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Profiling Tropospheric CO2 using the Aura TES and TCCON instruments
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Le Kuai1, John Worden1, Susan Kulawik1, Kevin Bowman1, Sebastien Biraud4, Vijay Natraj1, Christian
Frankenberg1, Debra Wunch3, Brian Connor2, Charles Miller1, Run-Lie Shia3, and Yuk Yung3
1.
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Mail
stop: 233-200, Pasadena, CA 91109, USA
2.
BC Consulting Ltd., 6 Fairway Dr, Alexandra 9320, New Zealand
3.
California Institute of Technology, 1200 E. California Blvd., Pasadena, CA, 91125, USA
4.
Lawrence Berkeley National Laboratories, Berkeley, CA, 94720, USA
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Abstract
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Monitoring the global distribution and long-term variations of CO2 sources and sinks
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is required for characterizing the global carbon budget. Although total column
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measurements will be useful for estimating large regional fluxes, model transport
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error remains a significant error source, particularly for local sources and sinks. To
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improve the capability of estimating regional fluxes, we estimate near-surface CO2
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values from ground-based near infrared (NIR) measurements with space-based
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thermal infrared (TIR) measurements. The NIR measurements are obtained from
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the Total Carbon Column Observing Network (TCCON) of solar measurements,
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which provide an estimate of the total CO2 atmospheric column amount. Estimates
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of tropospheric CO2 that are co-located with TCCON are obtained by assimilating
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Tropospheric Emission Spectrometer (TES) free-tropospheric CO2 estimates into
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the GEOS-Chem model. Estimates of the boundary layer CO2 are obtained through
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simple subtraction as the CO2 estimation problem is linear.
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We find that the calculated random uncertainties in total column and boundary
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layer estimates are consistent with actual uncertainties as compared to aircraft data.
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For the total column estimates, the random uncertainty is about 0.67 ppm with a
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bias of -5.71 ppm, consistent with previously published results. After accounting for
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the total column bias, the bias in the boundary layer CO2 estimates is 0.32 ppm with
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a precision of 1.44 ppm. This work shows that a combination of NIR and IR
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measurements can profile CO2 with the precisions and accuracy needed to quantify
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near-surface CO2 variability.
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I. Introduction
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Our ability to infer surface carbon fluxes depends critically on interpreting spatial
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and temporal variations of atmospheric CO2 and relating them back to surface
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fluxes. For example, surface CO2 fluxes are typically calculated using surface or near
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surface CO2 measurements with a combination of aircraft data (2011; Bousquet et
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al., 2000; Chevallier et al., 2010; Chevallier et al., 2011; Gurney et al., 2002; Keppel-
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Aleks et al., 2012; Law and Rayner, 1999; Rayner et al., 2011; Rayner et al., 2008;
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Rayner and O'Brien, 2001). More recently it has been shown that total column CO2
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measurements derived from ground-based or satellite observations can be used to
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place constraints on continental-scale flux estimates (e.g., GOSAT/OCO)(Chevallier,
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2007; Chevallier et al., 2011; Keppel-Aleks et al., 2012; O'Brien and Rayner, 2002).
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However, because CO2 is a long-lived greenhouse gas, measurements of the total
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column CO2 is primarily sensitive to synoptic scale fluxes as discussed in Keppel-
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Aleks (2011). They show that variations in the total column are only partly driven
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by local surface fluxes because of transport of CO2 from remote locations (Keppel-
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Aleks et al., 2011; Rayner, 2001). In the free troposphere, the temporal and spatial
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variations of atmospheric CO2 are associated with synoptic atmospheric
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phenomenon and only partly connected to the surface. In contrast, the variations
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caused by the surface source and sinks are largest in planetary boundary layer
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(PBL) CO2 (Sarrat et al., 2007). They used their mesoscale transport model to
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interpret a regional scale database including frequent vertical profiles and aircraft
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transection. The boundary layer CO2 variability is explained by the regional surface
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fluxes related to the land cover and the mesoscale circulation across the boundary
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layer. In another study, Stephen et al., (2007) concludes that most of the current
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models over-predicts the annual-mean midday vertical gradients and consequently
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lead to an overestimated carbon uptake in northern lands and underestimated
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carbon uptake over tropical forests. For these reasons we could expect that vertical
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profile estimates of CO2 will improve constraints on the distributions of carbon flux.
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Therefore, we are motivated to derive a method to estimate the PBL CO2 from
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current available column and free tropospheric observations.
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Total column CO2 data are calculated by the solar near infrared (NIR) measurements
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from the Total Carbon Column Observatory Network (TCCON) (Wunch et al., 2011a;
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Wunch et al., 2010), as well as the space-borne instruments, starting from GOSAT
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(Crisp et al., 2004; O'Dell et al., 2012; Wunch et al., 2011b; Yokota et al., 2009;
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Yoshida et al., 2009). The similar space-borne instruments are OCO-2, which is
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expected to be launched this decade (Crisp et al., 2004) and several other
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instruments such as Carbonsat (Velazco et al., 2011) and GOSAT-2 (Yokota et al.,
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2009; Yoshida et al., 2009), which are also expected to be launched in near future.
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The ground-based measurements have high precision and accuracy but limited
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spatial coverage. Satellite observations have lower precision and accuracy relative
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to the ground-based data, but obtain continuous global measurements of
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atmospheric CO2. In addition, there are free tropospheric CO2 measurements from
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satellite instruments such as TES (Kulawik, 2012; Kulawik et al., 2010) and AIRS
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(Chahine et al., 2005).
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In this paper, we present a method to estimate the PBL CO2 by combining column
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and free tropospheric CO2 from two data sources: TCCON and TES GEOS-Chem
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assimilation. We do not use the profiling approach discussed in Christi and Stephens
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(2004) because spectroscopic errors and sampling error due to poor co-location of
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the NIR and IR data result in unphysical profiles. The measurements used in this
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study are described in section 2. The estimates of column CO2 are obtained by
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TCCON profile retrieval and free tropospheric CO2 is derived from assimilation of
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the TES CO2 estimates into the GEOS-Chem global chemical transport model (Beer et
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al., 2001). The comparisons of estimates against aircraft data are used to evaluate
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the quality of the data. As long as the retrievals converge and the estimated states
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are close to the true states, the problem of subtracting free tropospheric column
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amount from total column amount is a linear problem with well characterized
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uncertainties. Section 3 describes the derivation to extract PBL CO2 from column
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data using free tropospheric measurements. The retrieval approach and error
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analysis is described in section 4. The results are discussed in section 5. It is
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followed with the summary in section 6.
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2. Measurements
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2.1 Ground-Based Total Column CO2 Measurements from TCCON:
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The column data used to derive PBL CO2 in this study are from TCCON observations.
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A Fourier Transform Spectrometer instrument, with a precise solar tracking system,
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measures incoming sunlight with high spectral resolution (0.02 cm-1) and high
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signal to noise ratio (SNR) between 500 and 885, depending on the spectral region
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observed (Washenfelder et al., 2006). The recorded spectral region ranges from
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4000 to 15,000 cm-1. It provides a long-term observation of column-averaged
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abundance of greenhouse gases, such as CO2, CH4, N2O and other trace gases (e.g.
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CO) over twenty TCCON sites around the world including both operational and
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future sites (Deutscher et al., 2010; Messerschmidt et al., 2011; Washenfelder et al.,
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2006; Wunch et al., 2010; Yang et al., 2002).
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As discussed in Wunch et al., (2011a; 2010), total column-averaged abundances
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using TCCON data can be estimated using a non-linear least squares approach that
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compares a forward model spectrum that depends on CO2, temperature, H2O, and
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instrument parameters against the observed spectrum. The retrieval approach
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adjusts atmospheric CO2 concentrations by scaling an a priori CO2 profile (as well as
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the other discussed parameters) until the observed and modeled spectra agree
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within the noise levels. The precision in the column-averaged CO2 dry air mole
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fraction from the scaling retrievals is better than 0.25% (Wunch et al., 2011a;
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Wunch et al., 2010). The absolute accuracy is ~1% and after calibration by aircraft
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data, it can reach 0.25% (Wunch et al., 2011a; Wunch et al., 2010). In this paper, we
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develop a profile retrieval algorithm that scales multiple levels of the CO2 profile
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instead of the whole profile. We find that the precision of retrieved column averages
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using this approach (0.18%) is consistent with the scaling retrievals. Fig. 1 shows a
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measurement at 1.6 μm CO2 absorption band, which is used for the profile retrieval.
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The profile retrieval algorithm is described in section 4.1.
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2.2 Satellite-Based free tropospheric CO2 measurements from TES:
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The free tropospheric CO2 estimates are from the Aura Tropospheric Emission
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Spectrometer (TES) (Beer et al., 2001). The TES instrument measures the infrared
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radiance emitted by Earth’s surface and atmospheric gases and particles from space.
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These measurements have peak sensitivity to the mid-tropospheric CO2 at ~500 hPa
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(Kulawik, 2012). Because the sampling for the TES CO2 measurements is sparse
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(e.g., 1 measurement every 200 km approximately) and passing over the Lamont
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TCCON site ~ every 16 days, we assimilated the CO2 measurements into the GEOS-
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Chem model, a global 3-D chemical transport model (CTM) (Beer et al., 2001;
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Kulawik, 2011; Kulawik et al., 2010; Nassar et al., 2010). We use the results from the
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assimilation as our free-tropospheric estimates of CO2.
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Details of the assimilation approach are discussed in the Supplemental section and
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uncertainties in the assimilation fields are calculated by the comparison to aircraft
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data as discussed in Section 5.2.
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2.3 Flight measurements:
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Aircraft data are used as our standard to access the quality of the CO2 estimates. The
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aircrafts measure the CO2 profiles up to 6 km and sometimes up to 15 km. They are
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considered the best estimates of the true state of atmospheric CO2. We collected
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profile observations during different aircraft campaigns, such as HIPPO (Wofsy et
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al.,
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http://www.esrl.noaa.gov/gmd/ccgg/aircraft/qc.html), at the Southern Great Plains
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(SGP) ARM site (Kulawik, 2012; Kulawik et al., 2010) over the year 2009
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(http://www.arm.gov/campaigns/aaf2008acme). They are comparable to the
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TCCON observations at Lamont site, Oklahoma (36.6°N, 97.5°W).
2011)
and
Learjet
(Abshire
et
al.,
2010;
Wunch
et
al.,
2010)(
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3. Calculation of column and PBL CO2
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The approach discussed in this paper is to estimate PBL CO2 by subtracting TES
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GEOS-Chem assimilated free tropospheric CO2 partial column amount from TCCON
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total column amount. The total column amount is usually obtained by integrating
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the gas concentration profile from surface to the top of atmosphere.
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∞
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𝑑𝑟𝑦
𝐶𝑔 = ∫ 𝒇𝑔 (𝒛) ∙ 𝝆(𝒛) ∙ 𝑑𝑧
(1)
𝑧𝑠
10
11
where Cg is total vertical column amount for gas ‘g’ and 𝝆(𝒛) represents the number
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𝑑𝑟𝑦
density vertical profile and 𝒇𝑔 (𝒛) is dry-air gas concentration profile as a function
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of altitude (z).
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𝑑𝑟𝑦
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𝒇𝑔 (𝒛) =
𝒇𝑔 (𝒛)
1 − 𝒇𝐻2 𝑂 (𝒛)
(2)
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The ratio of total column between gas and air will give dry-air column-averaged
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abundance, e.g. for CO2:
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𝑋𝐶𝑂2 =
𝐶𝐶𝑂2
𝐶𝑎𝑖𝑟
(3)
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Here we use 𝑋𝐶𝑂2 to refer to dry-air column-averaged mole fraction of CO2 and we
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simply call it column-averaged CO2 or column averages.
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Since TCCON also provides precise measurements of O2, dividing by the retrieved O2
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using spectral measurements from the same instrument improves the precision of
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𝑋𝐶𝑂2 by significantly reducing the effects of instrumental or measurement errors
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that are common in both gases (e.g. solar tracker pointing errors, zero level offsets,
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1
instrument line shape errors, etc.) (Wunch et al., 2010). We remove the water
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fraction by normalizing simultaneously retrieved O2 (Wunch et al., 2010). Since we
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retrieve the CO2 profile, we can remove the water component layer by layer.
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𝑑𝑟𝑦
𝑓𝐶𝑂2 (𝑧) =
𝑓𝐶𝑂2 (𝑧)
× 0.2095
𝑓𝑂2 (𝑧)
(4)
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Then the column amount (𝐶𝐶𝑂2 ) and the column average (𝑋𝐶𝑂2 ) can be computed
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using Eq. (1) and (3) respectively.
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As mentioned by Wunch et al., (2010), the precision of column estimates using O2 as
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the dry air standard will be improved but the bias specific for O2 will be transferred
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to 𝑋𝐶𝑂2 (Fig. 2). The precision of 𝑋𝐶𝑂2 is improved from 1.49 ppm (remove water
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using Eq. (2)) to 0.49 ppm (remove water using Eq. (4)) versus the bias increase
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from 0.73 ppm to −5.02 ppm (Fig. 2). This bias is due to the spectroscopic bias from
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O2 absorption coefficient. It negligibly varies over time and over different sites.
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The total column amounts (𝐶𝐶𝑂2 ) can be computed from the retrieved TCCON 𝑋𝐶𝑂2
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𝑇𝑅𝑂𝑃
by profile retrieval and free tropospheric partial column amount (𝐶𝐶𝑂
) are
2
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estimated by integrating TES GEOS-Chem assimilated data above the boundary layer
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(i.e. 600 hPa). Since O2 normalized estimates of 𝑋𝐶𝑂2 have higher precision but about
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1% negative bias, we need remove the mean bias in TCCON 𝑋𝐶𝑂2 when estimating
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the total column amount:
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𝐶𝐶𝑂2
𝑇𝐶𝐶𝑂𝑁
𝑋𝐶𝑂
2
= 𝐶𝑎𝑖𝑟 (
)
𝛼
(6)
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where 𝛼 is a correction factor to remove the bias in TCCON column retrievals. The
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𝑇𝑅𝑂𝑃
partial vertical column amount of CO2 in free troposphere and above (𝐶𝐶𝑂
) is
2
7
1
estimated by integrating TES GEOS-Chem assimilated profile (𝒇𝑇𝐸𝑆
𝐶𝑂2 ) above the
2
boundary layer (600 hPa).
3
0
4
𝑇𝑅𝑂𝑃
𝐶𝐶𝑂
= ∫ 𝒇𝑇𝐸𝑆
𝐶𝑂2 (𝒑) ∙ 𝒏(𝒑) ∙ 𝑑𝑝
2
(7)
600
5
6
Then partial vertical column amount of CO2 in PBL can be computed as the
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difference between the total column amount (Eq. 6) and partial free tropospheric
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column amount (Eq. 7):
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𝑃𝐵𝐿
𝐶𝐶𝑂
2
𝑇𝐶𝐶𝑂𝑁
0
𝑋𝐶𝑂
2
= 𝐶𝑎𝑖𝑟 (
) − ∫ 𝒇𝑇𝐸𝑆
𝐶𝑂2 (𝒑) ∙ 𝒏(𝒑) ∙ 𝑑𝑝
𝛼
600
(8)
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Applying Eq. (3) within the boundary layer give the estimates of the PBL CO2 mole
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𝑃𝐵𝐿
𝑃𝐵𝐿
fraction (𝑋𝐶𝑂
), the ratio of partial vertical column between CO2 (𝐶𝐶𝑂
) and air
2
2
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𝑃𝐵𝐿
(𝐶𝑎𝑖𝑟
= ∫𝑝
600
𝑠
1 ∙ 𝒏(𝒑) ∙ 𝑑𝑝) is
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𝑃𝐵𝐿
𝑋𝐶𝑂
2
𝑇𝐶𝐶𝑂𝑁
𝑋𝐶𝑂
0
0
2
1
∙
𝒏(𝒑)
∙
𝑑𝑝
−
𝒇𝑇𝐸𝑆 (𝒑) ∙ 𝒏(𝒑) ∙ 𝑑𝑝
∫
∫
𝑝𝑠
600 𝐶𝑂2
𝛼
=
600
∫𝑝 1 ∙ 𝒏(𝒑) ∙ 𝑑𝑝
(9)
𝑠
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From now on, we simply call it TES/TCCON PBL CO2. These estimates are then
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compared to the integrated partial column-averaged CO2 measured by aircraft
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within the boundary layer (surface to 600 hPa). As long as the retrievals converge
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and the estimated states are close to the true states, we can use the linear retrieval
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equations to attribute the errors.
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4. Retrieval Approach and Error Characterization
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2
4.1 Retrieval approach for TCCON CO2 profile:
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In this study, we develop a profile retrieval algorithm that is based on the scaling
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retrieval discussed in Wunch et al., (2011a; 2010). The profile of atmospheric CO2 is
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obtained by optimal estimation (Rodgers, 2000) using a line-by-line radiative
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transfer model in GFIT developed at JPL. It computes simulated spectra using 71
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vertical levels with 1 km intervals for the input atmospheric state (e.g. CO2, H2O,
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HDO, CH4, O2, P, T and etc.). The details about the TCCON instrument setup and GFIT
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are also described in Deutscher et al., (2010); Geibel et al., (2010); Washenfelder et
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al., (2006); Wunch et al., (2011a; 2010); Yang et al., (2002). The retrievals in this
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study use one of TCCON-measured CO2 absorption bands, centered at 6220.00 cm-1
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with a window width of 80.00 cm-1 (Fig. 1).
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In the scaling retrieval discussed by Wunch et al. (2011a; 2010), when the target gas
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is CO2, the retrieved state vector (𝜸 ) includes the eight constant scaling factors for
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four absorption gases (CO2, H2O, HDO, and CH4) and four instrument parameters
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(continuoum level: ‘cl’, continuoum tilt: ‘ct’, frequency shift: ‘fs’, and zero level offset:
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‘zo’).
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𝛾[𝐶𝑂2 ]
𝛾[𝐻2 𝑂]
𝛾[𝐻𝐷𝑂]
𝛾
𝜸 = [𝐶𝐻4 ]
𝛾𝑐𝑙
𝛾𝑐𝑡
𝛾𝑓𝑠
[ 𝛾𝑧𝑜 ]
(11)
21
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Each element of 𝜸 is a ratio between the state vector (x) and its a priori (xa). In the
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profile retrieval, for the target gas CO2, we estimate the altitude dependent scaling
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factors instead. For other interfering gases, a single scaling factor is retrieved. Ten
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levels are chosen for CO2 (see Fig. 3 a) to capture its vertical variation:
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9
𝛾1[𝐶𝑂2 ]
⋮
𝛾10[𝐶𝑂2]
𝛾[𝐻2 𝑂]
𝜸 = 𝛾[𝐻𝐷𝑂]
𝛾[𝐶𝐻4 ]
𝛾𝑐𝑙
𝛾𝑐𝑡
𝛾𝑓𝑠
[ 𝛾𝑧𝑜 ]
1
(12)
2
3
To obtain concentration profile, the retrieved scaling factors need to be first mapped
4
from retrieval grid (i.e. 10 levels for CO2 and 1 level for other three gases) to the 71
5
forward model levels.
6
7
𝜷 = 𝐌𝜸
(13)
8
9
where 𝐌 =
𝝏𝜷
𝝏𝜸
is a linear mapping matrix relating retrieval level to the forward
10
model altitude grid. Multiplying the scaling factor (𝜷) on the forward model level to
11
𝐌𝒙 = 𝝏𝜷, a diagonal matrix of the concentration a priori (𝒙𝒂 ), gives the truth state of
12
gas profile:
𝝏𝒙
13
14
𝒙 = 𝐌𝒙 𝜷
(14)
15
16
̂=
According to the definition, a priori profile is 𝒙𝒂 = 𝐌𝒙 𝜷𝒂 and estimated state is 𝒙
17
̂ . The non-diagonal CO2 covariance matrix used for the constraint matrix has
𝐌𝒙 𝜷
18
larger variance in boundary layer and decreases with altitude. The square root of
19
the diagonal of this covariance is approximately 2% in the boundary layer, 1% in the
20
free troposphere, and less than 1% in the stratosphere (Fig. 3 a). The off-diagonal
21
correlations are shown in Fig. 3 b. This covariance is generated using the GEOS-
22
Chem model as guidance. However, because atmospheric CO2 typically show lower
23
variability near surface than it is described in the covariance, we scaled the variance
24
down to make it match the variability of the surface observations. Although the SNR
10
1
of the TCCON instrument is better than 500, we use an SNR of approximately 200
2
because spectroscopic uncertainties degrade the comparison (O'Dell et al., 2011;
3
Wunch et al., 2011a) and consequently, this SNR results in a chi-square in our
4
retrievals about 1.
5
6
To obtain the best estimate of the state vector that minimize the difference between
7
the observed spectral radiances (𝒚𝒐 ) and the forward model spectral radiances (𝒚𝒎 )
8
we perform Bayesian optimization by minimizing the cost function, 𝜒(𝜸):
9
10
𝜒(𝜸) = (𝒚𝒎 − 𝒚𝒐 )T 𝐒𝑒−1 (𝒚𝒎 − 𝒚𝒐 ) + (𝜸 − 𝜸𝒂 )T 𝐒𝐚−1 (𝜸 − 𝜸𝒂 )
(15)
11
12
13
14
4.2 Error characterization for TCCON column-averaged CO2:
15
The comparison to the aircraft derived values evaluates our estimates based on
16
following assumptions. The measurement noise is a zero-mean random variable.
17
The temperature uncertainty is likely not to vary much for a time scale shorter than
18
a day but become random variable from day to day. Since aircraft only measures up
19
to a limited altitude (e.g. 6 km), in order to use it to estimate the total column
20
average as a validation standard, above the available aircraft measurements, the
21
TCCON a priori is scaled to the aircraft measurement so that the profile is
22
continuously extended up to 71 km. This is because the free tropospheric CO2 is well
23
mixed and aircraft measurement provides a better constraint. Combining aircraft
24
value and a priori profile shape reduces the uncertainties in the upper atmospheric
25
estimates.
26
27
In this section, we characterize the error in the TCCON profile retrieved column
28
averages in order to further understand the uncertainties in the derived PBL CO2.
29
The details of all the derivations are in Appendix.
30
31
The averaging kernel for the forward model dimension scaling vector 𝜷 is
11
1
2
(16)
𝐀 𝜷 = 𝐌𝐆𝜸 𝐊 𝜷
3
4
where 𝐊 𝜷 is the Jacobian of 𝜷 with respect to the radiance and 𝐆𝜸 is the gain matrix
5
in retrieval dimension (Eq. A1. 8). Consequently, the averaging kernel for 𝒙 is 𝐀 𝑥 =
6
𝐌𝒙 𝐀 𝜷 𝐌𝒙−𝟏 . The estimated state in forward model grids for a single measurement
7
can be expressed as a linear retrieval equation:
8
9
̂ = 𝜷𝒂 + 𝐀 𝜷 (𝜷 − 𝜷𝒂 ) + 𝐌𝐆𝜸 𝜺𝒏 + ∑ 𝐌𝐆𝜸 𝐊 𝒍𝒃 ∆𝒃𝒍
𝜷
(17)
𝒍
10
11
where 𝜺𝒏 is a zero-mean Gaussian spectral noise vector with covariance 𝐒𝐞 and the
12
vector ∆𝒃𝒍 is the error in true state of parameters (l) that also affect the modeled
13
radiance, e.g. temperature, interfering gases, etc. 𝐊 𝒍𝒃 is the Jacobian of parameter (𝒍).
14
In this study, the primary uncertainties (∆𝒃𝒍 ) are found due to temperature
15
̅̅̅,
(𝜺𝑻 ~ 𝑵(𝜺
𝑻 𝐒𝑻 )) and spectroscopic error (e.g. O2 absorption cross section bias)
16
̅̅̅,
(𝜺𝑳 ~ 𝑵(𝜺
𝑳 𝐒𝑳 )). If we want to convert above equation to the state vector of
17
̂ by 𝐌𝒙 to obtain:
̂), according Eq. (14) we simply multiply 𝜷
concentration (𝒙
18
19
̂ = 𝒙𝒂 + 𝐀 𝒙 (𝒙 − 𝒙𝒂 ) + 𝐌𝒙 𝐌𝐆𝜸 𝜺𝒏 + 𝐌𝒙 𝐌𝐆𝜸 𝐊 𝑻 𝜺𝑳
𝒙
20
+𝐌𝒙 𝐌𝐆𝜸 𝐊 𝑳 𝜺𝑳
(18)
21
22
where 𝐀 𝒙 = 𝐌𝒙 𝐀 𝜷 𝐌𝒙−𝟏 .
23
24
To evaluate our estimates, the aircraft measurements are used as the best estimates
25
of the true state (𝒙). Most of the measurements only go up to 6 km, but three of
26
them go up to 10 km or higher. In order to use them to estimate the total column
27
average as a validation standard, above the available aircraft measurements, the
28
TCCON a priori is scaled to value at the top of aircraft measurement so that the
29
profile is continuously extended up to 71 km (see Eq. (A1.11)). This is because the
12
1
free tropospheric CO2 is well mixed (vertical variations in free troposphere is less
2
than 1 ppm). In addition, aircraft measurement provides a better constraint.
3
Therefore, combining aircraft value and a priori profile shape reduces the
4
uncertainties in the upper atmosphere.
5
6
In order to do an inter-comparison of the measurements from two different
7
instruments, we apply a smoothing operator described in Rodgers and Connor
8
(2003) to the complete aircraft profile (𝒙𝑭𝑳𝑻 ) so that it is smoothed by the averaging
9
kernel and a priori constraint from the TCCON profile retrieval:
10
11
̂𝑭𝑳𝑻 = 𝒙𝒂 + 𝐀 𝒙 (𝒙𝑭𝑳𝑻 − 𝒙𝒂 )
𝒙
(19)
12
13
̂𝑭𝑳𝑻 is the profile that would be
𝒙𝑭𝑳𝑻 is the aircraft profile combining a priori. 𝒙
14
retrieved from TCCON measurements for the same air sampled by the aircraft
15
without the presence of other errors.
16
17
The error for single measurement is estimated by comparing to the derived aircraft
18
profile.
19
20
̂=𝒙
̂−𝒙
̂𝑭𝑳𝑻 = 𝐀 𝒙 (𝒙 − 𝒙𝑭𝑳𝑻 ) + 𝐌𝒙 𝐌𝐆𝜸 𝜺𝒏
𝜹𝒙
21
+𝐌𝒙 𝐌𝐆𝜸 𝐊 𝑻 𝜺𝑳 + 𝐌𝒙 𝐌𝐆𝜸 𝐊 𝑳 𝜺𝑳
(20)
22
23
We determine a short time window (e.g. 4 hours), which is short enough so that we
24
can assume the atmospheric state hasn’t changed but is also long enough there are
25
enough samples of retrievals for good statistics (e.g. ~100 samples). These
26
measurements should agree with the representation of the “truth”, 𝒙, within the
27
uncertainties. For example, given each aircraft profile as the validation standard, we
28
select the TCCON retrievals within 4-hr time window centered as the aircraft
29
measurement was taken. The estimated bias error is the difference between the
30
average of the multiple retrieved 𝑋𝑪𝑶𝟐 to the truth (or one aircraft measurement):
13
1
2
𝒉𝒓
𝑬(𝛿𝑋𝑪𝑶
) = 𝒉𝑻 [𝐀(𝒙 − 𝒙𝑭𝑳𝑻 )] + 𝒉𝑻 (𝐌𝒙 𝐌𝐆𝐊 𝑻 ̅̅̅)
𝜺𝑻
𝟐
3
+𝒉𝑻 (𝐌𝒙 𝐌𝐆𝐊 𝑳 ̅̅̅)
𝜺𝑳
(21)
4
5
where 𝒉 is a column-averaging operator, a pressure weighting function (Rodgers
6
and Connor, 2003). The second term describes the potential sources of bias error
7
due to temperature uncertainty. When the temperature profile does not vary a lot in
8
a short time scale (i.e. 4-hr), we can assume the temperature uncertainty stays as a
9
constant but it becomes a pseudo-random variable for a time scale of multiple days
10
when observing the different air masses. Therefore, the second term in Eq. (21) has
11
contribution to the bias error for measurements within a 4-hr time window but
12
varies over multiple days. The third term is the bias error due to spectroscopic error
13
and does not vary.
14
The random error in retrieved column averages is predicted by the measurement
15
error covariance:
16
17
𝒉𝒓
𝝈(𝛿𝑋𝑪𝑶
) ≈ √𝒉𝑻 𝐒̂𝐦 𝒉
𝟐
(22)
18
19
It should be consistent with the standard derivation of the real retrieved column
20
averaged within 4-hr time window. 𝐒̂𝐦 is the measurement error covariance:
21
22
𝐒̂𝐦 = 𝐌𝒙 𝐌𝐆𝐒𝐞 (𝐌𝒙 𝐌𝐆)𝐓
(23)
23
24
We also defined the systematic covariance as
25
26
𝐒̂𝑻 = 𝐌𝒙 𝐌𝐆𝐊 𝑻 𝐒𝑻𝒉𝒓 (𝐌𝒙 𝐌𝐆𝐊 𝑻 )𝐓
(24)
𝐒̂𝑳 = 𝐌𝒙 𝐌𝐆𝐊 𝑳 𝐒𝑳𝒉𝒓 (𝐌𝒙 𝐌𝐆𝐊 𝑳 )𝐓
(25)
27
28
29
14
1
and a smoothing error covariance as
2
3
𝐒̂𝐬𝐦 = 𝐀 𝒙 𝐒𝜹𝒙𝑭𝑳𝑻 𝐀𝑻𝒙
(26)
4
5
𝐒𝜹𝒙𝑭𝑳𝑻 is the aircraft error covariance defined in Eq. (A1.12). See supplement for
6
detailed derivations. The systematic error covariance matrices are approximately a
7
zero-matrix for the multiple measurements of the same air mass in 4-hr time
8
window since uncertainties due to temperature are effectively constant for several
9
measurements taken during a day but the temperature error covariance is non-zero
10
when observing multiple air parcels (over several days) because temperature varies
11
in these multiple air parcels. However, the spectroscopic error is consistent over
12
days. Therefore, its covariance is almost zero-matrix on both time scales.
13
14
We have estimated the bias error and random error for the measurements within 4-
15
hr time windows and next we will discuss the error on multiple-day time scale. The
16
former can be considered as the multiple observations of the same air mass while
17
the later is the case of the measurements for different air masses. For example, we
18
have about fifty aircraft measurements as our validation standard. What are the
19
sources of the mean bias error and random error for these fifty comparisons? In a
20
multiple-day time scale, the expected mean bias error over time is
21
22
𝒅𝒂𝒚
𝑻
𝑻
̅̅̅̅̅̅̅̅
̅
̅
𝑬(𝛿𝑋𝑪𝑶𝟐 ) = 𝒉𝑻 [𝐀𝜹𝒙
𝑭𝑳𝑻 ] + 𝒉 (𝐌𝒙 𝐌𝐆𝐊 𝑻 𝜺𝑻 ) + 𝒉 (𝐌𝒙 𝐌𝐆𝐊 𝑳 𝜺𝑳 )
(27)
23
24
and the precision error is predicted by
25
26
𝒅𝒂𝒚
𝝈(𝛿𝑋𝑪𝑶𝟐 ) ≈ √𝒉𝑻 (𝐒̂𝐦 + 𝐒̂𝐓 )𝒉
(28)
27
28
In summary, for a 4-hr time window, we have multiple retrievals compare to one
29
representation of the “truth” (one aircraft measurement). The mean bias error is
15
1
driven by temperature error and O2 spectroscopic error. The variability of the
2
retrievals is driven by the measurement noise. For multiple-day time scale, the
3
multiple comparisons of mean retrievals within 4-hr window to the aircraft
4
estimates for their truth states suggest the mean bias error is consistently primarily
5
driven by the O2 spectroscopic error over time and different sites. The random error
6
across multiple days is mainly due to the temperature uncertainties together with
7
the contribution of measurement noise.
8
9
10
4.3 Error characterization for TES/TCCON PBL CO2
11
To understand the potential sources of the uncertainties in the TES/TCCON PBL CO2
12
estimates, we separate the boundary layer from the free troposphere. To make
13
estimated PBL CO2 useful for carbon cycle science we have to understand the
14
potential source of the bias error and random errors in the PBL CO2 product. Since
15
the mean bias error in total column from TCCON has been removed before it is
16
applied to PBL estimates and the objective of GEOS-Chem assimilation with TES
17
data is to improve the bias error and uncertainty, the mean bias error in the
18
TES/TCCON estimated PBL CO2 is found to be quite small as expected. Its random
19
error can only be driven by TES assimilated free tropospheric CO2 estimates
20
together with the TCCON total column estimates.
21
22
𝑃𝐵𝐿
𝑇𝐸𝑆
𝑇𝐶𝐶𝑂𝑁
𝜎 2 (𝛿𝑋𝐶𝑂
) = 𝜎 2 (𝛿𝑋𝐶𝑂
) + 𝜎 2 (𝛿𝑋𝐶𝑂
)
2
2
2
(29)
23
24
The TES uncertainty is estimated by the comparison to the aircraft data and the
25
TCCON total column uncertainty has been discussed in previous section, which is
26
primarily driven by TCCON measurement noise and TCCON temperature
27
uncertainties. Comparing Eq. (A2.1) to the actual uncertainty in the estimated
28
TES/TCCON PBL CO2 can confirm the robustness of estimation by this method.
29
30
16
1
5. Results
2
3
5.1 Quality of the column-averaged CO2 estimates:
4
To understand the quality of the retrieved product, we compared the TCCON
5
column-averaged estimates with the aircraft column-integrated data to obtain the
6
bias error and precision error in a 4-hr time scale and a day-to-day time scale. We
7
show that these errors derived empirically are consistent with the calculated errors
8
discussed in section 4.2.
9
10
There are fifty SGP aircraft measured CO2 profiles in 2009. We show examples of
11
them comparing with TES assimilated profiles in Fig. 4. Most of aircraft
12
measurements only go up to 6 km except three profiles are obtained up to 10 Km
13
(July 31, August 2nd and 3rd). To estimate the total column, the missing observations
14
above the top of aircraft measurement are replace by shifted TCCON CO2 a priori.
15
The simultaneous observations by TCCON are measured at Lamont. The
16
comparisons between TCCON column averages and the derived aircraft column
17
averages are summarized in Fig. 5 and Table 1.
18
19
The TCCON retrievals within a 4-hr time window about the mid time during each
20
flight measurement are selected as the simultaneous measurements. We choose 4-
21
hr time window so that it is long enough to have large sample size for statistics and
22
short enough so that the air mass is not changed. The actual variability of the
23
retrieved 𝑋𝐶𝑂2 within the 4-hr time window, defined by one standard deviation (1 ×
24
𝜎), is the uncertainties of the retrievals for the same air parcel. Table 1 lists the
25
statistics for these fifty comparisons both with and without cloud filter. To remove
26
the unclear sky measurements, we dismiss the retrievals when the parameter ‘fvsi’
27
(fractional variation in solar intensity) is greater than 5%, which suggests that there
28
was some cloud cover during the spectra measurements. This will result in poor
29
sample size. For these cases, the agreement with aircraft is sometimes worse than
30
clear sky. For the clear sky cases, the variability in the total column retrievals within
17
1
the 4-hr time window corresponding to each aircraft is approximately 0.39 ppm.
2
This variability is consistent with the expected uncertainty due to the measurement
3
𝒉𝒓
error (Eq. 21) which is also listed in Table 1 (column for 𝝈(𝛿𝑋𝑪𝑶
)). They range from
𝟐
4
0.27 to 0.34 ppm. It suggests that the measurement error is the dominant source of
5
the variability for the errors in the retrieved column averages during this 4-hr time
6
window. In Table 1, there are some inconsistent cases (highlighted in pink: 1 × 𝜎 >
7
1.0 ppm and in yellow: 0.5 < 1 × 𝜎 < 1.0 ppm). These inconsistencies are due to the
8
cloud coverage during the measurements. After applying the cloud filter, most of
9
them are corrected to be more consistent with the expected uncertainty
10
(highlighted in green: 0.0 < 1 × 𝜎 < 0.5 ppm). There are still seven of them
11
remaining inconsistent because of their poor sample number (<50 retrievals).
12
13
The comparisons of the mean retrieved column averages in 4-hr window to the
14
aircraft derived column averages are plotted in Fig. 5. The difference between the
15
mean retrievals within the 4-hr time window and the derived aircraft 𝑋𝐶𝑂2 is the
16
bias error of that estimate (Table 1). The biases across multiple days are the offsets
17
of solid line to the one-to-one dash line in Fig. 5. The vertical error bars for TCCON
18
column averages are the sum of calculated measurement uncertainty and systematic
19
errors by temperature. Without removing the retrievals under cloudy skies, the
20
TCCON column averages underestimate the flight data by -5.78(±0.78) ppm. The
21
cloud filter has no significant influence on the mean bias and its variability over
22
multiple days, remaining as -5.71(±0.67) ppm. This mean bias value is consistent
23
with the bias estimated discussed in Wunch et al. (2010), which is constant over
24
time and sites. The RMS of the difference between column estimates from TCCON
25
(after the bias correction) and from the aircraft is 0.67 or 0.78 ppm for with or
26
without cloud filter; this precision error is consistent with the expected uncertainty
27
(column of 𝜎(𝛿𝑋𝑪𝑶𝟐 ) in table 2), the sum of the measurement error covariance and
28
temperature error covariance (0.78 ppm). The contribution by the temperature
29
uncertainty is larger than the measurement error.
𝒅𝒂𝒚
30
18
1
5.2 Quality of the PBL CO2 estimates:
2
In Fig. 7, we plot the comparisons of TCCON a priori PBL CO2 to the aircraft
3
estimates in (a) and the comparisons of TES/TCCON derived PBL CO2 to aircraft PBL
4
CO2 in (b). Since we removed the mean bias in total column before the subtraction,
5
TES/TCCON derived PBL CO2 are mostly close to the one-to-one line with a
6
remained mean bias of 0.32 (±1.44) ppm. The factor (𝛼) in Eq. (9) for removing -
7
5.78 ppm bias in TCCON column CO2 is 0.986. TES GEOS-Chem assimilated free
8
tropospheric CO2 is biased high relative to aircraft free tropospheric data by 0.38
9
(±1.66) ppm. Since the bias in TCCON column data is removed in advance, the 0.32-
10
ppm bias in derived PBL CO2 estimates is driven by TES assimilated free
11
tropospheric estimates. The agreement to the derived aircraft PBL CO2 is much
12
better in TES/TCCON PBL estimates than that from TCCON a priori integrating from
13
surface to 600 hPa. The improvement in the comparison is mainly during summer
14
time when surface CO2 are low because the biosphere is more active than in winter.
15
16
The precision error of the TES/TCCON PBL CO2 is 1.44 ppm, which is consistent
17
with the expected precision error of 1.83 ppm by Eq. (30), including the sources
18
from TES assimilated free tropospheric errors, TCCON measurement and systematic
19
errors. It is smaller than the uncertainties of the PBL estimates from both TCCON a
20
priori (2.07 ppm) (in Fig. 6 a) and TES GEOS-Chem assimilations (2.86 ppm) (not
21
plotted here). It suggests that the derived estimates of PBL CO2 by TES/TCCON data
22
reduce the uncertainties in the PBL estimates and improve our knowledge of the
23
variability in the boundary layer CO2. The precision of the estimates is sufficient to
24
capture the season variability which will be discussed in section 5.3.
25
26
As mentioned in section 5.1, the cloud coverage has a strong impact on the quality of
27
the TCCON column data. Under clear skies, there are on average 100 retrieval
28
samples in the 4-hr time window. For cloudy days when there is only limited
29
number of clear sky measurements available, the variability in the TCCON column
30
estimates is larger than on clear days. By excluding those data with sample number
31
less than 50, the averages of 1 × 𝜎 of bias in column-averaged CO2 is reduced from
19
1
0.78 ppm to 0.61 ppm and consequently that in PBL CO2 is reduced from 1.44 ppm
2
to 1.29 ppm.
3
4
In the above analysis, we separate PBL and free troposphere at 600 hPa because
5
TES retrieved CO2 has its peak sensitivity at 511 hPa and Fig. 4 shows that TES
6
GEOS-Chem assimilated profiles agree better with the aircraft profiles above 4 Km
7
(about 600 hPa) than below. If we use TES assimilated profiles above 800 hPa
8
instead to estimate the free tropospheric CO2, we get slightly improved bias in PBL
9
CO2 of 0.06 ppm, but the uncertainty in PBL CO2 is increased to 4.20 ppm. This is
10
because the agreement between the estimates of TES assimilated free tropospheric
11
CO2 and aircraft measurements between 600 to 800 hPa is not as well as it is above
12
600 hPa (Fig. 4). Therefore additional uncertainties in the derived PBL CO2 bias
13
error is driven by the TES assimilated free tropospheric estimates between 600 to
14
800 hPa.
15
16
Table 2 lists the accuracy and precisions by the estimates using different datasets. It
17
shows how information is improved. The accuracy and precision are all calculated
18
using aircraft profile as the validation standard. For total column averages, after the
19
retrieval, a 5-ppm O2 bias is induced but the precisions is improved from 1.50 ppm
20
to 0.67 ppm compared to the estimates from TCCON a priori. To estimate the PBL
21
CO2, the combination of TCCON and TES assimilated data gives the best accuracy
22
and precision. If we both use the TCCON retrieved column but replace TES
23
assimilated free tropospheric estimates by TCCON a priori, not only the uncertainty
24
is enlarged but also the bias increases. Similarly, keeping the free tropospheric
25
estimates from TES assimilation but replacing TCCON retrieved column with the
26
TCCON a priori column, both the accuracy and precision is worse than the
27
TES/TCCON PBL CO2. It confirms that both TCCON and TES assimilation adds the
28
information to reduce the uncertainty in PBL CO2.
29
30
5.3 Seasonal variability of PBL CO2 compared to column CO2.
20
1
The aircraft, TCCON, and TES assimilated estimates of atmospheric CO2 have
2
sufficient temporal density to provide an estimate of CO2 variability over the year. In
3
Figure 7 we show the monthly averaged total column averages and the partial
4
column averages (surface to 600 hPa) calculated from the aircraft data and the same
5
quantities derived from the TCCON data and the TCCON minus TES assimilated data
6
respectively. The TCCON profile retrieved column averages (black dots) and
7
TES/TCCON derived PBL data (red dots) are consistent with the similar aircraft
8
estimates (black line and red line) within the expected uncertainties indicating that
9
the estimates are robust. Based on these fifty flight profiles, there are about 3 to 5
10
days’ to be averaged in each month of the year except September and October, both
11
of which only have one available aircraft profile. Therefore, the comparisons for
12
these two months are not shown. Both TCCON column averages and TES/TCCON
13
PBL CO2 capture the seasonal variability in the similar estimates by aircraft
14
measurements.
15
16
The response of the season variability in PBL CO2 is more than twice of that in the
17
column averages. It is 14 ppm peak-to-peak in PBL CO2 and 5 ppm in the column-
18
averaged CO2 because there is a rapid drawdown in PBL CO2 at the growing season
19
onset over mid latitude due to the biosphere uptake but the vertical mixing dilute
20
the surface flux signature in the column CO2. The difference between the PBL CO2
21
and column CO2 changes from positive (about 3 ppm) to large negative (lower than -
22
4 ppm) over the year (Fig. 7 b solid line by flight and dots by TES/TCCON estimates).
23
These results empirically suggests that these estimated PBL CO2 will provide
24
improved sensitivity to local fluxes than the total column (Keppel-Aleks et al., 2011).
25
26
27
28
6. Summary
29
Total column estimates of atmospheric CO2 and partial column estimates of CO2 in
30
the boundary layer (surface to 600 hPa) are calculated using TCCON and Aura TES
31
assimilated data. In order to determine if the retrieval approach, forward model,
21
1
and understanding of uncertainties are robust, it is crucial to determine if the
2
calculated uncertainties are consistent with the actual uncertainties. In addition, we
3
need to assess any biases in the estimates and ideally attribute these biases errors in
4
the measurement system. The actual bias and its uncertainties in TCCON column-
5
averaged CO2 have to be explained in two different time scales, 4-hr time window
6
and day-to-day time scales. We find that for multiple retrievals of the same air
7
parcel within a 4-hr time window, the mean bias is from the uncertainties of
8
atmospheric states (i.e. temperature or interference gases) or spectroscopy
9
parameters. The variability of the collection of total column estimates within the 4-
10
hr time window is consistent with the calculated random error of about 0.3 ppm.
11
When comparing the TCCON total column estimates to aircraft data over several
12
days, we can assume that the daily systematic errors due to temperature or other
13
interference error is pseudo-random. For example, the estimated mean bias across
14
multiple days is -5.78(±0.78) ppm without cloud filter and -5.71(±0.67) ppm with
15
cloud filter. The standard deviation of the bias error of approximately 0.78 ppm (all
16
data) or 0.67 ppm (clear sky only data) is consistent with the expected estimates of
17
0.78 ppm, which is the square root of the sum of measurement error covariance and
18
temperature error covariance. Because the daily systematic error (largely due to
19
temperature) is larger than the random error, we find that it is the temperature
20
error that is likely responsible for the uncertainties in the bias estimate.
21
22
Comparisons of the aircraft data to free tropospheric CO2, calculated by assimilating
23
Aura TES CO2 estimates into the GEOS-Chem model (Nassar et al., 2011) suggest
24
that the TES assimilated data has bias error of 0.38(±1.66) ppm in the free
25
troposphere. We calculated a boundary layer estimate (surface to 600 hPa) of the
26
CO2 amount by subtracting the TES assimilated free tropospheric estimate from the
27
TCCON total column amount estimates. Comparisons of these boundary layer
28
estimates from TES/TCCON data to those from aircraft data are consistent after the
29
bias in the TCCON is removed. The precision in the derived PBL CO2 is 1.44 ppm,
30
which is consistent with the calculated precision of 1.83 ppm. The dominant sources
31
of the error in the PBL estimates are due to uncertainties in the free troposphere
22
1
data from TES assimilation and the temperature error in column averages from
2
TCCON. We show that this precision is sufficient to characterize the seasonal
3
boundary layer variability of CO2 over the TCCON sites.
4
5
This study highlights the potential of combining simultaneous measurements from
6
different instruments to obtain vertical information of the CO2 profile (e.g., Christi
7
and Stephens 2004). The present TCCON network is relatively sparse but has a good
8
latitudinal coverage. It provides temporal dense long-term accurate observations of
9
column abundance of CO2. Column estimates of CO2 by space measurement are
10
currently available from GOSAT and SCIAMACHY data (Schneising et al., 2012;
11
Schneising et al., 2011) and are expected from OCO-2. They have better global
12
coverage and could provide both spatially and temporally dense column data sets.
13
Column CO2 together with the boundary layer CO2 estimates are anticipated to
14
provide complementary constraints to infer CO2 fluxes and advance the ability to
15
study the carbon cycle problem by providing constraints on near-surface CO2
16
variations and atmospheric mixing (Sarrat et al., 2007).
17
18
Acknowledgements:
19
The authors wish to thank *** for insightful and constructive comments and
20
suggestions. We acknowledge financial support of
21
SGP data was supported by the Office of Biological and Environmental Research of
22
the US Department of Energy under contract No. DE-AC02-05CH11231 as part of the
23
Atmospheric Radiation Measurement Program. US funding for TCCON comes from
24
NASA’s Terrestrial Ecology Program, grant number NNX11AG01G, the Orbiting
25
Carbon Observatory Program, the Atmospheric CO2 Observations from Space
26
(ACOS) Program and the DOE/ARM Program.
27
28
29
30
31
23
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
References:
22
23
24
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