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1 !==============================================================
2 !
3 ! SYNOPSIS OF subroutineS TB, TBATMOS
4 !
5 !===============================================================
6 ! subroutine TBATMOS(ifREQ,THETA,P0,WV,HWV,TA,GAMMA,LW,ZCLD,TBUP,
7 ! TBDN,TAUATM)
8 !
9 ! This routine calculates the upwelling and downwelling microwave
10 ! atmospheric brightness temperatures and transmittance at SSM/I
11 ! frequencies. It is a generalization of "TBCLEAR" and includes a
12 ! cloud layer of known height and total liquid water content.
13 !------------------------------------------
14 ! Input : ifREQ = (1,2,3, or 4 ) for (19.35, 22.235, 37, or 85.5 GHz)
15 ! THETA = incidence angle (deg.)
16 !
17 ! ( approximate range )
18 ! P0 = surface pressure (mb) (940 -1030)
19 ! WV = precipitable water (kg/m**2) (0 - 70)
20 ! HWV = water vapor density scale height (km) (0.5 - 3.0)
21 ! TA, GAMMA = "effective" surface air temperature
22 ! and lapse rate (K ; km)
23 ! T(z) = Ta - gamma*z (263 - 303 ; 4.0 - 6.5)
24 !
25 ! LW, ZCLD = total cloud liquid water content (kg/m**2) and height (km)
26 !
27 ! Output : TBUP, TBDN = atmospheric component of upwelling and downwelling
28 ! brightness temperature (K)
29 ! TAUATM = total atmospheric transmittance at specified incidence angle.
30 !
31 ! Subroutines called : EFFHT, SIGMA_V
32 !
33 !
34 !===================================================================
35 !
36 ! NOTES
37 !
38 !===================================================================
39 !
40 !
41 ! 1) This model is described in detail by Petty (1990).
42 ! Frequency dependent
43 ! coefficients of the model are based on radiative transfer
44 ! integrations of 16,893 radiosonde profiles from 29 ships, islands and
45 ! coastal stations, representing all major climatic regimes and all
46 ! seasons. Absorption coefficients used in these integrations were
47 ! obtained from an adaptation of the Millimeter-wave Propagation Model
48 ! (MPM) of Liebe (1985) with updated line parameters (Liebe 1988,
49 ! personal communication). Empirical corrections to total water
50 ! absorption values have been added, based on comparisons with
51 ! radiosondes.
52 !
53 ! 2) The frequency-dependent component of the model is only
54 ! intended to give meaningful results for
55 ! combinations of input parameters which are meteorologically and
56 ! physically reasonable under coastal or maritime conditions near sea
57 ! level. The user must ensure that input values are not only
58 ! individually reasonable, but also are mutually consistent. See
59 ! Petty (1990) for details.
60 !
61 ! 3) Computed brightness temperatures from this model are generally
62 ! valid only for (gaseous optical depth)/cos(theta) of order unity or
63 ! less. This is usually of concern only for theta > 75 deg. in a moist
64 ! atmosphere at 22 and 85 GHz. An ad hoc correction has been added to
65 ! TBCLEAR which greatly improves the calculated downwelling brightness
66 ! temperature for near-grazing angles, so that its contribution to the
67 ! diffuse reflected component from the sea surface may be correctly
68 ! estimated. No such correction is applied to upwelling brightness
69 ! temperatures, since there is no contribution to SSM/I observations
70 ! from angles other than at the nadir angle. The correction is also
71 ! not yet available for downwelling brightness temperatures from
72 ! TBATMOS.
73 !
74 !
75 ! The author welcomes feedback from other workers concerning the
76 ! accuracy and overall performance of the routines presented here.
77 !
78 !
79 ! References:
80 !
81 ! Liebe, H.J., 1985 : An updated model for millimeter
82 ! wave propagation in moist air. Radio Science, 20, pp. 1069-1089
83 !
84 ! Liebe, H.J., 1988, personal communication: updated absorption line
85 ! parameters.
86 !
87 ! Petty, G.W. 1990: On the Response of the SSM/I to the
88 ! Marine Environment --- Implications for Atmospheric Parameter
89 ! Retrievals. Ph.D. Dissertation, Dept. of Atmospheric Sciences,
90 ! University of Washington
91 !
92 ! Petty, G.W., and K.B. Katsaros, 1992: The response
93 ! of the Special Sensor Microwave/Imager to the
94 ! marine environment. Part I: An analytic model for
95 ! the atmospheric component of observed brightness
96 ! temperatures. J. Atmos. Ocean. Tech., 9, 746--761
97 !
98 ! Petty, G.W., and K.B. Katsaros, 1993: The response
99 ! of the Special Sensor Microwave/Imager to the
100 ! marine environment. Part II: A parameterization of
101 ! roughness effects on sea surface emission and
102 ! reflection. Submitted to J. Atmos. Ocean. Tech.
103 !
104 !
105 !===============================================================
106 !
107 ! fortran source code listings for TBATMOS,
108 ! SIGMA_V, EFFHT
109 !
110 !===============================================================
111 ! subroutine TBATMOS(ifREQ,THETA,P0,WV,HWV,TA,GAMMA,LW,ZCLD,TBUP,
112 ! TBDN,TAUATM)
113 !
114 ! This routine calculates the upwelling and downwelling microwave
115 ! atmospheric brightness temperatures and transmittance at an SSM/I
116 ! frequency. It is a generalization of "TBCLEAR" and includes a
117 ! cloud layer of known height and total liquid water content.
118 !
119 ! Input : ifREQ = (1,2,3, or 4 ) for (19.35, 22.235, 37, or 85.5 GHz)
120 ! THETA = incidence angle (deg.)
121 !
122 ! ( approximate range )
123 ! P0 = surface pressure (mb) (940 -1030)
124 ! WV = precipitable water (kg/m**2) (0 - 70)
125 ! HWV = water vapor density scale height (km) (0.5 - 3.0)
126 ! TA, GAMMA = "effective" surface air temperature
127 ! and lapse rate (K ; km)
128 ! T(z) = Ta - gamma*z (263 - 303 ; 4.0 - 6.5)
129 !
130 ! LW, ZCLD = total cloud liquid water content (kg/m**2) and height (km)
131 !
132 ! Output : TBUP, TBDN = atmospheric component of upwelling and downwelling
133 ! brightness temperature (K)
134 ! TAUATM = total atmospheric transmittance at specified incidence angle.
135 !
136 ! Subroutines called : EFFHT, SIGMA_V
137 !------------------------------------------------------------
138 subroutine tbatmos(ifreq,theta,p0,wv,hwv,ta,gamma,lw,zcld, &
139 tbup,tbdn,tauatm)
140 integer ifreq
141 real theta,p0,wv,hwv,ta,gamma,lw,zcld,tbup,tbdn,tauatm
142 real mu,hdn,hup,hdninf,hupinf
143 !
144 real b1(4),b2(4),b3(4)
145 real c(4),d1(4),d2(4),d3(4),zeta(4),kw0(4),kw1(4),kw2(4),kw3(4)
146 real tau,tau1,tau2,taucld
147 real tcld,tc,em,em1
148 real sigv,sigo,sig,sig1,sigcld
149 real teff1dn,teff1up,teffdn,teffup
150 real tbcld,tbclrdn,tbclrup,tb1dn,tb1up,tb2dn,tb2up
151 real otbar,tc2,tc3,hv,ho,alph
152 !
153 data b1/-.46847e-1,-.57752e-1,-.18885,.10990/
154 data b2/.26640e-4,.31662e-4,.9832e-4,.60531e-4/
155 data b3/.87560e+1,.10961e+2,.36678e+2,-.37578e+2/
156 data c/ .9207, 1.208, .8253, .8203/
157 data zeta/4.2,4.2,4.2,2.9/
158 data d1/-.35908e+1,-.38921e+1,-.43072e+1,-.17020e+0/
159 data d2/ .29797e-1, .31054e-1, .32801e-1, .13610e-1/
160 data d3/-.23174e-1,-.23543e-1,-.24101e-1,-.15776e+0/
161 data kw0/ .786e-1, .103, .267, .988/
162 data kw1/-.230e-2,-.296e-2,-.673e-2,-.107e-1/
163 data kw2/ .448e-4, .557e-4, .975e-4,-.535e-4/
164 data kw3/-.464e-6,-.558e-6,-.724e-6, .115e-5/
165 ! mu = secant(theta)
166 mu = 1.0/cos(theta*0.0174533)
167 ! get water vapor optical depth
168 !=====
169 call cal_sigma_v(ifreq,p0,wv,hwv,ta,gamma,sigv)
170 ! otbar = one over "mean" temperature
171 otbar = 1.0/(ta - gamma*zeta(ifreq))
172 ! sigo = dry air optical depth
173 sigo = b1(ifreq) + b2(ifreq)*p0 + b3(ifreq)*otbar
174 ! cloud parameters
175 tcld = ta - gamma*zcld
176 tc = tcld - t_kelvin
177 tc2 = tc*tc
178 tc3 = tc2*tc
179 sigcld = (kw0(ifreq) + tc*kw1(ifreq) + tc2*kw2(ifreq) + &
180 tc3*kw3(ifreq))*lw
181 taucld = exp(-mu*sigcld)
182 tbcld = (1.0 - taucld)*tcld
183 ! hv, ho = effective absorber scale heights for vapor, dry air
184 hv = c(ifreq)*hwv
185 ho = d1(ifreq) + d2(ifreq)*ta + d3(ifreq)*gamma
186 ! get effective emission heights for layer 1 and total atmosphere
187 call effht(ho,hv,sigo,sigv,mu,zcld,hdn,hup, &
188 hdninf,hupinf)
189 ! atmospheric transmittances in layer one and two, and combined
190 sig = sigo + sigv
191 sig1 = sigo*(1.0-exp(-zcld/ho)) + sigv*(1.0-exp(-zcld/hv))
192 tau = exp(-mu*sig)
193 tau1 = exp(-mu*sig1)
194 tau2 = tau/tau1
195 ! atmospheric "emissivity"
196 em1 = 1.0 - tau1
197 em = 1.0 - tau
198 ! downwelling and upwelling brightness temperature for each layer
199 teff1dn = ta - gamma*hdn
200 teff1up = ta - gamma*hup
201 teffdn = ta - gamma*hdninf
202 teffup = ta - gamma*hupinf
203 tbclrdn = teffdn*em
204 tbclrup = teffup*em
205 !
206 tb1dn = em1*teff1dn
207 tb1up = em1*teff1up
208 tb2dn = (tbclrdn - tb1dn)/tau1
209 tb2up = tbclrup - tau2*tb1up
210 ! total downwelling and upwelling brightness temperature and transmittance
211 tbdn = tb1dn + tau1*(tbcld + taucld*tb2dn)
212 tbup = tb2up + tau2*(tbcld + taucld*tb1up)
213 tauatm = tau*taucld
214 !
215 ! the following lines apply an ad hoc correction to improve fit
216 ! at large angles and/or high gaseous opacities
217 ! (downwelling brightness temperatures only)
219 alph = (0.636619*atan(mu*sig))**2
220 tbdn = (1.0-alph)*tbdn + em*alph*ta
221 !
222 end subroutine tbatmos