Reply to Reviewers’ Comments in Italics.
“Vertically Constrained CO2 Retrievals from TCCON Measurements”
Reviewers' comments:
===================
Reviewer #1:
General:
The article touches an interesting and important subject: profile retrievals for CO2
and other greenhouse gases from ground-based FTIR measurements. However, I
think that the authors only took the first steps and did not go far enough along that
road. In the conclusions they claim:
"With this study, we demonstrate that the profile retrieval works equally well as the
scaling retrieval and sometimes better."
I do not think that this study has really demonstrated this yet. The authors have only
taken a few hand-selected test cases, varied the data only a little and have not
explained their method thoroughly enough. For example, it remains unclear how the
different altitude layers in Fig. 3 were selected or how exactly the partial columns
were derived from the "true" profiles. It is also not very convincing that all the
results can be summarized in four figures, two of which are only example plots of
spectra.
To be more specific: in section 3.1 you test the quality of the retrieval by adding
different noise to the same spectrum. Obviously, this works well. However, this is no
surprise, as (Gaussian) noise can be handled well with many retrieval methods. The
effects of scaling and bias on the spectrum or - much more realistic - ensembles of
spectra derived from different CO2 altitude profiles would tell us a lot more. This
seems to be missing. Even the aircraft profiles used in 3.2 do not provide the full
range of variability that you will find in real-world data.
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To prove that their method would work equally well under different meteorological
conditions and for all the other TCCON stations, would require additional efforts. I
would suggest that the authors take their synthetic data retrieval setup and simulate
an ensemble of different cases: TCCON stations at different locations, different
meteorological conditions, more variable CO2 profiles. This should be a fairly simple
exercise that would improve the article a lot.
We thank the reviewer for the thoughtful comments. We agree that further study is
required. The reviewer has illustrated most of our current CO2 retrieval challenges.
However, the main purpose of this paper is as a demonstration of a CO2 profile
retrieval and its application to TCCON data. In this process, we learned that the main
challenge to this work, as mentioned by the reviewer, is the systematic errors in TCCON
spectral residuals. Therefore, using realistic TCCON measurements, we propose to
retrieve only three partial column-averages in the troposphere to provide some
vertical constraints. This study provides a baseline to guide the next generation of
remote sensing measurements. We do not intend to validate the profile-retrieved
product using TCCON in this paper. The suggestions by this reviewer will be the focus
of a future paper.
Minor comments:
- From my experience, words like "Figure", "Table" etc. should always be capitalized.
Many journals require you to spell out the full word ("Figure") at the beginning of a
sentence and use an abbreviated form ("Fig.") within a sentence.
Thank you. We have made these changes.
- I noticed that the quality of the plots in the PDF file is not very good. When you
zoom in, lines and letters become pixeled.
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We apologize for this. We have improved the quality of the figures.
- p. 4, l. 15: "The difference between column-averaged CO2 ( <CHI> CO 2 ) and
surface CO2 can vary from 2 to 10 ppm depending on the location and the time of
the year [7]."
In fact, the difference can be much larger. Geibel et al. (Atmos. Meas. Tech., 3, 13631375, 2010, their Fig. 15) show an example where the surface CO2 vmr is ~60 ppmv
larger than total column averaged CO2 vmr in the morning. Within two hours, the
surface value drops very quickly and reaches similiar values as the total column
measurement.
We agree. Thanks for providing the reference. We have improved the words as below:
“The difference between column-averaged CO2 (𝑋𝐶𝑂2 ) and surface CO2 can vary from 2
to 10 ppmv or even larger depending on the location and the time of the year [Olsen
and Randerson, 2004; Geibel et al., 2010].”
- p. 5, l. 12-20:
Your reference [13] (Messerschmidt et al.) should also be mentioned here in the
context of quality assurance as well as aircraft calibration. BTW: reference [13]
should be updated as it has been published in ACP by now.
Thank you. We have updated the reference.
- p. 12, last paragraph:
You refer the reader to reference [25]. However, this reference is not accessible. You
should provide more information about the scheme here (or use a different
reference).
We have rewritten the part about how to determine the depth of three partial layers
and remove the words causing confusion:
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“Since the NIR CO2 absorption band has its maximum sensitivity in the lower
troposphere, and most of the information must come from this part of atmosphere, we
can retrieve one layer below 2 km representing the boundary layer, one layer from 3 to
5 km in the lower free troposphere and the third layer is above 6 km.”
- p. 17, l. 6:
Should be "In this paper, we expand the standard scaling retrieval of XCO2 to three
partial columns."
Yes, we agree. It has been revised as suggested.
- Table 1:
Sorry, I do not understand the column "Information content". It is also not explained
in the text. Please be more specific.
We apologize for that. We have added a few words to explain “information content” as
below:
“We applied Rodgers’ information theory analysis to understand how much
information we could gain from the retrieval using TCCON-like measurements[31]. It
provides a method to calculate the degrees of freedom (d_s) and information content
(H). The degrees of freedom describes how many independent pieces of information
there are in a measurement. The information content of a measurement can be defined
qualitatively as the factor by which knowledge of a quantity is improved by making the
measurement. It is a scalar quantity. The units of information content are ‘bits’.”
- Figure 2: "Star indicates the frequency measured."
Do you mean the OCO-2 channel center frequency? This is somewhat confusing as
the axis is in wavenumbers.
It is our Fig. 1 now. We have made the statement more consistent as below:
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“Fig. 1 Absorption lines centered at 6243.9 cm-1. (a) measured by OCO-2, sza=17 and
(b) by TCCON, sza=22.5. Star indicates the wavenumber measured. Their
corresponding Jacobian (K = d[Tr]/d[ln(CO2]) profiles are plotted in the two bottom
panels (c) for OCO-2 and (d) for TCCON. The weak absorption channels are in red;
intermediate absorption channels are in green; strong absorption channels are in
blue.”
- Figure 3: "The error bar is one standard deviation of 100 retrieved partial <CHI>
CO2." Sorry, I do not understand what the error bar is. Is there a unit missing?
We have rewritten the caption as below:
“Fig. 3. Partial column for the true profile (black stars) compared with the mean of the
partial columns for 100 retrievals (red dots). The error bar (in units of ppm) is one
standard deviation of the 100 partial columns. SNR = 885. Dotted lines indicate the top
of each scaling layer.”
=================
Reviewer #2:
Review of Le et al., "Vertically Constrained CO2 Retrievals from TCCON
Measurements"
Le et al demonstrate a method to retrieve the partial column abundance of
atmospheric CO2 from high resolution FTS spectra obtained by the TCCON network.
Such a capability is extremely desirable, as coincident observations of boundary
layer CO2 abundance along with the total column abundance would yield more
robust flux estimates. Le et al use information theory to predict that three pieces of
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vertical information can be retrieved from high resolution near infrared (NIR) FTS
spectra. The authors then demonstrate using synthetic and observed spectra that
the partial column CO2 mixing ratio can be retrieved at three levels.
Given that the ability to retrieve partial column abundance of atmospheric CO2 from
high resolution, near infrared spectra would represent a significant advance for
carbon cycle science, it is important that the authors more carefully examine
potential sources for bias in their retrieval before this study can be published.
Because variations in atmospheric CO2 are small, both in space and time, small
biases in the retrievals can translate into huge misappropriations in surface flux
when these data are used in, for instance, an inverse model. Without proper
examination of the error introduced by partial column retrievals, the paper does not
advance the ability to use such retrievals for carbon cycle science.
I think the fundamental answer that the authors must answer is "Can you calibrate
the error in the profile retrievals in order to make the partial column retrievals
useful for carbon cycle science?". The paper does not answer this question, nor does
it ask the questions that will allow the authors to answer this question. The authors
note that bias in the partial column retrieval is smaller than the bias in the total
column retrieval, BUT the total column retrievals have been shown to be consistent
across several sites and several seasons, making it possible to calibrate the bias. I
am concerned by the fact that the science conclusions of the study draw from only
three days, and the authors have not demonstrated that their retrieval methodology
is robust or that we can trust their conclusions for long-term monitoring of CO2.
We are grateful to the reviewer for the careful reading and the many insightful
comments. We have incorporated most of the reviewer’s suggestions. We totally agree
with the reviewer that characterization of the bias error is important to the
application of the retrieval data into the inversion problem of the carbon flux. This
needs to be done when the profile retrieval algorithm is applied to all the TCCON sites.
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We are still in the early stage of the profile retrieval. More work needs to be done to
develop our retrieval algorithm and minimize the uncertainties in other parameters.
One large source of potential bias in the retrievals that the authors do not explore is
the effect of solar zenith angle (SZA) on the partial column retrievals. The solar
zenith angle at which measurements are obtained changes as a function of season at
any given site, and also varies from site to site at different latitudes, meaning that
there could be strong covariance with patterns in atmospheric CO2. Therefore, if a
profile retrieval were to be useful for the TCCON network, the effect of SZA would
have to be negligible or readily quantifiable.
This present paper is to demonstrate the possibility of obtaining vertical information
using TCCON measurement. We haven’t reached the point concerning the SZA effect on
the retrieval yet.
The authors have also written the study assuming complete knowledge of the
atmospheric state (i.e., the only uncertainty is the profile of CO2). This is obviously
unrealistic, and the authors need to show the magnitude of the effect of incomplete
information regarding e.g., atmospheric temperature and specific humidity. On page
10, the authors discuss the sensitivity of the 6220 cm-1 CO2 band to the
temperature profile. The sensitivity they quote, 0.35% per 5 K error in temperature,
is for the total column. The more relevant, and unexplored, question is: What is the
temperature sensitivity for the partial column retrieval? The authors also state that
the relatively small temperature sensitivity is due to the fact that the NIR absorption
band is less sensitive to temperature than the thermal IR band. Although this is a
statement of fact, it is not a causal relationship for the relatively smaller
temperature sensitivity of the NIR band. On page 11, the authors assume that the
forward model is perfect. How valid of an assumption is this? Particularly, since the
profile retrieval relies on pressure broadening to provide the vertically resolved
information, what error does the assumption of the ILS fold into the profile
retrievals and does this error vary systematically?
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We thank the reviewer for their thoughtful comments. We did the synthetic
simulations with temperature uncertainties. We found the influence in the CO 2 on the
sub-layer is larger than we thought, i.e. 1 K error in temperature profile could have
more than 5-ppm bias on some layers. However, the partial column averages would be
smaller and the total column average bias would be even smaller, i.e. 1 ppm for 5 K.
We mentioned the assumption of the perfect forward model in the synthetic retrievals
for the ideal test case. In realist retrievals, we understand that the forward model
needs to be improved. For example, implementing other line shape models..
In addition to my concerns regarding the content of the analysis, the details
provided in the paper are incomplete. The introduction does not address why a
partial column retrieval is more difficult from NIR spectra, such as those obtained by
TCCON, than for mid-IR spectra, such as those obtained by NDACC. Nor does it
provide a compelling description of how partial column retrievals from high
resolution spectra would be useful for carbon cycle science. I am not an expert on
information theory analysis, and feel that more details are needed as to how the
degrees of freedom for the TCCON spectra are determined. At the very least, the
authors must provide a citation. The method for determining the layers for the
profile retrieval is quite vague. What is the sensitivity to the layers picked? How
would the retrievals change if the layers were chosen to be 0-1 km and 2-4 km? The
authors discuss using the cumulative degrees of freedom to determine the layers for
the profile retrieval. How does the CO2 abundance retrieved for the lowest layer in
this approach compare to the integrated CO2 abundance for the lowest two layers in
the approach the authors pick? Finally, the details in the methods section are sparse
and do not provide much information about how the methodology behind the
retrievals.
We apologize for not describing the information theory in detail. We have added a few
sentences about the definition of information content and degree of freedom in
addition to the reference.
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“We applied Rodgers information theory analysis to understand how much
information we could gain from the retrieval using TCCON-like measurements[31]. It
provides a method to calculate the degree of freedom (𝑑𝑠 ) and information content
(𝐻). The degree of freedom describes how many independent pieces of information
there are in a measurement. The information content of a measurement can be defined
qualitatively as the factor by which knowledge of a quantity is improved by making the
measurement. It is a scalar quantity. The units of information content are ‘bits’.”
We are sorry that the description about how the three partial columns were divided
are confusing. We have rephrased them as below:
“The NIR CO2 absorption band has its maximum sensitivity in the lower troposphere.
All three pieces of information come from the troposphere. Our information analysis
suggests that the first piece of information is from the layer below 2 km, which
represents the boundary layer. Another piece of information is from the layer from 3 to
5 km, which covers the lower free troposphere and the rest is from the layer above 6
km. Fig. 3 shows how the three partial columns are distributed.”
In light of the fact that a partial column retrieval from high resolution near infrared
spectra would represent a significant improvement in remote sensing constraints
on carbon fluxes, I encourage the authors to address the issues above before
publication of this research.
I suggest replacing Figure 3 with a table that shows
the retrieval errors not just for the simple case the authors have chosen, but also for
a case with e.g., a +/- 5 K temperature bias, a +/- 10% specific humidity bias, and
also sensitivity to synthetic spectra representing different seasons or latitudes,
when the water column, temperature profile, and solar zenith angle will all be
completely different. Not only does this retrieval approach needs to be tried with
synthetic spectra with systematically different atmospheric states, but the retrieval
could also be tried with real data, since many more than three aircraft profiles have
been obtained over TCCON sites since summer 2004.
Has this been done? What is the response?
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Minor and grammatical considerations:
-Page 4, Fourier transfer spectrometers --> Fourier transform spectrometers
Thank you. We have corrected it.
-Page 4, high-quality and high quality are both used; please be consistent with
hyphenation
There is no longer an inconsistency.
-Page 4, N2O is also a greenhouse gas
We have changed the wording as below:
“Although unevenly distributed over the world, the ensemble of sites retrieve the longterm column-averaged abundance of greenhouse gases, such as carbon dioxide (CO2),
methane (CH4), Nitrous oxide (N2O), and other trace gases (e.g. CO) with high
accuracy and high precision [Washenfelder et al., 2006; Wunch et al., 2011; Wunch et
al., 2010; Yang et al., 2002].”
-Page 4, perhaps review Keppel-Aleks et al., 2011 ACP for a more recent paper on
the information in total column retrievals
Thanks. We have added a reference to this paper.
“Compared to surface values, the seasonal variation of 𝑋𝐶𝑂2 generally has a time lag in
phase with less variability due to the time delay caused by the vertical mixing. The
variations in total column are only partly driven by the local flux. Meanwhile, the
synoptic activity has a large impact on the variations in 𝑋𝐶𝑂2 due to larger-scale eddy
flux and the meridional gradient. The simulations by Keppel-Aleks et al., 2011
illustrate that the sources of 𝑋𝐶𝑂2 variations are related to the north-south gradients
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of 𝑋𝐶𝑂2 and the flux on continental scales [9]. In another study, Stephens et al., (2007)
concludes that most of the current models overpredict the annual-mean midday
vertical gradients and consequently lead to an overestimated carbon uptake in
northern lands and underestimated carbon uptake over tropical forests[10].
Therefore, the vertical profile information of atmospheric CO2 is required for
estimating the regional sources and sinks, understanding the transport, and
determining the exchange between the surface and atmosphere.”
-Page 7, "The aircraft in situ measurements have higher precision. " --> relative to
what?
We have revised the sentence as below:
“The aircraft in situ measurements of CO2 profiles have higher precision (~0.2 ppm)
and higher accuracy (~0.2 ppm) [5] than the TCCON and spacecraft instruments.”
-Page 7 "lowest measured value was at X m" --> please fill in the missing value
Sorry. We have filled the values.
“The lowest measured value is at approximately 450 m above the surface, and it is
assumed to be the surface value.”
-Page 8: How were the SNR determined? How does this change over time? What
impact does this have on the partial column retrieval?
The SNR from a real measured spectrum can be determined by estimating the random
noise at the spectral region without any gas absorption. However, we set the SNR for
the retrievals so that the chi-square of the spectral residual is about 1. For the TCCON
profile retrieval, we assumed the variability of the SNR over time is quite stable for this
instrument.
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-Page 9: "The information theory analysis. three pieces of vertical information" -->
This sentence is redundant
We have combined two sentences “The information theory analysis suggests that the
CO2 retrieval from TCCON measurements has at least three pieces of independent
information. Its high spectral resolution and high SNR are sufficient to yield three
pieces of vertical information.” into one “Information theory analysis suggests that the
CO2 retrieval from TCCON measurements has at least three pieces of vertical
information.”
-Figure 1: The left and right panels should be switched, since TCCON and then OCO
are discussed in the text.
Thank you. We have made the changes in plots and paragraph.
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Fig. 1 The same absorption line centered at 6243.9 cm-1. (a) by TCCON, SZA=22.5° (b)
measured by OCO-2, SZA=17°. Dot indicates the wavenumber measured. Their
corresponding unitless Jacobian (K = d[Tr]/d[ln(CO2)]) profiles are plotted in the two
bottom panels (c) for TCCON and (d) for OCO-2. The weak absorption channels are in
red; the intermediate absorption channels are in green; the strong absorption
channels are in blue.
“Fig. 1 shows the CO2 Jacobian profiles for the frequencies at the same absorption lines
but measured by two instruments with different spectral resolutions (TCCON and OCO2). Due to the high spectral resolution, TCCON measurements capture the strong
absorption channels that are very close to the line center (blue lines in Fig. 1 b), the
Jacobian profiles have broader peaks, and have sensitivity to CO2 in the middle and
upper troposphere. Some of the intermediate absorption channels (green lines) can
have stronger peaks than both the weak and strong absorption channels and are
located in the lower troposphere. The weak absorption channels have the sensitivity
near surface. In contrast, the Jacobians from the channels measured by OCO-2 all
maximize near the surface because its spectral resolution is not sufficient to capture
the channels close enough to the line center that could provide complementary
information higher up (Fig. 1 b and d).”
-Page 11: "a prior constraints" --> " a priori constraints"
Thanks. We have corrected it.
“The advantage of a synthetic study is that with the knowledge of the right answer, it
can help us evaluate the precision of the retrievals with different SNR and different a
priori constraints.”
-Page 13: how many spectra were obtained during the two hour window during
which the aircraft profile was obtained?
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There are about 100 spectra recorded in ~2 hours. This number depends on the
weather conditions and the scan speed of the instrument.
-Page 15: "Large uncertainties in the upper atmosphere. stratospheric uncertainty is
a significant component of the total error." --> as written, I think this misrepresents
the nature of the error.
In Wunch et al., there are no direct observations of
stratospheric CO2, so assumptions must be made about the stratospheric
composition in order to integrate the aircraft profile for comparison with total
column observations.
-Page 15: "precisions are less than 1 ppm" --> "precisions are better than 1 ppm"
We have made the changes to “The precision is better than 1 ppm.”
-Page 16: "The ratio of the XCO2 determined from FTS scaling. " I think this whole
section (through the end of the paragraph) comes out of the blue, and would be
better suited to the methods section.
-Fig. 2: might not be necessary
We disagree. Fig. 2 shows the absorption band measured by TCCON which is used in
our retrieval. But why is the figure necessary? Is it insufficient to state which band is
being used in the text?
-Fig 4: legend needs to be more clear
We are sorry for the confusing legend. We have made it clearer.
“Fig. 4 Examples of profile retrievals from the same spectrum but with three different a
priori profiles. Solid lines with three different colors in (a) to (c) are the profile
retrieved CO2. The differences from the aircraft profile for each case are plotted below
them in (d) to (f). The diamonds represent the differences in the partial columns of
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CO2.. This figure demonstrates that the differences in some sub layers can be as large
as 4 ppm but the residuals in the partial column averages are smaller (< 3 ppm).”
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