Seasonal variability of the temperature structure of Uranus is modeled for all latitudes in the .0004 to 2 bar pressure range in anticipation of the Voyager encounter in January 1986. Atmospheric heating in the model results on the one hand from an internal heat source and, on the other hand, from absorption of solar energy by methane and by non-conservative aerosols located between the 0.5 and 2 bar levels. Various cases for the behavior of the internal heat flux are investigated, such as constant with latitude or constrained to yield a time-averaged thermal emission independent of latitude. Meridional transport of heat in the stably stratified atmosphere is not taken into account. The results indicate that the Voyager encounter time, very small north-south temperature asymmetry should be expected. Moreover, the northern hemisphere, although not illuminated, should emit as much energy (within one percent) as the southern hemisphere at this date. At a given latitude, extreme temperatures are reached at the equinoxes. At the poles, seasonal amplitudes of about 10 K in the upper stratosphere and 6 K at the 0.6 bar level are predicted, and the variation with time of the emission to space is found to be at most 20 percent. The atmosphere of Uranus appears to be characterized by very long radiative response times (mainly due to its cold temperature) which inhibit the large seasonal variations that one could otherwise expect in view of the high obliquity of the planet and its long orbital period

Bezard, B.

Gautier, D.

English

NASA Technical Reports Server

wN87-17642
A MODEL OF THE SPATIAL AND TEMPORAL VARIATION OF THE
URANUS THERMAL STRUCTURE
B. Bezard and D. Gautier
Observatoire de Meudon
Seasonal variability of the temperature structure of Uranus is
modeled for all latitudes in the 10 -4 to 2 bar pressure range in
anticipation of the Voyager encounter in January 1986. Atmospheric
heating in the model results on the one hand from an internal heat
source and, on the other hand, from absorption of solar energy by
methane and by non-conservative aerosols located between the 0.5 and
2 bar levels. Various cases for the behavior of the internal heat
flux are investigated, such as constant with latitude or constrained
to yield a time-averaged thermal emission independent of latitude.
Meridional transport of heat in the stably stratified atmosphere is
not taken into account. The results indicate that at the Voyager
encounter time, very small north-south temperature asymmetry should
be expected. Moreover, the northern hemisphere, although not
illuminated, should emit as much energy (within one percent) as the
southern hemisphere at this date. At a given latitude, extreme
temperatures are reached at the equinoxes. At the poles, seasonal
amplitudes of about I0 K in the upper stratosphere and 6 K at the 0.6
bar level are predicted, and the variation with time of the emission
to space is found to be at most 20 percent. The atmosphere of Uranus
appears to be characterized by very long radiative response times
Cmainly due to its cold temperature) which inhibit the large seasonal
variations that one could otherwise expect in view of the high
obliquity of the planet and its long orbital period.
We have developed a seasonal radiative model for the atmosphere of Uranus. It
is in fact an adaptation of previous modeling for Saturn's stratosphere
(Bezard and Gautier, 1985). In such a seasonal model, temperature for a given
pressure level p and at a given time t is derived from the simple equation:
dT(p,t) = mg dF(p,t) (I)
dt Cp dp '
where m is the mean molecular weight, g is the gravitational acceleration, Cp
is the specific heat, and F is the net upward flux.
Temporal variation of temperature is then directly related to the variation of
the total flux with pressure. The flux consists of two parts: the thermal
flux essentially in the far-infrared (_ >7_m), and the solar flux which is
predominantly absorbed in the visible and near-infrared.
254
https://ntrs.nasa.gov/search.jsp?R=19870008209 2020-03-20T12:36:22+00:00Z
To compute the solar heating, we first consider absorption by methane bands
(0.45-1.5, 1.7, 2.3 and 3.3 _m groups). Methane is constrained to follow the
saturation law in the troposphere above the condensation level, and a constant
mixing ratio is assumed above the temperature minimum. We also include
deposition of solar flux by non-conservative aerosols located below the 0.5
bar level following the model of Bergstralh and Baines (1984).
The second part of the flux, the part concerned with thermal emission, is
calculated through a _ultilayer monochromatic radiative transfer treatment for
wavelengths longer than 7 _m. Calculations incorporate opacity due to CH4,
H2-H 2 and H2-He for a H2 mole fraction of 0.90. This approach is quite
different from that adopted by Wallace (1983) to model the seasonal variation
of the thermal emission over Uranus' disk. Wallace's model is essentially a
grey atmosphere model. Moreover, the use of the Rosseland mean opacity _R
restricts its validity to deep atmospheric levels where _R >>I, which
corresponds to pressure higher than 1-2 bar.
When the calculated temperature profile is found to be unstable, the tempera-
ture lapse rate is set to the adiabatic value, and this criterion then defines
the location of the convective zone. On the other hand, the internal heat
flux behaves as a lower boundary condition in the calculation of the layer-by-
layer transfer of energy. Three different assumptions have been investigated
in this work. In the first case (I), the thermal structure in convective
layers is not allowed to vary with time or latitude. Some meridional heat
transfer thus takes place through the convective zone. In the second case (2),
the heat flux is taken to be independent of latitude, and we adopted a value of
70 erg s-lcm -2 consistent with ground-based measurements. Such a model does
not incorporate any kind of pole-to-equator transport of heat and will yield a
thermal emission-to-space which is dependent on latitude. Finally, a third
case (3) has been investigated in which a latitude-dependent heat flux is set
at the base of the model so that the annual average of the emisslon-to-space
does not vary over the disk. Meridional heat transfer thus occurs in the deep
interior. Note that in any case horizontal advectlon of heat in the radiatively-
controlled region is not taken into account. The model is also constrained to
match some observational constraints: the Bond albedo A b = 0.35±0.05, the
effective temperature as measured from the Earth in 1977-1982 Te = 58.5±2 K, and
a methane abundance CH4/H 2 _ 0.03 with large uncertainties.
The solid line in Fig. 1 indicates the synthetic temperature profile corres-
ponding to an average over the southern hemisphere--the one which is presently
sunlit--and was as well for year 1982.* That year, Moseley et a2. (1985) made
far-infrared measurements of Uranus, and the temperature profile they retrieved
is displayed here as a dashed line. It is about 3 K warmer than the theoretical
profile in the vicinity of the tropopause. This discrepancy may reveal the need
for additional atmospheric heating at these levels, possibly by absorption of
*This is consistent with the conventional definition which identifies the
pole corresponding to the direction of the positive angular momentum vector of
rotation for Uranus as the South Pole because that vector direction is less
than 90 degrees from the South Ecliptic Pole.
255
solar flux by dust particles as discussed by John Appleby in the preceding
paper. The model exhibits a temperature minimumlocated around the 50 mb level
with a very shallow lapse rate in the vicinity (10-100 mb). The temperature
lapse rate reaches the adiabatic value near the 0.45 bar level, but it is
noteworthy that it becomessubadiabatic again at the deepest layers of the
model below the 1.5 bar level. In fact this special feature occurs because at
these levels the solar flux no longer penetrates efficiently so that solar
heating is negligible, and on the other hand the internal heat flux is too weak
to maintain alone an adiabatic lapse rate. However, at even deeper layers
corresponding to high far infrared optical depths, the lapse rate is likely to
be adiabatic again for a non-zero internal heat flux.
-4
I0
10-s
0- 2
10-1
I -
40
/
I
Appleby (1980)
Moseley et al. (1985)
Figure i. Synthetic temperature profile (solid line)
corresponding to an average over the southern hemi-
sphere compared to the result obtained by Appleby (1980)
and the retrieved profile by Moseley et al. (1985).
256
Whenyou perform ground-based spectrophotometry of Uranus to determine its ef-
fective temperature, a potential error might be introduced in that you measure
the thermal emission of the sunlit hemisphere, which maydiffer from the glo-
bal planetary emission. Wehave therefore compared, in the framework of this
seasonal model, the actual planetary effective temperature to that measured
from the Earth as a function of time. In Fig. 2 the curves labelled i, 2 and
3 correspond to the above mentioned cases concerning the behavior of the
internal heat source. The corresponding dashed lines indicate the expected
seasonal variation of observations from Earth as estimated by our model. One
can see that, at most, the discrepancy between the "true" and the "apparent"
effective temperature is less than 2 K and thus lies within the typical uncer-
tainties associated with ground-based measurements. The maximumdiscrepancy
corresponds to no more than a I0 percent variation in the emitted flux; it is
reached at the equinoxes, and in case i or 2 at the solstices to a lesser
extent. We can then conclude that fortunately the inference of Uranus' effec-
tive temperature from ground-based studies is not too strongly biased despite
the nature of the planetary seasonal cycle.
60
59
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uJ
nr 60
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n- 59
Ld
n
_J 58
I-
l.iJ
> 57
F-
u. 59
I.L
W
58
! I | I
%
\ / ::i1\
_\ /\ /
_ \ / \ /
\ 2 / \ / -
- \ _ /
- \ / \ / -
\ / \ /
- \ I \ I _
_ \
\
/
/
\ /
\j57-
56 i I i I
1900 1920 1940
\ /_
\ /
\ /
VOYAGER
E N COUNTE R_'--_
I I i I ,_
1960 1980
YEAR
Figure 2. Seasonally dependent effective
temperature for cases 1-3. The solid
llne curve indicates the actual planetary
effective temperature, and the dashed
line shows that predicted to be measured
from Earth.
257
Figure 3 showsthe predicted seasonal cycles of polar and equatorial tempera-
tures for the 0.35 bar level for cases 1 and 2. This level is close to the
emission-to-space level. Maximumseasonal variations occur at the poles with
amplitudes at 0.35 bar in the range I-3.5 K depending on the assumedredistri-
bution of heat at deeper levels. Larger seasonal changes, typically 5-10 K,
are predicted in the high stratosphere. The variation with time of the
e_sslon-to-space is at most 25 percent. At the equator, the 0.35 bar
temperature does not vary by more than 0.1 K, and seasonal changes do not
exceed I K at any atmospheric level. Twoimportant characteristics should be
noted. First, the seasonal cycle of the atmosphere is lagging behind the
solar heating by approximately one-quarter of the orbital period, so maximum
north to south asymmetryoccurs at the equinoxes and minimumat the solstices.
Secondly, the temporal variations of temperature are indeed very weak in view
of the high obliquity of Uranus, its small internal heat source if any, and
its 10ng orbital period (84 years). These characteristics result from the
very long radiative response time of the Uranian atmosphere mainly due to its
cold temperature.
The Voyager 2 spacecraft encounters Uranus in January 1986, only four months
after the summersolstice for the southern hemisphere. Because of the phase
lag between the insolation cycle and the response of the atmosphere, very
small north-south asymmetryshould be expected. Within the atmospheric range
which will be soundedby the infrared spectrometer IRIS (approximately 0.1-0.6
bar), the difference is expected to be less than 2 K at any level.
64
62
v 60
W
58
n_ 56
UJ
Q_
54
i,i
_- 52
50
CONSTANT CONVECTIVE
_ ZONE STRUCTURE
B
Eq.
B N _
NIFORM INTERNAL HEAT FLUX
-- S
Eq.
VOYAGER VOYAGER
ENCOUNTER '- ENCOUNTER _
i i i I , I I i i '
1920 1940 1960 1980 1920 1940 1960 1980
YEAR
Figure 3. Predicted seasonal cycles of polar and equatorial
temperatures for the 0.35 bar level for cases I and 2.
258
The lack of north-south asymmetry is also illustrated in Fig. 4 where the cal-
culated local effective temperature is plotted as a function of latitude for
the time of Voyager encounter. For any redistribution of heat at deep levels(case I, 2 or 3), the two hemispheres are predicted to emit the sameamount of
energy within one percent. However, a pole-to-equator gradient as high as 6 K
would result if no redistribution of heat takes place to compensatefor the
minimuminsolation at low latitudes (case 2). This difference is less than 0.5
K if sometransfer of energy takes place Jn the upper convective layers (case
I) or through the deep interior (case 3). Now, it only remains to be seen
whether seasonal radiative models give a realistic representation of the actual
thermal structure of Uranus. Undoubtedly, the forthcoming Voyager encounter
will give important clues towards the answer to that question.
60
58
56
60
58
V--
o 56
U_
U..
W
J 60-
0
J
58 -
-90
I I I I I
oo _
*, 2 ¢
m _
3
I I I I I
-60 -30 0 50 60 90
LATITUDE
Figure 4. Local effective temperature for the three
model cases as a function of latitude for the time of
Voyager encounter.
259
REFERENCES
Bergstralh, J. T., and K. H. Baines (1984). Properties of the upper tropo-
spheres of Uranus and Neptune derived from observations at visible to
near-infrared wavelengths. In Uranus and Neptune (Ed. J. T. Bergstralh),
pp. 179-212. NASA CP 2330.
Bezard, B., and D. Gautier (1985). A seasonal climate model of the atmospheres
of the giant planets at the Voyager encounter time: I. Saturn's strato-
sphere. Icarus 61, 296-310.
Moseley, H., B. Conrath, and R. F. Silverberg (1985). Atmospheric temperature
profiles of Uranus and Neptune. Astrophys. J. 292, L83-L86.
Wallace, L. (1983). The seasonal variation of the thermal structure of the
atmosphere of Uranus. Icarus 54, 110-132.
DR. STOKER: Isn't the radiative time constant, even at the levels you are
looking at, longer than the seasonal time scale? How can you get seasonal
variations, or how can you account for that by your models?
DR. BEZARD: Yes, in fact that was the problem. The radiative time constants
are very long at any level. That is why you see only weak variations of
temperature along the Uranian year. We still have some variation because
there is a very long day and a very long night, and also a negligible internal
heat flux.
DR. INGERSOLL: I think you are saying that the big variation in the middle
curve (Fig. 4) is not a seasonal variation at all. It's just the Sun coming
onto the equator and then the pole.
DR. BEZARD: Yes. There is no north to south asymmetry predicted for Voyager
encounter.
260


A model of the spatial and temporal variation of the Uranus thermal structure

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