
---|
1027 | |
---|
1028 | tend(k,j,i) = tend(k,j,i) - kh(k,j,i) * g / vpt(k,j,i) * & |
---|
1029 | ( k1 * ( pt(k+1,j,i)-pt(k-1,j,i) ) + & |
---|
1030 | k2 * ( q(k+1,j,i) - q(k-1,j,i) ) & |
---|
1031 | ) * dd2zu(k) |
---|
1032 | ENDDO |
---|
1033 | |
---|
1034 | IF ( use_surface_fluxes ) THEN |
---|
1035 | k = nzb_diff_s_inner(j,i)-1 |
---|
1036 | |
---|
1037 | IF ( .NOT. cloud_physics ) THEN |
---|
1038 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
1039 | k2 = 0.61 * pt(k,j,i) |
---|
1040 | ELSE |
---|
1041 | IF ( ql(k,j,i) == 0.0 ) THEN |
---|
1042 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
1043 | k2 = 0.61 * pt(k,j,i) |
---|
1044 | ELSE |
---|
1045 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
---|
1046 | temp = theta * t_d_pt(k) |
---|
1047 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
---|
1048 | ( q(k,j,i) - ql(k,j,i) ) * & |
---|
1049 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
---|
1050 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
---|
1051 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
---|
1052 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
---|
1053 | ENDIF |
---|
1054 | ENDIF |
---|
1055 | |
---|
1056 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
---|
1057 | ( k1* shf(j,i) + k2 * qsws(j,i) ) |
---|
1058 | ENDIF |
---|
1059 | |
---|
1060 | IF ( use_top_fluxes ) THEN |
---|
1061 | k = nzt |
---|
1062 | |
---|
1063 | IF ( .NOT. cloud_physics ) THEN |
---|
1064 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
1065 | k2 = 0.61 * pt(k,j,i) |
---|
1066 | ELSE |
---|
1067 | IF ( ql(k,j,i) == 0.0 ) THEN |
---|
1068 | k1 = 1.0 + 0.61 * q(k,j,i) |
---|
1069 | k2 = 0.61 * pt(k,j,i) |
---|
1070 | ELSE |
---|
1071 | theta = pt(k,j,i) + pt_d_t(k) * l_d_cp * ql(k,j,i) |
---|
1072 | temp = theta * t_d_pt(k) |
---|
1073 | k1 = ( 1.0 - q(k,j,i) + 1.61 * & |
---|
1074 | ( q(k,j,i) - ql(k,j,i) ) * & |
---|
1075 | ( 1.0 + 0.622 * l_d_r / temp ) ) / & |
---|
1076 | ( 1.0 + 0.622 * l_d_r * l_d_cp * & |
---|
1077 | ( q(k,j,i) - ql(k,j,i) ) / ( temp * temp ) ) |
---|
1078 | k2 = theta * ( l_d_cp / temp * k1 - 1.0 ) |
---|
1079 | ENDIF |
---|
1080 | ENDIF |
---|
1081 | |
---|
1082 | tend(k,j,i) = tend(k,j,i) + g / vpt(k,j,i) * & |
---|
1083 | ( k1* tswst(j,i) + k2 * qswst(j,i) ) |
---|
1084 | ENDIF |
---|
1085 | |
---|
1086 | ENDIF |
---|
1087 | |
---|
1088 | END SUBROUTINE production_e_ij |
---|
1089 | |
---|
1090 | |
---|
1091 | SUBROUTINE production_e_init |
---|
1092 | |
---|
1093 | USE arrays_3d |
---|
1094 | USE control_parameters |
---|
1095 | USE grid_variables |
---|
1096 | USE indices |
---|
1097 | |
---|
1098 | IMPLICIT NONE |
---|
1099 | |
---|
1100 | INTEGER :: i, j, ku, kv |
---|
1101 | |
---|
1102 | IF ( prandtl_layer ) THEN |
---|
1103 | |
---|
1104 | IF ( first_call ) THEN |
---|
1105 | ALLOCATE( u_0(nys-1:nyn+1,nxl-1:nxr+1), & |
---|
1106 | v_0(nys-1:nyn+1,nxl-1:nxr+1) ) |
---|
1107 | first_call = .FALSE. |
---|
1108 | ENDIF |
---|
1109 | |
---|
1110 | ! |
---|
1111 | !-- Calculate a virtual velocity at the surface in a way that the |
---|
1112 | !-- vertical velocity gradient at k = 1 (u(k+1)-u_0) matches the |
---|
1113 | !-- Prandtl law (-w'u'/km). This gradient is used in the TKE shear |
---|
1114 | !-- production term at k=1 (see production_e_ij). |
---|
1115 | !-- The velocity gradient has to be limited in case of too small km |
---|
1116 | !-- (otherwise the timestep may be significantly reduced by large |
---|
1117 | !-- surface winds). |
---|
1118 | !-- Upper bounds are nxr+1 and nyn+1 because otherwise these values are |
---|
1119 | !-- not available in case of non-cyclic boundary conditions. |
---|
1120 | !-- WARNING: the exact analytical solution would require the determination |
---|
1121 | !-- of the eddy diffusivity by km = u* * kappa * zp / phi_m. |
---|
1122 | !$OMP PARALLEL DO PRIVATE( ku, kv ) |
---|
1123 | DO i = nxl, nxr+1 |
---|
1124 | DO j = nys, nyn+1 |
---|
1125 | |
---|
1126 | ku = nzb_u_inner(j,i)+1 |
---|
1127 | kv = nzb_v_inner(j,i)+1 |
---|
1128 | |
---|
1129 | u_0(j,i) = u(ku+1,j,i) + usws(j,i) * ( zu(ku+1) - zu(ku-1) ) / & |
---|
1130 | ( 0.5 * ( km(ku,j,i) + km(ku,j,i-1) ) + & |
---|
1131 | 1.0E-20 ) |
---|
1132 | ! ( us(j,i) * kappa * zu(1) ) |
---|
1133 | v_0(j,i) = v(kv+1,j,i) + vsws(j,i) * ( zu(kv+1) - zu(kv-1) ) / & |
---|
1134 | ( 0.5 * ( km(kv,j,i) + km(kv,j-1,i) ) + & |
---|
1135 | 1.0E-20 ) |
---|
1136 | ! ( us(j,i) * kappa * zu(1) ) |
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1137 | |
---|
1138 | IF ( ABS( u(ku+1,j,i) - u_0(j,i) ) > & |
---|
1139 | ABS( u(ku+1,j,i) - u(ku-1,j,i) ) ) u_0(j,i) = u(ku-1,j,i) |
---|
1140 | IF ( ABS( v(kv+1,j,i) - v_0(j,i) ) > & |
---|
1141 | ABS( v(kv+1,j,i) - v(kv-1,j,i) ) ) v_0(j,i) = v(kv-1,j,i) |
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1142 | |
---|
1143 | ENDDO |
---|
1144 | ENDDO |
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1145 | |
---|
1146 | CALL exchange_horiz_2d( u_0 ) |
---|
1147 | CALL exchange_horiz_2d( v_0 ) |
---|
1148 | |
---|
1149 | ENDIF |
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1150 | |
---|
1151 | END SUBROUTINE production_e_init |
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1152 | |
---|
1153 | END MODULE production_e_mod |
---|