!> @file diffusion_s.f90 !--------------------------------------------------------------------------------------------------! ! This file is part of the PALM model system. ! ! 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 1997-2021 Leibniz Universitaet Hannover !--------------------------------------------------------------------------------------------------! ! ! Description: ! ------------ !> Diffusion term of scalar quantities (temperature and water content) !--------------------------------------------------------------------------------------------------! MODULE diffusion_s_mod PRIVATE PUBLIC diffusion_s INTERFACE diffusion_s MODULE PROCEDURE diffusion_s MODULE PROCEDURE diffusion_s_ij END INTERFACE diffusion_s CONTAINS !--------------------------------------------------------------------------------------------------! ! Description: ! ------------ !> Call for all grid points !--------------------------------------------------------------------------------------------------! SUBROUTINE diffusion_s( s, s_flux_def_h_up, s_flux_def_h_down, & s_flux_t, & s_flux_lsm_h_up, s_flux_lsm_h_down, & s_flux_usm_h_up, s_flux_usm_h_down, & s_flux_def_v_north, s_flux_def_v_south, & s_flux_def_v_east, s_flux_def_v_west, & s_flux_lsm_v_north, s_flux_lsm_v_south, & s_flux_lsm_v_east, s_flux_lsm_v_west, & s_flux_usm_v_north, s_flux_usm_v_south, & s_flux_usm_v_east, s_flux_usm_v_west ) USE arrays_3d, & ONLY: ddzu, ddzw, kh, tend, drho_air, rho_air_zw USE control_parameters, & ONLY: use_surface_fluxes, use_top_fluxes USE grid_variables, & ONLY: ddx, ddx2, ddy, ddy2 USE indices, & ONLY: nxl, nxlg, nxr, nxrg, nyn, nyng, nys, nysg, nzb, nzt, topo_flags USE kinds USE surface_mod, & ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v IMPLICIT NONE INTEGER(iwp) :: i !< running index x direction INTEGER(iwp) :: j !< running index y direction INTEGER(iwp) :: k !< running index z direction INTEGER(iwp) :: m !< running index surface elements INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint REAL(wp) :: flag !< flag to mask topography grid points REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface REAL(wp) :: mask_east !< flag to mask vertical surface east of the grid point REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface REAL(wp) :: mask_west !< flag to mask vertical surface west of the grid point REAL(wp), DIMENSION(1:surf_def_h(0)%ns) :: s_flux_def_h_up !< flux at horizontal upward-facing default-type surfaces REAL(wp), DIMENSION(1:surf_def_h(1)%ns) :: s_flux_def_h_down !< flux at horizontal donwward-facing default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(2)%ns) :: s_flux_def_v_east !< flux at east-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(0)%ns) :: s_flux_def_v_north !< flux at north-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(1)%ns) :: s_flux_def_v_south !< flux at south-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(3)%ns) :: s_flux_def_v_west !< flux at west-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_lsm_h(0)%ns) :: s_flux_lsm_h_up !< flux at horizontal upward-facing natural-type surfaces REAL(wp), DIMENSION(1:surf_lsm_h(1)%ns) :: s_flux_lsm_h_down !< flux at horizontal downward-facing natural-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(2)%ns) :: s_flux_lsm_v_east !< flux at east-facing vertical natural-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(0)%ns) :: s_flux_lsm_v_north !< flux at north-facing vertical natural-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(1)%ns) :: s_flux_lsm_v_south !< flux at south-facing vertical natural-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(3)%ns) :: s_flux_lsm_v_west !< flux at west-facing vertical natural-type surfaces REAL(wp), DIMENSION(1:surf_usm_h(0)%ns) :: s_flux_usm_h_up !< flux at horizontal upward-facing urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_h(1)%ns) :: s_flux_usm_h_down !< flux at horizontal downward-facing urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(2)%ns) :: s_flux_usm_v_east !< flux at east-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(0)%ns) :: s_flux_usm_v_north !< flux at north-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(1)%ns) :: s_flux_usm_v_south !< flux at south-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(3)%ns) :: s_flux_usm_v_west !< flux at west-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_def_h(2)%ns) :: s_flux_t !< flux at model top REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s !< treated scalar !$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k, m) & !$ACC PRIVATE(surf_e, surf_s, flag, mask_top, mask_bottom) & !$ACC PRIVATE(mask_north, mask_south, mask_west, mask_east) & !$ACC PRESENT(topo_flags, kh) & !$ACC PRESENT(s) & !$ACC PRESENT(ddzu, ddzw, drho_air, rho_air_zw) & !$ACC PRESENT(surf_def_h(0:2), surf_def_v(0:3)) & !$ACC PRESENT(surf_lsm_h(0:1), surf_lsm_v(0:3)) & !$ACC PRESENT(surf_usm_h(0:1), surf_usm_v(0:3)) & !$ACC PRESENT(s_flux_def_h_up, s_flux_def_h_down) & !$ACC PRESENT(s_flux_t) & !$ACC PRESENT(s_flux_def_v_north, s_flux_def_v_south) & !$ACC PRESENT(s_flux_def_v_east, s_flux_def_v_west) & !$ACC PRESENT(s_flux_lsm_h_up, s_flux_lsm_h_down) & !$ACC PRESENT(s_flux_lsm_v_north, s_flux_lsm_v_south) & !$ACC PRESENT(s_flux_lsm_v_east, s_flux_lsm_v_west) & !$ACC PRESENT(s_flux_usm_h_up, s_flux_usm_h_down) & !$ACC PRESENT(s_flux_usm_v_north, s_flux_usm_v_south) & !$ACC PRESENT(s_flux_usm_v_east, s_flux_usm_v_west) & !$ACC PRESENT(tend) DO i = nxl, nxr DO j = nys,nyn ! !-- Compute horizontal diffusion DO k = nzb+1, nzt ! !-- Predetermine flag to mask topography and wall-bounded grid points flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 0 ) ) ! !-- Predetermine flag to mask wall-bounded grid points, equivalent to former s_outer !-- array mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i-1), 0 ) ) mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i+1), 0 ) ) mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j-1,i), 0 ) ) mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j+1,i), 0 ) ) tend(k,j,i) = tend(k,j,i) & + 0.5_wp * ( & mask_east * ( kh(k,j,i) + kh(k,j,i+1) ) & * ( s(k,j,i+1) - s(k,j,i) ) & - mask_west * ( kh(k,j,i) + kh(k,j,i-1) ) & * ( s(k,j,i) - s(k,j,i-1) ) & ) * ddx2 * flag & + 0.5_wp * ( & mask_north * ( kh(k,j,i) + kh(k,j+1,i) ) & * ( s(k,j+1,i) - s(k,j,i) ) & - mask_south * ( kh(k,j,i) + kh(k,j-1,i) ) & * ( s(k,j,i) - s(k,j-1,i) ) & ) * ddy2 * flag ENDDO ! !-- Apply prescribed horizontal wall heatflux where necessary. First, determine start and !-- end index for respective (j,i)-index. Please note, in the flat case following loop will !-- not be entered, as surf_s=1 and surf_e=0. Furtermore, note, no vertical natural !-- surfaces so far. !-- First, for default-type surfaces. !-- North-facing vertical default-type surfaces surf_s = surf_def_v(0)%start_index(j,i) surf_e = surf_def_v(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_north(m) * ddy ENDDO ! !-- South-facing vertical default-type surfaces surf_s = surf_def_v(1)%start_index(j,i) surf_e = surf_def_v(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_south(m) * ddy ENDDO ! !-- East-facing vertical default-type surfaces surf_s = surf_def_v(2)%start_index(j,i) surf_e = surf_def_v(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(2)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_east(m) * ddx ENDDO ! !-- West-facing vertical default-type surfaces surf_s = surf_def_v(3)%start_index(j,i) surf_e = surf_def_v(3)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(3)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_west(m) * ddx ENDDO ! !-- Now, for natural-type surfaces. !-- North-facing surf_s = surf_lsm_v(0)%start_index(j,i) surf_e = surf_lsm_v(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_north(m) * ddy ENDDO ! !-- South-facing surf_s = surf_lsm_v(1)%start_index(j,i) surf_e = surf_lsm_v(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_south(m) * ddy ENDDO ! !-- East-facing surf_s = surf_lsm_v(2)%start_index(j,i) surf_e = surf_lsm_v(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(2)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_east(m) * ddx ENDDO ! !-- West-facing surf_s = surf_lsm_v(3)%start_index(j,i) surf_e = surf_lsm_v(3)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(3)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_west(m) * ddx ENDDO ! !-- Now, for urban-type surfaces. !-- North-facing surf_s = surf_usm_v(0)%start_index(j,i) surf_e = surf_usm_v(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_north(m) * ddy ENDDO ! !-- South-facing surf_s = surf_usm_v(1)%start_index(j,i) surf_e = surf_usm_v(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_south(m) * ddy ENDDO ! !-- East-facing surf_s = surf_usm_v(2)%start_index(j,i) surf_e = surf_usm_v(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(2)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_east(m) * ddx ENDDO ! !-- West-facing surf_s = surf_usm_v(3)%start_index(j,i) surf_e = surf_usm_v(3)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(3)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_west(m) * ddx ENDDO ! !-- Compute vertical diffusion. In case that surface fluxes have been prescribed or !-- computed at bottom and/or top, index k starts/ends at nzb+2 or nzt-1, respectively. !-- Model top is also mask if top flux is given. DO k = nzb+1, nzt ! !-- Determine flags to mask topography below and above. Flag 0 is used to mask !-- topography in general, and flag 8 implies information about use_surface_fluxes. !-- Flag 9 is used to control flux at model top. mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k-1,j,i), 8 ) ) mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 8 ) ) * & MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 9 ) ) flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 0 ) ) tend(k,j,i) = tend(k,j,i) & + 0.5_wp * ( & ( kh(k,j,i) + kh(k+1,j,i) ) * & ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) & * rho_air_zw(k) & * mask_top & - ( kh(k,j,i) + kh(k-1,j,i) ) * & ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) & * rho_air_zw(k-1) & * mask_bottom & ) * ddzw(k) * drho_air(k) & * flag ENDDO ! !-- Vertical diffusion at horizontal walls. IF ( use_surface_fluxes ) THEN ! !-- Default-type surfaces, upward-facing surf_s = surf_def_h(0)%start_index(j,i) surf_e = surf_def_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_h_up(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Default-type surfaces, downward-facing surf_s = surf_def_h(1)%start_index(j,i) surf_e = surf_def_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_h_down(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, upward-facing surf_s = surf_lsm_h(0)%start_index(j,i) surf_e = surf_lsm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_h_up(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, downward-facing surf_s = surf_lsm_h(1)%start_index(j,i) surf_e = surf_lsm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_h_down(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, upward-facing surf_s = surf_usm_h(0)%start_index(j,i) surf_e = surf_usm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_h_up(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, downward-facing surf_s = surf_usm_h(1)%start_index(j,i) surf_e = surf_usm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_h_down(m) * ddzw(k) * drho_air(k) ENDDO ENDIF ! !-- Vertical diffusion at the last computational gridpoint along z-direction IF ( use_top_fluxes ) THEN surf_s = surf_def_h(2)%start_index(j,i) surf_e = surf_def_h(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(2)%k(m) tend(k,j,i) = tend(k,j,i) + ( - s_flux_t(m) ) * ddzw(k) * drho_air(k) ENDDO ENDIF ENDDO ENDDO END SUBROUTINE diffusion_s !--------------------------------------------------------------------------------------------------! ! Description: ! ------------ !> Call for grid point i,j !--------------------------------------------------------------------------------------------------! SUBROUTINE diffusion_s_ij( i, j, s, & s_flux_def_h_up, s_flux_def_h_down, & s_flux_t, & s_flux_lsm_h_up, s_flux_lsm_h_down, & s_flux_usm_h_up, s_flux_usm_h_down, & s_flux_def_v_north, s_flux_def_v_south, & s_flux_def_v_east, s_flux_def_v_west, & s_flux_lsm_v_north, s_flux_lsm_v_south, & s_flux_lsm_v_east, s_flux_lsm_v_west, & s_flux_usm_v_north, s_flux_usm_v_south, & s_flux_usm_v_east, s_flux_usm_v_west ) USE arrays_3d, & ONLY: ddzu, ddzw, kh, tend, drho_air, rho_air_zw USE control_parameters, & ONLY: use_surface_fluxes, use_top_fluxes USE grid_variables, & ONLY: ddx, ddx2, ddy, ddy2 USE indices, & ONLY: nxlg, nxrg, nyng, nysg, nzb, nzt, topo_flags USE kinds USE surface_mod, & ONLY : surf_def_h, surf_def_v, surf_lsm_h, surf_lsm_v, surf_usm_h, surf_usm_v IMPLICIT NONE INTEGER(iwp) :: i !< running index x direction INTEGER(iwp) :: j !< running index y direction INTEGER(iwp) :: k !< running index z direction INTEGER(iwp) :: m !< running index surface elements INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint REAL(wp) :: flag !< flag to mask topography grid points REAL(wp) :: mask_bottom !< flag to mask vertical upward-facing surface REAL(wp) :: mask_east !< flag to mask vertical surface east of the grid point REAL(wp) :: mask_north !< flag to mask vertical surface north of the grid point REAL(wp) :: mask_south !< flag to mask vertical surface south of the grid point REAL(wp) :: mask_top !< flag to mask vertical downward-facing surface REAL(wp) :: mask_west !< flag to mask vertical surface west of the grid point REAL(wp), DIMENSION(1:surf_def_h(1)%ns) :: s_flux_def_h_down !< flux at horizontal donwward-facing default-type surfaces REAL(wp), DIMENSION(1:surf_def_h(0)%ns) :: s_flux_def_h_up !< flux at horizontal upward-facing default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(2)%ns) :: s_flux_def_v_east !< flux at east-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(0)%ns) :: s_flux_def_v_north !< flux at north-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(1)%ns) :: s_flux_def_v_south !< flux at south-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_def_v(3)%ns) :: s_flux_def_v_west !< flux at west-facing vertical default-type surfaces REAL(wp), DIMENSION(1:surf_lsm_h(0)%ns) :: s_flux_lsm_h_up !< flux at horizontal upward-facing natural-type surfaces REAL(wp), DIMENSION(1:surf_lsm_h(1)%ns) :: s_flux_lsm_h_down !< flux at horizontal downward-facing natural-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(2)%ns) :: s_flux_lsm_v_east !< flux at east-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(0)%ns) :: s_flux_lsm_v_north !< flux at north-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(1)%ns) :: s_flux_lsm_v_south !< flux at south-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_lsm_v(3)%ns) :: s_flux_lsm_v_west !< flux at west-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_h(0)%ns) :: s_flux_usm_h_up !< flux at horizontal upward-facing urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_h(1)%ns) :: s_flux_usm_h_down !< flux at horizontal downward-facing urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(2)%ns) :: s_flux_usm_v_east !< flux at east-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(0)%ns) :: s_flux_usm_v_north !< flux at north-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(1)%ns) :: s_flux_usm_v_south !< flux at south-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_usm_v(3)%ns) :: s_flux_usm_v_west !< flux at west-facing vertical urban-type surfaces REAL(wp), DIMENSION(1:surf_def_h(2)%ns) :: s_flux_t !< flux at model top REAL(wp), DIMENSION(nzb:nzt+1,nysg:nyng,nxlg:nxrg) :: s !< treated scalar ! !-- Compute horizontal diffusion DO k = nzb+1, nzt ! !-- Predetermine flag to mask topography and wall-bounded grid points flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 0 ) ) ! !-- Predetermine flag to mask wall-bounded grid points, equivalent to former s_outer array mask_west = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i-1), 0 ) ) mask_east = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i+1), 0 ) ) mask_south = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j-1,i), 0 ) ) mask_north = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j+1,i), 0 ) ) ! !-- Finally, determine flag to mask both topography itself as well as wall-bounded grid !-- points, which will be treated further below tend(k,j,i) = tend(k,j,i) & + 0.5_wp * ( & mask_east * ( kh(k,j,i) + kh(k,j,i+1) ) & * ( s(k,j,i+1) - s(k,j,i) ) & - mask_west * ( kh(k,j,i) + kh(k,j,i-1) ) & * ( s(k,j,i) - s(k,j,i-1) ) & ) * ddx2 * flag & + 0.5_wp * ( & mask_north * ( kh(k,j,i) + kh(k,j+1,i) ) & * ( s(k,j+1,i) - s(k,j,i) ) & - mask_south * ( kh(k,j,i) + kh(k,j-1,i) ) & * ( s(k,j,i) - s(k,j-1,i) ) & ) * ddy2 * flag ENDDO ! !-- Apply prescribed horizontal wall heatflux where necessary. First, determine start and end !-- index for respective (j,i)-index. Please note, in the flat case following loops will not be !-- entered, as surf_s=1 and surf_e=0. Furtermore, note, no vertical natural surfaces so far. !-- First, for default-type surfaces. !-- North-facing vertical default-type surfaces surf_s = surf_def_v(0)%start_index(j,i) surf_e = surf_def_v(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_north(m) * ddy ENDDO ! !-- South-facing vertical default-type surfaces surf_s = surf_def_v(1)%start_index(j,i) surf_e = surf_def_v(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_south(m) * ddy ENDDO ! !-- East-facing vertical default-type surfaces surf_s = surf_def_v(2)%start_index(j,i) surf_e = surf_def_v(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(2)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_east(m) * ddx ENDDO ! !-- West-facing vertical default-type surfaces surf_s = surf_def_v(3)%start_index(j,i) surf_e = surf_def_v(3)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_v(3)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_v_west(m) * ddx ENDDO ! !-- Now, for natural-type surfaces !-- North-facing surf_s = surf_lsm_v(0)%start_index(j,i) surf_e = surf_lsm_v(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_north(m) * ddy ENDDO ! !-- South-facing surf_s = surf_lsm_v(1)%start_index(j,i) surf_e = surf_lsm_v(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_south(m) * ddy ENDDO ! !-- East-facing surf_s = surf_lsm_v(2)%start_index(j,i) surf_e = surf_lsm_v(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(2)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_east(m) * ddx ENDDO ! !-- West-facing surf_s = surf_lsm_v(3)%start_index(j,i) surf_e = surf_lsm_v(3)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_v(3)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_v_west(m) * ddx ENDDO ! !-- Now, for urban-type surfaces !-- North-facing surf_s = surf_usm_v(0)%start_index(j,i) surf_e = surf_usm_v(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_north(m) * ddy ENDDO ! !-- South-facing surf_s = surf_usm_v(1)%start_index(j,i) surf_e = surf_usm_v(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_south(m) * ddy ENDDO ! !-- East-facing surf_s = surf_usm_v(2)%start_index(j,i) surf_e = surf_usm_v(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(2)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_east(m) * ddx ENDDO ! !-- West-facing surf_s = surf_usm_v(3)%start_index(j,i) surf_e = surf_usm_v(3)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_v(3)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_v_west(m) * ddx ENDDO ! !-- Compute vertical diffusion. In case that surface fluxes have been prescribed or computed at !-- bottom and/or top, index k starts/ends at nzb+2 or nzt-1, respectively. Model top is also !-- mask if top flux is given. DO k = nzb+1, nzt ! !-- Determine flags to mask topography below and above. Flag 0 is used to mask topography in !-- general, and flag 8 implies information about use_surface_fluxes. Flag 9 is used to !-- control flux at model top. mask_bottom = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k-1,j,i), 8 ) ) mask_top = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 8 ) ) * & MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k+1,j,i), 9 ) ) flag = MERGE( 1.0_wp, 0.0_wp, BTEST( topo_flags(k,j,i), 0 ) ) tend(k,j,i) = tend(k,j,i) & + 0.5_wp * ( & ( kh(k,j,i) + kh(k+1,j,i) ) * & ( s(k+1,j,i)-s(k,j,i) ) * ddzu(k+1) & * rho_air_zw(k) & * mask_top & - ( kh(k,j,i) + kh(k-1,j,i) ) * & ( s(k,j,i)-s(k-1,j,i) ) * ddzu(k) & * rho_air_zw(k-1) & * mask_bottom & ) * ddzw(k) * drho_air(k) & * flag ENDDO ! !-- Vertical diffusion at horizontal walls. !-- TO DO: Adjust for downward facing walls and mask already in main loop IF ( use_surface_fluxes ) THEN ! !-- Default-type surfaces, upward-facing surf_s = surf_def_h(0)%start_index(j,i) surf_e = surf_def_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_h_up(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Default-type surfaces, downward-facing surf_s = surf_def_h(1)%start_index(j,i) surf_e = surf_def_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_def_h_down(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, upward-facing surf_s = surf_lsm_h(0)%start_index(j,i) surf_e = surf_lsm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_h_up(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Natural-type surfaces, downward-facing surf_s = surf_lsm_h(1)%start_index(j,i) surf_e = surf_lsm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_lsm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_lsm_h_down(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, upward-facing surf_s = surf_usm_h(0)%start_index(j,i) surf_e = surf_usm_h(0)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(0)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_h_up(m) * ddzw(k) * drho_air(k) ENDDO ! !-- Urban-type surfaces, upward-facing surf_s = surf_usm_h(1)%start_index(j,i) surf_e = surf_usm_h(1)%end_index(j,i) DO m = surf_s, surf_e k = surf_usm_h(1)%k(m) tend(k,j,i) = tend(k,j,i) + s_flux_usm_h_down(m) * ddzw(k) * drho_air(k) ENDDO ENDIF ! !-- Vertical diffusion at the last computational gridpoint along z-direction IF ( use_top_fluxes ) THEN surf_s = surf_def_h(2)%start_index(j,i) surf_e = surf_def_h(2)%end_index(j,i) DO m = surf_s, surf_e k = surf_def_h(2)%k(m) tend(k,j,i) = tend(k,j,i) + ( - s_flux_t(m) ) * ddzw(k) * drho_air(k) ENDDO ENDIF END SUBROUTINE diffusion_s_ij END MODULE diffusion_s_mod