| 1 | SUBROUTINE prandtl_fluxes |
|---|
| 2 | |
|---|
| 3 | !------------------------------------------------------------------------------! |
|---|
| 4 | ! Current revisions: |
|---|
| 5 | ! ----------------- |
|---|
| 6 | ! |
|---|
| 7 | ! |
|---|
| 8 | ! Former revisions: |
|---|
| 9 | ! ----------------- |
|---|
| 10 | ! $Id: prandtl_fluxes.f90 979 2012-08-09 08:50:11Z hoffmann $ |
|---|
| 11 | ! |
|---|
| 12 | ! 978 2012-08-09 08:28:32Z fricke |
|---|
| 13 | ! roughness length for scalar quantities z0h added |
|---|
| 14 | ! |
|---|
| 15 | ! 759 2011-09-15 13:58:31Z raasch |
|---|
| 16 | ! Bugfix for ts limitation |
|---|
| 17 | ! |
|---|
| 18 | ! 709 2011-03-30 09:31:40Z raasch |
|---|
| 19 | ! formatting adjustments |
|---|
| 20 | ! |
|---|
| 21 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
|---|
| 22 | ! Changed surface boundary conditions for u and v from mirror to Dirichlet. |
|---|
| 23 | ! Therefore u(uzb,:,:) and v(nzb,:,:) are now representative for height z0. |
|---|
| 24 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
|---|
| 25 | ! |
|---|
| 26 | ! 315 2009-05-13 10:57:59Z raasch |
|---|
| 27 | ! Saturation condition at (sea) surface is not used in precursor runs (only |
|---|
| 28 | ! in the following coupled runs) |
|---|
| 29 | ! Bugfix: qsws was calculated in case of constant heatflux = .FALSE. |
|---|
| 30 | ! |
|---|
| 31 | ! 187 2008-08-06 16:25:09Z letzel |
|---|
| 32 | ! Bugfix: modification of the calculation of the vertical turbulent momentum |
|---|
| 33 | ! fluxes u'w' and v'w' |
|---|
| 34 | ! Bugfix: change definition of us_wall from 1D to 2D |
|---|
| 35 | ! Change: modification of the integrated version of the profile function for |
|---|
| 36 | ! momentum for unstable stratification (does not effect results) |
|---|
| 37 | ! |
|---|
| 38 | ! 108 2007-08-24 15:10:38Z letzel |
|---|
| 39 | ! assume saturation at k=nzb_s_inner(j,i) for atmosphere coupled to ocean |
|---|
| 40 | ! |
|---|
| 41 | ! 75 2007-03-22 09:54:05Z raasch |
|---|
| 42 | ! moisture renamed humidity |
|---|
| 43 | ! |
|---|
| 44 | ! RCS Log replace by Id keyword, revision history cleaned up |
|---|
| 45 | ! |
|---|
| 46 | ! Revision 1.19 2006/04/26 12:24:35 raasch |
|---|
| 47 | ! +OpenMP directives and optimization (array assignments replaced by DO loops) |
|---|
| 48 | ! |
|---|
| 49 | ! Revision 1.1 1998/01/23 10:06:06 raasch |
|---|
| 50 | ! Initial revision |
|---|
| 51 | ! |
|---|
| 52 | ! |
|---|
| 53 | ! Description: |
|---|
| 54 | ! ------------ |
|---|
| 55 | ! Diagnostic computation of vertical fluxes in the Prandtl layer from the |
|---|
| 56 | ! values of the variables at grid point k=1 |
|---|
| 57 | !------------------------------------------------------------------------------! |
|---|
| 58 | |
|---|
| 59 | USE arrays_3d |
|---|
| 60 | USE control_parameters |
|---|
| 61 | USE grid_variables |
|---|
| 62 | USE indices |
|---|
| 63 | |
|---|
| 64 | IMPLICIT NONE |
|---|
| 65 | |
|---|
| 66 | INTEGER :: i, j, k |
|---|
| 67 | REAL :: a, b, e_q, rifm, uv_total, z_p |
|---|
| 68 | |
|---|
| 69 | ! |
|---|
| 70 | !-- Compute theta* |
|---|
| 71 | IF ( constant_heatflux ) THEN |
|---|
| 72 | ! |
|---|
| 73 | !-- For a given heat flux in the Prandtl layer: |
|---|
| 74 | !-- for u* use the value from the previous time step |
|---|
| 75 | !$OMP PARALLEL DO |
|---|
| 76 | DO i = nxlg, nxrg |
|---|
| 77 | DO j = nysg, nyng |
|---|
| 78 | ts(j,i) = -shf(j,i) / ( us(j,i) + 1E-30 ) |
|---|
| 79 | ! |
|---|
| 80 | !-- ts must be limited, because otherwise overflow may occur in case of |
|---|
| 81 | !-- us=0 when computing rif further below |
|---|
| 82 | IF ( ts(j,i) < -1.05E5 ) ts(j,i) = -1.0E5 |
|---|
| 83 | IF ( ts(j,i) > 1.0E5 ) ts(j,i) = 1.0E5 |
|---|
| 84 | ENDDO |
|---|
| 85 | ENDDO |
|---|
| 86 | |
|---|
| 87 | ELSE |
|---|
| 88 | ! |
|---|
| 89 | !-- For a given surface temperature: |
|---|
| 90 | !-- (the Richardson number is still the one from the previous time step) |
|---|
| 91 | !$OMP PARALLEL DO PRIVATE( a, b, k, z_p ) |
|---|
| 92 | DO i = nxlg, nxrg |
|---|
| 93 | DO j = nysg, nyng |
|---|
| 94 | |
|---|
| 95 | k = nzb_s_inner(j,i) |
|---|
| 96 | z_p = zu(k+1) - zw(k) |
|---|
| 97 | |
|---|
| 98 | IF ( rif(j,i) >= 0.0 ) THEN |
|---|
| 99 | ! |
|---|
| 100 | !-- Stable stratification |
|---|
| 101 | ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / ( & |
|---|
| 102 | LOG( z_p / z0h(j,i) ) + & |
|---|
| 103 | 5.0 * rif(j,i) * ( z_p - z0h(j,i) ) / z_p & |
|---|
| 104 | ) |
|---|
| 105 | ELSE |
|---|
| 106 | ! |
|---|
| 107 | !-- Unstable stratification |
|---|
| 108 | a = SQRT( 1.0 - 16.0 * rif(j,i) ) |
|---|
| 109 | b = SQRT( 1.0 - 16.0 * rif(j,i) * z0h(j,i) / z_p ) |
|---|
| 110 | |
|---|
| 111 | ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) / ( & |
|---|
| 112 | LOG( z_p / z0h(j,i) ) - & |
|---|
| 113 | 2.0 * LOG( ( 1.0 + a ) / ( 1.0 + b ) ) ) |
|---|
| 114 | ENDIF |
|---|
| 115 | |
|---|
| 116 | ENDDO |
|---|
| 117 | ENDDO |
|---|
| 118 | ENDIF |
|---|
| 119 | |
|---|
| 120 | ! |
|---|
| 121 | !-- Compute z_p/L (corresponds to the Richardson-flux number) |
|---|
| 122 | IF ( .NOT. humidity ) THEN |
|---|
| 123 | !$OMP PARALLEL DO PRIVATE( k, z_p ) |
|---|
| 124 | DO i = nxlg, nxrg |
|---|
| 125 | DO j = nysg, nyng |
|---|
| 126 | k = nzb_s_inner(j,i) |
|---|
| 127 | z_p = zu(k+1) - zw(k) |
|---|
| 128 | rif(j,i) = z_p * kappa * g * ts(j,i) / & |
|---|
| 129 | ( pt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) ) |
|---|
| 130 | ! |
|---|
| 131 | !-- Limit the value range of the Richardson numbers. |
|---|
| 132 | !-- This is necessary for very small velocities (u,v --> 0), because |
|---|
| 133 | !-- the absolute value of rif can then become very large, which in |
|---|
| 134 | !-- consequence would result in very large shear stresses and very |
|---|
| 135 | !-- small momentum fluxes (both are generally unrealistic). |
|---|
| 136 | IF ( rif(j,i) < rif_min ) rif(j,i) = rif_min |
|---|
| 137 | IF ( rif(j,i) > rif_max ) rif(j,i) = rif_max |
|---|
| 138 | ENDDO |
|---|
| 139 | ENDDO |
|---|
| 140 | ELSE |
|---|
| 141 | !$OMP PARALLEL DO PRIVATE( k, z_p ) |
|---|
| 142 | DO i = nxlg, nxrg |
|---|
| 143 | DO j = nysg, nyng |
|---|
| 144 | k = nzb_s_inner(j,i) |
|---|
| 145 | z_p = zu(k+1) - zw(k) |
|---|
| 146 | rif(j,i) = z_p * kappa * g * & |
|---|
| 147 | ( ts(j,i) + 0.61 * pt(k+1,j,i) * qs(j,i) ) / & |
|---|
| 148 | ( vpt(k+1,j,i) * ( us(j,i)**2 + 1E-30 ) ) |
|---|
| 149 | ! |
|---|
| 150 | !-- Limit the value range of the Richardson numbers. |
|---|
| 151 | !-- This is necessary for very small velocities (u,v --> 0), because |
|---|
| 152 | !-- the absolute value of rif can then become very large, which in |
|---|
| 153 | !-- consequence would result in very large shear stresses and very |
|---|
| 154 | !-- small momentum fluxes (both are generally unrealistic). |
|---|
| 155 | IF ( rif(j,i) < rif_min ) rif(j,i) = rif_min |
|---|
| 156 | IF ( rif(j,i) > rif_max ) rif(j,i) = rif_max |
|---|
| 157 | ENDDO |
|---|
| 158 | ENDDO |
|---|
| 159 | ENDIF |
|---|
| 160 | |
|---|
| 161 | ! |
|---|
| 162 | !-- Compute u* at the scalars' grid points |
|---|
| 163 | !$OMP PARALLEL DO PRIVATE( a, b, k, uv_total, z_p ) |
|---|
| 164 | DO i = nxl, nxr |
|---|
| 165 | DO j = nys, nyn |
|---|
| 166 | |
|---|
| 167 | k = nzb_s_inner(j,i) |
|---|
| 168 | z_p = zu(k+1) - zw(k) |
|---|
| 169 | |
|---|
| 170 | ! |
|---|
| 171 | !-- Compute the absolute value of the horizontal velocity |
|---|
| 172 | !-- (relative to the surface) |
|---|
| 173 | uv_total = SQRT( ( 0.5 * ( u(k+1,j,i) + u(k+1,j,i+1) & |
|---|
| 174 | - u(k,j,i) - u(k,j,i+1) ) )**2 + & |
|---|
| 175 | ( 0.5 * ( v(k+1,j,i) + v(k+1,j+1,i) & |
|---|
| 176 | - v(k,j,i) - v(k,j+1,i) ) )**2 ) |
|---|
| 177 | |
|---|
| 178 | |
|---|
| 179 | IF ( rif(j,i) >= 0.0 ) THEN |
|---|
| 180 | ! |
|---|
| 181 | !-- Stable stratification |
|---|
| 182 | us(j,i) = kappa * uv_total / ( & |
|---|
| 183 | LOG( z_p / z0(j,i) ) + & |
|---|
| 184 | 5.0 * rif(j,i) * ( z_p - z0(j,i) ) / z_p & |
|---|
| 185 | ) |
|---|
| 186 | ELSE |
|---|
| 187 | ! |
|---|
| 188 | !-- Unstable stratification |
|---|
| 189 | a = SQRT( SQRT( 1.0 - 16.0 * rif(j,i) ) ) |
|---|
| 190 | b = SQRT( SQRT( 1.0 - 16.0 * rif(j,i) / z_p * z0(j,i) ) ) |
|---|
| 191 | |
|---|
| 192 | us(j,i) = kappa * uv_total / ( & |
|---|
| 193 | LOG( z_p / z0(j,i) ) - & |
|---|
| 194 | LOG( ( 1.0 + a )**2 * ( 1.0 + a**2 ) / ( & |
|---|
| 195 | ( 1.0 + b )**2 * ( 1.0 + b**2 ) ) ) + & |
|---|
| 196 | 2.0 * ( ATAN( a ) - ATAN( b ) ) & |
|---|
| 197 | ) |
|---|
| 198 | ENDIF |
|---|
| 199 | ENDDO |
|---|
| 200 | ENDDO |
|---|
| 201 | |
|---|
| 202 | ! |
|---|
| 203 | !-- Values of us at ghost point locations are needed for the evaluation of usws |
|---|
| 204 | !-- and vsws. |
|---|
| 205 | CALL exchange_horiz_2d( us ) |
|---|
| 206 | ! |
|---|
| 207 | !-- Compute u'w' for the total model domain. |
|---|
| 208 | !-- First compute the corresponding component of u* and square it. |
|---|
| 209 | !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p ) |
|---|
| 210 | DO i = nxl, nxr |
|---|
| 211 | DO j = nys, nyn |
|---|
| 212 | |
|---|
| 213 | k = nzb_u_inner(j,i) |
|---|
| 214 | z_p = zu(k+1) - zw(k) |
|---|
| 215 | |
|---|
| 216 | ! |
|---|
| 217 | !-- Compute Richardson-flux number for this point |
|---|
| 218 | rifm = 0.5 * ( rif(j,i-1) + rif(j,i) ) |
|---|
| 219 | IF ( rifm >= 0.0 ) THEN |
|---|
| 220 | ! |
|---|
| 221 | !-- Stable stratification |
|---|
| 222 | usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) )/ ( & |
|---|
| 223 | LOG( z_p / z0(j,i) ) + & |
|---|
| 224 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
|---|
| 225 | ) |
|---|
| 226 | ELSE |
|---|
| 227 | ! |
|---|
| 228 | !-- Unstable stratification |
|---|
| 229 | a = SQRT( SQRT( 1.0 - 16.0 * rifm ) ) |
|---|
| 230 | b = SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) ) |
|---|
| 231 | |
|---|
| 232 | usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) / ( & |
|---|
| 233 | LOG( z_p / z0(j,i) ) - & |
|---|
| 234 | LOG( (1.0 + a )**2 * ( 1.0 + a**2 ) / ( & |
|---|
| 235 | (1.0 + b )**2 * ( 1.0 + b**2 ) ) ) + & |
|---|
| 236 | 2.0 * ( ATAN( a ) - ATAN( b ) ) & |
|---|
| 237 | ) |
|---|
| 238 | ENDIF |
|---|
| 239 | usws(j,i) = -usws(j,i) * 0.5 * ( us(j,i-1) + us(j,i) ) |
|---|
| 240 | ENDDO |
|---|
| 241 | ENDDO |
|---|
| 242 | |
|---|
| 243 | ! |
|---|
| 244 | !-- Compute v'w' for the total model domain. |
|---|
| 245 | !-- First compute the corresponding component of u* and square it. |
|---|
| 246 | !$OMP PARALLEL DO PRIVATE( a, b, k, rifm, z_p ) |
|---|
| 247 | DO i = nxl, nxr |
|---|
| 248 | DO j = nys, nyn |
|---|
| 249 | |
|---|
| 250 | k = nzb_v_inner(j,i) |
|---|
| 251 | z_p = zu(k+1) - zw(k) |
|---|
| 252 | |
|---|
| 253 | ! |
|---|
| 254 | !-- Compute Richardson-flux number for this point |
|---|
| 255 | rifm = 0.5 * ( rif(j-1,i) + rif(j,i) ) |
|---|
| 256 | IF ( rifm >= 0.0 ) THEN |
|---|
| 257 | ! |
|---|
| 258 | !-- Stable stratification |
|---|
| 259 | vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) / ( & |
|---|
| 260 | LOG( z_p / z0(j,i) ) + & |
|---|
| 261 | 5.0 * rifm * ( z_p - z0(j,i) ) / z_p & |
|---|
| 262 | ) |
|---|
| 263 | ELSE |
|---|
| 264 | ! |
|---|
| 265 | !-- Unstable stratification |
|---|
| 266 | a = SQRT( SQRT( 1.0 - 16.0 * rifm ) ) |
|---|
| 267 | b = SQRT( SQRT( 1.0 - 16.0 * rifm / z_p * z0(j,i) ) ) |
|---|
| 268 | |
|---|
| 269 | vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) / ( & |
|---|
| 270 | LOG( z_p / z0(j,i) ) - & |
|---|
| 271 | LOG( (1.0 + a )**2 * ( 1.0 + a**2 ) / ( & |
|---|
| 272 | (1.0 + b )**2 * ( 1.0 + b**2 ) ) ) + & |
|---|
| 273 | 2.0 * ( ATAN( a ) - ATAN( b ) ) & |
|---|
| 274 | ) |
|---|
| 275 | ENDIF |
|---|
| 276 | vsws(j,i) = -vsws(j,i) * 0.5 * ( us(j-1,i) + us(j,i) ) |
|---|
| 277 | ENDDO |
|---|
| 278 | ENDDO |
|---|
| 279 | |
|---|
| 280 | ! |
|---|
| 281 | !-- If required compute q* |
|---|
| 282 | IF ( humidity .OR. passive_scalar ) THEN |
|---|
| 283 | IF ( constant_waterflux ) THEN |
|---|
| 284 | ! |
|---|
| 285 | !-- For a given water flux in the Prandtl layer: |
|---|
| 286 | !$OMP PARALLEL DO |
|---|
| 287 | DO i = nxlg, nxrg |
|---|
| 288 | DO j = nysg, nyng |
|---|
| 289 | qs(j,i) = -qsws(j,i) / ( us(j,i) + 1E-30 ) |
|---|
| 290 | ENDDO |
|---|
| 291 | ENDDO |
|---|
| 292 | |
|---|
| 293 | ELSE |
|---|
| 294 | !$OMP PARALLEL DO PRIVATE( a, b, k, z_p ) |
|---|
| 295 | DO i = nxlg, nxrg |
|---|
| 296 | DO j = nysg, nyng |
|---|
| 297 | |
|---|
| 298 | k = nzb_s_inner(j,i) |
|---|
| 299 | z_p = zu(k+1) - zw(k) |
|---|
| 300 | |
|---|
| 301 | ! |
|---|
| 302 | !-- Assume saturation for atmosphere coupled to ocean (but not |
|---|
| 303 | !-- in case of precursor runs) |
|---|
| 304 | IF ( coupling_mode == 'atmosphere_to_ocean' .AND. run_coupled )& |
|---|
| 305 | THEN |
|---|
| 306 | e_q = 6.1 * & |
|---|
| 307 | EXP( 0.07 * ( MIN(pt(0,j,i),pt(1,j,i)) - 273.15 ) ) |
|---|
| 308 | q(k,j,i) = 0.622 * e_q / ( surface_pressure - e_q ) |
|---|
| 309 | ENDIF |
|---|
| 310 | IF ( rif(j,i) >= 0.0 ) THEN |
|---|
| 311 | ! |
|---|
| 312 | !-- Stable stratification |
|---|
| 313 | qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / ( & |
|---|
| 314 | LOG( z_p / z0h(j,i) ) + & |
|---|
| 315 | 5.0 * rif(j,i) * ( z_p - z0h(j,i) ) / z_p & |
|---|
| 316 | ) |
|---|
| 317 | ELSE |
|---|
| 318 | ! |
|---|
| 319 | !-- Unstable stratification |
|---|
| 320 | a = SQRT( 1.0 - 16.0 * rif(j,i) ) |
|---|
| 321 | b = SQRT( 1.0 - 16.0 * rif(j,i) * z0h(j,i) / z_p ) |
|---|
| 322 | |
|---|
| 323 | qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) / ( & |
|---|
| 324 | LOG( z_p / z0h(j,i) ) - & |
|---|
| 325 | 2.0 * LOG( (1.0 + a ) / ( 1.0 + b ) ) ) |
|---|
| 326 | ENDIF |
|---|
| 327 | |
|---|
| 328 | ENDDO |
|---|
| 329 | ENDDO |
|---|
| 330 | ENDIF |
|---|
| 331 | ENDIF |
|---|
| 332 | |
|---|
| 333 | ! |
|---|
| 334 | !-- Exchange the boundaries for the momentum fluxes (only for sake of |
|---|
| 335 | !-- completeness) |
|---|
| 336 | CALL exchange_horiz_2d( usws ) |
|---|
| 337 | CALL exchange_horiz_2d( vsws ) |
|---|
| 338 | IF ( humidity .OR. passive_scalar ) CALL exchange_horiz_2d( qsws ) |
|---|
| 339 | |
|---|
| 340 | ! |
|---|
| 341 | !-- Compute the vertical kinematic heat flux |
|---|
| 342 | IF ( .NOT. constant_heatflux ) THEN |
|---|
| 343 | !$OMP PARALLEL DO |
|---|
| 344 | DO i = nxlg, nxrg |
|---|
| 345 | DO j = nysg, nyng |
|---|
| 346 | shf(j,i) = -ts(j,i) * us(j,i) |
|---|
| 347 | ENDDO |
|---|
| 348 | ENDDO |
|---|
| 349 | ENDIF |
|---|
| 350 | |
|---|
| 351 | ! |
|---|
| 352 | !-- Compute the vertical water/scalar flux |
|---|
| 353 | IF ( .NOT. constant_waterflux .AND. ( humidity .OR. passive_scalar ) ) THEN |
|---|
| 354 | !$OMP PARALLEL DO |
|---|
| 355 | DO i = nxlg, nxrg |
|---|
| 356 | DO j = nysg, nyng |
|---|
| 357 | qsws(j,i) = -qs(j,i) * us(j,i) |
|---|
| 358 | ENDDO |
|---|
| 359 | ENDDO |
|---|
| 360 | ENDIF |
|---|
| 361 | |
|---|
| 362 | ! |
|---|
| 363 | !-- Bottom boundary condition for the TKE |
|---|
| 364 | IF ( ibc_e_b == 2 ) THEN |
|---|
| 365 | !$OMP PARALLEL DO |
|---|
| 366 | DO i = nxlg, nxrg |
|---|
| 367 | DO j = nysg, nyng |
|---|
| 368 | e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.1 )**2 |
|---|
| 369 | ! |
|---|
| 370 | !-- As a test: cm = 0.4 |
|---|
| 371 | ! e(nzb_s_inner(j,i)+1,j,i) = ( us(j,i) / 0.4 )**2 |
|---|
| 372 | e(nzb_s_inner(j,i),j,i) = e(nzb_s_inner(j,i)+1,j,i) |
|---|
| 373 | ENDDO |
|---|
| 374 | ENDDO |
|---|
| 375 | ENDIF |
|---|
| 376 | |
|---|
| 377 | |
|---|
| 378 | END SUBROUTINE prandtl_fluxes |
|---|
