!> @file model_1d_mod.f90 !------------------------------------------------------------------------------! ! This file is part of PALM. ! ! PALM is free software: you can redistribute it and/or modify it under the ! terms of the GNU General Public License as published by the Free Software ! Foundation, either version 3 of the License, or (at your option) any later ! version. ! ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. ! ! You should have received a copy of the GNU General Public License along with ! PALM. If not, see . ! ! Copyright 1997-2017 Leibniz Universitaet Hannover !------------------------------------------------------------------------------! ! ! Current revisions: ! ----------------- ! ! ! Former revisions: ! ----------------- ! $Id: model_1d_mod.f90 2339 2017-08-07 13:55:26Z scharf $ ! corrected timestamp in header ! ! 2338 2017-08-07 12:15:38Z gronemeier ! renamed init_1d_model to model_1d_mod and and formatted it as a module; ! reformatted output of profiles ! ! 2337 2017-08-07 08:59:53Z gronemeier ! revised calculation of mixing length ! removed rounding of time step ! corrected calculation of virtual potential temperature ! ! 2334 2017-08-04 11:57:04Z gronemeier ! set c_m = 0.4 according to Detering and Etling (1985) ! ! 2299 2017-06-29 10:14:38Z maronga ! Removed german text ! ! 2101 2017-01-05 16:42:31Z suehring ! ! 2059 2016-11-10 14:20:40Z maronga ! Corrected min/max values of Rif. ! ! 2000 2016-08-20 18:09:15Z knoop ! Forced header and separation lines into 80 columns ! ! 1960 2016-07-12 16:34:24Z suehring ! Remove passive_scalar from IF-statements, as 1D-scalar profile is effectively ! not used. ! Formatting adjustment ! ! 1808 2016-04-05 19:44:00Z raasch ! routine local_flush replaced by FORTRAN statement ! ! 1709 2015-11-04 14:47:01Z maronga ! Set initial time step to 10 s to avoid instability of the 1d model for small ! grid spacings ! ! 1697 2015-10-28 17:14:10Z raasch ! small E- and F-FORMAT changes to avoid informative compiler messages about ! insufficient field width ! ! 1691 2015-10-26 16:17:44Z maronga ! Renamed prandtl_layer to constant_flux_layer. rif is replaced by ol and zeta. ! ! 1682 2015-10-07 23:56:08Z knoop ! Code annotations made doxygen readable ! ! 1353 2014-04-08 15:21:23Z heinze ! REAL constants provided with KIND-attribute ! ! 1346 2014-03-27 13:18:20Z heinze ! Bugfix: REAL constants provided with KIND-attribute especially in call of ! intrinsic function like MAX, MIN, SIGN ! ! 1322 2014-03-20 16:38:49Z raasch ! REAL functions provided with KIND-attribute ! ! 1320 2014-03-20 08:40:49Z raasch ! ONLY-attribute added to USE-statements, ! kind-parameters added to all INTEGER and REAL declaration statements, ! kinds are defined in new module kinds, ! revision history before 2012 removed, ! comment fields (!:) to be used for variable explanations added to ! all variable declaration statements ! ! 1036 2012-10-22 13:43:42Z raasch ! code put under GPL (PALM 3.9) ! ! 1015 2012-09-27 09:23:24Z raasch ! adjustment of mixing length to the Prandtl mixing length at first grid point ! above ground removed ! ! 1001 2012-09-13 14:08:46Z raasch ! all actions concerning leapfrog scheme removed ! ! 996 2012-09-07 10:41:47Z raasch ! little reformatting ! ! 978 2012-08-09 08:28:32Z fricke ! roughness length for scalar quantities z0h1d added ! ! Revision 1.1 1998/03/09 16:22:10 raasch ! Initial revision ! ! ! Description: ! ------------ !> 1D-model to initialize the 3D-arrays. !> The temperature profile is set as steady and a corresponding steady solution !> of the wind profile is being computed. !> All subroutines required can be found within this file. !> !> @todo harmonize code with new surface_layer_fluxes module !> @bug 1D model crashes when using small grid spacings in the order of 1 m !------------------------------------------------------------------------------! MODULE model_1d_mod USE arrays_3d, & ONLY: dd2zu, ddzu, ddzw, dzu, l_grid, pt_init, q_init, ug, u_init, & vg, v_init, zu USE control_parameters, & ONLY: constant_diffusion, constant_flux_layer, dissipation_1d, f, g, & humidity, ibc_e_b, intermediate_timestep_count, & intermediate_timestep_count_max, kappa, km_constant, & message_string, mixing_length_1d, prandtl_number, & roughness_length, run_description_header, simulated_time_chr, timestep_scheme, tsc, z0h_factor USE indices, & ONLY: nzb, nzb_diff, nzt USE kinds USE pegrid IMPLICIT NONE INTEGER(iwp) :: current_timestep_number_1d = 0 !< current timestep number (1d-model) INTEGER(iwp) :: damp_level_ind_1d !< lower grid index of damping layer (1d-model) !# LOGICAL :: run_control_header_1d = .FALSE. !< flag for output of run control header (1d-model) LOGICAL :: stop_dt_1d = .FALSE. !< termination flag, used in case of too small timestep (1d-model) REAL(wp) :: c_m = 0.4_wp !< model constant, 0.4 according to Detering and Etling (1985) REAL(wp) :: damp_level_1d = -1.0_wp !< namelist parameter !# REAL(wp) :: dt_1d = 60.0_wp !< dynamic timestep (1d-model) REAL(wp) :: dt_max_1d = 300.0_wp !< timestep limit (1d-model) REAL(wp) :: dt_pr_1d = 9999999.9_wp !< namelist parameter !# REAL(wp) :: dt_run_control_1d = 60.0_wp !< namelist parameter !# REAL(wp) :: end_time_1d = 864000.0_wp !< namelist parameter !# REAL(wp) :: qs1d !< characteristic humidity scale (1d-model) REAL(wp) :: simulated_time_1d = 0.0_wp !< updated simulated time (1d-model) REAL(wp) :: time_pr_1d = 0.0_wp !< updated simulated time for profile output (1d-model) REAL(wp) :: time_run_control_1d = 0.0_wp !< updated simulated time for run-control output (1d-model) REAL(wp) :: ts1d !< characteristic temperature scale (1d-model) REAL(wp) :: us1d !< friction velocity (1d-model) !# REAL(wp) :: usws1d !< u-component of the momentum flux (1d-model) !# REAL(wp) :: vsws1d !< v-component of the momentum flux (1d-model) !# REAL(wp) :: z01d !< roughness length for momentum (1d-model) REAL(wp) :: z0h1d !< roughness length for scalars (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d !< tke (1d-model) !# REAL(wp), DIMENSION(:), ALLOCATABLE :: e1d_p !< prognostic value of tke (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: kh1d !< turbulent diffusion coefficient for heat (1d-model) !# REAL(wp), DIMENSION(:), ALLOCATABLE :: km1d !< turbulent diffusion coefficient for momentum (1d-model)!# REAL(wp), DIMENSION(:), ALLOCATABLE :: l_black !< mixing length Blackadar (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d !< mixing length for turbulent diffusion coefficients (1d-model) !# REAL(wp), DIMENSION(:), ALLOCATABLE :: l1d_diss !< mixing length for dissipation (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: rif1d !< Richardson flux number (1d-model) !# REAL(wp), DIMENSION(:), ALLOCATABLE :: te_e !< tendency of e (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: te_em !< weighted tendency of e for previous sub-timestep (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: te_u !< tendency of u (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: te_um !< weighted tendency of u for previous sub-timestep (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: te_v !< tendency of v (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: te_vm !< weighted tendency of v for previous sub-timestep (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d !< u-velocity component (1d-model) !# REAL(wp), DIMENSION(:), ALLOCATABLE :: u1d_p !< prognostic value of u-velocity component (1d-model) REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d !< v-velocity component (1d-model) !# REAL(wp), DIMENSION(:), ALLOCATABLE :: v1d_p !< prognostic value of v-velocity component (1d-model) ! !-- Initialize 1D model INTERFACE init_1d_model MODULE PROCEDURE init_1d_model END INTERFACE init_1d_model ! !-- Print profiles INTERFACE print_1d_model MODULE PROCEDURE print_1d_model END INTERFACE print_1d_model ! !-- Print run control information INTERFACE run_control_1d MODULE PROCEDURE run_control_1d END INTERFACE run_control_1d ! !-- Main procedure INTERFACE time_integration_1d MODULE PROCEDURE time_integration_1d END INTERFACE time_integration_1d ! !-- Calculate time step INTERFACE timestep_1d MODULE PROCEDURE timestep_1d END INTERFACE timestep_1d SAVE PRIVATE ! !-- Public interfaces PUBLIC init_1d_model ! !-- Public variables PUBLIC damp_level_1d, damp_level_ind_1d, dt_pr_1d, dt_run_control_1d, & e1d, end_time_1d, kh1d, km1d, l1d, rif1d, u1d, us1d, usws1d, v1d, & vsws1d CONTAINS SUBROUTINE init_1d_model IMPLICIT NONE CHARACTER (LEN=9) :: time_to_string !< INTEGER(iwp) :: k !< REAL(wp) :: lambda !< ! !-- Allocate required 1D-arrays ALLOCATE( e1d(nzb:nzt+1), e1d_p(nzb:nzt+1), kh1d(nzb:nzt+1), & km1d(nzb:nzt+1), l_black(nzb:nzt+1), l1d(nzb:nzt+1), & l1d_diss(nzb:nzt+1), rif1d(nzb:nzt+1), te_e(nzb:nzt+1), & te_em(nzb:nzt+1), te_u(nzb:nzt+1), te_um(nzb:nzt+1), & te_v(nzb:nzt+1), te_vm(nzb:nzt+1), u1d(nzb:nzt+1), & u1d_p(nzb:nzt+1), v1d(nzb:nzt+1), v1d_p(nzb:nzt+1) ) ! !-- Initialize arrays IF ( constant_diffusion ) THEN km1d = km_constant kh1d = km_constant / prandtl_number ELSE e1d = 0.0_wp; e1d_p = 0.0_wp kh1d = 0.0_wp; km1d = 0.0_wp rif1d = 0.0_wp ! !-- Compute the mixing length l_black(nzb) = 0.0_wp IF ( TRIM( mixing_length_1d ) == 'blackadar' ) THEN ! !-- Blackadar mixing length IF ( f /= 0.0_wp ) THEN lambda = 2.7E-4_wp * SQRT( ug(nzt+1)**2 + vg(nzt+1)**2 ) / & ABS( f ) + 1E-10_wp ELSE lambda = 30.0_wp ENDIF DO k = nzb+1, nzt+1 l_black(k) = kappa * zu(k) / ( 1.0_wp + kappa * zu(k) / lambda ) ENDDO ELSEIF ( TRIM( mixing_length_1d ) == 'as_in_3d_model' ) THEN ! !-- Use the same mixing length as in 3D model l_black(1:nzt) = l_grid l_black(nzt+1) = l_black(nzt) ENDIF ENDIF l1d = l_black l1d_diss = l_black u1d = u_init u1d_p = u_init v1d = v_init v1d_p = v_init ! !-- Set initial horizontal velocities at the lowest grid levels to a very small !-- value in order to avoid too small time steps caused by the diffusion limit !-- in the initial phase of a run (at k=1, dz/2 occurs in the limiting formula!) u1d(0:1) = 0.1_wp u1d_p(0:1) = 0.1_wp v1d(0:1) = 0.1_wp v1d_p(0:1) = 0.1_wp ! !-- For u*, theta* and the momentum fluxes plausible values are set IF ( constant_flux_layer ) THEN us1d = 0.1_wp ! without initial friction the flow would not change ELSE e1d(nzb+1) = 1.0_wp km1d(nzb+1) = 1.0_wp us1d = 0.0_wp ENDIF ts1d = 0.0_wp usws1d = 0.0_wp vsws1d = 0.0_wp z01d = roughness_length z0h1d = z0h_factor * z01d IF ( humidity ) qs1d = 0.0_wp ! !-- Tendencies must be preset in order to avoid runtime errors within the !-- first Runge-Kutta step te_em = 0.0_wp te_um = 0.0_wp te_vm = 0.0_wp ! !-- Set model constant IF ( dissipation_1d == 'as_in_3d_model' ) c_m = 0.1_wp ! !-- Set start time in hh:mm:ss - format simulated_time_chr = time_to_string( simulated_time_1d ) ! !-- Integrate the 1D-model equations using the Runge-Kutta scheme CALL time_integration_1d END SUBROUTINE init_1d_model !------------------------------------------------------------------------------! ! Description: ! ------------ !> Runge-Kutta time differencing scheme for the 1D-model. !------------------------------------------------------------------------------! SUBROUTINE time_integration_1d IMPLICIT NONE CHARACTER (LEN=9) :: time_to_string !< INTEGER(iwp) :: k !< loop index REAL(wp) :: a !< auxiliary variable REAL(wp) :: b !< auxiliary variable REAL(wp) :: dissipation !< dissipation of TKE REAL(wp) :: dpt_dz !< vertical temperature gradient REAL(wp) :: flux !< vertical temperature gradient REAL(wp) :: kmzm !< Km(z-dz/2) REAL(wp) :: kmzp !< Km(z+dz/2) REAL(wp) :: l_stable !< mixing length for stable case REAL(wp) :: pt_0 !< reference temperature REAL(wp) :: uv_total !< horizontal wind speed ! !-- Determine the time step at the start of a 1D-simulation and !-- determine and printout quantities used for run control dt_1d = 10.0_wp CALL run_control_1d ! !-- Start of time loop DO WHILE ( simulated_time_1d < end_time_1d .AND. .NOT. stop_dt_1d ) ! !-- Depending on the timestep scheme, carry out one or more intermediate !-- timesteps intermediate_timestep_count = 0 DO WHILE ( intermediate_timestep_count < & intermediate_timestep_count_max ) intermediate_timestep_count = intermediate_timestep_count + 1 CALL timestep_scheme_steering ! !-- Compute all tendency terms. If a Prandtl-layer is simulated, k starts !-- at nzb+2. DO k = nzb_diff, nzt kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) ! !-- u-component te_u(k) = f * ( v1d(k) - vg(k) ) + ( & kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) & - kmzm * ( u1d(k) - u1d(k-1) ) * ddzu(k) & ) * ddzw(k) ! !-- v-component te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) & - kmzm * ( v1d(k) - v1d(k-1) ) * ddzu(k) & ) * ddzw(k) ENDDO IF ( .NOT. constant_diffusion ) THEN DO k = nzb_diff, nzt ! !-- TKE kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) IF ( .NOT. humidity ) THEN pt_0 = pt_init(k) flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) ELSE pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & 0.61_wp * ( pt_init(k+1) * q_init(k+1) - & pt_init(k-1) * q_init(k-1) ) & ) * dd2zu(k) ENDIF IF ( dissipation_1d == 'detering' ) THEN ! !-- According to Detering, c_e=c_m^3 dissipation = c_m**3 * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN dissipation = ( 0.19_wp & + 0.74_wp * l1d_diss(k) / l_grid(k) & ) * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) ENDIF te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2& + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2& ) & - g / pt_0 * kh1d(k) * flux & + ( & kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & ) * ddzw(k) & - dissipation ENDDO ENDIF ! !-- Tendency terms at the top of the Prandtl-layer. !-- Finite differences of the momentum fluxes are computed using half the !-- normal grid length (2.0*ddzw(k)) for the sake of enhanced accuracy IF ( constant_flux_layer ) THEN k = nzb+1 kmzm = 0.5_wp * ( km1d(k-1) + km1d(k) ) kmzp = 0.5_wp * ( km1d(k) + km1d(k+1) ) IF ( .NOT. humidity ) THEN pt_0 = pt_init(k) flux = ( pt_init(k+1)-pt_init(k-1) ) * dd2zu(k) ELSE pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) flux = ( ( pt_init(k+1) - pt_init(k-1) ) + & 0.61_wp * ( pt_init(k+1) * q_init(k+1) - & pt_init(k-1) * q_init(k-1) ) & ) * dd2zu(k) ENDIF IF ( dissipation_1d == 'detering' ) THEN ! !-- According to Detering, c_e=0.064 dissipation = 0.064_wp * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) ELSEIF ( dissipation_1d == 'as_in_3d_model' ) THEN dissipation = ( 0.19_wp + 0.74_wp * l1d_diss(k) / l_grid(k) ) & * e1d(k) * SQRT( e1d(k) ) / l1d_diss(k) ENDIF ! !-- u-component te_u(k) = f * ( v1d(k) - vg(k) ) + ( & kmzp * ( u1d(k+1) - u1d(k) ) * ddzu(k+1) + usws1d & ) * 2.0_wp * ddzw(k) ! !-- v-component te_v(k) = -f * ( u1d(k) - ug(k) ) + ( & kmzp * ( v1d(k+1) - v1d(k) ) * ddzu(k+1) + vsws1d & ) * 2.0_wp * ddzw(k) ! !-- TKE te_e(k) = km1d(k) * ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & ) & - g / pt_0 * kh1d(k) * flux & + ( & kmzp * ( e1d(k+1) - e1d(k) ) * ddzu(k+1) & - kmzm * ( e1d(k) - e1d(k-1) ) * ddzu(k) & ) * ddzw(k) & - dissipation ENDIF ! !-- Prognostic equations for all 1D variables DO k = nzb+1, nzt u1d_p(k) = u1d(k) + dt_1d * ( tsc(2) * te_u(k) + & tsc(3) * te_um(k) ) v1d_p(k) = v1d(k) + dt_1d * ( tsc(2) * te_v(k) + & tsc(3) * te_vm(k) ) ENDDO IF ( .NOT. constant_diffusion ) THEN DO k = nzb+1, nzt e1d_p(k) = e1d(k) + dt_1d * ( tsc(2) * te_e(k) + & tsc(3) * te_em(k) ) ENDDO ! !-- Eliminate negative TKE values, which can result from the !-- integration due to numerical inaccuracies. In such cases the TKE !-- value is reduced to 10 percent of its old value. WHERE ( e1d_p < 0.0_wp ) e1d_p = 0.1_wp * e1d ENDIF ! !-- Calculate tendencies for the next Runge-Kutta step IF ( timestep_scheme(1:5) == 'runge' ) THEN IF ( intermediate_timestep_count == 1 ) THEN DO k = nzb+1, nzt te_um(k) = te_u(k) te_vm(k) = te_v(k) ENDDO IF ( .NOT. constant_diffusion ) THEN DO k = nzb+1, nzt te_em(k) = te_e(k) ENDDO ENDIF ELSEIF ( intermediate_timestep_count < & intermediate_timestep_count_max ) THEN DO k = nzb+1, nzt te_um(k) = -9.5625_wp * te_u(k) + 5.3125_wp * te_um(k) te_vm(k) = -9.5625_wp * te_v(k) + 5.3125_wp * te_vm(k) ENDDO IF ( .NOT. constant_diffusion ) THEN DO k = nzb+1, nzt te_em(k) = -9.5625_wp * te_e(k) + 5.3125_wp * te_em(k) ENDDO ENDIF ENDIF ENDIF ! !-- Boundary conditions for the prognostic variables. !-- At the top boundary (nzt+1) u,v and e keep their initial values !-- (ug(nzt+1), vg(nzt+1), 0). !-- At the bottom boundary, Dirichlet condition is used for u and v (0) !-- and Neumann condition for e (e(nzb)=e(nzb+1)). u1d_p(nzb) = 0.0_wp v1d_p(nzb) = 0.0_wp ! !-- Swap the time levels in preparation for the next time step. u1d = u1d_p v1d = v1d_p IF ( .NOT. constant_diffusion ) THEN e1d = e1d_p ENDIF ! !-- Compute diffusion quantities IF ( .NOT. constant_diffusion ) THEN ! !-- First compute the vertical fluxes in the Prandtl-layer IF ( constant_flux_layer ) THEN ! !-- Compute theta* using Rif numbers of the previous time step IF ( rif1d(nzb+1) >= 0.0_wp ) THEN ! !-- Stable stratification ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & ( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * & ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & ) ELSE ! !-- Unstable stratification a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & zu(nzb+1) * z0h1d ) ts1d = kappa * ( pt_init(nzb+1) - pt_init(nzb) ) / & LOG( (a-1.0_wp) / (a+1.0_wp) * & (b+1.0_wp) / (b-1.0_wp) ) ENDIF ENDIF ! constant_flux_layer ! !-- Compute the Richardson-flux numbers, !-- first at the top of the Prandtl-layer using u* of the previous !-- time step (+1E-30, if u* = 0), then in the remaining area. There !-- the rif-numbers of the previous time step are used. IF ( constant_flux_layer ) THEN IF ( .NOT. humidity ) THEN pt_0 = pt_init(nzb+1) flux = ts1d ELSE pt_0 = pt_init(nzb+1) * ( 1.0_wp + 0.61_wp * q_init(nzb+1) ) flux = ts1d + 0.61_wp * pt_init(k) * qs1d ENDIF rif1d(nzb+1) = zu(nzb+1) * kappa * g * flux / & ( pt_0 * ( us1d**2 + 1E-30_wp ) ) ENDIF DO k = nzb_diff, nzt IF ( .NOT. humidity ) THEN pt_0 = pt_init(k) flux = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) ELSE pt_0 = pt_init(k) * ( 1.0_wp + 0.61_wp * q_init(k) ) flux = ( ( pt_init(k+1) - pt_init(k-1) ) & + 0.61_wp & * ( pt_init(k+1) * q_init(k+1) & - pt_init(k-1) * q_init(k-1) ) & ) * dd2zu(k) ENDIF IF ( rif1d(k) >= 0.0_wp ) THEN rif1d(k) = g / pt_0 * flux / & ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & + 1E-30_wp & ) ELSE rif1d(k) = g / pt_0 * flux / & ( ( ( u1d(k+1) - u1d(k-1) ) * dd2zu(k) )**2 & + ( ( v1d(k+1) - v1d(k-1) ) * dd2zu(k) )**2 & + 1E-30_wp & ) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp ENDIF ENDDO ! !-- Richardson-numbers must remain restricted to a realistic value !-- range. It is exceeded excessively for very small velocities !-- (u,v --> 0). WHERE ( rif1d < -5.0_wp ) rif1d = -5.0_wp WHERE ( rif1d > 1.0_wp ) rif1d = 1.0_wp ! !-- Compute u* from the absolute velocity value IF ( constant_flux_layer ) THEN uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) IF ( rif1d(nzb+1) >= 0.0_wp ) THEN ! !-- Stable stratification us1d = kappa * uv_total / ( & LOG( zu(nzb+1) / z01d ) + 5.0_wp * rif1d(nzb+1) * & ( zu(nzb+1) - z01d ) / zu(nzb+1) & ) ELSE ! !-- Unstable stratification a = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) ) b = 1.0_wp / SQRT( SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & zu(nzb+1) * z01d ) ) us1d = kappa * uv_total / ( & LOG( (1.0_wp+b) / (1.0_wp-b) * (1.0_wp-a) / & (1.0_wp+a) ) + & 2.0_wp * ( ATAN( b ) - ATAN( a ) ) & ) ENDIF ! !-- Compute the momentum fluxes for the diffusion terms usws1d = - u1d(nzb+1) / uv_total * us1d**2 vsws1d = - v1d(nzb+1) / uv_total * us1d**2 ! !-- Boundary condition for the turbulent kinetic energy at the top !-- of the Prandtl-layer. c_m = 0.4 according to Detering. !-- Additional Neumann condition de/dz = 0 at nzb is set to ensure !-- compatibility with the 3D model. IF ( ibc_e_b == 2 ) THEN e1d(nzb+1) = ( us1d / c_m )**2 ENDIF e1d(nzb) = e1d(nzb+1) IF ( humidity ) THEN ! !-- Compute q* IF ( rif1d(nzb+1) >= 0.0_wp ) THEN ! !-- Stable stratification qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & ( LOG( zu(nzb+1) / z0h1d ) + 5.0_wp * rif1d(nzb+1) * & ( zu(nzb+1) - z0h1d ) / zu(nzb+1) & ) ELSE ! !-- Unstable stratification a = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) ) b = SQRT( 1.0_wp - 16.0_wp * rif1d(nzb+1) / & zu(nzb+1) * z0h1d ) qs1d = kappa * ( q_init(nzb+1) - q_init(nzb) ) / & LOG( (a-1.0_wp) / (a+1.0_wp) * & (b+1.0_wp) / (b-1.0_wp) ) ENDIF ELSE qs1d = 0.0_wp ENDIF ENDIF ! constant_flux_layer ! !-- Compute the diabatic mixing length. The unstable stratification !-- must not be considered for l1d (km1d) as it is already considered !-- in the dissipation of TKE via l1d_diss. Otherwise, km1d would be !-- too large. IF ( mixing_length_1d == 'blackadar' ) THEN DO k = nzb+1, nzt IF ( rif1d(k) >= 0.0_wp ) THEN l1d(k) = l_black(k) / ( 1.0_wp + 5.0_wp * rif1d(k) ) l1d_diss(k) = l1d(k) ELSE l1d(k) = l_black(k) l1d_diss(k) = l_black(k) * & SQRT( 1.0_wp - 16.0_wp * rif1d(k) ) ENDIF ENDDO ELSEIF ( mixing_length_1d == 'as_in_3d_model' ) THEN DO k = nzb+1, nzt dpt_dz = ( pt_init(k+1) - pt_init(k-1) ) * dd2zu(k) IF ( dpt_dz > 0.0_wp ) THEN l_stable = 0.76_wp * SQRT( e1d(k) ) / & SQRT( g / pt_init(k) * dpt_dz ) + 1E-5_wp ELSE l_stable = l_grid(k) ENDIF l1d(k) = MIN( l_grid(k), l_stable ) l1d_diss(k) = l1d(k) ENDDO ENDIF ! !-- Compute the diffusion coefficients for momentum via the !-- corresponding Prandtl-layer relationship and according to !-- Prandtl-Kolmogorov, respectively IF ( constant_flux_layer ) THEN IF ( rif1d(nzb+1) >= 0.0_wp ) THEN km1d(nzb+1) = us1d * kappa * zu(nzb+1) / & ( 1.0_wp + 5.0_wp * rif1d(nzb+1) ) ELSE km1d(nzb+1) = us1d * kappa * zu(nzb+1) * & ( 1.0_wp - 16.0_wp * rif1d(nzb+1) )**0.25_wp ENDIF ENDIF DO k = nzb_diff, nzt km1d(k) = c_m * SQRT( e1d(k) ) * l1d(k) ENDDO ! !-- Add damping layer DO k = damp_level_ind_1d+1, nzt+1 km1d(k) = 1.1_wp * km1d(k-1) km1d(k) = MIN( km1d(k), 10.0_wp ) ENDDO ! !-- Compute the diffusion coefficient for heat via the relationship !-- kh = phim / phih * km DO k = nzb+1, nzt IF ( rif1d(k) >= 0.0_wp ) THEN kh1d(k) = km1d(k) ELSE kh1d(k) = km1d(k) * ( 1.0_wp - 16.0_wp * rif1d(k) )**0.25_wp ENDIF ENDDO ENDIF ! .NOT. constant_diffusion ENDDO ! intermediate step loop ! !-- Increment simulated time and output times current_timestep_number_1d = current_timestep_number_1d + 1 simulated_time_1d = simulated_time_1d + dt_1d simulated_time_chr = time_to_string( simulated_time_1d ) time_pr_1d = time_pr_1d + dt_1d time_run_control_1d = time_run_control_1d + dt_1d ! !-- Determine and print out quantities for run control IF ( time_run_control_1d >= dt_run_control_1d ) THEN CALL run_control_1d time_run_control_1d = time_run_control_1d - dt_run_control_1d ENDIF ! !-- Profile output on file IF ( time_pr_1d >= dt_pr_1d ) THEN CALL print_1d_model time_pr_1d = time_pr_1d - dt_pr_1d ENDIF ! !-- Determine size of next time step CALL timestep_1d ENDDO ! time loop END SUBROUTINE time_integration_1d !------------------------------------------------------------------------------! ! Description: ! ------------ !> Compute and print out quantities for run control of the 1D model. !------------------------------------------------------------------------------! SUBROUTINE run_control_1d USE constants, & ONLY: pi IMPLICIT NONE INTEGER(iwp) :: k !< loop index REAL(wp) :: alpha !< angle of wind vector at top of constant-flux layer REAL(wp) :: energy !< kinetic energy REAL(wp) :: umax !< maximum of u REAL(wp) :: uv_total !< horizontal wind speed REAL(wp) :: vmax !< maximum of v ! !-- Output IF ( myid == 0 ) THEN ! !-- If necessary, write header IF ( .NOT. run_control_header_1d ) THEN CALL check_open( 15 ) WRITE ( 15, 100 ) run_control_header_1d = .TRUE. ENDIF ! !-- Compute control quantities !-- grid level nzp is excluded due to mirror boundary condition umax = 0.0_wp; vmax = 0.0_wp; energy = 0.0_wp DO k = nzb+1, nzt+1 umax = MAX( ABS( umax ), ABS( u1d(k) ) ) vmax = MAX( ABS( vmax ), ABS( v1d(k) ) ) energy = energy + 0.5_wp * ( u1d(k)**2 + v1d(k)**2 ) ENDDO energy = energy / REAL( nzt - nzb + 1, KIND=wp ) uv_total = SQRT( u1d(nzb+1)**2 + v1d(nzb+1)**2 ) IF ( ABS( v1d(nzb+1) ) < 1.0E-5_wp ) THEN alpha = ACOS( SIGN( 1.0_wp , u1d(nzb+1) ) ) ELSE alpha = ACOS( u1d(nzb+1) / uv_total ) IF ( v1d(nzb+1) <= 0.0_wp ) alpha = 2.0_wp * pi - alpha ENDIF alpha = alpha / ( 2.0_wp * pi ) * 360.0_wp WRITE ( 15, 101 ) current_timestep_number_1d, simulated_time_chr, & dt_1d, umax, vmax, us1d, alpha, energy ! !-- Write buffer contents to disc immediately FLUSH( 15 ) ENDIF ! !-- formats 100 FORMAT (///'1D run control output:'/ & &'------------------------------'// & &'ITER. HH:MM:SS DT UMAX VMAX U* ALPHA ENERG.'/ & &'-------------------------------------------------------------') 101 FORMAT (I5,2X,A9,1X,F6.2,2X,F6.2,1X,F6.2,1X,F6.3,2X,F5.1,2X,F7.2) END SUBROUTINE run_control_1d !------------------------------------------------------------------------------! ! Description: ! ------------ !> Compute the time step w.r.t. the diffusion criterion !------------------------------------------------------------------------------! SUBROUTINE timestep_1d IMPLICIT NONE INTEGER(iwp) :: k !< loop index REAL(wp) :: dt_diff !< time step accorind to diffusion criterion REAL(wp) :: fac !< factor of criterion REAL(wp) :: value !< auxiliary variable ! !-- Compute the currently feasible time step according to the diffusion !-- criterion. At nzb+1 the half grid length is used. fac = 0.35_wp dt_diff = dt_max_1d DO k = nzb+2, nzt value = fac * dzu(k) * dzu(k) / ( km1d(k) + 1E-20_wp ) dt_diff = MIN( value, dt_diff ) ENDDO value = fac * zu(nzb+1) * zu(nzb+1) / ( km1d(nzb+1) + 1E-20_wp ) dt_1d = MIN( value, dt_diff ) ! !-- Set flag when the time step becomes too small IF ( dt_1d < ( 0.00001_wp * dt_max_1d ) ) THEN stop_dt_1d = .TRUE. WRITE( message_string, * ) 'timestep has exceeded the lower limit &', & 'dt_1d = ',dt_1d,' s simulation stopped!' CALL message( 'timestep_1d', 'PA0192', 1, 2, 0, 6, 0 ) ENDIF END SUBROUTINE timestep_1d !------------------------------------------------------------------------------! ! Description: ! ------------ !> List output of profiles from the 1D-model !------------------------------------------------------------------------------! SUBROUTINE print_1d_model IMPLICIT NONE INTEGER(iwp) :: k !< loop parameter LOGICAL, SAVE :: write_first = .TRUE. !< flag for writing header IF ( myid == 0 ) THEN ! !-- Open list output file for profiles from the 1D-model CALL check_open( 17 ) ! !-- Write Header IF ( write_first ) THEN WRITE ( 17, 100 ) TRIM( run_description_header ) write_first = .FALSE. ENDIF ! !-- Write the values WRITE ( 17, 104 ) TRIM( simulated_time_chr ) WRITE ( 17, 101 ) WRITE ( 17, 102 ) WRITE ( 17, 101 ) DO k = nzt+1, nzb, -1 WRITE ( 17, 103) k, zu(k), u1d(k), v1d(k), pt_init(k), e1d(k), & rif1d(k), km1d(k), kh1d(k), l1d(k), zu(k), k ENDDO WRITE ( 17, 101 ) WRITE ( 17, 102 ) WRITE ( 17, 101 ) ! !-- Write buffer contents to disc immediately FLUSH( 17 ) ENDIF ! !-- Formats 100 FORMAT ('# ',A/'#',10('-')/'# 1d-model profiles') 104 FORMAT (//'# Time: ',A) 101 FORMAT ('#',79('-')) 102 FORMAT ('# k zu u v pt e rif Km Kh ', & 'l zu k') 103 FORMAT (1X,I4,1X,F7.1,1X,F6.2,1X,F6.2,1X,F6.2,1X,F6.2,1X,F5.2,1X,F5.2, & 1X,F5.2,1X,F6.2,1X,F7.1,2X,I4) END SUBROUTINE print_1d_model END MODULE