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jmc |
1.1 |
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module diffusivity_mod |
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!======================================================================= |
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! |
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! DIFFUSIVITY MODULE |
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! |
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! Routines for computing atmospheric diffusivities in the |
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! planetary boundary layer and in the free atmosphere |
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! |
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!======================================================================= |
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use gcm_params_mod, only: gcm_LEN_MBUF, gcm_SQZ_R, gcm_stdMsgUnit |
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use constants_mod, only : grav, vonkarm, cp_air, rdgas, rvgas |
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!use fms_mod, only: error_mesg, FATAL, file_exist, & |
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! check_nml_error, open_namelist_file, & |
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! mpp_pe, mpp_root_pe, close_file, stdlog, & |
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! write_version_number |
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use monin_obukhov_mod, only : mo_diff |
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implicit none |
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private |
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! public interfaces |
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!======================================================================= |
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public diffusivity, pbl_depth, molecular_diff |
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!======================================================================= |
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! form of iterfaces |
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!======================================================================= |
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! subroutine diffusivity (t, q, u, v, p_full, p_half, z_full, z_half, |
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! u_star, b_star, h, k_m, k_t) |
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! input: |
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! t : real, dimension(:,:,:) -- (:,:,pressure), third index running |
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! from top of atmosphere to bottom |
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! temperature (K) |
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! |
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! q : real, dimension(:,:,:) |
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! water vapor specific humidity (nondimensional) |
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! |
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! u : real, dimension(:,:) |
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! zonal wind (m/s) |
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! |
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! v : real, dimension(:,:,:) |
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! meridional wind (m/s) |
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! |
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! z_full : real, dimension(:,:,: |
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! height of full levels (m) |
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! 1 = top of atmosphere; size(p_half,3) = surface |
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! size(z_full,3) = size(t,3) |
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! |
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! z_half : real, dimension(:,:,:) |
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! height of half levels (m) |
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! size(z_half,3) = size(t,3) +1 |
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! z_half(:,:,size(z_half,3)) must be height of surface! |
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! (if you are not using eta-model) |
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! |
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! u_star: real, dimension(:,:) |
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! friction velocity (m/s) |
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! |
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! b_star: real, dimension(:,:) |
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! buoyancy scale (m/s**2) |
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! (u_star and b_star can be obtained by calling |
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! mo_drag in monin_obukhov_mod) |
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! output: |
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! h : real, dimension(:,:,) |
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! depth of planetary boundary layer (m) |
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! |
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! k_m : real, dimension(:,:,:) |
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! diffusivity for momentum (m**2/s) |
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! |
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! defined at half-levels |
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! size(k_m,3) should be at least as large as size(t,3) |
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! only the returned values at |
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! levels 2 to size(t,3) are meaningful |
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! other values will be returned as zero |
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! |
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! k_t : real, dimension(:,:,:) |
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! diffusivity for temperature and scalars (m**2/s) |
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! |
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! |
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!======================================================================= |
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!--------------------- version number ---------------------------------- |
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jmc |
1.2 |
character(len=128) :: version = '$Id: diffusivity_mod.F90,v 1.1 2012/09/11 03:53:05 jmc Exp $' |
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character(len=128) :: tag = '$Name: $' |
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jmc |
1.1 |
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!======================================================================= |
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! DEFAULT VALUES OF NAMELIST PARAMETERS: |
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logical :: fixed_depth = .false. |
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logical :: do_virtual_non_mcm = .false. ! applies only to non-'mcm' pbl scheme |
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real :: depth_0 = 5000.0 |
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real :: frac_inner = 0.1 |
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real :: rich_crit_pbl = 1.0 |
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real :: entr_ratio = 0.2 |
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real :: parcel_buoy = 2.0 |
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real :: znom = 1000.0 |
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logical :: free_atm_diff = .false. |
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logical :: free_atm_skyhi_diff = .false. |
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logical :: pbl_mcm = .false. |
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real :: rich_crit_diff = 0.25 |
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real :: mix_len = 30. |
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real :: rich_prandtl = 1.00 |
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real :: background_m = 0.0 |
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real :: background_t = 0.0 |
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logical :: ampns = .false. ! include delta z factor in |
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! defining ri ? |
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real :: ampns_max = 1.0E20 ! limit to reduction factor |
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! applied to ri due to delta z |
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! factor |
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namelist /diffusivity_nml/ fixed_depth, depth_0, frac_inner,& |
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rich_crit_pbl, entr_ratio, parcel_buoy,& |
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znom, free_atm_diff, free_atm_skyhi_diff,& |
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pbl_mcm, rich_crit_diff, mix_len, rich_prandtl,& |
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background_m, background_t, ampns, ampns_max, & |
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do_virtual_non_mcm |
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!======================================================================= |
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! OTHER MODULE VARIABLES |
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real :: small = 1.e-04 |
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real :: gcp = grav/cp_air |
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logical :: init = .false. |
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real :: beta = 1.458e-06 |
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real :: rbop1 = 110.4 |
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real :: rbop2 = 1.405 |
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real, parameter :: d608 = (rvgas-rdgas)/rdgas |
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contains |
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!======================================================================= |
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subroutine diffusivity_init(myThid) |
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integer, intent(in) :: myThid |
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integer :: unit, ierr, io |
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integer :: iUnit |
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CHARACTER*(gcm_LEN_MBUF) :: msgBuf |
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!------------------- read namelist input ------------------------------- |
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! read namelist and copy to logfile |
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! _BARRIER |
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! _BEGIN_MASTER(myThid) |
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CALL BARRIER(myThid) |
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IF ( myThid.EQ.1 ) THEN |
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WRITE(msgBuf,'(A)') 'DIFFUSIVITY_INIT: opening data.atm_gray' |
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CALL PRINT_MESSAGE( msgBuf, gcm_stdMsgUnit, gcm_SQZ_R, myThid ) |
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CALL OPEN_COPY_DATA_FILE( & |
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'data.atm_gray', 'DIFFUSIVITY_INIT', & |
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iUnit, & |
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myThid ) |
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! Read parameters from open data file |
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READ(UNIT=iUnit,NML=diffusivity_nml) |
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WRITE(msgBuf,'(A)') & |
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'DIFFUSIVITY_INIT: finished reading data.atm_gray' |
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CALL PRINT_MESSAGE( msgBuf, gcm_stdMsgUnit, gcm_SQZ_R, myThid ) |
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! Close the open data file |
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CLOSE(iUnit) |
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! if (file_exist('input.nml')) then |
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! unit = open_namelist_file () |
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! ierr=1; do while (ierr /= 0) |
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! read (unit, nml=diffusivity_nml, iostat=io, end=10) |
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! ierr = check_nml_error(io,'diffusivity_nml') |
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! enddo |
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! 10 call close_file (unit) |
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!------------------- dummy checks -------------------------------------- |
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if (frac_inner .le. 0. .or. frac_inner .ge. 1.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'frac_inner must be between 0 and 1', myThid) |
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! call error_mesg ('diffusivity_init', & |
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! 'frac_inner must be between 0 and 1', FATAL) |
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if (rich_crit_pbl .lt. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'rich_crit_pbl must be greater than or equal to zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'rich_crit_pbl must be greater than or equal to zero', FATAL) |
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if (entr_ratio .lt. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'entr_ratio must be greater than or equal to zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'entr_ratio must be greater than or equal to zero', FATAL) |
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if (znom .le. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'znom must be greater than zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'znom must be greater than zero', FATAL) |
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if (.not.free_atm_diff .and. free_atm_skyhi_diff)& |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'free_atm_diff must be set to true if '//& |
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'free_atm_skyhi_diff = .true.', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'free_atm_diff must be set to true if '//& |
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! 'free_atm_skyhi_diff = .true.', FATAL) |
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if (rich_crit_diff .le. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'rich_crit_diff must be greater than zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'rich_crit_diff must be greater than zero', FATAL) |
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if (mix_len .lt. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'mix_len must be greater than or equal to zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'mix_len must be greater than or equal to zero', FATAL) |
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if (rich_prandtl .lt. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'rich_prandtl must be greater than or equal to zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'rich_prandtl must be greater than or equal to zero', FATAL) |
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if (background_m .lt. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'background_m must be greater than or equal to zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'background_m must be greater than or equal to zero', FATAL) |
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if (background_t .lt. 0.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'background_t must be greater than or equal to zero', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'background_t must be greater than or equal to zero', FATAL) |
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if (ampns_max .lt. 1.) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'ampns_max must be greater than or equal to one', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'ampns_max must be greater than or equal to one', FATAL) |
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if (ampns .and. .not. free_atm_skyhi_diff) & |
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CALL PRINT_ERROR( 'diffusivity_init'// & |
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'ampns is only valid when free_atm_skyhi_diff is & also true', myThid ) |
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! call error_mesg ('diffusivity_init', & |
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! 'ampns is only valid when free_atm_skyhi_diff is & |
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! & also true', FATAL) |
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! endif !end of reading input.nml |
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!---------- output namelist to log------------------------------------- |
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! call write_version_number(version, tag) |
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! if ( mpp_pe() == mpp_root_pe() ) write (stdlog(), nml=diffusivity_nml) |
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init = .true. |
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ENDIF |
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CALL BARRIER(myThid) |
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return |
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end subroutine diffusivity_init |
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!======================================================================= |
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subroutine diffusivity(t, q, u, v, p_full, p_half, z_full, z_half, & |
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u_star, b_star, h, k_m, k_t, myThid, kbot) |
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real, intent(in), dimension(:,:,:) :: t, q, u, v |
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real, intent(in), dimension(:,:,:) :: p_full, p_half |
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real, intent(in), dimension(:,:,:) :: z_full, z_half |
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real, intent(in), dimension(:,:) :: u_star, b_star |
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real, intent(inout), dimension(:,:,:) :: k_m, k_t |
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real, intent(out), dimension(:,:) :: h |
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integer, intent (in) :: myThid |
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integer, intent(in), optional, dimension(:,:) :: kbot |
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real, dimension(size(t,1),size(t,2),size(t,3)) :: svcp,z_full_ag, & |
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k_m_save, k_t_save |
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real, dimension(size(t,1),size(t,2),size(t,3)+1):: z_half_ag |
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real, dimension(size(t,1),size(t,2)) :: z_surf |
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integer :: i,j,k,nlev,nlat,nlon |
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| 291 |
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if(.not.init) call diffusivity_init(myThid) |
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| 293 |
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nlev = size(t,3) |
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k_m_save = k_m |
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k_t_save = k_t |
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| 298 |
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!compute height of surface |
| 299 |
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if (present(kbot)) then |
| 300 |
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nlat = size(t,2) |
| 301 |
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nlon = size(t,1) |
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do j=1,nlat |
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do i=1,nlon |
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z_surf(i,j) = z_half(i,j,kbot(i,j)+1) |
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enddo |
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enddo |
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else |
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z_surf(:,:) = z_half(:,:,nlev+1) |
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end if |
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| 312 |
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!compute density profile, and heights relative to surface |
| 313 |
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do k = 1, nlev |
| 314 |
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| 315 |
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z_full_ag(:,:,k) = z_full(:,:,k) - z_surf(:,:) |
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z_half_ag(:,:,k) = z_half(:,:,k) - z_surf(:,:) |
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| 318 |
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if (do_virtual_non_mcm) then |
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svcp(:,:,k) = t(:,:,k)*(1. + d608*q(:,:,k)) + gcp*(z_full_ag(:,:,k)) |
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else |
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svcp(:,:,k) = t(:,:,k) + gcp*(z_full_ag(:,:,k)) |
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endif |
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end do |
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z_half_ag(:,:,nlev+1) = z_half(:,:,nlev+1) - z_surf(:,:) |
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| 328 |
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if(fixed_depth) then |
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h = depth_0 |
| 330 |
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else |
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call pbl_depth(svcp,u,v,z_full_ag,u_star,b_star,h, myThid, kbot=kbot) |
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end if |
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if(pbl_mcm) then |
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call diffusivity_pbl_mcm (u,v, t, p_full, p_half, & |
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z_full_ag, z_half_ag, h, k_m, k_t, myThid) |
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else |
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call diffusivity_pbl (svcp, u, v, z_half_ag, h, u_star, b_star,& |
| 339 |
|
|
k_m, k_t, myThid, kbot=kbot) |
| 340 |
|
|
end if |
| 341 |
|
|
if(free_atm_diff) & |
| 342 |
|
|
call diffusivity_free (svcp, u, v, z_full_ag, z_half_ag, h, k_m, k_t, myThid) |
| 343 |
|
|
|
| 344 |
|
|
k_m = k_m + k_m_save |
| 345 |
|
|
k_t = k_t + k_t_save |
| 346 |
|
|
|
| 347 |
|
|
!NOTE THAT THIS LINE MUST FOLLOW DIFFUSIVITY_FREE SO THAT ENTRAINMENT |
| 348 |
|
|
!K's DO NOT GET OVERWRITTEN IN DIFFUSIVITY_FREE SUBROUTINE |
| 349 |
|
|
if(entr_ratio .gt. 0. .and. .not. fixed_depth) & |
| 350 |
|
|
call diffusivity_entr(svcp,z_full_ag,h,u_star,b_star,k_m,k_t, myThid) |
| 351 |
|
|
|
| 352 |
|
|
!set background diffusivities |
| 353 |
|
|
if(background_m.gt.0.0) k_m = max(k_m,background_m) |
| 354 |
|
|
if(background_t.gt.0.0) k_t = max(k_t,background_t) |
| 355 |
|
|
|
| 356 |
|
|
|
| 357 |
|
|
return |
| 358 |
|
|
end subroutine diffusivity |
| 359 |
|
|
|
| 360 |
|
|
!======================================================================= |
| 361 |
|
|
|
| 362 |
|
|
subroutine pbl_depth(t, u, v, z, u_star, b_star, h, myThid, kbot) |
| 363 |
|
|
|
| 364 |
|
|
|
| 365 |
|
|
real, intent(in) , dimension(:,:,:) :: t, u, v, z |
| 366 |
|
|
real, intent(in) , dimension(:,:) :: u_star,b_star |
| 367 |
|
|
real, intent(out), dimension(:,:) :: h |
| 368 |
|
|
integer, intent(in) :: myThid |
| 369 |
|
|
integer,intent(in) , optional, dimension(:,:) :: kbot |
| 370 |
|
|
|
| 371 |
|
|
real, dimension(size(t,1),size(t,2),size(t,3)) :: rich |
| 372 |
|
|
real, dimension(size(t,1),size(t,2)) :: ws,k_t_ref,& |
| 373 |
|
|
h_inner,tbot |
| 374 |
|
|
real :: rich1, rich2,& |
| 375 |
|
|
h1,h2,svp,t1,t2 |
| 376 |
|
|
integer, dimension(size(t,1),size(t,2)) :: ibot |
| 377 |
|
|
integer :: i,j,k,nlon,& |
| 378 |
|
|
nlat, nlev |
| 379 |
|
|
|
| 380 |
|
|
nlev = size(t,3) |
| 381 |
|
|
nlat = size(t,2) |
| 382 |
|
|
nlon = size(t,1) |
| 383 |
|
|
|
| 384 |
|
|
!assign ibot, compute tbot (virtual temperature at lowest level) |
| 385 |
|
|
if (present(kbot)) then |
| 386 |
|
|
ibot(:,:) = kbot |
| 387 |
|
|
do j = 1,nlat |
| 388 |
|
|
do i = 1,nlon |
| 389 |
|
|
tbot(i,j) = t(i,j,ibot(i,j)) |
| 390 |
|
|
enddo |
| 391 |
|
|
enddo |
| 392 |
|
|
else |
| 393 |
|
|
ibot(:,:) = nlev |
| 394 |
|
|
tbot(:,:) = t(:,:,nlev) |
| 395 |
|
|
end if |
| 396 |
|
|
|
| 397 |
|
|
|
| 398 |
|
|
!compute richardson number for use in pbl depth of neutral/stable side |
| 399 |
|
|
do k = 1,nlev |
| 400 |
|
|
rich(:,:,k) = z(:,:,k)*grav*(t(:,:,k)-tbot(:,:))/tbot(:,:)& |
| 401 |
|
|
/(u(:,:,k)*u(:,:,k) + v(:,:,k)*v(:,:,k) + small ) |
| 402 |
|
|
end do |
| 403 |
|
|
|
| 404 |
|
|
!compute ws to be used in evaluating parcel buoyancy |
| 405 |
|
|
!ws = u_star / phi(h_inner,u_star,b_star) . To find phi |
| 406 |
|
|
!a call to mo_diff is made. |
| 407 |
|
|
|
| 408 |
|
|
h_inner(:,:)=frac_inner*znom |
| 409 |
|
|
call mo_diff(h_inner, u_star, b_star, ws, k_t_ref, myThid ) |
| 410 |
|
|
ws = max(small,ws/vonkarm/h_inner) |
| 411 |
|
|
|
| 412 |
|
|
|
| 413 |
|
|
do j = 1, nlat |
| 414 |
|
|
do i = 1, nlon |
| 415 |
|
|
|
| 416 |
|
|
!do neutral or stable case |
| 417 |
|
|
if (b_star(i,j).le.0.) then |
| 418 |
|
|
|
| 419 |
|
|
h1 = z(i,j,ibot(i,j)) |
| 420 |
|
|
h(i,j) = h1 |
| 421 |
|
|
rich1 = rich(i,j,ibot(i,j)) |
| 422 |
|
|
do k = ibot(i,j)-1, 1, -1 |
| 423 |
|
|
rich2 = rich(i,j,k) |
| 424 |
|
|
h2 = z(i,j,k) |
| 425 |
|
|
if(rich2.gt.rich_crit_pbl) then |
| 426 |
|
|
h(i,j) = h2 + (h1 - h2)*(rich2 - rich_crit_pbl)& |
| 427 |
|
|
/(rich2 - rich1 ) |
| 428 |
|
|
go to 10 |
| 429 |
|
|
endif |
| 430 |
|
|
rich1 = rich2 |
| 431 |
|
|
h1 = h2 |
| 432 |
|
|
enddo |
| 433 |
|
|
|
| 434 |
|
|
!do unstable case |
| 435 |
|
|
else |
| 436 |
|
|
|
| 437 |
|
|
svp = tbot(i,j)*(1.+ & |
| 438 |
|
|
(parcel_buoy*u_star(i,j)*b_star(i,j)/grav/ws(i,j)) ) |
| 439 |
|
|
h1 = z(i,j,ibot(i,j)) |
| 440 |
|
|
h(i,j) = h1 |
| 441 |
|
|
t1 = tbot(i,j) |
| 442 |
|
|
do k = ibot(i,j)-1 , 1, -1 |
| 443 |
|
|
h2 = z(i,j,k) |
| 444 |
|
|
t2 = t(i,j,k) |
| 445 |
|
|
if (t2.gt.svp) then |
| 446 |
|
|
h(i,j) = h2 + (h1 - h2)*(t2 - svp)/(t2 - t1 ) |
| 447 |
|
|
go to 10 |
| 448 |
|
|
end if |
| 449 |
|
|
h1 = h2 |
| 450 |
|
|
t1 = t2 |
| 451 |
|
|
enddo |
| 452 |
|
|
|
| 453 |
|
|
end if |
| 454 |
|
|
10 continue |
| 455 |
|
|
enddo |
| 456 |
|
|
enddo |
| 457 |
|
|
|
| 458 |
|
|
return |
| 459 |
|
|
end subroutine pbl_depth |
| 460 |
|
|
|
| 461 |
|
|
!======================================================================= |
| 462 |
|
|
|
| 463 |
|
|
subroutine diffusivity_pbl(t, u, v, z_half, h, u_star, b_star, & |
| 464 |
|
|
k_m, k_t, myThid, kbot) |
| 465 |
|
|
|
| 466 |
|
|
real, intent(in) , dimension(:,:,:) :: t, u, v, z_half |
| 467 |
|
|
real, intent(in) , dimension(:,:) :: h, u_star, b_star |
| 468 |
|
|
real, intent(inout) , dimension(:,:,:) :: k_m, k_t |
| 469 |
|
|
integer, intent (in) :: myThid |
| 470 |
|
|
integer, intent(in) , optional, dimension(:,:) :: kbot |
| 471 |
|
|
|
| 472 |
|
|
real, dimension(size(t,1),size(t,2)) :: h_inner, k_m_ref,& |
| 473 |
|
|
k_t_ref, factor |
| 474 |
|
|
real, dimension(size(t,1),size(t,2),size(t,3)+1) :: zm |
| 475 |
|
|
real :: h_inner_max |
| 476 |
|
|
integer :: i,j, k, kk, nlev |
| 477 |
|
|
|
| 478 |
|
|
|
| 479 |
|
|
nlev = size(t,3) |
| 480 |
|
|
|
| 481 |
|
|
!assign z_half to zm, and set to zero any values of zm < 0. |
| 482 |
|
|
!the setting to zero is necessary so that when using eta model |
| 483 |
|
|
!below ground half levels will have zero k_m and k_t |
| 484 |
|
|
zm = z_half |
| 485 |
|
|
if (present(kbot)) then |
| 486 |
|
|
where(zm < 0.) |
| 487 |
|
|
zm = 0. |
| 488 |
|
|
end where |
| 489 |
|
|
end if |
| 490 |
|
|
|
| 491 |
|
|
h_inner = frac_inner*h |
| 492 |
|
|
h_inner_max = maxval(h_inner) |
| 493 |
|
|
|
| 494 |
|
|
kk = nlev |
| 495 |
|
|
do k = 2, nlev |
| 496 |
|
|
if( minval(zm(:,:,k)) < h_inner_max) then |
| 497 |
|
|
kk = k |
| 498 |
|
|
exit |
| 499 |
|
|
end if |
| 500 |
|
|
end do |
| 501 |
|
|
|
| 502 |
|
|
k_m = 0.0 |
| 503 |
|
|
k_t = 0.0 |
| 504 |
|
|
|
| 505 |
|
|
call mo_diff(h_inner , u_star, b_star, k_m_ref , k_t_ref, myThid ) |
| 506 |
|
|
call mo_diff(zm(:,:,kk:nlev), u_star, b_star, k_m(:,:,kk:nlev), k_t(:,:,kk:nlev), & |
| 507 |
|
|
myThid ) |
| 508 |
|
|
|
| 509 |
|
|
do k = 2, nlev |
| 510 |
|
|
where(zm(:,:,k) >= h_inner .and. zm(:,:,k) < h) |
| 511 |
|
|
factor = (zm(:,:,k)/h_inner)* & |
| 512 |
|
|
(1.0 - (zm(:,:,k) - h_inner)/(h - h_inner))**2 |
| 513 |
|
|
k_m(:,:,k) = k_m_ref*factor |
| 514 |
|
|
k_t(:,:,k) = k_t_ref*factor |
| 515 |
|
|
end where |
| 516 |
|
|
end do |
| 517 |
|
|
|
| 518 |
|
|
return |
| 519 |
|
|
end subroutine diffusivity_pbl |
| 520 |
|
|
|
| 521 |
|
|
!======================================================================= |
| 522 |
|
|
|
| 523 |
|
|
subroutine diffusivity_pbl_mcm(u, v, t, p_full, p_half, z_full, z_half, & |
| 524 |
|
|
h, k_m, k_t, myThid) |
| 525 |
|
|
|
| 526 |
|
|
real, intent(in) , dimension(:,:,:) :: u, v, t, z_full, z_half |
| 527 |
|
|
real, intent(in) , dimension(:,:,:) :: p_full, p_half |
| 528 |
|
|
real, intent(in) , dimension(:,:) :: h |
| 529 |
|
|
real, intent(inout) , dimension(:,:,:) :: k_m, k_t |
| 530 |
|
|
integer, intent(in) :: myThid |
| 531 |
|
|
|
| 532 |
|
|
integer :: k, nlev |
| 533 |
|
|
real, dimension(size(z_full,1),size(z_full,2)) :: elmix, htcrit |
| 534 |
|
|
real, dimension(size(z_full,1),size(z_full,2)) :: delta_u, delta_v, delta_z |
| 535 |
|
|
|
| 536 |
|
|
real :: htcrit_ss |
| 537 |
|
|
real :: h_ss |
| 538 |
|
|
real, dimension(size(z_full,1),size(z_full,2)) :: sig_half, z_half_ss, elmix_ss |
| 539 |
|
|
|
| 540 |
|
|
! htcrit_ss = height at which mixing length is a maximum (75m) |
| 541 |
|
|
|
| 542 |
|
|
|
| 543 |
|
|
! h_ss = height at which mixing length vanishes (4900m) |
| 544 |
|
|
! elmix_ss = mixing length |
| 545 |
|
|
|
| 546 |
|
|
! Define some constants: |
| 547 |
|
|
! salaps = standard atmospheric lapse rate (K/m) |
| 548 |
|
|
! tsfc = idealized global mean surface temperature (15C) |
| 549 |
|
|
real :: tsfc = 288.16 |
| 550 |
|
|
real :: salaps = -6.5e-3 |
| 551 |
|
|
|
| 552 |
|
|
nlev = size(z_full,3) |
| 553 |
|
|
|
| 554 |
|
|
k_m = 0. |
| 555 |
|
|
|
| 556 |
|
|
h_ss = depth_0 |
| 557 |
|
|
htcrit_ss = frac_inner*h_ss |
| 558 |
|
|
|
| 559 |
|
|
do k = 2, nlev |
| 560 |
|
|
|
| 561 |
|
|
! TK mods 8/13/01: (code derived from SS) |
| 562 |
|
|
! Compute the height of each half level assuming a constant |
| 563 |
|
|
! standard lapse rate using the above procedure. |
| 564 |
|
|
! WARNING: These should be used with caution. They will |
| 565 |
|
|
! have large errors above the tropopause. |
| 566 |
|
|
|
| 567 |
|
|
! In order to determine the height, the layer mean temperature |
| 568 |
|
|
! from the surface to that level is required. A surface |
| 569 |
|
|
! temperature of 15 deg Celsius and a standard lapse rate of |
| 570 |
|
|
! -6.5 deg/km will be used to estimate an average temperature |
| 571 |
|
|
! profile. |
| 572 |
|
|
|
| 573 |
|
|
sig_half = p_half(:,:,k)/p_half(:,:,nlev+1) |
| 574 |
|
|
z_half_ss = -rdgas * .5*(tsfc+tsfc*(sig_half**(-rdgas*salaps/grav))) * alog(sig_half)/grav |
| 575 |
|
|
|
| 576 |
|
|
!compute mixing length as in SS (no geographical variation) |
| 577 |
|
|
elmix_ss = 0. |
| 578 |
|
|
|
| 579 |
|
|
where (z_half_ss < htcrit_ss .and. z_half_ss > 0.) |
| 580 |
|
|
elmix_ss = vonkarm*z_half_ss |
| 581 |
|
|
endwhere |
| 582 |
|
|
where (z_half_ss >= htcrit_ss .and. z_half_ss < h_ss) |
| 583 |
|
|
elmix_ss = vonkarm*htcrit_ss*(h_ss-z_half_ss)/(h_ss-htcrit_ss) |
| 584 |
|
|
endwhere |
| 585 |
|
|
|
| 586 |
|
|
delta_z = rdgas*0.5*(t(:,:,k)+t(:,:,k-1))*(p_full(:,:,k)-p_full(:,:,k-1))/& |
| 587 |
|
|
(grav*p_half(:,:,k)) |
| 588 |
|
|
delta_u = u(:,:,k-1) - u(:,:,k) |
| 589 |
|
|
delta_v = v(:,:,k-1) - v(:,:,k) |
| 590 |
|
|
|
| 591 |
|
|
k_m(:,:,k) = elmix_ss * elmix_ss *& |
| 592 |
|
|
sqrt(delta_u*delta_u + delta_v*delta_v)/delta_z |
| 593 |
|
|
|
| 594 |
|
|
end do |
| 595 |
|
|
|
| 596 |
|
|
k_t = k_m |
| 597 |
|
|
|
| 598 |
|
|
return |
| 599 |
|
|
end subroutine diffusivity_pbl_mcm |
| 600 |
|
|
|
| 601 |
|
|
!======================================================================= |
| 602 |
|
|
|
| 603 |
|
|
subroutine diffusivity_free(t, u, v, z, zz, h, k_m, k_t, myThid) |
| 604 |
|
|
|
| 605 |
|
|
real, intent(in) , dimension(:,:,:) :: t, u, v, z, zz |
| 606 |
|
|
real, intent(in) , dimension(:,:) :: h |
| 607 |
|
|
real, intent(inout) , dimension(:,:,:) :: k_m, k_t |
| 608 |
|
|
integer, intent(in) :: myThid |
| 609 |
|
|
|
| 610 |
|
|
real, dimension(size(t,1),size(t,2)) :: dz, b, speed2, rich, fri, & |
| 611 |
|
|
alpz, fri2 |
| 612 |
|
|
integer :: k |
| 613 |
|
|
|
| 614 |
|
|
do k = 2, size(t,3) |
| 615 |
|
|
|
| 616 |
|
|
!---------------------------------------------------------------------- |
| 617 |
|
|
! define the richardson number. set it to zero if it is negative. save |
| 618 |
|
|
! a copy of it for later use (rich2). |
| 619 |
|
|
!---------------------------------------------------------------------- |
| 620 |
|
|
dz = z(:,:,k-1) - z(:,:,k) |
| 621 |
|
|
b = grav*(t(:,:,k-1)-t(:,:,k))/t(:,:,k) |
| 622 |
|
|
speed2 = (u(:,:,k-1) - u(:,:,k))**2 + (v(:,:,k-1) - v(:,:,k))**2 |
| 623 |
|
|
rich= b*dz/(speed2+small) |
| 624 |
|
|
rich = max(rich, 0.0) |
| 625 |
|
|
|
| 626 |
|
|
if (free_atm_skyhi_diff) then |
| 627 |
|
|
!--------------------------------------------------------------------- |
| 628 |
|
|
! limit the standard richardson number to between 0 and the critical |
| 629 |
|
|
! value (rich2). compute the richardson number factor needed in the |
| 630 |
|
|
! eddy mixing coefficient using this standard richardson number. |
| 631 |
|
|
!--------------------------------------------------------------------- |
| 632 |
|
|
where (rich(:,:) >= rich_crit_diff) |
| 633 |
|
|
fri2(:,:) = 0.0 |
| 634 |
|
|
elsewhere |
| 635 |
|
|
fri2(:,:) = (1.0 - rich/rich_crit_diff)**2 |
| 636 |
|
|
endwhere |
| 637 |
|
|
endif |
| 638 |
|
|
|
| 639 |
|
|
!--------------------------------------------------------------------- |
| 640 |
|
|
! if ampns is activated, compute the delta z factor. define rich |
| 641 |
|
|
! including this factor. |
| 642 |
|
|
!--------------------------------------------------------------------- |
| 643 |
|
|
if (ampns) then |
| 644 |
|
|
alpz(:,:) = MIN ( (1. + 1.e-04*(dz(:,:)**1.5)), ampns_max) |
| 645 |
|
|
rich(:,:) = rich(:,:) / alpz(:,:) |
| 646 |
|
|
endif |
| 647 |
|
|
|
| 648 |
|
|
!--------------------------------------------------------------------- |
| 649 |
|
|
! compute the richardson number factor to be used in the eddy |
| 650 |
|
|
! mixing coefficient. if ampns is on, this value includes it; other- |
| 651 |
|
|
! wise it does not. |
| 652 |
|
|
!--------------------------------------------------------------------- |
| 653 |
|
|
fri(:,:) = (1.0 - rich/rich_crit_diff)**2 |
| 654 |
|
|
|
| 655 |
|
|
!--------------------------------------------------------------------- |
| 656 |
|
|
! compute the eddy mixing coefficients in the free atmosphere ( zz |
| 657 |
|
|
! > h). in the non-ampns case, values are obtained only when the |
| 658 |
|
|
! standard richardson number is sub-critical; in the ampns case values |
| 659 |
|
|
! are obtained only when the richardson number computed with the |
| 660 |
|
|
! ampns factor is sub critical. when the ampns factor is activated, |
| 661 |
|
|
! it is also included in the mixing coefficient. the value of mixing |
| 662 |
|
|
! for temperature, etc. is reduced dependent on the ri stability |
| 663 |
|
|
! factor calculated without the ampns factor. |
| 664 |
|
|
!--------------------------------------------------------------------- |
| 665 |
|
|
if (free_atm_skyhi_diff) then |
| 666 |
|
|
|
| 667 |
|
|
!--------------------------------------------------------------------- |
| 668 |
|
|
! this is the skyhi-like formulation -- possible ampns factor, ratio |
| 669 |
|
|
! of k_m to k_t defined based on computed stability factor. |
| 670 |
|
|
!--------------------------------------------------------------------- |
| 671 |
|
|
if (ampns) then |
| 672 |
|
|
where (rich < rich_crit_diff .and. zz(:,:,k) > h) |
| 673 |
|
|
k_m(:,:,k) = mix_len*mix_len*sqrt(speed2)*fri(:,:)* & |
| 674 |
|
|
( 1. + 1.e-04*(dz(:,:)**1.5))/dz |
| 675 |
|
|
k_t(:,:,k) = k_m(:,:,k)* (0.1 + 0.9*fri2(:,:)) |
| 676 |
|
|
end where |
| 677 |
|
|
else |
| 678 |
|
|
where (rich < rich_crit_diff .and. zz(:,:,k) > h) |
| 679 |
|
|
k_m(:,:,k) = mix_len*mix_len*sqrt(speed2)*fri(:,:)/dz |
| 680 |
|
|
k_t(:,:,k) = k_m(:,:,k)* (0.1 + 0.9*fri2(:,:)) |
| 681 |
|
|
end where |
| 682 |
|
|
endif |
| 683 |
|
|
else |
| 684 |
|
|
|
| 685 |
|
|
!--------------------------------------------------------------------- |
| 686 |
|
|
! this is the non-skyhi-like formulation -- no ampns factor, ratio |
| 687 |
|
|
! of k_m to k_t defined by rich_prandtl. |
| 688 |
|
|
!--------------------------------------------------------------------- |
| 689 |
|
|
where (rich < rich_crit_diff .and. zz(:,:,k) > h) |
| 690 |
|
|
k_t(:,:,k) = mix_len*mix_len*sqrt(speed2)*fri(:,:)/dz |
| 691 |
|
|
k_m(:,:,k) = k_t(:,:,k)*rich_prandtl |
| 692 |
|
|
end where |
| 693 |
|
|
end if |
| 694 |
|
|
end do |
| 695 |
|
|
|
| 696 |
|
|
|
| 697 |
|
|
end subroutine diffusivity_free |
| 698 |
|
|
|
| 699 |
|
|
!======================================================================= |
| 700 |
|
|
|
| 701 |
|
|
subroutine molecular_diff ( temp, press, k_m, k_t, myThid) |
| 702 |
|
|
|
| 703 |
|
|
real, intent(in), dimension (:,:,:) :: temp, press |
| 704 |
|
|
real, intent(inout), dimension (:,:,:) :: k_m, k_t |
| 705 |
|
|
integer, intent(in) :: myThid |
| 706 |
|
|
|
| 707 |
|
|
real, dimension (size(temp,1), size(temp,2)) :: temp_half, & |
| 708 |
|
|
rho_half, rbop2d |
| 709 |
|
|
integer :: k |
| 710 |
|
|
|
| 711 |
|
|
!--------------------------------------------------------------------- |
| 712 |
|
|
|
| 713 |
|
|
do k=2,size(temp,3) |
| 714 |
|
|
temp_half(:,:) = 0.5*(temp(:,:,k) + temp(:,:,k-1)) |
| 715 |
|
|
rho_half(:,:) = press(:,:,k)/(rdgas*temp_half(:,:) ) |
| 716 |
|
|
rbop2d(:,:) = beta*temp_half(:,:)*sqrt(temp_half(:,:))/ & |
| 717 |
|
|
(rho_half(:,:)*(temp_half(:,:)+rbop1)) |
| 718 |
|
|
k_m(:,:,k) = rbop2d(:,:) |
| 719 |
|
|
k_t(:,:,k) = rbop2d(:,:)*rbop2 |
| 720 |
|
|
end do |
| 721 |
|
|
|
| 722 |
|
|
k_m(:,:,1) = 0.0 |
| 723 |
|
|
k_t(:,:,1) = 0.0 |
| 724 |
|
|
|
| 725 |
|
|
|
| 726 |
|
|
|
| 727 |
|
|
end subroutine molecular_diff |
| 728 |
|
|
|
| 729 |
|
|
|
| 730 |
|
|
|
| 731 |
|
|
!======================================================================= |
| 732 |
|
|
|
| 733 |
|
|
subroutine diffusivity_entr(t, z, h, u_star, b_star, k_m, k_t, myThid) |
| 734 |
|
|
|
| 735 |
|
|
real, intent(in) , dimension(:,:,:) :: t, z |
| 736 |
|
|
real, intent(in) , dimension(:,:) :: h, u_star, b_star |
| 737 |
|
|
real, intent(inout) , dimension(:,:,:) :: k_m, k_t |
| 738 |
|
|
integer, intent(in) :: myThid |
| 739 |
|
|
|
| 740 |
|
|
integer :: k, nlev |
| 741 |
|
|
|
| 742 |
|
|
nlev=size(t,3) |
| 743 |
|
|
|
| 744 |
|
|
do k = 2,nlev |
| 745 |
|
|
where (b_star .gt. 0. .and. z(:,:,k-1) .gt. h .and. & |
| 746 |
|
|
z(:,:,k) .le. h) |
| 747 |
|
|
k_t(:,:,k) = (z(:,:,k-1)-z(:,:,k))*entr_ratio*t(:,:,k)* & |
| 748 |
|
|
u_star*b_star/grav/max(small,t(:,:,k-1)-t(:,:,k)) |
| 749 |
|
|
k_m(:,:,k) = k_t(:,:,k) |
| 750 |
|
|
end where |
| 751 |
|
|
enddo |
| 752 |
|
|
end subroutine diffusivity_entr |
| 753 |
|
|
|
| 754 |
|
|
!======================================================================= |
| 755 |
|
|
|
| 756 |
|
|
end module diffusivity_mod |
| 757 |
|
|
|
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