#define WRF_PORT #define MODAL_AERO ! Updated to CESM1.0.3 (CAM5.1.01) by Balwinder.Singh@pnnl.gov module diffusion_solver !------------------------------------------------------------------------------------ ! ! Module to solve vertical diffusion equations using a tri-diagonal solver. ! ! The module will also apply countergradient fluxes, and apply molecular ! ! diffusion for constituents. ! ! ! ! Public interfaces : ! ! init_vdiff initializes time independent coefficients ! ! compute_vdiff solves diffusion equations ! ! vd_lu_solve tridiagonal solver also used by gwd (should be private) ! ! vd_lu_decomp tridiagonal solver also used by gwd (should be private) ! ! vdiff_selector type for storing fields selected to be diffused ! ! vdiff_select selects fields to be diffused ! ! operator(.not.) extends .not. to operate on type vdiff_selector ! ! any provides functionality of intrinsic any for type vdiff_selector ! ! ! !------------------------------------ Code History ---------------------------------- ! ! Initial subroutines : B. Boville and others, 1991-2004 ! ! Modularization : J. McCaa, September 2004 ! ! Most Recent Code : Sungsu Park, Aug. 2006, Dec. 2008, Jan. 2010. ! !------------------------------------------------------------------------------------ ! #ifndef WRF_PORT use cam_logfile, only : iulog #else use module_cam_support, only : iulog #endif implicit none private save integer, parameter :: r8 = selected_real_kind(12) ! 8 byte real ! ----------------- ! ! Public interfaces ! ! ----------------- ! public init_vdiff ! Initialization public compute_vdiff ! Full routine public vd_lu_solve ! Tridiagonal solver also used by gwd ( should be private! ) public vd_lu_decomp ! Tridiagonal solver also used by gwd ( should be private! ) public vdiff_selector ! Type for storing fields selected to be diffused public vdiff_select ! Selects fields to be diffused public operator(.not.) ! Extends .not. to operate on type vdiff_selector public any ! Provides functionality of intrinsic any for type vdiff_selector integer, public :: nbot_molec ! Bottom level where molecular diffusivity is applied ! Below stores logical array of fields to be diffused type vdiff_selector private logical, pointer, dimension(:) :: fields end type vdiff_selector ! Below extends .not. to operate on type vdiff_selector interface operator(.not.) module procedure not end interface ! Below provides functionality of intrinsic any for type vdiff_selector interface any module procedure my_any end interface ! ------------ ! ! Private data ! ! ------------ ! real(r8), private :: cpair ! Specific heat of dry air real(r8), private :: gravit ! Acceleration due to gravity real(r8), private :: rair ! Gas constant for dry air real(r8), private :: zvir ! rh2o/rair - 1 real(r8), private :: latvap ! Latent heat of vaporization real(r8), private :: karman ! von Karman constant ! Parameters used for Turbulent Mountain Stress real(r8), parameter :: z0fac = 0.025_r8 ! Factor determining z_0 from orographic standard deviation real(r8), parameter :: z0max = 100._r8 ! Max value of z_0 for orography real(r8), parameter :: horomin = 10._r8 ! Min value of subgrid orographic height for mountain stress real(r8), parameter :: dv2min = 0.01_r8 ! Minimum shear squared real(r8), private :: oroconst ! Converts from standard deviation to height contains ! =============================================================================== ! ! ! ! =============================================================================== ! subroutine init_vdiff( kind, ncnst, rair_in, gravit_in, fieldlist_wet, fieldlist_dry, errstring ) integer, intent(in) :: kind ! Kind used for reals integer, intent(in) :: ncnst ! Number of constituents real(r8), intent(in) :: rair_in ! Input gas constant for dry air real(r8), intent(in) :: gravit_in ! Input gravititational acceleration type(vdiff_selector), intent(out) :: fieldlist_wet ! List of fields to be diffused using moist mixing ratio type(vdiff_selector), intent(out) :: fieldlist_dry ! List of fields to be diffused using dry mixing ratio character(128), intent(out) :: errstring ! Output status errstring = '' if( kind .ne. r8 ) then write(iulog,*) 'KIND of reals passed to init_vdiff -- exiting.' #ifdef WRF_PORT call wrf_message(iulog) #endif errstring = 'init_vdiff' return endif rair = rair_in gravit = gravit_in allocate( fieldlist_wet%fields( 3 + ncnst ) ) fieldlist_wet%fields(:) = .false. allocate( fieldlist_dry%fields( 3 + ncnst ) ) fieldlist_dry%fields(:) = .false. end subroutine init_vdiff ! =============================================================================== ! ! ! ! =============================================================================== ! subroutine compute_vdiff( lchnk , & pcols , pver , ncnst , ncol , pmid , & pint , rpdel , t , ztodt , taux , & tauy , shflx , cflx , ntop , nbot , & kvh , kvm , kvq , cgs , cgh , & zi , ksrftms , qmincg , fieldlist , & u , v , q , dse , & tautmsx , tautmsy , dtk , topflx , errstring , & tauresx , tauresy , itaures , & do_molec_diff , compute_molec_diff , vd_lu_qdecomp ) !-------------------------------------------------------------------------- ! ! Driver routine to compute vertical diffusion of momentum, moisture, trace ! ! constituents and dry static energy. The new temperature is computed from ! ! the diffused dry static energy. ! ! Turbulent diffusivities and boundary layer nonlocal transport terms are ! ! obtained from the turbulence module. ! !-------------------------------------------------------------------------- ! #ifndef WRF_PORT use phys_debug_util, only : phys_debug_col use time_manager, only : is_first_step, get_nstep use phys_control, only : phys_getopts #endif ! Modification : Ideally, we should diffuse 'liquid-ice static energy' (sl), not the dry static energy. ! Also, vertical diffusion of cloud droplet number concentration and aerosol number ! concentration should be done very carefully in the future version. ! --------------- ! ! Input Arguments ! ! --------------- ! integer, intent(in) :: lchnk integer, intent(in) :: pcols integer, intent(in) :: pver integer, intent(in) :: ncnst integer, intent(in) :: ncol ! Number of atmospheric columns integer, intent(in) :: ntop ! Top interface level to which vertical diffusion is applied ( = 1 ). integer, intent(in) :: nbot ! Bottom interface level to which vertical diffusion is applied ( = pver ). integer, intent(in) :: itaures ! Indicator determining whether 'tauresx,tauresy' is updated (1) or non-updated (0) in this subroutine. real(r8), intent(in) :: pmid(pcols,pver) ! Mid-point pressures [ Pa ] real(r8), intent(in) :: pint(pcols,pver+1) ! Interface pressures [ Pa ] real(r8), intent(in) :: rpdel(pcols,pver) ! 1./pdel real(r8), intent(in) :: t(pcols,pver) ! Temperature [ K ] real(r8), intent(in) :: ztodt ! 2 delta-t [ s ] real(r8), intent(in) :: taux(pcols) ! Surface zonal stress. Input u-momentum per unit time per unit area into the atmosphere [ N/m2 ] real(r8), intent(in) :: tauy(pcols) ! Surface meridional stress. Input v-momentum per unit time per unit area into the atmosphere [ N/m2 ] real(r8), intent(in) :: shflx(pcols) ! Surface sensible heat flux [ W/m2 ] real(r8), intent(in) :: cflx(pcols,ncnst) ! Surface constituent flux [ kg/m2/s ] real(r8), intent(in) :: zi(pcols,pver+1) ! Interface heights [ m ] real(r8), intent(in) :: ksrftms(pcols) ! Surface drag coefficient for turbulent mountain stress. > 0. [ kg/s/m2 ] real(r8), intent(in) :: qmincg(ncnst) ! Minimum constituent mixing ratios from cg fluxes logical, intent(in) :: do_molec_diff ! Flag indicating multiple constituent diffusivities integer, external, optional :: compute_molec_diff ! Constituent-independent moleculuar diffusivity routine integer, external, optional :: vd_lu_qdecomp ! Constituent-dependent moleculuar diffusivity routine type(vdiff_selector), intent(in) :: fieldlist ! Array of flags selecting which fields to diffuse ! ---------------------- ! ! Input-Output Arguments ! ! ---------------------- ! real(r8), intent(inout) :: kvh(pcols,pver+1) ! Eddy diffusivity for heat [ m2/s ] real(r8), intent(inout) :: kvm(pcols,pver+1) ! Eddy viscosity ( Eddy diffusivity for momentum ) [ m2/s ] real(r8), intent(inout) :: kvq(pcols,pver+1) ! Eddy diffusivity for constituents real(r8), intent(inout) :: cgs(pcols,pver+1) ! Counter-gradient star [ cg/flux ] real(r8), intent(inout) :: cgh(pcols,pver+1) ! Counter-gradient term for heat real(r8), intent(inout) :: u(pcols,pver) ! U wind. This input is the 'raw' input wind to PBL scheme without iterative provisional update. [ m/s ] real(r8), intent(inout) :: v(pcols,pver) ! V wind. This input is the 'raw' input wind to PBL scheme without iterative provisional update. [ m/s ] real(r8), intent(inout) :: q(pcols,pver,ncnst) ! Moisture and trace constituents [ kg/kg, #/kg ? ] real(r8), intent(inout) :: dse(pcols,pver) ! Dry static energy [ J/kg ] real(r8), intent(inout) :: tauresx(pcols) ! Input : Reserved surface stress at previous time step real(r8), intent(inout) :: tauresy(pcols) ! Output : Reserved surface stress at current time step ! ---------------- ! ! Output Arguments ! ! ---------------- ! real(r8), intent(out) :: dtk(pcols,pver) ! T tendency from KE dissipation real(r8), intent(out) :: tautmsx(pcols) ! Implicit zonal turbulent mountain surface stress [ N/m2 = kg m/s /s/m2 ] real(r8), intent(out) :: tautmsy(pcols) ! Implicit meridional turbulent mountain surface stress [ N/m2 = kg m/s /s/m2 ] real(r8), intent(out) :: topflx(pcols) ! Molecular heat flux at the top interface character(128), intent(out) :: errstring ! Output status ! --------------- ! ! Local Variables ! ! --------------- ! integer :: i, k, m, icol ! Longitude, level, constituent indices integer :: status ! Status indicator integer :: ntop_molec ! Top level where molecular diffusivity is applied logical :: lqtst(pcols) ! Adjust vertical profiles logical :: need_decomp ! Whether to compute a new decomposition logical :: cnst_fixed_ubc(ncnst) ! Whether upper boundary condition is fixed logical :: do_iss ! Use implicit turbulent surface stress computation real(r8) :: tmpm(pcols,pver) ! Potential temperature, ze term in tri-diag sol'n real(r8) :: ca(pcols,pver) ! - Upper diag of tri-diag matrix real(r8) :: cc(pcols,pver) ! - Lower diag of tri-diag matrix real(r8) :: dnom(pcols,pver) ! 1./(1. + ca(k) + cc(k) - cc(k)*ze(k-1)) real(r8) :: tmp1(pcols) ! Temporary storage real(r8) :: tmpi1(pcols,pver+1) ! Interface KE dissipation real(r8) :: tint(pcols,pver+1) ! Interface temperature real(r8) :: rhoi(pcols,pver+1) ! rho at interfaces real(r8) :: tmpi2(pcols,pver+1) ! dt*(g*rho)**2/dp at interfaces real(r8) :: rrho(pcols) ! 1./bottom level density real(r8) :: zero(pcols) ! Zero array for surface heat exchange coefficients real(r8) :: tautotx(pcols) ! Total surface stress ( zonal ) real(r8) :: tautoty(pcols) ! Total surface stress ( meridional ) real(r8) :: dinp_u(pcols,pver+1) ! Vertical difference at interfaces, input u real(r8) :: dinp_v(pcols,pver+1) ! Vertical difference at interfaces, input v real(r8) :: dout_u ! Vertical difference at interfaces, output u real(r8) :: dout_v ! Vertical difference at interfaces, output v real(r8) :: dse_top(pcols) ! dse on top boundary real(r8) :: cc_top(pcols) ! Lower diagonal at top interface real(r8) :: cd_top(pcols) ! real(r8) :: rghd(pcols,pver+1) ! (1/H_i - 1/H) *(g*rho)^(-1) real(r8) :: qtm(pcols,pver) ! Temporary copy of q real(r8) :: kq_scal(pcols,pver+1) ! kq_fac*sqrt(T)*m_d/rho for molecular diffusivity real(r8) :: mw_fac(ncnst) ! sqrt(1/M_q + 1/M_d) for this constituent real(r8) :: cnst_mw(ncnst) ! Molecular weight [ kg/kmole ] real(r8) :: ubc_mmr(pcols,ncnst) ! Upper boundary mixing ratios [ kg/kg ] real(r8) :: ubc_t(pcols) ! Upper boundary temperature [ K ] real(r8) :: ws(pcols) ! Lowest-level wind speed [ m/s ] real(r8) :: tau(pcols) ! Turbulent surface stress ( not including mountain stress ) real(r8) :: ksrfturb(pcols) ! Surface drag coefficient of 'normal' stress. > 0. Virtual mass input per unit time per unit area [ kg/s/m2 ] real(r8) :: ksrf(pcols) ! Surface drag coefficient of 'normal' stress + Surface drag coefficient of 'tms' stress. > 0. [ kg/s/m2 ] real(r8) :: usum_in(pcols) ! Vertical integral of input u-momentum. Total zonal momentum per unit area in column [ sum of u*dp/g = kg m/s m-2 ] real(r8) :: vsum_in(pcols) ! Vertical integral of input v-momentum. Total meridional momentum per unit area in column [ sum of v*dp/g = kg m/s m-2 ] real(r8) :: usum_mid(pcols) ! Vertical integral of u-momentum after adding explicit residual stress real(r8) :: vsum_mid(pcols) ! Vertical integral of v-momentum after adding explicit residual stress real(r8) :: usum_out(pcols) ! Vertical integral of u-momentum after doing implicit diffusion real(r8) :: vsum_out(pcols) ! Vertical integral of v-momentum after doing implicit diffusion real(r8) :: tauimpx(pcols) ! Actual net stress added at the current step other than mountain stress real(r8) :: tauimpy(pcols) ! Actual net stress added at the current step other than mountain stress real(r8) :: wsmin ! Minimum sfc wind speed for estimating frictional transfer velocity ksrf. [ m/s ] real(r8) :: ksrfmin ! Minimum surface drag coefficient [ kg/s/m^2 ] real(r8) :: timeres ! Relaxation time scale of residual stress ( >= dt ) [ s ] real(r8) :: ramda ! dt/timeres [ no unit ] real(r8) :: psum real(r8) :: u_in, u_res, tauresx_in real(r8) :: v_in, v_res, tauresy_in ! ------------------------------------------------ ! ! Parameters for implicit surface stress treatment ! ! ------------------------------------------------ ! wsmin = 1._r8 ! Minimum wind speed for ksrfturb computation [ m/s ] ksrfmin = 1.e-4_r8 ! Minimum surface drag coefficient [ kg/s/m^2 ] timeres = 7200._r8 ! Relaxation time scale of residual stress ( >= dt ) [ s ] #ifndef WRF_PORT call phys_getopts( do_iss_out = do_iss ) #else do_iss = .true. !hardwired to true #endif ! ----------------------- ! ! Main Computation Begins ! ! ----------------------- ! errstring = '' if( ( diffuse(fieldlist,'u') .or. diffuse(fieldlist,'v') ) .and. .not. diffuse(fieldlist,'s') ) then errstring = 'diffusion_solver.compute_vdiff: must diffuse s if diffusing u or v' return end if zero(:) = 0._r8 ! Compute 'rho' and 'dt*(g*rho)^2/dp' at interfaces tint(:ncol,1) = t(:ncol,1) rhoi(:ncol,1) = pint(:ncol,1) / (rair*tint(:ncol,1)) do k = 2, pver do i = 1, ncol tint(i,k) = 0.5_r8 * ( t(i,k) + t(i,k-1) ) rhoi(i,k) = pint(i,k) / (rair*tint(i,k)) tmpi2(i,k) = ztodt * ( gravit*rhoi(i,k) )**2 / ( pmid(i,k) - pmid(i,k-1) ) end do end do tint(:ncol,pver+1) = t(:ncol,pver) rhoi(:ncol,pver+1) = pint(:ncol,pver+1) / ( rair*tint(:ncol,pver+1) ) rrho(:ncol) = rair * t(:ncol,pver) / pmid(:ncol,pver) tmp1(:ncol) = ztodt * gravit * rpdel(:ncol,pver) !--------------------------------------- ! ! Computation of Molecular Diffusivities ! !--------------------------------------- ! ! Modification : Why 'kvq' is not changed by molecular diffusion ? if( do_molec_diff ) then if( (.not.present(compute_molec_diff)) .or. (.not.present(vd_lu_qdecomp)) ) then errstring = 'compute_vdiff: do_molec_diff true but compute_molec_diff or vd_lu_qdecomp missing' return endif ! The next subroutine 'compute_molec_diff' : ! Modifies : kvh, kvm, tint, rhoi, and tmpi2 ! Returns : kq_scal, ubc_t, ubc_mmr, dse_top, cc_top, cd_top, cnst_mw, ! cnst_fixed_ubc , mw_fac , ntop_molec status = compute_molec_diff( lchnk , & pcols , pver , ncnst , ncol , t , pmid , pint , & zi , ztodt , kvh , kvm , tint , rhoi , tmpi2 , & kq_scal , ubc_t , ubc_mmr , dse_top , cc_top , cd_top , cnst_mw , & cnst_fixed_ubc , mw_fac , ntop_molec , nbot_molec ) else kq_scal(:,:) = 0._r8 cd_top(:) = 0._r8 cc_top(:) = 0._r8 endif !---------------------------- ! ! Diffuse Horizontal Momentum ! !---------------------------- ! if( diffuse(fieldlist,'u') .or. diffuse(fieldlist,'v') ) then ! Compute the vertical upward differences of the input u,v for KE dissipation ! at each interface. ! Velocity = 0 at surface, so difference at the bottom interface is -u,v(pver) ! These 'dinp_u, dinp_v' are computed using the non-diffused input wind. do i = 1, ncol dinp_u(i,1) = 0._r8 dinp_v(i,1) = 0._r8 dinp_u(i,pver+1) = -u(i,pver) dinp_v(i,pver+1) = -v(i,pver) end do do k = 2, pver do i = 1, ncol dinp_u(i,k) = u(i,k) - u(i,k-1) dinp_v(i,k) = v(i,k) - v(i,k-1) end do end do ! -------------------------------------------------------------- ! ! Do 'Implicit Surface Stress' treatment for numerical stability ! ! in the lowest model layer. ! ! -------------------------------------------------------------- ! if( do_iss ) then ! Compute surface drag coefficient for implicit diffusion ! including turbulent turbulent mountain stress. do i = 1, ncol ws(i) = max( sqrt( u(i,pver)**2._r8 + v(i,pver)**2._r8 ), wsmin ) tau(i) = sqrt( taux(i)**2._r8 + tauy(i)**2._r8 ) ksrfturb(i) = max( tau(i) / ws(i), ksrfmin ) end do ksrf(:ncol) = ksrfturb(:ncol) + ksrftms(:ncol) ! Do all surface stress ( normal + tms ) implicitly ! Vertical integration of input momentum. ! This is total horizontal momentum per unit area [ kg*m/s/m2 ] in each column. ! Note (u,v) are the raw input to the PBL scheme, not the ! provisionally-marched ones within the iteration loop of the PBL scheme. do i = 1, ncol usum_in(i) = 0._r8 vsum_in(i) = 0._r8 do k = 1, pver usum_in(i) = usum_in(i) + (1._r8/gravit)*u(i,k)/rpdel(i,k) vsum_in(i) = vsum_in(i) + (1._r8/gravit)*v(i,k)/rpdel(i,k) end do end do ! Add residual stress of previous time step explicitly into the lowest ! model layer with a relaxation time scale of 'timeres'. ramda = ztodt / timeres u(:ncol,pver) = u(:ncol,pver) + tmp1(:ncol)*tauresx(:ncol)*ramda v(:ncol,pver) = v(:ncol,pver) + tmp1(:ncol)*tauresy(:ncol)*ramda ! Vertical integration of momentum after adding explicit residual stress ! into the lowest model layer. do i = 1, ncol usum_mid(i) = 0._r8 vsum_mid(i) = 0._r8 do k = 1, pver usum_mid(i) = usum_mid(i) + (1._r8/gravit)*u(i,k)/rpdel(i,k) vsum_mid(i) = vsum_mid(i) + (1._r8/gravit)*v(i,k)/rpdel(i,k) end do end do ! Debug ! icol = phys_debug_col(lchnk) ! if ( icol > 0 .and. get_nstep() .ge. 1 ) then ! tauresx_in = tauresx(icol) ! tauresy_in = tauresy(icol) ! u_in = u(icol,pver) - tmp1(icol) * tauresx(icol) * ramda ! v_in = v(icol,pver) - tmp1(icol) * tauresy(icol) * ramda ! u_res = u(icol,pver) ! v_res = v(icol,pver) ! endif ! Debug else ! In this case, do 'turbulent mountain stress' implicitly, ! but do 'normal turbulent stress' explicitly. ! In this case, there is no 'redisual stress' as long as 'tms' is ! treated in a fully implicit wway, which is true. ! 1. Do 'tms' implicitly ksrf(:ncol) = ksrftms(:ncol) ! 2. Do 'normal stress' explicitly u(:ncol,pver) = u(:ncol,pver) + tmp1(:ncol)*taux(:ncol) v(:ncol,pver) = v(:ncol,pver) + tmp1(:ncol)*tauy(:ncol) end if ! End of 'do iss' ( implicit surface stress ) ! --------------------------------------------------------------------------------------- ! ! Diffuse horizontal momentum implicitly using tri-diagnonal matrix. ! ! The 'u,v' are input-output: the output 'u,v' are implicitly diffused winds. ! ! For implicit 'normal' stress : ksrf = ksrftms + ksrfturb, ! ! u(pver) : explicitly include 'redisual normal' stress ! ! For explicit 'normal' stress : ksrf = ksrftms ! ! u(pver) : explicitly include 'normal' stress ! ! Note that in all the two cases above, 'tms' is fully implicitly treated. ! ! --------------------------------------------------------------------------------------- ! call vd_lu_decomp( pcols , pver , ncol , & ksrf , kvm , tmpi2 , rpdel , ztodt , zero , & ca , cc , dnom , tmpm , ntop , nbot ) call vd_lu_solve( pcols , pver , ncol , & u , ca , tmpm , dnom , ntop , nbot , zero ) call vd_lu_solve( pcols , pver , ncol , & v , ca , tmpm , dnom , ntop , nbot , zero ) ! ---------------------------------------------------------------------- ! ! Calculate 'total' ( tautotx ) and 'tms' ( tautmsx ) stresses that ! ! have been actually added into the atmosphere at the current time step. ! ! Also, update residual stress, if required. ! ! ---------------------------------------------------------------------- ! do i = 1, ncol ! Compute the implicit 'tms' using the updated winds. ! Below 'tautmsx(i),tautmsy(i)' are pure implicit mountain stresses ! that has been actually added into the atmosphere both for explicit ! and implicit approach. tautmsx(i) = -ksrftms(i)*u(i,pver) tautmsy(i) = -ksrftms(i)*v(i,pver) if( do_iss ) then ! Compute vertical integration of final horizontal momentum usum_out(i) = 0._r8 vsum_out(i) = 0._r8 do k = 1, pver usum_out(i) = usum_out(i) + (1._r8/gravit)*u(i,k)/rpdel(i,k) vsum_out(i) = vsum_out(i) + (1._r8/gravit)*v(i,k)/rpdel(i,k) end do ! Compute net stress added into the atmosphere at the current time step. ! Note that the difference between 'usum_in' and 'usum_out' are induced ! by 'explicit residual stress + implicit total stress' for implicit case, while ! by 'explicit normal stress + implicit tms stress' for explicit case. ! Here, 'tautotx(i)' is net stress added into the air at the current time step. tauimpx(i) = ( usum_out(i) - usum_in(i) ) / ztodt tauimpy(i) = ( vsum_out(i) - vsum_in(i) ) / ztodt tautotx(i) = tauimpx(i) tautoty(i) = tauimpy(i) ! Compute redisual stress and update if required. ! Note that the total stress we should have added at the current step is ! the sum of 'taux(i) - ksrftms(i)*u(i,pver) + tauresx(i)'. if( itaures .eq. 1 ) then tauresx(i) = taux(i) + tautmsx(i) + tauresx(i) - tauimpx(i) tauresy(i) = tauy(i) + tautmsy(i) + tauresy(i) - tauimpy(i) endif else tautotx(i) = tautmsx(i) + taux(i) tautoty(i) = tautmsy(i) + tauy(i) tauresx(i) = 0._r8 tauresy(i) = 0._r8 end if ! End of 'do_iss' routine end do ! End of 'do i = 1, ncol' routine ! Debug ! icol = phys_debug_col(lchnk) ! if ( icol > 0 .and. get_nstep() .ge. 1 ) then ! write(iulog,*) ! write(iulog,*) 'diffusion_solver debug' ! write(iulog,*) ! write(iulog,*) 'u_in, u_res, u_out' ! write(iulog,*) u_in, u_res, u(icol,pver) ! write(iulog,*) 'tauresx_in, tautmsx, tauimpx(actual), tauimpx(derived), tauresx_out, taux' ! write(iulog,*) tauresx_in, tautmsx(icol), tauimpx(icol), -ksrf(icol)*u(icol,pver), tauresx(icol), taux(icol) ! write(iulog,*) ! write(iulog,*) 'v_in, v_res, v_out' ! write(iulog,*) v_in, v_res, v(icol,pver) ! write(iulog,*) 'tauresy_in, tautmsy, tauimpy(actual), tauimpy(derived), tauresy_out, tauy' ! write(iulog,*) tauresy_in, tautmsy(icol), tauimpy(icol), -ksrf(icol)*v(icol,pver), tauresy(icol), tauy(icol) ! write(iulog,*) ! write(iulog,*) 'itaures, ksrf, ksrfturb, ksrftms' ! write(iulog,*) itaures, ksrf(icol), ksrfturb(icol), ksrftms(icol) ! write(iulog,*) ! endif ! Debug ! ------------------------------------ ! ! Calculate kinetic energy dissipation ! ! ------------------------------------ ! ! Modification : In future, this should be set exactly same as ! the ones in the convection schemes ! 1. Compute dissipation term at interfaces ! Note that 'u,v' are already diffused wind, and 'tautotx,tautoty' are ! implicit stress that has been actually added. On the other hand, ! 'dinp_u, dinp_v' were computed using non-diffused input wind. ! Modification : I should check whether non-consistency between 'u' and 'dinp_u' ! is correctly intended approach. I think so. k = pver + 1 do i = 1, ncol tmpi1(i,1) = 0._r8 tmpi1(i,k) = 0.5_r8 * ztodt * gravit * & ( (-u(i,k-1) + dinp_u(i,k))*tautotx(i) + (-v(i,k-1) + dinp_v(i,k))*tautoty(i) ) end do do k = 2, pver do i = 1, ncol dout_u = u(i,k) - u(i,k-1) dout_v = v(i,k) - v(i,k-1) tmpi1(i,k) = 0.25_r8 * tmpi2(i,k) * kvm(i,k) * & ( dout_u**2 + dout_v**2 + dout_u*dinp_u(i,k) + dout_v*dinp_v(i,k) ) end do end do ! 2. Compute dissipation term at midpoints, add to dry static energy do k = 1, pver do i = 1, ncol dtk(i,k) = ( tmpi1(i,k+1) + tmpi1(i,k) ) * rpdel(i,k) dse(i,k) = dse(i,k) + dtk(i,k) end do end do end if ! End of diffuse horizontal momentum, diffuse(fieldlist,'u') routine !-------------------------- ! ! Diffuse Dry Static Energy ! !-------------------------- ! ! Modification : In future, we should diffuse the fully conservative ! moist static energy,not the dry static energy. if( diffuse(fieldlist,'s') ) then ! Add counter-gradient to input static energy profiles do k = 1, pver dse(:ncol,k) = dse(:ncol,k) + ztodt * rpdel(:ncol,k) * gravit * & ( rhoi(:ncol,k+1) * kvh(:ncol,k+1) * cgh(:ncol,k+1) & - rhoi(:ncol,k ) * kvh(:ncol,k ) * cgh(:ncol,k ) ) end do ! Add the explicit surface fluxes to the lowest layer dse(:ncol,pver) = dse(:ncol,pver) + tmp1(:ncol) * shflx(:ncol) ! Diffuse dry static energy call vd_lu_decomp( pcols , pver , ncol , & zero , kvh , tmpi2 , rpdel , ztodt , cc_top, & ca , cc , dnom , tmpm , ntop , nbot ) call vd_lu_solve( pcols , pver , ncol , & dse , ca , tmpm , dnom , ntop , nbot , cd_top ) ! Calculate flux at top interface ! Modification : Why molecular diffusion does not work for dry static energy in all layers ? if( do_molec_diff ) then topflx(:ncol) = - kvh(:ncol,ntop_molec) * tmpi2(:ncol,ntop_molec) / (ztodt*gravit) * & ( dse(:ncol,ntop_molec) - dse_top(:ncol) ) end if endif !---------------------------- ! ! Diffuse Water Vapor Tracers ! !---------------------------- ! ! Modification : For aerosols, I need to use separate treatment ! for aerosol mass and aerosol number. ! Loop through constituents need_decomp = .true. do m = 1, ncnst if( diffuse(fieldlist,'q',m) ) then ! Add the nonlocal transport terms to constituents in the PBL. ! Check for neg q's in each constituent and put the original vertical ! profile back if a neg value is found. A neg value implies that the ! quasi-equilibrium conditions assumed for the countergradient term are ! strongly violated. qtm(:ncol,:pver) = q(:ncol,:pver,m) do k = 1, pver q(:ncol,k,m) = q(:ncol,k,m) + & ztodt * rpdel(:ncol,k) * gravit * ( cflx(:ncol,m) * rrho(:ncol) ) * & ( rhoi(:ncol,k+1) * kvh(:ncol,k+1) * cgs(:ncol,k+1) & - rhoi(:ncol,k ) * kvh(:ncol,k ) * cgs(:ncol,k ) ) end do lqtst(:ncol) = all(q(:ncol,1:pver,m) >= qmincg(m), 2) do k = 1, pver q(:ncol,k,m) = merge( q(:ncol,k,m), qtm(:ncol,k), lqtst(:ncol) ) end do ! Add the explicit surface fluxes to the lowest layer q(:ncol,pver,m) = q(:ncol,pver,m) + tmp1(:ncol) * cflx(:ncol,m) ! Diffuse constituents. if( need_decomp ) then call vd_lu_decomp( pcols , pver , ncol , & zero , kvq , tmpi2 , rpdel , ztodt , zero , & ca , cc , dnom , tmpm , ntop , nbot ) if( do_molec_diff ) then ! Update decomposition in molecular diffusion range, include separation velocity term status = vd_lu_qdecomp( pcols , pver , ncol , cnst_fixed_ubc(m), cnst_mw(m), ubc_mmr(:,m), & kvq , kq_scal, mw_fac(m) , tmpi2 , rpdel , & ca , cc , dnom , tmpm , rhoi , & tint , ztodt , ntop_molec, nbot_molec , cd_top ) else need_decomp = .false. endif end if call vd_lu_solve( pcols , pver , ncol , & q(1,1,m) , ca, tmpm , dnom , ntop , nbot , cd_top ) end if end do return end subroutine compute_vdiff ! =============================================================================== ! ! ! ! =============================================================================== ! subroutine vd_lu_decomp( pcols, pver, ncol , & ksrf , kv , tmpi , rpdel, ztodt , cc_top, & ca , cc , dnom , ze , ntop , nbot ) !---------------------------------------------------------------------- ! ! Determine superdiagonal (ca(k)) and subdiagonal (cc(k)) coeffs of the ! ! tridiagonal diffusion matrix. ! ! The diagonal elements (1+ca(k)+cc(k)) are not required by the solver. ! ! Also determine ze factor and denominator for ze and zf (see solver). ! !---------------------------------------------------------------------- ! ! --------------------- ! ! Input-Output Argument ! ! --------------------- ! integer, intent(in) :: pcols ! Number of allocated atmospheric columns integer, intent(in) :: pver ! Number of allocated atmospheric levels integer, intent(in) :: ncol ! Number of computed atmospheric columns integer, intent(in) :: ntop ! Top level to operate on integer, intent(in) :: nbot ! Bottom level to operate on real(r8), intent(in) :: ksrf(pcols) ! Surface "drag" coefficient [ kg/s/m2 ] real(r8), intent(in) :: kv(pcols,pver+1) ! Vertical diffusion coefficients [ m2/s ] real(r8), intent(in) :: tmpi(pcols,pver+1) ! dt*(g/R)**2/dp*pi(k+1)/(.5*(tm(k+1)+tm(k))**2 real(r8), intent(in) :: rpdel(pcols,pver) ! 1./pdel (thickness bet interfaces) real(r8), intent(in) :: ztodt ! 2 delta-t [ s ] real(r8), intent(in) :: cc_top(pcols) ! Lower diagonal on top interface (for fixed ubc only) real(r8), intent(out) :: ca(pcols,pver) ! Upper diagonal real(r8), intent(out) :: cc(pcols,pver) ! Lower diagonal real(r8), intent(out) :: dnom(pcols,pver) ! 1./(1. + ca(k) + cc(k) - cc(k)*ze(k-1)) real(r8), intent(out) :: ze(pcols,pver) ! Term in tri-diag. matrix system ! --------------- ! ! Local Variables ! ! --------------- ! integer :: i ! Longitude index integer :: k ! Vertical index ! ----------------------- ! ! Main Computation Begins ! ! ----------------------- ! ! Determine superdiagonal (ca(k)) and subdiagonal (cc(k)) coeffs of the ! tridiagonal diffusion matrix. The diagonal elements (cb=1+ca+cc) are ! a combination of ca and cc; they are not required by the solver. do k = nbot - 1, ntop, -1 do i = 1, ncol ca(i,k ) = kv(i,k+1) * tmpi(i,k+1) * rpdel(i,k ) cc(i,k+1) = kv(i,k+1) * tmpi(i,k+1) * rpdel(i,k+1) end do end do ! The bottom element of the upper diagonal (ca) is zero (element not used). ! The subdiagonal (cc) is not needed in the solver. do i = 1, ncol ca(i,nbot) = 0._r8 end do ! Calculate e(k). This term is ! required in solution of tridiagonal matrix defined by implicit diffusion eqn. do i = 1, ncol dnom(i,nbot) = 1._r8/(1._r8 + cc(i,nbot) + ksrf(i)*ztodt*gravit*rpdel(i,nbot)) ze(i,nbot) = cc(i,nbot)*dnom(i,nbot) end do do k = nbot - 1, ntop + 1, -1 do i = 1, ncol dnom(i,k) = 1._r8/(1._r8 + ca(i,k) + cc(i,k) - ca(i,k)*ze(i,k+1)) ze(i,k) = cc(i,k)*dnom(i,k) end do end do do i = 1, ncol dnom(i,ntop) = 1._r8/(1._r8 + ca(i,ntop) + cc_top(i) - ca(i,ntop)*ze(i,ntop+1)) end do return end subroutine vd_lu_decomp ! =============================================================================== ! ! ! ! =============================================================================== ! subroutine vd_lu_solve( pcols , pver , ncol , & q , ca , ze , dnom , ntop , nbot , cd_top ) !----------------------------------------------------------------------------------- ! ! Solve the implicit vertical diffusion equation with zero flux boundary conditions. ! ! Procedure for solution of the implicit equation follows Richtmyer and ! ! Morton (1967,pp 198-200). ! ! ! ! The equation solved is ! ! ! ! -ca(k)*q(k+1) + cb(k)*q(k) - cc(k)*q(k-1) = d(k), ! ! ! ! where d(k) is the input profile and q(k) is the output profile ! ! ! ! The solution has the form ! ! ! ! q(k) = ze(k)*q(k-1) + zf(k) ! ! ! ! ze(k) = cc(k) * dnom(k) ! ! ! ! zf(k) = [d(k) + ca(k)*zf(k+1)] * dnom(k) ! ! ! ! dnom(k) = 1/[cb(k) - ca(k)*ze(k+1)] = 1/[1 + ca(k) + cc(k) - ca(k)*ze(k+1)] ! ! ! ! Note that the same routine is used for temperature, momentum and tracers, ! ! and that input variables are replaced. ! ! ---------------------------------------------------------------------------------- ! ! --------------------- ! ! Input-Output Argument ! ! --------------------- ! integer, intent(in) :: pcols ! Number of allocated atmospheric columns integer, intent(in) :: pver ! Number of allocated atmospheric levels integer, intent(in) :: ncol ! Number of computed atmospheric columns integer, intent(in) :: ntop ! Top level to operate on integer, intent(in) :: nbot ! Bottom level to operate on real(r8), intent(in) :: ca(pcols,pver) ! -Upper diag coeff.of tri-diag matrix real(r8), intent(in) :: ze(pcols,pver) ! Term in tri-diag solution real(r8), intent(in) :: dnom(pcols,pver) ! 1./(1. + ca(k) + cc(k) - ca(k)*ze(k+1)) real(r8), intent(in) :: cd_top(pcols) ! cc_top * ubc value real(r8), intent(inout) :: q(pcols,pver) ! Constituent field ! --------------- ! ! Local Variables ! ! --------------- ! real(r8) :: zf(pcols,pver) ! Term in tri-diag solution integer i, k ! Longitude, vertical indices ! ----------------------- ! ! Main Computation Begins ! ! ----------------------- ! ! Calculate zf(k). Terms zf(k) and ze(k) are required in solution of ! tridiagonal matrix defined by implicit diffusion equation. ! Note that only levels ntop through nbot need be solved for. do i = 1, ncol zf(i,nbot) = q(i,nbot)*dnom(i,nbot) end do do k = nbot - 1, ntop + 1, -1 do i = 1, ncol zf(i,k) = (q(i,k) + ca(i,k)*zf(i,k+1))*dnom(i,k) end do end do ! Include boundary condition on top element k = ntop do i = 1, ncol zf(i,k) = (q(i,k) + cd_top(i) + ca(i,k)*zf(i,k+1))*dnom(i,k) end do ! Perform back substitution do i = 1, ncol q(i,ntop) = zf(i,ntop) end do do k = ntop + 1, nbot, +1 do i = 1, ncol q(i,k) = zf(i,k) + ze(i,k)*q(i,k-1) end do end do return end subroutine vd_lu_solve ! =============================================================================== ! ! ! ! =============================================================================== ! character(128) function vdiff_select( fieldlist, name, qindex ) ! --------------------------------------------------------------------- ! ! This function sets the field with incoming name as one to be diffused ! ! --------------------------------------------------------------------- ! type(vdiff_selector), intent(inout) :: fieldlist character(*), intent(in) :: name integer, intent(in), optional :: qindex vdiff_select = '' select case (name) case ('u','U') fieldlist%fields(1) = .true. case ('v','V') fieldlist%fields(2) = .true. case ('s','S') fieldlist%fields(3) = .true. case ('q','Q') if( present(qindex) ) then fieldlist%fields(3 + qindex) = .true. else fieldlist%fields(4) = .true. endif case default write(vdiff_select,*) 'Bad argument to vdiff_index: ', name end select return end function vdiff_select type(vdiff_selector) function not(a) ! ------------------------------------------------------------- ! ! This function extends .not. to operate on type vdiff_selector ! ! ------------------------------------------------------------- ! type(vdiff_selector), intent(in) :: a allocate(not%fields(size(a%fields))) not%fields(:) = .not. a%fields(:) end function not logical function my_any(a) ! -------------------------------------------------- ! ! This function extends the intrinsic function 'any' ! ! to operate on type vdiff_selector ! ! -------------------------------------------------- ! type(vdiff_selector), intent(in) :: a my_any = any(a%fields) end function my_any logical function diffuse(fieldlist,name,qindex) ! ---------------------------------------------------------------------------- ! ! This function reports whether the field with incoming name is to be diffused ! ! ---------------------------------------------------------------------------- ! type(vdiff_selector), intent(in) :: fieldlist character(*), intent(in) :: name integer, intent(in), optional :: qindex select case (name) case ('u','U') diffuse = fieldlist%fields(1) case ('v','V') diffuse = fieldlist%fields(2) case ('s','S') diffuse = fieldlist%fields(3) case ('q','Q') if( present(qindex) ) then diffuse = fieldlist%fields(3 + qindex) else diffuse = fieldlist%fields(4) endif case default diffuse = .false. end select return end function diffuse end module diffusion_solver