!==============================================================
!
! SYNOPSIS OF subroutineS TB, TBATMOS
!
!===============================================================
! subroutine TBATMOS(ifREQ,THETA,P0,WV,HWV,TA,GAMMA,LW,ZCLD,TBUP,
! TBDN,TAUATM)
!
! This routine calculates the upwelling and downwelling microwave
! atmospheric brightness temperatures and transmittance at SSM/I
! frequencies. It is a generalization of "TBCLEAR" and includes a
! cloud layer of known height and total liquid water content.
!------------------------------------------
! Input : ifREQ = (1,2,3, or 4 ) for (19.35, 22.235, 37, or 85.5 GHz)
! THETA = incidence angle (deg.)
!
! ( approximate range )
! P0 = surface pressure (mb) (940 -1030)
! WV = precipitable water (kg/m**2) (0 - 70)
! HWV = water vapor density scale height (km) (0.5 - 3.0)
! TA, GAMMA = "effective" surface air temperature
! and lapse rate (K ; km)
! T(z) = Ta - gamma*z (263 - 303 ; 4.0 - 6.5)
!
! LW, ZCLD = total cloud liquid water content (kg/m**2) and height (km)
!
! Output : TBUP, TBDN = atmospheric component of upwelling and downwelling
! brightness temperature (K)
! TAUATM = total atmospheric transmittance at specified incidence angle.
!
! Subroutines called : EFFHT, SIGMA_V
!
!
!===================================================================
!
! NOTES
!
!===================================================================
!
!
! 1) This model is described in detail by Petty (1990).
! Frequency dependent
! coefficients of the model are based on radiative transfer
! integrations of 16,893 radiosonde profiles from 29 ships, islands and
! coastal stations, representing all major climatic regimes and all
! seasons. Absorption coefficients used in these integrations were
! obtained from an adaptation of the Millimeter-wave Propagation Model
! (MPM) of Liebe (1985) with updated line parameters (Liebe 1988,
! personal communication). Empirical corrections to total water
! absorption values have been added, based on comparisons with
! radiosondes.
!
! 2) The frequency-dependent component of the model is only
! intended to give meaningful results for
! combinations of input parameters which are meteorologically and
! physically reasonable under coastal or maritime conditions near sea
! level. The user must ensure that input values are not only
! individually reasonable, but also are mutually consistent. See
! Petty (1990) for details.
!
! 3) Computed brightness temperatures from this model are generally
! valid only for (gaseous optical depth)/cos(theta) of order unity or
! less. This is usually of concern only for theta > 75 deg. in a moist
! atmosphere at 22 and 85 GHz. An ad hoc correction has been added to
! TBCLEAR which greatly improves the calculated downwelling brightness
! temperature for near-grazing angles, so that its contribution to the
! diffuse reflected component from the sea surface may be correctly
! estimated. No such correction is applied to upwelling brightness
! temperatures, since there is no contribution to SSM/I observations
! from angles other than at the nadir angle. The correction is also
! not yet available for downwelling brightness temperatures from
! TBATMOS.
!
!
! The author welcomes feedback from other workers concerning the
! accuracy and overall performance of the routines presented here.
!
!
! References:
!
! Liebe, H.J., 1985 : An updated model for millimeter
! wave propagation in moist air. Radio Science, 20, pp. 1069-1089
!
! Liebe, H.J., 1988, personal communication: updated absorption line
! parameters.
!
! Petty, G.W. 1990: On the Response of the SSM/I to the
! Marine Environment --- Implications for Atmospheric Parameter
! Retrievals. Ph.D. Dissertation, Dept. of Atmospheric Sciences,
! University of Washington
!
! Petty, G.W., and K.B. Katsaros, 1992: The response
! of the Special Sensor Microwave/Imager to the
! marine environment. Part I: An analytic model for
! the atmospheric component of observed brightness
! temperatures. J. Atmos. Ocean. Tech., 9, 746--761
!
! Petty, G.W., and K.B. Katsaros, 1993: The response
! of the Special Sensor Microwave/Imager to the
! marine environment. Part II: A parameterization of
! roughness effects on sea surface emission and
! reflection. Submitted to J. Atmos. Ocean. Tech.
!
!
!===============================================================
!
! fortran source code listings for TBATMOS,
! SIGMA_V, EFFHT
!
!===============================================================
! subroutine TBATMOS(ifREQ,THETA,P0,WV,HWV,TA,GAMMA,LW,ZCLD,TBUP,
! TBDN,TAUATM)
!
! This routine calculates the upwelling and downwelling microwave
! atmospheric brightness temperatures and transmittance at an SSM/I
! frequency. It is a generalization of "TBCLEAR" and includes a
! cloud layer of known height and total liquid water content.
!
! Input : ifREQ = (1,2,3, or 4 ) for (19.35, 22.235, 37, or 85.5 GHz)
! THETA = incidence angle (deg.)
!
! ( approximate range )
! P0 = surface pressure (mb) (940 -1030)
! WV = precipitable water (kg/m**2) (0 - 70)
! HWV = water vapor density scale height (km) (0.5 - 3.0)
! TA, GAMMA = "effective" surface air temperature
! and lapse rate (K ; km)
! T(z) = Ta - gamma*z (263 - 303 ; 4.0 - 6.5)
!
! LW, ZCLD = total cloud liquid water content (kg/m**2) and height (km)
!
! Output : TBUP, TBDN = atmospheric component of upwelling and downwelling
! brightness temperature (K)
! TAUATM = total atmospheric transmittance at specified incidence angle.
!
! Subroutines called : EFFHT, SIGMA_V
!------------------------------------------------------------
subroutine tbatmos(ifreq,theta,p0,wv,hwv,ta,gamma,lw,zcld, &
tbup,tbdn,tauatm)
integer ifreq
real theta,p0,wv,hwv,ta,gamma,lw,zcld,tbup,tbdn,tauatm
real mu,hdn,hup,hdninf,hupinf
!
real b1(4),b2(4),b3(4)
real c(4),d1(4),d2(4),d3(4),zeta(4),kw0(4),kw1(4),kw2(4),kw3(4)
real tau,tau1,tau2,taucld
real tcld,tc,em,em1
real sigv,sigo,sig,sig1,sigcld
real teff1dn,teff1up,teffdn,teffup
real tbcld,tbclrdn,tbclrup,tb1dn,tb1up,tb2dn,tb2up
real otbar,tc2,tc3,hv,ho,alph
!
data b1/-.46847e-1,-.57752e-1,-.18885,.10990/
data b2/.26640e-4,.31662e-4,.9832e-4,.60531e-4/
data b3/.87560e+1,.10961e+2,.36678e+2,-.37578e+2/
data c/ .9207, 1.208, .8253, .8203/
data zeta/4.2,4.2,4.2,2.9/
data d1/-.35908e+1,-.38921e+1,-.43072e+1,-.17020e+0/
data d2/ .29797e-1, .31054e-1, .32801e-1, .13610e-1/
data d3/-.23174e-1,-.23543e-1,-.24101e-1,-.15776e+0/
data kw0/ .786e-1, .103, .267, .988/
data kw1/-.230e-2,-.296e-2,-.673e-2,-.107e-1/
data kw2/ .448e-4, .557e-4, .975e-4,-.535e-4/
data kw3/-.464e-6,-.558e-6,-.724e-6, .115e-5/
! mu = secant(theta)
mu = 1.0/cos(theta*0.0174533)
! get water vapor optical depth
!=====
call cal_sigma_v(ifreq,p0,wv,hwv,ta,gamma,sigv)
! otbar = one over "mean" temperature
otbar = 1.0/(ta - gamma*zeta(ifreq))
! sigo = dry air optical depth
sigo = b1(ifreq) + b2(ifreq)*p0 + b3(ifreq)*otbar
! cloud parameters
tcld = ta - gamma*zcld
tc = tcld - t_kelvin
tc2 = tc*tc
tc3 = tc2*tc
sigcld = (kw0(ifreq) + tc*kw1(ifreq) + tc2*kw2(ifreq) + &
tc3*kw3(ifreq))*lw
taucld = exp(-mu*sigcld)
tbcld = (1.0 - taucld)*tcld
! hv, ho = effective absorber scale heights for vapor, dry air
hv = c(ifreq)*hwv
ho = d1(ifreq) + d2(ifreq)*ta + d3(ifreq)*gamma
! get effective emission heights for layer 1 and total atmosphere
call effht(ho,hv,sigo,sigv,mu,zcld,hdn,hup, &
hdninf,hupinf)
! atmospheric transmittances in layer one and two, and combined
sig = sigo + sigv
sig1 = sigo*(1.0-exp(-zcld/ho)) + sigv*(1.0-exp(-zcld/hv))
tau = exp(-mu*sig)
tau1 = exp(-mu*sig1)
tau2 = tau/tau1
! atmospheric "emissivity"
em1 = 1.0 - tau1
em = 1.0 - tau
! downwelling and upwelling brightness temperature for each layer
teff1dn = ta - gamma*hdn
teff1up = ta - gamma*hup
teffdn = ta - gamma*hdninf
teffup = ta - gamma*hupinf
tbclrdn = teffdn*em
tbclrup = teffup*em
!
tb1dn = em1*teff1dn
tb1up = em1*teff1up
tb2dn = (tbclrdn - tb1dn)/tau1
tb2up = tbclrup - tau2*tb1up
! total downwelling and upwelling brightness temperature and transmittance
tbdn = tb1dn + tau1*(tbcld + taucld*tb2dn)
tbup = tb2up + tau2*(tbcld + taucld*tb1up)
tauatm = tau*taucld
!
! the following lines apply an ad hoc correction to improve fit
! at large angles and/or high gaseous opacities
! (downwelling brightness temperatures only)
alph = (0.636619*atan(mu*sig))**2
tbdn = (1.0-alph)*tbdn + em*alph*ta
!
end subroutine tbatmos