Characterization of TCCON column CO2 and boundary layer CO2 by combining
TCCON and TES data
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 global sources
and sinks (Rayner and O’Brien, GRL, 2001, Olsen and Randerson, JGR, 2004) but are
less sensitive to regional scale sources and sinks because CO2 is a long-lived gas
which makes it challenging to identify local sources from CO2 transported into the
observed air parcel (Keppel-Aleks et al., BGD, 2011). In this study we explore the use
of total column measurements with estimates of the free tropospheric CO2 by TES to
distinguish boundary layer CO2 and free tropospheric CO2 because quantify the
vertical gradient between the free troposphere and boundary layer is critical for
estimating CO2 fluxes (Stephens, Science, 2007) and near surface CO2 should be
more sensitive to local fluxes than the total column CO2.
CO2 profiles are estimated from the Total Carbon Column Observing Network
(TCCON) measurements and integrated into a column-averaged concentration.
These column data agree with aircraft integrated data within root mean square
(RMS) of 0.46 ppm, consistent with the uncertainties due to measurement noise and
temperature. There is a bias of about -5 ppm, agreeing with Wunch et al. (Atmos.
Meas. Tech. 2010).
Free troposphere estimates of CO2 are obtained from the GEOS-Chem model that has
assimilated CO2 measurements from Aura Tropospheric Emission Spectrometer.
The boundary layer CO2 estimates are calculated by subtracting TES free
tropospheric CO2 from TCCON column CO2. This estimate of boundary layer CO2
agrees well with aircraft data with RMS of 1.46 ppm for the sixteen PBL CO 2
estimates we compared. This work shows that total column from NIR
measurements (GOSAT, TCCON and OCO-2) and free troposphere measurement
from TIR (e.g. TES and AIRS) can be used to profile CO2 and obtain PBL CO2 with
precision necessary to capture the atmospheric CO2 variability. It also shows
potential of joint retrieval of NIR and TIR. The CO2 surface flux can be better
quantified by monitoring a long-term boundary layer CO2.
I. Introduction
The spatial and temporal distribution of uptake remains large uncertainties.
Why boundary layer and tropospheric CO2 is important
The difference between column-averaged CO2 ( C CO2 ) and surface CO2 can vary from
2 to 10 ppm depending on the location and the time of the year (Olsen and
Randerson 2004). Compared to surface values, the seasonal variation of C CO2
generally has a time lag in phase with less variability due to the time delay caused
by the vertical mixing. The advantage of the column measurements is that they are
less affected by the variability due to the vertical transport, but they are also less
1
sensitive to surface sources and sinks. The advantage of the column measurements
is that they are less affected by the variability due to the vertical transport, but they
are also less sensitive to surface sources and sinks. Higher surface concentrations
usually occur at nighttime or in winter due to CO2 buildup in a shallow planetary
boundary layer (PBL), while surface uptake due to plant growth occurs during the
daytime or in summer. Therefore, the vertical profile information of atmospheric
CO2 is required for estimating the regional source and sink, understanding the
vertical transport, and determining the exchange between the surface and
atmosphere.
Current co2 data are column-weighted or mid/upper tropospheric CO2
Column-weighted CO2, ignoring the vertical mixing, is good for the study in
global scale but has limited sensitivity to local carbon flux. It is hard to determine
whether the column variation is due to the surface-atmosphere exchanging or
horizontal transportation.
Boundary layer CO2 variations are greatly affected by the local source and
sinks.
Combining boundary layer and column co2 can determine the vertical
gradient between boundary layer and free tropospheric co2 and further to infer the
local sources or sinks.
II. Method
The column amount is obtained by integrating the concentration profile fg(z) from
surface to the top of atmosphere.
∞
𝑇𝑉𝐶𝑔 = ∫𝑧 𝑓𝑔 (𝑧) ∙ 𝑛(𝑧) ∙ 𝑑𝑧
(1)
𝑠
where TVCg is total vertical column for gas ‘g’ and n(z) represents the number
density vertical profile. If fg(z) is dry concentration profile as a function of altitude
(z), the ratio of total column between gas and air will give dry-air column-averaged
abundance:
𝑇𝑉𝐶𝐶𝑂
𝑋𝐶𝑂2 = 𝑇𝑉𝐶 2
(2)
𝐴𝐼𝑅
Here we use 𝑋𝐶𝑂2 to refer to dry-air column-averaged CO2. The aim of this paper is
to determine PBL CO2 by subtracting TES free tropospheric CO2 from TCCON
retrieved total column amount of CO2. Partial vertical column amount of CO2 in free
TROP
troposphere and up are given by TES assimilated data ( PVCCO
). Then partial
2
vertical column amount of CO2 in PBL can be computed as the difference between
the column amount and partial free tropospheric amount:
𝑃𝐵𝐿
𝑇𝑅𝑂𝑃
𝑃𝑉𝐶𝐶𝑂
= 𝑇𝑉𝐶𝐶𝑂2 − 𝑃𝑉𝐶𝐶𝑂
2
2
(3)
The ratio of partial vertical column between CO2 and air gives the PBL CO2
PBL
concentration pXCO
.
2
pX
PBL
CO2
=
PBL
PVCCO
2
BL
PVCAIR
(4)
2
III. Measurements
1. Bottom-up measurement (TCCON):
The Total Carbon Column Observing Network (TCCON) is a ground-base network of
precise solar tracking system which measures incoming sunlight with high spectral
resolution (0.02 cm-1) and high signal to noise ratio (SNR) (e.g. 885 for the InGaAs
detector and 500 for the Si diode detector [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, methane (CH4),
and other trace gases (e.g. CO, N2O) over 16 TCCON sites around the world
including both operational and future sites (Washenfelder et al. 2006; Wunch et al.
2010, 2011; Yang et al. 2002).
The precision in CO2 total column measurements from TCCON standard scaling
retrieval is achieved to better than 0.25% (Wunch et al. 2010, 2011). The absolute
accuracy is ~1% (Wunch et al. 2010). In this work, we developed a profile retrieval
algorithm, which sometimes performs better than the scaling retrievals. It doesn’t
reduce the bias in column CO2 but improve the precision to 0.18%.
Figure 2. CO2 band at 1.6 m observed on June 17, 2008 by TCCON at Park Falls
(Wisconsin) with solar zenith angle of 22.5.
3
2. Top-down measurement (TES):
Aura Tropospheric Emission Spectrometer (TES) measures the infrared radiance
emitted by Earth’s surface and atmospheric gases and particles. These
measurements have peak sensitivity to mid-tropospheric CO2 at 511 hPa. Here, we
use TES Geos-chem assimilated CO2 in free troposphere to separate the PBL CO2
from column data by TCCON profile retrievals.
3. Flight measurements:
Aircraft measures the CO2 profiles up to 6 Km and sometimes to 10 Km. It is
considered the best estimates of the true state of atmospheric CO2. We collected
profile observations by different aircrafts, such as HIPPO and Learjet, at the
Southern Great Plains (SCP) ARM site mostly in 2009, to calibrate our derived
column and PBL CO2 data at Lamont site.
IV. Results
1. Estimates of column CO2
a) Retrieval approach:
The profile of atmospheric CO2 is obtained by a nonlinear least-square spectral
fitting using a line-by-line spectral fitting algorithm (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. The details about the TCCON
instrument setup and GFIT code are also 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 (figure 2). In standard
scaling retrieval, a constant scaling factor γ is estimated to shift a priori profile so
that the model computed spectrum has the best fit of observation. In our retrieval,
we retrieve altitude dependent scaling factors γ(z) to perturb a priori profile in
order to minimize the cost function.
Ten retrieval levels are selected with increasing spacing going up. The non-diagonal
covariance matrix for a priori has larger variance (about 10 ppm) in boundary layer
and decrease with altitude. There are tight constrains in the stratosphere. Off
diagonal values provide dependency between the levels. SNR is chosen to be 200 to
obtain chi-square about 1.
Column-averaged dry-air mole fractions are derived using retrieved O2 columns
𝑓
𝑑𝑟𝑦
𝑓𝐶𝑂2 = 𝑓𝐶𝑂2 × 0.2094
(5)
𝑂2
There a few more advantages of normalizing O2 column other than remove water.
Dividing by retrieved O2 using spectra measurements from same instruments
improves the precision of column CO2 by significantly reducing the effects of
instrumental or measurement errors that are common to both gases (e.g. solar
tracker pointing errors, zero level offsets, instrument line shape errors, etc. (Wunch
4
et al., 2010). However, errors specific for O2 will be transferred to column-averaged
CO2. We found a bias is introduced by using O2 as a measure of the dry air column.
b) Characterization of estimates:
Derivation of averaging kernel
We retrieve a parameter 𝛾 called scaling factor, which is a ratio between the state
vector of gas concentration profile x and its a priori xa. To obtain estimates such as a
CO2 profile, the scaling factors need to be first mapped from retrieval grid point to
forward model levels:
𝛽 = 𝑀𝛾
(6)
and then multiply the scaling factor on forward model level 𝛽 to the concentration a
priori xa, which gives the estimate of the gas profile:
𝑥 = 𝛽𝑥𝑎
(7)
where M is a linear mapping matrix. The Jacobian of retrieved parameter with
respect to the radiance is
𝜕𝐿(𝑀𝛾)
𝐾𝛾 = 𝜕𝛾
(8)
Using the chain rule, we can obtain the equation relating the retrieval Jacobian to
the full-state Jacobian
𝜕𝐿
𝜕𝐿 𝜕𝛽
= 𝜕𝛽 𝜕𝛾
(9)
𝜕𝛾
or
𝐾𝛾 = 𝐾𝛽 𝑀
(10)
If the estimates by retrieval are close to the actual state, then the estimated state can
be expressed as a linear retrieval equation:
𝛽̂ = 𝛽𝑎 + 𝐴𝛽 (𝛽 − 𝛽𝑎 ) + 𝑀𝐺𝛾 𝑛 + ∑𝑖 𝑀𝐺𝛾 𝐾𝑏𝑖 (𝑏 𝑖 − 𝑏𝑎𝑖 )
(11)
where n is a zero-mean Gaussian spectral noise vector with covariance 𝑆𝑒 and the
vector b is the true state of non-retrieved parameters that also affect the modeled
radiance, e.g. temperature, interfering gases, etc. The vector ba is a priori values for
vector b and Kb is the Jacobian of vector b. If we want to convert above equation to
the state vector of concentration (x), we simply multiply the equation by xa to
obtain:
𝑥̂ = 𝛽𝑎 𝑥𝑎 + 𝐴𝛽 (𝑥 − 𝛽𝑎 𝑥𝑎 ) + 𝑥𝑎 𝑀𝐺𝛾 𝑛 + ∑𝑖 𝑥𝑎 𝑀𝐺𝛾 𝐾𝑏𝑖 (𝑏 𝑖 − 𝑏𝑎𝑖 )
(12)
where 𝐺𝛾 is the gain matrix, which is defined by
𝜕𝛾
𝐺𝛾 = 𝜕𝐿 = (𝐾𝛾𝑇 𝑆𝑒−1 𝐾𝛾 + 𝑆𝑎−1 )−1 𝐾𝛾𝑇 𝑆𝑒−1.
(13)
Then the averaging kernel in forward model dimension is
𝐴𝛽 = 𝑀𝐺𝛾 𝐾𝛽
(14)
The mean of N TCCON column observations within time window of each flight
measurement is simply:
1
𝑥̂𝑁 = 𝑁 ∑𝑁
̂𝑖
(15)
𝑖=1 𝑥
The estimated bias error when observing the same air mass is
̅ )(𝛽𝑎 𝑥𝑎 − 𝑥)
𝑥̃𝑁 = 𝑥̂𝑁 − 𝑥 = (𝐼 − 𝐴𝛽𝑁
1
1 𝑁
𝑖,𝑙 𝑖,𝑙 𝑖,𝑙
𝑖,𝑙
𝑖
+ 𝑁 ∑𝑁
(16)
𝑖=1 𝑥𝑎 𝑀𝐺𝛾 𝑛𝑖 + 𝑁 ∑𝑖=1 ∑𝑙 𝑥𝑎 𝑀𝐺𝛾 𝐾𝑏 (𝑏 − 𝑏𝑎 )
5
̅ = 1 ∑𝑁
where xa is the same for all observations and 𝐴𝛽𝑁
𝐴 . We assume that both
𝑁 𝑖=1 𝛽𝑖
ni and 𝑏 𝑖,𝑙 − 𝑏𝑎𝑖,𝑙 are zero-mean, and they are independent, identically distributed
random variables for all N observations. The expected mean bias error is
̅ )(𝛽𝑎 𝑥𝑎 − 𝑥)
𝐸[𝑥̃𝑁 ] = 𝐸[𝑥̂𝑁 ] − 𝑥 = (𝐼 − 𝐴𝛽𝑁
(17)
The covariance of the estimated bias error can be expressed as
1
𝑖
𝑖 𝑇
𝑆𝑥̃ = 𝐸[(𝑥̂𝑁 − 𝐸[𝑥̃𝑁 ])(𝑥̂𝑁 − 𝐸[𝑥̃𝑁 ])𝑇 ] = 𝑁2 ∑𝑁
𝑖=1 𝑥𝑎 𝑀𝐺𝛾 𝑆𝑒 (𝑥𝑎 𝑀𝐺𝛾 ) +
1
𝑖,𝑙 𝑖,𝑙 𝑙
𝑖,𝑙 𝑖,𝑙 𝑇
∑𝑁
(18)
𝑖=1 ∑𝑙 𝑥𝑎 𝑀𝐺𝛾 𝐾𝑏 𝑆𝑏 (𝑥𝑎 𝑀𝐺𝛾 𝐾𝑏 )
where Sb is the covariance of the measurement error on vector b, and the spectral
noise and systematic errors are assumed to be uncorrelated. With the assumption
for all i, 𝐺𝛾𝑖 = 𝐺 and 𝐾𝑏𝑖,𝑙 = 𝐾𝑏𝑙 , then covariance of the estimated bias error reduces to
1
1
𝑆𝑥̃ = 𝑁 𝑥𝑎 𝑀𝐺𝑆𝑒 (𝑥𝑎 𝑀𝐺)𝑇 + 𝑁 ∑𝑙 𝑥𝑎 𝑀𝐺𝐾𝑏𝑙 𝑆𝑏𝑙 (𝑥𝑎 𝑀𝐺𝐾𝑏𝑙 )𝑇 .
(19)
The actual variability in TCCON column CO2 can be calculated as
1
𝑆̂ = 𝑁−1 (𝑋̂ − 𝑋̅̂ )(𝑋̂ − 𝑋̅̂ )𝑇
(20)
where 𝑋̂ is a vector of the retrieved TCCON column CO2, 𝑋̅̂ is the mean value of
retrieval samples. Under the assumption of small variability of 𝐺𝛾 and 𝐾𝑏𝑙 over the
TCCON observations, then
𝑇
𝑁
𝑆̂ = 𝑁−1 [(𝑥𝑎 𝑀𝐺𝑆𝑒 (𝑥𝑎 𝑀𝐺)𝑇 + ∑𝑙 𝑥𝑎 𝑀𝐺𝐾𝑏𝑙 𝑆𝑏𝑙 (𝑥𝑎 𝑀𝐺𝐾𝑏𝑙 ) ]
(21)
If N is large number, the observation error covariance is
𝑇
𝑆̂ ≈ 𝑥𝑎 𝑀𝐺𝑆𝑒 (𝑥𝑎 𝑀𝐺)𝑇 + ∑𝑙 𝑥𝑎 𝑀𝐺𝐾𝑏𝑙 𝑆𝑏𝑙 (𝑥𝑎 𝑀𝐺𝐾𝑏𝑙 )
(22)
The estimated variability of bias error can be calculated by applying column
operator to the square root of the diagonal of the observation error covariance. The
first term describes the source from random noise and the second term represent
the source from systematic errors. We can compare them to the RMS of the
collection of retrieved column relative to their mean and examine how well the
estimated random and systematic covariance matrix represent the actual variability
in TCCON retrievals.
𝑁2
To compare TCCON CO2 profile with aircraft measurements, we have to apply the
operator described in Rodgers and Connor (2003). The aircraft profile is first
mapped to the forward model pressure level in TCCON retrieval and then apply the
operator combining the averaging kernel and a priori constraint from the TCCON
profile retrieval:
𝑥̂𝐹𝐿𝑇 = 𝑥𝑎 + 𝐴𝛾 (𝑥𝐹𝐿𝑇 − 𝑥𝑎 ).
(23)
𝑥̂𝐹𝐿𝑇 is the profile that would be retrieved from TCCON measurements for the same
air sampled by the aircraft without the presence of other errors. Applying the
column operator to 𝑥̂𝐹𝐿𝑇 gives estimates of smoothed aircraft 𝑋𝐶𝑂2 .
6
c) Quality of the profile retrieved column CO2:
We have about fifty SGP aircraft measured CO2 profiles in 2009. Most of them go up
to 6 Km except three profiles are measured up to 10 Km. For the column calculation,
we used TCCON CO2 a priori as the assumption above the ceiling of aircraft
observations. Figure xx shows their comparisons between TCCON data and the
smoothed aircraft data. The total column-averaged CO2 is plotted in black dot. The
TCCON data within each 4-hour window about the mid time of flight duration are
selected as the simultaneous measurements. Most of the TCCON 𝑋𝐶𝑂2 variations in
time window by one standard deviation is about 0.3 ppm which is consistent with
the expected error estimated by random noise covariance matrix (0.32 ppm). There
are ten of them larger than 1 ppm and nine of them between 0.5 and 1 ppm. These
data with larger variations are due to the cloudy coverage during the
measurements. By removing the retrievals under unclear sky, five of those with
variations larger than 1 are reduced to about 0.3 ppm and three of them are found
with no observations under clear sky. Seven out of nine days with variations
between 0.5 and 1 are improved to nearly 0.3 ppm by exclusive unclear sky
7
retrievals. There are three days, which have larger variations of 1 ppm on
September 1st and December 27th and 0.66 ppm on November 11th. The reason for
larger errors for some of retrievals during these days might be that systematic
errors become large in these days, such as temperature or other interfering gases
are not well estimated as usual. The average of variations within time windows is
reduced from 0.67 to 0.38 ppm by removing unclear sky retrievals. In general, the
actual variations of TCCON 𝑋𝐶𝑂2 within time window are due to the random noise.
The averaged TCCON 𝑋𝐶𝑂2 within time window are comparable to the smoothed
aircraft 𝑋𝐶𝑂2 . The mean of these difference estimates a bias in TCCON 𝑋𝐶𝑂2 . A
negative bias of 5.7 ppm is found in profile retrieved 𝑋𝐶𝑂2 . It is consistent with that
was estimated in standard scaling retrieved 𝑋𝐶𝑂2 by Wunch et al., 2010. By filtering
unclear sky retrievals, the bias stay the same but the one standard deviation of day
to day bias decreased from 0.75 ppm to 0.69 ppm. This value is consistent with the
estimate by combining terms of random noise and systematic error in equation (*),
which is calculated to be 0.75 pm. We estimate the systematic error from the
temperature covariance matrix.
2. Estimates of PBL CO2
a) General approach
As described in section (II), PBL CO2 can be estimated by combining TCCON and TES
data. The total column amount 𝑇𝑉𝐶𝐶𝑂2 in equation (3) are given by TCCON profile
𝑇𝑅𝑂𝑃
retrievals and free tropospheric partial column amount 𝑃𝑉𝐶𝐶𝑂
are estimated by
2
TES assimilated data. Since O2 normalized estimates of 𝑋𝐶𝑂2 has higher precision but
about 1% bias, we need corrected TCCON 𝑋𝐶𝑂2 first to remove the bias to get the
total column:
𝑇𝑉𝐶𝐶𝑂2 = 𝑋𝐶𝑂2 /0.986 × 𝑇𝑉𝐶𝐴𝐼𝑅 .
(24)
Then using equation (3) and (4) gives the estimates of the PBL CO2.
2 (this work under the assumption of linearity of the free troposphere
and total column and boundary layer estimate. ) K#dx=dL
b) Characterization of estimates
1) Derivation Error analysis, calculated errors
2) Compare TES assimilated to aircraft (free trop) to obtain
uncertainty of free tropospheric co2
c) Quality of BDL CO2
compared with flight BDL CO2.
d) Seasonal variability of boundary layer co2 compared to column co2. Study the
seasonal variations of co2 emissions and uptake.
it is strong correlated with bias in column CO2 from tccon. The rms of bias in both
PBL co2 and column co2 are reduced when remove the case of bias in a priori larger
than 5 ppm. Exclusive days with small number of samples has minor improvement
in bias of both column and PBL co2.
8
When remove the retrievals under unclear sky, the scattering of column co2
within time window in most days are reduced to about 0.3 ppm. So most of days,
rms of xco2 agrees with the calculated error by random measurement noise. And
slightly reduction of bias in both column and PBL co2 is found when remove unclear
sky retrievals. The RMS of PBL CO2 is larger than that of XCO2 because error in PBL
CO2 is not only from TCCON’s column CO2 but also from TES free tropospheric CO2.
Here are the plots for cloudy sky included:
http://web.gps.caltech.edu/~kl/research/co2/tccon/ggg/lamont/lamont/pl
otdaily/SGP-ak.window4hr/output.cloudy/SGP.600.pdf
Clear sky only:
http://web.gps.caltech.edu/~kl/research/co2/tccon/ggg/lamont/lamont/pl
otdaily/SGP-ak.window4hr/output.clear/SGP.600.pdf
V. Conclusions
We are able to obtain boundary layer and free tropospheric co2. Calculated
error and actual error are consistent. Boundary layer estimates capture range of
seasonal variability of co2 within calculated co2 uncertainties.
VI. Acknowledgements
References
9