Profiling Tropospheric CO2 using the Aura TES and TCCON instruments
Le Kuai1, John Worden1, Susan Kulawik1, Kevin Bowman1, Christian Frankenberg1, Edward Olsen1,
Debra Wunch3, Run-Lie Shia3, Brian Connor2, Charles Miller1, and Yuk Yung3
1.
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Mail
stop: 233-200, Pasadena, CA 91109
2.
BC Consulting Ltd., 6 Fairway Dr, Alexandra 9320, New Zealand
3.
California Institute of Technology, 1200 E. California Blvd., Pasadena, CA, 91125
Abstract
Monitoring the global distribution and long-term variations of CO2 sources and sinks
is required for characterizing the global carbon budget. Measurements of the total
column of CO2 by ground or by satellite have the potential to estimate continental
scale sources and sinks but are less sensitive to regional and local scale sources and
sinks because CO2 is a long-lived gas which makes it challenging to identify local
sources from CO2 transported from elsewhere. For this reason we are exploring the
use of ground-based near infrared (NIR) measurements with space based thermal
IR measurements (TIR) for distinguishing planetary boundary layer CO2 from total
column estimates. The NIR measurements are obtained from the Total Carbon
Column Observing Network (TCCON) solar measurements, which provide an
estimate of the total CO2 atmospheric column amount. Estimates of tropospheric
CO2 that are co-located with TCCON are obtained by assimilating Tropospheric
Emission Spectrometer (TES) free-tropospheric CO2 estimates into the GEOS-Chem
model.
Estimates of the boundary layer CO2 are obtained through simple
subtraction as the CO2 estimation problem is linear.
We find that the calculated random uncertainties due to noise and temperature
variability for the total column and boundary layer estimates are consistent with
actual uncertainties as compared to aircraft data.(ref for aircraft???) For the total
1
column estimates the random uncertainty is about 0.7 ppm with a bias of -5 ppm,
consistent with previously published results. For the boundary layer CO2 estimates
the RMS is 1.46 ppm and the bias is 0.32 ppm after accounting for the total column
bias of -5 ppm.
This work shows that total column from NIR measurements, e.g. Greenhouse gases
Observing SATellite "IBUKI" (GOSAT), Orbiting Carbon Observatory (OCO-2) and
TCCON, as well as the free troposphere measurement from TIR, e.g. TES and
Atmospheric Infrared Sounder (AIRS) can be used to profile CO2 and obtain
boundary layer CO2 with precision necessary to capture the atmospheric CO2
variability.
I. Introduction
Our ability to infer surface carbon fluxes depends critically on interpreting spatial
and temporal gradients of atmospheric CO2 and relating them back to surface fluxes.
For example, surface CO2 fluxes are typically calculated using surface or near surface
CO2 measurements with a combination of aircraft data (e.g., Chevalier et al.,
2010need lots of references here). More recently it has been shown that total
column CO2 measurements, such as can be measured by satellite can be used to
place constraints on continental-scale flux estimates (e.g., Gurney et al., 2002; Baker
et al., ; Chevalier et al., 2007, 2011).
However, because CO2 is a long-lived
greenhouse gas, measurements of the total column CO2 is primarily sensitive to
large-scale fluxes (need a number here???) as discussed in Keppel-Aleks (2011).
They show that variations in the total column are only partly driven by local surface
fluxes because of transport of CO2 from remote locations (Rayner et al. 2001,
Keppel-Aleks et al., 2011). In the free troposphere, the temporal and spatial
variations of atmospheric CO2 are associated with synoptic atmospheric
phenomenon and only partly connected to the surface. In contrast, the variations in
planetary boundary layer (PBL) CO2 are more related to local flux (e.g., Sarrat et al.,
2
2007). They used their mesoscale transport model to interpret a regional scale
database including frequent vertical profiles and aircraft transection. 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,
Stephen 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. For these reasons we could expect that improved vertical profile estimates
of CO2 will improve constraints on the distributions of carbon flux. Therefore, we
are motivated to derive a method to estimate the PBL CO2 from current available
column and free tropospheric observations.
Total column CO2 data are calculated by solar near infrared (NIR) measurements
from the Total Carbon Column Observatory Network (TCCON) (Wunch et al., 2010
and 2011), as well as the space-borne instruments, starting from GOSAT (Crisp et al.,
2004; Yokota et al., 2009; Wunch et al., 2011; O’Dell et al., 2011). The similar spaceborne instruments are OCO-2, which is expected to be launched this decade (Crisp et
al., 2004) and several other instruments such as Carbonsat (reference???) and
GOSAT-2 (reference), which are expected to be launched. The ground-based
measurements have high precision and accuracy but limited spatial coverage.
Satellite observations have lower precision and accuracy relative to the groundbased data, but obtain continuous global measurements of atmospheric CO2. In
addition, there are free tropospheric CO2 measurements from satellite instruments
such as TES (Kulawik S, et al., 2009) and AIRS (Chahine et al., 2005); They measure
CO2 using the thermal infrared CO2 band. These datasets contribute the view of the
global and temporal variability of atmospheric CO2 in the middle and upper
troposphere.
In this paper, we present a method to estimate the PBL CO2 by combining column
and free tropospheric CO2 from two data source: TCCON and TES. The
measurements used in this study are described in section 2. The estimates of
3
column CO2 are obtained by TCCON profile retrieval and free tropospheric CO2 is
derived from assimilation of the TES CO2 estimates into the GEOS-chem global
chemical transport model (Bey et al., 2001). The comparisons of estimates against
aircraft data are used to evaluate the quality of the data. Section 3 describes the
derivation of extract PBL CO2 from column data using free tropospheric
measurements. The retrieval approach and error analysis is described in section 4.
The results are discussed in section 5. It is followed with the conclusions in section
6.
2. Measurements
2.1 Ground-Based Total Column CO2 Measurements from TCCON:
The column data used to derive PBL CO2 in this study are from TCCON observations.
A Fourier Transform Spectrometer instrument, with a precise solar tracking system,
measures incoming sunlight with high spectral resolution (0.02 cm-1) and high
signal to noise ratio (SNR) between 500 and 885, depending on the spectral region
observed Washenfelder et al. [2006]. The recorded spectral region covers from
4000 to 6000 cm-1. It provides a long-term observation of column-averaged
abundance of greenhouse gases, such as CO2, CH4, N2O and other trace gases (e.g.
CO) over sixteen TCCON sites around the world including both operational and
future sites (Washenfelder et al., 2006; Wunch et al., 2010, 2011; Yang et al., 2002).
As discussed in Wunch et al., (2010, 2011), total column abundances using TCCON
data can be estimated using a non-linear least squares approach that compares a
forward model spectrum that depends on CO2, temperature, H2O, and instrument
parameters against the observed spectrum. The retrieval approach described in
Wunch et al., (2010, 2011) adjusts atmospheric CO2 concentrations by simply
scaling an a priori CO2 profile (as well as the other discussed parameters) until the
observed and modeled spectra agree within the noise levels. The precision in their
column-averaged CO2 dry air mole fraction from the scaling retrievals is better than
0.25% (Wunch et al., 2010, 2011). The absolute accuracy is ~1% and after
calibration by aircraft data, it can reach 0.25% (Wunch et al., 2010). In this paper,
we developed a profile retrieval algorithm that scales multiply levels of the CO2
4
profile instead of the whole profile. We find that this approach can improve the
precision to 0.18%. Fig. 1 shows a measurement at 1.6 μm CO2 absorption band,
which is used for the profile retrieval. The profile retrieval algorithm is briefly
described in section 4.1 and the details will be discussed in a separate paper.
Fig. 1. CO2 band at 1.6 m observed on June 17, 2008 by TCCON at Park Falls
(Wisconsin) with solar zenith angle of 22.5.
2.2 Satellite-Based free tropospheric CO2 measurements from TES:
The free tropospheric CO2 estimates are retrieved from the Aura Tropospheric
Emission Spectrometer (TES) (Beer et al., 2001). The TES instrument measures the
infrared radiance emitted by Earth’s surface and atmospheric gases and particles
from the space. These measurements have peak sensitivity to the mid-tropospheric
CO2 at 511 hPa (Kulawik S, et al., 2012). Because the sampling for the TES CO2
measurements is sparse (e.g., 1 measurement every 200 km approximately), we
assimilated the TES CO2 measurements into the Geos-chem model, a global 3-D
5
chemical transport model (CTM) (Bey et al., 2001; Nassar et al., 2010; Kulawik et al.,
2011). We use the results from the assimilation as our free-tropospheric estimates
of CO2.
Details of the assimilation approach are discussed in the Supplemental section and
uncertainties in the assimilation fields are calculated by the comparison to aircraft
data as discussed in Section 4.2.
2.3 Flight measurements:
Aircraft data are used as our standard to access the quality of the CO2 estimates. The
aircrafts measure the CO2 profiles up to 6 km and sometimes up to 10 km. They are
considered as the best estimates of the true state of atmospheric CO2. We collected
profile observations by different aircrafts, such as HIPPO (Wofsy, 2011) and Learjet,
at the Southern Great Plains (SGP) ARM site (Fischer et al., 2007; Riley et al., 2009)
over the year 2009. They are comparable to the TCCON observations at Lamont site,
Oklahoma (36.6°N, 97.5°W).
3. Calculation of column and PBL CO2
The approach discussed in this paper is to estimate PBL CO2 by subtracting TES
GEOS-chem assimilated free tropospheric CO2 partial column amount from TCCON
total column amount. The total column amount is usually obtained by integrating
the gas concentration profile from surface to the top of atmosphere.
∞
𝑑𝑟𝑦
𝐶𝑔 = ∫ 𝒇𝑔 (𝒛) ∙ 𝒏(𝒛) ∙ 𝑑𝑧
(1)
𝑧𝑠
where Cg is total vertical column amount for gas ‘g’ and 𝒏(𝒛) represents the number
𝑑𝑟𝑦
density vertical profile and 𝒇𝑔 (𝒛) is dry-air gas concentration profile as a function
of altitude (z).
6
𝑑𝑟𝑦
𝒇𝑔 (𝒛) =
𝒇𝑔 (𝒛)
1 − 𝒇𝐻2 𝑂 (𝒛)
(2)
The ratio of total column between gas and air will give dry-air column-averaged
abundance, e.g. for CO2:
𝑋𝐶𝑂2 =
𝐶𝐶𝑂2
𝐶𝐴𝐼𝑅
(3)
Here we use 𝑋𝐶𝑂2 to refer to dry-air column-averaged mole fraction of CO2 and we
simply called it column-averaged CO2.
Since TCCON also provide the precise measurement of O2, dividing by the retrieved
O2 using spectra measurements from same instruments improves the precision of
𝑋𝐶𝑂2 by significantly reducing the effects of instrumental or measurement errors
that are common in both gases (e.g. solar tracker pointing errors, zero level offsets,
instrument line shape errors, etc.) (Wunch et al., 2010). We remove the water
fraction by normalizing simultaneously retrieved O2 but in slightly different order
from Wunch et al., 2010. The retrieved profile is first converted to the dry-air CO2
concentration layer by layer.
𝑑𝑟𝑦
𝑓𝐶𝑂2 (𝑧) =
𝑓𝐶𝑂2 (𝑧)
× 0.2095
𝑓𝑂2 (𝑧)
(4)
Then the column amount (𝐶𝐶𝑂2 ) and the column average (𝑋𝐶𝑂2 ) can be computed
using equation (1) and (3) respectively. While in Wunch et al., 2010, they integral
the profile for column amount and then computed 𝑋𝐶𝑂2 by ratio the column amount
between CO2 and O2 using
𝑋𝐶𝑂2 =
𝐶𝐶𝑂2
× 0.2095
𝐶𝑂2
(5)
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The improvement in precision is also found in profile retrieval. However, the bias
specific for O2 will be transferred to 𝑋𝐶𝑂2 . The test using equation (2) and (4)
suggest that a larger bias of about -5 ppm in 𝑋𝐶𝑂2 is mainly induced by normalizing
O2 as a measure of the dry air column. However, the precision of 𝑋𝐶𝑂2 is remarkably
reduced from 1.73 ppm to 0.5 ppm (Fig. 2).
Fig. 2. Calibration curve of CO2. Red points for using H2O as dry air standard; Black
points for using O2 as dry air standard. Dots for Parkfalls site and diamonds for
Lamont site.
𝑇𝑅𝑂𝑃
The partial vertical column amount of CO2 in free troposphere and above (𝐶𝐶𝑂
) is
2
estimated by TES GEOS-chem assimilated data. Then partial vertical column amount
of CO2 in PBL can be computed as the difference between the total column amount
and partial free tropospheric column amount:
𝑃𝐵𝐿
𝑇𝑅𝑂𝑃
𝐶𝐶𝑂
= 𝐶𝐶𝑂2 − 𝐶𝐶𝑂
2
2
(6)
8
The ratio of partial vertical column between CO2 and air gives the PBL CO2 mole
𝑃𝐵𝐿
fraction (𝑝𝑋𝐶𝑂
)
2
𝑃𝐵𝐿
𝑝𝑋𝐶𝑂
=
2
𝑇𝑅𝑂𝑃
𝐶𝐶𝑂2 − 𝐶𝐶𝑂
2
(7)
𝑃𝐵𝐿
𝐶𝐴𝐼𝑅
The total column amount 𝐶𝐶𝑂2 can be inverted from TCCON profile retrieved 𝑋𝐶𝑂2
𝑇𝑅𝑂𝑃
and free tropospheric partial column amount 𝐶𝐶𝑂
are estimated by integrating
2
TES GEOS-chem assimilated data above the top of boundary layer. Since O2
normalized estimates of 𝑋𝐶𝑂2 has higher precision but about 1% negative bias, we
need remove the mean bias in TCCON 𝑋𝐶𝑂2 when estimating the total column
amount:
𝐶𝐶𝑂2 =
𝑋𝐶𝑂2
𝐶
𝛼 𝐴𝐼𝑅
(8)
where 𝛼 is a correction factor to remove the bias in column data. Then applying
equation (3) within the boundary layer give the estimates of the PBL CO2. It is
comparable to the integrated partial column-averaged CO2 by aircraft within the
boundary layer.
This work is under the assumption of the linearity of the boundary layer, free
troposphere and total column estimates. In Fig. 3, we show that it is a reasonable to
assume that the changes in spectra (∆𝑳) due to the change of PBL CO2 (∆𝒙) is
linearly related to the changes of PBL CO2:
𝑳(𝒙 + ∆𝒙) − 𝑳(𝒙) ≈ 𝐊∆𝒙
(9)
where K is the Jacobians of x and ∆𝒙 is the change of CO2 in boundary layer (Fig. 3
(a, b)). The difference of the two calculated radiance is consistent with the expected
estimates of the changes in radiance using Jacobians K. The residual (~10-7)
9
between the actual difference and expected perturbation are much smaller than the
noise level (~10-4).
10
Fig. 3. (a) Original CO2 profile in black line and perturbed CO2 profile in blue line. (b)
Changes of CO2 (∆𝑥) are mostly in boundary layer. (c) Calculated differences of the
radiances. Black is the difference of two forward model simulations. The red is the
estimates of the difference using linear equation (9). Their residuals plotted in (d)
are three orders of magnitude smaller than the noise level (dotted line in c).
4. Retrieval Approach and Error Characterization
4.1 Retrieval approach for TCCON CO2 profile:
In this study, we develop a profile retrieval algorithm that is based on the scaling
retrieval discussed in Wunch et al., (2010, 2011). The profile of atmospheric CO2 is
obtained by optimal estimation (Rodgers, 2000) using a line-by-line radiative
transfer model in GFIT developed at JPL. It computes simulated spectra using 71
vertical levels with 1 km intervals for the input atmospheric state (e.g. CO2, H2O,
CH4, O2, P, T and etc.). The details about the TCCON instrument setup and GFIT code
are described in Deutscher et al., 2010; Geibel et al., 2010; Washenfelder et al., 2006;
Wunch et al., 2010, 2011; Yang et al., 2002. The retrievals in this study use one of
TCCON-measured CO2 absorption bands, centered at 6220.00 cm-1 with a window
width of 80.00 cm-1 (Fig. 1).
In the scaling retrieval discussed by Wunch et al. (2010, 2011), when the target gas
is CO2, the retrieved state vector (𝜸 ) includes the eight constant scaling factors for
four absorption gases (CO2, H2O, HDO, and CH4) and four spectroscopic parameters
(continuous level: ‘cl’, continuous title: ‘ct’, frequency shift: ‘fs’, and zero level offset:
‘zo’).
𝛾[𝐶𝑂2 ]
𝛾[𝐻2 𝑂]
𝛾[𝐻𝐷𝑂]
𝛾
𝜸 = [𝐶𝐻4 ]
𝛾𝑐𝑙
𝛾𝑐𝑡
𝛾𝑓𝑠
[ 𝛾𝑧𝑜 ]
(10)
11
It is estimated to shift whole a priori profile so that the model computed spectrum
has the best fit of observation. In the profile retrieval, we estimate the altitude
dependent scaling factors for CO2 while the other constant scaling factors are still
retrieved for other interfering gases and spectroscopic parameters. Ten levels are
chosen for CO2 (e.g., see Fig. 4 a):
𝛾1[𝐶𝑂2 ]
⋮
𝛾10[𝐶𝑂2]
𝛾[𝐻2 𝑂]
𝜸 = 𝛾[𝐻𝐷𝑂]
𝛾[𝐶𝐻4 ]
𝛾𝑐𝑙
𝛾𝑐𝑡
𝛾𝑓𝑠
[ 𝛾𝑧𝑜 ]
(11)
Each element of 𝜸 is a ratio between the state vector (x) and its a priori (xa). To
obtain concentration profile, the scaling factors need to be first mapped from
retrieval grids (i.e. 10 levels for CO2 and 1 level for other three gases) to the 71
forward model levels.
𝜷 = 𝐌𝜸
where 𝐌 =
𝝏𝜷
𝝏𝜸
(12)
is a linear mapping matrix relating retrieval level to the forward
model altitude grid. Multiplying the scaling factor (𝜷) on the forward model level to
the concentration a priori (𝒙𝒂 ) gives the estimates of the gas profile:
̂ 𝒙𝒂
̂=𝜷
𝒙
(13)
The non-diagonal CO2 covariance matrix used for the constraint matrix has larger
variance in boundary layer and decrease with altitude. The square root of the
12
diagonal of this covariance is approximately 2% in the boundary layer, 1% in the
free troposphere, and less than 1% in the stratosphere (Fig. 4 a). Off diagonal values
assume the correlation between the levels (Fig. 4 b). This covariance is generated
using the GEOS-Chem model as guidance. However, because aircraft data typically
show higher variability than the GEOS-Chem model, we increase the variance.
Although the SNR of the TCCON instrument is better than 500, we use an SNR of
approximately 200 because spectroscopic uncertainties degrade the comparison
(e.g., Wunch et al., 2011; O’ Dell et al., 2011) and it obtains the chi-square in our
retrievals about 1.
To obtain the best estimate of state vector that minimize the difference between the
observed spectral radiances (𝒚𝒐 ) and the forward model spectral radiances (𝒚𝒎 ) we
perform Bayesian optimization by minimizing the cost function, 𝜒(𝜸):
𝜒(𝜸) = (𝒚𝒎 − 𝒚𝒐 )𝑇 𝐒𝑒−1 (𝒚𝒎 − 𝒚𝒐 ) + (𝜸 − 𝜸𝒂 )𝑇 𝐒𝐚−1 (𝜸 − 𝜸𝒂 )
(14)
13
Fig. 4 (a) The square root of the diagonal in CO2 covariance matrix. (b) The 2-D plot
of the CO2 covariance matrix.
4.2 Error characterization for TCCON column-averaged CO2:
In this section, we characterize the error in the TCCON profile retrievals in order to
understand the uncertainties in the derived PBL CO2. The details of all the
derivations are in Appendix. The averaging kernel for the forward model dimension
scaling vector 𝜷 is
𝐀 𝜷 = 𝐌𝐆𝜸 𝐊 𝜷
(15)
14
where 𝐊 𝜷 is the Jacobian of 𝜷 with respect to the radiance and 𝐆𝜸 is the gain matrix
(Eq. A**). The estimated state for a single measurement can be expressed as a linear
retrieval equation:
̂ = 𝜷𝒂 + 𝐀 𝜷 (𝜷 − 𝜷𝒂 ) + 𝐌𝐆𝜸 𝒏 + ∑ 𝐌𝐆𝜸 𝐊 𝒍𝒃 ∆𝒃𝒍
𝜷
(16)
𝒍
where n is a zero-mean Gaussian spectral noise vector with covariance 𝐒𝐞 and the
vector ∆𝒃𝒍 is the error in true state of parameters (l) that also affect the modeled
radiance, e.g. temperature, interfering gases, etc. 𝐊 𝒍𝒃 is the Jacobian of parameter (𝒍).
̂ . If we want to convert above
̂ = 𝐌𝒙 𝜷
According to the definition, 𝒙𝒂 = 𝐌𝒙 𝜷𝒂 and 𝒙
̂ by 𝐌𝒙 , where
̂), we simply multiply 𝜷
equation to the state vector of concentration (𝒙
𝝏𝒙
𝐌𝒙 = 𝝏𝜷 and 𝐌𝒙 is simply a diagonal matrix filled by the concentration a priori (𝒙𝒂 ),
to obtain:
̂ = 𝒙𝒂 + 𝐀 𝜷 (𝒙 − 𝒙𝒂 ) + 𝐌𝒙 𝐌𝐆𝜸 𝒏 + ∑ 𝐌𝒙 𝐌𝐆𝜸 𝐊 𝒍𝒃 ∆𝒃𝒍
𝒙
(17)
𝒍
The estimated bias error for multiple measurements of the column averages is
obtained by applying a column operator (𝑪), such as a pressure weighting function
(Connor et al., 2003):
̅ 𝑵 )(𝒙𝒂 − 𝒙) + ∑ 𝐌𝒙 𝐆𝐌𝐊 𝒍𝒃 ∆𝒃𝒍 ]
𝑋̃𝐶𝑂2 = 𝑪 [(𝐈 − 𝐀
(18)
𝒍
The second term describes the potential sources of biases due to systematic errors,
such as light path or temperature uncertainty. They stay the same for the same air
mass (e.g. measurements within a day) but can be assumed to be pseudo-random
for the measurements of different air mass (e.g. measurements across multiple day).
The variance of the bias can be described in two terms:
15
𝟏
𝛔(𝐒̂𝐦 + 𝐒̂𝐬 ) = (𝑪𝑻 𝐒̂𝐦 𝑪 + 𝑪𝑻 𝐒̂𝐬 𝑪)𝟐
(19)
where 𝐒̂𝐦 is the measurement error covariance:
𝐒̂𝐦 = 𝐌𝒙 𝐌𝐆𝐒𝐞 (𝐌𝒙 𝐌𝐆)𝐓
(20)
and 𝐒̂𝐬 is the systematic error covariance:
𝐓
𝐒̂𝐬 = ∑ 𝐌𝒙 𝐌𝐆𝐊 𝒍𝒃 𝐒𝒃𝒍 (𝐌𝒙 𝐌𝐆𝐊 𝒍𝒃 )
(21)
𝒍
The systematic error covariance matrices are less important compare to the
measurement error covariance for the time scale shorter than one day but they
become significant for the time scale longer than day. For example, our uncertainties
to temperature is about the constant within a day but could be pseudo random
across multiple days.
To estimate the actual bias, the aircraft measurements are used as the best
estimates of the true state (𝒙). The aircraft profile is first mapped to the forward
model pressure levels in TCCON retrieval and then it is applied a smoothing
operator using the averaging kernel and a priori constraint from the TCCON profile
retrieval (Rodgers and Connor, 2003):
̂𝑭𝑳𝑻 = 𝒙𝒂 + 𝐀 𝜷 (𝒙𝑭𝑳𝑻 − 𝒙𝒂 )
𝒙
(22)
̂𝑭𝑳𝑻 is the profile that would be retrieved from TCCON measurements for the same
𝒙
air sampled by the aircraft without the presence of other errors. Applying the
̂𝑭𝑳𝑻 gives estimates of smoothed aircraft:
column operator (C) to 𝒙
16
𝐹𝐿𝑇
𝑋̂𝐶𝑂
= 𝑪𝑻 𝒙𝒂 + 𝑪𝑻 𝐀 𝜷 (𝒙𝑭𝑳𝑻 − 𝒙𝒂 )
2
(23)
The bias becomes
𝑇𝐶𝐶𝑂𝑁
𝐹𝐿𝑇
𝑋̃𝐶𝑂2 = 𝑋̂𝐶𝑂
− 𝑋̂𝐶𝑂
= 𝑪𝑻 ∑𝒍 𝐌𝒙 𝐆𝐌𝐊 𝒍𝒃 ∆𝒃𝒍
2
2
(24)
Fig. 5 CO2 profiles measured by aircraft (black) and TES GEOS-chem assimilation
(red) at SGP on the same day in 2009. Their best agreements are mostly above 600
hPa in free troposphere.
17
Fig. 6 The comparison of TCCON total column CO2 with smoothed aircraft CO2
(black) and the comparison of PBL CO2 by TCCON/TES with smoothed aircraft PBL
CO2 (red). Similar comparison of PBL CO2 by TCCON a priori is also plotted in blue to
provide a view of improvement by combining TCCON and TES data.
4.3 Error characterization for TCCON-TES PBL CO2
To understand the potential sources of the bias in the TCCON/TES PBL CO2 product,
we start with decomposing the averaging kernel matrix into four sub-matrices to
represent the boundary layer, free troposphere and their correlations (see Appendix
II). By separating the boundary layer from the free troposphere, the expected PBL
CO2 bias includes the bias from TES free tropospheric CO2 and two terms from
TCCON column-averaged estimate:
18
𝑝𝑋̃𝐶𝑂2 = 𝑪𝑭 𝐀 𝐅 (𝒙𝑭 − 𝒙𝑭𝑻𝑬𝑺 ) + 𝑪𝐆𝒏 + 𝑪𝐆𝐊 𝒃 ∆𝒃
(25)
where superscript ‘B’ represents the boundary layer and ‘F’ represents the free
troposphere. The derivation is in Appendix II.
The variance of the bias error in derived PBL CO2 is composed by covariance from
TES free tropospheric CO2, TCCON measurement error and systematic error:
𝟏
𝐅
𝐓𝐂𝐂𝐎𝐍
𝛔(𝑝𝑋̃𝐶𝑂2 ) = [(𝑪𝑭 )𝐓 𝐒̂𝐓𝐄𝐒
𝑪𝑭 + 𝑪𝑻 𝐒̂𝐦
𝑪 + 𝑪𝑻 𝐒̂𝐬𝐓𝐂𝐂𝐎𝐍 𝑪]𝟐
(26)
5. Results
5.1 Quality of the column-averaged CO2 estimates:
To understand the quality of the retrieved product, we compared the TCCON
column-averaged estimates to the column-integrated aircraft data to obtain the bias
error and precision error in a 4-hr time scale and a day-to-day time scale. It is
expected to show that the actual calculations are consistent with the expected
estimates in section 4.2.
There are fifty SGP aircraft measured CO2 profiles in 2009. We show some examples
of them in Fig. 5. Most of measurements go up to 6 km except three profiles are
obtained up to 10 Km (July 31, August 2nd and 3rd). To estimate the column, the
missing observations above the ceiling of aircraft profile are replace by TCCON CO2 a
priori. The simultaneous observations by TCCON are measured at Lamont. The
comparisons between TCCON column averages and the smoothed aircraft column
averages are summarized in Fig. 6 and Table 1.
The TCCON retrievals within a 4-hour window about the mid time during each flight
measurement are selected as the simultaneous measurements. The actual variability
of the retrieved 𝑿𝐶𝑂2 within the 4-hr window, defined by one standard deviation
(1 × 𝜎), is the uncertainties of the retrievals for the same air parcel. Table 1 lists the
19
statistics for these fifty comparisons both with and without cloud filter. The
variability of 4-hr window retrieval is mostly about 0.3 ppm. It is consistent with the
expected 𝜎(𝐒̂𝐦 ) due to the covariance of measurement error (Eq 20), which is also
listed in Table 1. They range from 0.27 to 0.34 ppm, which is due to the small
variability in Jacobian and averaging kernel. It suggests that the measurement error
is the dominant source of the variability of the multiply retrieved column averages
for 4-hr window time scale. In Table 1, the actual 1 × 𝜎 more than 1 ppm together
with the sample number less than 50 are highlighted in pink (1 × 𝜎 > 1.0 ppm). In
addition, the actual 1 × 𝜎 between 0.5 and 1 ppm are highlighted in yellow. After
applying the cloud filter, most of pink values are corrected to be green (0.0 < 1 ×
𝜎 < 0.3 ppm), consistent with the expected 𝜎(𝐒̂𝐦 ). There are seven of them remain
as pink because they only has small sample number (<50) within the time window
after cloud filter.
The difference between the mean of TCCON multiply retrievals within the time
window and the smoothed aircraft 𝑋𝐶𝑂2 is the estimates the bias error in that day
(Table 1). The biases across multiple days are the offsets of black dots to the one-toone line in Fig. 6. The vertical error bar of black dot is the actual 1 × 𝜎 without cloud
filter. Without removing the retrievals under unclear sky, the TCCON column
averages underestimate the flight data by -5.78(±0.78) ppm. The cloud filter has no
significant influence on the mean bias and its 1 × 𝜎 over multiple days, remaining as
-5.71(±0.67) ppm. This mean bias value is consistent with that was estimated in
standard scaling retrieved 𝑋𝐶𝑂2 by Wunch et al., 2010. It is noticed that the bias 1 ×
𝜎 over multiple days (0.67 or 0.78 ppm for with or without cloud filter) is consistent
with expected 𝜎(𝐒̂𝐦 + 𝐒̂𝐬 ), the sum of the measurement error covariance and
systematic error covariance (0.78 ppm). The systematic term is calculated using
temperature covariance. It suggests that for the variability of bias across the
multiple days, the systematic error plays an additional important role.
5.2 Quality of the PBL CO2 estimates:
20
In Fig. 6, we also plot the TES/TCCON derived PBL CO2 with respect to smoothed
aircraft PBL CO2 in red dots. They are mostly close to one-to-one line with a small
mean bias of 0.32 (±1.44) ppm. The correct factor (𝛼) in Eq (8) for removing bias in
TCCON column CO2 is 0.986. The comparison of TES GEOS-chem assimilated free
tropospheric CO2 to aircraft free tropospheric data obtains a bias of 0.38 (±1.66)
ppm. It is not removed when deriving the PBL CO2, and lead to a major component
of 0.32 ppm bias from TES data.
The variance of the derived PBL CO2 bias is 1.44 ppm. It is consistent with the
expected variance of 1.83 ppm by Eq (26), which includes the source from TES error
covariance, TCCON measurement error covariance and systematic error covariance.
It is smaller than the variance of bias in both a priori PBL CO2 (2.07 ppm) (blue dots
in Fig. 6) and TES GEOS-chem assimilated PBL CO2 (2.86 ppm) (not plotted here). It
suggests that the derived estimates of PBL CO2 by TCCON and TES data improve our
knowledge of the boundary layer CO2.
Since the retrieved column CO2 has strong constrain to the a priori to prevent the
retrievals to go too far away from a priori, it is noticed that for some retrievals when
a priori is quite off the aircraft measurements, the derived PBL estimates attempt to
move towards the one-to-one line but still have larger error. By removing those data
that a priori PBL CO2 are more than 5 ppm away from aircraft PBL estimates, the
mean bias in column CO2 does not have significant changes but its 1 × 𝜎 is reduced
from 0.78 ppm to 0.58 ppm. The bias of PBL CO2 is improved from 0.32 ppm to 0.08
ppm and the 1 × 𝜎 of the bias is further reduced from 1.44 pm to 0.92 ppm.
As discussed in section 5.1, the cloud coverage has a strong impact on the quality of
the TCCON column data. For a clear sky, there are on average about 100 retrieval
samples in the 4-hr window. For the cloudy days when there is only limited number
of clear sky measurements available, the scattering in TCCON column averages
become large. By exclusive those data with sample number less than 50, the 1 × 𝜎 of
bias in column-averaged CO2 is reduced from 0.78 ppm to 0.61 ppm and
21
consequently that in PBL CO2 is reduced from 1.44 ppm to 1.29 ppm. A strong
positive correlation is also found between the bias errors in the column and PBL
CO2, which suggests that the variability of the bias in PBL CO2 is related to the bias in
column estimates by TCCON.
In above analysis, we separate PBL and free troposphere at 600 hPa because TES
retrieved CO2 has the peak sensitivity at 511 hPa and Fig. 5 shows that TES Geoschem assimilated profiles agree better with the aircraft profiles above 4 Km (about
600 hPa). If we use TES assimilated profiles above 800 hPa to estimate the free
tropospheric CO2, we get slightly improved bias in PBL CO2 of 0.06 ppm, but larger
1 × 𝜎 of bias of 4.20 ppm. This indicates that additional variability of bias errors are
induced by the disagreement of TES free tropospheric CO2 with aircraft
measurements between 600 to 800 hPa. In addition, the correlation between the
TCCON column bias and PBL bias cannot be found anymore. It suggests that the bias
error in TES free tropospheric CO2 become dominant. Removing unrealistic a priori
points reduces the 1 × 𝜎 of PBL bias but remain as large as 3.35 ppm.
5.3 Seasonal variability of PBL CO2 compared to column CO2.
Given the comparison against the aircraft data over a year, it provides us an initial
view of seasonal variability in PBL CO2 compared with column-averaged data. We
plotted the monthly average by aircraft of both column-averaged data in black curve
and PBL data in red lines (Fig. 7). The TCCON retrieved column averages and
TCCON/TES derived PBL data in dots with error bars follow their comparable
aircraft estimates in solid lines quite well. There are about 3 to 5 days’ to be
averaged in each month of the year except September and October, both of which
only have one available aircraft profile. Therefore, these two months estimates are
not plotted. Both TCCON column averages and TCCON/TES PBL CO2 capture the
seasonal variability in aircraft measurements. More aircraft comparisons are
expected, especially in September and October.
22
Fig. 7 (a) Monthly mean column averages and PBL CO2 in 2009 at Lamont. Flight
column-averaged estimates in black solid line. TCCON column averages in black
dots. Flight PBL estimates in red solid line and TCCON/TES PBL estimates in red
dots. (b) The difference of PBL CO2 and column-averaged CO2 by flight (solid line)
and by TCCON/TES (dots). The agreements to the flight estimated differences are
better.
23
It is also noticed that in Fig. 7 (a) the amplitude of seasonal cycle is larger in PBL CO2
(14 ppm peak-to-peak) than the column-averaged CO2 (5 ppm) because there is a
rapid drawdown in PBL CO2 at the growing season onset at mid latitude due to the
biosphere uptake but the vertical mixing dilute the surface flux signature in the
column CO2. They reach their summer minima both in July without showing any
phase lag in current available data for monthly average. The contrast between the
PBL CO2 and column CO2 are negative and large in the middle of the growing season
(>4 ppm) but positive during mid-winter (about 3 ppm) (Fig. 7 b solid line by flight).
It is well captured by derived data in winter but not in the middle of summer (Fig. 7
b dots with error bars).
6. Conclusions
We obtained estimates of column-averaged CO2 by TCCON profile retrievals and free
tropospheric CO2 by TES GEOS-chem assimilation. Using these two dataset, we also
derived PBL CO2 estimates. It is crucial to attribute the source of the bias and the
measurement uncertainties.
The actual bias and its uncertainties in TCCON column-averaged CO2 have to be
explained in two different time scales, 4-hr window and day-to-day time scales. For
multiply retrievals of the same air parcel within 4-hr window, the mean bias is from
the uncertainties of atmospheric states (i.e. temperature or interference gases) or
spectroscopy parameters. Because these uncertainties are less variable within this
short time scale, the systematic error covariance is less important than the
measurement error covariance. The actual 1 × 𝜎 of the bias under the clear sky is
consistent with the expected estimates by the measurement error covariance of
about 0.3 ppm. The mean bias across the multiply days are -5.78(±0.78) ppm
without cloud filter and -5.71(±0.67) ppm with cloud filter. The actual 1 × 𝜎 of the
bias on multiple day scale is consistent with the expected estimates of 0.78 ppm,
which is the sum of measurement error covariance and systematic error covariance.
Because for a day-to-day time scale, the systematic errors can be assumed to be
pseudo random and is an additional source in bias uncertainties. We found that the
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profile retrieval has difficulty in capture the true state under the cloudy sky or with
unrealistic a priori.
Comparing to the flight free tropospheric CO2, we found TES data has a bias of
0.38(±1.66) ppm. Accurate estimation of the error in column CO2 and free
tropospheric CO2 ensures that the major source of variations in PBL is captured
because the potential sources for the bias in PBL estimates are the TES GEOS-chem
assimilated free tropospheric CO2 as well as TCCON column-averaged estimates due
to the measurement error and systematic error. Since the bias in TCCON column
averages are removed before combining with TES data, the actual bias remained in
derived PBL CO2 is about 0.32 ppm, which is consistent with the estimates of bias in
the TES GEOS-chem assimilated free tropospheric CO2. Its actual 1 × 𝜎 of the bias is
1.44 ppm, which is consistent with the expected estimates of 1.83 ppm. The
dominant sources of the bias variability are error covariance of free troposphere
data from TES and the systematic error in column averages from TCCON.
We confirm that the derived PBL CO2 improve our knowledge of boundary layer CO2
compared to the estimates from the assumed a priori or TES Geos-chem
assimilation. The bias uncertainty is smaller than that by both the a priori (2.07
ppm) and the TES Geos-chem assimilated data (2.86 ppm).
The evaluation of the estimates is based on the comparison with the estimates by
aircraft measurements made during 2009 over Southern Great Plains (SCP) ARM
site and the error analysis of the expected estimates representing the actual
estimates. We show that the derived PBL CO2 also capture the range of seasonal
variability within calculated uncertainties except September and October for limited
aircraft profiles. The PBL CO2 has seasonal amplitude larger than the columnaveraged CO2. The phase shift is not found yet with limited current aircraft data. The
contrast between the PBL CO2 and column CO2 is large negative in summer and
small positive in winter. Lower PBL CO2 than the column CO2 suggests positive
vertical gradient in the boundary layer and a strong sink near the surface.
25
This study highlights the potential of combining simultaneous measurements from
different instruments to obtain vertical information of CO2 profile. The present
TCCON network is relatively sparse but has a good latitudinal coverage. It provides
temporal dense long-term accurate observations of column abundance of CO2. The
next generation of column observation is the satellite column measurements by
GOSAT and OCO-2. They have better global coverage and could provide both
spatially and temporally dense column data sets. Applying our method to achieve
the simultaneous PBL CO2 from these column data improves the usefulness of spaceborne monitoring of the CO2 column. The column CO2 measurements constrain the
total mass and PBL CO2 estimates constrain how much of the total amount are
distributed in the boundary layer where has direct signature of the surfaceatmosphere exchange. Given the derived PBL CO2 coupled with the column CO2, it is
anticipated to provide complementary constraint to infer CO2 flux and advance the
ability to study the carbon cycle problem.
26