| 1 | !> @file microphysics_mod.f90 |
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| 2 | !------------------------------------------------------------------------------! |
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| 3 | ! This file is part of PALM. |
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| 4 | ! |
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| 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 6 | ! terms of the GNU General Public License as published by the Free Software |
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| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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| 8 | ! version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2017 Leibniz Universitaet Hannover |
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| 18 | !------------------------------------------------------------------------------! |
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| 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ------------------ |
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| 22 | ! Adjustments to new topography and surface concept |
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| 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: microphysics_mod.f90 2232 2017-05-30 17:47:52Z suehring $ |
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| 27 | ! |
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| 28 | ! 2155 2017-02-21 09:57:40Z hoffmann |
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| 29 | ! Bugfix in the calculation of microphysical quantities on ghost points. |
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| 30 | ! |
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| 31 | ! 2031 2016-10-21 15:11:58Z knoop |
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| 32 | ! renamed variable rho to rho_ocean |
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| 33 | ! |
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| 34 | ! 2000 2016-08-20 18:09:15Z knoop |
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| 35 | ! Forced header and separation lines into 80 columns |
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| 36 | ! |
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| 37 | ! 1850 2016-04-08 13:29:27Z maronga |
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| 38 | ! Module renamed |
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| 39 | ! Adapted for modularization of microphysics. |
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| 40 | ! |
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| 41 | ! 1845 2016-04-08 08:29:13Z raasch |
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| 42 | ! nzb_2d replaced by nzb_s_inner, Kessler precipitation is stored at surface |
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| 43 | ! point (instead of one point above surface) |
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| 44 | ! |
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| 45 | ! 1831 2016-04-07 13:15:51Z hoffmann |
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| 46 | ! turbulence renamed collision_turbulence, |
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| 47 | ! drizzle renamed cloud_water_sedimentation. cloud_water_sedimentation also |
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| 48 | ! avaialble for microphysics_kessler. |
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| 49 | ! |
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| 50 | ! 1822 2016-04-07 07:49:42Z hoffmann |
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| 51 | ! Unused variables removed. |
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| 52 | ! Kessler scheme integrated. |
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| 53 | ! |
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| 54 | ! 1691 2015-10-26 16:17:44Z maronga |
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| 55 | ! Added new routine calc_precipitation_amount. The routine now allows to account |
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| 56 | ! for precipitation due to sedimenation of cloud (fog) droplets |
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| 57 | ! |
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| 58 | ! 1682 2015-10-07 23:56:08Z knoop |
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| 59 | ! Code annotations made doxygen readable |
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| 60 | ! |
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| 61 | ! 1646 2015-09-02 16:00:10Z hoffmann |
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| 62 | ! Bugfix: Wrong computation of d_mean. |
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| 63 | ! |
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| 64 | ! 1361 2014-04-16 15:17:48Z hoffmann |
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| 65 | ! Bugfix in sedimentation_rain: Index corrected. |
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| 66 | ! Vectorized version of adjust_cloud added. |
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| 67 | ! Little reformatting of the code. |
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| 68 | ! |
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| 69 | ! 1353 2014-04-08 15:21:23Z heinze |
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| 70 | ! REAL constants provided with KIND-attribute |
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| 71 | ! |
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| 72 | ! 1346 2014-03-27 13:18:20Z heinze |
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| 73 | ! Bugfix: REAL constants provided with KIND-attribute especially in call of |
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| 74 | ! intrinsic function like MAX, MIN, SIGN |
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| 75 | ! |
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| 76 | ! 1334 2014-03-25 12:21:40Z heinze |
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| 77 | ! Bugfix: REAL constants provided with KIND-attribute |
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| 78 | ! |
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| 79 | ! 1322 2014-03-20 16:38:49Z raasch |
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| 80 | ! REAL constants defined as wp-kind |
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| 81 | ! |
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| 82 | ! 1320 2014-03-20 08:40:49Z raasch |
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| 83 | ! ONLY-attribute added to USE-statements, |
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| 84 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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| 85 | ! kinds are defined in new module kinds, |
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| 86 | ! comment fields (!:) to be used for variable explanations added to |
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| 87 | ! all variable declaration statements |
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| 88 | ! |
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| 89 | ! 1241 2013-10-30 11:36:58Z heinze |
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| 90 | ! hyp and rho_ocean have to be calculated at each time step if data from external |
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| 91 | ! file LSF_DATA are used |
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| 92 | ! |
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| 93 | ! 1115 2013-03-26 18:16:16Z hoffmann |
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| 94 | ! microphyical tendencies are calculated in microphysics_control in an optimized |
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| 95 | ! way; unrealistic values are prevented; bugfix in evaporation; some reformatting |
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| 96 | ! |
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| 97 | ! 1106 2013-03-04 05:31:38Z raasch |
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| 98 | ! small changes in code formatting |
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| 99 | ! |
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| 100 | ! 1092 2013-02-02 11:24:22Z raasch |
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| 101 | ! unused variables removed |
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| 102 | ! file put under GPL |
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| 103 | ! |
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| 104 | ! 1065 2012-11-22 17:42:36Z hoffmann |
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| 105 | ! Sedimentation process implemented according to Stevens and Seifert (2008). |
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| 106 | ! Turbulence effects on autoconversion and accretion added (Seifert, Nuijens |
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| 107 | ! and Stevens, 2010). |
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| 108 | ! |
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| 109 | ! 1053 2012-11-13 17:11:03Z hoffmann |
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| 110 | ! initial revision |
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| 111 | ! |
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| 112 | ! Description: |
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| 113 | ! ------------ |
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| 114 | !> Calculate bilk cloud microphysics. |
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| 115 | !------------------------------------------------------------------------------! |
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| 116 | MODULE microphysics_mod |
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| 117 | |
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| 118 | USE kinds |
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| 119 | |
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| 120 | IMPLICIT NONE |
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| 121 | |
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| 122 | LOGICAL :: cloud_water_sedimentation = .FALSE. !< cloud water sedimentation |
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| 123 | LOGICAL :: limiter_sedimentation = .TRUE. !< sedimentation limiter |
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| 124 | LOGICAL :: collision_turbulence = .FALSE. !< turbulence effects |
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| 125 | LOGICAL :: ventilation_effect = .TRUE. !< ventilation effect |
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| 126 | |
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| 127 | REAL(wp) :: a_1 = 8.69E-4_wp !< coef. in turb. parametrization (cm-2 s3) |
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| 128 | REAL(wp) :: a_2 = -7.38E-5_wp !< coef. in turb. parametrization (cm-2 s3) |
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| 129 | REAL(wp) :: a_3 = -1.40E-2_wp !< coef. in turb. parametrization |
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| 130 | REAL(wp) :: a_term = 9.65_wp !< coef. for terminal velocity (m s-1) |
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| 131 | REAL(wp) :: a_vent = 0.78_wp !< coef. for ventilation effect |
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| 132 | REAL(wp) :: b_1 = 11.45E-6_wp !< coef. in turb. parametrization (m) |
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| 133 | REAL(wp) :: b_2 = 9.68E-6_wp !< coef. in turb. parametrization (m) |
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| 134 | REAL(wp) :: b_3 = 0.62_wp !< coef. in turb. parametrization |
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| 135 | REAL(wp) :: b_term = 9.8_wp !< coef. for terminal velocity (m s-1) |
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| 136 | REAL(wp) :: b_vent = 0.308_wp !< coef. for ventilation effect |
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| 137 | REAL(wp) :: beta_cc = 3.09E-4_wp !< coef. in turb. parametrization (cm-2 s3) |
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| 138 | REAL(wp) :: c_1 = 4.82E-6_wp !< coef. in turb. parametrization (m) |
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| 139 | REAL(wp) :: c_2 = 4.8E-6_wp !< coef. in turb. parametrization (m) |
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| 140 | REAL(wp) :: c_3 = 0.76_wp !< coef. in turb. parametrization |
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| 141 | REAL(wp) :: c_const = 0.93_wp !< const. in Taylor-microscale Reynolds number |
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| 142 | REAL(wp) :: c_evap = 0.7_wp !< constant in evaporation |
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| 143 | REAL(wp) :: c_term = 600.0_wp !< coef. for terminal velocity (m-1) |
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| 144 | REAL(wp) :: diff_coeff_l = 0.23E-4_wp !< diffusivity of water vapor (m2 s-1) |
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| 145 | REAL(wp) :: eps_sb = 1.0E-10_wp !< threshold in two-moments scheme |
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| 146 | REAL(wp) :: k_cc = 9.44E09_wp !< const. cloud-cloud kernel (m3 kg-2 s-1) |
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| 147 | REAL(wp) :: k_cr0 = 4.33_wp !< const. cloud-rain kernel (m3 kg-1 s-1) |
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| 148 | REAL(wp) :: k_rr = 7.12_wp !< const. rain-rain kernel (m3 kg-1 s-1) |
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| 149 | REAL(wp) :: k_br = 1000.0_wp !< const. in breakup parametrization (m-1) |
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| 150 | REAL(wp) :: k_st = 1.2E8_wp !< const. in drizzle parametrization (m-1 s-1) |
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| 151 | REAL(wp) :: kappa_rr = 60.7_wp !< const. in collision kernel (kg-1/3) |
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| 152 | REAL(wp) :: kin_vis_air = 1.4086E-5_wp !< kin. viscosity of air (m2 s-1) |
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| 153 | REAL(wp) :: prec_time_const = 0.001_wp !< coef. in Kessler scheme (s-1) |
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| 154 | REAL(wp) :: ql_crit = 0.0005_wp !< coef. in Kessler scheme (kg kg-1) |
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| 155 | REAL(wp) :: schmidt_p_1d3=0.8921121_wp !< Schmidt number**0.33333, 0.71**0.33333 |
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| 156 | REAL(wp) :: sigma_gc = 1.3_wp !< geometric standard deviation cloud droplets |
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| 157 | REAL(wp) :: thermal_conductivity_l = 2.43E-2_wp !< therm. cond. air (J m-1 s-1 K-1) |
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| 158 | REAL(wp) :: w_precipitation = 9.65_wp !< maximum terminal velocity (m s-1) |
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| 159 | REAL(wp) :: x0 = 2.6E-10_wp !< separating drop mass (kg) |
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| 160 | REAL(wp) :: xrmin = 2.6E-10_wp !< minimum rain drop size (kg) |
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| 161 | REAL(wp) :: xrmax = 5.0E-6_wp !< maximum rain drop site (kg) |
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| 162 | |
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| 163 | REAL(wp) :: c_sedimentation = 2.0_wp !< Courant number of sedimentation process |
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| 164 | REAL(wp) :: dpirho_l !< 6.0 / ( pi * rho_l ) |
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| 165 | REAL(wp) :: dt_micro !< microphysics time step |
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| 166 | REAL(wp) :: nc_const = 70.0E6_wp !< cloud droplet concentration |
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| 167 | REAL(wp) :: dt_precipitation = 100.0_wp !< timestep precipitation (s) |
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| 168 | REAL(wp) :: sed_qc_const !< const. for sedimentation of cloud water |
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| 169 | REAL(wp) :: pirho_l !< pi * rho_l / 6.0; |
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| 170 | |
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| 171 | REAL(wp), DIMENSION(:), ALLOCATABLE :: nc_1d !< |
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| 172 | REAL(wp), DIMENSION(:), ALLOCATABLE :: nr_1d !< |
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| 173 | REAL(wp), DIMENSION(:), ALLOCATABLE :: pt_1d !< |
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| 174 | REAL(wp), DIMENSION(:), ALLOCATABLE :: qc_1d !< |
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| 175 | REAL(wp), DIMENSION(:), ALLOCATABLE :: qr_1d !< |
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| 176 | REAL(wp), DIMENSION(:), ALLOCATABLE :: q_1d !< |
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| 177 | |
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| 178 | SAVE |
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| 179 | |
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| 180 | PRIVATE |
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| 181 | PUBLIC microphysics_control, microphysics_init |
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| 182 | |
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| 183 | PUBLIC cloud_water_sedimentation, collision_turbulence, c_sedimentation, & |
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| 184 | dt_precipitation, limiter_sedimentation, nc_const, sigma_gc, & |
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| 185 | ventilation_effect |
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| 186 | |
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| 187 | INTERFACE microphysics_control |
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| 188 | MODULE PROCEDURE microphysics_control |
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| 189 | MODULE PROCEDURE microphysics_control_ij |
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| 190 | END INTERFACE microphysics_control |
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| 191 | |
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| 192 | INTERFACE adjust_cloud |
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| 193 | MODULE PROCEDURE adjust_cloud |
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| 194 | MODULE PROCEDURE adjust_cloud_ij |
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| 195 | END INTERFACE adjust_cloud |
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| 196 | |
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| 197 | INTERFACE autoconversion |
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| 198 | MODULE PROCEDURE autoconversion |
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| 199 | MODULE PROCEDURE autoconversion_ij |
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| 200 | END INTERFACE autoconversion |
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| 201 | |
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| 202 | INTERFACE autoconversion_kessler |
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| 203 | MODULE PROCEDURE autoconversion_kessler |
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| 204 | MODULE PROCEDURE autoconversion_kessler_ij |
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| 205 | END INTERFACE autoconversion_kessler |
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| 206 | |
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| 207 | INTERFACE accretion |
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| 208 | MODULE PROCEDURE accretion |
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| 209 | MODULE PROCEDURE accretion_ij |
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| 210 | END INTERFACE accretion |
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| 211 | |
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| 212 | INTERFACE selfcollection_breakup |
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| 213 | MODULE PROCEDURE selfcollection_breakup |
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| 214 | MODULE PROCEDURE selfcollection_breakup_ij |
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| 215 | END INTERFACE selfcollection_breakup |
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| 216 | |
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| 217 | INTERFACE evaporation_rain |
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| 218 | MODULE PROCEDURE evaporation_rain |
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| 219 | MODULE PROCEDURE evaporation_rain_ij |
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| 220 | END INTERFACE evaporation_rain |
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| 221 | |
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| 222 | INTERFACE sedimentation_cloud |
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| 223 | MODULE PROCEDURE sedimentation_cloud |
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| 224 | MODULE PROCEDURE sedimentation_cloud_ij |
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| 225 | END INTERFACE sedimentation_cloud |
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| 226 | |
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| 227 | INTERFACE sedimentation_rain |
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| 228 | MODULE PROCEDURE sedimentation_rain |
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| 229 | MODULE PROCEDURE sedimentation_rain_ij |
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| 230 | END INTERFACE sedimentation_rain |
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| 231 | |
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| 232 | INTERFACE calc_precipitation_amount |
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| 233 | MODULE PROCEDURE calc_precipitation_amount |
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| 234 | MODULE PROCEDURE calc_precipitation_amount_ij |
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| 235 | END INTERFACE calc_precipitation_amount |
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| 236 | |
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| 237 | CONTAINS |
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| 238 | !------------------------------------------------------------------------------! |
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| 239 | ! Description: |
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| 240 | ! ------------ |
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| 241 | !> Initialization of bulk microphysics |
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| 242 | !------------------------------------------------------------------------------! |
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| 243 | SUBROUTINE microphysics_init |
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| 244 | |
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| 245 | USE arrays_3d, & |
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| 246 | ONLY: dzu |
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| 247 | |
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| 248 | USE constants, & |
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| 249 | ONLY: pi |
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| 250 | |
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| 251 | USE cloud_parameters, & |
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| 252 | ONLY: rho_l |
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| 253 | |
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| 254 | USE control_parameters, & |
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| 255 | ONLY: microphysics_seifert |
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| 256 | |
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| 257 | USE indices, & |
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| 258 | ONLY: nzb, nzt |
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| 259 | |
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| 260 | IMPLICIT NONE |
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| 261 | |
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| 262 | ! |
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| 263 | !-- constant for the sedimentation of cloud water (2-moment cloud physics) |
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| 264 | sed_qc_const = k_st * ( 3.0_wp / ( 4.0_wp * pi * rho_l ) & |
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| 265 | )**( 2.0_wp / 3.0_wp ) * & |
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| 266 | EXP( 5.0_wp * LOG( sigma_gc )**2 ) |
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| 267 | |
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| 268 | ! |
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| 269 | !-- Calculate timestep according to precipitation |
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| 270 | IF ( microphysics_seifert ) THEN |
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| 271 | dt_precipitation = c_sedimentation * MINVAL( dzu(nzb+2:nzt) ) / & |
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| 272 | w_precipitation |
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| 273 | ENDIF |
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| 274 | |
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| 275 | ! |
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| 276 | !-- Pre-calculate frequently calculated fractions of pi and rho_l |
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| 277 | pirho_l = pi * rho_l / 6.0_wp |
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| 278 | dpirho_l = 1.0_wp / pirho_l |
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| 279 | |
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| 280 | ! |
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| 281 | !-- Allocate 1D microphysics arrays |
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| 282 | ALLOCATE ( nc_1d(nzb:nzt+1), pt_1d(nzb:nzt+1), q_1d(nzb:nzt+1), & |
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| 283 | qc_1d(nzb:nzt+1) ) |
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| 284 | |
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| 285 | IF ( microphysics_seifert ) THEN |
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| 286 | ALLOCATE ( nr_1d(nzb:nzt+1), qr_1d(nzb:nzt+1) ) |
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| 287 | ENDIF |
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| 288 | |
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| 289 | ! |
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| 290 | !-- Initialze nc_1d with nc_const |
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| 291 | nc_1d = nc_const |
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| 292 | |
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| 293 | END SUBROUTINE microphysics_init |
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| 294 | |
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| 295 | |
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| 296 | !------------------------------------------------------------------------------! |
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| 297 | ! Description: |
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| 298 | ! ------------ |
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| 299 | !> Control of microphysics for all grid points |
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| 300 | !------------------------------------------------------------------------------! |
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| 301 | SUBROUTINE microphysics_control |
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| 302 | |
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| 303 | USE arrays_3d, & |
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| 304 | ONLY: hyp, pt_init, prr, zu |
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| 305 | |
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| 306 | USE cloud_parameters, & |
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| 307 | ONLY: cp, hyrho, pt_d_t, r_d, t_d_pt |
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| 308 | |
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| 309 | USE control_parameters, & |
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| 310 | ONLY: call_microphysics_at_all_substeps, dt_3d, g, & |
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| 311 | intermediate_timestep_count, large_scale_forcing, & |
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| 312 | lsf_surf, microphysics_kessler, microphysics_seifert, & |
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| 313 | pt_surface, rho_surface,surface_pressure |
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| 314 | |
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| 315 | USE indices, & |
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| 316 | ONLY: nzb, nzt |
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| 317 | |
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| 318 | USE kinds |
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| 319 | |
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| 320 | USE statistics, & |
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| 321 | ONLY: weight_pres |
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| 322 | |
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| 323 | IMPLICIT NONE |
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| 324 | |
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| 325 | INTEGER(iwp) :: k !< |
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| 326 | |
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| 327 | REAL(wp) :: t_surface !< |
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| 328 | |
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| 329 | IF ( large_scale_forcing .AND. lsf_surf ) THEN |
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| 330 | ! |
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| 331 | !-- Calculate: |
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| 332 | !-- pt / t : ratio of potential and actual temperature (pt_d_t) |
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| 333 | !-- t / pt : ratio of actual and potential temperature (t_d_pt) |
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| 334 | !-- p_0(z) : vertical profile of the hydrostatic pressure (hyp) |
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| 335 | t_surface = pt_surface * ( surface_pressure / 1000.0_wp )**0.286_wp |
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| 336 | DO k = nzb, nzt+1 |
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| 337 | hyp(k) = surface_pressure * 100.0_wp * & |
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| 338 | ( ( t_surface - g / cp * zu(k) ) / & |
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| 339 | t_surface )**(1.0_wp / 0.286_wp) |
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| 340 | pt_d_t(k) = ( 100000.0_wp / hyp(k) )**0.286_wp |
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| 341 | t_d_pt(k) = 1.0_wp / pt_d_t(k) |
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| 342 | hyrho(k) = hyp(k) / ( r_d * t_d_pt(k) * pt_init(k) ) |
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| 343 | ENDDO |
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| 344 | |
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| 345 | ! |
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| 346 | !-- Compute reference density |
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| 347 | rho_surface = surface_pressure * 100.0_wp / ( r_d * t_surface ) |
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| 348 | ENDIF |
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| 349 | |
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| 350 | ! |
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| 351 | !-- Compute length of time step |
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| 352 | IF ( call_microphysics_at_all_substeps ) THEN |
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| 353 | dt_micro = dt_3d * weight_pres(intermediate_timestep_count) |
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| 354 | ELSE |
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| 355 | dt_micro = dt_3d |
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| 356 | ENDIF |
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| 357 | |
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| 358 | ! |
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| 359 | !-- Reset precipitation rate |
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| 360 | IF ( intermediate_timestep_count == 1 ) prr = 0.0_wp |
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| 361 | |
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| 362 | ! |
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| 363 | !-- Compute cloud physics |
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| 364 | IF ( microphysics_kessler ) THEN |
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| 365 | |
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| 366 | CALL autoconversion_kessler |
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| 367 | IF ( cloud_water_sedimentation ) CALL sedimentation_cloud |
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| 368 | |
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| 369 | ELSEIF ( microphysics_seifert ) THEN |
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| 370 | |
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| 371 | CALL adjust_cloud |
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| 372 | CALL autoconversion |
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| 373 | CALL accretion |
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| 374 | CALL selfcollection_breakup |
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| 375 | CALL evaporation_rain |
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| 376 | CALL sedimentation_rain |
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| 377 | IF ( cloud_water_sedimentation ) CALL sedimentation_cloud |
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| 378 | |
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| 379 | ENDIF |
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| 380 | |
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| 381 | CALL calc_precipitation_amount |
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| 382 | |
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| 383 | END SUBROUTINE microphysics_control |
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| 384 | |
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| 385 | !------------------------------------------------------------------------------! |
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| 386 | ! Description: |
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| 387 | ! ------------ |
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| 388 | !> Adjust number of raindrops to avoid nonlinear effects in sedimentation and |
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| 389 | !> evaporation of rain drops due to too small or too big weights |
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| 390 | !> of rain drops (Stevens and Seifert, 2008). |
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| 391 | !------------------------------------------------------------------------------! |
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| 392 | SUBROUTINE adjust_cloud |
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| 393 | |
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| 394 | USE arrays_3d, & |
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| 395 | ONLY: qr, nr |
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| 396 | |
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| 397 | USE cloud_parameters, & |
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| 398 | ONLY: hyrho |
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| 399 | |
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| 400 | USE cpulog, & |
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| 401 | ONLY: cpu_log, log_point_s |
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| 402 | |
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| 403 | USE indices, & |
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| 404 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
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| 405 | |
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| 406 | USE kinds |
|---|
| 407 | |
|---|
| 408 | IMPLICIT NONE |
|---|
| 409 | |
|---|
| 410 | INTEGER(iwp) :: i !< |
|---|
| 411 | INTEGER(iwp) :: j !< |
|---|
| 412 | INTEGER(iwp) :: k !< |
|---|
| 413 | |
|---|
| 414 | CALL cpu_log( log_point_s(54), 'adjust_cloud', 'start' ) |
|---|
| 415 | |
|---|
| 416 | DO i = nxlg, nxrg |
|---|
| 417 | DO j = nysg, nyng |
|---|
| 418 | DO k = nzb+1, nzt |
|---|
| 419 | IF ( qr(k,j,i) <= eps_sb ) THEN |
|---|
| 420 | qr(k,j,i) = 0.0_wp |
|---|
| 421 | nr(k,j,i) = 0.0_wp |
|---|
| 422 | ELSE |
|---|
| 423 | IF ( nr(k,j,i) * xrmin > qr(k,j,i) * hyrho(k) ) THEN |
|---|
| 424 | nr(k,j,i) = qr(k,j,i) * hyrho(k) / xrmin * & |
|---|
| 425 | MERGE( 1.0_wp, 0.0_wp, & |
|---|
| 426 | BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 427 | ELSEIF ( nr(k,j,i) * xrmax < qr(k,j,i) * hyrho(k) ) THEN |
|---|
| 428 | nr(k,j,i) = qr(k,j,i) * hyrho(k) / xrmax * & |
|---|
| 429 | MERGE( 1.0_wp, 0.0_wp, & |
|---|
| 430 | BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 431 | ENDIF |
|---|
| 432 | ENDIF |
|---|
| 433 | ENDDO |
|---|
| 434 | ENDDO |
|---|
| 435 | ENDDO |
|---|
| 436 | |
|---|
| 437 | CALL cpu_log( log_point_s(54), 'adjust_cloud', 'stop' ) |
|---|
| 438 | |
|---|
| 439 | END SUBROUTINE adjust_cloud |
|---|
| 440 | |
|---|
| 441 | |
|---|
| 442 | !------------------------------------------------------------------------------! |
|---|
| 443 | ! Description: |
|---|
| 444 | ! ------------ |
|---|
| 445 | !> Autoconversion rate (Seifert and Beheng, 2006). |
|---|
| 446 | !------------------------------------------------------------------------------! |
|---|
| 447 | SUBROUTINE autoconversion |
|---|
| 448 | |
|---|
| 449 | USE arrays_3d, & |
|---|
| 450 | ONLY: diss, dzu, nr, qc, qr |
|---|
| 451 | |
|---|
| 452 | USE cloud_parameters, & |
|---|
| 453 | ONLY: hyrho |
|---|
| 454 | |
|---|
| 455 | USE control_parameters, & |
|---|
| 456 | ONLY: rho_surface |
|---|
| 457 | |
|---|
| 458 | USE cpulog, & |
|---|
| 459 | ONLY: cpu_log, log_point_s |
|---|
| 460 | |
|---|
| 461 | USE grid_variables, & |
|---|
| 462 | ONLY: dx, dy |
|---|
| 463 | |
|---|
| 464 | USE indices, & |
|---|
| 465 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 466 | |
|---|
| 467 | USE kinds |
|---|
| 468 | |
|---|
| 469 | IMPLICIT NONE |
|---|
| 470 | |
|---|
| 471 | INTEGER(iwp) :: i !< |
|---|
| 472 | INTEGER(iwp) :: j !< |
|---|
| 473 | INTEGER(iwp) :: k !< |
|---|
| 474 | |
|---|
| 475 | REAL(wp) :: alpha_cc !< |
|---|
| 476 | REAL(wp) :: autocon !< |
|---|
| 477 | REAL(wp) :: dissipation !< |
|---|
| 478 | REAL(wp) :: flag !< flag to mask topography grid points |
|---|
| 479 | REAL(wp) :: k_au !< |
|---|
| 480 | REAL(wp) :: l_mix !< |
|---|
| 481 | REAL(wp) :: nu_c !< |
|---|
| 482 | REAL(wp) :: phi_au !< |
|---|
| 483 | REAL(wp) :: r_cc !< |
|---|
| 484 | REAL(wp) :: rc !< |
|---|
| 485 | REAL(wp) :: re_lambda !< |
|---|
| 486 | REAL(wp) :: sigma_cc !< |
|---|
| 487 | REAL(wp) :: tau_cloud !< |
|---|
| 488 | REAL(wp) :: xc !< |
|---|
| 489 | |
|---|
| 490 | CALL cpu_log( log_point_s(55), 'autoconversion', 'start' ) |
|---|
| 491 | |
|---|
| 492 | DO i = nxlg, nxrg |
|---|
| 493 | DO j = nysg, nyng |
|---|
| 494 | DO k = nzb+1, nzt |
|---|
| 495 | ! |
|---|
| 496 | !-- Predetermine flag to mask topography |
|---|
| 497 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 498 | |
|---|
| 499 | IF ( qc(k,j,i) > eps_sb ) THEN |
|---|
| 500 | |
|---|
| 501 | k_au = k_cc / ( 20.0_wp * x0 ) |
|---|
| 502 | ! |
|---|
| 503 | !-- Intern time scale of coagulation (Seifert and Beheng, 2006): |
|---|
| 504 | !-- (1.0_wp - qc(k,j,i) / ( qc(k,j,i) + qr(k,j,i) )) |
|---|
| 505 | tau_cloud = 1.0_wp - qc(k,j,i) / ( qr(k,j,i) + qc(k,j,i) ) |
|---|
| 506 | ! |
|---|
| 507 | !-- Universal function for autoconversion process |
|---|
| 508 | !-- (Seifert and Beheng, 2006): |
|---|
| 509 | phi_au = 600.0_wp * tau_cloud**0.68_wp * & |
|---|
| 510 | ( 1.0_wp - tau_cloud**0.68_wp )**3 |
|---|
| 511 | ! |
|---|
| 512 | !-- Shape parameter of gamma distribution (Geoffroy et al., 2010): |
|---|
| 513 | !-- (Use constant nu_c = 1.0_wp instead?) |
|---|
| 514 | nu_c = 1.0_wp !MAX( 0.0_wp, 1580.0_wp * hyrho(k) * qc(k,j,i) - 0.28_wp ) |
|---|
| 515 | ! |
|---|
| 516 | !-- Mean weight of cloud droplets: |
|---|
| 517 | xc = hyrho(k) * qc(k,j,i) / nc_const |
|---|
| 518 | ! |
|---|
| 519 | !-- Parameterized turbulence effects on autoconversion (Seifert, |
|---|
| 520 | !-- Nuijens and Stevens, 2010) |
|---|
| 521 | IF ( collision_turbulence ) THEN |
|---|
| 522 | ! |
|---|
| 523 | !-- Weight averaged radius of cloud droplets: |
|---|
| 524 | rc = 0.5_wp * ( xc * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 525 | |
|---|
| 526 | alpha_cc = ( a_1 + a_2 * nu_c ) / ( 1.0_wp + a_3 * nu_c ) |
|---|
| 527 | r_cc = ( b_1 + b_2 * nu_c ) / ( 1.0_wp + b_3 * nu_c ) |
|---|
| 528 | sigma_cc = ( c_1 + c_2 * nu_c ) / ( 1.0_wp + c_3 * nu_c ) |
|---|
| 529 | ! |
|---|
| 530 | !-- Mixing length (neglecting distance to ground and |
|---|
| 531 | !-- stratification) |
|---|
| 532 | l_mix = ( dx * dy * dzu(k) )**( 1.0_wp / 3.0_wp ) |
|---|
| 533 | ! |
|---|
| 534 | !-- Limit dissipation rate according to Seifert, Nuijens and |
|---|
| 535 | !-- Stevens (2010) |
|---|
| 536 | dissipation = MIN( 0.06_wp, diss(k,j,i) ) |
|---|
| 537 | ! |
|---|
| 538 | !-- Compute Taylor-microscale Reynolds number: |
|---|
| 539 | re_lambda = 6.0_wp / 11.0_wp * & |
|---|
| 540 | ( l_mix / c_const )**( 2.0_wp / 3.0_wp ) * & |
|---|
| 541 | SQRT( 15.0_wp / kin_vis_air ) * & |
|---|
| 542 | dissipation**( 1.0_wp / 6.0_wp ) |
|---|
| 543 | ! |
|---|
| 544 | !-- The factor of 1.0E4 is needed to convert the dissipation |
|---|
| 545 | !-- rate from m2 s-3 to cm2 s-3. |
|---|
| 546 | k_au = k_au * ( 1.0_wp + & |
|---|
| 547 | dissipation * 1.0E4_wp * & |
|---|
| 548 | ( re_lambda * 1.0E-3_wp )**0.25_wp * & |
|---|
| 549 | ( alpha_cc * EXP( -1.0_wp * ( ( rc - & |
|---|
| 550 | r_cc ) / & |
|---|
| 551 | sigma_cc )**2 & |
|---|
| 552 | ) + beta_cc & |
|---|
| 553 | ) & |
|---|
| 554 | ) |
|---|
| 555 | ENDIF |
|---|
| 556 | ! |
|---|
| 557 | !-- Autoconversion rate (Seifert and Beheng, 2006): |
|---|
| 558 | autocon = k_au * ( nu_c + 2.0_wp ) * ( nu_c + 4.0_wp ) / & |
|---|
| 559 | ( nu_c + 1.0_wp )**2 * qc(k,j,i)**2 * xc**2 * & |
|---|
| 560 | ( 1.0_wp + phi_au / ( 1.0_wp - tau_cloud )**2 ) * & |
|---|
| 561 | rho_surface |
|---|
| 562 | autocon = MIN( autocon, qc(k,j,i) / dt_micro ) |
|---|
| 563 | |
|---|
| 564 | qr(k,j,i) = qr(k,j,i) + autocon * dt_micro * flag |
|---|
| 565 | qc(k,j,i) = qc(k,j,i) - autocon * dt_micro * flag |
|---|
| 566 | nr(k,j,i) = nr(k,j,i) + autocon / x0 * hyrho(k) * dt_micro & |
|---|
| 567 | * flag |
|---|
| 568 | |
|---|
| 569 | ENDIF |
|---|
| 570 | |
|---|
| 571 | ENDDO |
|---|
| 572 | ENDDO |
|---|
| 573 | ENDDO |
|---|
| 574 | |
|---|
| 575 | CALL cpu_log( log_point_s(55), 'autoconversion', 'stop' ) |
|---|
| 576 | |
|---|
| 577 | END SUBROUTINE autoconversion |
|---|
| 578 | |
|---|
| 579 | |
|---|
| 580 | !------------------------------------------------------------------------------! |
|---|
| 581 | ! Description: |
|---|
| 582 | ! ------------ |
|---|
| 583 | !> Autoconversion process (Kessler, 1969). |
|---|
| 584 | !------------------------------------------------------------------------------! |
|---|
| 585 | SUBROUTINE autoconversion_kessler |
|---|
| 586 | |
|---|
| 587 | USE arrays_3d, & |
|---|
| 588 | ONLY: dzw, pt, prr, q, qc |
|---|
| 589 | |
|---|
| 590 | USE cloud_parameters, & |
|---|
| 591 | ONLY: l_d_cp, pt_d_t |
|---|
| 592 | |
|---|
| 593 | USE indices, & |
|---|
| 594 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 595 | |
|---|
| 596 | USE kinds |
|---|
| 597 | |
|---|
| 598 | |
|---|
| 599 | IMPLICIT NONE |
|---|
| 600 | |
|---|
| 601 | INTEGER(iwp) :: i !< |
|---|
| 602 | INTEGER(iwp) :: j !< |
|---|
| 603 | INTEGER(iwp) :: k !< |
|---|
| 604 | INTEGER(iwp) :: k_wall !< topgraphy top index |
|---|
| 605 | |
|---|
| 606 | REAL(wp) :: dqdt_precip !< |
|---|
| 607 | REAL(wp) :: flag !< flag to mask topography grid points |
|---|
| 608 | |
|---|
| 609 | DO i = nxlg, nxrg |
|---|
| 610 | DO j = nysg, nyng |
|---|
| 611 | ! |
|---|
| 612 | !-- Determine vertical index of topography top |
|---|
| 613 | k_wall = MAXLOC( & |
|---|
| 614 | MERGE( 1, 0, & |
|---|
| 615 | BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) & |
|---|
| 616 | ), DIM = 1 & |
|---|
| 617 | ) - 1 |
|---|
| 618 | DO k = nzb+1, nzt |
|---|
| 619 | ! |
|---|
| 620 | !-- Predetermine flag to mask topography |
|---|
| 621 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 622 | |
|---|
| 623 | IF ( qc(k,j,i) > ql_crit ) THEN |
|---|
| 624 | dqdt_precip = prec_time_const * ( qc(k,j,i) - ql_crit ) |
|---|
| 625 | ELSE |
|---|
| 626 | dqdt_precip = 0.0_wp |
|---|
| 627 | ENDIF |
|---|
| 628 | |
|---|
| 629 | qc(k,j,i) = qc(k,j,i) - dqdt_precip * dt_micro * flag |
|---|
| 630 | q(k,j,i) = q(k,j,i) - dqdt_precip * dt_micro * flag |
|---|
| 631 | pt(k,j,i) = pt(k,j,i) + dqdt_precip * dt_micro * l_d_cp * & |
|---|
| 632 | pt_d_t(k) * flag |
|---|
| 633 | |
|---|
| 634 | ! |
|---|
| 635 | !-- Compute the rain rate (stored on surface grid point) |
|---|
| 636 | prr(k_wall,j,i) = prr(k_wall,j,i) + dqdt_precip * dzw(k) * flag |
|---|
| 637 | |
|---|
| 638 | ENDDO |
|---|
| 639 | ENDDO |
|---|
| 640 | ENDDO |
|---|
| 641 | |
|---|
| 642 | END SUBROUTINE autoconversion_kessler |
|---|
| 643 | |
|---|
| 644 | |
|---|
| 645 | !------------------------------------------------------------------------------! |
|---|
| 646 | ! Description: |
|---|
| 647 | ! ------------ |
|---|
| 648 | !> Accretion rate (Seifert and Beheng, 2006). |
|---|
| 649 | !------------------------------------------------------------------------------! |
|---|
| 650 | SUBROUTINE accretion |
|---|
| 651 | |
|---|
| 652 | USE arrays_3d, & |
|---|
| 653 | ONLY: diss, qc, qr |
|---|
| 654 | |
|---|
| 655 | USE cloud_parameters, & |
|---|
| 656 | ONLY: hyrho |
|---|
| 657 | |
|---|
| 658 | USE control_parameters, & |
|---|
| 659 | ONLY: rho_surface |
|---|
| 660 | |
|---|
| 661 | USE cpulog, & |
|---|
| 662 | ONLY: cpu_log, log_point_s |
|---|
| 663 | |
|---|
| 664 | USE indices, & |
|---|
| 665 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 666 | |
|---|
| 667 | USE kinds |
|---|
| 668 | |
|---|
| 669 | IMPLICIT NONE |
|---|
| 670 | |
|---|
| 671 | INTEGER(iwp) :: i !< |
|---|
| 672 | INTEGER(iwp) :: j !< |
|---|
| 673 | INTEGER(iwp) :: k !< |
|---|
| 674 | |
|---|
| 675 | REAL(wp) :: accr !< |
|---|
| 676 | REAL(wp) :: flag !< flag to mask topography grid points |
|---|
| 677 | REAL(wp) :: k_cr !< |
|---|
| 678 | REAL(wp) :: phi_ac !< |
|---|
| 679 | REAL(wp) :: tau_cloud !< |
|---|
| 680 | |
|---|
| 681 | CALL cpu_log( log_point_s(56), 'accretion', 'start' ) |
|---|
| 682 | |
|---|
| 683 | DO i = nxlg, nxrg |
|---|
| 684 | DO j = nysg, nyng |
|---|
| 685 | DO k = nzb+1, nzt |
|---|
| 686 | ! |
|---|
| 687 | !-- Predetermine flag to mask topography |
|---|
| 688 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 689 | |
|---|
| 690 | IF ( ( qc(k,j,i) > eps_sb ) .AND. ( qr(k,j,i) > eps_sb ) ) THEN |
|---|
| 691 | ! |
|---|
| 692 | !-- Intern time scale of coagulation (Seifert and Beheng, 2006): |
|---|
| 693 | tau_cloud = 1.0_wp - qc(k,j,i) / ( qc(k,j,i) + qr(k,j,i) ) |
|---|
| 694 | ! |
|---|
| 695 | !-- Universal function for accretion process (Seifert and |
|---|
| 696 | !-- Beheng, 2001): |
|---|
| 697 | phi_ac = ( tau_cloud / ( tau_cloud + 5.0E-5_wp ) )**4 |
|---|
| 698 | ! |
|---|
| 699 | !-- Parameterized turbulence effects on autoconversion (Seifert, |
|---|
| 700 | !-- Nuijens and Stevens, 2010). The factor of 1.0E4 is needed to |
|---|
| 701 | !-- convert the dissipation rate (diss) from m2 s-3 to cm2 s-3. |
|---|
| 702 | IF ( collision_turbulence ) THEN |
|---|
| 703 | k_cr = k_cr0 * ( 1.0_wp + 0.05_wp * & |
|---|
| 704 | MIN( 600.0_wp, & |
|---|
| 705 | diss(k,j,i) * 1.0E4_wp )**0.25_wp & |
|---|
| 706 | ) |
|---|
| 707 | ELSE |
|---|
| 708 | k_cr = k_cr0 |
|---|
| 709 | ENDIF |
|---|
| 710 | ! |
|---|
| 711 | !-- Accretion rate (Seifert and Beheng, 2006): |
|---|
| 712 | accr = k_cr * qc(k,j,i) * qr(k,j,i) * phi_ac * & |
|---|
| 713 | SQRT( rho_surface * hyrho(k) ) |
|---|
| 714 | accr = MIN( accr, qc(k,j,i) / dt_micro ) |
|---|
| 715 | |
|---|
| 716 | qr(k,j,i) = qr(k,j,i) + accr * dt_micro * flag |
|---|
| 717 | qc(k,j,i) = qc(k,j,i) - accr * dt_micro * flag |
|---|
| 718 | |
|---|
| 719 | ENDIF |
|---|
| 720 | |
|---|
| 721 | ENDDO |
|---|
| 722 | ENDDO |
|---|
| 723 | ENDDO |
|---|
| 724 | |
|---|
| 725 | CALL cpu_log( log_point_s(56), 'accretion', 'stop' ) |
|---|
| 726 | |
|---|
| 727 | END SUBROUTINE accretion |
|---|
| 728 | |
|---|
| 729 | |
|---|
| 730 | !------------------------------------------------------------------------------! |
|---|
| 731 | ! Description: |
|---|
| 732 | ! ------------ |
|---|
| 733 | !> Collisional breakup rate (Seifert, 2008). |
|---|
| 734 | !------------------------------------------------------------------------------! |
|---|
| 735 | SUBROUTINE selfcollection_breakup |
|---|
| 736 | |
|---|
| 737 | USE arrays_3d, & |
|---|
| 738 | ONLY: nr, qr |
|---|
| 739 | |
|---|
| 740 | USE cloud_parameters, & |
|---|
| 741 | ONLY: hyrho |
|---|
| 742 | |
|---|
| 743 | USE control_parameters, & |
|---|
| 744 | ONLY: rho_surface |
|---|
| 745 | |
|---|
| 746 | USE cpulog, & |
|---|
| 747 | ONLY: cpu_log, log_point_s |
|---|
| 748 | |
|---|
| 749 | USE indices, & |
|---|
| 750 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 751 | |
|---|
| 752 | USE kinds |
|---|
| 753 | |
|---|
| 754 | IMPLICIT NONE |
|---|
| 755 | |
|---|
| 756 | INTEGER(iwp) :: i !< |
|---|
| 757 | INTEGER(iwp) :: j !< |
|---|
| 758 | INTEGER(iwp) :: k !< |
|---|
| 759 | |
|---|
| 760 | REAL(wp) :: breakup !< |
|---|
| 761 | REAL(wp) :: dr !< |
|---|
| 762 | REAL(wp) :: flag !< flag to mask topography grid points |
|---|
| 763 | REAL(wp) :: phi_br !< |
|---|
| 764 | REAL(wp) :: selfcoll !< |
|---|
| 765 | |
|---|
| 766 | CALL cpu_log( log_point_s(57), 'selfcollection', 'start' ) |
|---|
| 767 | |
|---|
| 768 | DO i = nxlg, nxrg |
|---|
| 769 | DO j = nysg, nyng |
|---|
| 770 | DO k = nzb+1, nzt |
|---|
| 771 | ! |
|---|
| 772 | !-- Predetermine flag to mask topography |
|---|
| 773 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 774 | |
|---|
| 775 | IF ( qr(k,j,i) > eps_sb ) THEN |
|---|
| 776 | ! |
|---|
| 777 | !-- Selfcollection rate (Seifert and Beheng, 2001): |
|---|
| 778 | selfcoll = k_rr * nr(k,j,i) * qr(k,j,i) * & |
|---|
| 779 | SQRT( hyrho(k) * rho_surface ) |
|---|
| 780 | ! |
|---|
| 781 | !-- Weight averaged diameter of rain drops: |
|---|
| 782 | dr = ( hyrho(k) * qr(k,j,i) / & |
|---|
| 783 | nr(k,j,i) * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 784 | ! |
|---|
| 785 | !-- Collisional breakup rate (Seifert, 2008): |
|---|
| 786 | IF ( dr >= 0.3E-3_wp ) THEN |
|---|
| 787 | phi_br = k_br * ( dr - 1.1E-3_wp ) |
|---|
| 788 | breakup = selfcoll * ( phi_br + 1.0_wp ) |
|---|
| 789 | ELSE |
|---|
| 790 | breakup = 0.0_wp |
|---|
| 791 | ENDIF |
|---|
| 792 | |
|---|
| 793 | selfcoll = MAX( breakup - selfcoll, -nr(k,j,i) / dt_micro ) |
|---|
| 794 | nr(k,j,i) = nr(k,j,i) + selfcoll * dt_micro * flag |
|---|
| 795 | |
|---|
| 796 | ENDIF |
|---|
| 797 | ENDDO |
|---|
| 798 | ENDDO |
|---|
| 799 | ENDDO |
|---|
| 800 | |
|---|
| 801 | CALL cpu_log( log_point_s(57), 'selfcollection', 'stop' ) |
|---|
| 802 | |
|---|
| 803 | END SUBROUTINE selfcollection_breakup |
|---|
| 804 | |
|---|
| 805 | |
|---|
| 806 | !------------------------------------------------------------------------------! |
|---|
| 807 | ! Description: |
|---|
| 808 | ! ------------ |
|---|
| 809 | !> Evaporation of precipitable water. Condensation is neglected for |
|---|
| 810 | !> precipitable water. |
|---|
| 811 | !------------------------------------------------------------------------------! |
|---|
| 812 | SUBROUTINE evaporation_rain |
|---|
| 813 | |
|---|
| 814 | USE arrays_3d, & |
|---|
| 815 | ONLY: hyp, nr, pt, q, qc, qr |
|---|
| 816 | |
|---|
| 817 | USE cloud_parameters, & |
|---|
| 818 | ONLY: hyrho, l_d_cp, l_d_r, l_v, r_v, t_d_pt |
|---|
| 819 | |
|---|
| 820 | USE constants, & |
|---|
| 821 | ONLY: pi |
|---|
| 822 | |
|---|
| 823 | USE cpulog, & |
|---|
| 824 | ONLY: cpu_log, log_point_s |
|---|
| 825 | |
|---|
| 826 | USE indices, & |
|---|
| 827 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 828 | |
|---|
| 829 | USE kinds |
|---|
| 830 | |
|---|
| 831 | IMPLICIT NONE |
|---|
| 832 | |
|---|
| 833 | INTEGER(iwp) :: i !< |
|---|
| 834 | INTEGER(iwp) :: j !< |
|---|
| 835 | INTEGER(iwp) :: k !< |
|---|
| 836 | |
|---|
| 837 | REAL(wp) :: alpha !< |
|---|
| 838 | REAL(wp) :: dr !< |
|---|
| 839 | REAL(wp) :: e_s !< |
|---|
| 840 | REAL(wp) :: evap !< |
|---|
| 841 | REAL(wp) :: evap_nr !< |
|---|
| 842 | REAL(wp) :: f_vent !< |
|---|
| 843 | REAL(wp) :: flag !< flag to mask topography grid points |
|---|
| 844 | REAL(wp) :: g_evap !< |
|---|
| 845 | REAL(wp) :: lambda_r !< |
|---|
| 846 | REAL(wp) :: mu_r !< |
|---|
| 847 | REAL(wp) :: mu_r_2 !< |
|---|
| 848 | REAL(wp) :: mu_r_5d2 !< |
|---|
| 849 | REAL(wp) :: nr_0 !< |
|---|
| 850 | REAL(wp) :: q_s !< |
|---|
| 851 | REAL(wp) :: sat !< |
|---|
| 852 | REAL(wp) :: t_l !< |
|---|
| 853 | REAL(wp) :: temp !< |
|---|
| 854 | REAL(wp) :: xr !< |
|---|
| 855 | |
|---|
| 856 | CALL cpu_log( log_point_s(58), 'evaporation', 'start' ) |
|---|
| 857 | |
|---|
| 858 | DO i = nxlg, nxrg |
|---|
| 859 | DO j = nysg, nyng |
|---|
| 860 | DO k = nzb+1, nzt |
|---|
| 861 | ! |
|---|
| 862 | !-- Predetermine flag to mask topography |
|---|
| 863 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 864 | |
|---|
| 865 | IF ( qr(k,j,i) > eps_sb ) THEN |
|---|
| 866 | ! |
|---|
| 867 | !-- Actual liquid water temperature: |
|---|
| 868 | t_l = t_d_pt(k) * pt(k,j,i) |
|---|
| 869 | ! |
|---|
| 870 | !-- Saturation vapor pressure at t_l: |
|---|
| 871 | e_s = 610.78_wp * EXP( 17.269_wp * ( t_l - 273.16_wp ) / & |
|---|
| 872 | ( t_l - 35.86_wp ) & |
|---|
| 873 | ) |
|---|
| 874 | ! |
|---|
| 875 | !-- Computation of saturation humidity: |
|---|
| 876 | q_s = 0.622_wp * e_s / ( hyp(k) - 0.378_wp * e_s ) |
|---|
| 877 | alpha = 0.622_wp * l_d_r * l_d_cp / ( t_l * t_l ) |
|---|
| 878 | q_s = q_s * ( 1.0_wp + alpha * q(k,j,i) ) / & |
|---|
| 879 | ( 1.0_wp + alpha * q_s ) |
|---|
| 880 | ! |
|---|
| 881 | !-- Supersaturation: |
|---|
| 882 | sat = ( q(k,j,i) - qr(k,j,i) - qc(k,j,i) ) / q_s - 1.0_wp |
|---|
| 883 | ! |
|---|
| 884 | !-- Evaporation needs only to be calculated in subsaturated regions |
|---|
| 885 | IF ( sat < 0.0_wp ) THEN |
|---|
| 886 | ! |
|---|
| 887 | !-- Actual temperature: |
|---|
| 888 | temp = t_l + l_d_cp * ( qc(k,j,i) + qr(k,j,i) ) |
|---|
| 889 | |
|---|
| 890 | g_evap = 1.0_wp / ( ( l_v / ( r_v * temp ) - 1.0_wp ) * & |
|---|
| 891 | l_v / ( thermal_conductivity_l * temp ) & |
|---|
| 892 | + r_v * temp / ( diff_coeff_l * e_s ) & |
|---|
| 893 | ) |
|---|
| 894 | ! |
|---|
| 895 | !-- Mean weight of rain drops |
|---|
| 896 | xr = hyrho(k) * qr(k,j,i) / nr(k,j,i) |
|---|
| 897 | ! |
|---|
| 898 | !-- Weight averaged diameter of rain drops: |
|---|
| 899 | dr = ( xr * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 900 | ! |
|---|
| 901 | !-- Compute ventilation factor and intercept parameter |
|---|
| 902 | !-- (Seifert and Beheng, 2006; Seifert, 2008): |
|---|
| 903 | IF ( ventilation_effect ) THEN |
|---|
| 904 | ! |
|---|
| 905 | !-- Shape parameter of gamma distribution (Milbrandt and Yau, |
|---|
| 906 | !-- 2005; Stevens and Seifert, 2008): |
|---|
| 907 | mu_r = 10.0_wp * ( 1.0_wp + TANH( 1.2E3_wp * & |
|---|
| 908 | ( dr - 1.4E-3_wp ) ) ) |
|---|
| 909 | ! |
|---|
| 910 | !-- Slope parameter of gamma distribution (Seifert, 2008): |
|---|
| 911 | lambda_r = ( ( mu_r + 3.0_wp ) * ( mu_r + 2.0_wp ) * & |
|---|
| 912 | ( mu_r + 1.0_wp ) & |
|---|
| 913 | )**( 1.0_wp / 3.0_wp ) / dr |
|---|
| 914 | |
|---|
| 915 | mu_r_2 = mu_r + 2.0_wp |
|---|
| 916 | mu_r_5d2 = mu_r + 2.5_wp |
|---|
| 917 | |
|---|
| 918 | f_vent = a_vent * gamm( mu_r_2 ) * & |
|---|
| 919 | lambda_r**( -mu_r_2 ) + b_vent * & |
|---|
| 920 | schmidt_p_1d3 * SQRT( a_term / kin_vis_air ) *& |
|---|
| 921 | gamm( mu_r_5d2 ) * lambda_r**( -mu_r_5d2 ) * & |
|---|
| 922 | ( 1.0_wp - & |
|---|
| 923 | 0.5_wp * ( b_term / a_term ) * & |
|---|
| 924 | ( lambda_r / ( c_term + lambda_r ) & |
|---|
| 925 | )**mu_r_5d2 - & |
|---|
| 926 | 0.125_wp * ( b_term / a_term )**2 * & |
|---|
| 927 | ( lambda_r / ( 2.0_wp * c_term + lambda_r ) & |
|---|
| 928 | )**mu_r_5d2 - & |
|---|
| 929 | 0.0625_wp * ( b_term / a_term )**3 * & |
|---|
| 930 | ( lambda_r / ( 3.0_wp * c_term + lambda_r ) & |
|---|
| 931 | )**mu_r_5d2 - & |
|---|
| 932 | 0.0390625_wp * ( b_term / a_term )**4 * & |
|---|
| 933 | ( lambda_r / ( 4.0_wp * c_term + lambda_r ) & |
|---|
| 934 | )**mu_r_5d2 & |
|---|
| 935 | ) |
|---|
| 936 | |
|---|
| 937 | nr_0 = nr(k,j,i) * lambda_r**( mu_r + 1.0_wp ) / & |
|---|
| 938 | gamm( mu_r + 1.0_wp ) |
|---|
| 939 | ELSE |
|---|
| 940 | f_vent = 1.0_wp |
|---|
| 941 | nr_0 = nr(k,j,i) * dr |
|---|
| 942 | ENDIF |
|---|
| 943 | ! |
|---|
| 944 | !-- Evaporation rate of rain water content (Seifert and |
|---|
| 945 | !-- Beheng, 2006): |
|---|
| 946 | evap = 2.0_wp * pi * nr_0 * g_evap * f_vent * sat / & |
|---|
| 947 | hyrho(k) |
|---|
| 948 | evap = MAX( evap, -qr(k,j,i) / dt_micro ) |
|---|
| 949 | evap_nr = MAX( c_evap * evap / xr * hyrho(k), & |
|---|
| 950 | -nr(k,j,i) / dt_micro ) |
|---|
| 951 | |
|---|
| 952 | qr(k,j,i) = qr(k,j,i) + evap * dt_micro * flag |
|---|
| 953 | nr(k,j,i) = nr(k,j,i) + evap_nr * dt_micro * flag |
|---|
| 954 | |
|---|
| 955 | ENDIF |
|---|
| 956 | ENDIF |
|---|
| 957 | |
|---|
| 958 | ENDDO |
|---|
| 959 | ENDDO |
|---|
| 960 | ENDDO |
|---|
| 961 | |
|---|
| 962 | CALL cpu_log( log_point_s(58), 'evaporation', 'stop' ) |
|---|
| 963 | |
|---|
| 964 | END SUBROUTINE evaporation_rain |
|---|
| 965 | |
|---|
| 966 | |
|---|
| 967 | !------------------------------------------------------------------------------! |
|---|
| 968 | ! Description: |
|---|
| 969 | ! ------------ |
|---|
| 970 | !> Sedimentation of cloud droplets (Ackermann et al., 2009, MWR). |
|---|
| 971 | !------------------------------------------------------------------------------! |
|---|
| 972 | SUBROUTINE sedimentation_cloud |
|---|
| 973 | |
|---|
| 974 | USE arrays_3d, & |
|---|
| 975 | ONLY: ddzu, dzu, pt, prr, q, qc |
|---|
| 976 | |
|---|
| 977 | USE cloud_parameters, & |
|---|
| 978 | ONLY: hyrho, l_d_cp, pt_d_t |
|---|
| 979 | |
|---|
| 980 | USE control_parameters, & |
|---|
| 981 | ONLY: call_microphysics_at_all_substeps, intermediate_timestep_count |
|---|
| 982 | |
|---|
| 983 | USE cpulog, & |
|---|
| 984 | ONLY: cpu_log, log_point_s |
|---|
| 985 | |
|---|
| 986 | USE indices, & |
|---|
| 987 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 988 | |
|---|
| 989 | USE kinds |
|---|
| 990 | |
|---|
| 991 | USE statistics, & |
|---|
| 992 | ONLY: weight_substep |
|---|
| 993 | |
|---|
| 994 | |
|---|
| 995 | IMPLICIT NONE |
|---|
| 996 | |
|---|
| 997 | INTEGER(iwp) :: i !< |
|---|
| 998 | INTEGER(iwp) :: j !< |
|---|
| 999 | INTEGER(iwp) :: k !< |
|---|
| 1000 | |
|---|
| 1001 | REAL(wp) :: flag !< flag to mask topography grid points |
|---|
| 1002 | REAL(wp), DIMENSION(nzb:nzt+1) :: sed_qc !< |
|---|
| 1003 | |
|---|
| 1004 | CALL cpu_log( log_point_s(59), 'sed_cloud', 'start' ) |
|---|
| 1005 | |
|---|
| 1006 | sed_qc(nzt+1) = 0.0_wp |
|---|
| 1007 | |
|---|
| 1008 | DO i = nxlg, nxrg |
|---|
| 1009 | DO j = nysg, nyng |
|---|
| 1010 | DO k = nzt, nzb+1, -1 |
|---|
| 1011 | ! |
|---|
| 1012 | !-- Predetermine flag to mask topography |
|---|
| 1013 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1014 | |
|---|
| 1015 | IF ( qc(k,j,i) > eps_sb ) THEN |
|---|
| 1016 | sed_qc(k) = sed_qc_const * nc_const**( -2.0_wp / 3.0_wp ) * & |
|---|
| 1017 | ( qc(k,j,i) * hyrho(k) )**( 5.0_wp / 3.0_wp ) * & |
|---|
| 1018 | flag |
|---|
| 1019 | ELSE |
|---|
| 1020 | sed_qc(k) = 0.0_wp |
|---|
| 1021 | ENDIF |
|---|
| 1022 | |
|---|
| 1023 | sed_qc(k) = MIN( sed_qc(k), hyrho(k) * dzu(k+1) * q(k,j,i) / & |
|---|
| 1024 | dt_micro + sed_qc(k+1) & |
|---|
| 1025 | ) * flag |
|---|
| 1026 | |
|---|
| 1027 | q(k,j,i) = q(k,j,i) + ( sed_qc(k+1) - sed_qc(k) ) * & |
|---|
| 1028 | ddzu(k+1) / hyrho(k) * dt_micro * flag |
|---|
| 1029 | qc(k,j,i) = qc(k,j,i) + ( sed_qc(k+1) - sed_qc(k) ) * & |
|---|
| 1030 | ddzu(k+1) / hyrho(k) * dt_micro * flag |
|---|
| 1031 | pt(k,j,i) = pt(k,j,i) - ( sed_qc(k+1) - sed_qc(k) ) * & |
|---|
| 1032 | ddzu(k+1) / hyrho(k) * l_d_cp * & |
|---|
| 1033 | pt_d_t(k) * dt_micro * flag |
|---|
| 1034 | |
|---|
| 1035 | ! |
|---|
| 1036 | !-- Compute the precipitation rate due to cloud (fog) droplets |
|---|
| 1037 | IF ( call_microphysics_at_all_substeps ) THEN |
|---|
| 1038 | prr(k,j,i) = prr(k,j,i) + sed_qc(k) / hyrho(k) & |
|---|
| 1039 | * weight_substep(intermediate_timestep_count) & |
|---|
| 1040 | * flag |
|---|
| 1041 | ELSE |
|---|
| 1042 | prr(k,j,i) = prr(k,j,i) + sed_qc(k) / hyrho(k) * flag |
|---|
| 1043 | ENDIF |
|---|
| 1044 | |
|---|
| 1045 | ENDDO |
|---|
| 1046 | ENDDO |
|---|
| 1047 | ENDDO |
|---|
| 1048 | |
|---|
| 1049 | CALL cpu_log( log_point_s(59), 'sed_cloud', 'stop' ) |
|---|
| 1050 | |
|---|
| 1051 | END SUBROUTINE sedimentation_cloud |
|---|
| 1052 | |
|---|
| 1053 | |
|---|
| 1054 | !------------------------------------------------------------------------------! |
|---|
| 1055 | ! Description: |
|---|
| 1056 | ! ------------ |
|---|
| 1057 | !> Computation of sedimentation flux. Implementation according to Stevens |
|---|
| 1058 | !> and Seifert (2008). Code is based on UCLA-LES. |
|---|
| 1059 | !------------------------------------------------------------------------------! |
|---|
| 1060 | SUBROUTINE sedimentation_rain |
|---|
| 1061 | |
|---|
| 1062 | USE arrays_3d, & |
|---|
| 1063 | ONLY: ddzu, dzu, nr, pt, prr, q, qr |
|---|
| 1064 | |
|---|
| 1065 | USE cloud_parameters, & |
|---|
| 1066 | ONLY: hyrho, l_d_cp, pt_d_t |
|---|
| 1067 | |
|---|
| 1068 | USE control_parameters, & |
|---|
| 1069 | ONLY: call_microphysics_at_all_substeps, intermediate_timestep_count |
|---|
| 1070 | USE cpulog, & |
|---|
| 1071 | ONLY: cpu_log, log_point_s |
|---|
| 1072 | |
|---|
| 1073 | USE indices, & |
|---|
| 1074 | ONLY: nxlg, nxrg, nyng, nysg, nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 1075 | |
|---|
| 1076 | USE kinds |
|---|
| 1077 | |
|---|
| 1078 | USE statistics, & |
|---|
| 1079 | ONLY: weight_substep |
|---|
| 1080 | |
|---|
| 1081 | USE surface_mod, & |
|---|
| 1082 | ONLY : bc_h |
|---|
| 1083 | |
|---|
| 1084 | IMPLICIT NONE |
|---|
| 1085 | |
|---|
| 1086 | INTEGER(iwp) :: i !< running index x direction |
|---|
| 1087 | INTEGER(iwp) :: j !< running index y direction |
|---|
| 1088 | INTEGER(iwp) :: k !< running index z direction |
|---|
| 1089 | INTEGER(iwp) :: k_run !< |
|---|
| 1090 | INTEGER(iwp) :: l !< running index of surface type |
|---|
| 1091 | INTEGER(iwp) :: m !< running index surface elements |
|---|
| 1092 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
|---|
| 1093 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
|---|
| 1094 | |
|---|
| 1095 | REAL(wp) :: c_run !< |
|---|
| 1096 | REAL(wp) :: d_max !< |
|---|
| 1097 | REAL(wp) :: d_mean !< |
|---|
| 1098 | REAL(wp) :: d_min !< |
|---|
| 1099 | REAL(wp) :: dr !< |
|---|
| 1100 | REAL(wp) :: flux !< |
|---|
| 1101 | REAL(wp) :: flag !< flag to mask topography grid points |
|---|
| 1102 | REAL(wp) :: lambda_r !< |
|---|
| 1103 | REAL(wp) :: mu_r !< |
|---|
| 1104 | REAL(wp) :: z_run !< |
|---|
| 1105 | |
|---|
| 1106 | REAL(wp), DIMENSION(nzb:nzt+1) :: c_nr !< |
|---|
| 1107 | REAL(wp), DIMENSION(nzb:nzt+1) :: c_qr !< |
|---|
| 1108 | REAL(wp), DIMENSION(nzb:nzt+1) :: nr_slope !< |
|---|
| 1109 | REAL(wp), DIMENSION(nzb:nzt+1) :: qr_slope !< |
|---|
| 1110 | REAL(wp), DIMENSION(nzb:nzt+1) :: sed_nr !< |
|---|
| 1111 | REAL(wp), DIMENSION(nzb:nzt+1) :: sed_qr !< |
|---|
| 1112 | REAL(wp), DIMENSION(nzb:nzt+1) :: w_nr !< |
|---|
| 1113 | REAL(wp), DIMENSION(nzb:nzt+1) :: w_qr !< |
|---|
| 1114 | |
|---|
| 1115 | CALL cpu_log( log_point_s(60), 'sed_rain', 'start' ) |
|---|
| 1116 | |
|---|
| 1117 | ! |
|---|
| 1118 | !-- Compute velocities |
|---|
| 1119 | DO i = nxlg, nxrg |
|---|
| 1120 | DO j = nysg, nyng |
|---|
| 1121 | DO k = nzb+1, nzt |
|---|
| 1122 | ! |
|---|
| 1123 | !-- Predetermine flag to mask topography |
|---|
| 1124 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1125 | |
|---|
| 1126 | IF ( qr(k,j,i) > eps_sb ) THEN |
|---|
| 1127 | ! |
|---|
| 1128 | !-- Weight averaged diameter of rain drops: |
|---|
| 1129 | dr = ( hyrho(k) * qr(k,j,i) / & |
|---|
| 1130 | nr(k,j,i) * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 1131 | ! |
|---|
| 1132 | !-- Shape parameter of gamma distribution (Milbrandt and Yau, 2005; |
|---|
| 1133 | !-- Stevens and Seifert, 2008): |
|---|
| 1134 | mu_r = 10.0_wp * ( 1.0_wp + TANH( 1.2E3_wp * & |
|---|
| 1135 | ( dr - 1.4E-3_wp ) ) ) |
|---|
| 1136 | ! |
|---|
| 1137 | !-- Slope parameter of gamma distribution (Seifert, 2008): |
|---|
| 1138 | lambda_r = ( ( mu_r + 3.0_wp ) * ( mu_r + 2.0_wp ) * & |
|---|
| 1139 | ( mu_r + 1.0_wp ) )**( 1.0_wp / 3.0_wp ) / dr |
|---|
| 1140 | |
|---|
| 1141 | w_nr(k) = MAX( 0.1_wp, MIN( 20.0_wp, & |
|---|
| 1142 | a_term - b_term * ( 1.0_wp + & |
|---|
| 1143 | c_term / & |
|---|
| 1144 | lambda_r )**( -1.0_wp * & |
|---|
| 1145 | ( mu_r + 1.0_wp ) ) & |
|---|
| 1146 | ) & |
|---|
| 1147 | ) * flag |
|---|
| 1148 | |
|---|
| 1149 | w_qr(k) = MAX( 0.1_wp, MIN( 20.0_wp, & |
|---|
| 1150 | a_term - b_term * ( 1.0_wp + & |
|---|
| 1151 | c_term / & |
|---|
| 1152 | lambda_r )**( -1.0_wp * & |
|---|
| 1153 | ( mu_r + 4.0_wp ) ) & |
|---|
| 1154 | ) & |
|---|
| 1155 | ) * flag |
|---|
| 1156 | ELSE |
|---|
| 1157 | w_nr(k) = 0.0_wp |
|---|
| 1158 | w_qr(k) = 0.0_wp |
|---|
| 1159 | ENDIF |
|---|
| 1160 | ENDDO |
|---|
| 1161 | ! |
|---|
| 1162 | !-- Adjust boundary values using surface data type. |
|---|
| 1163 | !-- Upward-facing |
|---|
| 1164 | surf_s = bc_h(0)%start_index(j,i) |
|---|
| 1165 | surf_e = bc_h(0)%end_index(j,i) |
|---|
| 1166 | DO m = surf_s, surf_e |
|---|
| 1167 | k = bc_h(0)%k(m) |
|---|
| 1168 | w_nr(k-1) = w_nr(k) |
|---|
| 1169 | w_qr(k-1) = w_qr(k) |
|---|
| 1170 | ENDDO |
|---|
| 1171 | ! |
|---|
| 1172 | !-- Downward-facing |
|---|
| 1173 | surf_s = bc_h(1)%start_index(j,i) |
|---|
| 1174 | surf_e = bc_h(1)%end_index(j,i) |
|---|
| 1175 | DO m = surf_s, surf_e |
|---|
| 1176 | k = bc_h(1)%k(m) |
|---|
| 1177 | w_nr(k+1) = w_nr(k) |
|---|
| 1178 | w_qr(k+1) = w_qr(k) |
|---|
| 1179 | ENDDO |
|---|
| 1180 | ! |
|---|
| 1181 | !-- Model top boundary value |
|---|
| 1182 | w_nr(nzt+1) = 0.0_wp |
|---|
| 1183 | w_qr(nzt+1) = 0.0_wp |
|---|
| 1184 | ! |
|---|
| 1185 | !-- Compute Courant number |
|---|
| 1186 | DO k = nzb+1, nzt |
|---|
| 1187 | ! |
|---|
| 1188 | !-- Predetermine flag to mask topography |
|---|
| 1189 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1190 | |
|---|
| 1191 | c_nr(k) = 0.25_wp * ( w_nr(k-1) + & |
|---|
| 1192 | 2.0_wp * w_nr(k) + w_nr(k+1) ) * & |
|---|
| 1193 | dt_micro * ddzu(k) * flag |
|---|
| 1194 | c_qr(k) = 0.25_wp * ( w_qr(k-1) + & |
|---|
| 1195 | 2.0_wp * w_qr(k) + w_qr(k+1) ) * & |
|---|
| 1196 | dt_micro * ddzu(k) * flag |
|---|
| 1197 | ENDDO |
|---|
| 1198 | ! |
|---|
| 1199 | !-- Limit slopes with monotonized centered (MC) limiter (van Leer, 1977): |
|---|
| 1200 | IF ( limiter_sedimentation ) THEN |
|---|
| 1201 | |
|---|
| 1202 | DO k = nzb+1, nzt |
|---|
| 1203 | ! |
|---|
| 1204 | !-- Predetermine flag to mask topography |
|---|
| 1205 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1206 | |
|---|
| 1207 | d_mean = 0.5_wp * ( qr(k+1,j,i) - qr(k-1,j,i) ) |
|---|
| 1208 | d_min = qr(k,j,i) - MIN( qr(k+1,j,i), qr(k,j,i), qr(k-1,j,i) ) |
|---|
| 1209 | d_max = MAX( qr(k+1,j,i), qr(k,j,i), qr(k-1,j,i) ) - qr(k,j,i) |
|---|
| 1210 | |
|---|
| 1211 | qr_slope(k) = SIGN(1.0_wp, d_mean) * MIN ( 2.0_wp * d_min, & |
|---|
| 1212 | 2.0_wp * d_max, & |
|---|
| 1213 | ABS( d_mean ) ) & |
|---|
| 1214 | * flag |
|---|
| 1215 | |
|---|
| 1216 | d_mean = 0.5_wp * ( nr(k+1,j,i) - nr(k-1,j,i) ) |
|---|
| 1217 | d_min = nr(k,j,i) - MIN( nr(k+1,j,i), nr(k,j,i), nr(k-1,j,i) ) |
|---|
| 1218 | d_max = MAX( nr(k+1,j,i), nr(k,j,i), nr(k-1,j,i) ) - nr(k,j,i) |
|---|
| 1219 | |
|---|
| 1220 | nr_slope(k) = SIGN(1.0_wp, d_mean) * MIN ( 2.0_wp * d_min, & |
|---|
| 1221 | 2.0_wp * d_max, & |
|---|
| 1222 | ABS( d_mean ) ) |
|---|
| 1223 | ENDDO |
|---|
| 1224 | |
|---|
| 1225 | ELSE |
|---|
| 1226 | |
|---|
| 1227 | nr_slope = 0.0_wp |
|---|
| 1228 | qr_slope = 0.0_wp |
|---|
| 1229 | |
|---|
| 1230 | ENDIF |
|---|
| 1231 | |
|---|
| 1232 | sed_nr(nzt+1) = 0.0_wp |
|---|
| 1233 | sed_qr(nzt+1) = 0.0_wp |
|---|
| 1234 | ! |
|---|
| 1235 | !-- Compute sedimentation flux |
|---|
| 1236 | DO k = nzt, nzb+1, -1 |
|---|
| 1237 | ! |
|---|
| 1238 | !-- Predetermine flag to mask topography |
|---|
| 1239 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1240 | ! |
|---|
| 1241 | !-- Sum up all rain drop number densities which contribute to the flux |
|---|
| 1242 | !-- through k-1/2 |
|---|
| 1243 | flux = 0.0_wp |
|---|
| 1244 | z_run = 0.0_wp ! height above z(k) |
|---|
| 1245 | k_run = k |
|---|
| 1246 | c_run = MIN( 1.0_wp, c_nr(k) ) |
|---|
| 1247 | DO WHILE ( c_run > 0.0_wp .AND. k_run <= nzt ) |
|---|
| 1248 | flux = flux + hyrho(k_run) * & |
|---|
| 1249 | ( nr(k_run,j,i) + nr_slope(k_run) * & |
|---|
| 1250 | ( 1.0_wp - c_run ) * 0.5_wp ) * c_run * dzu(k_run) & |
|---|
| 1251 | * flag |
|---|
| 1252 | z_run = z_run + dzu(k_run) * flag |
|---|
| 1253 | k_run = k_run + 1 * flag |
|---|
| 1254 | c_run = MIN( 1.0_wp, c_nr(k_run) - z_run * ddzu(k_run) ) & |
|---|
| 1255 | * flag |
|---|
| 1256 | ENDDO |
|---|
| 1257 | ! |
|---|
| 1258 | !-- It is not allowed to sediment more rain drop number density than |
|---|
| 1259 | !-- available |
|---|
| 1260 | flux = MIN( flux, & |
|---|
| 1261 | hyrho(k) * dzu(k+1) * nr(k,j,i) + sed_nr(k+1) * & |
|---|
| 1262 | dt_micro & |
|---|
| 1263 | ) |
|---|
| 1264 | |
|---|
| 1265 | sed_nr(k) = flux / dt_micro * flag |
|---|
| 1266 | nr(k,j,i) = nr(k,j,i) + ( sed_nr(k+1) - sed_nr(k) ) * & |
|---|
| 1267 | ddzu(k+1) / hyrho(k) * dt_micro * flag |
|---|
| 1268 | ! |
|---|
| 1269 | !-- Sum up all rain water content which contributes to the flux |
|---|
| 1270 | !-- through k-1/2 |
|---|
| 1271 | flux = 0.0_wp |
|---|
| 1272 | z_run = 0.0_wp ! height above z(k) |
|---|
| 1273 | k_run = k |
|---|
| 1274 | c_run = MIN( 1.0_wp, c_qr(k) ) |
|---|
| 1275 | |
|---|
| 1276 | DO WHILE ( c_run > 0.0_wp .AND. k_run <= nzt ) |
|---|
| 1277 | |
|---|
| 1278 | flux = flux + hyrho(k_run) * ( qr(k_run,j,i) + & |
|---|
| 1279 | qr_slope(k_run) * ( 1.0_wp - c_run ) * & |
|---|
| 1280 | 0.5_wp ) * c_run * dzu(k_run) * flag |
|---|
| 1281 | z_run = z_run + dzu(k_run) * flag |
|---|
| 1282 | k_run = k_run + 1 * flag |
|---|
| 1283 | c_run = MIN( 1.0_wp, c_qr(k_run) - z_run * ddzu(k_run) ) & |
|---|
| 1284 | * flag |
|---|
| 1285 | |
|---|
| 1286 | ENDDO |
|---|
| 1287 | ! |
|---|
| 1288 | !-- It is not allowed to sediment more rain water content than |
|---|
| 1289 | !-- available |
|---|
| 1290 | flux = MIN( flux, & |
|---|
| 1291 | hyrho(k) * dzu(k) * qr(k,j,i) + sed_qr(k+1) * & |
|---|
| 1292 | dt_micro & |
|---|
| 1293 | ) |
|---|
| 1294 | |
|---|
| 1295 | sed_qr(k) = flux / dt_micro * flag |
|---|
| 1296 | |
|---|
| 1297 | qr(k,j,i) = qr(k,j,i) + ( sed_qr(k+1) - sed_qr(k) ) * & |
|---|
| 1298 | ddzu(k+1) / hyrho(k) * dt_micro * flag |
|---|
| 1299 | q(k,j,i) = q(k,j,i) + ( sed_qr(k+1) - sed_qr(k) ) * & |
|---|
| 1300 | ddzu(k+1) / hyrho(k) * dt_micro * flag |
|---|
| 1301 | pt(k,j,i) = pt(k,j,i) - ( sed_qr(k+1) - sed_qr(k) ) * & |
|---|
| 1302 | ddzu(k+1) / hyrho(k) * l_d_cp * & |
|---|
| 1303 | pt_d_t(k) * dt_micro * flag |
|---|
| 1304 | ! |
|---|
| 1305 | !-- Compute the rain rate |
|---|
| 1306 | IF ( call_microphysics_at_all_substeps ) THEN |
|---|
| 1307 | prr(k,j,i) = prr(k,j,i) + sed_qr(k) / hyrho(k) & |
|---|
| 1308 | * weight_substep(intermediate_timestep_count) & |
|---|
| 1309 | * flag |
|---|
| 1310 | ELSE |
|---|
| 1311 | prr(k,j,i) = prr(k,j,i) + sed_qr(k) / hyrho(k) * flag |
|---|
| 1312 | ENDIF |
|---|
| 1313 | |
|---|
| 1314 | ENDDO |
|---|
| 1315 | ENDDO |
|---|
| 1316 | ENDDO |
|---|
| 1317 | |
|---|
| 1318 | CALL cpu_log( log_point_s(60), 'sed_rain', 'stop' ) |
|---|
| 1319 | |
|---|
| 1320 | END SUBROUTINE sedimentation_rain |
|---|
| 1321 | |
|---|
| 1322 | |
|---|
| 1323 | !------------------------------------------------------------------------------! |
|---|
| 1324 | ! Description: |
|---|
| 1325 | ! ------------ |
|---|
| 1326 | !> Computation of the precipitation amount due to gravitational settling of |
|---|
| 1327 | !> rain and cloud (fog) droplets |
|---|
| 1328 | !------------------------------------------------------------------------------! |
|---|
| 1329 | SUBROUTINE calc_precipitation_amount |
|---|
| 1330 | |
|---|
| 1331 | USE arrays_3d, & |
|---|
| 1332 | ONLY: precipitation_amount, prr |
|---|
| 1333 | |
|---|
| 1334 | USE cloud_parameters, & |
|---|
| 1335 | ONLY: hyrho |
|---|
| 1336 | |
|---|
| 1337 | USE control_parameters, & |
|---|
| 1338 | ONLY: call_microphysics_at_all_substeps, dt_do2d_xy, dt_3d, & |
|---|
| 1339 | intermediate_timestep_count, intermediate_timestep_count_max,& |
|---|
| 1340 | precipitation_amount_interval, time_do2d_xy |
|---|
| 1341 | |
|---|
| 1342 | USE indices, & |
|---|
| 1343 | ONLY: nxl, nxr, nys, nyn, nzb, nzt, wall_flags_0 |
|---|
| 1344 | |
|---|
| 1345 | USE kinds |
|---|
| 1346 | |
|---|
| 1347 | USE surface_mod, & |
|---|
| 1348 | ONLY : bc_h |
|---|
| 1349 | |
|---|
| 1350 | IMPLICIT NONE |
|---|
| 1351 | |
|---|
| 1352 | INTEGER(iwp) :: i !< running index x direction |
|---|
| 1353 | INTEGER(iwp) :: j !< running index y direction |
|---|
| 1354 | INTEGER(iwp) :: k !< running index y direction |
|---|
| 1355 | INTEGER(iwp) :: m !< running index surface elements |
|---|
| 1356 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
|---|
| 1357 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
|---|
| 1358 | |
|---|
| 1359 | IF ( ( dt_do2d_xy - time_do2d_xy ) < precipitation_amount_interval .AND.& |
|---|
| 1360 | ( .NOT. call_microphysics_at_all_substeps .OR. & |
|---|
| 1361 | intermediate_timestep_count == intermediate_timestep_count_max ) ) & |
|---|
| 1362 | THEN |
|---|
| 1363 | ! |
|---|
| 1364 | !-- Run over all upward-facing surface elements, i.e. non-natural, |
|---|
| 1365 | !-- natural and urban |
|---|
| 1366 | DO m = 1, bc_h(0)%ns |
|---|
| 1367 | i = bc_h(0)%i(m) |
|---|
| 1368 | j = bc_h(0)%j(m) |
|---|
| 1369 | k = bc_h(0)%k(m) |
|---|
| 1370 | precipitation_amount(j,i) = precipitation_amount(j,i) + & |
|---|
| 1371 | prr(k,j,i) * hyrho(k) * dt_3d |
|---|
| 1372 | ENDDO |
|---|
| 1373 | |
|---|
| 1374 | ENDIF |
|---|
| 1375 | |
|---|
| 1376 | END SUBROUTINE calc_precipitation_amount |
|---|
| 1377 | |
|---|
| 1378 | |
|---|
| 1379 | !------------------------------------------------------------------------------! |
|---|
| 1380 | ! Description: |
|---|
| 1381 | ! ------------ |
|---|
| 1382 | !> Control of microphysics for grid points i,j |
|---|
| 1383 | !------------------------------------------------------------------------------! |
|---|
| 1384 | |
|---|
| 1385 | SUBROUTINE microphysics_control_ij( i, j ) |
|---|
| 1386 | |
|---|
| 1387 | USE arrays_3d, & |
|---|
| 1388 | ONLY: hyp, nr, pt, pt_init, prr, q, qc, qr, zu |
|---|
| 1389 | |
|---|
| 1390 | USE cloud_parameters, & |
|---|
| 1391 | ONLY: cp, hyrho, pt_d_t, r_d, t_d_pt |
|---|
| 1392 | |
|---|
| 1393 | USE control_parameters, & |
|---|
| 1394 | ONLY: call_microphysics_at_all_substeps, dt_3d, g, & |
|---|
| 1395 | intermediate_timestep_count, large_scale_forcing, & |
|---|
| 1396 | lsf_surf, microphysics_seifert, microphysics_kessler, & |
|---|
| 1397 | pt_surface, rho_surface, surface_pressure |
|---|
| 1398 | |
|---|
| 1399 | USE indices, & |
|---|
| 1400 | ONLY: nzb, nzt |
|---|
| 1401 | |
|---|
| 1402 | USE kinds |
|---|
| 1403 | |
|---|
| 1404 | USE statistics, & |
|---|
| 1405 | ONLY: weight_pres |
|---|
| 1406 | |
|---|
| 1407 | IMPLICIT NONE |
|---|
| 1408 | |
|---|
| 1409 | INTEGER(iwp) :: i !< |
|---|
| 1410 | INTEGER(iwp) :: j !< |
|---|
| 1411 | INTEGER(iwp) :: k !< |
|---|
| 1412 | |
|---|
| 1413 | REAL(wp) :: t_surface !< |
|---|
| 1414 | |
|---|
| 1415 | IF ( large_scale_forcing .AND. lsf_surf ) THEN |
|---|
| 1416 | ! |
|---|
| 1417 | !-- Calculate: |
|---|
| 1418 | !-- pt / t : ratio of potential and actual temperature (pt_d_t) |
|---|
| 1419 | !-- t / pt : ratio of actual and potential temperature (t_d_pt) |
|---|
| 1420 | !-- p_0(z) : vertical profile of the hydrostatic pressure (hyp) |
|---|
| 1421 | t_surface = pt_surface * ( surface_pressure / 1000.0_wp )**0.286_wp |
|---|
| 1422 | DO k = nzb, nzt+1 |
|---|
| 1423 | hyp(k) = surface_pressure * 100.0_wp * & |
|---|
| 1424 | ( ( t_surface - g / cp * zu(k) ) / t_surface )**(1.0_wp / 0.286_wp) |
|---|
| 1425 | pt_d_t(k) = ( 100000.0_wp / hyp(k) )**0.286_wp |
|---|
| 1426 | t_d_pt(k) = 1.0_wp / pt_d_t(k) |
|---|
| 1427 | hyrho(k) = hyp(k) / ( r_d * t_d_pt(k) * pt_init(k) ) |
|---|
| 1428 | ENDDO |
|---|
| 1429 | ! |
|---|
| 1430 | !-- Compute reference density |
|---|
| 1431 | rho_surface = surface_pressure * 100.0_wp / ( r_d * t_surface ) |
|---|
| 1432 | ENDIF |
|---|
| 1433 | |
|---|
| 1434 | ! |
|---|
| 1435 | !-- Compute length of time step |
|---|
| 1436 | IF ( call_microphysics_at_all_substeps ) THEN |
|---|
| 1437 | dt_micro = dt_3d * weight_pres(intermediate_timestep_count) |
|---|
| 1438 | ELSE |
|---|
| 1439 | dt_micro = dt_3d |
|---|
| 1440 | ENDIF |
|---|
| 1441 | |
|---|
| 1442 | ! |
|---|
| 1443 | !-- Use 1d arrays |
|---|
| 1444 | q_1d(:) = q(:,j,i) |
|---|
| 1445 | pt_1d(:) = pt(:,j,i) |
|---|
| 1446 | qc_1d(:) = qc(:,j,i) |
|---|
| 1447 | nc_1d(:) = nc_const |
|---|
| 1448 | IF ( microphysics_seifert ) THEN |
|---|
| 1449 | qr_1d(:) = qr(:,j,i) |
|---|
| 1450 | nr_1d(:) = nr(:,j,i) |
|---|
| 1451 | ENDIF |
|---|
| 1452 | |
|---|
| 1453 | ! |
|---|
| 1454 | !-- Reset precipitation rate |
|---|
| 1455 | IF ( intermediate_timestep_count == 1 ) prr(:,j,i) = 0.0_wp |
|---|
| 1456 | |
|---|
| 1457 | ! |
|---|
| 1458 | !-- Compute cloud physics |
|---|
| 1459 | IF( microphysics_kessler ) THEN |
|---|
| 1460 | |
|---|
| 1461 | CALL autoconversion_kessler( i,j ) |
|---|
| 1462 | IF ( cloud_water_sedimentation ) CALL sedimentation_cloud( i,j ) |
|---|
| 1463 | |
|---|
| 1464 | ELSEIF ( microphysics_seifert ) THEN |
|---|
| 1465 | |
|---|
| 1466 | CALL adjust_cloud( i,j ) |
|---|
| 1467 | CALL autoconversion( i,j ) |
|---|
| 1468 | CALL accretion( i,j ) |
|---|
| 1469 | CALL selfcollection_breakup( i,j ) |
|---|
| 1470 | CALL evaporation_rain( i,j ) |
|---|
| 1471 | CALL sedimentation_rain( i,j ) |
|---|
| 1472 | IF ( cloud_water_sedimentation ) CALL sedimentation_cloud( i,j ) |
|---|
| 1473 | |
|---|
| 1474 | ENDIF |
|---|
| 1475 | |
|---|
| 1476 | CALL calc_precipitation_amount( i,j ) |
|---|
| 1477 | |
|---|
| 1478 | ! |
|---|
| 1479 | !-- Store results on the 3d arrays |
|---|
| 1480 | q(:,j,i) = q_1d(:) |
|---|
| 1481 | pt(:,j,i) = pt_1d(:) |
|---|
| 1482 | IF ( microphysics_seifert ) THEN |
|---|
| 1483 | qr(:,j,i) = qr_1d(:) |
|---|
| 1484 | nr(:,j,i) = nr_1d(:) |
|---|
| 1485 | ENDIF |
|---|
| 1486 | |
|---|
| 1487 | END SUBROUTINE microphysics_control_ij |
|---|
| 1488 | |
|---|
| 1489 | !------------------------------------------------------------------------------! |
|---|
| 1490 | ! Description: |
|---|
| 1491 | ! ------------ |
|---|
| 1492 | !> Adjust number of raindrops to avoid nonlinear effects in |
|---|
| 1493 | !> sedimentation and evaporation of rain drops due to too small or |
|---|
| 1494 | !> too big weights of rain drops (Stevens and Seifert, 2008). |
|---|
| 1495 | !> The same procedure is applied to cloud droplets if they are determined |
|---|
| 1496 | !> prognostically. Call for grid point i,j |
|---|
| 1497 | !------------------------------------------------------------------------------! |
|---|
| 1498 | SUBROUTINE adjust_cloud_ij( i, j ) |
|---|
| 1499 | |
|---|
| 1500 | USE cloud_parameters, & |
|---|
| 1501 | ONLY: hyrho |
|---|
| 1502 | |
|---|
| 1503 | USE indices, & |
|---|
| 1504 | ONLY: nzb, nzt, wall_flags_0 |
|---|
| 1505 | |
|---|
| 1506 | USE kinds |
|---|
| 1507 | |
|---|
| 1508 | IMPLICIT NONE |
|---|
| 1509 | |
|---|
| 1510 | INTEGER(iwp) :: i !< |
|---|
| 1511 | INTEGER(iwp) :: j !< |
|---|
| 1512 | INTEGER(iwp) :: k !< |
|---|
| 1513 | |
|---|
| 1514 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 1515 | |
|---|
| 1516 | DO k = nzb+1, nzt |
|---|
| 1517 | ! |
|---|
| 1518 | !-- Predetermine flag to mask topography |
|---|
| 1519 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1520 | |
|---|
| 1521 | IF ( qr_1d(k) <= eps_sb ) THEN |
|---|
| 1522 | qr_1d(k) = 0.0_wp |
|---|
| 1523 | nr_1d(k) = 0.0_wp |
|---|
| 1524 | ELSE |
|---|
| 1525 | ! |
|---|
| 1526 | !-- Adjust number of raindrops to avoid nonlinear effects in |
|---|
| 1527 | !-- sedimentation and evaporation of rain drops due to too small or |
|---|
| 1528 | !-- too big weights of rain drops (Stevens and Seifert, 2008). |
|---|
| 1529 | IF ( nr_1d(k) * xrmin > qr_1d(k) * hyrho(k) ) THEN |
|---|
| 1530 | nr_1d(k) = qr_1d(k) * hyrho(k) / xrmin * flag |
|---|
| 1531 | ELSEIF ( nr_1d(k) * xrmax < qr_1d(k) * hyrho(k) ) THEN |
|---|
| 1532 | nr_1d(k) = qr_1d(k) * hyrho(k) / xrmax * flag |
|---|
| 1533 | ENDIF |
|---|
| 1534 | |
|---|
| 1535 | ENDIF |
|---|
| 1536 | |
|---|
| 1537 | ENDDO |
|---|
| 1538 | |
|---|
| 1539 | END SUBROUTINE adjust_cloud_ij |
|---|
| 1540 | |
|---|
| 1541 | |
|---|
| 1542 | !------------------------------------------------------------------------------! |
|---|
| 1543 | ! Description: |
|---|
| 1544 | ! ------------ |
|---|
| 1545 | !> Autoconversion rate (Seifert and Beheng, 2006). Call for grid point i,j |
|---|
| 1546 | !------------------------------------------------------------------------------! |
|---|
| 1547 | SUBROUTINE autoconversion_ij( i, j ) |
|---|
| 1548 | |
|---|
| 1549 | USE arrays_3d, & |
|---|
| 1550 | ONLY: diss, dzu |
|---|
| 1551 | |
|---|
| 1552 | USE cloud_parameters, & |
|---|
| 1553 | ONLY: hyrho |
|---|
| 1554 | |
|---|
| 1555 | USE control_parameters, & |
|---|
| 1556 | ONLY: rho_surface |
|---|
| 1557 | |
|---|
| 1558 | USE grid_variables, & |
|---|
| 1559 | ONLY: dx, dy |
|---|
| 1560 | |
|---|
| 1561 | USE indices, & |
|---|
| 1562 | ONLY: nzb, nzt, wall_flags_0 |
|---|
| 1563 | |
|---|
| 1564 | USE kinds |
|---|
| 1565 | |
|---|
| 1566 | IMPLICIT NONE |
|---|
| 1567 | |
|---|
| 1568 | INTEGER(iwp) :: i !< |
|---|
| 1569 | INTEGER(iwp) :: j !< |
|---|
| 1570 | INTEGER(iwp) :: k !< |
|---|
| 1571 | |
|---|
| 1572 | REAL(wp) :: alpha_cc !< |
|---|
| 1573 | REAL(wp) :: autocon !< |
|---|
| 1574 | REAL(wp) :: dissipation !< |
|---|
| 1575 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 1576 | REAL(wp) :: k_au !< |
|---|
| 1577 | REAL(wp) :: l_mix !< |
|---|
| 1578 | REAL(wp) :: nu_c !< |
|---|
| 1579 | REAL(wp) :: phi_au !< |
|---|
| 1580 | REAL(wp) :: r_cc !< |
|---|
| 1581 | REAL(wp) :: rc !< |
|---|
| 1582 | REAL(wp) :: re_lambda !< |
|---|
| 1583 | REAL(wp) :: sigma_cc !< |
|---|
| 1584 | REAL(wp) :: tau_cloud !< |
|---|
| 1585 | REAL(wp) :: xc !< |
|---|
| 1586 | |
|---|
| 1587 | DO k = nzb+1, nzt |
|---|
| 1588 | ! |
|---|
| 1589 | !-- Predetermine flag to mask topography |
|---|
| 1590 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1591 | |
|---|
| 1592 | IF ( qc_1d(k) > eps_sb ) THEN |
|---|
| 1593 | |
|---|
| 1594 | k_au = k_cc / ( 20.0_wp * x0 ) |
|---|
| 1595 | ! |
|---|
| 1596 | !-- Intern time scale of coagulation (Seifert and Beheng, 2006): |
|---|
| 1597 | !-- (1.0_wp - qc(k,j,i) / ( qc(k,j,i) + qr_1d(k) )) |
|---|
| 1598 | tau_cloud = 1.0_wp - qc_1d(k) / ( qr_1d(k) + qc_1d(k) ) |
|---|
| 1599 | ! |
|---|
| 1600 | !-- Universal function for autoconversion process |
|---|
| 1601 | !-- (Seifert and Beheng, 2006): |
|---|
| 1602 | phi_au = 600.0_wp * tau_cloud**0.68_wp * ( 1.0_wp - tau_cloud**0.68_wp )**3 |
|---|
| 1603 | ! |
|---|
| 1604 | !-- Shape parameter of gamma distribution (Geoffroy et al., 2010): |
|---|
| 1605 | !-- (Use constant nu_c = 1.0_wp instead?) |
|---|
| 1606 | nu_c = 1.0_wp !MAX( 0.0_wp, 1580.0_wp * hyrho(k) * qc_1d(k) - 0.28_wp ) |
|---|
| 1607 | ! |
|---|
| 1608 | !-- Mean weight of cloud droplets: |
|---|
| 1609 | xc = hyrho(k) * qc_1d(k) / nc_1d(k) |
|---|
| 1610 | ! |
|---|
| 1611 | !-- Parameterized turbulence effects on autoconversion (Seifert, |
|---|
| 1612 | !-- Nuijens and Stevens, 2010) |
|---|
| 1613 | IF ( collision_turbulence ) THEN |
|---|
| 1614 | ! |
|---|
| 1615 | !-- Weight averaged radius of cloud droplets: |
|---|
| 1616 | rc = 0.5_wp * ( xc * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 1617 | |
|---|
| 1618 | alpha_cc = ( a_1 + a_2 * nu_c ) / ( 1.0_wp + a_3 * nu_c ) |
|---|
| 1619 | r_cc = ( b_1 + b_2 * nu_c ) / ( 1.0_wp + b_3 * nu_c ) |
|---|
| 1620 | sigma_cc = ( c_1 + c_2 * nu_c ) / ( 1.0_wp + c_3 * nu_c ) |
|---|
| 1621 | ! |
|---|
| 1622 | !-- Mixing length (neglecting distance to ground and stratification) |
|---|
| 1623 | l_mix = ( dx * dy * dzu(k) )**( 1.0_wp / 3.0_wp ) |
|---|
| 1624 | ! |
|---|
| 1625 | !-- Limit dissipation rate according to Seifert, Nuijens and |
|---|
| 1626 | !-- Stevens (2010) |
|---|
| 1627 | dissipation = MIN( 0.06_wp, diss(k,j,i) ) |
|---|
| 1628 | ! |
|---|
| 1629 | !-- Compute Taylor-microscale Reynolds number: |
|---|
| 1630 | re_lambda = 6.0_wp / 11.0_wp * & |
|---|
| 1631 | ( l_mix / c_const )**( 2.0_wp / 3.0_wp ) * & |
|---|
| 1632 | SQRT( 15.0_wp / kin_vis_air ) * & |
|---|
| 1633 | dissipation**( 1.0_wp / 6.0_wp ) |
|---|
| 1634 | ! |
|---|
| 1635 | !-- The factor of 1.0E4 is needed to convert the dissipation rate |
|---|
| 1636 | !-- from m2 s-3 to cm2 s-3. |
|---|
| 1637 | k_au = k_au * ( 1.0_wp + & |
|---|
| 1638 | dissipation * 1.0E4_wp * & |
|---|
| 1639 | ( re_lambda * 1.0E-3_wp )**0.25_wp * & |
|---|
| 1640 | ( alpha_cc * EXP( -1.0_wp * ( ( rc - r_cc ) / & |
|---|
| 1641 | sigma_cc )**2 & |
|---|
| 1642 | ) + beta_cc & |
|---|
| 1643 | ) & |
|---|
| 1644 | ) |
|---|
| 1645 | ENDIF |
|---|
| 1646 | ! |
|---|
| 1647 | !-- Autoconversion rate (Seifert and Beheng, 2006): |
|---|
| 1648 | autocon = k_au * ( nu_c + 2.0_wp ) * ( nu_c + 4.0_wp ) / & |
|---|
| 1649 | ( nu_c + 1.0_wp )**2 * qc_1d(k)**2 * xc**2 * & |
|---|
| 1650 | ( 1.0_wp + phi_au / ( 1.0_wp - tau_cloud )**2 ) * & |
|---|
| 1651 | rho_surface |
|---|
| 1652 | autocon = MIN( autocon, qc_1d(k) / dt_micro ) |
|---|
| 1653 | |
|---|
| 1654 | qr_1d(k) = qr_1d(k) + autocon * dt_micro * flag |
|---|
| 1655 | qc_1d(k) = qc_1d(k) - autocon * dt_micro * flag |
|---|
| 1656 | nr_1d(k) = nr_1d(k) + autocon / x0 * hyrho(k) * dt_micro * flag |
|---|
| 1657 | |
|---|
| 1658 | ENDIF |
|---|
| 1659 | |
|---|
| 1660 | ENDDO |
|---|
| 1661 | |
|---|
| 1662 | END SUBROUTINE autoconversion_ij |
|---|
| 1663 | |
|---|
| 1664 | !------------------------------------------------------------------------------! |
|---|
| 1665 | ! Description: |
|---|
| 1666 | ! ------------ |
|---|
| 1667 | !> Autoconversion process (Kessler, 1969). |
|---|
| 1668 | !------------------------------------------------------------------------------! |
|---|
| 1669 | SUBROUTINE autoconversion_kessler_ij( i, j ) |
|---|
| 1670 | |
|---|
| 1671 | USE arrays_3d, & |
|---|
| 1672 | ONLY: dzw, prr |
|---|
| 1673 | |
|---|
| 1674 | USE cloud_parameters, & |
|---|
| 1675 | ONLY: l_d_cp, pt_d_t |
|---|
| 1676 | |
|---|
| 1677 | USE indices, & |
|---|
| 1678 | ONLY: nzb, nzb_max, nzt, wall_flags_0 |
|---|
| 1679 | |
|---|
| 1680 | USE kinds |
|---|
| 1681 | |
|---|
| 1682 | |
|---|
| 1683 | IMPLICIT NONE |
|---|
| 1684 | |
|---|
| 1685 | INTEGER(iwp) :: i !< |
|---|
| 1686 | INTEGER(iwp) :: j !< |
|---|
| 1687 | INTEGER(iwp) :: k !< |
|---|
| 1688 | INTEGER(iwp) :: k_wall !< topography top index |
|---|
| 1689 | |
|---|
| 1690 | REAL(wp) :: dqdt_precip !< |
|---|
| 1691 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 1692 | |
|---|
| 1693 | ! |
|---|
| 1694 | !-- Determine vertical index of topography top |
|---|
| 1695 | k_wall = MAXLOC( & |
|---|
| 1696 | MERGE( 1, 0, & |
|---|
| 1697 | BTEST( wall_flags_0(nzb:nzb_max,j,i), 12 ) & |
|---|
| 1698 | ), DIM = 1 & |
|---|
| 1699 | ) - 1 |
|---|
| 1700 | DO k = nzb+1, nzt |
|---|
| 1701 | ! |
|---|
| 1702 | !-- Predetermine flag to mask topography |
|---|
| 1703 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1704 | |
|---|
| 1705 | IF ( qc_1d(k) > ql_crit ) THEN |
|---|
| 1706 | dqdt_precip = prec_time_const * ( qc_1d(k) - ql_crit ) |
|---|
| 1707 | ELSE |
|---|
| 1708 | dqdt_precip = 0.0_wp |
|---|
| 1709 | ENDIF |
|---|
| 1710 | |
|---|
| 1711 | qc_1d(k) = qc_1d(k) - dqdt_precip * dt_micro * flag |
|---|
| 1712 | q_1d(k) = q_1d(k) - dqdt_precip * dt_micro * flag |
|---|
| 1713 | pt_1d(k) = pt_1d(k) + dqdt_precip * dt_micro * l_d_cp * pt_d_t(k) * flag |
|---|
| 1714 | |
|---|
| 1715 | ! |
|---|
| 1716 | !-- Compute the rain rate (stored on surface grid point) |
|---|
| 1717 | prr(k_wall,j,i) = prr(k_wall,j,i) + dqdt_precip * dzw(k) * flag |
|---|
| 1718 | |
|---|
| 1719 | ENDDO |
|---|
| 1720 | |
|---|
| 1721 | END SUBROUTINE autoconversion_kessler_ij |
|---|
| 1722 | |
|---|
| 1723 | !------------------------------------------------------------------------------! |
|---|
| 1724 | ! Description: |
|---|
| 1725 | ! ------------ |
|---|
| 1726 | !> Accretion rate (Seifert and Beheng, 2006). Call for grid point i,j |
|---|
| 1727 | !------------------------------------------------------------------------------! |
|---|
| 1728 | SUBROUTINE accretion_ij( i, j ) |
|---|
| 1729 | |
|---|
| 1730 | USE arrays_3d, & |
|---|
| 1731 | ONLY: diss |
|---|
| 1732 | |
|---|
| 1733 | USE cloud_parameters, & |
|---|
| 1734 | ONLY: hyrho |
|---|
| 1735 | |
|---|
| 1736 | USE control_parameters, & |
|---|
| 1737 | ONLY: rho_surface |
|---|
| 1738 | |
|---|
| 1739 | USE indices, & |
|---|
| 1740 | ONLY: nzb, nzt, wall_flags_0 |
|---|
| 1741 | |
|---|
| 1742 | USE kinds |
|---|
| 1743 | |
|---|
| 1744 | IMPLICIT NONE |
|---|
| 1745 | |
|---|
| 1746 | INTEGER(iwp) :: i !< |
|---|
| 1747 | INTEGER(iwp) :: j !< |
|---|
| 1748 | INTEGER(iwp) :: k !< |
|---|
| 1749 | |
|---|
| 1750 | REAL(wp) :: accr !< |
|---|
| 1751 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 1752 | REAL(wp) :: k_cr !< |
|---|
| 1753 | REAL(wp) :: phi_ac !< |
|---|
| 1754 | REAL(wp) :: tau_cloud !< |
|---|
| 1755 | |
|---|
| 1756 | DO k = nzb+1, nzt |
|---|
| 1757 | ! |
|---|
| 1758 | !-- Predetermine flag to mask topography |
|---|
| 1759 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1760 | |
|---|
| 1761 | IF ( ( qc_1d(k) > eps_sb ) .AND. ( qr_1d(k) > eps_sb ) ) THEN |
|---|
| 1762 | ! |
|---|
| 1763 | !-- Intern time scale of coagulation (Seifert and Beheng, 2006): |
|---|
| 1764 | tau_cloud = 1.0_wp - qc_1d(k) / ( qc_1d(k) + qr_1d(k) ) |
|---|
| 1765 | ! |
|---|
| 1766 | !-- Universal function for accretion process |
|---|
| 1767 | !-- (Seifert and Beheng, 2001): |
|---|
| 1768 | phi_ac = ( tau_cloud / ( tau_cloud + 5.0E-5_wp ) )**4 |
|---|
| 1769 | ! |
|---|
| 1770 | !-- Parameterized turbulence effects on autoconversion (Seifert, |
|---|
| 1771 | !-- Nuijens and Stevens, 2010). The factor of 1.0E4 is needed to |
|---|
| 1772 | !-- convert the dissipation rate (diss) from m2 s-3 to cm2 s-3. |
|---|
| 1773 | IF ( collision_turbulence ) THEN |
|---|
| 1774 | k_cr = k_cr0 * ( 1.0_wp + 0.05_wp * & |
|---|
| 1775 | MIN( 600.0_wp, & |
|---|
| 1776 | diss(k,j,i) * 1.0E4_wp )**0.25_wp & |
|---|
| 1777 | ) |
|---|
| 1778 | ELSE |
|---|
| 1779 | k_cr = k_cr0 |
|---|
| 1780 | ENDIF |
|---|
| 1781 | ! |
|---|
| 1782 | !-- Accretion rate (Seifert and Beheng, 2006): |
|---|
| 1783 | accr = k_cr * qc_1d(k) * qr_1d(k) * phi_ac * SQRT( rho_surface * hyrho(k) ) |
|---|
| 1784 | accr = MIN( accr, qc_1d(k) / dt_micro ) |
|---|
| 1785 | |
|---|
| 1786 | qr_1d(k) = qr_1d(k) + accr * dt_micro * flag |
|---|
| 1787 | qc_1d(k) = qc_1d(k) - accr * dt_micro * flag |
|---|
| 1788 | |
|---|
| 1789 | ENDIF |
|---|
| 1790 | |
|---|
| 1791 | ENDDO |
|---|
| 1792 | |
|---|
| 1793 | END SUBROUTINE accretion_ij |
|---|
| 1794 | |
|---|
| 1795 | |
|---|
| 1796 | !------------------------------------------------------------------------------! |
|---|
| 1797 | ! Description: |
|---|
| 1798 | ! ------------ |
|---|
| 1799 | !> Collisional breakup rate (Seifert, 2008). Call for grid point i,j |
|---|
| 1800 | !------------------------------------------------------------------------------! |
|---|
| 1801 | SUBROUTINE selfcollection_breakup_ij( i, j ) |
|---|
| 1802 | |
|---|
| 1803 | USE cloud_parameters, & |
|---|
| 1804 | ONLY: hyrho |
|---|
| 1805 | |
|---|
| 1806 | USE control_parameters, & |
|---|
| 1807 | ONLY: rho_surface |
|---|
| 1808 | |
|---|
| 1809 | USE indices, & |
|---|
| 1810 | ONLY: nzb, nzt, wall_flags_0 |
|---|
| 1811 | |
|---|
| 1812 | USE kinds |
|---|
| 1813 | |
|---|
| 1814 | IMPLICIT NONE |
|---|
| 1815 | |
|---|
| 1816 | INTEGER(iwp) :: i !< |
|---|
| 1817 | INTEGER(iwp) :: j !< |
|---|
| 1818 | INTEGER(iwp) :: k !< |
|---|
| 1819 | |
|---|
| 1820 | REAL(wp) :: breakup !< |
|---|
| 1821 | REAL(wp) :: dr !< |
|---|
| 1822 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 1823 | REAL(wp) :: phi_br !< |
|---|
| 1824 | REAL(wp) :: selfcoll !< |
|---|
| 1825 | |
|---|
| 1826 | DO k = nzb+1, nzt |
|---|
| 1827 | ! |
|---|
| 1828 | !-- Predetermine flag to mask topography |
|---|
| 1829 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1830 | |
|---|
| 1831 | IF ( qr_1d(k) > eps_sb ) THEN |
|---|
| 1832 | ! |
|---|
| 1833 | !-- Selfcollection rate (Seifert and Beheng, 2001): |
|---|
| 1834 | selfcoll = k_rr * nr_1d(k) * qr_1d(k) * SQRT( hyrho(k) * rho_surface ) |
|---|
| 1835 | ! |
|---|
| 1836 | !-- Weight averaged diameter of rain drops: |
|---|
| 1837 | dr = ( hyrho(k) * qr_1d(k) / nr_1d(k) * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 1838 | ! |
|---|
| 1839 | !-- Collisional breakup rate (Seifert, 2008): |
|---|
| 1840 | IF ( dr >= 0.3E-3_wp ) THEN |
|---|
| 1841 | phi_br = k_br * ( dr - 1.1E-3_wp ) |
|---|
| 1842 | breakup = selfcoll * ( phi_br + 1.0_wp ) |
|---|
| 1843 | ELSE |
|---|
| 1844 | breakup = 0.0_wp |
|---|
| 1845 | ENDIF |
|---|
| 1846 | |
|---|
| 1847 | selfcoll = MAX( breakup - selfcoll, -nr_1d(k) / dt_micro ) |
|---|
| 1848 | nr_1d(k) = nr_1d(k) + selfcoll * dt_micro * flag |
|---|
| 1849 | |
|---|
| 1850 | ENDIF |
|---|
| 1851 | ENDDO |
|---|
| 1852 | |
|---|
| 1853 | END SUBROUTINE selfcollection_breakup_ij |
|---|
| 1854 | |
|---|
| 1855 | |
|---|
| 1856 | !------------------------------------------------------------------------------! |
|---|
| 1857 | ! Description: |
|---|
| 1858 | ! ------------ |
|---|
| 1859 | !> Evaporation of precipitable water. Condensation is neglected for |
|---|
| 1860 | !> precipitable water. Call for grid point i,j |
|---|
| 1861 | !------------------------------------------------------------------------------! |
|---|
| 1862 | SUBROUTINE evaporation_rain_ij( i, j ) |
|---|
| 1863 | |
|---|
| 1864 | USE arrays_3d, & |
|---|
| 1865 | ONLY: hyp |
|---|
| 1866 | |
|---|
| 1867 | USE cloud_parameters, & |
|---|
| 1868 | ONLY: hyrho, l_d_cp, l_d_r, l_v, r_v, t_d_pt |
|---|
| 1869 | |
|---|
| 1870 | USE constants, & |
|---|
| 1871 | ONLY: pi |
|---|
| 1872 | |
|---|
| 1873 | USE indices, & |
|---|
| 1874 | ONLY: nzb, nzt, wall_flags_0 |
|---|
| 1875 | |
|---|
| 1876 | USE kinds |
|---|
| 1877 | |
|---|
| 1878 | IMPLICIT NONE |
|---|
| 1879 | |
|---|
| 1880 | INTEGER(iwp) :: i !< |
|---|
| 1881 | INTEGER(iwp) :: j !< |
|---|
| 1882 | INTEGER(iwp) :: k !< |
|---|
| 1883 | |
|---|
| 1884 | REAL(wp) :: alpha !< |
|---|
| 1885 | REAL(wp) :: dr !< |
|---|
| 1886 | REAL(wp) :: e_s !< |
|---|
| 1887 | REAL(wp) :: evap !< |
|---|
| 1888 | REAL(wp) :: evap_nr !< |
|---|
| 1889 | REAL(wp) :: f_vent !< |
|---|
| 1890 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 1891 | REAL(wp) :: g_evap !< |
|---|
| 1892 | REAL(wp) :: lambda_r !< |
|---|
| 1893 | REAL(wp) :: mu_r !< |
|---|
| 1894 | REAL(wp) :: mu_r_2 !< |
|---|
| 1895 | REAL(wp) :: mu_r_5d2 !< |
|---|
| 1896 | REAL(wp) :: nr_0 !< |
|---|
| 1897 | REAL(wp) :: q_s !< |
|---|
| 1898 | REAL(wp) :: sat !< |
|---|
| 1899 | REAL(wp) :: t_l !< |
|---|
| 1900 | REAL(wp) :: temp !< |
|---|
| 1901 | REAL(wp) :: xr !< |
|---|
| 1902 | |
|---|
| 1903 | DO k = nzb+1, nzt |
|---|
| 1904 | ! |
|---|
| 1905 | !-- Predetermine flag to mask topography |
|---|
| 1906 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 1907 | |
|---|
| 1908 | IF ( qr_1d(k) > eps_sb ) THEN |
|---|
| 1909 | ! |
|---|
| 1910 | !-- Actual liquid water temperature: |
|---|
| 1911 | t_l = t_d_pt(k) * pt_1d(k) |
|---|
| 1912 | ! |
|---|
| 1913 | !-- Saturation vapor pressure at t_l: |
|---|
| 1914 | e_s = 610.78_wp * EXP( 17.269_wp * ( t_l - 273.16_wp ) / & |
|---|
| 1915 | ( t_l - 35.86_wp ) & |
|---|
| 1916 | ) |
|---|
| 1917 | ! |
|---|
| 1918 | !-- Computation of saturation humidity: |
|---|
| 1919 | q_s = 0.622_wp * e_s / ( hyp(k) - 0.378_wp * e_s ) |
|---|
| 1920 | alpha = 0.622_wp * l_d_r * l_d_cp / ( t_l * t_l ) |
|---|
| 1921 | q_s = q_s * ( 1.0_wp + alpha * q_1d(k) ) / ( 1.0_wp + alpha * q_s ) |
|---|
| 1922 | ! |
|---|
| 1923 | !-- Supersaturation: |
|---|
| 1924 | sat = ( q_1d(k) - qr_1d(k) - qc_1d(k) ) / q_s - 1.0_wp |
|---|
| 1925 | ! |
|---|
| 1926 | !-- Evaporation needs only to be calculated in subsaturated regions |
|---|
| 1927 | IF ( sat < 0.0_wp ) THEN |
|---|
| 1928 | ! |
|---|
| 1929 | !-- Actual temperature: |
|---|
| 1930 | temp = t_l + l_d_cp * ( qc_1d(k) + qr_1d(k) ) |
|---|
| 1931 | |
|---|
| 1932 | g_evap = 1.0_wp / ( ( l_v / ( r_v * temp ) - 1.0_wp ) * l_v / & |
|---|
| 1933 | ( thermal_conductivity_l * temp ) + & |
|---|
| 1934 | r_v * temp / ( diff_coeff_l * e_s ) & |
|---|
| 1935 | ) |
|---|
| 1936 | ! |
|---|
| 1937 | !-- Mean weight of rain drops |
|---|
| 1938 | xr = hyrho(k) * qr_1d(k) / nr_1d(k) |
|---|
| 1939 | ! |
|---|
| 1940 | !-- Weight averaged diameter of rain drops: |
|---|
| 1941 | dr = ( xr * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 1942 | ! |
|---|
| 1943 | !-- Compute ventilation factor and intercept parameter |
|---|
| 1944 | !-- (Seifert and Beheng, 2006; Seifert, 2008): |
|---|
| 1945 | IF ( ventilation_effect ) THEN |
|---|
| 1946 | ! |
|---|
| 1947 | !-- Shape parameter of gamma distribution (Milbrandt and Yau, 2005; |
|---|
| 1948 | !-- Stevens and Seifert, 2008): |
|---|
| 1949 | mu_r = 10.0_wp * ( 1.0_wp + TANH( 1.2E3_wp * ( dr - 1.4E-3_wp ) ) ) |
|---|
| 1950 | ! |
|---|
| 1951 | !-- Slope parameter of gamma distribution (Seifert, 2008): |
|---|
| 1952 | lambda_r = ( ( mu_r + 3.0_wp ) * ( mu_r + 2.0_wp ) * & |
|---|
| 1953 | ( mu_r + 1.0_wp ) & |
|---|
| 1954 | )**( 1.0_wp / 3.0_wp ) / dr |
|---|
| 1955 | |
|---|
| 1956 | mu_r_2 = mu_r + 2.0_wp |
|---|
| 1957 | mu_r_5d2 = mu_r + 2.5_wp |
|---|
| 1958 | |
|---|
| 1959 | f_vent = a_vent * gamm( mu_r_2 ) * lambda_r**( -mu_r_2 ) + & |
|---|
| 1960 | b_vent * schmidt_p_1d3 * & |
|---|
| 1961 | SQRT( a_term / kin_vis_air ) * gamm( mu_r_5d2 ) * & |
|---|
| 1962 | lambda_r**( -mu_r_5d2 ) * & |
|---|
| 1963 | ( 1.0_wp - & |
|---|
| 1964 | 0.5_wp * ( b_term / a_term ) * & |
|---|
| 1965 | ( lambda_r / ( c_term + lambda_r ) & |
|---|
| 1966 | )**mu_r_5d2 - & |
|---|
| 1967 | 0.125_wp * ( b_term / a_term )**2 * & |
|---|
| 1968 | ( lambda_r / ( 2.0_wp * c_term + lambda_r ) & |
|---|
| 1969 | )**mu_r_5d2 - & |
|---|
| 1970 | 0.0625_wp * ( b_term / a_term )**3 * & |
|---|
| 1971 | ( lambda_r / ( 3.0_wp * c_term + lambda_r ) & |
|---|
| 1972 | )**mu_r_5d2 - & |
|---|
| 1973 | 0.0390625_wp * ( b_term / a_term )**4 * & |
|---|
| 1974 | ( lambda_r / ( 4.0_wp * c_term + lambda_r ) & |
|---|
| 1975 | )**mu_r_5d2 & |
|---|
| 1976 | ) |
|---|
| 1977 | |
|---|
| 1978 | nr_0 = nr_1d(k) * lambda_r**( mu_r + 1.0_wp ) / & |
|---|
| 1979 | gamm( mu_r + 1.0_wp ) |
|---|
| 1980 | ELSE |
|---|
| 1981 | f_vent = 1.0_wp |
|---|
| 1982 | nr_0 = nr_1d(k) * dr |
|---|
| 1983 | ENDIF |
|---|
| 1984 | ! |
|---|
| 1985 | !-- Evaporation rate of rain water content (Seifert and Beheng, 2006): |
|---|
| 1986 | evap = 2.0_wp * pi * nr_0 * g_evap * f_vent * sat / hyrho(k) |
|---|
| 1987 | evap = MAX( evap, -qr_1d(k) / dt_micro ) |
|---|
| 1988 | evap_nr = MAX( c_evap * evap / xr * hyrho(k), & |
|---|
| 1989 | -nr_1d(k) / dt_micro ) |
|---|
| 1990 | |
|---|
| 1991 | qr_1d(k) = qr_1d(k) + evap * dt_micro * flag |
|---|
| 1992 | nr_1d(k) = nr_1d(k) + evap_nr * dt_micro * flag |
|---|
| 1993 | |
|---|
| 1994 | ENDIF |
|---|
| 1995 | ENDIF |
|---|
| 1996 | |
|---|
| 1997 | ENDDO |
|---|
| 1998 | |
|---|
| 1999 | END SUBROUTINE evaporation_rain_ij |
|---|
| 2000 | |
|---|
| 2001 | |
|---|
| 2002 | !------------------------------------------------------------------------------! |
|---|
| 2003 | ! Description: |
|---|
| 2004 | ! ------------ |
|---|
| 2005 | !> Sedimentation of cloud droplets (Ackermann et al., 2009, MWR). |
|---|
| 2006 | !> Call for grid point i,j |
|---|
| 2007 | !------------------------------------------------------------------------------! |
|---|
| 2008 | SUBROUTINE sedimentation_cloud_ij( i, j ) |
|---|
| 2009 | |
|---|
| 2010 | USE arrays_3d, & |
|---|
| 2011 | ONLY: ddzu, dzu, prr |
|---|
| 2012 | |
|---|
| 2013 | USE cloud_parameters, & |
|---|
| 2014 | ONLY: hyrho, l_d_cp, pt_d_t |
|---|
| 2015 | |
|---|
| 2016 | USE control_parameters, & |
|---|
| 2017 | ONLY: call_microphysics_at_all_substeps, intermediate_timestep_count |
|---|
| 2018 | |
|---|
| 2019 | USE indices, & |
|---|
| 2020 | ONLY: nzb, nzb, nzt, wall_flags_0 |
|---|
| 2021 | |
|---|
| 2022 | USE kinds |
|---|
| 2023 | |
|---|
| 2024 | USE statistics, & |
|---|
| 2025 | ONLY: weight_substep |
|---|
| 2026 | |
|---|
| 2027 | IMPLICIT NONE |
|---|
| 2028 | |
|---|
| 2029 | INTEGER(iwp) :: i !< |
|---|
| 2030 | INTEGER(iwp) :: j !< |
|---|
| 2031 | INTEGER(iwp) :: k !< |
|---|
| 2032 | |
|---|
| 2033 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 2034 | REAL(wp), DIMENSION(nzb:nzt+1) :: sed_qc !< |
|---|
| 2035 | |
|---|
| 2036 | sed_qc(nzt+1) = 0.0_wp |
|---|
| 2037 | |
|---|
| 2038 | DO k = nzt, nzb+1, -1 |
|---|
| 2039 | ! |
|---|
| 2040 | !-- Predetermine flag to mask topography |
|---|
| 2041 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 2042 | |
|---|
| 2043 | IF ( qc_1d(k) > eps_sb ) THEN |
|---|
| 2044 | sed_qc(k) = sed_qc_const * nc_1d(k)**( -2.0_wp / 3.0_wp ) * & |
|---|
| 2045 | ( qc_1d(k) * hyrho(k) )**( 5.0_wp / 3.0_wp ) * flag |
|---|
| 2046 | ELSE |
|---|
| 2047 | sed_qc(k) = 0.0_wp |
|---|
| 2048 | ENDIF |
|---|
| 2049 | |
|---|
| 2050 | sed_qc(k) = MIN( sed_qc(k), hyrho(k) * dzu(k+1) * q_1d(k) / & |
|---|
| 2051 | dt_micro + sed_qc(k+1) & |
|---|
| 2052 | ) * flag |
|---|
| 2053 | |
|---|
| 2054 | q_1d(k) = q_1d(k) + ( sed_qc(k+1) - sed_qc(k) ) * ddzu(k+1) / & |
|---|
| 2055 | hyrho(k) * dt_micro * flag |
|---|
| 2056 | qc_1d(k) = qc_1d(k) + ( sed_qc(k+1) - sed_qc(k) ) * ddzu(k+1) / & |
|---|
| 2057 | hyrho(k) * dt_micro * flag |
|---|
| 2058 | pt_1d(k) = pt_1d(k) - ( sed_qc(k+1) - sed_qc(k) ) * ddzu(k+1) / & |
|---|
| 2059 | hyrho(k) * l_d_cp * pt_d_t(k) * dt_micro * flag |
|---|
| 2060 | |
|---|
| 2061 | ! |
|---|
| 2062 | !-- Compute the precipitation rate of cloud (fog) droplets |
|---|
| 2063 | IF ( call_microphysics_at_all_substeps ) THEN |
|---|
| 2064 | prr(k,j,i) = prr(k,j,i) + sed_qc(k) / hyrho(k) * & |
|---|
| 2065 | weight_substep(intermediate_timestep_count) * flag |
|---|
| 2066 | ELSE |
|---|
| 2067 | prr(k,j,i) = prr(k,j,i) + sed_qc(k) / hyrho(k) * flag |
|---|
| 2068 | ENDIF |
|---|
| 2069 | |
|---|
| 2070 | ENDDO |
|---|
| 2071 | |
|---|
| 2072 | END SUBROUTINE sedimentation_cloud_ij |
|---|
| 2073 | |
|---|
| 2074 | |
|---|
| 2075 | !------------------------------------------------------------------------------! |
|---|
| 2076 | ! Description: |
|---|
| 2077 | ! ------------ |
|---|
| 2078 | !> Computation of sedimentation flux. Implementation according to Stevens |
|---|
| 2079 | !> and Seifert (2008). Code is based on UCLA-LES. Call for grid point i,j |
|---|
| 2080 | !------------------------------------------------------------------------------! |
|---|
| 2081 | SUBROUTINE sedimentation_rain_ij( i, j ) |
|---|
| 2082 | |
|---|
| 2083 | USE arrays_3d, & |
|---|
| 2084 | ONLY: ddzu, dzu, prr |
|---|
| 2085 | |
|---|
| 2086 | USE cloud_parameters, & |
|---|
| 2087 | ONLY: hyrho, l_d_cp, pt_d_t |
|---|
| 2088 | |
|---|
| 2089 | USE control_parameters, & |
|---|
| 2090 | ONLY: call_microphysics_at_all_substeps, intermediate_timestep_count |
|---|
| 2091 | |
|---|
| 2092 | USE indices, & |
|---|
| 2093 | ONLY: nzb, nzb, nzt, wall_flags_0 |
|---|
| 2094 | |
|---|
| 2095 | USE kinds |
|---|
| 2096 | |
|---|
| 2097 | USE statistics, & |
|---|
| 2098 | ONLY: weight_substep |
|---|
| 2099 | |
|---|
| 2100 | USE surface_mod, & |
|---|
| 2101 | ONLY : bc_h |
|---|
| 2102 | |
|---|
| 2103 | IMPLICIT NONE |
|---|
| 2104 | |
|---|
| 2105 | INTEGER(iwp) :: i !< running index x direction |
|---|
| 2106 | INTEGER(iwp) :: j !< running index y direction |
|---|
| 2107 | INTEGER(iwp) :: k !< running index z direction |
|---|
| 2108 | INTEGER(iwp) :: k_run !< |
|---|
| 2109 | INTEGER(iwp) :: m !< running index surface elements |
|---|
| 2110 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
|---|
| 2111 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
|---|
| 2112 | |
|---|
| 2113 | REAL(wp) :: c_run !< |
|---|
| 2114 | REAL(wp) :: d_max !< |
|---|
| 2115 | REAL(wp) :: d_mean !< |
|---|
| 2116 | REAL(wp) :: d_min !< |
|---|
| 2117 | REAL(wp) :: dr !< |
|---|
| 2118 | REAL(wp) :: flux !< |
|---|
| 2119 | REAL(wp) :: flag !< flag to indicate first grid level above surface |
|---|
| 2120 | REAL(wp) :: lambda_r !< |
|---|
| 2121 | REAL(wp) :: mu_r !< |
|---|
| 2122 | REAL(wp) :: z_run !< |
|---|
| 2123 | |
|---|
| 2124 | REAL(wp), DIMENSION(nzb:nzt+1) :: c_nr !< |
|---|
| 2125 | REAL(wp), DIMENSION(nzb:nzt+1) :: c_qr !< |
|---|
| 2126 | REAL(wp), DIMENSION(nzb:nzt+1) :: nr_slope !< |
|---|
| 2127 | REAL(wp), DIMENSION(nzb:nzt+1) :: qr_slope !< |
|---|
| 2128 | REAL(wp), DIMENSION(nzb:nzt+1) :: sed_nr !< |
|---|
| 2129 | REAL(wp), DIMENSION(nzb:nzt+1) :: sed_qr !< |
|---|
| 2130 | REAL(wp), DIMENSION(nzb:nzt+1) :: w_nr !< |
|---|
| 2131 | REAL(wp), DIMENSION(nzb:nzt+1) :: w_qr !< |
|---|
| 2132 | |
|---|
| 2133 | ! |
|---|
| 2134 | !-- Compute velocities |
|---|
| 2135 | DO k = nzb+1, nzt |
|---|
| 2136 | ! |
|---|
| 2137 | !-- Predetermine flag to mask topography |
|---|
| 2138 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 2139 | |
|---|
| 2140 | IF ( qr_1d(k) > eps_sb ) THEN |
|---|
| 2141 | ! |
|---|
| 2142 | !-- Weight averaged diameter of rain drops: |
|---|
| 2143 | dr = ( hyrho(k) * qr_1d(k) / nr_1d(k) * dpirho_l )**( 1.0_wp / 3.0_wp ) |
|---|
| 2144 | ! |
|---|
| 2145 | !-- Shape parameter of gamma distribution (Milbrandt and Yau, 2005; |
|---|
| 2146 | !-- Stevens and Seifert, 2008): |
|---|
| 2147 | mu_r = 10.0_wp * ( 1.0_wp + TANH( 1.2E3_wp * ( dr - 1.4E-3_wp ) ) ) |
|---|
| 2148 | ! |
|---|
| 2149 | !-- Slope parameter of gamma distribution (Seifert, 2008): |
|---|
| 2150 | lambda_r = ( ( mu_r + 3.0_wp ) * ( mu_r + 2.0_wp ) * & |
|---|
| 2151 | ( mu_r + 1.0_wp ) )**( 1.0_wp / 3.0_wp ) / dr |
|---|
| 2152 | |
|---|
| 2153 | w_nr(k) = MAX( 0.1_wp, MIN( 20.0_wp, & |
|---|
| 2154 | a_term - b_term * ( 1.0_wp + & |
|---|
| 2155 | c_term / lambda_r )**( -1.0_wp * & |
|---|
| 2156 | ( mu_r + 1.0_wp ) ) & |
|---|
| 2157 | ) & |
|---|
| 2158 | ) * flag |
|---|
| 2159 | w_qr(k) = MAX( 0.1_wp, MIN( 20.0_wp, & |
|---|
| 2160 | a_term - b_term * ( 1.0_wp + & |
|---|
| 2161 | c_term / lambda_r )**( -1.0_wp * & |
|---|
| 2162 | ( mu_r + 4.0_wp ) ) & |
|---|
| 2163 | ) & |
|---|
| 2164 | ) * flag |
|---|
| 2165 | ELSE |
|---|
| 2166 | w_nr(k) = 0.0_wp |
|---|
| 2167 | w_qr(k) = 0.0_wp |
|---|
| 2168 | ENDIF |
|---|
| 2169 | ENDDO |
|---|
| 2170 | ! |
|---|
| 2171 | !-- Adjust boundary values using surface data type. |
|---|
| 2172 | !-- Upward facing non-natural |
|---|
| 2173 | surf_s = bc_h(0)%start_index(j,i) |
|---|
| 2174 | surf_e = bc_h(0)%end_index(j,i) |
|---|
| 2175 | DO m = surf_s, surf_e |
|---|
| 2176 | k = bc_h(0)%k(m) |
|---|
| 2177 | w_nr(k-1) = w_nr(k) |
|---|
| 2178 | w_qr(k-1) = w_qr(k) |
|---|
| 2179 | ENDDO |
|---|
| 2180 | ! |
|---|
| 2181 | !-- Downward facing non-natural |
|---|
| 2182 | surf_s = bc_h(1)%start_index(j,i) |
|---|
| 2183 | surf_e = bc_h(1)%end_index(j,i) |
|---|
| 2184 | DO m = surf_s, surf_e |
|---|
| 2185 | k = bc_h(1)%k(m) |
|---|
| 2186 | w_nr(k+1) = w_nr(k) |
|---|
| 2187 | w_qr(k+1) = w_qr(k) |
|---|
| 2188 | ENDDO |
|---|
| 2189 | ! |
|---|
| 2190 | !-- Neumann boundary condition at model top |
|---|
| 2191 | w_nr(nzt+1) = 0.0_wp |
|---|
| 2192 | w_qr(nzt+1) = 0.0_wp |
|---|
| 2193 | ! |
|---|
| 2194 | !-- Compute Courant number |
|---|
| 2195 | DO k = nzb+1, nzt |
|---|
| 2196 | ! |
|---|
| 2197 | !-- Predetermine flag to mask topography |
|---|
| 2198 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 2199 | |
|---|
| 2200 | c_nr(k) = 0.25_wp * ( w_nr(k-1) + 2.0_wp * w_nr(k) + w_nr(k+1) ) * & |
|---|
| 2201 | dt_micro * ddzu(k) * flag |
|---|
| 2202 | c_qr(k) = 0.25_wp * ( w_qr(k-1) + 2.0_wp * w_qr(k) + w_qr(k+1) ) * & |
|---|
| 2203 | dt_micro * ddzu(k) * flag |
|---|
| 2204 | ENDDO |
|---|
| 2205 | ! |
|---|
| 2206 | !-- Limit slopes with monotonized centered (MC) limiter (van Leer, 1977): |
|---|
| 2207 | IF ( limiter_sedimentation ) THEN |
|---|
| 2208 | |
|---|
| 2209 | DO k = nzb+1, nzt |
|---|
| 2210 | ! |
|---|
| 2211 | !-- Predetermine flag to mask topography |
|---|
| 2212 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 2213 | |
|---|
| 2214 | d_mean = 0.5_wp * ( qr_1d(k+1) - qr_1d(k-1) ) |
|---|
| 2215 | d_min = qr_1d(k) - MIN( qr_1d(k+1), qr_1d(k), qr_1d(k-1) ) |
|---|
| 2216 | d_max = MAX( qr_1d(k+1), qr_1d(k), qr_1d(k-1) ) - qr_1d(k) |
|---|
| 2217 | |
|---|
| 2218 | qr_slope(k) = SIGN(1.0_wp, d_mean) * MIN ( 2.0_wp * d_min, & |
|---|
| 2219 | 2.0_wp * d_max, & |
|---|
| 2220 | ABS( d_mean ) ) * flag |
|---|
| 2221 | |
|---|
| 2222 | d_mean = 0.5_wp * ( nr_1d(k+1) - nr_1d(k-1) ) |
|---|
| 2223 | d_min = nr_1d(k) - MIN( nr_1d(k+1), nr_1d(k), nr_1d(k-1) ) |
|---|
| 2224 | d_max = MAX( nr_1d(k+1), nr_1d(k), nr_1d(k-1) ) - nr_1d(k) |
|---|
| 2225 | |
|---|
| 2226 | nr_slope(k) = SIGN(1.0_wp, d_mean) * MIN ( 2.0_wp * d_min, & |
|---|
| 2227 | 2.0_wp * d_max, & |
|---|
| 2228 | ABS( d_mean ) ) * flag |
|---|
| 2229 | ENDDO |
|---|
| 2230 | |
|---|
| 2231 | ELSE |
|---|
| 2232 | |
|---|
| 2233 | nr_slope = 0.0_wp |
|---|
| 2234 | qr_slope = 0.0_wp |
|---|
| 2235 | |
|---|
| 2236 | ENDIF |
|---|
| 2237 | |
|---|
| 2238 | sed_nr(nzt+1) = 0.0_wp |
|---|
| 2239 | sed_qr(nzt+1) = 0.0_wp |
|---|
| 2240 | ! |
|---|
| 2241 | !-- Compute sedimentation flux |
|---|
| 2242 | DO k = nzt, nzb+1, -1 |
|---|
| 2243 | ! |
|---|
| 2244 | !-- Predetermine flag to mask topography |
|---|
| 2245 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
|---|
| 2246 | ! |
|---|
| 2247 | !-- Sum up all rain drop number densities which contribute to the flux |
|---|
| 2248 | !-- through k-1/2 |
|---|
| 2249 | flux = 0.0_wp |
|---|
| 2250 | z_run = 0.0_wp ! height above z(k) |
|---|
| 2251 | k_run = k |
|---|
| 2252 | c_run = MIN( 1.0_wp, c_nr(k) ) |
|---|
| 2253 | DO WHILE ( c_run > 0.0_wp .AND. k_run <= nzt ) |
|---|
| 2254 | flux = flux + hyrho(k_run) * & |
|---|
| 2255 | ( nr_1d(k_run) + nr_slope(k_run) * ( 1.0_wp - c_run ) * & |
|---|
| 2256 | 0.5_wp ) * c_run * dzu(k_run) * flag |
|---|
| 2257 | z_run = z_run + dzu(k_run) * flag |
|---|
| 2258 | k_run = k_run + 1 * flag |
|---|
| 2259 | c_run = MIN( 1.0_wp, c_nr(k_run) - z_run * ddzu(k_run) ) * flag |
|---|
| 2260 | ENDDO |
|---|
| 2261 | ! |
|---|
| 2262 | !-- It is not allowed to sediment more rain drop number density than |
|---|
| 2263 | !-- available |
|---|
| 2264 | flux = MIN( flux, & |
|---|
| 2265 | hyrho(k) * dzu(k+1) * nr_1d(k) + sed_nr(k+1) * dt_micro ) |
|---|
| 2266 | |
|---|
| 2267 | sed_nr(k) = flux / dt_micro * flag |
|---|
| 2268 | nr_1d(k) = nr_1d(k) + ( sed_nr(k+1) - sed_nr(k) ) * ddzu(k+1) / & |
|---|
| 2269 | hyrho(k) * dt_micro * flag |
|---|
| 2270 | ! |
|---|
| 2271 | !-- Sum up all rain water content which contributes to the flux |
|---|
| 2272 | !-- through k-1/2 |
|---|
| 2273 | flux = 0.0_wp |
|---|
| 2274 | z_run = 0.0_wp ! height above z(k) |
|---|
| 2275 | k_run = k |
|---|
| 2276 | c_run = MIN( 1.0_wp, c_qr(k) ) |
|---|
| 2277 | |
|---|
| 2278 | DO WHILE ( c_run > 0.0_wp .AND. k_run <= nzt ) |
|---|
| 2279 | |
|---|
| 2280 | flux = flux + hyrho(k_run) * & |
|---|
| 2281 | ( qr_1d(k_run) + qr_slope(k_run) * ( 1.0_wp - c_run ) * & |
|---|
| 2282 | 0.5_wp ) * c_run * dzu(k_run) * flag |
|---|
| 2283 | z_run = z_run + dzu(k_run) * flag |
|---|
| 2284 | k_run = k_run + 1 * flag |
|---|
| 2285 | c_run = MIN( 1.0_wp, c_qr(k_run) - z_run * ddzu(k_run) ) * flag |
|---|
| 2286 | |
|---|
| 2287 | ENDDO |
|---|
| 2288 | ! |
|---|
| 2289 | !-- It is not allowed to sediment more rain water content than available |
|---|
| 2290 | flux = MIN( flux, & |
|---|
| 2291 | hyrho(k) * dzu(k) * qr_1d(k) + sed_qr(k+1) * dt_micro ) |
|---|
| 2292 | |
|---|
| 2293 | sed_qr(k) = flux / dt_micro * flag |
|---|
| 2294 | |
|---|
| 2295 | qr_1d(k) = qr_1d(k) + ( sed_qr(k+1) - sed_qr(k) ) * ddzu(k+1) / & |
|---|
| 2296 | hyrho(k) * dt_micro * flag |
|---|
| 2297 | q_1d(k) = q_1d(k) + ( sed_qr(k+1) - sed_qr(k) ) * ddzu(k+1) / & |
|---|
| 2298 | hyrho(k) * dt_micro * flag |
|---|
| 2299 | pt_1d(k) = pt_1d(k) - ( sed_qr(k+1) - sed_qr(k) ) * ddzu(k+1) / & |
|---|
| 2300 | hyrho(k) * l_d_cp * pt_d_t(k) * dt_micro * flag |
|---|
| 2301 | ! |
|---|
| 2302 | !-- Compute the rain rate |
|---|
| 2303 | IF ( call_microphysics_at_all_substeps ) THEN |
|---|
| 2304 | prr(k,j,i) = prr(k,j,i) + sed_qr(k) / hyrho(k) & |
|---|
| 2305 | * weight_substep(intermediate_timestep_count) * flag |
|---|
| 2306 | ELSE |
|---|
| 2307 | prr(k,j,i) = prr(k,j,i) + sed_qr(k) / hyrho(k) * flag |
|---|
| 2308 | ENDIF |
|---|
| 2309 | |
|---|
| 2310 | ENDDO |
|---|
| 2311 | |
|---|
| 2312 | END SUBROUTINE sedimentation_rain_ij |
|---|
| 2313 | |
|---|
| 2314 | |
|---|
| 2315 | !------------------------------------------------------------------------------! |
|---|
| 2316 | ! Description: |
|---|
| 2317 | ! ------------ |
|---|
| 2318 | !> This subroutine computes the precipitation amount due to gravitational |
|---|
| 2319 | !> settling of rain and cloud (fog) droplets |
|---|
| 2320 | !------------------------------------------------------------------------------! |
|---|
| 2321 | SUBROUTINE calc_precipitation_amount_ij( i, j ) |
|---|
| 2322 | |
|---|
| 2323 | USE arrays_3d, & |
|---|
| 2324 | ONLY: precipitation_amount, prr |
|---|
| 2325 | |
|---|
| 2326 | USE cloud_parameters, & |
|---|
| 2327 | ONLY: hyrho |
|---|
| 2328 | |
|---|
| 2329 | USE control_parameters, & |
|---|
| 2330 | ONLY: call_microphysics_at_all_substeps, dt_do2d_xy, dt_3d, & |
|---|
| 2331 | intermediate_timestep_count, intermediate_timestep_count_max,& |
|---|
| 2332 | precipitation_amount_interval, time_do2d_xy |
|---|
| 2333 | |
|---|
| 2334 | USE indices, & |
|---|
| 2335 | ONLY: nzb, nzt, wall_flags_0 |
|---|
| 2336 | |
|---|
| 2337 | USE kinds |
|---|
| 2338 | |
|---|
| 2339 | USE surface_mod, & |
|---|
| 2340 | ONLY : bc_h |
|---|
| 2341 | |
|---|
| 2342 | IMPLICIT NONE |
|---|
| 2343 | |
|---|
| 2344 | INTEGER(iwp) :: i !< running index x direction |
|---|
| 2345 | INTEGER(iwp) :: j !< running index y direction |
|---|
| 2346 | INTEGER(iwp) :: k !< running index z direction |
|---|
| 2347 | INTEGER(iwp) :: m !< running index surface elements |
|---|
| 2348 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
|---|
| 2349 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
|---|
| 2350 | |
|---|
| 2351 | IF ( ( dt_do2d_xy - time_do2d_xy ) < precipitation_amount_interval .AND.& |
|---|
| 2352 | ( .NOT. call_microphysics_at_all_substeps .OR. & |
|---|
| 2353 | intermediate_timestep_count == intermediate_timestep_count_max ) ) & |
|---|
| 2354 | THEN |
|---|
| 2355 | |
|---|
| 2356 | surf_s = bc_h(0)%start_index(j,i) |
|---|
| 2357 | surf_e = bc_h(0)%end_index(j,i) |
|---|
| 2358 | DO m = surf_s, surf_e |
|---|
| 2359 | k = bc_h(0)%k(m) |
|---|
| 2360 | precipitation_amount(j,i) = precipitation_amount(j,i) + & |
|---|
| 2361 | prr(k,j,i) * hyrho(k) * dt_3d |
|---|
| 2362 | ENDDO |
|---|
| 2363 | |
|---|
| 2364 | ENDIF |
|---|
| 2365 | |
|---|
| 2366 | END SUBROUTINE calc_precipitation_amount_ij |
|---|
| 2367 | |
|---|
| 2368 | !------------------------------------------------------------------------------! |
|---|
| 2369 | ! Description: |
|---|
| 2370 | ! ------------ |
|---|
| 2371 | !> This function computes the gamma function (Press et al., 1992). |
|---|
| 2372 | !> The gamma function is needed for the calculation of the evaporation |
|---|
| 2373 | !> of rain drops. |
|---|
| 2374 | !------------------------------------------------------------------------------! |
|---|
| 2375 | FUNCTION gamm( xx ) |
|---|
| 2376 | |
|---|
| 2377 | USE kinds |
|---|
| 2378 | |
|---|
| 2379 | IMPLICIT NONE |
|---|
| 2380 | |
|---|
| 2381 | INTEGER(iwp) :: j !< |
|---|
| 2382 | |
|---|
| 2383 | REAL(wp) :: gamm !< |
|---|
| 2384 | REAL(wp) :: ser !< |
|---|
| 2385 | REAL(wp) :: tmp !< |
|---|
| 2386 | REAL(wp) :: x_gamm !< |
|---|
| 2387 | REAL(wp) :: xx !< |
|---|
| 2388 | REAL(wp) :: y_gamm !< |
|---|
| 2389 | |
|---|
| 2390 | |
|---|
| 2391 | REAL(wp), PARAMETER :: stp = 2.5066282746310005_wp !< |
|---|
| 2392 | REAL(wp), PARAMETER :: cof(6) = (/ 76.18009172947146_wp, & |
|---|
| 2393 | -86.50532032941677_wp, & |
|---|
| 2394 | 24.01409824083091_wp, & |
|---|
| 2395 | -1.231739572450155_wp, & |
|---|
| 2396 | 0.1208650973866179E-2_wp, & |
|---|
| 2397 | -0.5395239384953E-5_wp /) !< |
|---|
| 2398 | |
|---|
| 2399 | x_gamm = xx |
|---|
| 2400 | y_gamm = x_gamm |
|---|
| 2401 | tmp = x_gamm + 5.5_wp |
|---|
| 2402 | tmp = ( x_gamm + 0.5_wp ) * LOG( tmp ) - tmp |
|---|
| 2403 | ser = 1.000000000190015_wp |
|---|
| 2404 | |
|---|
| 2405 | DO j = 1, 6 |
|---|
| 2406 | y_gamm = y_gamm + 1.0_wp |
|---|
| 2407 | ser = ser + cof( j ) / y_gamm |
|---|
| 2408 | ENDDO |
|---|
| 2409 | |
|---|
| 2410 | ! |
|---|
| 2411 | !-- Until this point the algorithm computes the logarithm of the gamma |
|---|
| 2412 | !-- function. Hence, the exponential function is used. |
|---|
| 2413 | ! gamm = EXP( tmp + LOG( stp * ser / x_gamm ) ) |
|---|
| 2414 | gamm = EXP( tmp ) * stp * ser / x_gamm |
|---|
| 2415 | |
|---|
| 2416 | RETURN |
|---|
| 2417 | |
|---|
| 2418 | END FUNCTION gamm |
|---|
| 2419 | |
|---|
| 2420 | END MODULE microphysics_mod |
|---|
