Brightness temperature spectra of Venus computed to determine amount of water vapor in lower atmospher

Pollack, J. B.

Wood, A. T., Jr.

English

NASA Technical Reports Server

/ 
Implications of Microwave Spectroscopy for  the 
Water-Vapor Content of the 
Venus Atmosphere 
J. B. Pollack and A. T. Wood, Jr. 
ff 653 J u l y 6 5  
May 1968 
Smithsonian Institution 
As trophy s i c a 1 Ob s e rva  to r y 
Cambridge, Massachusetts 021 38 
80 5 -44 
https://ntrs.nasa.gov/search.jsp?R=19680016401 2020-03-12T10:53:57+00:00Z
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Pollack- 1 
IMPLICATIONS OF MICROWAVE SPECTROSCOPY FOR THE 
WATER-VAPOR CONTENT O F  THE 
VENUS ATMOSPHERE 
805 -44 
Pollack- 2 
Abstract .  F r o m  a comparison of theoret ical  and observed microwave 
br ightness  tempera tures  of Venus at 1 .35  cm, the center  of a water-vapor  
line, we obtain an upper l imit  of 0 . 8  percent  to the water-vapor  mixing ra t io  
in the lower atmosphere.  This limit is consistent with the amount of water  
vapor detected by Venera 4, the existence of water  ice  clouds, and a green-  
house effect caused by water vapor and carbon dioxide. The computed spec t r a  
suggest that a sensi t ive procedure f o r  detecting water  vapor  is an examination 
of the 1 - c m  to 1 . 4 - c m  wavelength region. 
Pollack- 3 
As  a resu l t  of the data  obtained by the Venera 4 (1,z) and Mar ine r  V 
spacecraf t  ( 3 ) ,  - we now know the atmospheric  s t ruc tu re  of Venus sufficiently 
well to pe rmi t  the construction of rather unambiguous microwave spec t ra .  
In this paper we compute brightness tempera ture  spec t r a  s o  as to set limits 
on the amount of water  vapor in the lower atmosphere.  
compared with the amount of water vapor detected by Venera 4. 
These values a r e  
In accord with the high temperature  conditions found by Venera 4 and 
Mar ine r  V, we assumed that the radio emiss ion  f r o m  Venus emanates  
f r o m  a hot su r face  and atmosphere and that the decline in brightness t empera -  
t u r e  at wavelengths shortward of 3 c m  is attr ibutable t o  a tmospheric  opacity. 
W e  now descr ibe  our  method of calculation. 
To  compute the brightness temperature ,  we integrated analytically Eq. 3 
of a paper  by Pollack and Sagan (4) over the disk and used a constant soiid- 
angle average emissivity.  
microwave opacity a t  each  atmospheric level, the atmospheric  s t ruc ture ,  
and the sur face  emissivity.  
The brightness tempera ture  is a function of the 
We considered three sources  of microwave opacity: pressure- induced 
t ransi t ions of carbon dioxide and nitrogen, and permit ted,  rotational transit ions 
of water  vapor.  
mixture ,  we used the empir ical  formula of Ho et al. (5). B a r r e t t  and Staelin 
(6) presented an  equation fo r  the absorption coefficient of water  vapor, sug-  
gested by Chung (7). 
due to the 1. 35-cm line, and a nonresonant component, due to the overlapping 
wings of l ines at sho r t e r  wavelengths. 
theoretically and adjusted one parameter  to give a good f i t  with a laboratory 
spec t rum nea r  STP .  To tes t  the validity of the formula  at high p r e s s u r e s  
and elevated tempera tures  , we compared i t  with the laboratory resu l t s  of 
Ho et  al .  (5). At the high pressures  (45 to 125 atm),  t empera tures  (393°K to 
473"K), and wavelength (3.2 cm) used in the la t te r  measurement ,  the non- 
resonant  component is dominant; Ho et  al. have no d i r e c t  es t imate  of the 
resonant  t e r m .  
F o r  the absorption coefficient of a carbon dioxide-nitrogen 
-- - 
The absorption coefficient consis ts  of a resonant  term, 
Chung derived his  expression 
We find very  good agreement  between the two formulas  
Pollack-4 
near  room tempera ture ,  but marked disagreement  in the t empera tu re  depen- 
dence of the absorption coefficient. 
formula  in our  computations, with the tempera ture  dependence of the l ine- 
Accordingly, we have used Chung's 
width pa rame te r ,  Av, modified f rom T- o * 6 2 5 ,  a s  given by Chung, to T -2 .5  
> 
a s  found by Ho -- e t  al . (5). 
The atmospheric  s t ruc tu re  w a s  chosen to f i t  the measurements  of 
Venera 4 (1 ,2)  - - and Mar ine r  V (2) quite closely.  
s u r e s  a t  the position measured  by Mariner  V probably closely resemble  the 
average proper t ies  of the atmosphere:  
diurnal  variations (A), a s  would be expected on the bas i s  of the la rge  heat  
capacity of the atmosphere.  Fur thermore ,  the measurements  were  performed 
a t  a midlatitude position of 37". We w i l l  consider two models:  F o r  Model I, 
the average  su r face  tempera ture  equals the sur face  tempera ture  a t  the posi-  
tion viewed by Mar ine r  V. 
average su r face  tempera ture  2 5 "  K lower than does Model I. 
The tempera tures  and p r e s -  
The atmosphere exhibits no appreciable 
Model I1 differs  f r o m  Model I only in  having a n  
We now descr ibe  the detailed properties of Model I. The re  a r e  three 
tempera ture  domains:  
4 .05 a t m  and extending to the surface (2), a constant lapse r a t e  of 7 .9"K/km 
between the top of the adiabatic region and the tropopause tempera ture  point 
of 23O"K, and an i so thermal  profile above the tropopause (2). 
the carbon dioxide mixing rat io  was 85 percent ,  with the remainder  of the 
a tmosphere  consisting of water  vapor and nitrogen (l-,2,2). 
a t  the 5 .08  a tm level was chosen as  437°K (3). 
est imated the sur face  tempera ture  and p r e s s u r e  for  us  by means  of a com- 
puter p rogram fo r  adiabatic profiles, which allowed fo r  the var ia t ion of the 
rat io  of specif ic  heats with temperature  and p r e s s u r e .  Extrapolating f r o m  
the 5.08-atm point to the r a d a r  radius of Venus e), he obtained a sur face  
t empera tu re  of 747" K and a surface p r e s s u r e  of 91 .2  a tm.  
computer  p r o g r a m  a l so  allowed for  a var iable  specific heats ra t io  within the 
adiabatic portion of the atmosphere.  
an adiabatic regime beginning a t  the p r e s s u r e  level of 
We assumed 
The tempera ture  
Richard Wattson (8) 
We note that our  
We selected a value of 0 .82  for the sur face  emissivi ty:  The f r e sne l  
ref lect ivi ty  equations were  used to average over  solid angle a r a d a r  c r o s s  
sect ion of 0 .14 a t  70-cm wavelength (10). 
Pollack-  5 
A mos t  important feature  of our calculations was the allowance for  a 
rapid dec rease  in the water-vapor  mixing rat io  above the level a t  which 
saturat ion is first reached. Since the resonant  t e r m  of the water-vapor  
absorption coefficient var ies  inversely with p r e s s u r e  nea r  the 1 .35 -cm line 
center ,  regions of low p res su re  can significantly influence the microwave 
spec t rum near  this wavelength. 
relatively shallow dips in the brightness tempera ture  near  1. 35 cm. 
By allowing fo r  saturat ion,  we obtained only 
Once saturat ion is attained, condensation will occur  and the wa te r -  
vapor par t ia l  p r e s s u r e  will follow a saturat ion curve to the cloud tops. By 
analogy with the ea r th  (ll), the relative humidity in the s t ra tosphere  would 
probably be quite low. Finally,  a t  sufficiently high alt i tudes,  photodissociation 
of water  vapor will occur.  
by having the water-vapor  mixing ratio dec rease  exponentially above the 
saturat ion point with a 1 - k m  sca le  height, a value appropriate  f o r  the water -  
vapor saturat ion curve.  
of 4 did not significantly a l t e r  the computed spec t ra .  
We have attempted to s imulate  the above situation 
Changes in the value of the sca le  height by a factor  
We performed spec t ra l  calculations of br ightness  tempera ture  with a 
computer program writ ten initially by Andrea Dupree,  and modified sub-  
stantially by one of the authors (A. T. W. ). Integration s tep  s i zes  of 1 k m  
were  used in performing the vertical  integration. 
F igu res  1 and 2 present  the resul ts  of the calculated br ightness  tempera-  
tu re  spec t r a  for  s ix  values of the water-vapor mixing rat io:  0 percent,  0. 1 p e r -  
cent,  0 .  3 percent,  0 . 5  percent,  1 percent, and 3 percent.  Also given a r e  m e a s -  
urements  of br ightness  temperature  near  infer ior  conjunction with the es t i -  
mated e r r o r s ,  which were taken f r o m  a compilation by Dickel (12).  - 
puted curves  a r e  ra ther  insensitive to the exact  choice of input pa rame te r s ,  
especial ly  in the 0 .8 -cm to 1 .4-cm wavelength range. F o r  the cases  of l a r g e r  
water-vapor  mixing rat ios ,  l e s s  than a 15°K change in br ightness  tempera-  
t u r e  resul ted in this range when the following changes were  simultaneously 
made:  the sur face  tempera ture  decreased to 543°K (the value est imated by 
the Venera 4 exper imenters ) ;  the sur face  p r e s s u r e  lowered to  20 atm; the 
The corn- 
Pollack - 6 
emissivi ty  increased  t o  0.  9 ;  the carbon dioxide mixing ra t io  changed by 
f 15 percent,  a constant lapse r a t e  used between tropopause and sur face ;  
and the tropopause tempera ture  changed by 15°K. 
resul ted for  the cases  of lower water-vapor mixing rat io ,  especial ly  when 
the carbon dioxide mixing ratio o r  atmospheric s t ruc tu re  was al tered.  
Somewhat l a r g e r  changes 
An interesting fea ture  of F igs .  1 and 2 is the sl ight displacement  sho r t -  
ward of 1.  35 c m  of the center  of the absorption f ea tu re  fo r  c a s e s  of low 
water  -vapor mixing ratio.  
a t  1.  3 c m  for  the 0. 3 percent  case.  This resu l t s  f r o m  the influence of the* 
steady increase  in br ightness  temperature  toward longer wavelength supe r -  
imposed on the d e c r e a s e  caused by the resonance line. 
F o r  example, the absorption minimum is located 
We now s e t  l imits  on the water-vapor mixing rat io  in the lower a tmos-  
Because of the shallowness of the absorption feature  nea r  phere of Venus. 
1 .  35 c m  in the computed spec t ra ,  the depth of the fea ture  i s  not a very  useful 
discr iminant  with the p re sen t  s e t  of data. 
absolute value of the br ightness  tempera ture  at 1.  35 cm: The curves  of F igs .  
1 and 2 a r e  markedly different a t  this wavelength, and a s  mentioned above 
the values of the br ightness  temperature  he re  a r e  relatively independent of 
the exact  values of the input parameters .  
t u re s  have been measured  near  inferior conjunction a t  o r  quite c lose to 
1 .35  c m :  520 f 40°K (13), - 435 f 40°K (14), - 404 f 28°K (15), - 500 f 70°K and 
560 f 48°K (16),  - and 436 f 39°K (17). - Accordingly, the br ightness  tempera-  
tu re  a t  1 .35 cm is probably in excess  of 375°K and water-vapor  mixing ra t ios  
in the lower atmosphere g rea t e r  than 0 . 8  percent  can be excluded. 
tunately, the present  observations do not permi t  the sett ing of a lower bound 
other  than 0 percent.  
A m o r e  useful c r i te r ion  is the 
The following br ightness  tempera-  
Unfor- 
The above upper l imit  is compatible with a value of between 0 .1  percent  
and 0 . 7  percent  determined by the chemical  analysis  experiment  aboard 
Venera 4 ( i ,  - -  2). 
clouds in the upper a tmosphere of Venus. 
bottom tempera tures  below the equilibrium freezing point of water  and s o ,  
except fo r  possibly some supercooled droplets ,  they would consis t  of ice 
It  a lso does not exclude the presence  of water  condensation 
Such clouds would have cloud- 
Pollack-  7 
par t ic les .  
vapor ,  about 0 . 5  percent,  required fo r  a carbon dioxide, water-vapor  green-  
house effect (18). - 
Finally,  the above limit does not exclude mixing ra t ios  of water  
Above, we have considered models having water  -vapor mixing ra t ios  of 
0 .1  percent  o r  m o r e  for  which condensation can  be expected to occur  in  the 
upper  a tmosphere.  However, the occurrence of condensation for  ra t ios  
between 0.001 percent  and 0 .1  percent  is uncertain and depends on the exact 
choice of tropopause tempera ture .  
high s o  a s  to preclude condensation f o r  some of these ra t ios ,  these c a s e s  
could be immediately ruled out a s  being inconsistent with the smal l ,  spec t ro -  
scopically determined amounts of water vapor in the upper portion of the 
a tmosphere  (19). - 
0.001 percent ,  and conceivably spec t ra  produced f o r  such  models would con- 
tain ve ry  deep, nar row absorption fea tures  nea r  1 .35 c m .  However, the i r  
widths would be much s m a l l e r  than typical instrumental  bandwidths (17), - and 
s o  a much shallower line would result .  
prevent the formation of such an  intrinsically deep line by causing a depletion 
of water  vapor in the region of line formation. 
Were  the tropopause tempera ture  to be too 
Finally, no condensation will occur  with values l e s s  than 
In addition, photodissociation may 
The calculated spec t ra  show very broad, shallow depress ions  nea r  1.35 
cm.  
a t  wavelengths centered around and quite c lose  to 1 .35 cm. 
profitable procedure would be to investigate the region between 1 and 1 . 4  cm. 
F o r  example,  the brightness temperature  declines by 50°K for  the 0 percent  
c a s e  between 1 . 4  and 1 cm,  but increases  by 5°K fo r  the 0 . 5  percent  ca se .  
Table 1 presents  values of the ratio of the br ightness  tempera ture  a t  1 .4  c m  
to that a t  1 cm,  a s  well a s  the absolute value of the br ightness  t empera tu re  a t  
1 c m .  
Previous sea rches  fo r  the presence of water  vapor have been conducted 
Perhaps  a m o r e  
J. B. Pollack 
A. T. Wood, Jr .  
Smithsonian Astrophysical Observatory 
and 
Harvard  College Observatory, 
Cambridge, Mas sachus e tts 
Harvard College Observatory, 
Cambridge, Massachusetts 
Pollack- 8 
References and Notes 
1 .  P ravda  (24 Oct. and 1 Nov. 1967). 
2 .  V. S. Avduevskiy, M. Y. Marov, M. K.  Rozhdestvenskiy, "The Model 
of the a tmosphere  of the planet Venus on the  Results of measu remen t s  
made  by the  Soviet Automatic Interplanetary Station 'Venera 4'. 
(1 968). 
P rep r in t  
3. A.  Kliore,  D. L. Cain, G. S. Levy, G. Fjelbo, S. I. Rasoo1,"Structure 
of the  a tmosphere  of Venus derived f r o m  Mar ine r  V S-band measu re -  
ments. P resen ted  at the 1 l t h  COSPAR Meeting, Tokyo, Japan (1 968). 
4. J. B. Pollack and C. Sagan, Astrophys. J. 150 327 (1967). 
5. W. Ho, I. A. Kaufman, P. Thaddeus, J. Geophys. Res.  71 5091 (1966). 
-2 
6. A. H. Barre t t ,  D. H. Staelin, Space Sci. Rev. 109 (1964). 
7. V. K. Chung, "Microwave Spectra of the Planet  Venus." M a s t e r s  thesis ,  
-' 
M. I. T. (1962). 
8. R. Wattson, private communication (1968). 
9. M. E. Ash, I. I. Shapiro, W. B. Smith, Astron. J. 72 338 (1967). 
-mJ 
10. G. H. Pettingill,  R. B. Dyce, D. B. Campbell, Astron. J. E, 330 (1967). 
11. R .  M. Goody, Atmospheric Radiation. I. Theoretical  Basis  (Clarendon 
P r e s s ,  Oxford, 1966), p. 12. 
12. J. R. Dickel, Icarus  6, 417 (1967). 
13. 
14. , Radio Science m, 1577 (1965). 
15. D. H. Staelin and A. H. Barret t ,  Astrophys.  J. _1_44, 352 (1966). 
16. P. H. Gr i f f i th ,  D. D. Thornton, W. J. Welch, IcarusA,  175 (1967). 
17. S. E. Law and D. H. Staelin, "Measurements  of Venus and Jupiter n e a r  
- 
J. E. Gibson and H. H. Corbett, Astron. J. g, p. 74 (1963). 
1 - c m  wavelength. Submitted to Astrophys.  J. (1968). 
18. J. B. Pollack, Icarus ,  in preparation (1968). 
19 .  M. Belton, D. Hunter, R. M. Goody, in  The Atmospheres  of Venus and 
M a r s ,  J. C. Brandt and M. B. McElroy, Eds.  (Gordon and Breach,  
New York, 1968). 
Pollack-9 
20. We a r e  extremely grateful to Dr. Richard Wattson fo r  obtaining the 
sur face  boundary conditions, M r s .  Andrea Dupree fo r  the u s e  of he r  
computer program, Dr.  A. Kliore for  sending u s  a prepr in t  of the la tes t  
reductions of the Mar ine r  V resul ts ,  D r .  C a r l  Sagan fo r  helpful d i scus-  
s ions,  and Dr .  David Staelin f o r  sending us  a prepr in t  of his m o s t  recent  
resu l t s .  This work was supported in pa r t  by NASA Grant  No. 
NGR 09-015-023.  
Pollack-10 
Table 1. Computed br ightness  tempera tures  a t  a wavelength of 1 cm, 
T (1.0) and the ra t io  of br ightness  tempera tures  at 1 . 4  and 1 .0  cm, TB(1.4) /  
TB( l .  0).  B 
.I T B ( l o o )  (OK) T g ( l *  4 ) / T g ( l  0) 
aHZO Model t Model 
1. 
(percent) I II I I1 
0 483 459 1.102 1.107 
0 .1  4 64 442 1.061 1.064 
0 . 3  438 419 1.009 1.027 
0 . 5  421 403 0.976 0.996 
1 .0  395 378 0.939 0.962 
3.0 352 338 0.916 0.941 
.L I
Water-vapor  mixing ra t io  in the lower a tmosphere.  
'Model I uses  the value at the locale explored by Mar ine r  V as the average  
surface tempera ture ,  while Model I1 uses  a n  average  sur face  t empera tu r t  
that  is 25°K lower. 
H 
-I 
w 
n 
0 z 
0 0 0 0 0 
0 0 0 0 0 
b CD In * M 
)lo NI ‘1 
0 
0 cu 
0 
Pollack-1 1 
Pollack- 12 


Implications of microwave spectroscopy for the water-vapor content of the Venus atmosphere

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