!> @file surface_layer_fluxes_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: surface_layer_fluxes_mod.f90 2119 2017-01-17 16:51:50Z schwenkel $ ! ! 2118 2017-01-17 16:38:49Z raasch ! OpenACC directives and related code removed ! ! 2091 2016-12-21 16:38:18Z suehring ! Bugfix in calculation of vsws ( incorrect linear interpolation of us ) ! ! 2076 2016-12-02 13:54:20Z raasch ! further openmp bugfix for lookup method ! ! 2073 2016-11-30 14:34:05Z raasch ! openmp bugfix for lookup method ! ! 2037 2016-10-26 11:15:40Z knoop ! Anelastic approximation implemented ! ! 2011 2016-09-19 17:29:57Z kanani ! Flag urban_surface is now defined in module control_parameters. ! ! 2007 2016-08-24 15:47:17Z kanani ! Account for urban surface model in computation of vertical kinematic heatflux ! ! 2000 2016-08-20 18:09:15Z knoop ! Forced header and separation lines into 80 columns ! ! 1992 2016-08-12 15:14:59Z suehring ! Minor bug, declaration of look-up index as INTEGER ! ! 1960 2016-07-12 16:34:24Z suehring ! Treat humidity and passive scalar separately ! ! 1929 2016-06-09 16:25:25Z suehring ! Bugfix: avoid segmentation fault in case one grid point is horizontally ! completely surrounded by topography ! ! 1920 2016-05-30 10:50:15Z suehring ! Avoid segmentation fault (see change in 1915) by different initialization of ! us instead of adding a very small number in the denominator ! ! 1915 2016-05-27 11:05:02Z suehring ! Bugfix: avoid segmentation fault in case of most_method = 'circular' at first ! timestep ! ! 1850 2016-04-08 13:29:27Z maronga ! Module renamed ! ! ! 1822 2016-04-07 07:49:42Z hoffmann ! icloud_scheme replaced by microphysics_* ! ! 1788 2016-03-10 11:01:04Z maronga ! Added parameter z0q which replaces z0h in the similarity functions for ! humidity. ! Syntax layout improved. ! ! 1757 2016-02-22 15:49:32Z maronga ! Minor fixes. ! ! 1749 2016-02-09 12:19:56Z raasch ! further OpenACC adjustments ! ! 1747 2016-02-08 12:25:53Z raasch ! adjustments for OpenACC usage ! ! 1709 2015-11-04 14:47:01Z maronga ! Bugfix: division by zero could occur when calculating rib at low wind speeds ! Bugfix: calculation of uv_total for neutral = .T., initial value for ol for ! neutral = .T. ! ! 1705 2015-11-02 14:28:56Z maronga ! Typo removed ! ! 1697 2015-10-28 17:14:10Z raasch ! FORTRAN and OpenMP errors removed ! ! 1696 2015-10-27 10:03:34Z maronga ! Modularized and completely re-written version of prandtl_fluxes.f90. In the ! course of the re-writing two additional methods have been implemented. See ! updated description. ! ! 1551 2015-03-03 14:18:16Z maronga ! Removed land surface model part. The surface fluxes are now always calculated ! within prandtl_fluxes, based on the given surface temperature/humidity (which ! is either provided by the land surface model, by large scale forcing data, or ! directly prescribed by the user. ! ! 1496 2014-12-02 17:25:50Z maronga ! Adapted for land surface model ! ! 1494 2014-11-21 17:14:03Z maronga ! Bugfixes: qs is now calculated before calculation of Rif. calculation of ! buoyancy flux in Rif corrected (added missing humidity term), allow use of ! topography for coupled runs (not tested) ! ! 1361 2014-04-16 15:17:48Z hoffmann ! Bugfix: calculation of turbulent fluxes of rain water content (qrsws) and rain ! drop concentration (nrsws) added ! ! 1340 2014-03-25 19:45:13Z kanani ! REAL constants defined as wp-kind ! ! 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, ! old module precision_kind is removed, ! revision history before 2012 removed, ! comment fields (!:) to be used for variable explanations added to ! all variable declaration statements ! ! 1276 2014-01-15 13:40:41Z heinze ! Use LSF_DATA also in case of Dirichlet bottom boundary condition for scalars ! ! 1257 2013-11-08 15:18:40Z raasch ! openACC "kernels do" replaced by "kernels loop", "loop independent" added ! ! 1036 2012-10-22 13:43:42Z raasch ! code put under GPL (PALM 3.9) ! ! 1015 2012-09-27 09:23:24Z raasch ! OpenACC statements added ! ! 978 2012-08-09 08:28:32Z fricke ! roughness length for scalar quantities z0h added ! ! Revision 1.1 1998/01/23 10:06:06 raasch ! Initial revision ! ! ! Description: ! ------------ !> Diagnostic computation of vertical fluxes in the constant flux layer from the !> values of the variables at grid point k=1. Three different methods are !> available: !> 1) the "old" version (most_method = 'circular') which is fast, but inaccurate !> 2) a Newton iteration method (most_method = 'newton'), which is accurate, but !> slower !> 3) a method using a lookup table which is fast and accurate. Note, however, !> that this method cannot be used in case of roughness heterogeneity !> !> @todo (re)move large_scale_forcing actions !> @todo check/optimize OpenMP directives !------------------------------------------------------------------------------! MODULE surface_layer_fluxes_mod USE arrays_3d, & ONLY: e, kh, nr, nrs, nrsws, ol, pt, q, ql, qr, qrs, qrsws, qs, qsws, & s, shf, ss, ssws, ts, u, us, usws, v, vpt, vsws, zu, zw, z0, & z0h, z0q, drho_air_zw, rho_air_zw USE cloud_parameters, & ONLY: l_d_cp, pt_d_t USE constants, & ONLY: pi USE cpulog USE control_parameters, & ONLY: cloud_physics, constant_heatflux, constant_scalarflux, & constant_waterflux, coupling_mode, g, humidity, ibc_e_b, & ibc_pt_b, initializing_actions, kappa, & intermediate_timestep_count, & intermediate_timestep_count_max, large_scale_forcing, lsf_surf, & message_string, microphysics_seifert, most_method, neutral, & passive_scalar, pt_surface, q_surface, run_coupled, & surface_pressure, simulated_time, terminate_run, & urban_surface, & zeta_max, zeta_min USE indices, & ONLY: nxl, nxlg, nxr, nxrg, nys, nysg, nyn, nyng, nzb_s_inner, & nzb_u_inner, nzb_v_inner USE kinds USE pegrid USE land_surface_model_mod, & ONLY: land_surface, skip_time_do_lsm IMPLICIT NONE INTEGER(iwp) :: i !< loop index x direction INTEGER(iwp) :: j !< loop index y direction INTEGER(iwp) :: k !< loop index z direction INTEGER(iwp) :: l_bnd = 7500 !< Lookup table index of the last time step INTEGER(iwp), PARAMETER :: num_steps = 15000 !< number of steps in the lookup table LOGICAL :: coupled_run !< Flag for coupled atmosphere-ocean runs REAL(wp), DIMENSION(:,:), ALLOCATABLE :: pt1, & !< Potential temperature at first grid level (required for cloud_physics = .T.) qv1, & !< Specific humidity at first grid level (required for cloud_physics = .T.) uv_total !< Total velocity at first grid level REAL(wp), DIMENSION(0:num_steps-1) :: rib_tab, & !< Lookup table bulk Richardson number ol_tab !< Lookup table values of L REAL(wp) :: e_s, & !< Saturation water vapor pressure ol_max = 1.0E6_wp, & !< Maximum Obukhov length rib_max, & !< Maximum Richardson number in lookup table rib_min, & !< Minimum Richardson number in lookup table z_mo !< Height of the constant flux layer where MOST is assumed SAVE PRIVATE PUBLIC init_surface_layer_fluxes, pt1, qv1, surface_layer_fluxes, uv_total INTERFACE init_surface_layer_fluxes MODULE PROCEDURE init_surface_layer_fluxes END INTERFACE init_surface_layer_fluxes INTERFACE surface_layer_fluxes MODULE PROCEDURE surface_layer_fluxes END INTERFACE surface_layer_fluxes CONTAINS !------------------------------------------------------------------------------! ! Description: ! ------------ !> Main routine to compute the surface fluxes !------------------------------------------------------------------------------! SUBROUTINE surface_layer_fluxes IMPLICIT NONE ! !-- In case cloud physics is used, it is required to derive potential !-- temperature and specific humidity at first grid level from the fields pt !-- and q IF ( cloud_physics ) THEN CALL calc_pt_q ENDIF ! !-- First, calculate the new Obukhov length, then new friction velocity, !-- followed by the new scaling parameters (th*, q*, etc.), and the new !-- surface fluxes if required. The old routine ("circular") requires a !-- different order of calls as the scaling parameters from the previous time !-- steps are used to calculate the Obukhov length ! !-- Depending on setting of most_method use the "old" routine IF ( most_method == 'circular' ) THEN CALL calc_scaling_parameters CALL calc_uv_total IF ( .NOT. neutral ) THEN CALL calc_ol ENDIF CALL calc_us CALL calc_surface_fluxes ! !-- Use either Newton iteration or a lookup table for the bulk Richardson !-- number to calculate the Obukhov length ELSEIF ( most_method == 'newton' .OR. most_method == 'lookup' ) THEN CALL calc_uv_total IF ( .NOT. neutral ) THEN CALL calc_ol ENDIF CALL calc_us CALL calc_scaling_parameters CALL calc_surface_fluxes ENDIF END SUBROUTINE surface_layer_fluxes !------------------------------------------------------------------------------! ! Description: ! ------------ !> Initializing actions for the surface layer routine. Basically, this involves !> the preparation of a lookup table for the the bulk Richardson number vs !> Obukhov length L when using the lookup table method. !------------------------------------------------------------------------------! SUBROUTINE init_surface_layer_fluxes IMPLICIT NONE INTEGER(iwp) :: l, & !< Index for loop to create lookup table num_steps_n !< Number of non-stretched zeta steps LOGICAL :: terminate_run_l = .FALSE. !< Flag to terminate run (global) REAL(wp), PARAMETER :: zeta_stretch = -10.0_wp !< Start of stretching in the free convection limit REAL(wp), DIMENSION(:), ALLOCATABLE :: zeta_tmp REAL(wp) :: zeta_step, & !< Increment of zeta regr = 1.01_wp, & !< Stretching factor of zeta_step in the free convection limit regr_old = 1.0E9_wp, & !< Stretching factor of last iteration step z0h_min = 0.0_wp, & !< Minimum value of z0h to create table z0_min = 0.0_wp !< Minimum value of z0 to create table ! !-- When cloud physics is used, arrays for storing potential temperature and !-- specific humidity at first grid level are required IF ( cloud_physics ) THEN ALLOCATE ( pt1(nysg:nyng,nxlg:nxrg) ) ALLOCATE ( qv1(nysg:nyng,nxlg:nxrg) ) ENDIF ! !-- Allocate field for storing the horizontal velocity ALLOCATE ( uv_total(nysg:nyng,nxlg:nxrg) ) ! !-- In case of runs with neutral statification, set Obukhov length to a !-- large value IF ( neutral ) ol = 1.0E10_wp IF ( most_method == 'lookup' ) THEN ! !-- Check for roughness heterogeneity. In that case terminate run and !-- inform user IF ( MINVAL( z0h ) /= MAXVAL( z0h ) .OR. & MINVAL( z0 ) /= MAXVAL( z0 ) ) THEN terminate_run_l = .TRUE. ENDIF #if defined( __parallel ) ! !-- Make a logical OR for all processes. Force termiation of model if result !-- is TRUE IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) CALL MPI_ALLREDUCE( terminate_run_l, terminate_run, 1, MPI_LOGICAL, & MPI_LOR, comm2d, ierr ) #else terminate_run = terminate_run_l #endif IF ( terminate_run ) THEN message_string = 'most_method = "lookup" cannot be used in ' // & 'combination with a prescribed roughness ' // & 'heterogeneity' CALL message( 'surface_layer_fluxes', 'PA0417', 1, 2, 0, 6, 0 ) ENDIF ALLOCATE( zeta_tmp(0:num_steps-1) ) ! !-- Use the lowest possible value for z_mo k = MINVAL(nzb_s_inner) z_mo = zu(k+1) - zw(k) ! !-- Calculate z/L range from zeta_stretch to zeta_max using 90% of the !-- available steps (num_steps). The calculation is done with negative !-- values of zeta in order to simplify the stretching in the free !-- convection limit for the remaining 10% of steps. zeta_tmp(0) = - zeta_max num_steps_n = ( num_steps * 9 / 10 ) - 1 zeta_step = (zeta_max - zeta_stretch) / REAL(num_steps_n) DO l = 1, num_steps_n zeta_tmp(l) = zeta_tmp(l-1) + zeta_step ENDDO ! !-- Calculate stretching factor for the free convection range DO WHILE ( ABS( (regr-regr_old) / regr_old ) > 1.0E-10_wp ) regr_old = regr regr = ( 1.0_wp - ( -zeta_min / zeta_step ) * ( 1.0_wp - regr ) & )**( 10.0_wp / REAL(num_steps) ) ENDDO ! !-- Calculate z/L range from zeta_min to zeta_stretch DO l = num_steps_n+1, num_steps-1 zeta_tmp(l) = zeta_tmp(l-1) + zeta_step zeta_step = zeta_step * regr ENDDO ! !-- Save roughness lengths to temporary variables z0h_min = z0h(nys,nxl) z0_min = z0(nys,nxl) ! !-- Calculate lookup table for the Richardson number versus Obukhov length !-- The Richardson number (rib) is defined depending on the choice of !-- boundary conditions for temperature IF ( ibc_pt_b == 1 ) THEN DO l = 0, num_steps-1 ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l) rib_tab(l) = z_mo / ol_tab(l) / ( LOG( z_mo / z0_min ) & - psi_m( z_mo / ol_tab(l) ) & + psi_m( z0_min / ol_tab(l) ) & )**3 ENDDO ELSE DO l = 0, num_steps-1 ol_tab(l) = - z_mo / zeta_tmp(num_steps-1-l) rib_tab(l) = z_mo / ol_tab(l) * ( LOG( z_mo / z0h_min ) & - psi_h( z_mo / ol_tab(l) ) & + psi_h( z0h_min / ol_tab(l) ) & ) & / ( LOG( z_mo / z0_min ) & - psi_m( z_mo / ol_tab(l) ) & + psi_m( z0_min / ol_tab(l) ) & )**2 ENDDO ENDIF ! !-- Determine minimum values of rib in the lookup table. Set upper limit !-- to critical Richardson number (0.25) rib_min = MINVAL(rib_tab) rib_max = 0.25 !MAXVAL(rib_tab) DEALLOCATE( zeta_tmp ) ENDIF END SUBROUTINE init_surface_layer_fluxes !------------------------------------------------------------------------------! ! Description: ! ------------ !> Compute the absolute value of the horizontal velocity (relative to the !> surface). This is required by all methods !------------------------------------------------------------------------------! SUBROUTINE calc_uv_total IMPLICIT NONE !$OMP PARALLEL DO PRIVATE( k ) DO i = nxl, nxr DO j = nys, nyn k = nzb_s_inner(j,i) uv_total(j,i) = SQRT( ( 0.5_wp * ( u(k+1,j,i) + u(k+1,j,i+1) & - u(k,j,i) - u(k,j,i+1) ) )**2 + & ( 0.5_wp * ( v(k+1,j,i) + v(k+1,j+1,i) & - v(k,j,i) - v(k,j+1,i) ) )**2 ) ! !-- For too small values of the local wind, MOST does not work. A !-- threshold value is thus set if required ! uv_total(j,i) = MAX(0.01_wp,uv_total(j,i)) ENDDO ENDDO ! !-- Values of uv_total need to be exchanged at the ghost boundaries CALL exchange_horiz_2d( uv_total ) END SUBROUTINE calc_uv_total !------------------------------------------------------------------------------! ! Description: ! ------------ !> Calculate the Obukhov length (L) and Richardson flux number (z/L) !------------------------------------------------------------------------------! SUBROUTINE calc_ol IMPLICIT NONE INTEGER(iwp) :: iter, & !< Newton iteration step l !< look index REAL(wp), DIMENSION(nysg:nyng,nxlg:nxrg) :: rib !< Bulk Richardson number REAL(wp) :: f, & !< Function for Newton iteration: f = Ri - [...]/[...]^2 = 0 f_d_ol, & !< Derivative of f ol_l, & !< Lower bound of L for Newton iteration ol_m, & !< Previous value of L for Newton iteration ol_old, & !< Previous time step value of L ol_u !< Upper bound of L for Newton iteration IF ( TRIM( most_method ) /= 'circular' ) THEN !$OMP PARALLEL DO PRIVATE( k, z_mo ) DO i = nxl, nxr DO j = nys, nyn k = nzb_s_inner(j,i) z_mo = zu(k+1) - zw(k) ! !-- Evaluate bulk Richardson number (calculation depends on !-- definition based on setting of boundary conditions IF ( ibc_pt_b /= 1 ) THEN IF ( humidity ) THEN rib(j,i) = g * z_mo * ( vpt(k+1,j,i) - vpt(k,j,i) ) & / ( uv_total(j,i)**2 * vpt(k+1,j,i) + 1.0E-20_wp ) ELSE rib(j,i) = g * z_mo * ( pt(k+1,j,i) - pt(k,j,i) ) & / ( uv_total(j,i)**2 * pt(k+1,j,i) + 1.0E-20_wp ) ENDIF ELSE ! !-- When using Neumann boundary conditions, the buoyancy flux !-- is required but cannot be calculated at the surface, as pt !-- and q are not known at the surface. Hence the values at !-- first grid level are used to estimate the buoyancy flux IF ( humidity ) THEN rib(j,i) = - g * z_mo * ( ( 1.0_wp + 0.61_wp & * q(k+1,j,i) ) * shf(j,i) + 0.61_wp & * pt(k+1,j,i) * qsws(j,i) ) * drho_air_zw(k) & / ( uv_total(j,i)**3 * vpt(k+1,j,i) * kappa**2& + 1.0E-20_wp) ELSE rib(j,i) = - g * z_mo * shf(j,i) * drho_air_zw(k) & / ( uv_total(j,i)**3 * pt(k+1,j,i) * kappa**2 & + 1.0E-20_wp ) ENDIF ENDIF ENDDO ENDDO ENDIF ! !-- Calculate the Obukhov length either using a Newton iteration !-- method, via a lookup table, or using the old circular way IF ( TRIM( most_method ) == 'newton' ) THEN !$OMP PARALLEL DO PRIVATE( k, z_mo ) DO i = nxl, nxr DO j = nys, nyn k = nzb_s_inner(j,i) z_mo = zu(k+1) - zw(k) ! !-- Store current value in case the Newton iteration fails ol_old = ol(j,i) ! !-- Ensure that the bulk Richardson number and the Obukhov !-- lengtH have the same sign IF ( rib(j,i) * ol(j,i) < 0.0_wp .OR. & ABS( ol(j,i) ) == ol_max ) THEN IF ( rib(j,i) > 0.0_wp ) ol(j,i) = 0.01_wp IF ( rib(j,i) < 0.0_wp ) ol(j,i) = -0.01_wp ENDIF ! !-- Iteration to find Obukhov length iter = 0 DO iter = iter + 1 ! !-- In case of divergence, use the value of the previous time step IF ( iter > 1000 ) THEN ol(j,i) = ol_old EXIT ENDIF ol_m = ol(j,i) ol_l = ol_m - 0.001_wp * ol_m ol_u = ol_m + 0.001_wp * ol_m IF ( ibc_pt_b /= 1 ) THEN ! !-- Calculate f = Ri - [...]/[...]^2 = 0 f = rib(j,i) - ( z_mo / ol_m ) * ( LOG( z_mo / z0h(j,i) )& - psi_h( z_mo / ol_m ) & + psi_h( z0h(j,i) / ol_m ) & ) & / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol_m ) & + psi_m( z0(j,i) / ol_m ) & )**2 ! !-- Calculate df/dL f_d_ol = ( - ( z_mo / ol_u ) * ( LOG( z_mo / z0h(j,i) ) & - psi_h( z_mo / ol_u ) & + psi_h( z0h(j,i) / ol_u ) & ) & / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol_u ) & + psi_m( z0(j,i) / ol_u ) & )**2 & + ( z_mo / ol_l ) * ( LOG( z_mo / z0h(j,i) ) & - psi_h( z_mo / ol_l ) & + psi_h( z0h(j,i) / ol_l ) & ) & / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol_l ) & + psi_m( z0(j,i) / ol_l ) & )**2 & ) / ( ol_u - ol_l ) ELSE ! !-- Calculate f = Ri - 1 /[...]^3 = 0 f = rib(j,i) - ( z_mo / ol_m ) / ( LOG( z_mo / z0(j,i) )& - psi_m( z_mo / ol_m ) & + psi_m( z0(j,i) / ol_m ) & )**3 ! !-- Calculate df/dL f_d_ol = ( - ( z_mo / ol_u ) / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol_u ) & + psi_m( z0(j,i) / ol_u ) & )**3 & + ( z_mo / ol_l ) / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol_l ) & + psi_m( z0(j,i) / ol_l ) & )**3 & ) / ( ol_u - ol_l ) ENDIF ! !-- Calculate new L ol(j,i) = ol_m - f / f_d_ol ! !-- Ensure that the bulk Richardson number and the Obukhov !-- length have the same sign and ensure convergence. IF ( ol(j,i) * ol_m < 0.0_wp ) ol(j,i) = ol_m * 0.5_wp ! !-- If unrealistic value occurs, set L to the maximum !-- value that is allowed IF ( ABS( ol(j,i) ) > ol_max ) THEN ol(j,i) = ol_max EXIT ENDIF ! !-- Check for convergence IF ( ABS( ( ol(j,i) - ol_m ) / ol(j,i) ) < 1.0E-4_wp ) THEN EXIT ELSE CYCLE ENDIF ENDDO ENDDO ENDDO ELSEIF ( TRIM( most_method ) == 'lookup' ) THEN !$OMP PARALLEL DO PRIVATE( k, l, z_mo ) FIRSTPRIVATE( l_bnd ) LASTPRIVATE( l_bnd ) DO i = nxl, nxr DO j = nys, nyn ! !-- If the bulk Richardson number is outside the range of the lookup !-- table, set it to the exceeding threshold value IF ( rib(j,i) < rib_min ) rib(j,i) = rib_min IF ( rib(j,i) > rib_max ) rib(j,i) = rib_max ! !-- Find the correct index bounds for linear interpolation. As the !-- Richardson number will not differ very much from time step to !-- time step , use the index from the last step and search in the !-- correct direction l = l_bnd IF ( rib_tab(l) - rib(j,i) > 0.0_wp ) THEN DO WHILE ( rib_tab(l-1) - rib(j,i) > 0.0_wp .AND. l > 0 ) l = l-1 ENDDO ELSE DO WHILE ( rib_tab(l) - rib(j,i) < 0.0_wp & .AND. l < num_steps-1 ) l = l+1 ENDDO ENDIF l_bnd = l ! !-- Linear interpolation to find the correct value of z/L ol(j,i) = ( ol_tab(l-1) + ( ol_tab(l) - ol_tab(l-1) ) & / ( rib_tab(l) - rib_tab(l-1) ) & * ( rib(j,i) - rib_tab(l-1) ) ) ENDDO ENDDO ELSEIF ( TRIM( most_method ) == 'circular' ) THEN !$OMP PARALLEL DO PRIVATE( k, z_mo ) DO i = nxl, nxr DO j = nys, nyn k = nzb_s_inner(j,i) z_mo = zu(k+1) - zw(k) IF ( .NOT. humidity ) THEN ol(j,i) = ( pt(k+1,j,i) * us(j,i)**2 ) / ( kappa * g & * ts(j,i) + 1E-30_wp ) ELSEIF ( cloud_physics ) THEN ol(j,i) = ( vpt(k+1,j,i) * us(j,i)**2 ) / ( kappa * g & * ( ts(j,i) + 0.61_wp * pt1(j,i) * qs(j,i) & + 0.61_wp * qv1(j,i) * ts(j,i) - ts(j,i) & * ql(k+1,j,i) ) + 1E-30_wp ) ELSE ol(j,i) = ( vpt(k+1,j,i) * us(j,i)**2 ) / ( kappa * g & * ( ts(j,i) + 0.61_wp * pt(k+1,j,i) * qs(j,i) & + 0.61_wp * q(k+1,j,i) * ts(j,i) ) + 1E-30_wp ) ENDIF ! !-- Limit the value range of the Obukhov length. !-- This is necessary for very small velocities (u,v --> 0), because !-- the absolute value of ol can then become very small, which in !-- consequence would result in very large shear stresses and very !-- small momentum fluxes (both are generally unrealistic). IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) < zeta_min ) & ol(j,i) = z_mo / zeta_min IF ( ( z_mo / ( ol(j,i) + 1E-30_wp ) ) > zeta_max ) & ol(j,i) = z_mo / zeta_max ENDDO ENDDO ENDIF ! !-- Values of ol at ghost point locations are needed for the evaluation !-- of usws and vsws. CALL exchange_horiz_2d( ol ) END SUBROUTINE calc_ol ! !-- Calculate friction velocity u* SUBROUTINE calc_us IMPLICIT NONE !$OMP PARALLEL DO PRIVATE( k, z_mo ) DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i)+1 z_mo = zu(k+1) - zw(k) ! !-- Compute u* at the scalars' grid points us(j,i) = kappa * uv_total(j,i) / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol(j,i) ) & + psi_m( z0(j,i) / ol(j,i) ) ) ENDDO ENDDO END SUBROUTINE calc_us ! !-- Calculate potential temperature and specific humidity at first grid level SUBROUTINE calc_pt_q IMPLICIT NONE DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i)+1 pt1(j,i) = pt(k,j,i) + l_d_cp * pt_d_t(k) * ql(k,j,i) qv1(j,i) = q(k,j,i) - ql(k,j,i) ENDDO ENDDO END SUBROUTINE calc_pt_q ! !-- Calculate the other MOST scaling parameters theta*, q*, (qr*, nr*) SUBROUTINE calc_scaling_parameters IMPLICIT NONE ! !-- Compute theta* IF ( constant_heatflux ) THEN ! !-- For a given heat flux in the surface layer: !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) ts(j,i) = -shf(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp ) ! !-- ts must be limited, because otherwise overflow may occur in case !-- of us=0 when computing ol further below IF ( ts(j,i) < -1.05E5_wp ) ts(j,i) = -1.0E5_wp IF ( ts(j,i) > 1.0E5_wp ) ts(j,i) = 1.0E5_wp ENDDO ENDDO ELSE ! !-- For a given surface temperature: IF ( large_scale_forcing .AND. lsf_surf ) THEN !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) pt(k,j,i) = pt_surface ENDDO ENDDO ENDIF !$OMP PARALLEL DO PRIVATE( k, z_mo ) DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) z_mo = zu(k+1) - zw(k) IF ( cloud_physics ) THEN ts(j,i) = kappa * ( pt1(j,i) - pt(k,j,i) ) & / ( LOG( z_mo / z0h(j,i) ) & - psi_h( z_mo / ol(j,i) ) & + psi_h( z0h(j,i) / ol(j,i) ) ) ELSE ts(j,i) = kappa * ( pt(k+1,j,i) - pt(k,j,i) ) & / ( LOG( z_mo / z0h(j,i) ) & - psi_h( z_mo / ol(j,i) ) & + psi_h( z0h(j,i) / ol(j,i) ) ) ENDIF ENDDO ENDDO ENDIF ! !-- If required compute q* IF ( humidity ) THEN IF ( constant_waterflux ) THEN ! !-- For a given water flux in the surface layer !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) qs(j,i) = -qsws(j,i) * drho_air_zw(k) / ( us(j,i) + 1E-30_wp ) ENDDO ENDDO ELSE coupled_run = ( coupling_mode == 'atmosphere_to_ocean' .AND. & run_coupled ) IF ( large_scale_forcing .AND. lsf_surf ) THEN !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) q(k,j,i) = q_surface ENDDO ENDDO ENDIF !$OMP PARALLEL DO PRIVATE( e_s, k, z_mo ) DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) z_mo = zu(k+1) - zw(k) ! !-- Assume saturation for atmosphere coupled to ocean (but not !-- in case of precursor runs) IF ( coupled_run ) THEN e_s = 6.1_wp * & EXP( 0.07_wp * ( MIN(pt(k,j,i),pt(k+1,j,i)) & - 273.15_wp ) ) q(k,j,i) = 0.622_wp * e_s / ( surface_pressure - e_s ) ENDIF IF ( cloud_physics ) THEN qs(j,i) = kappa * ( qv1(j,i) - q(k,j,i) ) & / ( LOG( z_mo / z0q(j,i) ) & - psi_h( z_mo / ol(j,i) ) & + psi_h( z0q(j,i) / ol(j,i) ) ) ELSE qs(j,i) = kappa * ( q(k+1,j,i) - q(k,j,i) ) & / ( LOG( z_mo / z0q(j,i) ) & - psi_h( z_mo / ol(j,i) ) & + psi_h( z0q(j,i) / ol(j,i) ) ) ENDIF ENDDO ENDDO ENDIF ENDIF ! !-- If required compute s* IF ( passive_scalar ) THEN IF ( constant_scalarflux ) THEN ! !-- For a given water flux in the surface layer !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng ss(j,i) = -ssws(j,i) / ( us(j,i) + 1E-30_wp ) ENDDO ENDDO ENDIF ENDIF ! !-- If required compute qr* and nr* IF ( cloud_physics .AND. microphysics_seifert ) & THEN !$OMP PARALLEL DO PRIVATE( k, z_mo ) DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) z_mo = zu(k+1) - zw(k) qrs(j,i) = kappa * ( qr(k+1,j,i) - qr(k,j,i) ) & / ( LOG( z_mo / z0q(j,i) ) & - psi_h( z_mo / ol(j,i) ) & + psi_h( z0q(j,i) / ol(j,i) ) ) nrs(j,i) = kappa * ( nr(k+1,j,i) - nr(k,j,i) ) & / ( LOG( z_mo / z0q(j,i) ) & - psi_h( z_mo / ol(j,i) ) & + psi_h( z0q(j,i) / ol(j,i) ) ) ENDDO ENDDO ENDIF END SUBROUTINE calc_scaling_parameters ! !-- Calculate surface fluxes usws, vsws, shf, qsws, (qrsws, nrsws) SUBROUTINE calc_surface_fluxes IMPLICIT NONE REAL(wp) :: ol_mid !< Grid-interpolated L ! !-- Compute u'w' for the total model domain. !-- First compute the corresponding component of u* and square it. !$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo ) DO i = nxl, nxr DO j = nys, nyn k = nzb_u_inner(j,i) z_mo = zu(k+1) - zw(k) ! !-- Compute bulk Obukhov length for this point ol_mid = 0.5_wp * ( ol(j,i-1) + ol(j,i) ) IF ( ol_mid == 0.0_wp ) THEN ol_mid = MIN(ol(j,i-1), ol(j,i)) ENDIF usws(j,i) = kappa * ( u(k+1,j,i) - u(k,j,i) ) & / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol_mid ) & + psi_m( z0(j,i) / ol_mid ) ) usws(j,i) = -usws(j,i) * 0.5_wp * ( us(j,i-1) + us(j,i) ) & * rho_air_zw(k) ENDDO ENDDO ! !-- Compute v'w' for the total model domain. !-- First compute the corresponding component of u* and square it. !$OMP PARALLEL DO PRIVATE( k, ol_mid, z_mo ) DO i = nxl, nxr DO j = nys, nyn k = nzb_v_inner(j,i) z_mo = zu(k+1) - zw(k) ! !-- Compute bulk Obukhov length for this point ol_mid = 0.5_wp * ( ol(j-1,i) + ol(j,i) ) IF ( ol_mid == 0.0_wp ) THEN ol_mid = MIN(ol(j-1,i), ol(j-1,i)) ENDIF vsws(j,i) = kappa * ( v(k+1,j,i) - v(k,j,i) ) & / ( LOG( z_mo / z0(j,i) ) & - psi_m( z_mo / ol_mid ) & + psi_m( z0(j,i) / ol_mid ) ) vsws(j,i) = -vsws(j,i) * 0.5_wp * ( us(j-1,i) + us(j,i) ) & * rho_air_zw(k) ENDDO ENDDO ! !-- Exchange the boundaries for the momentum fluxes (is this still required?) CALL exchange_horiz_2d( usws ) CALL exchange_horiz_2d( vsws ) ! !-- Compute the vertical kinematic heat flux IF ( .NOT. constant_heatflux .AND. ( simulated_time <= & skip_time_do_lsm .OR. .NOT. land_surface ) .AND. & .NOT. urban_surface ) THEN !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) shf(j,i) = -ts(j,i) * us(j,i) * rho_air_zw(k) ENDDO ENDDO ENDIF ! !-- Compute the vertical water flux IF ( .NOT. constant_waterflux .AND. humidity .AND. & ( simulated_time <= skip_time_do_lsm & .OR. .NOT. land_surface ) ) THEN !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) qsws(j,i) = -qs(j,i) * us(j,i) * rho_air_zw(k) ENDDO ENDDO ENDIF ! !-- Compute the vertical scalar flux IF ( .NOT. constant_scalarflux .AND. passive_scalar .AND. & ( simulated_time <= skip_time_do_lsm & .OR. .NOT. land_surface ) ) THEN !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng ssws(j,i) = -ss(j,i) * us(j,i) ENDDO ENDDO ENDIF ! !-- Compute (turbulent) fluxes of rain water content and rain drop conc. IF ( cloud_physics .AND. microphysics_seifert ) THEN !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng qrsws(j,i) = -qrs(j,i) * us(j,i) nrsws(j,i) = -nrs(j,i) * us(j,i) ENDDO ENDDO ENDIF ! !-- Bottom boundary condition for the TKE IF ( ibc_e_b == 2 ) THEN !$OMP PARALLEL DO DO i = nxlg, nxrg DO j = nysg, nyng k = nzb_s_inner(j,i) e(k+1,j,i) = ( us(j,i) / 0.1_wp )**2 ! !-- As a test: cm = 0.4 ! e(k+1,j,i) = ( us(j,i) / 0.4_wp )**2 e(k,j,i) = e(k+1,j,i) ENDDO ENDDO ENDIF END SUBROUTINE calc_surface_fluxes ! !-- Integrated stability function for momentum FUNCTION psi_m( zeta ) USE kinds IMPLICIT NONE REAL(wp) :: psi_m !< Integrated similarity function result REAL(wp) :: zeta !< Stability parameter z/L REAL(wp) :: x !< dummy variable REAL(wp), PARAMETER :: a = 1.0_wp !< constant REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant REAL(wp), PARAMETER :: c = 5.0_wp !< constant REAL(wp), PARAMETER :: d = 0.35_wp !< constant REAL(wp), PARAMETER :: c_d_d = c / d !< constant REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant IF ( zeta < 0.0_wp ) THEN x = SQRT( SQRT( 1.0_wp - 16.0_wp * zeta ) ) psi_m = pi * 0.5_wp - 2.0_wp * ATAN( x ) + LOG( ( 1.0_wp + x )**2 & * ( 1.0_wp + x**2 ) * 0.125_wp ) ELSE psi_m = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - a * zeta & - bc_d_d ! !-- Old version for stable conditions (only valid for z/L < 0.5) !-- psi_m = - 5.0_wp * zeta ENDIF END FUNCTION psi_m ! !-- Integrated stability function for heat and moisture FUNCTION psi_h( zeta ) USE kinds IMPLICIT NONE REAL(wp) :: psi_h !< Integrated similarity function result REAL(wp) :: zeta !< Stability parameter z/L REAL(wp) :: x !< dummy variable REAL(wp), PARAMETER :: a = 1.0_wp !< constant REAL(wp), PARAMETER :: b = 0.66666666666_wp !< constant REAL(wp), PARAMETER :: c = 5.0_wp !< constant REAL(wp), PARAMETER :: d = 0.35_wp !< constant REAL(wp), PARAMETER :: c_d_d = c / d !< constant REAL(wp), PARAMETER :: bc_d_d = b * c / d !< constant IF ( zeta < 0.0_wp ) THEN x = SQRT( 1.0_wp - 16.0_wp * zeta ) psi_h = 2.0_wp * LOG( (1.0_wp + x ) / 2.0_wp ) ELSE psi_h = - b * ( zeta - c_d_d ) * EXP( -d * zeta ) - (1.0_wp & + 0.66666666666_wp * a * zeta )**1.5_wp - bc_d_d & + 1.0_wp ! !-- Old version for stable conditions (only valid for z/L < 0.5) !-- psi_h = - 5.0_wp * zeta ENDIF END FUNCTION psi_h END MODULE surface_layer_fluxes_mod