Title: Radiative Forcing of the Stratosphere of Jupiter, Part I: Atmospheric Cooling Rates
from Voyager to Cassini
Authors: Zhang, Nixon, Shia, West, Irwin, Yelle, Allen, and Yung
Dear Editor,
First we would like to acknowledge the reviewers for the comments, with the help of
which the manuscript has been improved. In the following paragraphs, we will first cite
the comments in blue, followed by our response in black and the changes of manuscript
in italics. We also mark all the changes in red in the revised manuscript.
$$$ do not use red if possible $$$
Thanks,
Xi Zhang, and co-authors
======
Reviewer #1: The manuscript by Zhang et al. presents interesting new calculations of the
cooling rates on Jupiter based upon the latest temperature and hydrocarbon profiles
obtained from Cassini/CIRS and Voyager/IRIS dataset. This work deserves publication
and will be of interest for PSS readers. Nevertheless I have a few important comments to
raise the reliability of the results and the clarity of their presentations.
Major comments:
- The authors used two different radiative transfer modelling methods: a correlated-k
model based on the spectral library implemented in NEMESIS for the data analysis and
the vertical profiles retrieval, and a line-by-line model for the cooling rates calculation
with spectral libraries which seem different from those used in NEMESIS (these latest
are not clearly stated in the manuscript). I am not advocating that one of these two
1
methods is better than the other, but rather that they would not be consistent with each
other. The differences in the spectral libraries, the different approximations used in the
line-by-line and the correlated-k models may lead to differences in inverted temperature
and chemical profiles, or differences in the cooling rates for a given atmospheric
structure. The strength of this paper is to used a very consistent database that is actually a
measure of Jupiter's cooling to space, but they jeopardize this advantage by using two
different radiative transfer models which may introduce a bias between the observations
and the cooling rate calculations.
First, the spectral libraries used in the latest NEMESIS were described in Nixon et al.
(2010), which are consistent with that we used for the cooling rate calculations. For
example, we both used the latest C2H6 spectroscopic data from Vander Auwera et al.
(2007) with H2 broadening line width, and CH4 and C2H2 data from the HITRAN dataset.
The only difference is that the H2-H2 collisional induced opacity in NEMESIS is from
Borysow et al. (1985, 1988) but in the cooling rate calculation we used the updated one
from Orton et al. (2007). However, from personal communication with Dr. Glenn Orton,
the correction from Orton et al. (2007) is only significant for the “cold” planets such as
Uranus. For a “warmer” planet like Jupiter, that correction is negligible. Therefore, the
spectral databases used in NEMESIS and the cooling rate calculations are consistent in
this study.
Second, about the accuracy of correlated-k versus LBL method, the correlated-k method
has negligible errors relative to LBL for our purposes, since everything is dominated by
the much larger unknowns, e.g. in the knowledge of the temperatures and gas abundances
at deeper and higher levels than reliable CIRS/IRIS measurements. We have always
found, on testing, that it is typically no more than a few percent, if 20 gaussian points are
used (which is typical). At this level, any numerical errors are typically as small or
smaller than errors on the absolute line intensities from the lab spectroscopy - where
pressures are difficult to measure accurately to better than a few percent due to variations
across the cell. For reference, the Nemesis paper (Irwin et al. 2008, p1140) estimates the
correlated-k error to be less than 5%. This difference is much smaller than that from
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uncertainties of the retrieved temperature and gas profiles.
In view of this, we think it is necessary to add one more paragraph at the end of section
3.1 (page 17) for clarification: “It should be noted that the spectral database used in the
LBL cooling rate calculations is consistent with that in NEMESIS because the
correlated-k coefficients in the retrieval are computed from the same spectral libraries
(Nixon et al., 2010) except for the H2-H2 CIA. However, the difference between the
opacity from Borysow et al. (1985; 1988, used in NEMESIS) and that from Orton et al.
(2007, used in the cooling rate calculations) is negligible under the temperature range of
Jupiter (personal communication of G. Orton). In addition, the error from correlated-k
approximation is usually below 5% with 20 quadrature points (Irwin, et al., 2008).
Therefore, the difference between the two radiative transfer methods used in this study is
negligible relative to the uncertainties of the retrieved temperature and gas profiles.”
- The authors pay very much attention to the CH4 abundance in the upper stratosphere,
i.e. to the homopause level. I find this point of little importance for their discussions
compared to the tropospheric or lower stratosphere CH4 abundance. In fact, the CIRS
and IRIS dataset constrain the temperature structure up to the 0.1-mbar level, hence 2-3
scale heights below the homopause level. Hence, the cooling rates calculation at the
homopause levels is rather speculative and not constrained by the available dataset. But
the deep methane abundance will affect not only the cooling rates in the lower
stratosphere, but also the heating rates!! So it deserves a dedicated discussion, and also
calculations with different assumptions. In the literature two different measurements are
available: the in situ Galileo value, which has error bars of 25% (Wong et al. 2004) and
the remote sensing value from Gautier al. (1982) (1.95-0.22e-3), slightly lower than the
in situ value. Overall the possible CH4/H2 mixing ratios stretch from 1.73e-3 to 2.94e-3.
It can have a dramatic effect on the calculations and this variable must be taken into
account.
Yes, the CH4 mixing ratio in the deep atmosphere from Galileo has been updated by
Wong et al. (2004). Note that the H2 mixing ratios in Gautier et al. (1982) and Wong et
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al. (2004) are also different. In order to cover the whole uncertainty range, we think the
CH4 mixing ratio (CH4/air) in the deep atmosphere of Jupiter ranges from 1.5e-3 to 2.5e3. We were using 1.81e-3 based on Niemann et al. (1998). In the revised manuscript we
have investigated the effects of the update CH4 values:
(1) We have modified Fig. 1 to include the deep CH4 data from Wong et al. (2004).
GMPS data is available from 1.25 to ~4 bar. Since the CH4 mixing ratio is nearly
constant below that pressure level, we just used 2 bar as a reference pressure level. Based
on that data point and its uncertainty, we re-calculated the CH4 profiles using the 1D
chemical transport model from Moses et al. (2005). The two new dashed curves
(compared to old Fig. 1) correspond to the deep CH4 mixing ratio 1.5e-3 and 2.5e-3,
respectively.
(2) We tested how the two new CH4 profiles affect our CIRS retrieval results in
NEMESIS. Those can be considered as two extreme cases. Since the CH4 profile is
prescribed, changing CH4 abundance may affect the temperature profile retrieval. But
changing the CH4 profile will not directly affect the C2H2 and C2H6 profile retrievals
because their spectral bands do not overlap with the CH4 bands. As before, we tried five a
priori temperature profiles (in Fig. 1) and different a priori uncertainties (correlation
4
length is one scale height since it does not matter significantly). We note that, changing
the prescribed CH4 profile does change the retrieved temperature profile. Specifically, if
we increase the CH4 mixing ratio, the retrieved temperature tends to be smaller, and vice
versa. However, we also note that the effect is not large, compared with the uncertainty
range of our old ensemble cases. For example, we have plotted the “new” retrieved
temperature profiles (global-mean, in red) on top of the “old” results (blue, see the old
Fig. 2), as shown by the figure below. It can be seen that the red curves are located within
the uncertainty range of the previous retrieved profiles (information is low above the
green line, roughly). That means our previous estimate of the uncertainty range in the
retrieved temperature is already large enough to include the effect from the uncertainty of
the deep CH4 abundances. Since we prescribed the temperature profiles in the retrievals
of C2H2 and C2H6, the gas retrievals would not affected either.
(3) We tested how the two new CH4 profiles affect our cooling rate calculations. Since
the temperature retrieval were not significantly affected, we fixed the temperature and
other gas abundances, and calculated the cooling rates associated with the five dashed
profiles in Fig. 1. The results are plotted in the figure below with dashed lines showing
the cooling rates by the CH4 𝜈4 bands alone, and solid lines showing the total cooling
rates. The black lines correspond to the case with the CH4 profile from the model C in
Moses et al. (2005). Although changing CH4 abundances by 10-40% has an observable
change in the CH4 cooling rates (in a log scale axis), the effect is still negligible in the
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total cooling rate because CH4 is not the major coolant of the stratosphere of Jupiter, as
we have pointed out in the manuscript.
(4) We tested how the two new CH4 profiles affect our gas heating rate calculations.
Because CH4 is the major heating source, the heating rate is affected, i.e., changing the
methane mixing ratio by 20-40% would change the stratospheric heating rate by as large
as ~20%. Meanwhile the vertical profile of the heating rate also changes with the CH4
change. For example, increasing CH4 abundances will increase the heating rate in the
lower pressure region (e.g., stratosphere) but reduce the heating rate in the higher
pressure region (e.g., troposphere) because of the self-shielding effect, although the
column integrated heating rate would not change as the total absorbed solar energy in the
near infrared does not change.
The total absorbed solar energy is actually constrained by the reflected spectra from the
ground-based measurements (e.g., Banfield et al., 1998) and Cassini ISS images. The I/F
spectra imply the existence of the aerosols in the stratosphere of Jupiter. Different
assumption of the CH4 abundances in the atmosphere may lead to different distributions
of the aerosols under the constraints of I/F spectra. Therefore, it is possible that the
heating rate change due to the CH4 change is (partly) compensated by the change of the
aerosol heating rate in the visible wavelengths, but as we have stated in the manuscript,
this is beyond the range of this current paper and will be discussed in the future paper
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(Part II). In the NIR wavelengths, since the reflected solar energy is less the 1 percent of
the total energy (Banfield et al., 1998), we can just ignore the effect of the aerosols.
We have updated the uncertainty range of the heating rate in Fig. 10 (see the figure
below). Due to the uncertainty of the deep CH4 mixing ratio, the uncertainty of the
heating rate has been enlarged, but this effect would not change our conclusion that the
gas heating rate is smaller than the cooling rate in the stratosphere of Jupiter.
Overall, this comment is much appreciated. Our revised manuscript has now incorporated
the updated CH4 value and its uncertainty range from Wong et al. (2004). We found the
major effect is on the heating rate, but much smaller effect on the cooling rate and
temperature retrieval. We have updated Fig. 1 and Fig. 10, and we added several
sentences on p. 8: “Below 1 bar, Gautier et al. (1982) derived the [CH4]/[H2] from IRIS
measurements and obtained ( 1.95 ± 0.22) × 10−3 with the H2 mixing ratio fixed as
0.897. The [CH4]/[H2] ratio derived from Galileo probe mass spectrometer (GPMS)
measurements by Niemann et al. (1998) is (2.1±0.4)× 10−3 and subsequently updated to
(2.37±0.57)× 10−3 by Wong et al. (2004), and the H2 mixing ratio from Wong et al.
7
(2004) is about 0.86-0.87. The model C from Moses et al. (2005) was based on the deep
CH4 mixing ratio (CH4/air) of 1.81 × 10−3 (from Niemann et al., 1998). In order to fully
investigate the uncertainty range of the previous measurements, we also create two
extreme cases, with the deep CH4 mixing ratio of 1.5× 10−3 and 2.5× 10−3 , respectively.”
Since we have updated Fig. 1 and tested two more CH4 profiles, we modified the
sentences on p. 10: “We wish to find all possible solutions in the full parameter space.
For the temperature retrieval at each latitude, our parameter space includes 5 CH4 profiles
(Fig. 1), 5 a priori temperature profiles based on the previous work described in Section
3.2.2, 4 a priori temperature uncertainties from 2.5 to 20 K, 3 vertical correlation lengths
from 1 to 3 scale heights, resulting in 5 × 5 × 4 × 3 distinct cases.”
And we also modified the sentences on p. 11:
“The CH4 profiles with different homopause levels only affect the retrieval results above
the 0.01 mbar pressure level, and CH4 profiles with different deep tropospheric values
within the GPMS uncertainty range do not seem to affect the temperature retrieval
significantly, so the different CH4 profiles essentially result in similar retrieved profiles
below 0.1 mbar.”
- Last important point, how reliable are the absolute flux calibration for the IRIS and
CIRS instrument. As shown, figure 11, the difference between the calculated heating and
cooling rates could be accounted for by a decrease of 20% CIRS flux. 20% is usually the
level of uncertainty given by engineers for a standard calibration methods. Getting
smaller uncertainties is difficult. It may have been performed by the CIRS and IRIS
teams, but the authors should state it and refer to refereed literature to prove it.
The flux calibrations were very briefly stated in Nixon et al. (2007) and Nixon et al.
(2010), but there is no published literature on the calibration errors, since it is usually
perceived to be small compared to the other uncertainties in the retrieval, and the random
noise (NESR). For CIRS, the instrument optics is thermostated to 170 K, with an
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accuracy of about +/- 0.1 K. So long as we believe our temperature sensors, that confirm
this thermostating with small variations at the level of 0.1 K across the instrument, then
the radiometric calibration follow from that. For example, at 1300 cm-1, a difference in
temperature from 150 K to 150.1K corresponds to about a 1% difference in flux. This
obviously varies depending on wavelength, and the brightness temperature of the target.
A radiometric calibration error of 20% would show up as a larger temperature error, e.g.
2 K at 150 K in 1300 cm-1, which is inconsistent with the agreement and repeatability
between CIRS and other instruments. Regarding IRIS, it is the precursor of CIRS and
designed in a similar way. Therefore, we think the 20% difference in the CIRS flux is
larger than our current calibration errors and should be considered as a robust result. In p.
28, we added one more sentence to make this statement more clear: “Reducing the lower
stratospheric temperature by 10 K will decrease the outgoing flux by 20% at the
wavelengths around 600 cm-1, which is much larger than the systematic errors such as the
flux calibration error.”
Minor comments:
- All manuscript: the authors are using the expression "above (or below) whatever mbar".
This is unclear. They should specify "above the whatever-mbar pressure level" or " at
pressures lower than whatever mbar".
We have modified all the unclear places.
- Page 4: The Lellouch et al. (2006) paper on CO2 and HCN distribution is also
advocating for both horizontal eddy diffusion and advection.
Yes. We modified that part as follows: “In fact, observations have shown that the
temperature change is much larger than can be explained by the instantaneous radiative
equilibrium model (Simon-Miller et al., 2006), possibly owing to the effect of the
stratospheric dynamics. The latitudinal distributions of HCN and CO2 after SL9 impact
suggest the existence of both horizontal eddy diffusion and advection (Lellouch et al.,
9
2006). The distributions of C2H2 and C2H6 from Nixon et al. (2010) also imply a possible
meridional circulation in the stratosphere of Jupiter because the two species also serve as
the tracers for transport. The opposite latitudinal trends of the short-lived species (C2H2)
and the long-lived species (C2H6) are a strong evidence of the horizontal advection, as
also suggested by the simulations using a chemistry-transport (Zhang et al., 2013).” And
we added Zhang et al. (2013) in the reference list.
- Page 9: The different C2H6 measured values do not always agree with each other as
rightly discussed by the authors. They should take into account that the C2H6 spectra
libraries have recently dramaticaly changed and that some of the old values may have
been different if the new spectral libraries would have been used for their retrieval.
We added one more sentence in the part: “It should be noted that the previously retrieved
values might be changed since the C2H6 spectral library has been greatly improved in
recent years (e.g., Vander Auwera et al., 2007; Orton et al., 2008).”
- Page 9, line 50: the sentence "The para-hydrogen fraction is calculated in the forward
model" is misleading since it could be understood that the fp is actually retrieved from
the data. I would prefer " The para hydrogen fraction is always assumed equal to its
thermodynamical equilibrium value."
We have modified the sentence to “The para-hydrogen fraction is assumed to be equal to
its thermodynamical equilibrium value according to the local temperature of each level,
with the value of 0.25 in the deep atmosphere.”
- page 10: The temperature is retrieved up to the 0.1-mbar level. It seems a bit high and
not consistent with Nixon et al. (2006) who stated that the T(p) profiles could be
constrained between 1-10 mbar using the same CIRS dataset as the present manuscript.
There is no Nixon et al. (2006). Simon-miller et al. (2006) constraint their retrieved
temperature profiles between 1-10 mbar. But later, Nixon et al. (2007) stated that the
10
information in the Q-branch lines of CH4 is sensitive to the temperature in the upper
stratosphere (5 microbar). Thus Nixon et al. (2007) and Nixon et al. (2010) extended the
retrieval region to the lower pressure level.
- page 15, line 4: scattered really?
The aerosols and clouds may scatter the mid-infrared photons in general although we
have not found a robust evidence for Jupiter.
- page 23, line 8: "much less variations". What kind of variations (vertical? latitudinal?)
We have changed “variation” to “meridional variation”.
- page 23, line 34: please a reference for the QBO-induced circulation in the terrestrial
atmosphere. Here a comparison with Saturn may also be appropriate, including the work
of Howett, Guerlet, Hesman, Greathouse, etc...
We added two references for the QBO-induced circulation: Reed (1964) and Plumb and
Bell (1982). We are not sure if there is a strong evidence on the similar induced
circulation on Saturn, so we do not cite the Saturn work here.
- page 24, the authors are using the Orton et al. CIA calculations for calculating the
cooling rates and the Borysow et al. calculations for the heating rates. Please verify that
the approach is consistent for the two windows.
Orton et al. CIA calculation is only available in the mid-infrared, which is important for
the cooling rates, but not for the heating rates which are mostly contributed by the NIR
CH4 absorption. So there is no conflict between the two datasets.
- page 35 isolation --> insolation
11
We have corrected those three words.
============
Reviewer #2:
This is a good paper that addresses the heating and cooling of Jupiter's
upper atmosphere using data from both Cassini and Voyager. The largest improvements
are (1) the use of Cassini CIRS data to extend the regions of the atmosphere that the
Voyager data sets were not able to, in addition to studying the temporal variability, (2)
improved numerical methods, with well-established codes, for extracting the temperature
and abundance as a function of both altitude and latitude for large number of cases, and
(3) use of up-to-date high resolution line-by-line calculations in which the
cooling/heating can be determined. Probably the weakest part is the latter portion of the
paper (sections 4.3 and 4.4) where they present an analytical model and estimates of
heating due to gravity wave breaking.
This is, however, an area that I have little
experience in (see my comment #20 below). That said, I would recommend this paper
for publication provided the authors address the following items.
Here is my list of comments/questions/corrections:
1.
Page 7, line 4: Clarify the magnitude of the errors comprising Se. I expect that this
a function of how many spectra are used in each latitude bin.
Our formal error bars are somewhat optimistic, as they include only the 'known
unknowns' (to quote Donald Rumsfeld), which are principally estimates of random errors
(noise), and not the 'unknown unknowns', which are principally systematic errors that are
hard to estimate. These include things like the radiometric uncertainty in the calibration,
errors in the intensities in the spectral line databases, and differences in the
latitudes/altitudes sounded by the FP3 and FP4 arrays. In this study, we estimated the
forward model error to be on the same order of magnitude as the measurement error. The
measurement errors depend on the number of spectra used in each latitude bin. Please see
Nixon et al. (2007) for details.
12
We have modified that part to: “A good retrieval profile should be able to match the
observations weighted by the measurement covariance matrix Se and also has sufficient
smoothing supplied by diagonal elements of the quantity 𝐾𝑛 𝑆𝑥 𝐾𝑛𝑇 , where 𝑆𝑥 is the error
covariance matrix of the a priori state vector and 𝐾𝑛 ??? is the Jacobian matrix or the
matrix of functional derivatives which measures the sensitivity of the forward model with
respect to the change of state vector. The measurement covariance matrix Se includes the
measurement errors (see Nixon et al., 2007 for details) and forward model errors. The
latter were estimated to be on the same order of magnitude as the measurement errors in
this study.”
2. Page 9, line 6: The authors state that "C2H2 at the ~10 mbar level are not consistent
with each other", referring to Figure 1. It seems to this reviewer that there is quite large
error bars on the values of C2H2. There also seems to be less agreement at high altitudes
(~0.01 mbar) . Please clarify?
Yes. The error bars are large but still not fully overlapping with each other. That is why
we (and Nixon et al. 2010) think they are inconsistent with each other. The C2H2 at 0.01
mbar pressure level is quite hard to retrieve from the nadir-viewed spectra so we do not
have more comments on that. Sometimes the values were obtained with the C2H2 values
fixed below (say, at ~1 mbar). So the readers should keep in mind that the previously
retrieved values might have larger errors than that showed in Fig.1. In the manuscript we
have already stated: “However, for C2H2 in the upper stratosphere (0.01 mbar),
measurements by the NASA Infrared Telescope Facility (IRTF) (Bézard, et al., 1997;
Yelle et al., 2001), ISO (Fouchet et al., 2000) and the recent New Horizons occultation
data (Greathouse et al., 2010) do not agree with each other.” In the revised manuscript,
we added the (0.01 mbar) to highlight the pressure range we mentioned.
3.
Page 9, line 41: "spanning from 70o S to 70oN". Is this due to foreshorting at high
latitudes?
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In the higher latitudes, the number of spectra is too few to satisfy a good signal to noise
ratio for our retrieval. Please see Nixon et al. (2007; 2010) for more details.
4.
Page 9, line 50: Para-/ortho- hydrogen is only mentioned briefly in this paper, even
though it is one of the parameters obtained from the retrieval software.
sensitivity on the para-/ortho- hydrogen abundance?
What is the
How does the transition non-
equilibrium abundances to equilibrium abundances impact heating/cooling rates?
As also mentioned by the other reviewer, this part was misleading. We did not retrieve
the para-/ortho- hydrogen ratio. We have modified the sentence to “The para-hydrogen
fraction is assumed equal to its thermodynamical equilibrium value according to the local
temperature of each level, with the value of 0.25 in the deep atmosphere.” On the other
hand, the non-equilibrium values (here means away from 0.25) have little impact on the
cooling rates of the lower stratosphere because the cross sections of the normal hydrogen
and the equilibrium hydrogen are not very different (Orton et al., 2007). For the solar
heating rate, the hydrogen contribution is almost negligible.
5.
Page 11, line 43: "CH4" is stated here, whereas Figure 3 only shows panels for T,
C2H2, and C2H6. Please clarify or fix.
We have modified the sentence to “Fig. 3 shows the global mean profile of temperature
and two-dimensional (latitude-altitude) maps of C2H2 and C2H6 from a typical CIRS
retrieval case.”
6.
Page 13, line 25: "CH4" is stated here, whereas Figure 3 only shows panels for T,
C2H2, and C2H6. Please clarify or fix.
We have modified the sentence to “Fig. 5 shows a typical case with the global mean
profile of temperature and two-dimensional maps of C2H2 and C2H6.”
7.
Page 12, line 19-20: What kind of circulation would cause C2H6 would increase
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towards the pole? Might an auroral source of C2H6 be a candidate? Also a bit confusing
is the increasing contrast mentioned on page 14, line 41. Perhaps an example or
reference?
Yes, the auroral source of C2H6 might be a cause too. We have added a sentence to this
part: “The C2H6 seems increasing from equator to pole, suggesting a transport-dominated
processes with an upward transport in the lower latitude and a downward transport in the
higher latitude (Nixon et al., 2007), or a possible aurora source of C2H6 in the polar
region (Zhang et al., 2013).”
For the increasing contrast of C2H6. We meant here that a stronger equator to pole
advection would transport more C2H6 to the polar region in a relatively short timescale so
as to increase the latitudinal contrast. On the other hand, for a short-lived species such as
C2H2, more advection would compensate the effect the local chemistry so that to reduce
the latitudinal contrast.
8.
Page 12, lines 40-41: Is this basically a sliding average? How much of will this
impact the lack of the QQO feature vs. the atmosphere being "less violent" (page 13, line
60.
The sliding average was used only for the CIRS data, but not the IRIS data. So for CIRS
the averaging width is 5 degrees, stepped by 5 degrees in center position. For IRIS, the
equivalent numbers are 10 and 5. So CIRS bins do not overlap but the IRIS ones do. The
QQO feature would be visible in the Voyager map if there is one, because the QQO
feature covers from 20°S to 20°N as shown in the CIRS map. The Voyager spectra are
only averaged in 10° width latitudinal bins so the spatial resolution is high enough to
resolve the QQO feature.
9.
Page 13, line 6: "uses" should be "use".
We have corrected it.
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10.
Page 16, line 19: Clarify what you mean by "spectrally resolved optical depth".
Do you mean the "cross section".
It is the monochromatic optical thickness of each atmospheric layer, not the cross section.
We have modified that part to “The spectrally resolved optical thickness for each
atmospheric layer is calculated using the Reference Forward Model (RFM,
http://www.atm.ox.ac.uk/RFM/#publications)…”
11.
Page 16, line 37: Add a reference or two after "previous calculations".
We have modified that part to “Our benchmark models achieved much higher spectral
resolution than the previous calculations (e.g., Yelle et al., 2001).”
12.
Page 16, lines 43-48. Please rewrite to clarify.
We have modified that part to “The pressure broadening of hydrocarbons in the hydrogen
atmosphere could be different from that in Earth’s atmosphere. The experimental data are
based on the recently updated C2H6 spectroscopic line parameters in the ν9 band (Vander
Auwera et al., 2007), with hydrogen-broadening widths adopted (Orton et al., 2008). ”
13.
Page 17, line 23: "CH4" is stated here, whereas Figure 3 only shows panels for T,
C2H2, and C2H6. Please clarify or fix.
We have modified that sentence to “Fig. 3 shows the global mean profile of temperature
and CH4, and two-dimensional maps of C2H2 and C2H6 from a typical retrieval case.”
14.
Page 18, line 19: What kind of error bars can you assign to these individual
cooling rates?
We did not calculate the error bars for the individual cooling rates. The error bars for the
CIA are mostly from the temperature uncertainty. Since the CIA cooling dominates the
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lower stratosphere, the error bars can be viewed from Fig. 10. The error bars for C2H2
and C2H6 dominate the error bars in the middle stratosphere in Fig. 10. Since we have
prescribed CH4 profile, the error bars of CH4 cooling are due to the temperature
uncertainty. In the upper stratosphere, the errors of the CH4 cooling rates are also from
the uncertainty of the CH4 profile. Overall, below 1 mbar pressure level, the uncertainties
of the individual cooling rates are about 30% of the cooling rate values.
15.
Page 19, lines 56-57: Please clarify what you mean with the last sentence.
The replenishment will increase the population of the 𝜈4 level so that the non-LTE effect
looks reduced. Please see Fig. 2 in Halthore et al. (1994).
16.
Page 20, lines 16-19: This sentence is confusing. If "the CIA component is
negligible" why does it necessary?
That was a typo. We have modified that sentence to “This modification is necessary since
in the higher atmosphere where the hydrocarbon abundances drop rapidly with pressure,
the CIA component is not negligible.”
17.
Page 22, lines 47-54: As with #8 above, how much of this is due to smoothing and
the larger FOV of IRIS compared to CIRS?
As we have stated in the above, we think the variations span more than 20 degrees
latitude, which is larger than the smoothing width of the Voyager data (10 degrees). So
the variation is robust and the difference between Voyager and Cassini data should be
considered as a temporal variation instead of the representative issue, as also supported
by more data on QQO variations in Friedson et al. (1999).
18.
Page 23, lines 39-41: I assume that the QQO can be modeled or has been observed
over time. Have you tried to assess the full seasonal impact of this on Jupiter's cooling
and do the CIRS and Voyage epochs fit in with this?
17
It would be of interest to do that. However, in order to simulate Jupiter’s cooling rate, the
vertical temperature profile is required. There are continuous observations of the 7.8
micron radiances that show the QQO-like variations (Friedson et al, 1999; Simon-miller
et al., 2006). So it might be possible to investigate the full seasonal impact of the QQO on
Jupiter’s cooling. We leave it to the future work. We added the following sentences in the
paragraph: “There are continuous observations of the 7.8 𝜇𝑚 radiances that show the
QQO variations over time (Friedson, 1999; Simon-miller et al., 2006). It might be
possible to assess the full seasonal impact of the QQO on Jupiter’s cooling rate in the
future study.”
19.
Page 26, lines 5-10. Fix and clarify.
We have modified that part to “But in the lowest stratosphere (10-100 mbar), it is clear
that the globally averaged heating rate does not match the cooling rates. The peak value
of the cooling rate is about 45 erg g−1 s−1 at 50 mbar, larger than the heating rate by a
factor of 2 at the same pressure level.”
20.
Page 30, lines 38-59. The magnitude of gravity wave breaking seems to be the
main unknown, although you conclude that they may be important. What is necessary to
prove that they indeed are important? Better modeling of the gravity waves? Specific
observations?
In the literature we have cited Young et al. (2005) and Greathouse et al. (2011) who
showed the possible evidences of the gravity waves, and Young et al. (2005) who
discussed the possible impact on the stratospheric heating on Jupiter. We did not
conclude that the wave heating must be important. It will be important only if we adopt
the calculation by Young et al. (2005). On the other hand, the wave heating is just one of
the possible heating source. The aerosol heating could be important too (as shown by
West et al., 1992).
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In order to avoid misunderstanding, we have changed that sentence to “If we adopt the
magnitude estimate from Young et al. (2005) and the natural correlation between the
slopes of the gravity wave heating rate and the gas cooling rate, the wave heating might
be important, and may help solve the seemingly imbalance above the 1 mbar pressure
level, if there is any.”
21.
Page 31, line 6: Add "heating" after "is aerosol".
22.
Page 32, line 39: Change "But" to "However,".
23.
Page 34, line 44: Change "as the altitude gets higher" to "with increasing".
24.
Page 34, line 50: Add "increasing" between "with" and "altitude".
21-24: We have corrected as the reviewer suggested.
25.
Page 35, lines 23 & 32: Do you mean to use "insolation" rather than "isolation"?
We have changed all the ‘isolation’ to “insolation”.
26.
Page 36, line 16: Change "still on debate" to "still open to debate".
We have corrected as the reviewer suggested.
27.
Page 37, Figure 4: The error bars for C2H6 look a bit odd to me given the small
spread in C2H6 (blue curves).
We have explained this in Page 14: “Although the error bars in the IRIS gases appear to
be smaller than the CIRS results from the plots, it is not appropriate to conclude the IRIS
gas retrievals in Fig. 4 are more accurate than the CIRS results, because the profile
retrieval of CIRS data distributes the error probability distribution in a much larger
parameter space.” Note that we have fixed the shape of C2H6 in the IRIS retrieval, so the
whole retrieved profiles are strongly constrained by the pressure levels that the spectra
are sensitive to (where we put the error bars). We do not have any information at the
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other pressure levels where the reviewer might have found the small spread.
28.
Page 1 of Appendix, line 10: "Substituting" is a bit misleading. Moments need to
be taken, etc. Please expand.
We have modified that part to “Taking the first and second moments of the Equation
(A.1) and substituting Equation (A.2), and we obtain:”
29.
Page 2 of Appendix, lines 32-34: It is a bit confusing as to whether you are using
monochromatic terms here or wavelength integrated. Please clarify.
We have modified the sentence to “where 𝜏𝑣 is the integrated optical depth at visible (or
near IR) band”.
30.
Page 2 of Appendix, line 36: Please insert the specific equation number from
Goody and Yung (1995).
This is basically the same as Equation (9.13) in Goody and Yung (1995).
31.
Page 3 of Appendix, line 41: "A.2" should be "A.3".
We have changed A.2 to A.3.
32.
Page 5 of Appendix, line 85: Please explain why.
2𝜋
𝜏
Because ∫0 𝑒 −𝑐𝑜𝑠𝜃 𝑑𝜃 - that is the form we will get in the expression of the zonallyaveraged heating rate, is not analytically integrable.
33.
Page 5 of Appendix, line 89: Please specify what equations you are deriving this
from.
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We have modified that sentence to “The IR Cooling Rate at 𝜏𝑖 (derived from Equation
(2.111) in Goody and Yung, 1995):”
34.
Page 9 of Appendix, line 166: With the errors relatively small for both numerical
scheme, what is your preferred method for this work?
We used two methods in this study and they are consistent. The figures in the paper are
based on the finite difference calculations, as stated in page 16.
35.
Page 10 of Appendix, line 186: By "levels", do you mean the boundaries between
layers?
Yes, as having defined in the first paragraph of Appendix B.
Other modifications:
1. p. 15, change “5 to 10 𝜇𝑚” to “5 to 100 𝜇𝑚”
2. We have added several references in the manuscript:
Borysow, A., Trafton, L., Frommhold, L., Birnbaum, G., 1985. Modeling of pressureinduced far-infrared absorption spectra:Molecular hydrogen pairs. Astrophys.
Journal 296, 644–654.
Friedson, A.J., 1999. New Observations and modelling of a QBO-like oscillationin
Jupiter’s stratosphere. Icarus 137, 34-55.
Gautier, D., Bézard,, B., Marten, A., Baluteau, J. P., Scott, N., Chedin, A., Kunde, V.,
Hanel, R., 1982. The C/H ratio in Jupiter from the Voyager infrared investigation.
The Astrophysical Journal 257, 901-912.
Niemann, H.B., Atreya, S.K., Carignan, G.R., Donahue, T.M., Haberman, J.A., Harpold,
D.N., Hartle, R.E., Hunten, D.M., Kasprzak, W.T., Mahaffy, P.R., Owen, T.C.,
Way, S.H., 1998. The composition of the Jovian atmosphere as determined by the
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Galileo probe mass spectrometer. Journal of Geophysical Research 103, 22831–
22845.
Plumb, R.A., Bell, R.C., 1982. A model of the quasi-biennial oscillation on an equatorial
beta-plane. Quarterly Journal of the Royal Meteorological Society 108, 335-352.
Reed, R.J., 1964. A tentative model of the 26-month oscillation in tropical latitudes.
Quarterly Journal of the Royal Meteorological Society 105, 441-466.
Zhang, X., R.-L. Shia, and Y. L. Yung. (2013) “Jovian stratosphere as a chemical
transport system: benchmark analytical solutions”, Astrophysical Journal, 767
172 (15pp), doi:10.1088/0004-637X/767/2/172
3. We wish to provide the digital data files of the retrieved temperatures, gas abundances
and heating and cooling rates in the online supplementary materials. So we added one
more sentence in the acknowledgment section: “The digital data files of the retrieved
temperatures, gas abundances and gas heating and cooling rates are available in the
online supplementary materials.”
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