module constants
!$$$ module documentation block
! . . . .
! module: constants
! prgmmr: treadon org: np23 date: 2003-09-25
!
! abstract: This module contains the definition of various constants
! used in the gsi code
!
! program history log:
! 2003-09-25 treadon - original code
! 2004-03-02 treadon - allow global and regional constants to differ
! 2004-06-16 treadon - update documentation
! 2004-10-28 treadon - replace parameter tiny=1.e-12 with tiny_r_kind
! and tiny_single
! 2004-11-16 treadon - add huge_single, huge_r_kind parameters
! 2005-08-24 derber - move cg_term to constants from qcmod
! 2006-03-07 treadon - add rd_over_cp_mass
! 2006-05-18 treadon - add huge_i_kind
! 2006-06-06 su - add var-qc wgtlim, change value to 0.25 (ECMWF)
! 2006-07-28 derber - add r1000
! 2007-03-20 rancic - add r3600
! 2009-02-05 cucurull - modify refractive indexes for gpsro data
! 2010-08-25 cucurull - add constants to compute compressibility factor
! - add option to use Rueger/Bevis refractive index coeffs
! 2010-12-20 pagowski - add max_varname_length=12
! 2010-04-01 li - add maximum diurnal thermocline thickness
! 2011-10-27 Huang - add i_missing and r_missing to detect missing values
! 2011-11-01 eliu - add minimum value for cloud water mixing ratio
! 2012-03-07 todling - define lower bound for trace-gases (arbitrary unit as long as small)
! 2016-02-15 Johnson, Y. Wang, X. Wang - define additional constant values for
! radar DA, POC: xuguang.wang@ou.edu
!
! Subroutines Included:
! sub init_constants_derived - compute derived constants
! sub init_constants - set regional/global constants
! sub gps_constants - set Rueger/Bevis refractive index coefficients
!
! Variable Definitions:
! see below
!
! attributes:
! language: f90
! machine: ibm RS/6000 SP
!
!$$$ end documentation block
use kinds, only: r_single,r_kind,i_kind,r_quad,i_long
implicit none
! set default as private
private
! set subroutines as public
public :: init_constants_derived
public :: init_constants
public :: gps_constants
! set passed variables to public
public :: one,two,half,zero,deg2rad,pi,three,quarter,one_tenth
public :: rad2deg,zero_quad,r3600,r1000,r60inv,five,four,rd_over_cp,grav
public :: rd,rv,rozcon,rearth_equator,zero_single,tiny_r_kind,tiny_single,ten
public :: omega,rcp,rearth,fv,h300,cp,cg_term,tpwcon,xb,ttp,psatk,xa,tmix
public :: xai,xbi,psat,eps,omeps,wgtlim,one_quad,two_quad,epsq,climit,epsm1,hvap
public :: hsub,cclimit,el2orc,elocp,h1000,cpr,pcpeff0,pcpeff2,delta,pcpeff1
public :: factor1,c0,pcpeff3,factor2,dx_inv,dx_min,rhcbot,rhctop,hfus,ke2
public :: rrow,cmr,cws,r60,huge_i_kind,huge_r_kind,t0c,rd_over_cp_mass
public :: somigliana,grav_equator,grav_ratio,flattening,semi_major_axis
public :: n_b,n_a,eccentricity,huge_single,constoz,g_over_rd,amsua_clw_d2
public :: amsua_clw_d1,n_c,rd_over_g,zero_ilong
public :: r10,r100,sqrt_tiny_r_kind,r2000,r4000
public :: r0_01,r0_02,r0_03,r0_04,r0_05,r400,r2400
public :: cpf_a0, cpf_a1, cpf_a2, cpf_b0, cpf_b1, cpf_c0, cpf_c1, cpf_d, cpf_e
public :: psv_a, psv_b, psv_c, psv_d
public :: ef_alpha, ef_beta, ef_gamma
public :: max_varname_length
public :: z_w_max,tfrozen
public :: qmin,qcmin,tgmin
public :: i_missing, r_missing
public :: izero, qimin, qsmin, qgmin,qrmin
public :: partialSnowThreshold
public :: soilmoistmin
! Declare derived constants
integer(i_kind):: huge_i_kind
integer(i_kind), parameter :: max_varname_length=32
real(r_single):: tiny_single, huge_single
real(r_kind):: xai, xa, xbi, xb, dldt, rozcon,ozcon,fv, tpwcon,eps, rd_over_g
real(r_kind):: el2orc, g_over_rd, rd_over_cp, cpr, omeps, epsm1, factor2
real(r_kind):: factor1, huge_r_kind, tiny_r_kind, deg2rad, pi, rad2deg, cg_term
real(r_kind):: eccentricity_linear, cv, rv, rd_over_cp_mass, cliq, rd, cp_mass
real(r_kind):: eccentricity, grav, rearth, r60inv
real(r_kind):: sqrt_tiny_r_kind
real(r_kind):: n_a, n_b, n_c
! Define constants common to global and regional applications
real(r_kind),parameter:: rearth_equator= 6.37813662e6_r_kind ! equatorial earth radius (m)
real(r_kind),parameter:: omega = 7.2921e-5_r_kind ! angular velocity of earth (1/s)
real(r_kind),parameter:: cp = 1.0046e+3_r_kind ! specific heat of air @pressure (J/kg/K)
real(r_kind),parameter:: cvap = 1.8460e+3_r_kind ! specific heat of h2o vapor (J/kg/K)
real(r_kind),parameter:: csol = 2.1060e+3_r_kind ! specific heat of solid h2o (ice)(J/kg/K)
real(r_kind),parameter:: hvap = 2.5000e+6_r_kind ! latent heat of h2o condensation (J/kg)
real(r_kind),parameter:: hfus = 3.3358e+5_r_kind ! latent heat of h2o fusion (J/kg)
real(r_kind),parameter:: psat = 6.1078e+2_r_kind ! pressure at h2o triple point (Pa)
real(r_kind),parameter:: t0c = 2.7315e+2_r_kind ! temperature at zero celsius (K)
real(r_kind),parameter:: ttp = 2.7316e+2_r_kind ! temperature at h2o triple point (K)
real(r_kind),parameter:: jcal = 4.1855e+0_r_kind ! joules per calorie ()
! real(r_kind),parameter:: stndrd_atmos_ps = 1013.25e2_r_kind ! 1976 US standard atmosphere ps (Pa)
! Numeric constants
integer(i_long),parameter:: zero_ilong = 0_i_long
real(r_single),parameter:: zero_single= 0.0_r_single
real(r_kind),parameter:: zero = 0.0_r_kind
real(r_kind),parameter:: r0_01 = 0.01_r_kind
real(r_kind),parameter:: r0_02 = 0.02_r_kind
real(r_kind),parameter:: r0_03 = 0.03_r_kind
real(r_kind),parameter:: r0_04 = 0.04_r_kind
real(r_kind),parameter:: r0_05 = 0.05_r_kind
real(r_kind),parameter:: one_tenth = 0.10_r_kind
real(r_kind),parameter:: quarter = 0.25_r_kind
real(r_kind),parameter:: one = 1.0_r_kind
real(r_kind),parameter:: two = 2.0_r_kind
real(r_kind),parameter:: three = 3.0_r_kind
real(r_kind),parameter:: four = 4.0_r_kind
real(r_kind),parameter:: five = 5.0_r_kind
real(r_kind),parameter:: ten = 10.0_r_kind
real(r_kind),parameter:: r10 = 10.0_r_kind
real(r_kind),parameter:: r60 = 60._r_kind
real(r_kind),parameter:: r100 = 100.0_r_kind
real(r_kind),parameter:: r400 = 400.0_r_kind
real(r_kind),parameter:: r1000 = 1000.0_r_kind
real(r_kind),parameter:: r2000 = 2000.0_r_kind
real(r_kind),parameter:: r2400 = 2400.0_r_kind
real(r_kind),parameter:: r4000 = 4000.0_r_kind
real(r_kind),parameter:: r3600 = 3600.0_r_kind
real(r_kind),parameter:: z_w_max = 30.0_r_kind ! maximum diurnal thermocline thickness
real(r_kind),parameter:: tfrozen = 271.2_r_kind ! sea water frozen point temperature
real(r_quad),parameter:: zero_quad = 0.0_r_quad
real(r_quad),parameter:: one_quad = 1.0_r_quad
real(r_quad),parameter:: two_quad = 2.0_r_quad
! Constants for compressibility factor (Davis et al 1992)
real(r_kind),parameter:: cpf_a0 = 1.58123e-6_r_kind ! K/Pa
real(r_kind),parameter:: cpf_a1 = -2.9331e-8_r_kind ! 1/Pa
real(r_kind),parameter:: cpf_a2 = 1.1043e-10_r_kind ! 1/K 1/Pa
real(r_kind),parameter:: cpf_b0 = 5.707e-6_r_kind ! K/Pa
real(r_kind),parameter:: cpf_b1 = -2.051e-8_r_kind ! 1/Pa
real(r_kind),parameter:: cpf_c0 = 1.9898e-4_r_kind ! K/Pa
real(r_kind),parameter:: cpf_c1 = -2.376e-6_r_kind ! 1/Pa
real(r_kind),parameter:: cpf_d = 1.83e-11_r_kind ! K2/Pa2
real(r_kind),parameter:: cpf_e = -0.765e-8_r_kind ! K2/Pa2
! Constants for vapor pressure at saturation
real(r_kind),parameter:: psv_a = 1.2378847e-5_r_kind ! (1/K2)
real(r_kind),parameter:: psv_b = -1.9121316e-2_r_kind ! (1/K)
real(r_kind),parameter:: psv_c = 33.93711047_r_kind !
real(r_kind),parameter:: psv_d = -6.3431645e+3_r_kind ! (K)
! Constants for enhancement factor to calculating the mole fraction of water vapor
real(r_kind),parameter:: ef_alpha = 1.00062_r_kind !
real(r_kind),parameter:: ef_beta = 3.14e-8_r_kind ! (1/Pa)
real(r_kind),parameter:: ef_gamma = 5.6e-7_r_kind ! (1/K2)
! Parameters below from WGS-84 model software inside GPS receivers.
real(r_kind),parameter:: semi_major_axis = 6378.1370e3_r_kind ! (m)
real(r_kind),parameter:: semi_minor_axis = 6356.7523142e3_r_kind ! (m)
real(r_kind),parameter:: grav_polar = 9.8321849378_r_kind ! (m/s2)
real(r_kind),parameter:: grav_equator = 9.7803253359_r_kind ! (m/s2)
real(r_kind),parameter:: earth_omega = 7.292115e-5_r_kind ! (rad/s)
real(r_kind),parameter:: grav_constant = 3.986004418e14_r_kind ! (m3/s2)
! Derived geophysical constants
real(r_kind),parameter:: flattening = (semi_major_axis-semi_minor_axis)/semi_major_axis
real(r_kind),parameter:: somigliana = &
(semi_minor_axis/semi_major_axis) * (grav_polar/grav_equator) - one
real(r_kind),parameter:: grav_ratio = (earth_omega*earth_omega * &
semi_major_axis*semi_major_axis * semi_minor_axis) / grav_constant
! Derived thermodynamic constants
real(r_kind),parameter:: dldti = cvap-csol
real(r_kind),parameter:: hsub = hvap+hfus
real(r_kind),parameter:: psatk = psat*0.001_r_kind
real(r_kind),parameter:: tmix = ttp-20._r_kind
real(r_kind),parameter:: elocp = hvap/cp
real(r_kind),parameter:: rcp = one/cp
! Constants used in GFS moist physics
real(r_kind),parameter:: h300 = 300._r_kind
real(r_kind),parameter:: half = 0.5_r_kind
real(r_kind),parameter:: cclimit = 0.001_r_kind
real(r_kind),parameter:: climit = 1.e-20_r_kind
real(r_kind),parameter:: epsq = 2.e-12_r_kind
real(r_kind),parameter:: h1000 = r1000
real(r_kind),parameter:: rhcbot=0.85_r_kind
real(r_kind),parameter:: rhctop=0.85_r_kind
real(r_kind),parameter:: dx_max=-8.8818363_r_kind
real(r_kind),parameter:: dx_min=-5.2574954_r_kind
real(r_kind),parameter:: dx_inv=one/(dx_max-dx_min)
real(r_kind),parameter:: c0=0.002_r_kind
real(r_kind),parameter:: delta=0.6077338_r_kind
real(r_kind),parameter:: pcpeff0=1.591_r_kind
real(r_kind),parameter:: pcpeff1=-0.639_r_kind
real(r_kind),parameter:: pcpeff2=0.0953_r_kind
real(r_kind),parameter:: pcpeff3=-0.00496_r_kind
real(r_kind),parameter:: cmr = one/0.0003_r_kind
real(r_kind),parameter:: cws = 0.025_r_kind
real(r_kind),parameter:: ke2 = 0.00002_r_kind
real(r_kind),parameter:: row = r1000
real(r_kind),parameter:: rrow = one/row
! real(r_kind),parameter:: qmin = 1.e-7_r_kind !lower bound on ges_q
! Constant used to process ozone
real(r_kind),parameter:: constoz = 604229.0_r_kind
! Constants used in cloud liquid water correction for AMSU-A
! brightness temperatures
real(r_kind),parameter:: amsua_clw_d1 = 0.754_r_kind
real(r_kind),parameter:: amsua_clw_d2 = -2.265_r_kind
! Constants used for variational qc
real(r_kind),parameter:: wgtlim = quarter ! Cutoff weight for concluding that obs has been
! rejected by nonlinear qc. This limit is arbitrary
! and DOES NOT affect nonlinear qc. It only affects
! the printout which "counts" the number of obs that
! "fail" nonlinear qc. Observations counted as failing
! nonlinear qc are still assimilated. Their weight
! relative to other observations is reduced. Changing
! wgtlim does not alter the analysis, only
! the nonlinear qc data "count"
! Minimum values for water vapor, cloud water mixing ratio, and trace gases
real(r_kind),parameter:: qmin = 1.e-07_r_kind ! lower bound on ges_q
real(r_kind),parameter:: qcmin = 0.0_r_kind ! lower bound on ges_cw
real(r_kind),parameter:: tgmin = 1.e-15_r_kind ! lower bound on trace gases
integer(i_kind),parameter:: izero = 0
real(r_kind),parameter:: qimin = 0.0_r_kind
real(r_kind),parameter:: qgmin = 0.0_r_kind
real(r_kind),parameter:: qsmin = 0.0_r_kind
real(r_kind),parameter:: qrmin = 0.0_r_kind
real(r_kind),parameter:: log10qcmin = -10_r_single
real(r_kind),parameter:: r10log10qcmin = 1.0e-10_r_single
real(r_kind),parameter:: log10qrmin = -6.0_r_single
real(r_kind),parameter:: r10log10qrmin = 1.0e-6_r_single
real(r_kind),parameter:: log10qimin = -8_r_single
real(r_kind),parameter:: r10log10qimin = 1.0e-8_r_single
real(r_kind),parameter:: log10qgmin = -8_r_single
real(r_kind),parameter:: r10log10qgmin = 1.0e-8_r_single
real(r_kind),parameter:: log10qsmin = -9_r_single
real(r_kind),parameter:: r10log10qsmin = 1.0e-9_r_single
! Minimum values for soil adjustment
real(r_single),parameter:: soilmoistmin = 0.002_r_single ! minimum soil
! moisture (sand)
real(r_kind), parameter :: partialSnowThreshold = 32._r_kind ! mm
! Constant used to detect missing input value
integer(i_kind),parameter:: i_missing=-9999
integer(r_kind),parameter:: r_missing=-9999._r_kind
contains
subroutine init_constants_derived
!$$$ subprogram documentation block
! . . . .
! subprogram: init_constants_derived set derived constants
! prgmmr: treadon org: np23 date: 2004-12-02
! ! abstract: This routine sets derived constants
!
! program history log:
! 2004-12-02 treadon
! 2005-03-03 treadon - add implicit none
! 2008-06-04 safford - rm unused vars
!
! input argument list:
!
! output argument list:
!
! attributes:
! language: f90
! machine: ibm rs/6000 sp
!
!$$$
implicit none
! Trigonometric constants
pi = acos(-one)
deg2rad = pi/180.0_r_kind
rad2deg = one/deg2rad
cg_term = (sqrt(two*pi))/two ! constant for variational qc
tiny_r_kind = tiny(zero)
sqrt_tiny_r_kind = r10*sqrt(tiny_r_kind)
huge_r_kind = huge(zero)
tiny_single = tiny(zero_single)
huge_single = huge(zero_single)
huge_i_kind = huge(0)
r60inv=one/r60
! Geophysical parameters used in conversion of geopotential to
! geometric height
eccentricity_linear = sqrt(semi_major_axis**2 - semi_minor_axis**2)
eccentricity = eccentricity_linear / semi_major_axis
return
end subroutine init_constants_derived
subroutine init_constants(regional)
!$$$ subprogram documentation block
! . . . .
! subprogram: init_constants set regional or global constants
! prgmmr: treadon org: np23 date: 2004-03-02
!
! abstract: This routine sets constants specific to regional or global
! applications of the gsi
!
! program history log:
! 2004-03-02 treadon
! 2004-06-16 treadon, documentation
! 2004-10-28 treadon - use intrinsic TINY function to set value
! for smallest machine representable positive
! number
! 2004-12-03 treadon - move derived constants to init_constants_derived
! 2005-03-03 treadon - add implicit none
!
! input argument list:
! regional - if .true., set regional gsi constants;
! otherwise (.false.), use global constants
!
! output argument list:
!
! attributes:
! language: f90
! machine: ibm rs/6000 sp
!
!$$$
implicit none
logical,intent(in ) :: regional
real(r_kind) reradius,g,r_d,r_v,cliq_wrf
! Define regional constants here
if (regional) then
! Name given to WRF constants
reradius = one/6370.e03_r_kind
g = 9.81_r_kind
r_d = 287.04_r_kind
r_v = 461.6_r_kind
cliq_wrf = 4190.0_r_kind
cp_mass = 1004.67_r_kind
! Transfer WRF constants into unified GSI constants
rearth = one/reradius
grav = g
rd = r_d
rv = r_v
cv = cp-r_d
cliq = cliq_wrf
! Define global constants here
else
rearth = 6.3712e+6_r_kind
grav = 9.80665e+0_r_kind
rd = 2.8705e+2_r_kind
rv = 4.6150e+2_r_kind
cv = 7.1760e+2_r_kind
cliq = 4.1855e+3_r_kind
cp_mass= cp
endif
! Now define derived constants which depend on constants
! which differ between global and regional applications.
! Constants related to ozone assimilation
rd_over_cp_mass = rd / cp_mass
ozcon = grav*21.4e-9_r_kind
rozcon= one/ozcon
! Constant used in vertical integral for precipitable water
tpwcon = 100.0_r_kind/grav
! Derived atmospheric constants
fv = rv/rd-one ! used in virtual temperature equation
dldt = cvap-cliq
xa = -(dldt/rv)
xai = -(dldti/rv)
xb = xa+hvap/(rv*ttp)
xbi = xai+hsub/(rv*ttp)
eps = rd/rv
epsm1 = rd/rv-one
omeps = one-eps
factor1 = (cvap-cliq)/rv
factor2 = hvap/rv-factor1*t0c
cpr = cp*rd
el2orc = hvap*hvap/(rv*cp)
rd_over_g = rd/grav
rd_over_cp = rd/cp
g_over_rd = grav/rd
return
end subroutine init_constants
subroutine gps_constants(use_compress)
!$$$ subprogram documentation block
! . . . .
! subprogram: gps_constants set Bevis or Rueger refractive index coeff
! prgmmr: cucurull org: np23 date: 2010-08-25
!
! abstract: This routine sets constants for the refractivity equation. GSI uses Bevis
! coefficients when the compressibility factors option is turned off
! and uses Rueger coefficients otherwise.
!
! program history log:
! 2010-08-25 cucurull
! 2010-08-25 cucurull, documentation
!
! input argument list:
! compress - if .true., set Rueger coefficients;
! otherwise (.false.), use Bevis coefficients
!
! output argument list:
!
! attributes:
! language: f90
! machine: ibm rs/6000 sp
!
!$$$
implicit none
logical,intent(in ) :: use_compress
! Define refractive index coefficients here
if (use_compress) then
! Constants for gpsro data (Rueger 2002)
n_a = 77.6890_r_kind ! K/mb
n_b = 3.75463e+5_r_kind ! K^2/mb
n_c = 71.2952_r_kind ! K/mb
else
! Constants for gpsro data (Bevis et al 1994)
n_a = 77.60_r_kind ! K/mb
n_b = 3.739e+5_r_kind ! K^2/mb
n_c = 70.4_r_kind ! K/mb
endif
return
end subroutine gps_constants
end module constants