1
Vertically Constrained CO2 Retrievals from TCCON Measurements
Le Kuai1, Debra Wunch1, Run-Lie Shia1, Brian Connor2,
Charles Miller3, and Yuk Yung1
1.
Division of Geological and Planetary Sciences, California Institute of Technology,
MC: 150-21, Pasadena, CA, 91125, USA. E-mail: kl@gps.caltech.edu
2.
BC Consulting Ltd., 6 Fairway Dr, Alexandra 9320, New Zealand
3.
Jet Propulsion Laboratory, California Institute of Technology
Submitted to JQRST
2
Abstract
Partial column-averaged carbon dioxide (CO2) mixing ratio in three tropospheric layers
have been retrieved from Total Carbon Column Observing Network (TCCON) spectra in
the 1.6 m CO2 absorption band. Information analysis suggests that a measurement with
about sixty absorption lines provides three or more pieces of independent information,
depending on the signal-to-noise ratio and solar zenith angle. This has been confirmed by
retrievals based on synthetic data. Realistic retrievals for both total and partial columnaveraged CO2 over Park Falls, Wisconsin on July 12, 15, and August 14, 2004, agree
with aircraft measurements. Furthermore, the retrieved total column averages are always
underestimated by less than 1%. The results above provide a basis for CO2 profile
retrievals using ground-based observations in the near-infrared region.
3
1 Introduction
Remote sensing observations improve our understanding of the spatial and temporal
distributions of carbon dioxide (CO2) in the atmosphere. The Total Carbon Column
Observing Network (TCCON) is a network of ground-based Fourier transform
spectrometers (FTS). An automated solar observatory measures high-quality incoming
solar
absorption
spectra
in
the
near-infrared
region
(4000−9000
cm-1)
(www.tccon.caltech.edu, [1, 2]). Each TCCON instrument has a precise solar tracking
system that allows the FTS to record direct sunlight. The high-quality spectra are
measured under clear skies and can be corrected by the recorded DC-signal for partly
cloudy skies [3]. There are 20 sites located worldwide, including both operational and
future sites. Although unevenly distributed over the world, the TCCON has good
latitudinal coverage and the ensemble of sites retrieve the long-term 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 [2, 46].
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 [7, 8]. Higher
surface concentrations usually occur at nighttime or in winter due to CO 2 build up in a
shallow planetary boundary layer (PBL), while surface uptake due to plant growth occurs
during the daytime or in summer. On the diurnal scales, the variations in 𝑋𝐶𝑂2 are smaller
than surface CO2 because they are remotely forced by local fluxes and depend on
4
advection. 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 𝑋𝐶𝑂2 are only partly driven by the local flux, and synoptic-scale activity
has a large impact on the variations in 𝑋𝐶𝑂2 due to larger-scale eddy fluxes 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 of 𝑋𝐶𝑂2 and the flux on
continental scales [9]. In contrast, the variations in boundary layer CO2 are directly
influenced by local flux [10]. They show that the boundary layer CO2 variability is
explained by the regional surface fluxes related to the land cover and the mesoscale
circulation across the boundary layer. 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 the northern lands and
underestimated carbon uptake over tropical forests [11]. Therefore, 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.
In this paper, we show that high-resolution spectra of the atmosphere can provide
information about the vertical distribution of CO2 in additional to the total column
abundance. In this work, three scaling factors along each CO2 profile are retrieved to
obtain the vertical distribution information. Other than the accurately retrieved total
column abundance, the vertical variation is given by the partial column averages in
different parts of the atmosphere.
5
The major uncertainty sources in the TCCON retrievals are spectroscopy, measurement
noise, instrument line shape function (ILS), temperature, surface pressure and zero level
offset. Significant effort has been undertaken to reduce the instrumental uncertainties of a
TCCON experiment [3, 12-15]. An overview of these uncertainties for TCCON
measurements is discussed in [2, 5]. The column measurements are calibrated and their
precision is quantified using in situ aircraft profiles [5, 16].
The main purpose of this paper is as a demonstration of a CO2 profile retrieval and its
application to TCCON data. This study provides a baseline to guide the next generation
of remote sensing measurements for profiling the atmospheric CO2. It is organized as
follows. TCCON and aircraft data, information analysis, and the setup of the vertically
constrained retrieval are described in section 2. A description of the profile retrieval
method, and its illustration using both synthetic and real spectra is discussed in section 3.
We use three of aircraft profiles, measured at Park Falls [4] on July 12, July 15, and
August 14 in 2004, to evaluate the partial column retrievals from coincident TCCON
spectra. The conclusions and discussions follow in section 4.
2 Data and Methodology
2.1 TCCON Data
The TCCON 𝑋𝐶𝑂2 measurements are precise to better than 0.25% [2, 5]. With this
precision, the monthly averaged column-integrated data are sufficient to reduce the
uncertainties in the global surface carbon sources and sinks [17]. The absolute accuracy
6
of the uncalibrated 𝑋𝐶𝑂2 measurements from TCCON is ~1% [5]. These measurements
have been calibrated to 0.25% accuracy using aircraft profile data that are themselves
calibrated to the World Metrological Organization (WMO) scale over nine TCCON sites
(Park Falls, Lamont, Darwin, Lauder, Tsukuba, Karlsruhe, Bremen, Bialystok, Orleans)
[5, 18] so that they can be used in combination with in situ measurements to provide
constraints on continental-scale flux estimates [19-22].
The 𝑋𝐶𝑂2 values retrieved from the TCCON spectra are an important validation source
for satellite observations from the Orbiting Carbon Observatory (OCO-2) [23], SCanning
Imaging Absorption SpectroMeter for Atmospheric CartograpHY (Sciamachy) [24], and
Greenhouse Gases Observing Satellite (GOSAT) [25-27]. In contrast to space-based
instruments such as SCIAMACHY, OCO-2, and GOSAT, which measure in the near
infrared spectral region but look down from space to measure reflected sunlight, the
retrievals from TCCON spectra have minimal influences from aerosol, uncertainty in
airmass, or variation in land surface properties [2], because the ground-based TCCON
instruments measure direct sunlight. Thus, TCCON data serves as a transfer standard
between satellite observations and in situ networks [1, 2, 5, 6, 28]. Because of their high
qualities, TCCON spectra are the best real data source for the challenging profile
retrieval.
2.2 Aircraft In Situ Profiles
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. We
7
consider these measurements to be the best observations of the true state of the
atmospheric CO2 profile. In this study, the remote sensing measurements of CO2 over
Park Falls, Wisconsin on July 12, 15 and August 14, 2004 [4] are compared with the
coincident in situ measurements during the Intercontinental Chemical Transport
Experiment––North America campaign (INTEX––NA) [29]. Highly precise (0.25 ppm)
CO2 profiles were obtained from 0.2 to 11.5 km in about a 20 km radius. Due to the
altitude floor and ceiling limitations of the aircraft measurements, additional information
for the surface and the stratosphere are required. The lowest measured value is at
approximately 200 m above the surface, and it is assumed to be the surface value. The
profile above the aircraft ceiling was derived from in situ measurements on high-altitude
balloons [5]. An excellent correlation between the integrated aircraft profiles and the FTS
retrieved 𝑋𝐶𝑂2 was found [4, 5, 18, 29, 30]. The calibration using aircraft data reduced the
uncertainty in the retrieved 𝑋𝐶𝑂2 by TCCON to 0.25% [2, 4, 5, 18, 29].
In this work, we also use aircraft measured CO2 profiles as our standard. In addition to
the comparison of 𝑋𝐶𝑂2 , we further look at the difference in the partial columns for three
scaling layers. The knowledge of the partial columns can improve our understanding of
the vertical distribution of total columns in the atmosphere.
2.3 Information Analysis
Recording direct solar spectra, the TCCON measures a high signal-to-noise ratio (SNR)
of about 885 on the InGaAs detector and 500 on the Si diode detector [4]. This is
significantly larger than the GOSAT and OCO-2 measurements of the same spectral
8
region (SNR ~ 300). We use the 1.6 m CO2 absorption band, which is measured using
the InGaAs detector by TCCON with a spectral resolution of 0.02 cm-1 (Fig. 1 a). This
band is also measured by GOSAT and OCO-2 from the space. However, the TCCON
measured spectra have a resolution that is about ten times finer than those from spacecraft
instruments (e.g. OCO-2 Fig. 1 b).
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 (𝑑𝑠 ) 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’.
The analysis shows that, assuming SNR to be 885 for TCCON measurements and the
diagonal value of a priori covariance matrix to be the square of 3% for CO2 variations,
the degrees of freedom for signal of the CO2 from TCCON retrieval is 3.6, 3.8 and 4.3 for
solar zenith angle (SZA) 22.5, 58 and 80 respectively (Table 1). The information
content is also listed in this table. The instrument noise level is a key parameter in most
retrievals [32]. However, even assuming SNR to be 300, there are still as many as 2.7 and
2.8 degrees of freedom from TCCON spectra with SZA 22.5 and 58. A similar
calculation for OCO-2 only gives 1.5 degrees of freedom because this measurement has
lower resolution and lower SNR than TCCON.
9
Profile information is known to be contained in the absorption line shape, such as
pressure broadening. The CO2 Jacobian profiles describe the sensitivity at the particular
frequency to the CO2 changes in different levels of the atmosphere. We found that the
Jacobian profiles for TCCON measurements have peaks located at different levels. 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 OCO-2).
Due to the high spectral resolution, TCCON measurements capture the strong absorption
channels that are very close to the line center. Their Jacobian profiles have broader peaks,
and have sensitivity to CO2 in the middle and upper troposphere (blue in Fig. 1 a and c).
Some of the intermediate absorption channels (green) 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 most 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)
We considered three major factors when we decide how to divide the three layers. The
first factor is that three layers could represent boundary layer, lower troposphere and
middle-upper troposphere respectively. The second is that the three pieces of information
would be distributed in three layers [33]. The last factor is that the pressure weighting for
these three layers couldn’t be differed too much. By considering all three factors we
chose the lowest layer below 2 km, which represents the boundary layer. It has about 0.8
degrees of freedom and account for 25% of pressure weighting of the total column.
10
Another layer is from 3 to 5 km, which covers the lower free troposphere along with
approximately 0.6 degrees of freedom and has another 25% of pressure weighting. The
third layer is above 6 km. It contains about 1.3 degrees of freedom and weights the
remaining 50% of the total column. Fig. 3 shows how the three partial columns are
distributed.
2.4 Retrievals
The slant column of each absorber is obtained by a nonlinear least-squares spectral fitting
routine that uses line-by-line spectroscopic calculations (GFIT, developed at JPL). The
radiative transfer model in GFIT computes simulated spectra using 71 vertical levels with
1 km intervals for the input atmospheric state. Details about GFIT are described in [2, 46, 8, 30].
The retrievals in this study use one of the TCCON-measured CO2 absorption bands,
centered at 6220.00 cm-1 with a window width of 80.00 cm-1 (Fig. 2), to estimate the
atmospheric CO2. A study of the temperature sensitivity of the CO2 retrieval suggests that
a systematic error of 5 K in temperature profile would cause 0.35% or about 1 ppm error
in 𝑋𝐶𝑂2 [6]. This is because the near infrared (NIR) CO2 absorption band is much less
sensitive to temperature than the thermal IR band (i.e., 15 m), which has 30 ppm error
in retrieved CO2 for 1 K uncertainty in temperature [34]. To minimize our temperature
error, we use the assimilated NCEP temperature, pressure, and humidity profile for local
noon for each day of measurements.
11
In the traditional scaling retrieval, given the best knowledge of the true atmospheric state
with minimized spectroscopic errors, instrument line shape functions, etc., a scaling
factor (γ) of the a priori profile (xa) is retrieved. The estimated state vector can be
calculated as
𝑥̂ = 𝛾𝑥𝑎
(1)
In this method, the a priori profile is uniformly scaled to find the best fit to the observed
spectrum. In this work, we improve on this scaling method by dividing the profile into
three scaling layers in the troposphere instead of retrieving one scaling factor for the
whole profile. Three scaling factors were chosen to match the information analysis (see
Section 2.3), and are retrieved to shift the a priori in three layers. By scaling the three
parts of the a priori profile, we can determine how the total column averaged CO2 is
vertically distributed in the atmosphere. To distinguish this retrieval method from the
scaling retrieval, we call it the “profile retrieval” in this paper.
The column amount is usually obtained by integrating the gas concentration profile from
𝑧1 to 𝑧2 .
𝑧2
𝐶𝑔 = ∫ 𝒇𝑔 (𝒛) ∙ 𝒏(𝒛) ∙ 𝑑𝑧
(2)
𝑧1
where Cg is vertical column amount for gas ‘g’ within layer 𝑧1 to 𝑧2 . When 𝑧1 = 0 and
𝑧2 = ∞ then Cg is the total column amount. 𝒏(𝒛) represents the number density vertical
profile and 𝒇𝑔 (𝒛) is gas concentration profile as a function of altitude (z).
12
The ratio of column amount between gas and air will give the column-averaged
abundance. The partial column-averaged CO2 is simply
𝑧
𝑝𝑋𝐶𝑂2
2
𝐶𝐶𝑂2 ∫𝑧1 𝒇𝐶𝑂2 (𝒛) ∙ 𝒏(𝒛) ∙ 𝑑𝑧
=
=
𝑧2
𝐶𝐴𝐼𝑅
∫ 1 ∙ 𝒏(𝒛) ∙ 𝑑𝑧
(3)
𝑧1
The total column-averaged CO2 is
∞
𝑋𝐶𝑂2
𝐶𝐶𝑂2 ∫0 𝒇𝐶𝑂2 (𝒛) ∙ 𝒏(𝒛) ∙ 𝑑𝑧
=
=
∞
𝐶𝐴𝐼𝑅
∫0 1 ∙ 𝒏(𝒛) ∙ 𝑑𝑧
(4)
𝒇𝐶𝑂2 is estimated in equation (1) by the TCCON profile retrieval.
3 Profile Retrievals
3.1 Synthetic Retrievals
Retrieval simulations using synthetic data enable us to test the retrieval algorithm. The
advantage of a synthetic study is that we know the “truth”, which will help us evaluate
the precision of the retrievals with different SNR and different a priori constraints. The
forward model is used both to generate the synthetic spectra and run the retrieval, thus,
no errors arise from the spectroscopy and instrument line shape. It also allows us to
estimate the errors induced by the uncertainties of the other interference parameters. It is
a useful tool to help us understand the ideal case and more complicated measurements.
13
A reference transmission spectrum at 6180 – 6260 cm-1 is simulated using the GFIT
forward model. Atmospheric profiles including pressure, temperature and humidity are
based on NCEP/NCAR reanalysis at Park Falls on July 12, 2004. One hundred synthetic
observational spectra are generated by adding to the reference spectrum some noise of
amplitude /SNR, where  is a pseudorandom number normally distributed.
Assuming there are no uncertainties in the true state of the atmosphere except the target
gas to be retrieved, and that the forward model is perfect, the mean errors (the difference
between the retrieved value and the true value) in total 𝑋𝐶𝑂2 varies from 0.06 to 0.08
ppm, depending on the selection of the depth of layers and SNR (885 to 300). Fig. 3
compares the averages of the 100 retrieved partial 𝑋𝐶𝑂2 (red dot) for SNR=885 to the
truth (black stars). Their residuals are less than 0.5 ppm. The error bars for the three
partial column averages are no more than 0.7 ppm. In this paper, we always use one
standard deviation to compute the error bar.
3.2 Realistic Retrievals
For comparison with the aircraft profile on July 12, 2004, the contemporaneous TCCON
measured spectra were selected within a 2-hour window centered on the time when the
aircraft measurements were taken. The averages of retrievals from these spectra are used,
with error bars equal to one standard deviation (std), to compare with the aircraft
measurements.
14
Three tests of the profile retrievals starting from different a priori profiles have been
studied. The first test is to use the a priori profile that is shifted by 1% from the aircraft
profile. Since aircraft data have temporal and spatial limitations, aircraft a priori profiles
will not be available at all TCCON sites and in all seasons. It is of interest to compare the
retrieval results using the GFIT a priori and aircraft profile a priori. Therefore, the
second test is to use the GFIT a priori [2, 35]. The CO2 a priori profiles are derived by an
empirical model based on fits to GLOBALVIEW data [36] and changes based on the
time of the year and the latitude of the site, for altitudes up to 10 km. In the stratosphere
an age-dependent CO2 profile is assumed [37]. This is done to obtain the best possible a
priori profiles for CO2 at all TCCON sites in all seasons. The third test is to assume that,
within each layer, CO2 is well mixed with a constant mixing ratio. The a priori profile in
this test is a constant CO2 of 375 ppm.
In all three tests, the retrieved CO2 profiles (colored lines in Fig. 4 a-c) converged to the
aircraft profile (‘+’ in Fig. 4 a-c). Compared with the aircraft measurements, the mean
biases in total 𝑋𝐶𝑂2 for three tests are listed along with their precision in table 2. In both
profile retrievals and scaling retrievals, the three tests underestimate the total 𝑋𝐶𝑂2 from
0.67 to 1.64 ppm, but the profile retrievals always have less bias (<1 ppm) than the
scaling retrievals (>1 ppm) for all three tests. In profile retrievals, there is a slightly
smaller bias in the first test (0.67 ppm) than the other two cases (~0.8 ppm) because the a
priori profile has the same shape as that measured by the aircraft. However, this
advantage does not lead to a significant improvement over the retrievals using other
reasonable a priori. It suggests the retrieval is robust and does not depend on the a priori.
15
This agrees with what was found by [5]. In their scaling retrievals for the total column
CO2, the GFIT a priori profiles do not introduce additional bias compared with the
results by replacing the aircraft profiles along with the best estimate of the stratospheric
profiles as a priori profiles.
The vertical resolution in the GFIT model is 1 km uniformly from the surface to 70 km
with 71 grid points in total. We divided them into three scaling layers (surface–2 km, 3–5
km and 6 km-top). This allowed us to keep the shape of the a priori profile within the
scaling layers. In the first test, because the shape of the a priori profile agrees perfectly
with the aircraft profile (Fig. 4 a), the difference between the retrieved profile and aircraft
profile within the same scaling layer do not vary much with altitude (Fig. 4 d colored
lines). This is not true in the other two tests where the a priori profiles have different
shapes from the true profiles (Fig. 4 b and c). Although larger differences can occur
where the shape of the a priori and true profile differs significantly (e.g., Fig. 4 e and f),
the biases in their partial column averaged CO2 (diamonds in Fig. 4 d, e and f) are much
reduced due to the compensation between the sub-layers. Biases and their error bars for
the total 𝑋𝐶𝑂2 and partial column averages for multiple retrievals within the ±2-hr
window are listed in table 3. The error bars in each partial column averages are no more
than 1 ppm. Since the first two layers close to the surface are thinner and therefore are
less weighted than the third layer, their bias in the partial column averages contribute
about 25% each in total column average’s bias according to pressure weighting function.
The third layer will account for the remaining 50% in total column average’s bias. Large
16
uncertainties in the upper atmosphere result from the lack of information in the
stratosphere.
The profile retrievals using the GFIT a priori profiles at Park Falls are also compared
with the aircraft measured data on July 15 and August 14, 2004. Table 4 lists the bias in
total and partial 𝑋𝐶𝑂2 with their error bars. It suggests that the total 𝑋𝐶𝑂2 biases are less
than 1 ppm for the three-day comparisons with 0.3-ppm precision. Most of the errors in
partial 𝑋𝐶𝑂2 are less than 1 ppm and some of them are between 1 and 2 ppm. Their
precisions are better than 1 ppm.
In the above studies, we show that in addition to the accurate estimates of the total𝑋𝐶𝑂2 ,
the profile retrievals can also provide some vertical information about the CO2
distribution in the atmosphere in the form of partial 𝑋𝐶𝑂2 .
4 Conclusions
TCCON provides long-term observations for the understanding of the CO2 variations at
different timescales and at different latitudes. In addition to the column measurements,
the information on the vertical distribution of CO2 can also be obtained from these
observations. Our retrieval simulations have confirmed their potential for retrieving the
CO2 profile. The realistic profile retrievals from TCCON spectra are compared to CO2
profiles measured by in situ aircraft. The comparison between the retrieved 𝑋𝐶𝑂2 and the
17
integration of the aircraft CO2 profiles show an underestimation from both scaling and
profile retrievals. This agrees with the conclusion from the previous work about the
calibration of TCCON data against the aircraft measurements. The ratio of the 𝑋𝐶𝑂2
determined from FTS scaling retrievals to that from integrated aircraft profiles gives a
correction factor of 0.991  0.002 (mean  standard deviation of the ratios of FTS to
aircraft 𝑋𝐶𝑂2 ) at Park Falls [4, 5]. However, Wunch et al. [5] also retrieved CO2 from the
another band at 6339 cm-1, and computed the average of two retrievals before they are
scaled by the retrieved O2 to a mean value of 0.2095 in order to get the dry air columnaveraged mole fractions [4, 5, 8, 30]. Here we just present the retrievals from one of two
windows mentioned above, which is centered at 6220 cm-1. The column-averaged dry-air
mole fraction is derived using the pressure weighting function which was introduced in
Connor et al., [38], instead of being scaled by simultaneously retrieved O2. The scaling
by retrieved O2 reduces systematic errors that are common to both CO2 and O2 (such as
pointing errors and ILS errors), but does not necessarily reduce the overall bias.
In this paper, we expand the standard scaling retrieval of 𝑋𝐶𝑂2 to three partial columns.
With this study, we demonstrate that profile retrievals are possible on high-resolution
spectra. It gives the consistent results as the scaling retrievals and adds extra information
about the vertical distribution of CO2. The retrieved partial column averages in the free
troposphere can be more readily compared with satellite retrievals from thermal infrared
spectra such as AIRS and TES that are more sensitive to the mid-troposphere. Long-term
profile data can be useful to address variability at different time scales and at different
18
altitudes. The direct use of profile data for inverse modeling can provide better
constraints on the CO2 sources and sinks on regional scales.
5 Acknowledgements
This research is supported in part by the Orbiting Carbon Observatory 2 (OCO-2) project,
a NASA Earth System Science Pathfinder (ESSP) mission and Project JPL.1382974 to
the California Institute of Technology. Support for TCCON and operations at Park Falls
Wisconsin are provided by a grant from NASA to the California Institute of Technology
(NNX11AG01G). We would like to thank Gretchen Keppel Aleks, Mimi Gerstell, Vijay
Natraj, Sally Newman, Jack Margolis, Xi Zhang, King-Fai Li, and Michael Line for
useful discussions and comments on the paper. Special thanks are given to G. Toon and
P. Wennberg for making available their code and data, and for valuable discussions.
19
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