AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-12-35-2019Using a speed-dependent Voigt line shape to retrieve O2 from Total
Carbon Column Observing Network solar spectra to improve measurements of
XCO2Improving the retrieval of O2 total columnsMendoncaJosephjoseph.mendonca@utoronto.caStrongKimberlyhttps://orcid.org/0000-0001-9947-1053WunchDebrahttps://orcid.org/0000-0002-4924-0377ToonGeoffrey C.LongDavid A.HodgesJoseph T.SironneauVincent T.FranklinJonathan E.Department of Physics, University of Toronto, Toronto, ON, CanadaJet Propulsion Laboratory, Pasadena, CA, USANational Institute of Standards and Technology, Gaithersburg, MD, USAHarvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, MA, USAJoseph Mendonca (joseph.mendonca@utoronto.ca)3January2019121355023February20183April201823August201817September2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://amt.copernicus.org/articles/12/35/2019/amt-12-35-2019.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/12/35/2019/amt-12-35-2019.pdf
High-resolution, laboratory, absorption spectra of
the a1Δg←X3Σg- oxygen (O2) band
measured using cavity ring-down spectroscopy were fitted using the Voigt and
speed-dependent Voigt line shapes. We found that the speed-dependent Voigt
line shape was better able to model the measured absorption coefficients than
the Voigt line shape. We used these line shape models to calculate absorption
coefficients to retrieve atmospheric total columns abundances of O2
from ground-based spectra from four Fourier transform spectrometers that are
a part of the Total Carbon Column Observing Network (TCCON). Lower O2
total columns were retrieved with the speed-dependent Voigt line shape, and
the difference between the total columns retrieved using the Voigt and
speed-dependent Voigt line shapes increased as a function of solar zenith
angle. Previous work has shown that carbon dioxide (CO2) total columns
are better retrieved using a speed-dependent Voigt line shape with line
mixing. The column-averaged dry-air mole fraction of CO2 (XCO2) was
calculated using the ratio between the columns of CO2 and O2
retrieved (from the same spectra) with both line shapes from measurements
taken over a 1-year period at the four sites. The inclusion of speed
dependence in the O2 retrievals significantly reduces the air mass
dependence of XCO2, and the bias between the TCCON measurements and
calibrated integrated aircraft profile measurements was reduced from 1 % to
0.4 %. These results suggest that speed dependence should be included in
the forward model when fitting near-infrared CO2 and O2
spectra to improve the accuracy of XCO2 measurements.
Introduction
Accurate remote sensing of greenhouse gases (GHGs) such as CO2, in
the Earth's atmosphere is important for studying the carbon cycle to better
understand and predict climate change. The absorption of solar radiation by
O2 in the Earth's atmosphere is important because it can be used to
study the properties of clouds and aerosols and to determine vertical
profiles of temperature and surface pressure. Wallace and
Livingston (1990) were the first to retrieve total columns of O2 from
some of the discrete lines of the a1Δg←X3Σg- band of O2 centred at 1.27 µm (which will be referred
to bellow as the 1.27 µm band) using atmospheric solar absorption
spectra from Kitt Peak National Observatory. Mlawer
et al. (1998) recorded solar absorption spectra in the near-infrared (NIR)
region to study collision-induced absorption (CIA) in the a1Δg←X3Σg- band as well as two other O2
bands. The spectra were compared to a line-by-line radiative transfer model
and the differences between the measured and calculated spectra showed the
need for better absorption coefficients in order to accurately model the
1.27 µm band (Mlawer et al., 1998).
Subsequently, spectroscopic parameters needed to calculate the absorption
coefficients from discrete transitions of the 1.27 µm band were
measured in multiple studies (Cheah
et al., 2000; Newman et al., 1999, 2000; Smith and Newnham, 2000), as was
collision-induced absorption (CIA) (Maté
et al., 1999; Smith and Newnham, 2000), while Smith et al. (2001) validated the
work done in Smith and Newnham (2000)
using solar absorption spectra.
The 1.27 µm band is of particular importance to the Total Carbon
Column Observing Network (TCCON) (Wunch et al., 2011). TCCON is a
ground-based remote sensing network that makes accurate and precise
measurements of GHGs for satellite validation and carbon cycle studies. Using
the O2 column retrieved from solar absorption spectra, the
column-averaged dry-air mole fraction of CO2 (XCO2) has
been shown to provide better precision than when using the surface pressure to
calculate XCO2 (Yang et al., 2002). The O2 column is
retrieved from the 1.27 µm band because of its close proximity to
the spectral lines used to retrieve CO2, thereby reducing the
impact of solar tracker mispointing and an imperfect instrument line shape
(ILS) (Washenfelder et al., 2006a). To improve the
retrievals of O2 from the 1.27 µm band, Washenfelder et
al. (2006a) found that adjusting the spectroscopic
parameters in HITRAN 2004 (Rothman et al., 2005) decreased the air mass and
temperature dependence of the O2 column. These revised
spectroscopic parameters were included in HITRAN 2008 (Rothman et al., 2009).
Atmospheric solar absorption measurements from this band taken at the Park
Falls TCCON site by Washenfelder et al. (2006a) were the
first measurements to observe the electric-quadrupole transitions (Gordon et
al., 2010). Leshchishina et al. (2011, 2010) subsequently used
cavity ring-down spectra to retrieve spectroscopic parameters for the
1.27 µm band using a Voigt spectral line shape and these parameters
were included in HITRAN 2012 (Rothman et al., 2013a).
Spectroscopic parameters for the discrete spectral lines of the O2
1.27 µm band from HITRAN 2016 (Gordon et al., 2017) are very
similar to HITRAN 2012 except that HITRAN2016 includes improved line
positions reported by Yu et al. (2014).
Extensive spectral line shape studies have been performed for the O2
A-band, which is centred at 762 nm and used by the Greenhouse Gases
Observing Satellite (GOSAT) (Yokota et al.,
2009) and the Orbiting Carbon Observatory-2 (OCO-2) satellite (Crisp et al., 2004)
to determine surface pressure. Studies have shown that the Voigt line shape
is inadequate to describe the spectral line shape of the discrete O2
lines in the A-band. Dicke narrowing occurs when the motion of the molecule
is diffusive due to collisions changing the velocity and direction of the
molecule during the time that it is excited. This diffusive motion is taken
into account by averaging over many different Doppler states, resulting in a
line width that is narrower than the Doppler width (Dicke,
1953). Long et
al. (2010) and Predoi-Cross et al. (2008) found it necessary to use a
spectral line shape model that accounted for Dicke narrowing when fitting
the discrete lines of the O2 A-band. Line mixing, which occurs when
collisions transfer intensity from one part of the spectral band to another
(Lévy et al., 1992), was shown to be prevalent in multiple
studies (Predoi-Cross
et al., 2008; Tran et al., 2006; Tran and Hartmann, 2008). Tran and Hartmann (2008) showed that including line
mixing when calculating the O2 A-band absorption coefficients reduced
the air mass dependence of the O2 column retrieved from TCCON spectra.
When fitting cavity ring-down spectra of the O2 A-band, Drouin et al. (2017) found
it necessary to use a speed-dependence Voigt line shape, which takes into
account different speeds at the time of collision (Shannon et al., 1986), with line mixing to
properly fit the discrete spectral lines of the O2 A-band.
The need to include non-Voigt effects when calculating absorption
coefficients for the O2 1.27 µm band was first shown in Hartmann et
al. (2013) and Lamouroux et al. (2014). In Hartmann et
al. (2013) and Lamouroux et al. (2014), Lorentzian widths were calculated
using the requantised classical molecular dynamics simulations (rCMDSs) and
used to fit cavity ring-down spectra with a Voigt line shape for some
isolated transitions in the O2 1.27 µm band. The studies
concluded that a Voigt line shape is insufficient for modelling the spectral
lines of the O2 1.27 µm band and that effects such as speed
dependence and Dicke narrowing should be included in the line shape
calculation.
In this study, air-broadened laboratory cavity ring-down spectra of the
O2 1.27 µm band were fitted using a spectral line shape that
takes into account speed dependence. The derived spectroscopic parameters
for the speed-dependent Voigt line shape were used to calculate absorption
coefficients when fitting high-resolution solar absorption spectra.
XCO2 was calculated from O2 total columns retrieved using the new
absorption coefficients and CO2 total columns retrieved with the line shape model
described in Mendonca et al. (2016). These new XCO2 values were compared
to the XCO2 retrieved using the Voigt line shape. Section 2 details the formulas used to
calculate absorption coefficients using different spectral line shapes. In
Sect. 3, we describe the retrieval of spectroscopic parameters from three
air-broadened cavity ring-down spectra fitted with a speed-dependent Voigt
line shape. For Sect. 4, the speed-dependent line shape along with the
retrieved spectroscopic parameters is used to fit solar absorption spectra
from four TCCON sites and retrieve total columns of O2, which is
compared to O2 retrieved using a Voigt line shape. In Sect. 5, we
investigate the change in the air mass dependence of XCO2 with the new
O2 retrievals. In Sect. 6, we discuss our results and their
implications for remote sensing of greenhouse gases.
Absorption coefficient calculationsVoigt line shape
The Voigt line shape is the convolution of the Lorentz and the Gaussian
profiles, which model pressure and Doppler broadening of the spectral line
respectively. The corresponding absorption coefficient, k, at a given
wave number v becomes
kv=N∑jSj1γDjln(2)π1/2Recv,xj,yj,
where N is the number density, Sj is the line intensity of spectral
line j, γDj is the Doppler half-width (HWHM), c is
the complex error function, and
xj=v-vjo-PδjoγDjln(2)1/2,yj=γLjγDjln(2)1/2.
Here, vjo is the position of the spectral line j, P is the
pressure, and δjo is the pressure-shift coefficient. The
Lorentz half-width, γLj, is calculated using the following:
γLjT=PγLjo296Tn,
where γLjo is the air-broadened Lorentz
half-width coefficient (at reference temperature 296 K) and n is the
exponent of temperature dependence. The Voigt line shape assumes that
pressure broadening is accurately represented by a Lorentz profile
calculated for the statistical average velocity at the time of collision.
Speed-dependent Voigt line shape
The speed-dependent Voigt line shape refines the pressure-broadening
component of the Voigt by calculating multiple Lorentz profiles for
different speeds at the time of collision. The final contribution from
pressure broadening to the speed-dependent Voigt is the weighted sum of
Lorentz profiles (weighted by the Maxwell–Boltzmann speed distribution)
calculated for different speeds at the time of collision. The
speed-dependent Voigt line shape (Ciuryło, 1998) with the
quadratic representation of the Lorentz width and pressure shift (Rohart et al., 1994) is as follows:
kv=N2π32∑jSj∫-∞∞e-V2Vtan-1xj-BaδjV2-1.5+Vyj1+aγLjV2-1.5dV,
where aγLj is the speed-dependent Lorentz width
parameter (unitless) for line j, aδj is the speed-dependent
pressure-shift parameter (unitless), B is ln(2)1/2γDj, V is the ratio of the absorbing
molecule's speed to the most probable speed of the absorbing molecule, and
all other variables were defined before.
(a) Cavity ring-down absorption coefficients for
O2 measured at the three pressures indicated in the legend at
approximately room temperature and a volume mixing ratio of 0.20720 (43). The
difference between measured absorption coefficients and those calculated using
(b) a Voigt line shape and (c) the speed-dependent Voigt
line shape. Note the difference in scale between panels (b) and
(c).
Fitting laboratory spectra
O2, unlike CO2 and CH4, cannot produce an electric dipole
moment and therefore should not be infrared active. However, O2 has two
unpaired electrons in the ground state that produce a magnetic dipole
moment. Due to the unpaired electrons in the ground state (X3Σg-) the rotational state (N) is split into three components which are
given by J=N-1, J=N and J=N+1, while in the upper state
(a1Δg), J=N. When labelling a transition, the following
nomenclature is used: ΔN(N′′)ΔJ(J′′) (Leshchishina et al., 2010), where
ΔNis the difference between N′ in the upper state and N′′ in the lower
state; ΔJ is the difference between J′ in the upper state and
J′′ in the lower state. The magnetic transitions of a1Δg←X3Σg- allow for ΔJ=0, ±1.
This leads to nine observed branches: P(N′′)Q(J′′), R(N′′)Q(J′′) and
Q(N′′)Q(J′′) for ΔJ=0; O(N′′)P(J′′), P(N′′)P(J′′), and
Q(N′′)P(J′′) for ΔJ=-1; and S(N′′)R(J′′),
R(N′′)R(J′′) and Q(N′′)R(J′′) for ΔJ=1.
Absorption coefficients for three room temperature air-broadened (NIST
Standard reference materal® 2659a containing 79.28 %
N2, 20.720 (43) % O2, 0.0029 % Ar, 0.00015 % H2O and
0.001 % other compounds) spectra were measured at the National Institute
of Standards and Technology (NIST) using the frequency-stabilised
cavity ring-down spectroscopy (FS-CRDS) technique (Hodges et al., 2004;
Hodges, 2005). The absorption spectra were acquired at pressures of 131,
99.3 and 66.9 kPa, at temperatures of 296.28, 296.34 and 296.30 K
respectively. Figure 1a shows the three measured absorption spectra. A more
detailed discussion of the present FS-CRDS spectrometer can be found in Lin et al. (2015).
The same as Fig. 1 but expanded to show four spectral lines in the
P branch of the O2 1.27 µm band.
The spectra were fitted individually using a Voigt line shape (Eq. 1), with
Sj, γLjo and δjo for the main
isotope of the magnetic dipole lines of the O2 1.27 µm
band for lines with an intensity greater than 7.0×10-28 cm-1 (molecule cm-2)-1.
The spectroscopic parameters measured in Leshchishina et al. (2011) for the
spectral lines of interest were used as the a priori for the retrieved
spectroscopic parameters. The line positions were left fixed to the values
measured in Leshchishina et al. (2011), and all other O2 spectral
lines (intensity less 7.0×10-28 cm-1 (molecule cm-2)-1) were calculated using a
Voigt line shape with spectroscopic parameters from HITRAN 2012 (Rothman et
al., 2013a). Spectral fits were done using the lsqnonlin
function in Matlab, with a user-defined Jacobian matrix. The Jacobian was
constructed by taking the derivative of the absorption coefficients with
respect to the parameters of interest. Using an analytical Jacobian instead
of the finite difference method is both computationally faster and more
accurate. The Voigt line shape was calculated using the Matlab code created
by Abrarov and Quine (2011) to calculate the complex error function and its
derivatives. To take collision-induced absorption (CIA) into account, a set
of 50 Legendre polynomials were added together by retrieving the weighting
coefficients needed to add the polynomials to fit the CIA for each spectrum.
Figure 1b shows the residual (measured minus calculated absorption
coefficients) when using a Voigt line shape with the retrieved spectroscopic
parameters. The plot shows that residual structure still remains for all
three spectra. The root mean square (rms) residual values for the spectra are
given by the legend at the side of the plot.
The averaged measured (a) intensity, (b) Lorentz
line width, (c) pressure shift and (d) speed-dependent
pressure shift retrieved from the three cavity ring-down spectra of the
1.27 µm band of O2. All data are plotted as a function of
m, which is m=-J for the P-branch lines, m=J for the Q branch and
m=J+1 for the R branch (where J is the lower state rotational
quantum number) and the uncertainties shown are 2σ.
Figure 2 is the same plot as Fig. 1 but for the P(11)P(11), P(11)Q(10),
P(9)P(9) and P(9)Q(8) spectral lines only. Figure 2b shows that for all
four spectral lines there is a W-shaped residual at the line centre. The
P(11)P(11) line was also measured by Hartmann et al. (2013) at pressures
ranging from 6.7 to 107 kPa. Figure 5 of Hartmann et al. (2013) shows the
P(11)P(11) line at a pressure of 66.7 kPa, which is approximately the
pressure of the 66.9 kPa spectrum (blue spectrum in Figs. 1 and 2). When
one compares the blue residual of the P(11)P(11) line in Fig. 2b to that
of the residual of the left panel of Fig. 5 of Hartmann et al. (2013), one can see that
the residuals are the same. Figure 6 of Hartmann et al. (2013) show that the
amplitude of the residual increases with decreasing pressure, which is also
seen in Fig. 2b. Figure 3 of Lamouroux
et al. (2014) shows the same W residual for the P(9)P(9) lines and that
the amplitude of the residual increases with decreasing pressure (although
for lower pressures), consistent with the results for the P(9)P(9) line in
Fig. 2b.
Figure 1c shows the residual when using the speed-dependent Voigt (Eq. 4) to
fit each spectrum individually. Using Eq. (4) requires integration over all
possible speeds, which is not computationally practical, so we employ the
simple numerical integration scheme as was done by Wehr (2005). When fitting the spectra, parameters
Sj, γLjo, δjo, aγLi and aδj were retrieved for lines of intensity
greater than 7.0×10-28 cm-1 (molecule cm-2)-1, while all other
O2 lines were calculated using a Voigt line shape and spectroscopic
parameters from HITRAN 2012 (Rothman
et al., 2013b). The retrieved spectroscopic parameters are available in the Supplement. The Jacobian matrix was created by taking the derivative
with respect to each parameter of interest, as was done with the Voigt fits.
By taking speed-dependent effects into account, the residuals were reduced to
25 times smaller than those for the Voigt fit and the rms residuals
(given in the legend of Fig. 1c) are 10 times smaller. However, some
residual structure still remains, which is more evident in the in the Q and
R branches than the P branch. Figure 2c shows the four lines in the P
branch, as discussed when analysing the Voigt fits. A small residual W
remains at the line centre as well as residuals from weak O2 lines.
Figure 3 shows the averaged intensity Lorentz width coefficient, pressure
shift coefficient and speed-dependent shift coefficient of the
1.27 µm O2 band, retrieved from the three spectra,
plotted as a function of quantum number m, which is m=-J (where J is the
lower state rotational quantum number) for the P-branch lines, m=J for
the Q-branch lines and m=J+1 for the R-branch lines. The intensity,
Lorentz widths and pressure shifts show a m dependence for these
parameters for the P and R sub-branches. The measured Lorentz widths and
pressure shifts for the Q sub-branches show a m dependence but are not as
strong as the P and R sub-branches. This is because the Q branch lines
are broadened enough to blend with each other, since they are spaced closer
together than the P or R branch lines. Figure 1c shows that some of the
residual structure in the Q branch increases with pressure and is partly
due to the blending of these transitions as the pressure increases. The weak
O2 absorption lines also blend in with the Q branch, contributing
to the residual structure in Fig. 1c. We tried retrieving the spectroscopic
parameters for the weak O2 absorption lines, but since they were
overlapping with the strong O2 lines, it was not possible.
Figure 4a shows the retrieved speed-dependent width parameter averaged over
the three spectra, plotted as a function of m, showing that it increases
with m. Error bars correspond to the 2σ standard deviation and are
large regardless of sub-branch. Figure 4b shows the retrieved speed-dependent
width for the PQ sub-branch for the different pressures. The
speed-dependent width shows the same m dependence regardless of pressure,
but also increases with decreasing pressure as is the case for sub-branches.
It should be noted that the speed-dependent width parameter should be
independent of pressure.
(a) The averaged measured speed-dependent width parameter
of the 1.27 µm band of O2 plotted as a function of m.
(b) The measured speed-dependent width parameter for spectral lines
that belong to the PQ sub-branch plotted as a function of m.
Fitting solar spectra
High-resolution solar absorption spectra were measured at four TCCON sites
using a Bruker IFS 125HR FTIR spectrometer with a room temperature InGaAs
detector at a spectral resolution of 0.02 cm-1 (45 cm maximum optical
path difference). The raw interferograms recorded by the instrument were
processed into spectra using the I2S software package (Wunch et al., 2015) that corrects solar
intensity variations (Keppel-Aleks et al., 2007), phase
errors (Mertz, 1967) and laser sampling errors (Wunch et al., 2015), and then performs a
fast Fourier transform to convert the interferograms into spectra (Bergland, 1969). The GGG software package
(Wunch et al., 2015) is used to retrieve
total columns of atmospheric trace gases. GFIT is the main code that
contains the forward model, which calculates a solar absorption spectrum
using a line-by-line radiative transfer model and an iterative non-linear
least square fitting algorithm that scales an a priori gas profile to obtain
the best fit to the measured spectrum. A priori profiles for GHGs are
created by an empirical model in GGG that is based on measurements from the
balloon-borne JPL MkIV Fourier transform spectrometer (FTS) (Toon, 1991), the Atmospheric Chemistry Experiment (ACE) FTS
instrument aboard the SCISAT satellite (Bernath
et al., 2005) and in situ GLOBALVIEW data (Wunch et al., 2011). Temperature and
pressure profiles, as well as H2O a priori profiles are generated from
the National Centers for Environmental Prediction (NCEP) data. The
calculations are performed for 71 atmospheric layers (0 to 70 km), so all
a priori profiles are generated on a vertical grid of 1 km.
(a) The residuals (measured minus calculated) for a
spectrum measured at Eureka on 27 March 2015 at a SZA of 81.32∘. The
red residual is the result of using the Voigt line shape and the blue is from
using the qSDV. (b) The measured (red dots) and calculated values (black
dots), with the qSDV spectrum, along with the gases included in the fit
(refer to the legend to the right) in the spectral window.
In the current GGG software package (Wunch et al., 2015), the forward model
of GFIT calculates absorption coefficients for the discrete lines of the
O2 1.27 µm band using a Voigt line shape and
spectroscopic parameters from Washenfelder et al. (2006a) and Gordon et
al. (2010). To take CIA into account, absorption coefficients are calculated
using a Voigt line shape and spectroscopic parameters from the
foreign-collision-induced absorption (FCIA) and self-collision-induced
absorption (SCIA) spectral line lists provided with the GGG software package
(Wunch et al., 2015). Spectroscopic parameters in the FCIA and SCIA line
lists were retrieved by Geoff C. Toon by fitting the laboratory spectra of Smith and
Newnham (2000). This was done by retrieving the integrated absorption at
every 1 cm-1 of the spectrum and using a Voigt line shape, with fixed
Lorentz width and no pressure shift. In GFIT, a volume scale factor is
retrieved for the CIA and discrete lines separately so that the O2
column is derived from the discrete lines of the 1.27 µm band only.
Airglow is not considered when fitting the 1.27 µm band, since the
spectrometer views the sun directly and airglow is overwhelmed by this a
bright source. The continuum level and tilt of the 100 % transmission
level is fitted using a weighted combination of the first two Legendre
polynomials. Absorption coefficient for all other trace gases are calculated
using a Voigt line shape and spectroscopic parameters from the atm.101 line
list (Toon, 2014a) and solar lines are fitted using the solar line list
(Toon, 2014b).
Figure 5 shows the spectral fit to a solar absorption spectrum recorded at
Eureka on 27 March 2015, at a solar zenith angle (SZA) of 81.32∘
(air mass of 6.3). This spectrum is an average of five Eureka scans. The TCCON
standard is single scan but five scans were averaged to decrease the noise. The
measured spectrum (red circles), calculated spectrum (black circles) and
transitions from all gases in the window (coloured lines, refer to the legend
for different gases) are shown in Fig. 5b. The residual obtained using a
Voigt line shape to calculate the discrete lines of the O2
1.27 µm band is shown in red in Fig. 5a. The blue residual is the
result of using a speed-dependent Voigt line shape with the spectroscopic
parameters retrieved from fitting the absorption coefficients in Section 3.
To decrease the amount of time it takes to calculate the absorption
coefficients, the quadratic speed-dependent Voigt (qSDV) computational
approach of Ngo et al. (2013) and Tran et al. (2013) was used instead of
Eq. (4) since it requires the Voigt calculation only twice, while Eq. (4)
requires numerical integration scheme with 33 iterations. The
temperature-dependent parameter of the Lorentz width of the discrete lines of
the O2 1.27 µm band reported in HITRAN 2012 was used to
take temperature dependence into account for γLjT. There was only a slight improvement in the fit residuals with the
new absorption coefficients (using the qSDV), as seen in Fig. 5a. Absorption
coefficients calculated with the qSDV were used to retrieve total columns of
O2 from solar spectra recorded over a 1-year period at TCCON
sites in Eureka (eu) (Nunavut, Canada) (Batchelor et al., 2009; Strong et
al., 2017), Park Falls (pa) (Wisconsin, USA) (Washenfelder et al.,
2006a; Wennberg et al., 2017a) ,
Lamont (oc) (Oklahoma, USA) (Wennberg et al., 2017b) and Darwin (db)
(Australia) (Deutscher et al., 2010; Griffith et al., 2017). In total
131 124 spectra were fitted using the qSDV and the average root mean square
(rms) residual of the fit only decreased by 0.5 %.
Impact of O2 columns on XCO2 measurements
The O2 column retrieved from the 1.27 µm band with a
Voigt line shape and spectroscopic parameters from the atm.101 line list
(Toon, 2014a) has an air mass dependence such that the O2 column
retrieved increases as a function of the solar zenith angle (or air mass). Using
spectra recorded from Eureka, Park Falls, Lamont and Darwin over 1-year
periods, total columns of O2 were retrieved using (1) a Voigt
spectral line shape with spectroscopic parameters from the atm.101 line list
and (2) the qSDV with the spectroscopic parameters determined in Sect. 3.
Figure 6 shows the percent difference calculated as the column from the qSDV
retrieval minus the column from the Voigt retrieval, which was then divided
by the latter and multiplied by 100, plotted as a function of solar zenith
angle (SZA). At the smallest SZA, the qSDV retrieves 0.75 % less
O2 than the Voigt, with the difference increasing to approximately
1.8 % as the SZA approaches 90∘. Figure 7 shows XAIR for the
entire data set plotted as a function of SZA. XAIR is the column of air
(determined using surface pressure recorded at the site) divided by the
column of O2 retrieved from the spectra and multiplied by 0.2095,
which is the dry-air mole fraction of O2 in the Earth's atmosphere.
Ideally XAIR should be 1 but when using O2 retrieved with a Voigt
line shape (Fig. 7a) to calculate XAIR the average XAIR value for the entire
data set is 0.977. Using O2 retrieved with the qSDV to calculate
XAIR, the average value is 0.986, which is closer to the expected value of 1.
However, XAIR has a dependence on SZA regardless of line shape used.
Figure 7a shows that XAIR decreases as a function of SZA (evident at SZA >75∘), which means that the retrieved column of O2 increases
as a function of SZA. Figure 7b shows that XAIR increases as a function of
SZA (evident at SZA >70∘), which means that the retrieved column
of O2 decreases as a function of SZA. Therefore retrieving total
columns of O2 with the qSDV changes the air mass dependence of the
O2 column, which in turn will impact the air mass dependence of
XCO2.
The percent difference between the O2 column retrieved
with the Voigt and qSDV line shapes for a year of measurements from Eureka
(eu), Park Falls (pa), Lamont (oc) and Darwin (db).
(a) XAIR as a function of SZA calculated using the total
column of O2 retrieved using the Voigt line shape.
Panel (b) is the same as panel (a) except the total column
of O2 was retrieved with the qSDV.
XCO2 calculated from the CO2 and O2
columns retrieved from Park Falls spectra recorded on 18 June 2013. The
CO2 columns were retrieved using either the Voigt line shape or
the qSDV with line mixing, while the O2 columns were retrieved
using either the Voigt or qSDV line shapes. XCO2 was calculated in
four ways: (1) both CO2 and O2 columns retrieved using
the Voigt line shape (red), (2) CO2 columns retrieved with the
Voigt and O2 columns retrieved with the qSDV (green),
(3) CO2 columns retrieved with the qSDV and line mixing and
O2 columns retrieved with the Voigt (cyan) and (4) CO2
columns retrieved with the qSDV and line mixing and O2 columns
retrieved with the qSDV (blue). The top x axis is the SZA that corresponds
to the hour on the bottom x axis.
Air mass dependence of XCO2
Since the standard TCCON XCO2 (and all other XGas) is calculated using
the column of O2 instead of the surface pressure, errors associated
with the retrieval of O2, such as the air mass dependence of the O2
column, will affect XCO2. Figure 8 is XCO2 calculated for four
different combinations pertaining to the two CO2 column retrievals and
the O2 column retrievals. The CO2 columns were retrieved with
either a Voigt line shape (the standard GGG2014 approach) or the qSDV with
line mixing as done in Mendonca et al. (2016), while the O2 columns were retrieved with either a Voigt (the
standard GGG2014 approach) or the new qSDV approach developed here. Figure 8
shows a spurious symmetric component to XCO2 when the total column of
O2 is retrieved with the Voigt line shape, regardless of line shape
used to retrieve CO2. When the qSDV is used to retrieve total columns
of O2, the symmetric component of XCO2 is dismissed regardless of
line shape used to retrieve CO2. This is because the air mass dependence
of the column of O2 retrieved using the qSDV is more consistent with
the air mass dependence of the column of CO2 (for both line shapes used
to retrieve CO2). Mendonca et al. (2016) showed that using the qSDV with line mixing results in better fits to
the CO2 windows and impacts the air mass dependence of the retrieved
column of CO2. When using a Voigt line shape the retrieved column
amount of CO2 decreases as air mass increases until the air mass is large
(SZA of about 82∘), at which point the retrieved column of CO2
increases as the air mass increases, changing the shape of the air mass
dependence of the CO2 column. When the qSDV with line mixing is used,
the retrieved column of CO2 decreases as a function of air mass (up
until the sun is above the horizon).
To correct for this, an empirical correction is applied to all TCCON
XCO2 (and XGas). The empirical correction determines the
antisymmetrical component of the day's XCO2, which is assumed to be the
true variation of XCO2 throughout the day, as well as the symmetrical
component, which is caused by the air mass dependence of the retrieved column
of the gas of interest and O2. We can, therefore, represent a
measurement as (Wunch et al., 2011)
yi=y^1+αSθi+βAti,
where y^ is the mean value of XCO2 measured that day, β
is the fitted coefficient of the antisymmetric function Ati and α is the fitted coefficient of the symmetric function
S(θi). The antisymmetric function is calculated by (Wunch et al., 2011)
Ati=sin2πti-tnoon,
where ti is the time of the measurement and tnoon is the time at
solar noon, both in units of days. The symmetric function is calculated by (Wunch et al., 2011)
Sθi=θi+13∘90∘+13∘3-45∘+13∘90∘+13∘3,
where θi is the SZA in degrees. To determine α for the
different line shapes, total columns of CO2 were retrieved using the
Voigt line shape (Wunch et al., 2015) and the
qSDV with line mixing (Mendonca et al.,
2016). Henceforth, we will refer to XCO2 calculated from O2 and
CO2 using the Voigt line shape as XCO2 Voigt and the qSDV line
shape as XCO2 qSDV.
Figure 9 shows the average α calculated for each season at Darwin,
Lamont and Park Falls. Eureka XCO2 cannot be used to determine α because Eureka measurements do not go through the same range of SZAs as
the other three sites due to its geolocation. The average α values
derived from XCO2 Voigt are represented by stars in Fig. 9, while the
squares indicate XCO2 qSDV. At all three sites, α is closer
to 0 when the qSDV line shape is used in the retrieval compared to the Voigt
retrieval, regardless of the season. The average α for XCO2
Voigt calculated from a year of measurements from Darwin, Park Falls and
Lamont is -0.0071±0.0057 and that for XCO2 qSDV is
-0.0012±0.0054.
For all four sites, α=-0.0071 is used to correct XCO2 Voigt
measurements. Figure 10a shows the XCO2 Voigt anomalies plotted as a
function of SZA. The data are expressed as the daily XCO2 anomaly, which
is the difference between the XCO2 value and the daily median value, in
order to remove the seasonal cycle. When XCO2 is left uncorrected for
air mass dependencies, XCO2 decreases as a function of SZA up to
approximately 82∘ and increases as a function of SZA at angles greater
than 82∘. Figure 10b shows XCO2 Voigt corrected for the air mass
dependence. This air mass correction works well only up to a SZA of
approximately 82∘. Figure 10c is the same as Fig. 10a but for the
uncorrected XCO2 qSDV measurements, while Fig. 10d is the same as Fig. 10b
but for the corrected XCO2 qSDV measurements. When the air mass
correction is applied to XCO2 qSDV, there is a small difference between
the corrected and uncorrected XCO2 qSDV measurements, with the
difference only noticeable for the Darwin measurements recorded at SZA >60∘. For XCO2 qSDV measurements taken at SZA >82∘, XCO2 does not increase with SZA as it does with
the Voigt.
The average air-mass-dependent correction factor for XCO2
derived from a year of spectra measured at Darwin, Lamont and Park Falls for
different seasons. The dashed lines with stars are the α for
XCO2 retrieved using a Voigt line shape for both CO2 and
O2 columns. The solid lines with squares are from XCO2
retrieved using the qSDV for both CO2 and O2 columns.
(a)XCO2 Voigt anomaly for a year of measurements
from the four TCCON sites. The XCO2 anomaly is the difference
between each XCO2 value and the daily median XCO2.
(b) The XCO2 Voigt anomaly after the air mass dependence
correction is applied to the XCO2 Voigt data.
(c)XCO2 qSDV anomaly. (d)XCO2 qSDV
anomaly after correction for the air mass dependence.
(a) Correlation between TCCON and aircraft XCO2
Voigt measurements for 13 TCCON sites. Each aircraft type is indicated by a
different symbol given by the legend in the top-left corner. Each site is
represented by a different colour given by the legend in the bottom right
corner. The grey line indicates the one-to-one line and the dashed line is
the line of best fit for the data. The slope of the line of best fit as well
as the error on the slope are given in the plot. (b) The same as
panel (a) but for XCO2 qSDV.
(a–d)XCO2 plotted as a function of day of the
year for Eureka (2014), Park Falls (2013), Lamont (2010) and Darwin (2006). The mostly hidden red boxes are XCO2 calculated from
using a Voigt line shape in the retrieval and the blue boxes are from using
the qSDV. (e–h) The difference between XCO2 Voigt and
XCO2 qSDV.
Accuracy of XCO2
To assess the accuracy of TCCON XCO2 measurements, they are compared to
aircraft XCO2 profile measurements using the method described in Wunch
et al. (2010). Figure 11a shows the comparison between the aircraft
XCO2 (Deutscher
et al., 2010; Lin et al., 2006; Messerschmidt et al., 2010; Singh et al.,
2006; Wofsy, 2011) measurements (legend at the top details the different
aircraft) and TCCON XCO2 Voigt measurements for 13 TCCON sites (given
by the colour-coded legend at the bottom right). The grey line indicates the
one-to-one line and the dashed line is the line of best fit. There is a bias
of 0.9897±0.0005 given by the slope of the line of best fit in
Fig. 11a for the XCO2 Voigt measurements. Figure 11b is the same as
Fig. 11a but for the XCO2 qSDV measurements. The bias between the aircraft
XCO2 measurements and the XCO2 qSDV measurements is 1.0041±0.0005 as given by the slope of the line of best fit in Fig. 11b. This
increase in the slope can be explained by an increase in the retrieved
column of CO2 when using the qSDV with line mixing as shown in Mendonca et al. (2016) as well as combined with a decrease in the retrieved O2 column
due to using the qSDV. As discussed previously (Sect. 5) the decrease in
the retrieved O2 column is an improvement but the expected column of
O2 is still approximately 1.2 % higher (at the smallest SZA) than it
should be. Therefore, the retrieved column of CO2 is higher than it
should be, and the slope would be greater if the retrieved column of O2
was 1.2 % lower. Nevertheless, using the qSDV to retrieve total columns
of CO2 and O2 reduces the difference between TCCON XCO2 and
aircraft XCO2 measurements by 0.62 %.
TCCON XCO2 measurements are divided by the scale factors (or bias
determined in Fig. 11) to calibrate to the WMO scale. For all TCCON
XCO2 measurements retrieved with a Voigt line shape, the air mass
correction is first applied to the data and the result is divided by the
determined bias factor, 0.9897. Figure 12a to d shows XCO2 Voigt (for
Eureka, Park Falls, Lamont and Darwin) indicated by red square
boxes in the plots. XCO2 Voigt measurements taken at SZA >82∘ have been filtered out because they cannot be corrected for the
air mass dependence. The blue boxes are XCO2 qSDV corrected for air mass
dependence and scaled by 1.0041. No filter was applied to the XCO2 qSDV
measurements for SZA since the air mass dependence correction works at all
SZA. Figure 12e–h shows the difference between XCO2 Voigt and
XCO2 qSDV for Eureka, Park Falls, Lamont and Darwin. The
mean differences for the data shown in Fig. 12e to h are 0.113±0.082, -0.102±0.223, -0.132±0.241 and -0.059±0.231µmol mol-1 (ppm) for Eureka, Park Falls, Lamont and Darwin respectively.
The difference throughout the day at Park Falls, Lamont and Darwin varies
between -0.6 and 0.2 µmol mol-1 and is SZA dependent.
(a)XCO2 from Park Falls retrieved from spectra
recorded on 18 June 2013. Retrieved XCO2 is plotted (1) with a
Voigt line shape and corrected for the air mass dependence (red squares),
(2) with the qSDV (cyan circles) and (3) with the qSDV and corrected for the
air mass dependence (blue squares). (b) The difference between the
corrected Voigt XCO2 and the qSDV XCO2 (cyan circles)
and the difference between the Voigt corrected XCO2 and the corrected qSDV
XCO2 (blue squares). The top x axis is the SZA that
corresponds to the hour on the bottom x axis.
Figure 13a shows XCO2 Voigt corrected for the air mass dependence, as
well as XCO2 qSDV, uncorrected and corrected for the air mass
dependence. These XCO2 measurements were retrieved from Park Falls
spectra recorded on 18 June 2013. For all three XCO2 measurements, the
amount of XCO2 decreases throughout the day. Figure 13b shows the
difference between the corrected Voigt XCO2 and the uncorrected qSDV
XCO2, as well as the difference between the corrected Voigt XCO2
and the corrected qSDV XCO2. The difference between the Voigt and the
qSDV (corrected and uncorrected) shows that at the start and end of the day,
more XCO2 is retrieved with the qSDV, while at midday less is
retrieved with the qSDV. The range in the differences seen in Fig. 12e to
h varies with SZA throughout the day as shown in Fig. 13b.
Discussion and conclusions
Using cavity ring-down spectra measured in the lab, we have shown that the
Voigt line shape is insufficient to model the line shape of O2 for the
1.27 µm band, consistent with the results of Hartmann
et al. (2013) and Lamouroux et al. (2014). By using the speed-dependent
Voigt line shape when calculating the absorption coefficients, we were
better able to reproduce the measured absorption coefficients than using the
Voigt line shape. However, some residual structure remains as seen Figs. 1
and 2. This is partly due to the blending of spectral lines (i.e. line
mixing) and the inability to retrieve the spectroscopic parameters for weak
O2 transitions. Fitting low-pressure spectra would help with isolating
spectral lines and decreasing the uncertainty on the retrieved spectroscopic
parameters for the Q branch lines.
Accurate measurements of the pressure shifts in the 1.27 µm band
have been hard to obtain as shown in Newman et al. (1999) and Hill et
al. (2003). While the retrieved pressure shifts show a dependence on quantum
number m (Fig. 3c) as one would expect, this dependence is not as strong as
the m dependence of the Lorentz widths (Fig. 3b). This can be explained by
the fact that line mixing, which is shown to be important for the
O2 A-band, was not considered when fitting the cavity ring-down
spectra. Neglecting line mixing usually produces an asymmetric residual in
the discrete lines as well as a broad residual feature associated with the
fact that collisions are transferring intensity from one part of the spectrum
to another. By fitting a set of Legendre polynomials for CIA, we could be
simultaneously fitting the broader-band feature associated with line mixing,
while the retrieved pressure shifts and speed-dependent pressure shifts
could be compensating for the asymmetric structure one would see in the
discrete lines when neglecting line mixing. The remaining structure, as seen
in Fig. 1c, could be due to neglecting line mixing, especially in the
Q branch, where the spacing between spectral lines is small (in comparison
to the P and R branches) and line mixing is most likely prevalent. The
large error bars for the measured pressure shifts and speed-dependent
pressure shifts as well as a deviation from a smooth m dependence of these
parameters could be due to neglecting line mixing when fitting the lab
spectra. Figure 3c and d show that the spectral lines that have large error
bars and deviate from an expected m dependence belong mainly to the
Q-branch spectral lines (which are mostly likely impacted by line mixing).
To achieve the results obtained in this study it is best to use the
parameters as they are instead of trying to apply an interpolation that depends on
m or even omitting them, unless one tests these changes on atmospheric
spectra that cover different range of conditions (i.e. seasons, dry/wet, SZA,
geographical locations). It is evident that the parameters might be
compensating for effects (such as line mixing) that were not included when
fitting the lab spectra, and changing these parameters (or omitting them)
could lead to degradation in the quality of the spectral fits of solar
spectra and a change in the air mass dependence of the retrieved column of
O2, which would impact the air mass dependence of XCO2.
The pressure dependence of the retrieved speed-dependent width parameter is
an indication that Dicke narrowing needs to be taken into account, as shown
by Bui et al. (2014) for CO2. When both speed dependence and Dicke
narrowing are present, a multispectrum fit needs to be used due to the
correlation between the parameters (Bui et al., 2014). Domysławska et
al. (2016) recommend using the qSDV to model the line shape of O2
based on multiple line shape studies of the O2 B-band. In these
studies, a multispectrum fit to low-pressure (0.27–5.87 kPa) cavity ring-down spectra was performed testing multiple line shapes that took
speed dependence and Dicke narrowing into account both separately and
simultaneously. They found that the line shapes that only used Dicke
narrowing were not good enough to model the line shape of the O2
B-band lines, but a line shape that included either speed dependence or both
speed dependence and Dicke narrowing produced similar quality fits,
ultimately concluding that speed dependence has a larger effect than Dicke
narrowing. It was noted in the study by Wójtewicz et al. (2014) that both
Dicke narrowing and speed-dependent effects might simultaneously play an
important role in modelling the line shape of the O2 B-band lines.
However, the speed-dependent and Dicke narrowing parameters are highly
correlated at low pressures. Reducing the correlation requires either a
multispectrum fit of spectra at low pressures with a high enough signal-to-noise ratio or spectra that cover a wide range of pressures (Wójtewicz et
al., 2014). So, by combining the high-pressure spectra used in this study
with low-pressure spectra in a multispectral fit, both the speed dependence
and Dicke narrowing parameters could be retrieved. The temperature dependence
of the Lorentz width coefficients of this band has never been measured
before, which could have an impact on the air mass dependence of O2.
Combining high-pressure cavity ring-down absorption coefficient measurements
with those for low pressures and different temperatures as done in Devi et
al. (2015, 2016) for CH4 would lead to more accurate line shape
parameters for O2.
By taking speed dependence into account for both CO2 (in the work of Mendonca et al.,
2016) and O2 (the work presented here), we were able to significantly
decrease the air mass dependence of TCCON XCO2 and the bias between
TCCON and aircraft XCO2. XAIR calculated with the column of O2
retrieved with the qSDV is now closer to the expected value of 1, but XAIR
still has an air mass dependence which is the result of the retrieved total
column of O2 decreasing as a function of SZA at large SZA. This
remaining air mass dependence could be due to neglecting effects such as
Dicke narrowing and line mixing in the absorption coefficient calculations,
as well as assuming a perfect instrument line shape in the retrieval
algorithm. However, retrieving O2 with the qSDV significantly decreases
the air mass dependence of XCO2. With the qSDV line shape, XCO2
measurements taken at SZA >82∘ no longer have to be
discarded. We recommend using the full range of SZA, which would result in
more XCO2 measurement available from all TCCON sites. This is
particularly important for high-latitude TCCON sites such as Eureka
because measurements taken from late February to late March and from late
September to mid-October are taken at SZA >82∘. Filtering
out these large SZA measurements thus limits the knowledge of the seasonal
cycle of XCO2 at high latitudes. The air mass dependence of the O2
column not only affects XCO2 but all trace gases measured by TCCON and
in the future the air mass dependence of all XGas will be determined with
these new O2 columns.
All TCCON data are available from the TCCON data archive hosted by CaltechDATA and located at
https://tccondata.org/ (last access: 19 December 2018).
Site-specific data used in this work can be obtained from the links in the relevant cited references. Solar absorption spectra can be
obtained by contacting the TCCON site PIs. Laboratory O2 cavity ring-down spectra can be obtained by contacting David Long at the
National Institute of Standards and Technology.
The supplement related to this article is available online at: https://doi.org/10.5194/amt-12-35-2019-supplement.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was primarily supported by the Canadian Space Agency (CSA) through
the GOSAT and CAFTON projects and the Natural Sciences and Engineering
Research Council of Canada (NSERC). The Eureka measurements were taken at the
Polar Environment Atmospheric Research Laboratory (PEARL) by the Canadian
Network for the Detection of Atmospheric Change (CANDAC), which has been
supported by the AIF/NSRIT, CFI, CFCAS, CSA, Environment Canada (EC),
Government of Canada IPY funding, NSERC, OIT, ORF, PCSP, and FQRNT. The
authors wish to thank the staff at EC's Eureka Weather Station and CANDAC
for the logistical and on-site support provided. Thanks to CANDAC Principal
Investigator James R. Drummond, PEARL Site Manager Pierre Fogal and
CANDAC/PEARL operators Mike Maurice and Peter McGovern for their invaluable
assistance in maintaining and operating the Bruker 125HR. The research at
the Jet Propulsion Laboratory (JPL), and California Institute of Technology
was performed under contracts and cooperative agreements with the National
Aeronautics and Space Administration (NASA). Geoffrey C. Toon and Debra Wunch
acknowledge support from NASA for the development of TCCON via grant number
NNX17AE15G. Darwin TCCON measurements are possible thanks to support from
NASA grants NAG5-12247 and NNG05-GD07G, the Australian Research Council
grants DP140101552, DP110103118, DP0879468 and LP0562346, and the DOE ARM
programme for technical support. The research at the National Institute of
Standards and Technology was performed with the support of the NIST
Greenhouse Gas Measurements and Climate Research Program. Certain commercial
equipment, instruments, or materials are identified in this paper in order
to specify the experimental procedure adequately. Such identification is not
intended to imply recommendation or endorsement by the National Institute of
Standards and Technology, nor is it intended to imply that the materials or
equipment identified are necessarily the best available for the purpose.
Edited by: Frank Hase
Reviewed by: two anonymous referees
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