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micro_pumas_utils.F90
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module micro_pumas_utils
!--------------------------------------------------------------------------
!
! This module contains process rates and utility functions used by the MG
! microphysics.
!
! Original MG authors: Andrew Gettelman, Hugh Morrison
! Contributions from: Peter Caldwell, Xiaohong Liu and Steve Ghan
!
! Separated from MG 1.5 by B. Eaton.
! Separated module switched to MG 2.0 and further changes by S. Santos.
!
! for questions contact Hugh Morrison, Andrew Gettelman
! e-mail: morrison@ucar.edu, andrew@ucar.edu
!
!--------------------------------------------------------------------------
!
! List of required external functions that must be supplied:
! gamma --> standard mathematical gamma function (if gamma is an
! intrinsic, define HAVE_GAMMA_INTRINSICS)
!
!--------------------------------------------------------------------------
!
! Constants that must be specified in the "init" method (module variables):
!
! kind kind of reals (to verify correct linkage only) -
! gravit acceleration due to gravity m s-2
! rair dry air gas constant for air J kg-1 K-1
! rh2o gas constant for water vapor J kg-1 K-1
! cpair specific heat at constant pressure for dry air J kg-1 K-1
! tmelt temperature of melting point for water K
! latvap latent heat of vaporization J kg-1
! latice latent heat of fusion J kg-1
!
!--------------------------------------------------------------------------
use pumas_kinds, only: r8=>kind_r8, i8=>kind_i8
#ifndef HAVE_GAMMA_INTRINSICS
use pumas_gamma_function, only: gamma=>pumas_gamma
#endif
implicit none
private
save
public :: &
micro_pumas_utils_init, &
size_dist_param_liq, &
size_dist_param_basic, &
avg_diameter, &
rising_factorial, &
ice_deposition_sublimation, &
ice_deposition_sublimation_mg4, & !! ktc
sb2001v2_liq_autoconversion,&
sb2001v2_accre_cld_water_rain,&
kk2000_liq_autoconversion, &
ice_autoconversion, &
immersion_freezing, &
contact_freezing, &
snow_self_aggregation, &
ice_self_aggregation, & !! mg4 added for using instead of snow_self_agg
accrete_cloud_water_snow, &
accrete_cloud_water_ice, & !! mg4 added for using instead of cloud_water_snow
secondary_ice_production, &
accrete_rain_snow, &
accrete_rain_ice, & !! mg4 added for using instead of rain_snow
heterogeneous_rain_freezing, &
accrete_cloud_water_rain, &
self_collection_rain, &
accrete_cloud_ice_snow, &
evaporate_sublimate_precip, &
bergeron_process_snow, &
graupel_collecting_snow, &
graupel_collecting_rain, &
graupel_collecting_cld_water, &
graupel_riming_liquid_snow, &
graupel_rain_riming_snow, &
graupel_rime_splintering, &
vapor_deposition_onto_snow, &
evaporate_sublimate_precip_graupel, &
evaporate_sublimate_precip_mg4, &
evaporate_sublimate_precip_graupel_mg4, &
access_lookup_table, & !! mg4
access_lookup_table_coll, & !! mg4
init_lookup_table, & !! mg4
avg_diameter_vec
integer, parameter, public :: VLENS = 128 ! vector length of a GPU compute kernel
public :: MGHydrometeorProps
type :: MGHydrometeorProps
! Density (kg/m^3)
real(r8) :: rho
! Information for size calculations.
! Basic calculation of mean size is:
! lambda = (shape_coef*nic/qic)^(1/eff_dim)
! Then lambda is constrained by bounds.
real(r8) :: eff_dim
real(r8) :: shape_coef
real(r8) :: lambda_bounds(2)
! Minimum average particle mass (kg).
! Limit is applied at the beginning of the size distribution calculations.
real(r8) :: min_mean_mass
end type MGHydrometeorProps
interface MGHydrometeorProps
module procedure NewMGHydrometeorProps
end interface
type(MGHydrometeorProps), public :: mg_liq_props
type(MGHydrometeorProps), public :: mg_ice_props
type(MGHydrometeorProps), public :: mg_rain_props
type(MGHydrometeorProps), public :: mg_snow_props
type(MGHydrometeorProps), public :: mg_graupel_props
type(MGHydrometeorProps), public :: mg_hail_props
interface size_dist_param_liq
module procedure size_dist_param_liq_2D
module procedure size_dist_param_liq_vect
module procedure size_dist_param_liq_line
end interface
interface size_dist_param_basic
module procedure size_dist_param_basic_2D
module procedure size_dist_param_basic_vect
module procedure size_dist_param_basic_line
end interface
interface calc_ab
module procedure calc_ab_line
module procedure calc_ab_vect
end interface
!=================================================
! Public module parameters (mostly for MG itself)
!=================================================
! Pi to 20 digits; more than enough to reach the limit of double precision.
real(r8), parameter, public :: pi = 3.14159265358979323846_r8
! "One minus small number": number near unity for round-off issues.
real(r8), parameter, public :: omsm = 1._r8 - 1.e-5_r8
! Smallest mixing ratio considered in microphysics.
real(r8), parameter, public :: qsmall = 1.e-18_r8
! minimum allowed cloud fraction
real(r8), parameter, public :: mincld = 0.0001_r8
real(r8), parameter, public :: rhosn = 250._r8 ! bulk density snow
real(r8), parameter, public :: rhoi = 500._r8 ! bulk density ice
real(r8), parameter, public :: rhow = 1000._r8 ! bulk density liquid
real(r8), parameter, public :: rhows = 917._r8 ! bulk density water solid
!Hail and Graupel (set in MG3)
real(r8), parameter, public :: rhog = 500._r8
real(r8), parameter, public :: rhoh = 900._r8
! fall speed parameters, V = aD^b (V is in m/s)
! droplets
real(r8), parameter, public :: ac = 3.e7_r8
real(r8), parameter, public :: bc = 2._r8
! snow
real(r8), parameter, public :: as = 11.72_r8
real(r8), parameter, public :: bs = 0.41_r8
! cloud ice
real(r8), parameter, public :: ai = 700._r8
real(r8), parameter, public :: bi = 1._r8
! small cloud ice (r< 10 um) - sphere, bulk density
real(r8), parameter, public :: aj = ac*((rhoi/rhows)**(bc/3._r8))*rhows/rhow
real(r8), parameter, public :: bj = bc
! rain
real(r8), parameter, public :: ar = 841.99667_r8
real(r8), parameter, public :: br = 0.8_r8
! graupel
real(r8), parameter, public :: ag = 19.3_r8
real(r8), parameter, public :: bg = 0.37_r8
! hail
real(r8), parameter, public :: ah = 114.5_r8
real(r8), parameter, public :: bh = 0.5_r8
! mass of new crystal due to aerosol freezing and growth (kg)
! Make this consistent with the lower bound, to support UTLS and
! stratospheric ice, and the smaller ice size limit.
real(r8), parameter, public :: mi0 = 4._r8/3._r8*pi*rhoi*(1.e-6_r8)**3
! mass of new graupel particle (assume same as mi0 for now, may want to make bigger?)
!real(r8), parameter, public :: mg0 = 4._r8/3._r8*pi*rhoi*(1.e-6_r8)**3
!or set based on M2005:
real(r8), parameter, public :: mg0 = 1.6e-10_r8
! radius of contact nuclei
real(r8), parameter, public :: mmult = 4._r8/3._r8*pi*rhoi*(5.e-6_r8)**3
!=================================================
! Private module parameters
!=================================================
! Signaling NaN bit pattern that represents a limiter that's turned off.
integer(i8), parameter :: limiter_off = int(Z'7FF1111111111111', i8)
! alternate threshold used for some in-cloud mmr
real(r8), parameter, public :: icsmall = 1.e-8_r8
! particle mass-diameter relationship
! currently we assume spherical particles for cloud ice/snow
! m = cD^d
! exponent
real(r8), parameter :: dsph = 3._r8
! Bounds for mean diameter for different constituents.
real(r8), parameter :: lam_bnd_rain(2) = 1._r8/[500.e-6_r8, 20.e-6_r8]
real(r8), parameter :: lam_bnd_snow(2) = 1._r8/[2000.e-6_r8, 10.e-6_r8]
! Minimum average mass of particles.
real(r8), parameter :: min_mean_mass_liq = 1.e-20_r8
real(r8), parameter :: min_mean_mass_ice = 1.e-20_r8
! ventilation parameters
! for snow
real(r8), parameter :: f1s = 0.86_r8
real(r8), parameter :: f2s = 0.28_r8
! for rain
real(r8), parameter :: f1r = 0.78_r8
real(r8), parameter :: f2r = 0.308_r8
! collection efficiencies
! aggregation of cloud ice and snow
real(r8), parameter :: eii = 0.5_r8
! collection efficiency, ice-droplet collisions
real(r8), parameter, public :: ecid = 0.7_r8
! collection efficiency between droplets/rain and snow/rain
real(r8), parameter, public :: ecr = 1.0_r8
! immersion freezing parameters, bigg 1953
real(r8), parameter :: bimm = 100._r8
real(r8), parameter :: aimm = 0.66_r8
! Mass of each raindrop created from autoconversion.
real(r8), parameter :: droplet_mass_25um = 4._r8/3._r8*pi*rhow*(25.e-6_r8)**3
real(r8), parameter :: droplet_mass_40um = 4._r8/3._r8*pi*rhow*(40.e-6_r8)**3
!!!!!!
! MG4 look up table parameters
!!!!!!
! ice microphysics lookup table array dimensions
integer, parameter, public :: tsize = 3
integer, parameter, public :: isize = 20
integer, parameter, public :: jsize = 20
integer, parameter, public :: rcollsize = 30
! number of ice microphysical quantities used from lookup table
integer, parameter, public :: tabsize = 14
! number of ice-rain collection microphysical quantities used from lookup table
integer, parameter, public :: colltabsize = 2
!ice lookup table values
real(r8) :: itab(tsize,isize,jsize,tabsize)
!ice lookup table values for ice-rain collision/collection
real(r8) :: itabcoll(tsize,isize,jsize,rcollsize,colltabsize)
private :: itab,itabcoll
!=========================================================
! Constants set in initialization
!=========================================================
! Set using arguments to micro_pumas_init
real(r8) :: rv ! water vapor gas constant
real(r8) :: cpp ! specific heat of dry air
real(r8) :: tmelt ! freezing point of water (K)
real(r8) :: ra ! dry air gas constant
! latent heats of:
real(r8) :: xxlv ! vaporization
real(r8) :: xlf ! freezing
real(r8) :: xxls ! sublimation
! additional constants to help speed up code
real(r8) :: gamma_bs_plus3
real(r8) :: gamma_half_br_plus5
real(r8) :: gamma_half_bs_plus5
real(r8) :: gamma_2bs_plus2
!$acc declare create (rv,cpp,tmelt,xxlv,xxls,gamma_bs_plus3, &
!$acc gamma_half_br_plus5,gamma_half_bs_plus5, &
!$acc gamma_2bs_plus2)
!=========================================================
! Utilities that are cheaper if the compiler knows that
! some argument is an integer.
!=========================================================
interface rising_factorial
module procedure rising_factorial_r8
module procedure rising_factorial_r8_vec
module procedure rising_factorial_integer
module procedure rising_factorial_integer_vec
end interface rising_factorial
interface var_coef
module procedure var_coef_r8
module procedure var_coef_r8_vect
module procedure var_coef_integer
module procedure var_coef_integer_vect
end interface var_coef
!==========================================================================
contains
!==========================================================================
! Initialize module variables.
!
! "kind" serves no purpose here except to check for unlikely linking
! issues; always pass in the kind for a double precision real.
!
! "errstring" is the only output; it is blank if there is no error, or set
! to a message if there is an error.
!
! Check the list at the top of this module for descriptions of all other
! arguments.
subroutine micro_pumas_utils_init( kind, rair, rh2o, cpair, tmelt_in, latvap, &
latice, dcs, errstring)
integer, intent(in) :: kind
real(r8), intent(in) :: rair
real(r8), intent(in) :: rh2o
real(r8), intent(in) :: cpair
real(r8), intent(in) :: tmelt_in
real(r8), intent(in) :: latvap
real(r8), intent(in) :: latice
real(r8), intent(in) :: dcs
character(128), intent(out) :: errstring
! Name this array to workaround an XLF bug (otherwise could just use the
! expression that sets it).
real(r8) :: ice_lambda_bounds(2)
!-----------------------------------------------------------------------
errstring = ' '
if( kind .ne. r8 ) then
errstring = 'micro_pumas_init: KIND of reals does not match'
return
endif
! declarations for MG code (transforms variable names)
rv = rh2o ! water vapor gas constant
cpp = cpair ! specific heat of dry air
tmelt = tmelt_in
ra = rair ! dry air gas constant
! latent heats
xxlv = latvap ! latent heat vaporization
xlf = latice ! latent heat freezing
xxls = xxlv + xlf ! latent heat of sublimation
! Define constants to help speed up code (this limits calls to gamma function)
gamma_bs_plus3 = gamma(3._r8+bs)
gamma_half_br_plus5 = gamma(5._r8/2._r8+br/2._r8)
gamma_half_bs_plus5 = gamma(5._r8/2._r8+bs/2._r8)
gamma_2bs_plus2 = gamma(2._r8*bs+2._r8)
! Don't specify lambda bounds for cloud liquid, as they are determined by
! pgam dynamically.
mg_liq_props = MGHydrometeorProps(rhow, dsph, &
min_mean_mass=min_mean_mass_liq)
! Mean ice diameter can not grow bigger than twice the autoconversion
! threshold for snow.
ice_lambda_bounds(1) = 1._r8/2._r8*dcs
ice_lambda_bounds(2) = 1._r8/1.e-6_r8
mg_ice_props = MGHydrometeorProps(rhoi, dsph, &
ice_lambda_bounds, min_mean_mass_ice)
mg_rain_props = MGHydrometeorProps(rhow, dsph, lam_bnd_rain)
mg_snow_props = MGHydrometeorProps(rhosn, dsph, lam_bnd_snow)
mg_graupel_props = MGHydrometeorProps(rhog, dsph, lam_bnd_snow)
mg_hail_props = MGHydrometeorProps(rhoh, dsph, lam_bnd_snow)
!$acc update device (rv,cpp,tmelt,xxlv,xxls,gamma_bs_plus3, &
!$acc gamma_half_br_plus5,gamma_half_bs_plus5, &
!$acc gamma_2bs_plus2)
end subroutine micro_pumas_utils_init
! Constructor for a constituent property object.
function NewMGHydrometeorProps(rho, eff_dim, lambda_bounds, min_mean_mass) &
result(res)
real(r8), intent(in) :: rho, eff_dim
real(r8), intent(in), optional :: lambda_bounds(2), min_mean_mass
type(MGHydrometeorProps) :: res
res%rho = rho
res%eff_dim = eff_dim
if (present(lambda_bounds)) then
res%lambda_bounds = lambda_bounds
else
res%lambda_bounds = no_limiter()
end if
if (present(min_mean_mass)) then
res%min_mean_mass = min_mean_mass
else
res%min_mean_mass = no_limiter()
end if
res%shape_coef = rho*pi*gamma(eff_dim+1._r8)/6._r8
end function NewMGHydrometeorProps
!========================================================================
!FORMULAS
!========================================================================
! Use gamma function to implement rising factorial extended to the reals.
subroutine rising_factorial_r8(x, n, res)
!$acc routine seq
real(r8), intent(in) :: x, n
real(r8), intent(out) :: res
res = gamma(x+n)/gamma(x)
end subroutine rising_factorial_r8
subroutine rising_factorial_r8_vec(x, n, res,vlen)
integer, intent(in) :: vlen
real(r8), intent(in) :: x(vlen), n
real(r8), intent(out) :: res(vlen)
integer :: i
real(r8) :: tmp
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i=1,vlen
tmp = x(i)+n
res(i) = gamma(tmp)
tmp = gamma(x(i))
res(i) = res(i)/tmp
end do
!$acc end parallel
end subroutine rising_factorial_r8_vec
! Rising factorial can be performed much cheaper if n is a small integer.
subroutine rising_factorial_integer(x, n, res)
!$acc routine seq
real(r8), intent(in) :: x
integer, intent(in) :: n
real(r8), intent(out) :: res
integer :: i
real(r8) :: factor
res = 1._r8
factor = x
!$acc loop seq
do i = 1, n
res = res * factor
factor = factor + 1._r8
end do
end subroutine rising_factorial_integer
subroutine rising_factorial_integer_vec(x, n, res,vlen)
integer, intent(in) :: vlen
real(r8), intent(in) :: x(vlen)
integer, intent(in) :: n
real(r8), intent(out) :: res(vlen)
integer :: i,j
real(r8) :: factor
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i=1,vlen
res(i) = 1._r8
factor = x(i)
if (n == 3) then
res(i) = res(i) * factor
factor = factor + 1._r8
res(i) = res(i) * factor
factor = factor + 1._r8
res(i) = res(i) * factor
elseif (n == 2) then
res(i) = res(i) * factor
factor = factor + 1._r8
res(i) = res(i) * factor
else
!$acc loop seq
do j = 1, n
res(i) = res(i) * factor
factor = factor + 1._r8
end do
end if
end do
!$acc end parallel
end subroutine rising_factorial_integer_vec
! Calculate correction due to latent heat for evaporation/sublimation
subroutine calc_ab_line(t, qv, xxl, ab)
!$acc routine seq
real(r8), intent(in) :: t ! Temperature
real(r8), intent(in) :: qv ! Saturation vapor pressure
real(r8), intent(in) :: xxl ! Latent heat
real(r8), intent(out) :: ab
real(r8) :: dqsdt
dqsdt = xxl*qv / (rv * t**2)
ab = 1._r8 + dqsdt*xxl/cpp
end subroutine calc_ab_line
! Calculate correction due to latent heat for evaporation/sublimation
subroutine calc_ab_vect(t, qv, xxl, ab, vlen)
integer, intent(in) :: vlen
real(r8), intent(in) :: t(vlen) ! Temperature
real(r8), intent(in) :: qv(vlen) ! Saturation vapor pressure
real(r8), intent(in) :: xxl ! Latent heat
real(r8), intent(out) :: ab(vlen)
real(r8) :: dqsdt
integer :: i
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i=1,vlen
dqsdt = xxl*qv(i) / (rv * t(i)**2)
ab(i) = 1._r8 + dqsdt*xxl/cpp
end do
!$acc end parallel
end subroutine calc_ab_vect
! get cloud droplet size distribution parameters
subroutine size_dist_param_liq_line(props, qcic, ncic, rho, pgam, lamc)
!$acc routine seq
type(MGHydrometeorProps), intent(in) :: props
real(r8), intent(in) :: qcic
real(r8), intent(inout) :: ncic
real(r8), intent(in) :: rho
real(r8), intent(out) :: pgam
real(r8), intent(out) :: lamc
! local variables
type(MGHydrometeorProps) :: props_loc
real(r8) :: tmp
if (qcic > qsmall) then
! Local copy of properties that can be modified.
! (Elemental routines that operate on arrays can't modify scalar
! arguments.)
props_loc = props
! Get pgam from fit Rotstayn and Liu 2003 (changed from Martin 1994 for CAM6)
pgam = 1.0_r8 - 0.7_r8 * exp(-0.008_r8*1.e-6_r8*ncic*rho)
pgam = 1._r8/(pgam**2) - 1._r8
pgam = max(pgam, 2._r8)
! Set coefficient for use in size_dist_param_basic.
! The 3D case is so common and optimizable that we specialize it:
if (props_loc%eff_dim == 3._r8) then
call rising_factorial(pgam+1._r8, 3, tmp)
props_loc%shape_coef = pi / 6._r8 * props_loc%rho * tmp
else
call rising_factorial(pgam+1._r8, props_loc%eff_dim, tmp)
props_loc%shape_coef = pi / 6._r8 * props_loc%rho * tmp
end if
! Limit to between 2 and 50 microns mean size.
props_loc%lambda_bounds(1) = (pgam+1._r8)*1._r8/50.e-6_r8
props_loc%lambda_bounds(2) = (pgam+1._r8)*1._r8/2.e-6_r8
call size_dist_param_basic(props_loc, qcic, ncic, lamc)
else
! pgam not calculated in this case, so set it to a value likely to
! cause an error if it is accidentally used
! (gamma function undefined for negative integers)
pgam = -100._r8
lamc = 0._r8
end if
end subroutine size_dist_param_liq_line
! get cloud droplet size distribution parameters
subroutine size_dist_param_liq_2D(props, qcic, ncic, rho, pgam, lamc, dim1, dim2)
type(mghydrometeorprops), intent(in) :: props
integer, intent(in) :: dim1, dim2
real(r8), dimension(dim1,dim2), intent(in) :: qcic
real(r8), dimension(dim1,dim2), intent(inout) :: ncic
real(r8), dimension(dim1,dim2), intent(in) :: rho
real(r8), dimension(dim1,dim2), intent(out) :: pgam
real(r8), dimension(dim1,dim2), intent(out) :: lamc
! local variables
integer :: i, k
real(r8) :: tmp(dim1,dim2),pgamp1(dim1,dim2)
real(r8) :: shapeC(dim1,dim2),lbnd(dim1,dim2),ubnd(dim1,dim2)
!$acc data create (tmp,pgamp1,shapeC,lbnd,ubnd)
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector collapse(2)
do k = 1, dim2
do i = 1, dim1
if (qcic(i,k) > qsmall) then
! Get pgam from fit Rotstayn and Liu 2003 (changed from Martin 1994 for CAM6)
pgam(i,k) = 1.0_r8 - 0.7_r8 * exp(-0.008_r8*1.e-6_r8*ncic(i,k)*rho(i,k))
pgam(i,k) = 1._r8/(pgam(i,k)**2) - 1._r8
pgam(i,k) = max(pgam(i,k), 2._r8)
pgamp1(i,k) = pgam(i,k)+1._r8
else
pgamp1(i,k) = 0._r8
end if
end do
end do
!$acc end parallel
! Set coefficient for use in size_dist_param_basic.
! The 3D case is so common and optimizable that we specialize it:
if (props%eff_dim == 3._r8) then
call rising_factorial_integer_vec(pgamp1,3,tmp,dim1*dim2)
else
call rising_factorial_r8_vec(pgamp1, props%eff_dim,tmp,dim1*dim2)
end if
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector collapse(2)
do k = 1, dim2
do i = 1, dim1
if (qcic(i,k) > qsmall) then
shapeC(i,k) = pi / 6._r8 * props%rho * tmp(i,k)
! Limit to between 2 and 50 microns mean size.
lbnd(i,k) = pgamp1(i,k)*1._r8/50.e-6_r8
ubnd(i,k) = pgamp1(i,k)*1._r8/2.e-6_r8
else
shapeC(i,k) = 0._r8
lbnd(i,k) = 0._r8
ubnd(i,k) = 0._r8
end if
end do
end do
!$acc end parallel
call size_dist_param_basic_vect2(props, qcic, ncic, shapeC, lbnd, ubnd, lamc, dim1*dim2)
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector collapse(2)
do k = 1, dim2
do i = 1, dim1
if (qcic(i,k) <= qsmall) then
! pgam not calculated in this case, so set it to a value likely to
! cause an error if it is accidentally used
! (gamma function undefined for negative integers)
pgam(i,k) = -100._r8
lamc(i,k) = 0._r8
end if
end do
end do
!$acc end parallel
!$acc end data
end subroutine size_dist_param_liq_2D
! get cloud droplet size distribution parameters
subroutine size_dist_param_liq_vect(props, qcic, ncic, rho, pgam, lamc, vlen)
type(mghydrometeorprops), intent(in) :: props
integer, intent(in) :: vlen
real(r8), dimension(vlen), intent(in) :: qcic
real(r8), dimension(vlen), intent(inout) :: ncic
real(r8), dimension(vlen), intent(in) :: rho
real(r8), dimension(vlen), intent(out) :: pgam
real(r8), dimension(vlen), intent(out) :: lamc
! local variables
integer :: i
real(r8) :: tmp(vlen),pgamp1(vlen)
real(r8) :: shapeC(vlen),lbnd(vlen),ubnd(vlen)
!$acc data create (tmp,pgamp1,shapeC,lbnd,ubnd)
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i = 1, vlen
if (qcic(i) > qsmall) then
! Get pgam from fit Rotstayn and Liu 2003 (changed from Martin 1994 for CAM6)
pgam(i) = 1.0_r8 - 0.7_r8 * exp(-0.008_r8*1.e-6_r8*ncic(i)*rho(i))
pgam(i) = 1._r8/(pgam(i)**2) - 1._r8
pgam(i) = max(pgam(i), 2._r8)
pgamp1(i) = pgam(i)+1._r8
else
pgamp1(i) = 0._r8
end if
end do
!$acc end parallel
! Set coefficient for use in size_dist_param_basic.
! The 3D case is so common and optimizable that we specialize it:
if (props%eff_dim == 3._r8) then
call rising_factorial_integer_vec(pgamp1,3,tmp,vlen)
else
call rising_factorial_r8_vec(pgamp1, props%eff_dim,tmp,vlen)
end if
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i = 1, vlen
if (qcic(i) > qsmall) then
shapeC(i) = pi / 6._r8 * props%rho * tmp(i)
! Limit to between 2 and 50 microns mean size.
lbnd(i) = pgamp1(i)*1._r8/50.e-6_r8
ubnd(i) = pgamp1(i)*1._r8/2.e-6_r8
else
shapeC(i) = 0._r8
lbnd(i) = 0._r8
ubnd(i) = 0._r8
end if
end do
!$acc end parallel
call size_dist_param_basic_vect2(props, qcic, ncic, shapeC, lbnd, ubnd, lamc, vlen)
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i = 1, vlen
if (qcic(i) <= qsmall) then
! pgam not calculated in this case, so set it to a value likely to
! cause an error if it is accidentally used
! (gamma function undefined for negative integers)
pgam(i) = -100._r8
lamc(i) = 0._r8
end if
end do
!$acc end parallel
!$acc end data
end subroutine size_dist_param_liq_vect
! Basic routine for getting size distribution parameters.
subroutine size_dist_param_basic_line(props, qic, nic, lam, n0)
!$acc routine seq
type(MGHydrometeorProps), intent(in) :: props
real(r8), intent(in) :: qic
real(r8), intent(inout) :: nic
real(r8), intent(out) :: lam
real(r8), intent(out), optional :: n0
logical :: present_n0
present_n0 = present(n0)
if (qic > qsmall) then
! add upper limit to in-cloud number concentration to prevent
! numerical error
if (limiter_is_on(props%min_mean_mass)) then
nic = min(nic, qic / props%min_mean_mass)
end if
! lambda = (c n/q)^(1/d)
lam = (props%shape_coef * nic/qic)**(1._r8/props%eff_dim)
! check for slope
! adjust vars
if (lam < props%lambda_bounds(1)) then
lam = props%lambda_bounds(1)
nic = lam**(props%eff_dim) * qic/props%shape_coef
else if (lam > props%lambda_bounds(2)) then
lam = props%lambda_bounds(2)
nic = lam**(props%eff_dim) * qic/props%shape_coef
end if
else
lam = 0._r8
end if
if (present_n0) n0 = nic * lam
end subroutine size_dist_param_basic_line
subroutine size_dist_param_basic_vect(props, qic, nic, lam, vlen, n0)
type (mghydrometeorprops), intent(in) :: props
integer, intent(in) :: vlen
real(r8), dimension(vlen), intent(in) :: qic
real(r8), dimension(vlen), intent(inout) :: nic
real(r8), dimension(vlen), intent(out) :: lam
real(r8), dimension(vlen), intent(out), optional :: n0
integer :: i
logical :: limiterActive, present_n0
real(r8) :: effDim,shapeCoef,ubnd,lbnd, minMass
limiterActive = limiter_is_on(props%min_mean_mass)
effDim = props%eff_dim
shapeCoef = props%shape_coef
lbnd = props%lambda_bounds(1)
ubnd = props%lambda_bounds(2)
minMass = props%min_mean_mass
present_n0 = present(n0)
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i = 1, vlen
if (qic(i) > qsmall) then
! add upper limit to in-cloud number concentration to prevent
! numerical error
if (limiterActive) then
nic(i) = min(nic(i), qic(i) / minMass)
end if
! lambda = (c n/q)^(1/d)
lam(i) = (shapeCoef * nic(i)/qic(i))**(1._r8/effDim)
! check for slope
! adjust vars
if (lam(i) < lbnd) then
lam(i) = lbnd
nic(i) = lam(i)**(effDim) * qic(i)/shapeCoef
else if (lam(i) > ubnd) then
lam(i) = ubnd
nic(i) = lam(i)**(effDim) * qic(i)/shapeCoef
end if
else
lam(i) = 0._r8
end if
if (present_n0) n0(i) = nic(i) * lam(i)
end do
!$acc end parallel
end subroutine size_dist_param_basic_vect
subroutine size_dist_param_basic_2D(props, qic, nic, lam, dim1, dim2, n0)
type (mghydrometeorprops), intent(in) :: props
integer, intent(in) :: dim1, dim2
real(r8), dimension(dim1,dim2), intent(in) :: qic
real(r8), dimension(dim1,dim2), intent(inout) :: nic
real(r8), dimension(dim1,dim2), intent(out) :: lam
real(r8), dimension(dim1,dim2), intent(out), optional :: n0
integer :: i, k
logical :: limiterActive, present_n0
real(r8) :: effDim,shapeCoef,ubnd,lbnd, minMass
limiterActive = limiter_is_on(props%min_mean_mass)
effDim = props%eff_dim
shapeCoef = props%shape_coef
lbnd = props%lambda_bounds(1)
ubnd = props%lambda_bounds(2)
minMass = props%min_mean_mass
present_n0 = present(n0)
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector collapse(2)
do k = 1, dim2
do i = 1, dim1
if (qic(i,k) > qsmall) then
! add upper limit to in-cloud number concentration to prevent
! numerical error
if (limiterActive) then
nic(i,k) = min(nic(i,k), qic(i,k) / minMass)
end if
! lambda = (c n/q)^(1/d)
lam(i,k) = (shapeCoef * nic(i,k)/qic(i,k))**(1._r8/effDim)
! check for slope
! adjust vars
if (lam(i,k) < lbnd) then
lam(i,k) = lbnd
nic(i,k) = lam(i,k)**(effDim) * qic(i,k)/shapeCoef
else if (lam(i,k) > ubnd) then
lam(i,k) = ubnd
nic(i,k) = lam(i,k)**(effDim) * qic(i,k)/shapeCoef
end if
else
lam(i,k) = 0._r8
end if
if (present_n0) n0(i,k) = nic(i,k) * lam(i,k)
end do
end do
!$acc end parallel
end subroutine size_dist_param_basic_2D
subroutine size_dist_param_basic_vect2(props, qic, nic, shapeC, lbnd, ubnd, lam, vlen, n0)
type (mghydrometeorprops), intent(in) :: props
integer, intent(in) :: vlen
real(r8), dimension(vlen), intent(in) :: qic
real(r8), dimension(vlen), intent(inout) :: nic
real(r8), dimension(vlen), intent(in) :: shapeC,lbnd,ubnd
real(r8), dimension(vlen), intent(out) :: lam
real(r8), dimension(vlen), intent(out), optional :: n0
integer :: i
integer :: cnt
logical :: limiterActive, present_n0
real(r8) :: effDim,shapeCoef, minMass
limiterActive = limiter_is_on(props%min_mean_mass)
effDim = props%eff_dim
minMass = props%min_mean_mass
present_n0 = present(n0)
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i=1,vlen
if (qic(i) > qsmall) then
! add upper limit to in-cloud number concentration to prevent
! numerical error
if (limiterActive) then
nic(i) = min(nic(i), qic(i) / minMass)
end if
! lambda = (c n/q)^(1/d)
lam(i) = (shapeC(i) * nic(i)/qic(i))**(1._r8/effDim)
! check for slope
! adjust vars
if (lam(i) < lbnd(i)) then
lam(i) = lbnd(i)
nic(i) = lam(i)**(effDim) * qic(i)/shapeC(i)
else if (lam(i) > ubnd(i)) then
lam(i) = ubnd(i)
nic(i) = lam(i)**(effDim) * qic(i)/shapeC(i)
end if
else
lam(i) = 0._r8
end if
if (present_n0) n0(i) = nic(i) * lam(i)
end do
!$acc end parallel
end subroutine size_dist_param_basic_vect2
real(r8) elemental function avg_diameter(q, n, rho_air, rho_sub)
! Finds the average diameter of particles given their density, and
! mass/number concentrations in the air.
! Assumes that diameter follows an exponential distribution.
real(r8), intent(in) :: q ! mass mixing ratio
real(r8), intent(in) :: n ! number concentration (per volume)
real(r8), intent(in) :: rho_air ! local density of the air
real(r8), intent(in) :: rho_sub ! density of the particle substance
avg_diameter = (q*rho_air/(pi * rho_sub * n))**(1._r8/3._r8)
end function avg_diameter
subroutine avg_diameter_vec (q, n, rho_air, rho_sub, avg_diameter, vlen)
! Finds the average diameter of particles given their density, and
! mass/number concentrations in the air.
! Assumes that diameter follows an exponential distribution.
integer, intent(in) :: vlen
real(r8), intent(in) :: q(vlen) ! mass mixing ratio
real(r8), intent(in) :: n(vlen) ! number concentration (per volume)
real(r8), intent(in) :: rho_air(vlen) ! local density of the air
real(r8), intent(in) :: rho_sub ! density of the particle substance
real(r8), intent(out) :: avg_diameter(vlen)
integer :: i
!$acc parallel vector_length(VLENS) default(present)
!$acc loop gang vector
do i=1,vlen
avg_diameter(i) = (q(i)*rho_air(i)/(pi * rho_sub * n(i)))**(1._r8/3._r8)
end do
!$acc end parallel
end subroutine avg_diameter_vec
subroutine var_coef_r8(relvar, a, res)
!$acc routine seq
! Finds a coefficient for process rates based on the relative variance
! of cloud water.
real(r8), intent(in) :: relvar
real(r8), intent(in) :: a
real(r8), intent(out) :: res
call rising_factorial(relvar, a, res)
res = res / relvar**a
end subroutine var_coef_r8
subroutine var_coef_r8_vect(relvar, a, res, vlen)