Profiling Tropospheric CO2 Using Aura TES and TCCON Instruments

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Atmos. Meas. Tech., 6, 63–79, 2013 www.atmos-meas-tech.net/6/63/2013/ Atmospheric doi:10.5194/amt-6-63-2013 Measurement © Author(s) 2013. CC Attribution 3.0 License. Techniques

Proﬁling tropospheric CO2 using Aura TES and TCCON instruments

L. Kuai1, J. Worden1, S. Kulawik1, K. Bowman1, M. Lee1, S. C. Biraud2, J. B. Abshire3, S. C. Wofsy4, V. Natraj1, C. Frankenberg1, D. Wunch5, B. Connor6, C. Miller1, C. Roehl5, R.-L. Shia5, and Y. Yung5 1Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Mail stop: 233-200, Pasadena, CA 91109, USA 2Lawrence Berkeley National Laboratories, Berkeley, CA 94720, USA 3NASA Goddard Space Flight Center, Greenbelt, MD, USA 4Harvard University, Cambridge, MA, USA 5California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA 6BC Consulting Ltd., 6 Fairway Dr., Alexandra, 9320, New Zealand

Correspondence to: L. Kuai (lkuai@jpl.nasa.gov)

Received: 30 May 2012 – Published in Atmos. Meas. Tech. Discuss.: 29 June 2012 Revised: 22 November 2012 – Accepted: 7 December 2012 – Published: 10 January 2013

Abstract. Monitoring the global distribution and long-term of 1.02 ppm. This precision is sufficient for capturing the variations of CO2 sources and sinks is required for charac- winter to summer variability of approximately 12 ppm in the terizing the global carbon budget. Total column measure- lower troposphere; double the variability of the total column. ments are useful for estimating regional-scale fluxes; how- This work shows that a combination of NIR and TIR mea- ever, model transport remains a significant error source, par- surements can profile CO2 with the precision and accuracy ticularly for quantifying local sources and sinks. To im- needed to quantify lower tropospheric CO2 variability. prove the capability of estimating regional fluxes, we estimate lower tropospheric CO2 concentrations from ground- based near-infrared (NIR) measurements with space-based thermal infrared (TIR) measurements. The NIR measure- 1 Introduction ments are obtained from the Total Carbon Column Observing Network (TCCON) of solar measurements, which provide an Our ability to infer surface carbon fluxes depends criti- cally on interpreting spatial and temporal variations of at- estimate of the total CO2 column amount. Estimates of tropo- mospheric CO and relating them back to surface fluxes. For spheric CO2 that are co-located with TCCON are obtained by 2 assimilating Tropospheric Emission Spectrometer (TES) free example, surface CO2 fluxes are typically calculated using surface or near-surface CO measurements along with air- tropospheric CO2 estimates into the GEOS-Chem model. We 2 craft data (Law and Rayner, 1999; Bousquet et al., 2000; find that quantifying lower tropospheric CO2 by subtracting Rayner and O’Brien, 2001; Gurney et al., 2002; Rayner et free tropospheric CO2 estimates from total column estimates is a linear problem, because the calculated random uncer- al., 2008, 2011; Baker et al., 2010; Chevallier et al., 2010, tainties in total column and lower tropospheric estimates are 2011; Keppel-Aleks et al., 2012). More recently it has been consistent with actual uncertainties as compared to aircraft shown that total column CO2 measurements derived from data. For the total column estimates, the random uncertainty ground-based or satellite observations can be used to place is about 0.55 ppm with a bias of −5.66 ppm, consistent with constraints on continental-scale flux estimates (O’Brien and previously published results. After accounting for the total Rayner, 2002; Chevallier, 2007; Chevallier et al., 2011; Keppel-Aleks et al., 2012). However, because CO is a long- column bias, the bias in the lower tropospheric CO2 esti- 2 mates is 0.26 ppm with a precision (one standard deviation) lived greenhouse gas, measurements of the total column CO2 are primarily sensitive to synoptic-scale fluxes (Baker et al.,

Published by Copernicus Publications on behalf of the European Geosciences Union. 64 L. Kuai et al.: Proﬁling tropospheric CO2 using Aura TES and TCCON instruments

2010; Keppel-Aleks et al., 2011); variations in the total column are only partly driven by local surface fluxes, because the total column depends on CO2 from remote locations. Furthermore, the variations caused by the surface source and sinks are largest in the lower tropospheric (LT) CO2 (Sarrat et al., 2007; Keppel-Aleks et al., 2011, 2012). Incorrect spec- ification of the vertical gradient of atmospheric CO2 can also lead to an overestimate of carbon uptake in northern lands and an underestimate of carbon uptake over tropical forests (Stephens et al., 2007). For these reasons we could expect that vertical profile estimates of CO2 will improve constraints on the distributions of carbon flux. Therefore, we are moti- vated to derive a method to estimate the LT CO2 (surface to 600 hPa) from current available column and free tropospheric (FT) observations. Fig. 1. Averaging kernel for TES retrieval (blue) and TCCON re- Total column CO2 data are calculated from solar near- trieval (red). infrared (NIR) measurements from the Total Carbon Col- umn Observing Network (TCCON) (Wunch et al., 2010, 2011a), as well as space-borne instruments, starting from tropospheric CO2, whereas the TCCON total column also SCIAMACHY (Schneising et al., 2011, 2012) and GOSAT has sensitivity to the lower tropospheric CO2. Consequently (Yoshida et al., 2009; Wunch et al., 2011b; Crisp et al., 2012; we expect that combining these measurements will allow for O’Dell et al., 2012). Similar space-borne instruments include estimation of lower tropospheric CO2. This approach has OCO-2 (Crisp et al., 2004) and GOSAT-2, which are ex- been used to estimate lower tropospheric ozone (Worden et pected to be launched in 2014 and later this decade respec- al., 2007; Fu et al., 2012) and carbon monoxide (CO) (Wor- tively. In addition, CarbonSat (Bovensmann et al., 2010; Ve- den et al., 2010). However, we do not use the direct profiling lazco et al., 2011) is a proposed instrument that could also be approach discussed in Christi and Stephens (2004), because launched in the next decade. Ground-based Fourier transfer we found that spectroscopic errors and sampling error due to spectrometer (FTS) measurements such as TCCON instru- poor co-location of the NIR and TIR data currently result in ments have high precision and accuracy compared to satel- unphysical retrieved CO2 profiles. Instead we simply subtract lite instruments but limited spatial coverage. TCCON mea- free tropospheric column estimates from total column esti- surements are therefore a valuable resource for validation of mates in order to quantify lower tropospheric CO2 column SCIAMACHY, GOSAT and OCO-2 satellite measurements. amounts. As long as the retrievals converge and the estimated In addition to the column CO2 from NIR measurements, free states are close to the true states, the problem of subtracting tropospheric CO2 measurements can be made from passive free tropospheric column amount from total column amount thermal infrared satellite instruments such as Tropospheric is a linear problem with well-characterized uncertainties. Emission Spectrometer (TES); (Kulawik et al., 2010, 2012) and AIRS (Chahine et al., 2005). All these measurements by different techniques play important roles in the carbon flux 2 Measurements inversion problem and provide complementary information of the atmospheric CO2 distribution. However, none of these 2.1 Ground-based total column CO2 measurements instruments measure the LT CO2. from TCCON In this paper, we present a method to estimate the LT CO2 by combining column and FT CO2 from two data sources: The column data used to derive LT CO2 in this study total column estimates from TCCON and free tropospheric are from TCCON observations. These observations are ob- estimates from TES data, assimilated into the GEOS-Chem tained by FTS with a precise solar tracking system, which model. We expect this approach to provide estimates of lower measures incoming sunlight with high spectral resolution −1 tropospheric CO2, because the TCCON and TES measure- (0.02 cm ) and high signal-to-noise ratio (SNR) (Washen- ments have complementary sensitivities to the vertical distri- felder et al., 2006). The recorded spectra range between −1 bution of CO2. For example, Fig. 1 shows that TCCON CO2 4000–15 000 cm . These data provide a long-term obser- estimates are sensitive to the total column CO2 as described vation of column-averaged abundance of greenhouse gases, by its averaging kernel. The averaging kernel indicates the such as CO2, CH4,N2O and other trace gases (e.g., CO) sensitivity of the retrieved estimate to the true distribution of over 20 TCCON sites around the world, including both op- CO2. The TES averaging kernel for an estimate of CO2, av- erational and future sites (Yang et al., 2002; Washenfelder et eraged from surface to top-of-atmosphere, is also shown in al., 2006; Deutscher et al., 2010; Wunch et al., 2010; Messer- Fig. 1. Both averaging kernels show sensitivity to the free schmidt et al., 2011). Figure 2 shows a sample measurement

Atmos. Meas. Tech., 6, 63–79, 2013 www.atmos-meas-tech.net/6/63/2013/ L. Kuai et al.: Proﬁling tropospheric CO2 using Aura TES and TCCON instruments 65

Table 1. Surface ﬂuxes used in GEOS-Chem model.

Biosphere CASA-GFED3-v2 (3 h) (cmsflux.jpl.nasa.gov) Biomass burning GFED3-Fire-v2 (daily) (cmsflux.jpl.nasa.gov) Bio fuel GFED3-fuel-v2 (monthly) (cmsflux.jpl.nasa.gov) Fossil fuel CDIAC (monthly) (Nassar et al., 2010) Ocean ECCO2-Darwin (daily) (cmsflux.jpl.nasa.gov) (Brix et al., 2012) Ship ICOADS (monthly) (Nassar et al., 2010) Chemical source GEOS-Chem-V8.2.1 (Nassar et al., 2010) (monthly) Plane emission GEOS-Chem-V8.2.1 (Nassar et al., 2010) (monthly) Chemical surface GEOS-Chem-V8.2.1 (Nassar et al., 2010) (monthly)

2.2 Satellite-based free tropospheric CO2 measurements from TES

Free tropospheric CO2 estimates are derived from thermal IR radiances measured by the Tropospheric Emission Spec- trometer (TES) aboard NASA’s Aura satellite (Beer et al., 2001). The TES instrument measures the infrared radiance emitted by Earth’s surface and atmospheric gases and par- ticles from space. These measurements have peak sensitivity to the mid-tropospheric CO2 at ∼ 500 hPa (Kulawik et al., 2012). The sampling for the TES CO2 measurements is Fig. 2. CO2 band at 1.6 µm observed on 17 June 2008 by TCCON at Park Falls (Wisconsin) with solar zenith angle of 22.5◦. sparse (e.g., 1 measurement every 100 km approximately), and the satellite passes over the Lamont TCCON site ∼ every 16 days (Beer et al., 2001). However, the spatial scales of in the 1.6-µm CO2 absorption band, which is used for analy- variability in the free troposphere are large, which suggests sis here. that TES data can provide useful constraints on free tropo- As discussed in Wunch et al. (2010, 2011a), total column- spheric CO2 over TCCON sites. In order to exploit these averaged abundances can be estimated from TCCON data large scales, we assimilated the TES CO2 measurements into using a non-linear least squares approach that compares a the GEOS-Chem model, a global 3-D chemistry transport forward model spectrum against the observed spectrum. The model (CTM). forward model is dependent on CO2, temperature, water GEOS-Chem (V8.2.1) is driven by assimilated meteoro- vapor (H2O), and instrument parameters. The retrieval ap- logical data from the Goddard Earth Observation System proach adjusts atmospheric CO2 concentrations by scaling an (GEOS) of the NASA Global Modeling and Assimilation Of- a priori CO2 profile until the observed and modeled spectra fice (GMAO). The model supports input data from GEOS-4 ◦ ◦ agree within the noise levels. The precision in the column- (1 × 1.25 horizontal resolution, 55 vertical levels), GEOS- ◦ ◦ averaged CO2 dry air mole fraction from the scaling re- 5 (0.5 × 0.67 , 72 levels), and MERRA (ibid.). The GEOS trievals is better than 0.25 % (Wunch et al., 2010, 2011a). meteorological data archive has a temporal resolution of 6 h The absolute accuracy is ∼ 1 %; after calibration by aircraft except for surface quantities and mixing depths that have ◦ ◦ ◦ ◦ data, the absolute accuracy can reach 0.25 % (Wunch et al., temporal resolution of 3 × 2.5 or 4 × 5 grid resolution 2010, 2011a). by aggregating GEOS meteorological data (Bey et al., 2001). In this paper, we use the optimal estimation method Convective transport in GEOS-Chem is computed from the (Rodgers, 2000) to retrieve a profile that scales multiple lev- convective mass fluxes in the meteorological archive, as de- els of the CO2 profile instead of the whole profile (Kuai scribed by Wu et al. (2007) for GEOS-4, GEOS-5, and et al., 2012). We find that the precision of retrieved col- GISS GCM 3. umn averages of the profile using this approach (0.55 ppm) The original CO2 simulation in GEOS-Chem was de- is consistent with the scaling retrievals described by Wunch scribed by Suntharalingam et al. (2004) and was updated et al. (2010). The profile retrieval algorithm is described in by Nassar et al. (2010). The “bottom-up” inventories used Sect. 4. to force GEOS-Chem are drawn from Nassar et al. (2010) and from the Carbon Monitoring System Flux Pilot Project (http://carbon.nasa.gov) and are available at http://cmsflux. jpl.nasa.gov. The specific inventories are described in Ta- ble 1. TES CO2 and flask measurements have been used to www.atmos-meas-tech.net/6/63/2013/ Atmos. Meas. Tech., 6, 63–79, 2013 66 L. Kuai et al.: Profiling tropospheric CO2 using Aura TES and TCCON instruments

dry constrain time-invariant global carbon fluxes in GEOS-Chem where fg (z) and ndry(z) are the vertical profiles of the dry- (Nassar et al., 2011). Both 3-D variational (3-D var) and 4- air gas volume mixing ratio and number density, respectively, D variational (4-D var) assimilation approaches have been as functions of altitude z. The dry-air column-averaged mole implemented in GEOS-Chem for full oxidant-aerosol chem- fraction of CO2, denoted by XCO2 , is defined as the ratio of istry as well as for CO (Henze et al., 2007, 2009; Kopacz the total dry-air column of CO2 to that of dry air: et al., 2009; Singh et al., 2011a,b). These techniques have C been used to assess the impact of precursors and emissions = CO2 XCO2 (2) on atmospheric composition (Zhang et al., 2009; Walker et Cair al., 2012; Parrington et al., 2012). The 3-D var assimilation where C and C are obtained by Eq. (1). algorithm used here is adapted from Singh et al. (2011b). CO2 air In real atmosphere where the amount of H O cannot be TES at all pressure levels between 40◦ S–40◦ N, along 2 f dry(z) with the predicted sensitivity and errors, was assimilated for neglected, g is formally defined as the year 2009 using 3-D var assimilation. We compare model dry fg(z) output with and without assimilation to surface-based in situ f (z) = . (3) g 1 − f (z) aircraft measurements from the US DOE Atmospheric Radi- H2O ation Measurement (ARM) Southern Great Plains (SGP) site However, the H2O concentration is usually highly variable during the ARM Airborne Carbon Measurements (Biraud dry and may introduce some uncertainties in fg (z). On the et al., 2012, http://www.arm.gov/campaigns/aaf2008acme) other hand, TCCON also provides precise measurements of and HIAPER Pole-to-Pole Observations-II (HIPPO-2; http: O2. Dividing by the retrieved O2 using spectral measure- //hippo.ucar.edu/) campaigns (Kulawik et al., 2012). We find ments from the same instrument improves the precision of model improvement in the seasonal cycle amplitude in the XCO2 by significantly reducing the effects of instrumen- mid-troposphere at the SGP site, but there are model discrep- tal/measurement errors that are common in both gases (e.g., ancies compared with HIPPO at remote oceanic sites, partic- solar tracker pointing errors, zero level offsets, instrument ularly outside of the latitude range of assimilation (Kulawik line shape errors, etc.) (Wunch et al., 2010). Therefore, we et al., 2012). introduce another definition of f dry(z) by normalizing simul- We use the results from the assimilation as our estimates g taneously retrieved O2: of free tropospheric CO2. The uncertainties in the assimilation fields are calculated as the difference from aircraft data dry fg(z) (Sect. 5.2). fg (z) = × 0.2095. (4) fO2 (z) 2.3 Flight measurements Consistent with the discussions in Wunch et al. (2010), the precision of column estimates using O as the dry air stan- Aircraft data are used as our standard to assess the quality of 2 dard will be improved, but the bias specific from the use the different CO estimates. The aircraft measure CO pro- 2 2 of the O band will be transferred to X . For example, files typically up to 6 km and sometimes to 10 km or higher. 2 CO2 Fig. 3 shows total column X estimates, retrieved from For comparison with the TCCON CO estimates, we col- CO2 2 our algorithm, corresponding to aircraft in which data were lected profile observations from different aircraft campaigns, taken from the surface past 10 km. Red points represent such as HIPPO (Wofsy et al., 2011) and Learjet (Abshire X , which is estimated using Eq. (3); black points repre- et al., 2010) (http://www.esrl.noaa.gov/gmd/ccgg/aircraft/qc. CO2 sent X , which is estimated using Eq. (4). Dots are used html), and ARM-SGP (Biraud et al., 2012) (http://www.arm. CO2 for Park Falls site, and diamonds are applied for Lamont site. gov/campaigns/aaf2008acme) over the year 2009. These data As evident from Fig. 3, X estimated using Eq. (4) with are compared to the TCCON CO observations at the Lam- CO2 2 the observed O column has higher precision, but it also has ont site, Oklahoma (36.6◦ N, 97.5◦ W). 2 ∼ 1 % negative bias (Wunch et al., 2010, 2011a). Because the bias is relatively constant over time and over different sites as 3 Calculation of total column and LT CO2 discussed in Wunch et al. (2010), we remove this mean bias in TCCON XCO2 when estimating the total column amount: Our approach is to estimate LT CO2 by subtracting estimates XTCCON ! of partial column CO2 in the free troposphere from the total CO2 CCO = Cair (5) column CO2. The total column of a gas “g”, denoted by Cg, 2 α is obtained by integrating the gas concentration profile from the surface to the top of atmosphere: where α is an empirical correction factor to remove the bias in TCCON column retrievals. ∝(p=0) Z dry Cg = fg (z) · ndry(z) · dz (1) 0

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4 CO2 proﬁle retrieval approach

In this section, we describe a profile retrieval algorithm that is based on the scaling retrieval discussed in Wunch et al. (2010, 2011a). Characterization of the errors, based on this retrieval approach, is discussed in the Appendix. The profile of atmospheric CO2 is obtained by optimal estimation (Rodgers, 2000) using the same line-by-line radiative transfer model discussed in Wunch et al. (2010) (or the standard TCCON retrieval algorithm: GFIT). It computes simulated spectra using 71 vertical levels with 1 km intervals for the input atmospheric state (e.g., CO2,H2O, HDO, CH4,O2, P, T, etc.). The details about the TCCON instrument setup and Fig. 3. Comparison of XCO2 estimates to derived aircraft column averages. Red points indicate that H2O is used as dry air standard. GFIT are also described in Yang et al. (2002), Washenfelder Black points indicate that O2 is used as dry air standard. Dots are et al. (2006), Deutscher et al. (2010), Geibel et al. (2010) for Park Falls site and diamonds for Lamont site. Error bars are not and Wunch et al. (2010, 2011a). The retrievals in this study shown in this figure. use one of TCCON-measured CO2 absorption bands, centered at 6220.00 cm−1 with a window width of 80.00 cm−1 (Fig. 2). Note that ultimately we do not use the full profiles The partial vertical column amount of CO2 in free tro- for this study as we find that spectroscopic or other errors in- posphere and above (CTROP) is estimated by integrating the CO2 troduce vertical oscillations into the estimated profiles with TES/GEOS-Chem assimilated profile (f TES) above 600 hPa. larger values than expected in the upper troposphere that are CO2 compensated by lower values than expected in the lower troposphere. The same effect is found in the GOSAT CO re- ∝(p=0) 2 Z trievals as discussed in O’Dell et al. (2012). This vertical os- CTROP = f TES(z) · n (z) · dz. (6) CO2 CO2 dry cillation is one of the potential issues in joint retrievals by z(p=600) combining NIR and TIR (thermal infrared) radiance in addition to the limitation of the coincident measurements from The partial vertical column amount of CO2 in the LT can two different instruments. However, the total columns of then be computed as the difference between the total column these profiles are still good estimates with well-characterized amount (Eq. 6) and partial free tropospheric column amount errors as discussed in Sect. 5.1. Therefore, the profiles are (Eq. 7): mapped into column amounts and are shown to be consistent with the results of Wunch et al. (2011a). We use a profile re- ∝(p=0) XTCCON ! Z trieval instead of standard TCCON column scaling retrieval LT CO2 TES C = Cair − f (z) · ndry(z) · dz. (7) CO2 α CO2 in order to understand the error characteristics of the CO2 z(p=600) retrieval. In the scaling retrieval discussed by Wunch et al. (2010, Applying Eq. (3) within the lower troposphere gives the esti- LT 2011a), the retrieved state vector (γ ) includes the eight con- mate of the LT CO2 mole fraction (X ); the ratio of partial CO2 stant scaling factors for four absorption gases (CO2,H2O, = z(p 600) HDO, and CH ) and four instrument parameters (continuum vertical column between CO (CLT ) and air (CLT = R 4 2 CO2 air 0 level: “cl”, continuum tilt: “ct”, frequency shift: “fs”, and 1 · ndry(z) · dz) is zero level offset: “zo”).

TCCON ∝(p=0) ∝(p=0)   XCO γ[ ] 2 R 1 · n (z) · dz − R f TES(z) · n (z) · dz CO2 α dry CO2 dry 0 z(p=600)  γ[H O]  XLT = (8) 2 CO2 600   R  γ[HDO]  1 · ndry(z) · dz   ps  γ[CH ]  γ =  4  (9)  γcl  LT   where X is defined as the TCCON/TES LT CO2. These  γct  CO2   estimates can be compared to the integrated partial column-  γfs  averaged CO2 measured by aircraft within the lower tropo- γzo sphere (surface to 600 hPa for Lamont). Each element of γ is a ratio between the state vector (x) and its a priori (xa). In the profile retrieval, for the target gas www.atmos-meas-tech.net/6/63/2013/ Atmos. Meas. Tech., 6, 63–79, 2013 68 L. Kuai et al.: Profiling tropospheric CO2 using Aura TES and TCCON instruments

According to the above deﬁnition, the a priori proﬁle is ˆ xa = Mx βa and estimated state is xˆ = Mx β. The non-linear least squares retrieval is a standard optimal estimation retrieval that employs an a priori constraint matrix to regularize the problem (Rodgers, 2000; Bowman et al., 2006). The non-diagonal CO2 covariance matrix used to generate the constraint matrix has larger variance in the lower troposphere and decreases with altitude. This covariance is generated using the GEOS-Chem model as guidance. However, we scale the diagonals of the covariance matrix in order to match the variability observed at the TCCON sites. The square root of the diagonal of this covariance is approximately 2 % (8 ppm) in the lower troposphere, 1 % (4 ppm) in the free troposphere, and less than 1 % (4 ppm) in the stratosphere (Fig. 4a). The off-diagonal correlations are shown in Fig. 4b. The elements of the a priori covariance corresponding to the other retrieved parameters (e.g., H2O) are set to be equivalent to 100 % uncertainty. The measurement noise, or signal-to-noise ratio (SNR) is used to weight the measurement relative to the a priori in the non-linear least squares retrieval. Although the SNR of the TCCON instrument is better than 500, we use a SNR of approximately 200, because spectroscopic uncertainties Fig. 4. (a) The square root of the diagonal in CO2 covariance ma- degrade the comparison (O’Dell et al., 2011; Wunch et al., trix. (b) The 2-D plot of the CO2 covariance matrix. 2011a); use of this SNR results in a chi-square in our retrievals of about 1. To obtain the best estimate of the state vector that mini- (CO2), we estimate the altitude-dependent scaling factors in- mizes the difference between the observed spectral radiances stead. For other interfering gases, a single scaling factor is (yo) and the forward model spectral radiances (ym), we per- retrieved. Ten levels are chosen for CO2 (see Fig. 4a) to cap- form Bayesian optimization by minimizing the cost function, ture its vertical variation: χ(γ ):   γ1[CO2] = − T −1 − + − T −1 −  .  χ(γ ) (ym yo) Se (ym yo) (γ γ a) Sa (γ γ a) (13)  .     γ10[CO ]  where S is chosen to be the covariance shown in Fig. 4 and  2  a  γ[H O]  S is the measurement noise covariance, a diagonal matrix  2  e =  γ[HDO]  with values of noise squared. Noise is inverse of SNR. γ  . (10)  γ[CH ]   4   γcl    5 Results  γct     γfs  5.1 Quality of the column-averaged CO2 estimates γzo

To obtain a profile of volume mixing ratio, the retrieved scal- To characterize the quality of the CO2 estimates, we com- ing factors need to be mapped from retrieval grid (i.e., 10 lev- pare the TCCON column-averaged estimates with the aircraft els for CO2 and 1 level for other three gases) to the 71 for- column-integrated data. Calculated errors (as derived in the ward model levels. Appendix) are compared to actual errors as derived empir- ically from comparison of the estimates to the aircraft data β = Mγ (11) and are shown to be consistent. ∂β There are 41 SGP aircraft-measured CO2 profiles in 2009 where M = ∂γ is a linear mapping matrix relating retrieval level to the forward model altitude grid. Multiplying the scal- (Fig. 5). Most aircraft measurements are from the surface to ∂x 6 km; however, three profiles have measurements from the ing factor (β) on the forward model level to Mx = , a diag- ∂β surface to 10 km or higher (31 July, 2 and 3 August). To es- onal matrix of the concentration a priori (xa), gives the true state of gas profile: timate the total column, the CO2 values for altitudes above the top of the aircraft measurements are replaced by the TC- x = Mx β. (12) CON CO2 a priori, shifted to match the mean aircraft value

Atmos. Meas. Tech., 6, 63–79, 2013 www.atmos-meas-tech.net/6/63/2013/ L. Kuai et al.: Proﬁling tropospheric CO2 using Aura TES and TCCON instruments 69

Fig. 5. Samples of CO2 profiles measured by aircraft (black) and TES/GEOS-Chem assimilation (red) at SGP. at the top of the aircraft profile. As discussed in the Appendix (A1.2.1), this approximation to the upper tropospheric CO2 values negligibly contributes to uncertainty in the compar- + ison between TCCON XCO2 estimates and the aircraft shifted upper troposphere a priori profiles. The comparisons between TCCON column averages and the derived aircraft column averages are summarized in Fig. 6 and Table 2.

TCCON XCO2 estimates are calculated within a 4-h time window, centered about the time corresponding to each aircraft profile. A 4-h time window is chosen to ensure that comparisons are statistically meaningful and also to ensure that variations in CO2 and temperature are small relative to calculated uncertainties. Comparisons between TCCON and Fig. 6. Comparison of X from TCCON profile retrievals to that aircraft X are shown in Table 2. Results listed in Ta- CO2 CO2 derived from aircraft. Black dots indicate comparison of TCCON ble 2 are only for clear-sky scenes, because it is difficult to estimates to aircraft that measure up to 6 km. Green dots are com- quantify the effect of clouds on the TCCON retrievals and parison of TCCON estimates to the three aircraft profiles that mea- errors. We find that the calculated precision for the collec- sure up to 12 km. tion of measurements within each 4-h time window encom- passing the aircraft is, on average, approximately 0.32 ppm. This precision is, on average, consistent with the variability average by −5.66 ± 0.55 ppm. The magnitude of this bias es- of the TCCON XCO2 estimates within this 4-h time window timate is consistent with that described in Wunch et al. (2010) of 0.35 ppm. The error on the mean will be arbitrarily small and is attributed to errors in the O2 spectroscopy. The error because of the large number of measurements within this 4-h in the bias (0.55 ppm) is consistent with the calculated error time window. Consequently, we expect that the XCO2 vari- due to temperature (0.69 ppm) and is a result of temperature ability within each 4-h time window is driven by noise and variations between aircraft measurements. not by variations in temperature and CO2. However, we calculate that errors in temperature lead to an error in XCO2 of approximately 0.69 ppm on average (last column, Table 2).

We ﬁnd that the TCCON XCO2 estimates are biased on www.atmos-meas-tech.net/6/63/2013/ Atmos. Meas. Tech., 6, 63–79, 2013 70 L. Kuai et al.: Proﬁling tropospheric CO2 using Aura TES and TCCON instruments

Table 2. Lists of bias error and its standard deviation (1 × σ ) of TCCON profile retrieved column averages within 4-h time window of each flight measurement. The expected uncertainties from measurement error covariance and the temperature error covariance are also listed in the last two columns. To remove the unclear sky spectra measurements, we dismiss the retrievals when the parameter “fvis” (fractional variation in solar intensity) is greater than 0.05, which suggests the cloud coverage during the spectra measurement. By applying the cloud filter, the consistency between the empirical error estimates and expected error estimates is improved. The columns for “n” are the total numbers of retrievals within 4-h time window.

Unit (ppm) With cloud ﬁlter Expected day Day (yyyymmdd) Bias + 5.66 (ppm) Actual (1 × σ ) n σ (δXh ) σ (δX ) CO2 CO2 20090108 0.66 0.30 161 0.27 0.74 20090116 0.45 0.30 171 0.33 0.74 20090129 0.36 0.30 169 0.34 0.77 20090204 0.58 0.26 169 0.33 0.74 20090211 0.69 0.49 90 0.33 0.75 20090219 0.39 0.38 96 0.33 0.76 20090221 0.67 0.42 130 0.34 0.77 20090308 0.25 0.39 132 0.32 0.71 20090314 0.98 0.42 102 0.33 0.73 20090316 0.00 0.27 154 0.32 0.69 20090318 0.26 0.44 112 0.32 0.69 20090329 −0.08 0.28 76 0.33 0.72 20090407 0.13 0.26 98 0.33 0.72 20090408 −0.03 0.40 121 0.32 0.69 20090420 −0.59 0.44 69 0.32 0.70 20090421 −0.32 0.29 130 0.32 0.70 20090423 −0.21 0.30 122 0.32 0.66 20090517 −0.19 0.32 130 0.32 0.70 20090518 0.82 0.32 131 0.32 0.68 20090520 0.60 0.50 75 0.32 0.67 20090526 −0.12 0.36 86 0.32 0.67 20090528 0.11 0.30 130 0.32 0.68 20090530 0.30 0.34 130 0.32 0.66 20090604 0.01 0.38 128 0.32 0.68 20090612 −0.96 0.35 72 0.32 0.66 20090616 −1.31 0.34 128 0.31 0.64 20090621 −0.85 0.28 95 0.31 0.63 20090623 −0.56 0.32 129 0.31 0.63 20090629 0.16 0.32 118 0.31 0.64 20090701 −0.24 0.46 119 0.31 0.65 20090706 0.85 0.33 43 0.32 0.66 20090731 0.31 0.34 125 0.32 0.66 20090802 0.26 0.29 131 0.31 0.65 20090803 −0.37 0.33 130 0.31 0.63 20090823 −0.74 0.38 130 0.31 0.65 20091101 −0.47 0.36 130 0.32 0.68 20091102 −0.68 0.33 131 0.32 0.69 20091103 −0.94 0.35 131 0.32 0.70 20091122 −0.38 0.39 68 0.32 0.71 20091218 −0.23 0.47 127 0.33 0.75 20091220 0.33 0.38 101 0.33 0.72 Mean 0.00 0.35 118 0.32 0.69 1 × σ 0.55

Atmos. Meas. Tech., 6, 63–79, 2013 www.atmos-meas-tech.net/6/63/2013/ L. Kuai et al.: Proﬁling tropospheric CO2 using Aura TES and TCCON instruments 71

Fig. 7. (a) Comparison of LT CO2 estimates derived from integrating from surface to 600 hPa by TCCON prior and aircraft. (b) Comparison of LT CO2 estimates derived from TCCON and TES with aircraft.

5.2 Quality of the LT CO2 estimates Table 3. Bias and precision comparisons.

In this section we examine the robustness of estimates of Unit (ppm) Bias Precision the LT CO (surface to 600 hPa) by comparison of the TC- Total column CO2 [TCCON prior] 1.04 1.50 2 [TCCON] −5.66 0.55 CON/TES LT CO2 to aircraft estimates. We separate the FT CO2 [TCCON prior] 0.23 1.33 lower troposphere from the free troposphere at the 600 hPa (Above 600 hPa) [TCCON] −1.62 1.50 pressure level, because the aircraft profiles indicate that the [GEOS-Chem] 0.91 1.22 [ ] variability in the free troposphere becomes “small” above TES/GEOS-Chem 0.38 0.71 LT CO2 [TCCON prior] 2.17 2.05 this pressure (Fig. 5) relative to the variability below this (Surface to 600 hPa) [TCCON] −4.91 1.39 level and it is well above the boundary layer height, which [GEOS-Chem] 0.13 1.92 varies depending on the location and time of the day. The [TES/GEOS-Chem] 0.73 2.86 [TCCON] − [TES/GEOS-Chem] 0.26 1.02 knowledge of the boundary layer height will affect the use of these LT estimates for quantifying surface fluxes, because boundary layer heights are typically at higher pressures than 600 hPa (von Engeln et al., 2005). Figure 7a compares the estimate compared to the TCCON priori, GEOS-Chem mod- LT CO2 estimates that are calculated from integrating TC- eling and TES/GEOS-Chem assimilation. In addition, the CON prior from surface to 600 hPa to the aircraft estimates. improvement in the TCCON/TES LT CO2 (1.02 ppm), rel- Figure 7b compares the LT CO2 estimates that are calcu- ative to the TCCON priori (2.0 ppm), is mainly during sum- lated from TCCON and TES data to the aircraft estimates. mertime when surface CO2 is low relative to wintertime, be- The root-mean-square (RMS) of the fitted line (1.02 ppm) cause the biosphere is more active in the summer (Fig. 7). in Fig. 7b is smaller than that if the TCCON prior data are With these uncertainties, the LT CO2 estimates are able to used in Fig. 7a (2.02 ppm). The −5.66 ppm bias (or factor α capture the seasonal variability of the lower troposphere as in Eq. 9) is removed from the TCCON total column before discussed next. computing the LT CO2 using TCCON data and TES data. As shown in Table 3, the average difference between TC- 5.3 Seasonal variability of LT CO2 compared to column CON/TES LT CO2 and aircraft values is 0.26 ± 1.02 ppm. CO2 The calculated uncertainty (Appendix A4, Eq. A28) depends on the quadratic sum of the uncertainties of TES free tro- The aircraft, TCCON, and TES assimilated estimates of at- pospheric estimates (∼ 0.71 ppm) and TCCON column es- mospheric CO2 have sufficient temporal density to provide timates (∼ 0.55), resulting in an estimate of uncertainty of an estimate of CO2 variability over most of the year. In Fig. 8 0.90 ppm. This calculated uncertainty of 0.90 ppm is consis- we show the monthly averaged total column averages and tent with the actual uncertainty of 1.02 ppm. For total column the partial column averages (surface to 600 hPa) calculated CO2, the retrieved value from TCCON measurement is a bet- from the aircraft data and the same quantities derived from ter estimate than TCCON prior. For free tropospheric CO2, the TCCON data and the TCCON minus TES assimilated the assimilated value from TES/GEOS-Chem has the small- data respectively. The TCCON column averages (black dots) est uncertainty (0.71 ppm) and is thus a better estimate com- and TCCON/TES derived LT data (red dots) are consistent pared to the other estimates (e.g., TCCON prior, TCCON re- with the aircraft measurement (black diamonds and red dia- trieval, or GEOS-Chem modeling). As a result, for LT CO2, monds) within the expected uncertainties indicating that the the retrieved value from the TCCON/TES retrieval is the best estimates are robust. We use a total of 41 aircraft profiles. www.atmos-meas-tech.net/6/63/2013/ Atmos. Meas. Tech., 6, 63–79, 2013 72 L. Kuai et al.: Profiling tropospheric CO2 using Aura TES and TCCON instruments

the measurement error. When comparing the TCCON total column estimates to aircraft data over several days, we can assume that the daily systematic errors due to temperature or other interference error are pseudo-random. For example, the estimated mean bias across multiple days is −5.66 (± 0.55) ppm. The standard deviation of the bias error of approximately 0.55 ppm is consistent with the expected error of 0.69 ppm, which is primarily driven by temperature error, because measurement error for these comparisons is arbitrarily small due to the large number of measurements used to calculate the mean CO2 estimate. Comparisons of the aircraft data to free tropospheric CO2, calculated by assimilating Aura TES CO2 estimates into the Fig. 8. Monthly mean XCO2 for total column and LT CO2 in 2009 at Lamont. Aircraft data (FLT) are indicated by diamonds (black GEOS-Chem model (Nassar et al., 2011), suggest that the TES assimilated data have a bias error of 0.38 (± 0.71) ppm for total XCO2 ; red for LT CO2) and TCCON or TCCON/TES estimates are indicated by black or red dots with error bars. in the free troposphere. We calculated a lower tropospheric estimate (surface to 600 hPa) of the CO2 amount by subtracting the TES assimilated free tropospheric estimate from Typically 3–5 profiles have been averaged in a month. How- the TCCON total column amount estimates. Comparisons of ever, September and October both have only one available these lower tropospheric estimates from TCCON/TES data aircraft profile, which were measured under cloudy skies. So to those from aircraft data are consistent after the bias in the September and October data cannot be used in this study. TCCON is removed. The precision in the derived LT CO2 is Therefore, the comparisons for these two months are not 1.02 ppm, which is consistent with the calculated precision shown. In Fig. 8, both TCCON column averages and TC- of 0.90 ppm. The dominant sources of the error in the LT es- CON/TES LT CO2 capture the seasonal variability. timates are due to uncertainties in the free troposphere data The response of the seasonal variability in LT CO2 is more from TES assimilation and the temperature-driven error in than twice that of the column averages with a 14-ppm peak- column averages from TCCON. We show that this precision to-trough in LT CO2 and 5 ppm in the column-averaged CO2. is sufficient to characterize the seasonal variability of lower This increased variability is due to a rapid drawdown in LT tropospheric CO2 over the Lamont TCCON site. CO2 at the growing season onset over mid-latitude due to the The approach described in this paper shows that the prob- biosphere uptake. lem of using independent total column and free tropospheric estimates to estimate lower tropospheric CO2 is a linear problem. This linear problem is in contrast to using a non-linear 6 Summary retrieval for quantifying lower tropospheric ozone (Worden et al., 2007) or CO (Worden et al., 2010) by using reflected Total column estimates of atmospheric CO2 and partial col- sunlight and thermal IR radiances and is likely, because umn estimates of CO2 in the lower troposphere (surface to ozone and CO can have much larger variance in the lower 600 hPa) are calculated using TCCON and Aura TES data. In troposphere than CO2. order to determine if the retrieval approach, forward model, The study shown here indicates that assimilating total col- and understanding of uncertainties are robust, it is crucial umn and free tropospheric CO2 will increase sensitivity to to determine if the calculated uncertainties are consistent surface fluxes by placing improved constraints on lower tro- with the actual uncertainties. In addition, we need to assess pospheric CO2. Furthermore, quantifying lower tropospheric any biases in the estimates and ideally attribute these bias CO2 using total column and free tropospheric estimates is errors in the measurement system. The bias and its uncer- useful for evaluating model estimates of lower troposphere. tainties in TCCON column-averaged CO2 are explained at This study also highlights the potential of combining si- two different time scales: 4-h time windows centered about multaneous measurements from NIR and IR sounding in- individual aircraft measurement and day-to-day time scales struments to obtain vertical information of atmospheric CO2 from comparison to the collection of 41 aircraft profiles. (Christi and Stephens, 2004). Column estimates of CO2 We find that, for multiple retrievals of the same air parcel by space are currently available from GOSAT (Yoshida et within a 4-h time window, the mean bias is from the un- al., 2009) and SCIAMACHY data (Schneising et al., 2011, certainties of atmospheric states (i.e., temperature or inter- 2012) and are expected from OCO-2. Column CO2 esti- ference gases) or spectroscopic parameters. The variability mates from these satellite data together with the free tropo- of the collection of total column estimates within the 4-h spheric CO2 estimates are anticipated to provide complemen- time window of 0.35 ppm is consistent with the calculated tary constraints to infer CO2 fluxes and advance the ability random error of about 0.32 ppm, which is associated with to study the carbon cycle problem by providing constraints

Atmos. Meas. Tech., 6, 63–79, 2013 www.atmos-meas-tech.net/6/63/2013/ L. Kuai et al.: Profiling tropospheric CO2 using Aura TES and TCCON instruments 73 on near-surface CO2 variations and atmospheric mixing. Our scaling factor (β) on the forward model level to the concen- future work will apply this method to combine GOSAT and tration a priori (xa) gives the estimates of the gas profile. We ∂x TES data to expand the spatial coverage of these lower tro- define Mx = ∂β where Mx is a diagonal matrix filled by the pospheric CO2 estimates. concentration a priori (xa): ˆ xˆ = Mx β. (A3) Appendix A From Eq. (A3), it follows that xa = Mx βa and x = Mx β. The Jacobian matrix of retrieved parameter with respect to the Error characterization radiance is ∂L(Mγ ) One of the reasons we used optimal estimation to retrieve the Kγ = . (A4) CO2 profile and then map the profile to the total column CO2 ∂γ instead of using the standard TCCON product is that the op- Using the chain rule, we can obtain the equation relating the timal estimation allows us to characterize the error budget. Jacobians on retrieval levels to the full-state Jacobian: This appendix estimates the expected errors and shows how ∂L ∂L ∂x ∂β = (A5) these terms compare to the actual errors. Careful characteri- ∂γ ∂x ∂β ∂γ zation of the errors is critical for evaluating the retrieval me- or chanics and for use of these data for scientific analysis. Kγ = Kx Mx M = Kβ M. (A6) A1 Errors in TCCON column-averaged CO2 If the estimated state is “close” to the true state, then the es- In this section, we develop the error characterization for timated state for a single measurement can be expressed as a (1) the estimates of TCCON CO2 column averages from the linear retrieval equation (Rodgers, 2000): profile retrievals for a 4-h time window around each aircraft ˆ X l l β = βa +Aβ (β − βa)+MGγ εn + MGγ Kb 1b (A7) CO2 profile measurement and (2) comparisons of TCCON l estimates against 41 aircraft profiles. where ε is a zero-mean noise vector with covariance S and In addition to CO , we also retrieve a column amount of n e 2 the vector 1bl is the error in true state of parameters (l) that H O, HDO and four instrument parameters. This set of re- 2 also affect the modeled radiance, e.g., temperature, interfer- trieval parameters is defined in the following retrieval vector ing gases, spectroscopy. The Kl is the Jacobian of parameter (see Sect. 4): b (l). In this study, we found the systematic error is primarily   due to the temperature uncertainty (ε ) and spectroscopic er- γ1[CO2] T  .  ror (εL). Gγ is the gain matrix, which is defined by  .  −1   ∂γ T −1 −1 T −1  γ10[CO2]  = = +   Gγ Kγ Se Kγ Sa Kγ Se . (A8)  γ[H O]  ∂L  2  =  γ[HDO]  The averaging kernel for β in forward model dimension is γ  . (A1)  γ[CH4]    Aβ = MGγ Kβ . (A9)  γcl    −1  γct  We can define Ax = Mx Aβ M as the averaging kernel for   x  γfs  the concentration profile x. In order to convert Eq. (A7) to γzo the state vector of concentration (xˆ ), we apply Eq. (A7) into Eq. (A3): Each element of γ is a ratio between the state vector (x) and xˆ = x + A (x − x ) + M MG ε its a priori (xa). For the target gas CO2, altitude-dependent a x a x γ n scaling factors are retrieved. For other interfering gases, a +Mx MGγ KT εT + Mx MGγ KL εL. (A10) constant scaling factor for the whole profile is retrieved. The The temperature uncertainty (εT ) and spectroscopic error last four are for the instrument parameters (continuum level: l (εL) represent the systematic errors (1b ). “cl”, continuum title: “ct”, frequency shift: “fs”, and zero level offset: “zo”). To obtain a concentration profile, the re- A2 Total error budget trieved scaling factors are mapped from the retrieval grid (i.e., 10 levels for CO2 and 1 level for other three gases) to The total error for a single retrieval is the difference between the 71 forward model levels. the estimated state vector (Eq. A10) and the true state vector (x): β = Mγ (A2) δxˆ = xˆ − x = (I − Ax)(xa − x) + Mx MGγ εn where M = ∂β is a linear mapping matrix relating retrieval ∂γ +Mx MGγ KT εT + Mx MGγ KL εL. (A11) levels to the forward model altitude grid. Multiplying the www.atmos-meas-tech.net/6/63/2013/ Atmos. Meas. Tech., 6, 63–79, 2013 74 L. Kuai et al.: Profiling tropospheric CO2 using Aura TES and TCCON instruments

The second-order statistics for the error is have a precision of 0.02 ppm. With the validation standard, the error in the retrieval (δxˆ ) can be estimated by the compar- ˆ ˆ ˆ ˆ Sδxˆ = Ssm + Sm + ST + SL (A12) ison of the retrieved state vector (xˆ ) to the validation standard (xˆ ). In order to do an inter-comparison of the measure- where the smoothing error covariance is std ments from two different instruments, we apply a smoothing ˆ T Ssm = (I − Ax) Sa (I − Ax) ; (A13) operator described in Rodgers and Connor (2003) to the complete profile (xFLT) based on aircraft measurement so that it a measurement error covariance is is smoothed by the averaging kernel and a priori constraint ˆ T from the TCCON profile retrieval: Sm = Mx MGSe (Mx MG) , (A14) xˆ std = xa + Ax (xFLT − xa). (A17) and two systematic error covariance matrices are xˆ is the profile that would be retrieved from TCCON mea- Sˆ = M MGK S (M MGK )T (A15) std T x T T x T surements for the same air sampled by the aircraft without ˆ = T SL Mx MGKL SL (Mx MGKL) . (A16) the presence of other errors. xFLT is the complete CO2 profile based on aircraft measurement. Sa is the a priori covariance for CO2, Se the covariance de- Several aircraft only measure CO2 up to approximately scribing the TCCON measurement noise (see Sect. 4), ST the a priori covariance for temperature and based on the a pri- 6 km, but three of them go up to 10 km or higher, which are ori covariance used for the Aura TES temperature retrievals measured by Learjet on 31 July, 2 and 3 August (Fig. 5). (Worden et al., 2004); this temperature covariance is based These three profiles show that the free troposphere is well on the expected uncertainty in the re-analysis fields that are mixed and the vertical gradient is small (Wofsy et al., 2011), less than 1 ppm km−1 on average between 600 hPa inputs to the TES retrievals. SL is the covariance associated with spectroscopic error. It has been found that spectroscopic and tropopause. Therefore, the lower part of xFLT is from inadequacies are common to all retrievals from TCCON ra- the direct aircraft measurements. Above that, the TCCON diances (e.g., line widths, neglect of line-mixing, inconsis- prior is scaled to the measured CO2 values at the top of the tencies in the relative strengths of weak and strong lines) aircraft measurement so that the profile is continuously ex- (Wunch et al., 2010). tended up to 71 km. Then the complete profile based on the aircraft measurement is A3 Individual error budget terms xmeas δxmeas x = FLT = x − δx = x − FLT (A18) FLT λxF FLT xF − λxF Considering different time scales, the uncertainties of the es- a a meas timates would be attributed to different error terms. In this where xFLT is the direct aircraft measurements in the lower section, we will discuss the error terms one by one. atmosphere, which has been mapped to forward model grid. meas For comparisons of TCCON retrievals to each aircraft pro- δxFLT is its unknown error relative to the “truth” and is of file, we choose the TCCON measurements taken within a 4-h the order of 0.02 ppm. λ is the ratio between the CO2 at the time window centered about the aircraft measurement. This top of aircraft measurement to the a priori CO2 on that level. F F time window is short enough so that we can assume the at- xa and x represent the a priori and “true” state above direct F mospheric state has not changed, but it is also long enough aircraft measurement in the free troposphere and above. λxa that there are enough samples of retrievals for good statistics is the shifted a priori to smoothly extend the profile up to (e.g., ∼ 100 samples). the stratosphere. xFLT represents the complete profile based There are 41 aircraft measurements that measured CO2 combining a priori. δxFLT is the unknown error in the xFLT profiles over Lamont in 2009. On any given day (or i-th to the true state. day), we have ni TCCON retrievals within a 4-h time win- Subtracting Eq. (A27) from Eq. (A10) results in the fol- dow around aircraft measurement where ni varies by day (or lowing expression: aircraft profile comparison). The difference of the mean of ˆ = ˆ − ˆ = + these retrievals to the aircraft measurement can be used to δx x xstd Ax δxFLT Mx MGγ εn compute the error of the mean estimate due to temperature. +Mx MGγ KT εT + Mx MGγ KL εL. (A19) The average of the errors from these 41 comparisons esti- The second-order statistics for the error in the complete mates the mean bias error. Which term contributes to the un- aircraft-based profile, δxFLT, is: certainties will be discussed in follow. T Sδ xFLT = E [δxFLT − E (δxFLT)][xFLT − E (δxFLT)] A3.1 Error due to extrapolation of CO2 above aircraft meas SFLT 0 profile = F . (A20) 0 Sa meas In reality, the true state (x) is unknown and can only be esti- SFLT is the error covariance for direct aircraft measurements, mated by our best measurements, such as by aircraft, which which is a diagonal matrix with a constant value of the square

Atmos. Meas. Tech., 6, 63–79, 2013 www.atmos-meas-tech.net/6/63/2013/ L. Kuai et al.: Profiling tropospheric CO2 using Aura TES and TCCON instruments 75 of 0.02 ppm (the precision of aircraft instruments) (Wunch et with a covariance of F al., 2010). Sa is the submatrix of TCCON prior covariance q matrix above the aircraft measurements. Since we scale the = T ˆ σT δXCO2 h ST h (A26) a priori to the aircraft data, the actual error covariance in the F ˆ upper atmosphere should be much smaller than Sa . where ST is from Eq. (A25). The estimate of this term is, on The uncertainty in retrieved column averages driven by the average, approximately 0.69 ppm. smoothing error can be estimated by A3.4 Spectroscopic error q T T σsm δXCO = h Ax Sδ xFLT A h. (A21) 2 x The spectroscopic error is another significant source of sys- The upper limit of this uncertainty is approximately 0.5 ppm tematic error. Different from temperature error, it does not when using the a priori covariance in the upper atmosphere vary significantly on any time scales or even over different where the aircraft measurement is missing (e.g., above 6 km). sites (Wunch et al., 2010). Therefore, its covariance is always Since the free troposphere is well mixed and the upper atmo- negligible. However, it is found to be the primary source of sphere is constrained by the aircraft measurement, the ac- the bias error. tual uncertainty for the validation standard should be much δX = hT M MG K ε . (A27) smaller than above estimates. For example, if we assume CO2 L x γ L L conservatively that the term S is half the size of the S δxFLT a The estimate of this term is about −5 ppm. It is mainly due used to describe our CO covariance, then this term becomes 2 to the error in O cross section. negligible relative to the temperature error. 2 A4 Errors in LT column-averaged CO A3.2 Measurement error 2 We estimate the LT CO by subtracting the TES assimilated The measurement noise vector ε is a zero-mean random 2 n free tropospheric CO from the TCCON total column CO . variable. In a 4-h time window, the measurement error co- 2 2 The TCCON dry-air total column estimated by weighting the variance will drive the variability of the retrieved column av- retrieved O column has a bias of approximately −5.66 ppm. erages. The uncertainty in retrieved column averages driven 2 Therefore, we remove the bias using Eq. (9) before subtract- by the measurement error can be estimated by ing the free tropospheric partial column amount. Because the q TCCON estimates and TES/GEOS-Chem estimates are in- σ δX = hT Sˆ h (A22) m CO2 m dependent estimates of CO2, the uncertainties in the lower ˆ tropospheric estimates are simply the uncertainties summed where Sm is defined in Eq. (A14). We calculate that this term in quadrature: is approximately 0.32 ppm. The error on the mean is related to the number of samples in 4-h time window: r σ δXLT = σ 2 δXTES + σ 2 δXTCCON . (A28) s CO2 CO2 CO2 T ˆ h Sm h σm δXCO = (A23) The estimate of this term is 0.90 ppm. The TES as- 2 n i similated free tropospheric bias error and uncertainty where ni is number of retrieval samples within 4-h on i-th (0.38 ± 0.71 ppm) is estimated by the comparison to the free day (listed in Table 2). tropospheric estimates from the aircraft-based profile (xFLT). The TCCON total column mean bias error and uncertainty A3.3 Temperature error (−5.66 ± 0.55 ppm) has been discussed in previous section.

Within a 4-h time window, we assume that variations in temperature do not result in variations in the CO2 estimate; however, the uncertainty in the temperature profiles will result in Acknowledgements. Part of this research was carried out at the Jet a bias: Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. T The GEOS-Chem model results with assimilated TES data was δXCO = h Mx MGγ KT εT . (A24) 2 Ti i funded by proposal No. 09-ACOS09-0010. US funding for TCCON comes from NASA’s Terrestrial Ecology Program, grant number However, εTi varies from day to day. The mean bias error from temperature uncertainties over days becomes NNX11AG01G, the Orbiting Carbon Observatory Program, the Atmospheric CO2 Observations from Space (ACOS) Program and m ! the DOE/ARM Program. SGP data was supported by the Office of 1 X δX = hT M MG K ε (A25) Biological and Environmental Research of the US Department of CO2 T x γ T m Ti i=1 Energy under contract No. DE-AC02-05CH11231 as part of the Atmospheric Radiation Measurement Program. The authors wish www.atmos-meas-tech.net/6/63/2013/ Atmos. Meas. Tech., 6, 63–79, 2013 76 L. Kuai et al.: Profiling tropospheric CO2 using Aura TES and TCCON instruments to thank G. Toon and P. Wennberg for making available their GFIT Chevallier, F., Ciais, P., Conway, T. J., Aalto, T., Anderson, B. E., code and TCCON data. Bousquet, P., Brunke, E. G., Ciattaglia, L., Esaki, Y., Frohlich, M., Gomez, A., Gomez-Pelaez, A. J., Haszpra, L., Krummel, P. Edited by: K. Strong B., Langenfelds, R. L., Leuenberger, M., Machida, T., Maignan, F., Matsueda, H., Morgui, J. A., Mukai, H., Nakazawa, T., Peylin, P., Ramonet, M., Rivier, L., Sawa, Y., Schmidt, M., Steele, L. P., Vay, S. A., Vermeulen, A. 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