| 1 | SUBROUTINE lpm_droplet_condensation |
|---|
| 2 | |
|---|
| 3 | !------------------------------------------------------------------------------! |
|---|
| 4 | ! Current revisions: |
|---|
| 5 | ! ------------------ |
|---|
| 6 | ! message text "advec_particles" replaced by " lpm_droplet_condensation" |
|---|
| 7 | ! |
|---|
| 8 | ! Former revisions: |
|---|
| 9 | ! ----------------- |
|---|
| 10 | ! $Id: lpm_droplet_condensation.f90 849 2012-03-15 10:35:09Z raasch $ |
|---|
| 11 | ! |
|---|
| 12 | ! |
|---|
| 13 | ! Description: |
|---|
| 14 | ! ------------ |
|---|
| 15 | ! Calculates change in droplet radius by condensation/evaporation, using |
|---|
| 16 | ! either an analytic formula or by numerically integrating the radius growth |
|---|
| 17 | ! equation including curvature and solution effects using Rosenbrocks method |
|---|
| 18 | ! (see Numerical recipes in FORTRAN, 2nd edition, p. 731). |
|---|
| 19 | ! The analytical formula and growth equation follow those given in |
|---|
| 20 | ! Rogers and Yau (A short course in cloud physics, 3rd edition, p. 102/103). |
|---|
| 21 | !------------------------------------------------------------------------------! |
|---|
| 22 | |
|---|
| 23 | USE arrays_3d |
|---|
| 24 | USE cloud_parameters |
|---|
| 25 | USE constants |
|---|
| 26 | USE control_parameters |
|---|
| 27 | USE cpulog |
|---|
| 28 | USE grid_variables |
|---|
| 29 | USE interfaces |
|---|
| 30 | USE lpm_collision_kernels_mod |
|---|
| 31 | USE particle_attributes |
|---|
| 32 | |
|---|
| 33 | IMPLICIT NONE |
|---|
| 34 | |
|---|
| 35 | INTEGER :: i, internal_timestep_count, j, jtry, k, n |
|---|
| 36 | |
|---|
| 37 | INTEGER, PARAMETER :: maxtry = 40 |
|---|
| 38 | |
|---|
| 39 | REAL :: aa, afactor, arg, bb, cc, dd, ddenom, delta_r, drdt, drdt_ini, & |
|---|
| 40 | drdt_m, dt_ros, dt_ros_last, dt_ros_next, dt_ros_sum, & |
|---|
| 41 | dt_ros_sum_ini, d2rdtdr, d2rdt2, errmax, err_ros, g1, g2, g3, g4, & |
|---|
| 42 | e_a, e_s, gg, new_r, p_int, pt_int, pt_int_l, pt_int_u, q_int, & |
|---|
| 43 | q_int_l, q_int_u, ql_int, ql_int_l, ql_int_u, r_ros, r_ros_ini, & |
|---|
| 44 | sigma, t_int, x, y |
|---|
| 45 | |
|---|
| 46 | ! |
|---|
| 47 | !-- Parameters for Rosenbrock method |
|---|
| 48 | REAL, PARAMETER :: a21 = 2.0, a31 = 48.0/25.0, a32 = 6.0/25.0, & |
|---|
| 49 | a2x = 1.0, a3x = 3.0/5.0, b1 = 19.0/9.0, b2 = 0.5, & |
|---|
| 50 | b3 = 25.0/108.0, b4 = 125.0/108.0, c21 = -8.0, & |
|---|
| 51 | c31 = 372.0/25.0, c32 = 12.0/5.0, & |
|---|
| 52 | c41 = -112.0/125.0, c42 = -54.0/125.0, & |
|---|
| 53 | c43 = -2.0/5.0, c1x = 0.5, c2x= -3.0/2.0, & |
|---|
| 54 | c3x = 121.0/50.0, c4x = 29.0/250.0, & |
|---|
| 55 | errcon = 0.1296, e1 = 17.0/54.0, e2 = 7.0/36.0, & |
|---|
| 56 | e3 = 0.0, e4 = 125.0/108.0, gam = 0.5, grow = 1.5, & |
|---|
| 57 | pgrow = -0.25, pshrnk = -1.0/3.0, shrnk = 0.5 |
|---|
| 58 | |
|---|
| 59 | |
|---|
| 60 | CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'start' ) |
|---|
| 61 | |
|---|
| 62 | DO n = 1, number_of_particles |
|---|
| 63 | ! |
|---|
| 64 | !-- Interpolate temperature and humidity. |
|---|
| 65 | !-- First determine left, south, and bottom index of the arrays. |
|---|
| 66 | i = particles(n)%x * ddx |
|---|
| 67 | j = particles(n)%y * ddy |
|---|
| 68 | k = ( particles(n)%z + 0.5 * dz * atmos_ocean_sign ) / dz & |
|---|
| 69 | + offset_ocean_nzt ! only exact if equidistant |
|---|
| 70 | |
|---|
| 71 | x = particles(n)%x - i * dx |
|---|
| 72 | y = particles(n)%y - j * dy |
|---|
| 73 | aa = x**2 + y**2 |
|---|
| 74 | bb = ( dx - x )**2 + y**2 |
|---|
| 75 | cc = x**2 + ( dy - y )**2 |
|---|
| 76 | dd = ( dx - x )**2 + ( dy - y )**2 |
|---|
| 77 | gg = aa + bb + cc + dd |
|---|
| 78 | |
|---|
| 79 | pt_int_l = ( ( gg - aa ) * pt(k,j,i) + ( gg - bb ) * pt(k,j,i+1) & |
|---|
| 80 | + ( gg - cc ) * pt(k,j+1,i) + ( gg - dd ) * pt(k,j+1,i+1) & |
|---|
| 81 | ) / ( 3.0 * gg ) |
|---|
| 82 | |
|---|
| 83 | pt_int_u = ( ( gg-aa ) * pt(k+1,j,i) + ( gg-bb ) * pt(k+1,j,i+1) & |
|---|
| 84 | + ( gg-cc ) * pt(k+1,j+1,i) + ( gg-dd ) * pt(k+1,j+1,i+1) & |
|---|
| 85 | ) / ( 3.0 * gg ) |
|---|
| 86 | |
|---|
| 87 | pt_int = pt_int_l + ( particles(n)%z - zu(k) ) / dz * & |
|---|
| 88 | ( pt_int_u - pt_int_l ) |
|---|
| 89 | |
|---|
| 90 | q_int_l = ( ( gg - aa ) * q(k,j,i) + ( gg - bb ) * q(k,j,i+1) & |
|---|
| 91 | + ( gg - cc ) * q(k,j+1,i) + ( gg - dd ) * q(k,j+1,i+1) & |
|---|
| 92 | ) / ( 3.0 * gg ) |
|---|
| 93 | |
|---|
| 94 | q_int_u = ( ( gg-aa ) * q(k+1,j,i) + ( gg-bb ) * q(k+1,j,i+1) & |
|---|
| 95 | + ( gg-cc ) * q(k+1,j+1,i) + ( gg-dd ) * q(k+1,j+1,i+1) & |
|---|
| 96 | ) / ( 3.0 * gg ) |
|---|
| 97 | |
|---|
| 98 | q_int = q_int_l + ( particles(n)%z - zu(k) ) / dz * & |
|---|
| 99 | ( q_int_u - q_int_l ) |
|---|
| 100 | |
|---|
| 101 | ql_int_l = ( ( gg - aa ) * ql(k,j,i) + ( gg - bb ) * ql(k,j,i+1) & |
|---|
| 102 | + ( gg - cc ) * ql(k,j+1,i) + ( gg - dd ) * ql(k,j+1,i+1) & |
|---|
| 103 | ) / ( 3.0 * gg ) |
|---|
| 104 | |
|---|
| 105 | ql_int_u = ( ( gg-aa ) * ql(k+1,j,i) + ( gg-bb ) * ql(k+1,j,i+1) & |
|---|
| 106 | + ( gg-cc ) * ql(k+1,j+1,i) + ( gg-dd ) * ql(k+1,j+1,i+1) & |
|---|
| 107 | ) / ( 3.0 * gg ) |
|---|
| 108 | |
|---|
| 109 | ql_int = ql_int_l + ( particles(n)%z - zu(k) ) / dz * & |
|---|
| 110 | ( ql_int_u - ql_int_l ) |
|---|
| 111 | |
|---|
| 112 | ! |
|---|
| 113 | !-- Calculate real temperature and saturation vapor pressure |
|---|
| 114 | p_int = hyp(k) + ( particles(n)%z - zu(k) ) / dz * ( hyp(k+1)-hyp(k) ) |
|---|
| 115 | t_int = pt_int * ( p_int / 100000.0 )**0.286 |
|---|
| 116 | |
|---|
| 117 | e_s = 611.0 * EXP( l_d_rv * ( 3.6609E-3 - 1.0 / t_int ) ) |
|---|
| 118 | |
|---|
| 119 | ! |
|---|
| 120 | !-- Current vapor pressure |
|---|
| 121 | e_a = q_int * p_int / ( 0.378 * q_int + 0.622 ) |
|---|
| 122 | |
|---|
| 123 | ! |
|---|
| 124 | !-- Thermal conductivity for water (from Rogers and Yau, Table 7.1), |
|---|
| 125 | !-- diffusivity for water vapor (after Hall und Pruppacher, 1976) |
|---|
| 126 | thermal_conductivity_l = 7.94048E-05 * t_int + 0.00227011 |
|---|
| 127 | diff_coeff_l = 0.211E-4 * ( t_int / 273.15 )**1.94 * & |
|---|
| 128 | ( 101325.0 / p_int) |
|---|
| 129 | ! |
|---|
| 130 | !-- Change in radius by condensation/evaporation |
|---|
| 131 | IF ( particles(n)%radius >= 1.0E-6 .OR. & |
|---|
| 132 | .NOT. curvature_solution_effects ) THEN |
|---|
| 133 | ! |
|---|
| 134 | !-- Approximation for large radii, where curvature and solution |
|---|
| 135 | !-- effects can be neglected |
|---|
| 136 | arg = particles(n)%radius**2 + 2.0 * dt_3d * & |
|---|
| 137 | ( e_a / e_s - 1.0 ) / & |
|---|
| 138 | ( ( l_d_rv / t_int - 1.0 ) * l_v * rho_l / t_int / & |
|---|
| 139 | thermal_conductivity_l + & |
|---|
| 140 | rho_l * r_v * t_int / diff_coeff_l / e_s ) |
|---|
| 141 | IF ( arg < 1.0E-16 ) THEN |
|---|
| 142 | new_r = 1.0E-8 |
|---|
| 143 | ELSE |
|---|
| 144 | new_r = SQRT( arg ) |
|---|
| 145 | ENDIF |
|---|
| 146 | ENDIF |
|---|
| 147 | |
|---|
| 148 | IF ( curvature_solution_effects .AND. & |
|---|
| 149 | ( ( particles(n)%radius < 1.0E-6 ) .OR. ( new_r < 1.0E-6 ) ) ) & |
|---|
| 150 | THEN |
|---|
| 151 | ! |
|---|
| 152 | !-- Curvature and solutions effects are included in growth equation. |
|---|
| 153 | !-- Change in Radius is calculated with 4th-order Rosenbrock method |
|---|
| 154 | !-- for stiff o.d.e's with monitoring local truncation error to adjust |
|---|
| 155 | !-- stepsize (see Numerical recipes in FORTRAN, 2nd edition, p. 731). |
|---|
| 156 | !-- For larger radii the simple analytic method (see ELSE) gives |
|---|
| 157 | !-- almost the same results. |
|---|
| 158 | ! |
|---|
| 159 | !-- Surface tension after (Straka, 2009) |
|---|
| 160 | sigma = 0.0761 - 0.00155 * ( t_int - 273.15 ) |
|---|
| 161 | |
|---|
| 162 | r_ros = particles(n)%radius |
|---|
| 163 | dt_ros_sum = 0.0 ! internal integrated time (s) |
|---|
| 164 | internal_timestep_count = 0 |
|---|
| 165 | |
|---|
| 166 | ddenom = 1.0 / ( rho_l * r_v * t_int / ( e_s * diff_coeff_l ) + & |
|---|
| 167 | ( l_v / ( r_v * t_int ) - 1.0 ) * & |
|---|
| 168 | rho_l * l_v / ( thermal_conductivity_l * t_int )& |
|---|
| 169 | ) |
|---|
| 170 | |
|---|
| 171 | afactor = 2.0 * sigma / ( rho_l * r_v * t_int ) |
|---|
| 172 | |
|---|
| 173 | IF ( particles(n)%rvar3 == -9999999.9 ) THEN |
|---|
| 174 | ! |
|---|
| 175 | !-- First particle timestep. Derivative has to be calculated. |
|---|
| 176 | drdt_m = ddenom / r_ros * ( e_a / e_s - 1.0 - & |
|---|
| 177 | afactor / r_ros + & |
|---|
| 178 | bfactor / r_ros**3 ) |
|---|
| 179 | ELSE |
|---|
| 180 | ! |
|---|
| 181 | !-- Take value from last PALM timestep |
|---|
| 182 | drdt_m = particles(n)%rvar3 |
|---|
| 183 | ENDIF |
|---|
| 184 | ! |
|---|
| 185 | !-- Take internal timestep values from the end of last PALM timestep |
|---|
| 186 | dt_ros_last = particles(n)%rvar1 |
|---|
| 187 | dt_ros_next = particles(n)%rvar2 |
|---|
| 188 | ! |
|---|
| 189 | !-- Internal timestep must not be larger than PALM timestep |
|---|
| 190 | dt_ros = MIN( dt_ros_next, dt_3d ) |
|---|
| 191 | ! |
|---|
| 192 | !-- Integrate growth equation in time unless PALM timestep is reached |
|---|
| 193 | DO WHILE ( dt_ros_sum < dt_3d ) |
|---|
| 194 | |
|---|
| 195 | internal_timestep_count = internal_timestep_count + 1 |
|---|
| 196 | |
|---|
| 197 | ! |
|---|
| 198 | !-- Derivative at starting value |
|---|
| 199 | drdt = ddenom / r_ros * ( e_a / e_s - 1.0 - afactor / r_ros + & |
|---|
| 200 | bfactor / r_ros**3 ) |
|---|
| 201 | drdt_ini = drdt |
|---|
| 202 | dt_ros_sum_ini = dt_ros_sum |
|---|
| 203 | r_ros_ini = r_ros |
|---|
| 204 | |
|---|
| 205 | ! |
|---|
| 206 | !-- Calculate time derivative of dr/dt |
|---|
| 207 | d2rdt2 = ( drdt - drdt_m ) / dt_ros_last |
|---|
| 208 | |
|---|
| 209 | ! |
|---|
| 210 | !-- Calculate radial derivative of dr/dt |
|---|
| 211 | d2rdtdr = ddenom * ( ( 1.0 - e_a/e_s ) / r_ros**2 + & |
|---|
| 212 | 2.0 * afactor / r_ros**3 - & |
|---|
| 213 | 4.0 * bfactor / r_ros**5 ) |
|---|
| 214 | ! |
|---|
| 215 | !-- Adjust stepsize unless required accuracy is reached |
|---|
| 216 | DO jtry = 1, maxtry+1 |
|---|
| 217 | |
|---|
| 218 | IF ( jtry == maxtry+1 ) THEN |
|---|
| 219 | message_string = 'maxtry > 40 in Rosenbrock method' |
|---|
| 220 | CALL message( 'lpm_droplet_condensation', 'PA0347', 2, 2, & |
|---|
| 221 | 0, 6, 0 ) |
|---|
| 222 | ENDIF |
|---|
| 223 | |
|---|
| 224 | aa = 1.0 / ( gam * dt_ros ) - d2rdtdr |
|---|
| 225 | g1 = ( drdt_ini + dt_ros * c1x * d2rdt2 ) / aa |
|---|
| 226 | r_ros = r_ros_ini + a21 * g1 |
|---|
| 227 | drdt = ddenom / r_ros * ( e_a / e_s - 1.0 - & |
|---|
| 228 | afactor / r_ros + & |
|---|
| 229 | bfactor / r_ros**3 ) |
|---|
| 230 | |
|---|
| 231 | g2 = ( drdt + dt_ros * c2x * d2rdt2 + c21 * g1 / dt_ros )& |
|---|
| 232 | / aa |
|---|
| 233 | r_ros = r_ros_ini + a31 * g1 + a32 * g2 |
|---|
| 234 | drdt = ddenom / r_ros * ( e_a / e_s - 1.0 - & |
|---|
| 235 | afactor / r_ros + & |
|---|
| 236 | bfactor / r_ros**3 ) |
|---|
| 237 | |
|---|
| 238 | g3 = ( drdt + dt_ros * c3x * d2rdt2 + & |
|---|
| 239 | ( c31 * g1 + c32 * g2 ) / dt_ros ) / aa |
|---|
| 240 | g4 = ( drdt + dt_ros * c4x * d2rdt2 + & |
|---|
| 241 | ( c41 * g1 + c42 * g2 + c43 * g3 ) / dt_ros ) / aa |
|---|
| 242 | r_ros = r_ros_ini + b1 * g1 + b2 * g2 + b3 * g3 + b4 * g4 |
|---|
| 243 | |
|---|
| 244 | dt_ros_sum = dt_ros_sum_ini + dt_ros |
|---|
| 245 | |
|---|
| 246 | IF ( dt_ros_sum == dt_ros_sum_ini ) THEN |
|---|
| 247 | message_string = 'zero stepsize in Rosenbrock method' |
|---|
| 248 | CALL message( 'lpm_droplet_condensation', 'PA0348', 2, 2, & |
|---|
| 249 | 0, 6, 0 ) |
|---|
| 250 | ENDIF |
|---|
| 251 | ! |
|---|
| 252 | !-- Calculate error |
|---|
| 253 | err_ros = e1*g1 + e2*g2 + e3*g3 + e4*g4 |
|---|
| 254 | errmax = 0.0 |
|---|
| 255 | errmax = MAX( errmax, ABS( err_ros / r_ros_ini ) ) / eps_ros |
|---|
| 256 | ! |
|---|
| 257 | !-- Leave loop if accuracy is sufficient, otherwise try again |
|---|
| 258 | !-- with a reduced stepsize |
|---|
| 259 | IF ( errmax <= 1.0 ) THEN |
|---|
| 260 | EXIT |
|---|
| 261 | ELSE |
|---|
| 262 | dt_ros = SIGN( MAX( ABS( 0.9 * dt_ros * errmax**pshrnk ), & |
|---|
| 263 | shrnk * ABS( dt_ros ) ), dt_ros ) |
|---|
| 264 | ENDIF |
|---|
| 265 | |
|---|
| 266 | ENDDO ! loop for stepsize adjustment |
|---|
| 267 | |
|---|
| 268 | ! |
|---|
| 269 | !-- Calculate next internal timestep |
|---|
| 270 | IF ( errmax > errcon ) THEN |
|---|
| 271 | dt_ros_next = 0.9 * dt_ros * errmax**pgrow |
|---|
| 272 | ELSE |
|---|
| 273 | dt_ros_next = grow * dt_ros |
|---|
| 274 | ENDIF |
|---|
| 275 | |
|---|
| 276 | ! |
|---|
| 277 | !-- Estimated timestep is reduced if the PALM time step is exceeded |
|---|
| 278 | dt_ros_last = dt_ros |
|---|
| 279 | IF ( ( dt_ros_next + dt_ros_sum ) >= dt_3d ) THEN |
|---|
| 280 | dt_ros = dt_3d - dt_ros_sum |
|---|
| 281 | ELSE |
|---|
| 282 | dt_ros = dt_ros_next |
|---|
| 283 | ENDIF |
|---|
| 284 | |
|---|
| 285 | drdt_m = drdt |
|---|
| 286 | |
|---|
| 287 | ENDDO |
|---|
| 288 | ! |
|---|
| 289 | !-- Store derivative and internal timestep values for next PALM step |
|---|
| 290 | particles(n)%rvar1 = dt_ros_last |
|---|
| 291 | particles(n)%rvar2 = dt_ros_next |
|---|
| 292 | particles(n)%rvar3 = drdt_m |
|---|
| 293 | |
|---|
| 294 | new_r = r_ros |
|---|
| 295 | ! |
|---|
| 296 | !-- Radius should not fall below 1E-8 because Rosenbrock method may |
|---|
| 297 | !-- lead to errors otherwise |
|---|
| 298 | new_r = MAX( new_r, 1.0E-8 ) |
|---|
| 299 | |
|---|
| 300 | ENDIF |
|---|
| 301 | |
|---|
| 302 | delta_r = new_r - particles(n)%radius |
|---|
| 303 | |
|---|
| 304 | ! |
|---|
| 305 | !-- Sum up the change in volume of liquid water for the respective grid |
|---|
| 306 | !-- volume (this is needed later in lpm_calc_liquid_water_content for |
|---|
| 307 | !-- calculating the release of latent heat) |
|---|
| 308 | i = ( particles(n)%x + 0.5 * dx ) * ddx |
|---|
| 309 | j = ( particles(n)%y + 0.5 * dy ) * ddy |
|---|
| 310 | k = particles(n)%z / dz + 1 + offset_ocean_nzt_m1 |
|---|
| 311 | ! only exact if equidistant |
|---|
| 312 | |
|---|
| 313 | ql_c(k,j,i) = ql_c(k,j,i) + particles(n)%weight_factor * & |
|---|
| 314 | rho_l * 1.33333333 * pi * & |
|---|
| 315 | ( new_r**3 - particles(n)%radius**3 ) / & |
|---|
| 316 | ( rho_surface * dx * dy * dz ) |
|---|
| 317 | IF ( ql_c(k,j,i) > 100.0 ) THEN |
|---|
| 318 | WRITE( message_string, * ) 'k=',k,' j=',j,' i=',i, & |
|---|
| 319 | ' ql_c=',ql_c(k,j,i), ' &part(',n,')%wf=', & |
|---|
| 320 | particles(n)%weight_factor,' delta_r=',delta_r |
|---|
| 321 | CALL message( 'lpm_droplet_condensation', 'PA0143', 2, 2, -1, 6, 1 ) |
|---|
| 322 | ENDIF |
|---|
| 323 | |
|---|
| 324 | ! |
|---|
| 325 | !-- Change the droplet radius |
|---|
| 326 | IF ( ( new_r - particles(n)%radius ) < 0.0 .AND. new_r < 0.0 ) & |
|---|
| 327 | THEN |
|---|
| 328 | WRITE( message_string, * ) '#1 k=',k,' j=',j,' i=',i, & |
|---|
| 329 | ' e_s=',e_s, ' e_a=',e_a,' t_int=',t_int, & |
|---|
| 330 | ' &delta_r=',delta_r, & |
|---|
| 331 | ' particle_radius=',particles(n)%radius |
|---|
| 332 | CALL message( 'lpm_droplet_condensation', 'PA0144', 2, 2, -1, 6, 1 ) |
|---|
| 333 | ENDIF |
|---|
| 334 | |
|---|
| 335 | ! |
|---|
| 336 | !-- Sum up the total volume of liquid water (needed below for |
|---|
| 337 | !-- re-calculating the weighting factors) |
|---|
| 338 | ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * new_r**3 |
|---|
| 339 | |
|---|
| 340 | particles(n)%radius = new_r |
|---|
| 341 | |
|---|
| 342 | ! |
|---|
| 343 | !-- Determine radius class of the particle needed for collision |
|---|
| 344 | IF ( ( hall_kernel .OR. wang_kernel ) .AND. use_kernel_tables ) & |
|---|
| 345 | THEN |
|---|
| 346 | particles(n)%class = ( LOG( new_r ) - rclass_lbound ) / & |
|---|
| 347 | ( rclass_ubound - rclass_lbound ) * & |
|---|
| 348 | radius_classes |
|---|
| 349 | particles(n)%class = MIN( particles(n)%class, radius_classes ) |
|---|
| 350 | particles(n)%class = MAX( particles(n)%class, 1 ) |
|---|
| 351 | ENDIF |
|---|
| 352 | |
|---|
| 353 | ENDDO |
|---|
| 354 | |
|---|
| 355 | CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'stop' ) |
|---|
| 356 | |
|---|
| 357 | |
|---|
| 358 | END SUBROUTINE lpm_droplet_condensation |
|---|
