| 1 | SUBROUTINE prandtl_fluxes |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Current revisions: |
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| 5 | ! ----------------- |
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| 6 | ! |
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| 7 | ! |
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| 8 | ! Former revisions: |
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| 9 | ! ----------------- |
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| 10 | ! $Id: prandtl_fluxes.f90 979 2012-08-09 08:50:11Z maronga $ |
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| 11 | ! |
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| 12 | ! 978 2012-08-09 08:28:32Z fricke |
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| 13 | ! roughness length for scalar quantities z0h added |
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| 14 | ! |
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| 15 | ! 759 2011-09-15 13:58:31Z raasch |
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| 16 | ! Bugfix for ts limitation |
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| 17 | ! |
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| 18 | ! 709 2011-03-30 09:31:40Z raasch |
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| 19 | ! formatting adjustments |
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| 20 | ! |
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| 21 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 22 | ! Changed surface boundary conditions for u and v from mirror to Dirichlet. |
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| 23 | ! Therefore u(uzb,:,:) and v(nzb,:,:) are now representative for height z0. |
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| 24 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
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| 25 | ! |
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| 26 | ! 315 2009-05-13 10:57:59Z raasch |
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| 27 | ! Saturation condition at (sea) surface is not used in precursor runs (only |
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| 28 | ! in the following coupled runs) |
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| 29 | ! Bugfix: qsws was calculated in case of constant heatflux = .FALSE. |
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| 30 | ! |
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| 31 | ! 187 2008-08-06 16:25:09Z letzel |
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| 32 | ! Bugfix: modification of the calculation of the vertical turbulent momentum |
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| 33 | ! fluxes u'w' and v'w' |
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| 34 | ! Bugfix: change definition of us_wall from 1D to 2D |
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| 35 | ! Change: modification of the integrated version of the profile function for |
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| 36 | ! momentum for unstable stratification (does not effect results) |
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| 37 | ! |
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| 38 | ! 108 2007-08-24 15:10:38Z letzel |
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| 39 | ! assume saturation at k=nzb_s_inner(j,i) for atmosphere coupled to ocean |
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| 40 | ! |
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| 41 | ! 75 2007-03-22 09:54:05Z raasch |
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| 42 | ! moisture renamed humidity |
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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 1.19 2006/04/26 12:24:35 raasch |
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| 47 | ! +OpenMP directives and optimization (array assignments replaced by DO loops) |
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| 48 | ! |
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| 49 | ! Revision 1.1 1998/01/23 10:06:06 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 | ! Diagnostic computation of vertical fluxes in the Prandtl layer from the |
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| 56 | ! values of the variables at grid point k=1 |
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| 57 | !------------------------------------------------------------------------------! |
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| 58 | |
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| 59 | USE arrays_3d |
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| 60 | USE control_parameters |
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| 61 | USE grid_variables |
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| 62 | USE indices |
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| 63 | |
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| 64 | IMPLICIT NONE |
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| 65 | |
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| 66 | INTEGER :: i, j, k |
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| 67 | REAL :: a, b, e_q, rifm, uv_total, z_p |
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| 68 | |
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| 69 | ! |
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| 70 | !-- Compute theta* |
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| 71 | IF ( constant_heatflux ) THEN |
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| 72 | ! |
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| 73 | !-- For a given heat flux in the Prandtl layer: |
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| 74 | !-- for u* use the value from the previous time step |
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| 75 | !$OMP PARALLEL DO |
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| 76 | DO i = nxlg, nxrg |
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| 77 | DO j = nysg, nyng |
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| 78 | ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30 ) |
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| 79 | ! |
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| 80 | !-- ts must be limited, because otherwise overflow may occur in case of |
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| 81 | !-- us=0 when computing rif further below |
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| 82 | IF ( ts(j,i) < -1.05E5 ) ts(j,i) = -1.0E5 |
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| 83 | IF ( ts(j,i) > 1.0E5 ) ts(j,i) = 1.0E5 |
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| 84 | ENDDO |
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| 85 | ENDDO |
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| 86 | |
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| 87 | ELSE |
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| 88 | ! |
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| 89 | !-- For a given surface temperature: |
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| 90 | !-- (the Richardson number is still the one from the previous time step) |
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| 91 | !$OMP PARALLEL DO PRIVATE( a, b, k, z_p ) |
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| 92 | DO i = nxlg, nxrg |
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| 93 | DO j = nysg, nyng |
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| 94 | |
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| 95 | k = nzb_s_inner(j,i) |
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| 96 | z_p = zu(k+1) - zw(k) |
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| 97 | |
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| 98 | IF ( rif(j,i) >= 0.0 ) THEN |
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| 99 | ! |
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| 100 | !-- Stable stratification |
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| 101 | ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / ( & |
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| 102 | LOG( z_p / z0h(j,i) ) + & |
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| 103 | 5.0 * rif(j,i) * ( z_p - z0h(j,i) ) / z_p & |
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| 104 | ) |
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| 105 | ELSE |
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| 106 | ! |
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| 107 | !-- Unstable stratification |
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| 108 | a = SQRT( 1.0 - 16.0 * rif(j,i) ) |
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| 109 | b = SQRT( 1.0 - 16.0 * rif(j,i) * z0h(j,i) / z_p ) |
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| 110 | |
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| 111 | ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / ( & |
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| 112 | LOG( z_p / z0h(j,i) ) - & |
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| 113 | 2.0 * LOG( ( 1.0 + a ) / ( 1.0 + b ) ) ) |
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| 114 | ENDIF |
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| 115 | |
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| 116 | ENDDO |
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| 117 | ENDDO |
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| 118 | ENDIF |
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| 119 | |
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| 120 | ! |
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| 121 | !-- Compute z_p/L (corresponds to the Richardson-flux number) |
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| 122 | IF ( .NOT. humidity ) THEN |
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| 123 | !$OMP PARALLEL DO PRIVATE( k, z_p ) |
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| 124 | DO i = nxlg, nxrg |
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| 125 | DO j = nysg, nyng |
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| 126 | k = nzb_s_inner(j,i) |
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| 127 | z_p = zu(k+1) - zw(k) |
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| 128 | rif(j,i) = z_p * kappa * g * ts(j,i) / & |
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| 129 | ( pt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) ) |
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| 130 | ! |
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| 131 | !-- Limit the value range of the Richardson numbers. |
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| 132 | !-- This is necessary for very small velocities (u,v --> 0), because |
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| 133 | !-- the absolute value of rif can then become very large, which in |
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| 134 | !-- consequence would result in very large shear stresses and very |
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| 135 | !-- small momentum fluxes (both are generally unrealistic). |
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| 136 | IF ( rif(j,i) < rif_min ) rif(j,i) = rif_min |
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| 137 | IF ( rif(j,i) > rif_max ) rif(j,i) = rif_max |
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| 138 | ENDDO |
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| 139 | ENDDO |
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| 140 | ELSE |
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| 141 | !$OMP PARALLEL DO PRIVATE( k, z_p ) |
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| 142 | DO i = nxlg, nxrg |
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| 143 | DO j = nysg, nyng |
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| 144 | k = nzb_s_inner(j,i) |
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| 145 | z_p = zu(k+1) - zw(k) |
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| 146 | rif(j,i) = z_p * kappa * g * & |
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| 147 | ( ts(j,i) + 0.61 * pt(k+1,j,i) * qs(j,i) ) / & |
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| 148 | ( vpt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) ) |
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| 149 | ! |
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| 150 | !-- Limit the value range of the Richardson numbers. |
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| 151 | !-- This is necessary for very small velocities (u,v --> 0), because |
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| 152 | !-- the absolute value of rif can then become very large, which in |
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| 153 | !-- consequence would result in very large shear stresses and very |
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| 154 | !-- small momentum fluxes (both are generally unrealistic). |
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| 155 | IF ( rif(j,i) < rif_min ) rif(j,i) = rif_min |
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| 156 | IF ( rif(j,i) > rif_max ) rif(j,i) = rif_max |
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| 157 | ENDDO |
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| 158 | ENDDO |
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| 159 | ENDIF |
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| 160 | |
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| 161 | ! |
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| 162 | !-- Compute u* at the scalars' grid points |
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| 163 | !$OMP PARALLEL DO PRIVATE( a, b, k, uv_total, z_p ) |
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| 164 | DO i = nxl, nxr |
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| 165 | DO j = nys, nyn |
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| 166 | |
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| 167 | k = nzb_s_inner(j,i) |
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| 168 | z_p = zu(k+1) - zw(k) |
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| 169 | |
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| 170 | ! |
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| 171 | !-- Compute the absolute value of the horizontal velocity |
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| 172 | !-- (relative to the surface) |
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| 173 | uv_total = SQRT( ( 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) & |
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| 174 | - u(k,j,i) - u(k,j,i+1) ) )**2 + & |
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| 175 | ( 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) & |
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| 176 | - v(k,j,i) - v(k,j+1,i) ) )**2 ) |
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| 177 | |
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| 178 | |
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| 179 | IF ( rif(j,i) >= 0.0 ) THEN |
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| 180 | ! |
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| 181 | !-- Stable stratification |
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| 182 | us(j,i) = kappa * uv_total / ( & |
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| 183 | LOG( z_p / z0(j,i) ) + & |
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| 184 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
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| 185 | ) |
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| 186 | ELSE |
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| 187 | ! |
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| 188 | !-- Unstable stratification |
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| 189 | a = SQRT( SQRT( 1.0 - 16.0 * rif(j,i) ) ) |
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| 190 | b = SQRT( SQRT( 1.0 - 16.0 * rif(j,i) / z_p * z0(j,i) ) ) |
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| 191 | |
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| 192 | us(j,i) = kappa * uv_total / ( & |
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| 193 | LOG( z_p / z0(j,i) ) - & |
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| 194 | LOG( ( 1.0 + a )**2 * ( 1.0 + a**2 ) / ( & |
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| 195 | ( 1.0 + b )**2 * ( 1.0 + b**2 ) ) ) + & |
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| 196 | 2.0 * ( ATAN( a ) - ATAN( b ) ) & |
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| 197 | ) |
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| 198 | ENDIF |
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| 199 | ENDDO |
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| 200 | ENDDO |
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| 201 | |
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| 202 | ! |
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| 203 | !-- Values of us at ghost point locations are needed for the evaluation of usws |
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| 204 | !-- and vsws. |
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| 205 | CALL exchange_horiz_2d( us ) |
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| 206 | ! |
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| 207 | !-- Compute u'w' for the total model domain. |
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| 208 | !-- First compute the corresponding component of u* and square it. |
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| 209 | !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p ) |
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| 210 | DO i = nxl, nxr |
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| 211 | DO j = nys, nyn |
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| 212 | |
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| 213 | k = nzb_u_inner(j,i) |
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| 214 | z_p = zu(k+1) - zw(k) |
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| 215 | |
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| 216 | ! |
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| 217 | !-- Compute Richardson-flux number for this point |
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| 218 | rifm = 0.5 * ( rif(j,i-1) + rif(j,i) ) |
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| 219 | IF ( rifm >= 0.0 ) THEN |
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| 220 | ! |
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| 221 | !-- Stable stratification |
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| 222 | usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) )/ ( & |
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| 223 | LOG( z_p / z0(j,i) ) + & |
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| 224 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
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| 225 | ) |
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| 226 | ELSE |
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| 227 | ! |
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| 228 | !-- Unstable stratification |
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| 229 | a = SQRT( SQRT( 1.0 - 16.0 * rifm ) ) |
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| 230 | b = SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) ) |
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| 231 | |
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| 232 | usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) / ( & |
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| 233 | LOG( z_p / z0(j,i) ) - & |
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| 234 | LOG( (1.0 + a )**2 * ( 1.0 + a**2 ) / ( & |
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| 235 | (1.0 + b )**2 * ( 1.0 + b**2 ) ) ) + & |
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| 236 | 2.0 * ( ATAN( a ) - ATAN( b ) ) & |
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| 237 | ) |
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| 238 | ENDIF |
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| 239 | usws(j,i) = -usws(j,i) * 0.5 * ( us(j,i-1) + us(j,i) ) |
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| 240 | ENDDO |
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| 241 | ENDDO |
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| 242 | |
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| 243 | ! |
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| 244 | !-- Compute v'w' for the total model domain. |
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| 245 | !-- First compute the corresponding component of u* and square it. |
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| 246 | !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p ) |
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| 247 | DO i = nxl, nxr |
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| 248 | DO j = nys, nyn |
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| 249 | |
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| 250 | k = nzb_v_inner(j,i) |
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| 251 | z_p = zu(k+1) - zw(k) |
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| 252 | |
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| 253 | ! |
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| 254 | !-- Compute Richardson-flux number for this point |
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| 255 | rifm = 0.5 * ( rif(j-1,i) + rif(j,i) ) |
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| 256 | IF ( rifm >= 0.0 ) THEN |
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| 257 | ! |
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| 258 | !-- Stable stratification |
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| 259 | vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) / ( & |
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| 260 | LOG( z_p / z0(j,i) ) + & |
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| 261 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
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| 262 | ) |
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| 263 | ELSE |
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| 264 | ! |
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| 265 | !-- Unstable stratification |
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| 266 | a = SQRT( SQRT( 1.0 - 16.0 * rifm ) ) |
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| 267 | b = SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) ) |
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| 268 | |
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| 269 | vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) / ( & |
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| 270 | LOG( z_p / z0(j,i) ) - & |
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| 271 | LOG( (1.0 + a )**2 * ( 1.0 + a**2 ) / ( & |
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| 272 | (1.0 + b )**2 * ( 1.0 + b**2 ) ) ) + & |
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| 273 | 2.0 * ( ATAN( a ) - ATAN( b ) ) & |
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| 274 | ) |
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| 275 | ENDIF |
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| 276 | vsws(j,i) = -vsws(j,i) * 0.5 * ( us(j-1,i) + us(j,i) ) |
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| 277 | ENDDO |
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| 278 | ENDDO |
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| 279 | |
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| 280 | ! |
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| 281 | !-- If required compute q* |
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| 282 | IF ( humidity .OR. passive_scalar ) THEN |
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| 283 | IF ( constant_waterflux ) THEN |
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| 284 | ! |
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| 285 | !-- For a given water flux in the Prandtl layer: |
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| 286 | !$OMP PARALLEL DO |
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| 287 | DO i = nxlg, nxrg |
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| 288 | DO j = nysg, nyng |
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| 289 | qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30 ) |
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| 290 | ENDDO |
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| 291 | ENDDO |
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| 292 | |
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| 293 | ELSE |
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| 294 | !$OMP PARALLEL DO PRIVATE( a, b, k, z_p ) |
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| 295 | DO i = nxlg, nxrg |
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| 296 | DO j = nysg, nyng |
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| 297 | |
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| 298 | k = nzb_s_inner(j,i) |
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| 299 | z_p = zu(k+1) - zw(k) |
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| 300 | |
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| 301 | ! |
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| 302 | !-- Assume saturation for atmosphere coupled to ocean (but not |
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| 303 | !-- in case of precursor runs) |
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| 304 | IF ( coupling_mode == 'atmosphere_to_ocean' .AND. run_coupled )& |
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| 305 | THEN |
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| 306 | e_q = 6.1 * & |
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| 307 | EXP( 0.07 * ( MIN(pt(0,j,i),pt(1,j,i)) - 273.15 ) ) |
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| 308 | q(k,j,i) = 0.622 * e_q / ( surface_pressure - e_q ) |
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| 309 | ENDIF |
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| 310 | IF ( rif(j,i) >= 0.0 ) THEN |
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| 311 | ! |
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| 312 | !-- Stable stratification |
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| 313 | qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / ( & |
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| 314 | LOG( z_p / z0h(j,i) ) + & |
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| 315 | 5.0 * rif(j,i) * ( z_p - z0h(j,i) ) / z_p & |
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| 316 | ) |
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| 317 | ELSE |
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| 318 | ! |
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| 319 | !-- Unstable stratification |
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| 320 | a = SQRT( 1.0 - 16.0 * rif(j,i) ) |
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| 321 | b = SQRT( 1.0 - 16.0 * rif(j,i) * z0h(j,i) / z_p ) |
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| 322 | |
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| 323 | qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / ( & |
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| 324 | LOG( z_p / z0h(j,i) ) - & |
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| 325 | 2.0 * LOG( (1.0 + a ) / ( 1.0 + b ) ) ) |
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| 326 | ENDIF |
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| 327 | |
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| 328 | ENDDO |
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| 329 | ENDDO |
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| 330 | ENDIF |
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| 331 | ENDIF |
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| 332 | |
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| 333 | ! |
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| 334 | !-- Exchange the boundaries for the momentum fluxes (only for sake of |
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| 335 | !-- completeness) |
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| 336 | CALL exchange_horiz_2d( usws ) |
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| 337 | CALL exchange_horiz_2d( vsws ) |
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| 338 | IF ( humidity .OR. passive_scalar ) CALL exchange_horiz_2d( qsws ) |
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| 339 | |
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| 340 | ! |
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| 341 | !-- Compute the vertical kinematic heat flux |
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| 342 | IF ( .NOT. constant_heatflux ) THEN |
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| 343 | !$OMP PARALLEL DO |
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| 344 | DO i = nxlg, nxrg |
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| 345 | DO j = nysg, nyng |
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| 346 | shf(j,i) = -ts(j,i) * us(j,i) |
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| 347 | ENDDO |
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| 348 | ENDDO |
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| 349 | ENDIF |
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| 350 | |
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| 351 | ! |
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| 352 | !-- Compute the vertical water/scalar flux |
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| 353 | IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) ) THEN |
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| 354 | !$OMP PARALLEL DO |
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| 355 | DO i = nxlg, nxrg |
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| 356 | DO j = nysg, nyng |
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| 357 | qsws(j,i) = -qs(j,i) * us(j,i) |
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| 358 | ENDDO |
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| 359 | ENDDO |
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| 360 | ENDIF |
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| 361 | |
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| 362 | ! |
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| 363 | !-- Bottom boundary condition for the TKE |
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| 364 | IF ( ibc_e_b == 2 ) THEN |
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| 365 | !$OMP PARALLEL DO |
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| 366 | DO i = nxlg, nxrg |
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| 367 | DO j = nysg, nyng |
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| 368 | e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1 )**2 |
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| 369 | ! |
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| 370 | !-- As a test: cm = 0.4 |
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| 371 | ! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4 )**2 |
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| 372 | e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i) |
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| 373 | ENDDO |
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| 374 | ENDDO |
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| 375 | ENDIF |
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| 376 | |
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| 377 | |
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| 378 | END SUBROUTINE prandtl_fluxes |
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