[1] | 1 | SUBROUTINE prandtl_fluxes |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Actual revisions: |
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| 5 | ! ----------------- |
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| 6 | ! |
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| 7 | ! |
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| 8 | ! Former revisions: |
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| 9 | ! ----------------- |
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| 10 | ! $Log: prandtl_fluxes.f90,v $ |
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| 11 | ! Revision 1.19 2006/04/26 12:24:35 raasch |
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| 12 | ! +OpenMP directives and optimization (array assignments replaced by DO loops) |
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| 13 | ! |
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| 14 | ! Revision 1.18 2006/02/23 12:49:32 raasch |
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| 15 | ! shf, ts, rif, us, usws, vsws, qs and qsws are now defined at the actual |
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| 16 | ! surface of the model domain, i.e. either at the bottom or at the height |
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| 17 | ! of the topography. Thus, zu(1) is replaced |
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| 18 | ! by zp = ( zu(nzb_[variable]_inner(j,i)+1 - zw(nzb_[variable]_inner(j,i) ), |
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| 19 | ! [variable](1,j,i) by [variable](nzb_[variable]_inner(j,i)+1,j,i) and |
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| 20 | ! [variable](0,j,i) by [variable](nzb_[variable]_inner(j,i) ,j,i). |
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| 21 | ! |
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| 22 | ! Revision 1.17 2004/04/30 12:43:50 raasch |
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| 23 | ! rif_m replaced by rif (they are the same when used here) |
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| 24 | ! |
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| 25 | ! Revision 1.16 2003/11/20 15:13:26 raasch |
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| 26 | ! Variable name (B) changed from capital to small |
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| 27 | ! |
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| 28 | ! Revision 1.15 2001/03/30 07:46:47 raasch |
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| 29 | ! Translation of remaining German identifiers (variables, subroutines, etc.) |
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| 30 | ! |
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| 31 | ! Revision 1.14 2001/01/29 12:33:38 raasch |
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| 32 | ! Passive scalar is considered |
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| 33 | ! |
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| 34 | ! Revision 1.13 2001/01/25 07:23:22 raasch |
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| 35 | ! Range of ts is limited, since otherwise overflow may occur on REAL*4 |
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| 36 | ! machines |
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| 37 | ! |
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| 38 | ! Revision 1.11 2001/01/22 07:50:34 raasch |
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| 39 | ! Module test_variables removed |
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| 40 | ! |
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| 41 | ! Revision 1.10 2000/04/13 13:44:41 schroeter |
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| 42 | ! + implentation of the Prandtl layer for the total water content |
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| 43 | ! |
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| 44 | ! Revision 1.9 2000/01/26 14:48:48 14:48:48 letzel (Marcus Letzel) |
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| 45 | ! correct wrong time level of rif in computation of theta*, |
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| 46 | ! all comments translated into English |
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| 47 | ! |
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| 48 | ! Revision 1.8 1998/09/22 17:27:15 raasch |
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| 49 | ! Testweise Randbedingung fuer TKE mit cm = 0.4, aber vorerst auskommentiert |
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| 50 | ! |
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| 51 | ! Revision 1.7 1998/08/05 06:54:23 raasch |
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| 52 | ! Begrenzung von rif ist jetzt variabel (rif_max, rif_min) |
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| 53 | ! |
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| 54 | ! Revision 1.6 1998/07/06 12:30:01 raasch |
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| 55 | ! + USE test_variables |
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| 56 | ! |
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| 57 | ! Revision 1.5 1998/04/15 11:22:58 raasch |
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| 58 | ! Berechnung von theta* ueber Oberflaechentemperatur moeglich |
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| 59 | ! |
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| 60 | ! Revision 1.4 1998/03/11 11:53:22 raasch |
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| 61 | ! Zusaetzliche untere Randbedingung fuer TKE ( (u*/0.1)**2 ) |
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| 62 | ! |
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| 63 | ! Revision 1.3 1998/02/10 15:08:53 raasch |
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| 64 | ! Grenzfall bei labiler Schichtung ( a=1, b=1 ) wird stabil gerechnet |
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| 65 | ! Begrenzung von rif aktiviert |
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| 66 | ! |
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| 67 | ! Revision 1.2 1998/02/04 16:09:29 raasch |
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| 68 | ! Berechnung der Waermefluesse |
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| 69 | ! |
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| 70 | ! Revision 1.1 1998/01/23 10:06:06 raasch |
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| 71 | ! Initial revision |
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| 72 | ! |
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| 73 | ! |
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| 74 | ! Description: |
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| 75 | ! ------------ |
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| 76 | ! Diagnostic computation of vertical fluxes in the Prandtl layer from the |
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| 77 | ! values of the variables at grid point k=1 |
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| 78 | !------------------------------------------------------------------------------! |
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| 79 | |
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| 80 | USE arrays_3d |
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| 81 | USE control_parameters |
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| 82 | USE grid_variables |
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| 83 | USE indices |
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| 84 | |
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| 85 | IMPLICIT NONE |
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| 86 | |
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| 87 | INTEGER :: i, j, k |
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| 88 | REAL :: a, b, rifm, uv_total, z_p |
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| 89 | |
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| 90 | ! |
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| 91 | !-- Compute theta* |
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| 92 | IF ( constant_heatflux ) THEN |
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| 93 | ! |
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| 94 | !-- For a given heat flux in the Prandtl layer: |
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| 95 | !-- for u* use the value from the previous time step |
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| 96 | !$OMP PARALLEL DO |
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| 97 | DO i = nxl-1, nxr+1 |
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| 98 | DO j = nys-1, nyn+1 |
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| 99 | ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30 ) |
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| 100 | ! |
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| 101 | !-- ts must be limited, because otherwise overflow may occur in case of |
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| 102 | !-- us=0 when computing rif further below |
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| 103 | IF ( ts(j,i) < -1.05E5 ) ts = -1.0E5 |
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| 104 | IF ( ts(j,i) > 1.0E5 ) ts = 1.0E5 |
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| 105 | ENDDO |
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| 106 | ENDDO |
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| 107 | |
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| 108 | ELSE |
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| 109 | ! |
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| 110 | !-- For a given surface temperature: |
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| 111 | !-- (the Richardson number is still the one from the previous time step) |
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| 112 | !$OMP PARALLEL DO PRIVATE( a, b, k, z_p ) |
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| 113 | DO i = nxl-1, nxr+1 |
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| 114 | DO j = nys-1, nyn+1 |
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| 115 | |
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| 116 | k = nzb_s_inner(j,i) |
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| 117 | z_p = zu(k+1) - zw(k) |
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| 118 | |
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| 119 | IF ( rif(j,i) >= 0.0 ) THEN |
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| 120 | ! |
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| 121 | !-- Stable stratification |
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| 122 | ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / ( & |
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| 123 | LOG( z_p / z0(j,i) ) + & |
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| 124 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
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| 125 | ) |
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| 126 | ELSE |
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| 127 | ! |
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| 128 | !-- Unstable stratification |
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| 129 | a = SQRT( 1.0 - 16.0 * rif(j,i) ) |
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| 130 | b = SQRT( 1.0 - 16.0 * rif(j,i) / z_p * z0(j,i) ) |
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| 131 | ! |
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| 132 | !-- If a borderline case occurs, the formula for stable |
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| 133 | !-- stratification must be used anyway, or else a zero division |
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| 134 | !-- would occur in the argument of the logarithm |
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| 135 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
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| 136 | ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / ( & |
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| 137 | LOG( z_p / z0(j,i) ) + & |
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| 138 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
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| 139 | ) |
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| 140 | ELSE |
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| 141 | ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / ( & |
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| 142 | LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) & |
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| 143 | ) |
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| 144 | ENDIF |
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| 145 | ENDIF |
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| 146 | |
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| 147 | ENDDO |
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| 148 | ENDDO |
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| 149 | ENDIF |
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| 150 | |
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| 151 | ! |
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| 152 | !-- Compute z_p/L (corresponds to the Richardson-flux number) |
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| 153 | IF ( .NOT. moisture ) THEN |
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| 154 | !$OMP PARALLEL DO PRIVATE( k, z_p ) |
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| 155 | DO i = nxl-1, nxr+1 |
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| 156 | DO j = nys-1, nyn+1 |
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| 157 | k = nzb_s_inner(j,i) |
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| 158 | z_p = zu(k+1) - zw(k) |
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| 159 | rif(j,i) = z_p * kappa * g * ts(j,i) / & |
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| 160 | ( pt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) ) |
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| 161 | ! |
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| 162 | !-- Limit the value range of the Richardson numbers. |
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| 163 | !-- This is necessary for very small velocities (u,v --> 0), because |
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| 164 | !-- the absolute value of rif can then become very large, which in |
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| 165 | !-- consequence would result in very large shear stresses and very |
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| 166 | !-- small momentum fluxes (both are generally unrealistic). |
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| 167 | IF ( rif(j,i) < rif_min ) rif(j,i) = rif_min |
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| 168 | IF ( rif(j,i) > rif_max ) rif(j,i) = rif_max |
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| 169 | ENDDO |
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| 170 | ENDDO |
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| 171 | ELSE |
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| 172 | !$OMP PARALLEL DO PRIVATE( k, z_p ) |
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| 173 | DO i = nxl-1, nxr+1 |
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| 174 | DO j = nys-1, nyn+1 |
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| 175 | k = nzb_s_inner(j,i) |
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| 176 | z_p = zu(k+1) - zw(k) |
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| 177 | rif(j,i) = z_p * kappa * g * & |
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| 178 | ( ts(j,i) + 0.61 * pt(k+1,j,i) * qs(j,i) ) / & |
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| 179 | ( vpt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) ) |
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| 180 | ! |
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| 181 | !-- Limit the value range of the Richardson numbers. |
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| 182 | !-- This is necessary for very small velocities (u,v --> 0), because |
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| 183 | !-- the absolute value of rif can then become very large, which in |
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| 184 | !-- consequence would result in very large shear stresses and very |
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| 185 | !-- small momentum fluxes (both are generally unrealistic). |
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| 186 | IF ( rif(j,i) < rif_min ) rif(j,i) = rif_min |
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| 187 | IF ( rif(j,i) > rif_max ) rif(j,i) = rif_max |
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| 188 | ENDDO |
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| 189 | ENDDO |
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| 190 | ENDIF |
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| 191 | |
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| 192 | ! |
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| 193 | !-- Compute u* at the scalars' grid points |
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| 194 | !$OMP PARALLEL DO PRIVATE( a, b, k, uv_total, z_p ) |
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| 195 | DO i = nxl, nxr |
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| 196 | DO j = nys, nyn |
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| 197 | |
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| 198 | k = nzb_s_inner(j,i) |
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| 199 | z_p = zu(k+1) - zw(k) |
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| 200 | |
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| 201 | ! |
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| 202 | !-- Compute the absolute value of the horizontal velocity |
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| 203 | uv_total = SQRT( ( 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) ) )**2 + & |
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| 204 | ( 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) ) )**2 & |
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| 205 | ) |
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| 206 | |
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| 207 | IF ( rif(j,i) >= 0.0 ) THEN |
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| 208 | ! |
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| 209 | !-- Stable stratification |
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| 210 | us(j,i) = kappa * uv_total / ( & |
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| 211 | LOG( z_p / z0(j,i) ) + & |
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| 212 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
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| 213 | ) |
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| 214 | ELSE |
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| 215 | ! |
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| 216 | !-- Unstable stratification |
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| 217 | a = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif(j,i) ) ) |
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| 218 | b = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rif(j,i) / z_p * z0(j,i) ) ) |
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| 219 | ! |
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| 220 | !-- If a borderline case occurs, the formula for stable stratification |
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| 221 | !-- must be used anyway, or else a zero division would occur in the |
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| 222 | !-- argument of the logarithm. |
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| 223 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
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| 224 | us(j,i) = kappa * uv_total / ( & |
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| 225 | LOG( z_p / z0(j,i) ) + & |
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| 226 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
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| 227 | ) |
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| 228 | ELSE |
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| 229 | us(j,i) = kappa * uv_total / ( & |
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| 230 | LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) + & |
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| 231 | 2.0 * ( ATAN( b ) - ATAN( a ) ) & |
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| 232 | ) |
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| 233 | ENDIF |
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| 234 | ENDIF |
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| 235 | ENDDO |
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| 236 | ENDDO |
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| 237 | |
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| 238 | ! |
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| 239 | !-- Compute u'w' for the total model domain. |
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| 240 | !-- First compute the corresponding component of u* and square it. |
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| 241 | !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p ) |
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| 242 | DO i = nxl, nxr |
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| 243 | DO j = nys, nyn |
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| 244 | |
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| 245 | k = nzb_u_inner(j,i) |
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| 246 | z_p = zu(k+1) - zw(k) |
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| 247 | |
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| 248 | ! |
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| 249 | !-- Compute Richardson-flux number for this point |
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| 250 | rifm = 0.5 * ( rif(j,i-1) + rif(j,i) ) |
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| 251 | IF ( rifm >= 0.0 ) THEN |
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| 252 | ! |
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| 253 | !-- Stable stratification |
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| 254 | usws(j,i) = kappa * u(k+1,j,i) / ( & |
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| 255 | LOG( z_p / z0(j,i) ) + & |
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| 256 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
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| 257 | ) |
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| 258 | ELSE |
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| 259 | ! |
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| 260 | !-- Unstable stratification |
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| 261 | a = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifm ) ) |
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| 262 | b = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) ) |
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| 263 | ! |
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| 264 | !-- If a borderline case occurs, the formula for stable stratification |
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| 265 | !-- must be used anyway, or else a zero division would occur in the |
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| 266 | !-- argument of the logarithm. |
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| 267 | IF ( a == 1.0 .OR. B == 1.0 ) THEN |
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| 268 | usws(j,i) = kappa * u(k+1,j,i) / ( & |
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| 269 | LOG( z_p / z0(j,i) ) + & |
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| 270 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
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| 271 | ) |
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| 272 | ELSE |
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| 273 | usws(j,i) = kappa * u(k+1,j,i) / ( & |
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| 274 | LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) + & |
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| 275 | 2.0 * ( ATAN( b ) - ATAN( a ) ) & |
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| 276 | ) |
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| 277 | ENDIF |
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| 278 | ENDIF |
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| 279 | usws(j,i) = -usws(j,i) * ABS( usws(j,i) ) |
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| 280 | ENDDO |
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| 281 | ENDDO |
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| 282 | |
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| 283 | ! |
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| 284 | !-- Compute v'w' for the total model domain. |
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| 285 | !-- First compute the corresponding component of u* and square it. |
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| 286 | !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p ) |
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| 287 | DO i = nxl, nxr |
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| 288 | DO j = nys, nyn |
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| 289 | |
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| 290 | k = nzb_v_inner(j,i) |
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| 291 | z_p = zu(k+1) - zw(k) |
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| 292 | |
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| 293 | ! |
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| 294 | !-- Compute Richardson-flux number for this point |
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| 295 | rifm = 0.5 * ( rif(j-1,i) + rif(j,i) ) |
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| 296 | IF ( rifm >= 0.0 ) THEN |
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| 297 | ! |
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| 298 | !-- Stable stratification |
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| 299 | vsws(j,i) = kappa * v(k+1,j,i) / ( & |
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| 300 | LOG( z_p / z0(j,i) ) + & |
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| 301 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
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| 302 | ) |
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| 303 | ELSE |
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| 304 | ! |
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| 305 | !-- Unstable stratification |
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| 306 | a = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifm ) ) |
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| 307 | b = 1.0 / SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) ) |
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| 308 | ! |
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| 309 | !-- If a borderline case occurs, the formula for stable stratification |
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| 310 | !-- must be used anyway, or else a zero division would occur in the |
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| 311 | !-- argument of the logarithm. |
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| 312 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
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| 313 | vsws(j,i) = kappa * v(k+1,j,i) / ( & |
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| 314 | LOG( z_p / z0(j,i) ) + & |
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| 315 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
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| 316 | ) |
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| 317 | ELSE |
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| 318 | vsws(j,i) = kappa * v(k+1,j,i) / ( & |
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| 319 | LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) + & |
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| 320 | 2.0 * ( ATAN( b ) - ATAN( a ) ) & |
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| 321 | ) |
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| 322 | ENDIF |
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| 323 | ENDIF |
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| 324 | vsws(j,i) = -vsws(j,i) * ABS( vsws(j,i) ) |
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| 325 | ENDDO |
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| 326 | ENDDO |
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| 327 | |
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| 328 | ! |
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| 329 | !-- If required compute q* |
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| 330 | IF ( moisture .OR. passive_scalar ) THEN |
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| 331 | IF ( constant_waterflux ) THEN |
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| 332 | ! |
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| 333 | !-- For a given water flux in the Prandtl layer: |
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| 334 | !$OMP PARALLEL DO |
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| 335 | DO i = nxl-1, nxr+1 |
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| 336 | DO j = nys-1, nyn+1 |
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| 337 | qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30 ) |
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| 338 | ENDDO |
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| 339 | ENDDO |
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| 340 | |
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| 341 | ELSE |
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| 342 | !$OMP PARALLEL DO PRIVATE( a, b, k, z_p ) |
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| 343 | DO i = nxl-1, nxr+1 |
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| 344 | DO j = nys-1, nyn+1 |
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| 345 | |
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| 346 | k = nzb_s_inner(j,i) |
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| 347 | z_p = zu(k+1) - zw(k) |
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| 348 | |
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| 349 | IF ( rif(j,i) >= 0.0 ) THEN |
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| 350 | ! |
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| 351 | !-- Stable stratification |
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| 352 | qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / ( & |
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| 353 | LOG( z_p / z0(j,i) ) + & |
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| 354 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
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| 355 | ) |
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| 356 | ELSE |
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| 357 | ! |
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| 358 | !-- Unstable stratification |
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| 359 | a = SQRT( 1.0 - 16.0 * rif(j,i) ) |
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| 360 | b = SQRT( 1.0 - 16.0 * rif(j,i) / z_p * z0(j,i) ) |
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| 361 | ! |
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| 362 | !-- If a borderline case occurs, the formula for stable |
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| 363 | !-- stratification must be used anyway, or else a zero division |
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| 364 | !-- would occur in the argument of the logarithm. |
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| 365 | IF ( a == 1.0 .OR. b == 1.0 ) THEN |
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| 366 | qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / ( & |
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| 367 | LOG( z_p / z0(j,i) ) + & |
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| 368 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
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| 369 | ) |
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| 370 | ELSE |
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| 371 | qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / ( & |
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| 372 | LOG( (1.0+b) / (1.0-b) * (1.0-a) / (1.0+a) ) & |
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| 373 | ) |
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| 374 | ENDIF |
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| 375 | ENDIF |
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| 376 | |
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| 377 | ENDDO |
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| 378 | ENDDO |
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| 379 | ENDIF |
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| 380 | ENDIF |
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| 381 | |
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| 382 | ! |
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| 383 | !-- Exchange the boundaries for u* and the momentum fluxes (fluxes only for |
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| 384 | !-- completeness's sake). |
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| 385 | CALL exchange_horiz_2d( us ) |
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| 386 | CALL exchange_horiz_2d( usws ) |
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| 387 | CALL exchange_horiz_2d( vsws ) |
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| 388 | IF ( moisture .OR. passive_scalar ) CALL exchange_horiz_2d( qsws ) |
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| 389 | |
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| 390 | ! |
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| 391 | !-- Compute the vertical kinematic heat flux |
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| 392 | IF ( .NOT. constant_heatflux ) THEN |
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| 393 | !$OMP PARALLEL DO |
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| 394 | DO i = nxl-1, nxr+1 |
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| 395 | DO j = nys-1, nyn+1 |
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| 396 | shf(j,i) = -ts(j,i) * us(j,i) |
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| 397 | ENDDO |
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| 398 | ENDDO |
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| 399 | ENDIF |
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| 400 | |
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| 401 | ! |
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| 402 | !-- Compute the vertical water/scalar flux |
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| 403 | IF ( .NOT. constant_heatflux .AND. ( moisture .OR. passive_scalar ) ) THEN |
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| 404 | !$OMP PARALLEL DO |
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| 405 | DO i = nxl-1, nxr+1 |
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| 406 | DO j = nys-1, nyn+1 |
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| 407 | qsws(j,i) = -qs(j,i) * us(j,i) |
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| 408 | ENDDO |
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| 409 | ENDDO |
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| 410 | ENDIF |
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| 411 | |
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| 412 | ! |
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| 413 | !-- Bottom boundary condition for the TKE |
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| 414 | IF ( ibc_e_b == 2 ) THEN |
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| 415 | !$OMP PARALLEL DO |
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| 416 | DO i = nxl-1, nxr+1 |
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| 417 | DO j = nys-1, nyn+1 |
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| 418 | e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1 )**2 |
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| 419 | ! |
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| 420 | !-- As a test: cm = 0.4 |
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| 421 | ! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4 )**2 |
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| 422 | e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i) |
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| 423 | ENDDO |
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| 424 | ENDDO |
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| 425 | ENDIF |
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| 426 | |
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| 427 | |
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| 428 | END SUBROUTINE prandtl_fluxes |
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