!============================================================== ! ! 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