1. Introduction

Carbon dioxide (CO₂), as the most important anthropogenic enhanced global greenhouse gas, and has continued to increase since the industrial revolution [1]. This CO₂ increase has been deeply influencing global climate, flora and fauna. From 2002 to 2011, the rate of increase in CO₂ is approximately 2.0 ± 0.1 ppm yr⁻¹, coinciding with emission reduction efforts worldwide [2]. In recent times, anthropogenic sources have emitted more than 9 GtC yr⁻¹ CO₂ into the atmosphere [2,3]. The anthropogenic CO₂ emission increase is mainly attributed to anthropogenic activities, like fossil fuel burning, industrial activity and land use-change [4]. Prediction of the evolution of atmospheric greenhouses requires detailed understanding of their sources and sinks [5]. Due to the complex seasonal variability of trace gas sources and transport pathways, the seasonal cycle of trace gases in the troposphere is different from the gases at the surface [6]. Accurate and continued observations of tropospheric CO₂ have given valuable insights on climate change, carbon cycle, model simulation and CO₂ emission sources [7]. The CO₂ concentrations throughout the troposphere can complement very well in situ results.

Recently several methods and techniques have been utilized to measure concentration of atmospheric CO₂. The in-situ technique offers high accuracy and precision, usually utilized to monitor tropospheric CO₂ [8]. Other examples include, nondispersive infrared gas analyzer (NDIR) and cavity ring-down spectroscopy (CRDS) used to monitor long-time variation of ground-surface CO₂, integrated-path differential absorption (IPDA) light detection and ranging (LIDAR) system to measure the column-averaged dry-air mixing ratio of CO₂ (XCO₂), and a differential absorption lidar (DIAL) system that could provide the CO₂ profile variation below the boundary layer [9–11]. However, these measurements are strongly influenced by local sources and small-scale processes [12]. The space-based measurements, such as the Greenhouse gases Observing SATellite (GOSAT), the Greenhouse gases Observing SATellite-2 (GOSAT-2), the Orbiting Carbon Observatory 2(OCO-2) and TanSat are tasked to observe the columns of atmospheric CO₂, which provide global atmosphere CO₂ concentrations [13–15]. But the satellite data must be validated by ground-based instruments, as satellite observations can be affected by surface properties and aerosols, measurement features that do not impact ground-based instruments. [16–18].

The ground-based high resolution Fourier transform spectrometer (FTIR) is increasingly used to observe total columns and vertical profiles of atmospheric trace gases [20–22]. The global Network for the Detection of Atmospheric Composition Change (NDACC) utilize middle-infrared Fourier transform infrared spectrometers to monitor the profiles of tropospheric and stratospheric trace gases [20,23–26]. Here we use a ground-based high resolution FTIR spectrometer to detect tropospheric CO₂.

In this paper, the objective is to use the mid-infrared solar spectra to retrieve vertical profiles and tropospheric CO₂ columns. The outline of the paper is as follows. In Sect. 2, we describe the measurement site, observation instrument and simulation model. Sect. 3 presents the retrieval setup for measurement spectra, retrieval results correction and error estimates. In addition, the time series of tropospheric CO₂ columns from FTIR observations and GEOS-chem simulations are presented and compared in Sect. 4. Sect. 5 summarizes our findings and conclusions.

2. Methods

2.1 Measurement site

The observation site (31.540 °N, 117.100° E, 35.5 m a.s.l.), adjacent to a reservoir named DongPu, is located in the north-west of Hefei city in eastern China. We installed the ground-based remote sensing system in 2014 (Fig. 1), consisting of a high-resolution FTIR instrument (Bruker IFS 125HR), which has nine scanner compartments (with a maximum spectral resolution of 0.00096 cm⁻¹), and a solar tracker (A547N) that is installed on the roof of the lab building and reflects the solar beam into the FTIR instrument (with the tracking precision of 0.1°), to monitor the atmospheric trace gas profiles and total columns. A meteorological station (ZENO, Coastal Environmental Systems, USA), on the roof of the lab building that is near the solar tracker, has recorded ground pressure, ground temperature, relative humidity, ground wind speed, ground wind direction, ground solar radiation, rain or snow and leaf wetness data since Sep. 2015 [27,28].

 

Fig. 1. The observed FTIR instrument system in Hefei site

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2.2 FTIR measurement

The FTIR instrument collects near-infrared and mid-infrared solar absorption spectra alternately on clear days. The FTIR instrument is equipped with a calcium fluoride (CaF2) beamsplitter and an indium gallium arsenide (InGaAs) detector, which can record near-infrared solar spectra (3800–11,000 cm⁻¹) with a spectral resolution of 0.02 cm⁻¹, according to the standard TCCON set up [27]. The mid-infrared spectra (600–4500 cm⁻¹), with a spectral resolution up to 0.005cm^-1, are collected by a potassium bromide (KBr) beamsplitter along with indium antimonide (InSb) and mercury cadmium telluride (MCT) detectors. Knowledge of the instrument line shape (ILS) is required to diagnose the alignment of the spectrometer and hence to retrieve total columns of gases from measurements accurately [27,29]. The ILS of the FTIR instrument is monitored by low-pressure HCl and HBr cell measurements [26,27]. The FTIR trace gases uncertainty estimates are computed by the standard deviation of the daily observed results. Aircraft measurements are used to calibrate the FTIR results within TCCON, and has yet to happen at our site, but we will do this work if we have the opportunity later [30,31].

2.3 GEOS-Chem model

The GEOS-Chem is a global 3-D chemical transport model, which has been used in a wide range of research topics on atmospheric composition, including CO₂, is driven by the Goddard Earth Observing System (GEOS) assimilated meteorological input data from the NASA Global Modeling and Assimilation Office [32,33]. In this study, we use a spatial resolution of 2° latitude × 2.5° longitude with 47 vertical layers [34]. For atmospheric CO₂ concentration, annual fossil fuel emissions in the model are estimated with the Multi-resolution Emission Inventory for China (MEIC) [35,36]. Biomass burning emissions are simulated from the Global Fire Emission Database (GFED2016) [37]. Ocean exchange and annual biofuel flux are acquired according to the paper of Takahashi (2009) [38], and Yevich and Logan (2003) [39], respectively. Balanced ecosystem exchange are calculated by the Carnegie-Ames-Stanford Approach (CASA) biosphere model [40]. It should be noted that the balanced ecosystem exchange contribute no net annual uptake of CO₂, but they make the greatest contribution to the seasonal cycle of atmospheric CO2 over most of the globe with the largest impact in the Northern Hemisphere[34]. Ship and plane emissions of CO₂ emission are estimated from the International Comprehensive Ocean Atmosphere Data Set (ICOADS) and System for assessing Aviations Global Emissions (SAGE) [40,41]. The concentration of atmospheric CO₂ in this study is calculated using these settings. The net ecosystem uptake, which is used to adjust net ecosystem exchange (NEE), are computed from TransCom climatology [42].

3. Tropospheric CO₂ retrieval

3.1 CO₂ retrieval setup

The tropospheric CO₂ concentrations are retrieved using SFIT4 (version 0.9.4.4), which is developed from SFIT2 [43]. The SFIT algorithm is based on the optimal estimation method to obtain the vertical profiles and columns of trace gases [44]. The CO₂ micro-windows are selected from mid-infrared spectra which contain strong and well-isolated CO₂ absorption lines [21,25,45]. The retrieval parameters and interfering gases for CO₂ at the Hefei site is listed in Table 1. Four absorption windows of CO₂ were fitted simultaneously. In addition to CO₂, the spectroscopic signatures of interfering gases are also considered to reduce fitting residuals. The interfering gases, H₂O and HDO, are considered as two different species for fitting. The a priori profile of CO₂ and other interfering gases except H₂O and HDO are derived from the Whole Atmosphere Community Climate Model (WACCM). The a priori profiles of atmospheric temperature, pressure and H₂O are adopted from National Centers for Environmental Protection (NCEP) reanalysis data [46]. The spectroscopic line parameters for CO₂ and interfering species are derived from the HITRAN 2012 linelist and recent updated versions [47]. The columns of H₂O, HDO, CH₄ and O₃ are also simulated during the CO₂ retrieval. A typical spectrum collected at 04:44 UTC 03 Feb. 2016, with a solar zenith angle of 48.82° is shown in Fig. 2. The fitting residuals of each window fluctuate within ± 0.2% and the averaged root-mean-square error is 0.069%, showing that the spectrum is well fitted.

 

Fig. 2. . The fittings for the CO₂ retrieval windows. Shown is a typical example of a spectral fitting at Hefei site (04:44 UTC, 03 Feb. 2016, solar zenith angle: 48.82°). For each window, the blue line is observed spectrum, red line the simulated spectrum, and the upper panel the fitting residuals.

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Table 1. The parameters setting for CO₂ retrieval.

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The averaging kernels are used to depict the sensitivity of height dependence of the retrieved profile to concentration perturbations at the various atmospheric levels [44]. The typical averaging kernel of CO₂ is shown in Fig. 3(a). The most sensitive height range of CO₂ is mainly located at 5-9 km and 12-25 km. The trace of averaging kernel matrix is characterized as the degrees of freedom for signal (DOFs). The typical DOFs for CO₂ over Hefei is about 2.86. This indicates that the retrieved profile can be separated into two independent partial columns, because the criterion for separating partial columns into separate layers is that the partial column DOFs of gases is greater than 1.0 [26,48]. To ensure accurate information from the CO₂ retrievals in the troposphere and minimize any stratosphere influence, i.e., the stratosphere–troposphere exchange, the upper altitude limit for the troposphere is set to 12 km, which is lower than the mean value of the tropopause (15 km) [26]. The red lines represent the averaging kernels above 12 km and the blue lines represent the averaging kernels in the troposphere (for altitudes < 12 km) in Fig. 2. The typical DOFs in the troposphere for CO₂ is 1.27.

 

Fig. 3. The typical averaging kernel matrix of the CO₂ retrieval at Hefei site (04:44 UTC, 03 Feb. 2016, solar zenith angle: 48.82°). (a): averaging kernel matrix without any correction (blue: tropospheric averaging kernels, red: stratospheric averaging kernels); (b): averaging kernel matrix obtained after applying the a posteriori optimization (blue: tropospheric averaging kernels, red: stratospheric averaging kernels).

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3.2 Posteriori optimization for the tropospheric CO₂ retrieval

Rodgers and Connor (2003) provide some mathematical background to a posteriori modification of a retrieval [44]. The profile retrievals are not necessarily perfect estimates of the desired quantity, including noise, but will have an averaging kernel that is not perfect [44]. As discussed in Sect.4 of Rodgers and Connor (2003), what is the best estimate of a function of the state vector. Since the tropospheric CO₂ has been considered as a function of the retrieved state vector: in the case of a retrieval that is based on the Bayesian theorem, one can simply apply the function to the retrieved state and get the expectation of the state, given the measurement (see Sect. 4.1 of Rodgers and Connor, 2003). However, in our case the a priori profile and its covariance are not completely known. Instead we use the WACCM simulated profile as the a priori and a constant covariance. We then calculate the tropospheric partial column of CO₂ from this approach. However, the tropospheric partial column of CO₂ can be better estimated with a posteriori modification. Equation (19) of Rodgers and Connor (2003) shows how this better estimator can be calculated from the retrieved state [44]. Sepulveda et al. (2014) also use this posteriori optimization method to eliminate the upper tropospheric/lower stratospheric (UTLS) influence on the tropospheric partial column of CH₄ [20].

As shown in Fig. 3(a), the peak of the tropospheric averaging kernels (blue lines) mainly appear in the troposphere and the peak of stratospheric averaging kernels (red lines) occur mainly in the stratosphere. However, the negative value for the tropospheric averaging kernels in stratosphere means that the stratosphere also contributes to the retrieved tropospheric CO₂ [20]. This means that the variation of stratospheric CO₂ will significantly affect the retrieved tropospheric CO₂. Therefore, we rewrite the retrieved averaging kernel matrix A as:

To reduce the cross-dependencies and separate the tropospheric column, that has a weak dependency on stratosphere, the a posteriori optimization method based on a simple matrix multiplication is used to correct the retrieval results. The matrix C can be written as:

I is the unit matrix. The dimension of the correction matrix C is identical to the averaging kernel matrix. The a posteriori optimized averaging kernel is obtained from C multiplied by the averaging kernel matrix:

The corrected averaging kernels matrix ${A_{corr}}$ is depicted in the Fig. 3(b). The overlap between the tropospheric averaging kernel and the stratosphere averaging kernels decreased between approximately 5 and 20 km, which means the corrected averaging kernel is much less affected by the stratosphere than the original averaging kernel [20]. The column averaging kernels in Fig. 4 are calculated based on the derived partial columns and averaging kernel [49]. The column averaging kernels have the property that they are 1 in the ideal case, but for a real retrieval can be more or less than one depending on the dominance of the apriori profile and other factors. The tropospheric partial column averaging kernel depicts this change in stratospheric cross-sensitivity clearly (Fig. 4). The kernel values improved significantly from negative to positive values in the range from 18-42 km. The shape of the sensitivity of the corrected and uncorrected partial column averaging kernels are similar in tropospheric region. It is apparent that this correction improved the separation between the retrieved tropospheric and stratospheric amounts.

 

Fig. 4. Comparison of the raw tropospheric partial column averaging kernel (red solid line) and corrected partial column averaging kernel (pink dashed line).

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3.3 Error estimations

The retrieved error covariance is calculated following the method of Rodgers and Conor (2003) [44]. The error components for error estimations are listed in Table 2. The square root of diagonal elements of the error covariance matrices, for a typical measurement spectrum (observed in 03:36 UTC, 23 Jun. 2019, with SZA 11.72°), are depicted in Fig. 5(a). The vertical structures of the error profiles reflect the effect of the propagation of different errors in the retrieval. As shown in Fig. 5, the dominant error sources are spectral and measurement error.

 

Fig. 5. Errors in the retrieved CO₂ due to the uncertainties as listed in Table 2. (a): errors calculated from profile retrieval without any correction; (b): errors after applying the a posteriori correction.

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Table 2. Error components used for error estimation. The second column gives the uncertainty value of each components and the third column gives the partitioning of this uncertainty between statistical and systematic sources.

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The error estimation for the a posteriori optimization is calculated by:

The small cross-dependency of the retrieved lower tropospheric mole fraction on the state of the stratosphere can significantly affect the quality of the lower tropospheric column product [20]. This means that cross-dependencies are one of the leading error sources. This error is referred to as the “sensitivity error”. This error covariance matrix is calculated as:

Table 3 summarizes DOFs values, sensitivity error and the total errors for the tropospheric partial column of CO₂ with and without a posteriori optimization. The total error include statistical and systematic errors. For the corrected results we get a sensitivity error that is still a significant fraction of the variability in the raw data. The a posterior optimization is more important for the sensitivity error so that the cross-talk between the partial columns is reduced without affecting the statistical and systematic errors. The DOFs value slightly decreases, but still meets the criterion of separating troposphere and stratosphere (DOFs greater than 1.0). The results show that the total error calculated from the error components list in Table 2 slightly decreases after correction in troposphere. The total error in this study is comparable to the error at the Karlsruhe site, which reported a total error of 4.24% [21]. The a posteriori optimization reduces the stratospheric influence on the tropospheric partial column from the CO₂ retrieval. This is reflected in the reduction of the sensitivity error (from 1.33% to 0.97%), but the DOFs also decrease, which is mainly losses in information at and above 12 km that were being folded into the troposphere. Since we separate the troposphere and stratosphere at 12 km, accordingly the tropospheric DOFs reduce (from 1.14 to 1.03). This is the classic trade-off between vertical resolution and profile accuracy: improve one and the other worsens. However in our case, this apparent reduction in DOFs may well be regarded as an improvement as the information loss of 0.11 was mainly a contribution to the tropospheric partial column from the stratosphere.

Table 3. Errors before and after considering correction in CO₂ for tropospheric partial column and for the total column.

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4. Results and discussion

4.1 Time series of tropospheric CO₂

The retrieved state is recalculated by considering the a posteriori optimization matrix C:

 

Fig. 6. CO₂ time series of the tropospheric column average mole fractions of the FTIR measurements at Hefei. The light-blue dots are the individual measurements of tropospheric CO₂; the blue dots represent the daily averaged CO₂; the error bars are daily CO₂ standard deviations; the black dash line is the annual trend line and the black dash dot line is the seasonal variation fitting curve.

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The DMF of tropospheric CO₂ time series show an obvious annual increase and seasonal variation in Fig. 6. The annual increase of CO₂ is due to the contribution of fossil fuel combustion. The CO₂ annual increase rate is 2.71 ± 0.36 ppm yr^-1. This rate is slightly higher than the values at other observation stations in the Northern Hemisphere. The annual increase rate of XCO₂ is 2.3 ppm yr^-1 from 2011 to 2015 at the Saga site, which is the TCCON site in Japan near to our site [51]. The annual increase rate of CO₂ is about 2 ppm yr^-1 from 2005 to 2009 at a rural site near Beijing and 2.05 ppm yr⁻¹ in Mauna Loa with in-situ observation [52], also similar to the value of 1.96 ppm yr^-1 from 2003 to 2011 in the Northern Hemisphere observed from SCIAMACHY [53]. This high increase rate is caused by the recent rapid rise of fossil fuel combustion in the Hefei area.

The CO₂ seasonality is also captured by the Fourier series fitting (Fig. 6). The annual peak value of CO₂ always appears in January, and then to a minimum in August. This seasonal variation amplitude of CO₂ is mainly caused by respiration and photosynthesis from plants. To clearly show the seasonal variation, we de-trend the tropospheric CO₂ time series. This de-trending is performed by subtracting the long-term trends, and the de-trended daily averaged CO₂ of each year are shown in Fig. 7. Table 4 summarizes the seasonal amplitude in each observation year. The seasonal amplitudes are different, i.e., the seasonal amplitude difference is 7.72 ppm between 2016 and 2017. This amplitude discrepancy is mainly due to the different temperature variation in different years because the CO₂ seasonal amplitude is strongly influenced by temperature [53–55]. The averaged seasonal amplitude of tropospheric CO₂ over observed period is 18.53 ± 3.07 ppm. The total column seasonal amplitude of XCO₂ are 8.31 and 13.56 ppm, respectively, over Hefei from 2014 to 2015 and from 2015 to 2016 [27]. The seasonal cycle was mainly driven by biosphere-atmosphere exchange, and it mostly happens near the surface, therefore this seasonal variability is more clearly captured in the troposphere compared with the total column.

 

Fig. 7. De-trend of DMF of tropospheric CO₂ for each year in 2016-2019. The error bars are daily CO₂ standard deviations.

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Table 4. Annual seasonal amplitude during in observed period

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4.2 Comparison with GEOS-Chem model

The FTIR DMF of tropospheric CO₂ time series was used to compare with GEOS-Chem model simulated results to evaluate the performance of GEOS-Chem model simulation in eastern China. We used the GEOS-Chem model to simulate the CO₂ mixing ratio profiles from July 2015 to December 2019 with 1 h time frequency. We sampled the simulation results at the grid cell covering the FTIR site, and interpolated them vertically to the vertical grid of FTIR retrieval [33]. To eliminate the influence of different a priori profiles and averaging kernel matrices, the profile from model simulation is smoothed by the FTIR retrieval averaging kernel [44]:

The daily averaged DMF of tropospheric CO₂ obtained by the FTIR instrument and the GEOS-Chem model are presented in Fig. 8. As shown in Fig. 8, the DMF of tropospheric CO₂ from GEOS-Chem simulation are in good agreement with the coincident FTS data. Figure 9 shows the GEOS-Chem model results comparisons with coincident FTIR data. The black line is the linear regression curve of the FTIR and GEOS-Chem results and the linear regression method according to York (2004) is used [56]. The GEOS-Chem model data are smoother than the FTIR measurements. Further, the FTIR and GEOS-Chem model result shows high correlation, with the correlation coefficient (r) of 0.89, but also show a bigger bias between FTIR and GEOS-Chem model data, especially in August and September. A positive CO₂ annual trend of 2.41 ppm yr^-1 is calculated from the GEOS-Chem data, comparable to the FTIR data (2.71 ± 0.36 ppm yr^-1). The model also has a good simulation record compared with other FTS and satellite CO₂ observation results [57,58]. The seasonal variations of GEOS-Chem model data is similar to the FTIR data, with the maximum and minimum of DMF of tropospheric CO₂ occurring in February and August, respectively. The mean bias between FTIR and GEOS-chem data, expressed as FTIR minus GEOS-chem, is -1.66 ± 7.31 ppm. The averaged seasonal amplitude of GEOS-chem is 10.68 ± 0.52 ppm and this is only one half of the FTIR seasonal amplitude (18.53 ± 3.07 ppm), which means GEOS-chem model underestimates the seasonal amplitude of the tropospheric CO₂ column. Because the model overestimates the minimum value and underestimates the peak value in each year (Fig. 8), especially the minimum value in August 2016, the average difference between FTIR and GEOS-chem is 13.97 ± 3.63 ppm. The mean biases of the minimum and maximum peaks between simulated and observed values are 8.07 ± 4.78 and 3.51 ± 1.44 ppm, respectively.

 

Fig. 8. The daily averaged DMF of tropospheric CO₂ observed by the FTIR instrument at Hefei and the GEOS-Chem model. The error bars are standard deviations for daily averaged CO₂. Top panel are the biases between the FTIR retrieval and GEOS-chem simulation.

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Fig. 9. Correlation plot of the coincident daily averaged DMF of tropospheric CO₂ from FTIR observation and GEOS-chem simulation. Black line is the linear regression curve between FTIR observation and GEOS-chem simulation. The blue line is the y = x line.

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The bias in the DMF of tropospheric CO₂ between the FTIR observations and GEOS-Chem simulations can be largely attributed to the following reasons: the grid cell and timing of the GEOS-Chem simulated data are not exactly the same as those of FTIR observations; and the accuracy of GEOS-Chem model simulation is affected by several factors, including the emission inventory (with an uncertainty of 31%), the atmosphere-biosphere model, and the meteorological conditions [33, 59–61]. Uncertainties in the model inputs and parameters result in the differences between the GEOS-Chem and the FTIR data.

4.3 Comparison with mole fraction of the total column and surface concentration

The total column abundances of CO₂ are retrieved from the near-infrared solar absorption spectra [19]. The retrieval strategies of total column CO₂ are harmonized with those of other TCCON sites. We use the GGG2014 software package to analyze the spectra [62]. The core of software is a nonlinear least squares spectral fitting algorithm (GFIT), which scales the a priori profile for the best fit based on the high-resolution transmission molecular absorption (HITRAN) database [63]. The column abundances of gases are then converted into column-averaged dry-air mole fractions (XCO₂) by dividing them by the total column of dry air. The division helps to cancel some potential systematic errors, including pointing errors, ILS uncertainty, zero level offsets, and source brightness fluctuation [19]. The method of determining the column of dry air is done by calculating the column of O₂ from the spectrum, divided by the dry-air mole fractions of O₂ (0.2095).

A wavelength-scanned cavity ring-down spectrometer (CRDS, Picarro model-2014i) has been used to measure surface CO₂ concentration since November 2015. To ensure the measurement stability, the CRDS instrument is placed inside the FTIR lab. Standard gases with three different concentrations are used to calibrate the measurement system once a month.

Time series of the daily averaged DMF of tropospheric CO₂ and XCO₂ are shown in Fig. 10. As show in Fig. 10, these data sets show obvious seasonal variation and an annual increase trend. The annual increase rate of CO₂ for the two datasets are in good agreement. The annual increase rate of DMF of tropospheric CO₂ and XCO₂ are 2.71 ± 0.36 ppm yr^-1 and 2.64 ± 0.13 ppm yr^-1, respectively. However, as show in Fig. 10, the annual maximum values of DMF of tropospheric CO₂ is higher than XCO₂ and the annual minima lower than XCO₂. The difference between daily averaged DMF of tropospheric CO₂ and XCO₂ is 17.79 ± 6.62 ppm, while the averaged seasonal amplitude of XCO₂ is 7.1 ± 0.98 ppm which is about 1/3 of DMF of tropospheric CO₂ seasonal amplitude (18.53 ± 3.07 ppm). The correlation coefficient (R) between the daily averaged DMF of tropospheric CO₂ and XCO₂ is 0.56 (p < 0.01) (Fig. 11).The seasonal variation of CO₂ is mainly dominated by the respiration and photosynthesis of plants, mostly happening at the surface. It would appear that the DMF of tropospheric CO₂ has a slightly better ability to capture this seasonality, due to the XCO₂ being slightly more diluted and influenced by stratospheric CO₂.

 

Fig. 10. The daily averaged DMF of tropospheric CO₂ column and XCO₂ observed by the FTIR instrument at Hefei. The error bars are standard deviations of daily averaged CO₂. Top panel are the biases between the DMF of tropospheric CO₂ column and XCO₂.

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Fig. 11. Correlation plot of the coincident daily averaged DMF of tropospheric CO₂ and XCO₂ from FTIR observation. Red line is the linear regression curve between DMF of tropospheric CO₂ and XCO₂. The black line is the y = x line.

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The time series of the daily means from the surface concentration, DMF of tropospheric CO₂ and XCO₂ are shown in Fig. 12. As shown in Fig. 12(a) and (c), the DMF of tropospheric has a smaller bias (8.12 ± 9.28 ppm)with the surface CO₂ than the total column derived XCO₂ (15.05 ± 9.33 ppm). Further, as show in Fig. 12(b) and (d), the correlation coefficient (R) between the DMF of tropospheric CO₂ and surface CO₂ is 0.61 (p < 0.01, with the slope of 0.62 ± 0.05), which is also higher than the correlation between XCO₂ and surface CO₂ (R = 0.54, with the slope of 1.71 ± 0.17). These results still show though that both the DMF of tropospheric CO₂ and XCO₂ are also influenced by sources in the mid and upper troposphere that are not sampled by the in-situ measurement.

 

Fig. 12. The time series of the daily means from the surface concentration, DMF of tropospheric and total column XCO₂ (a) surface concentration vs DMF of tropospheric column, the residual is absolute difference between surface concentration vs DMF of tropospheric column results, (b) daily means correlation between surface concentration vs DMF of tropospheric column; (c) tropospheric vs DMF of total column, the residual is absolute difference between tropospheric and DMF of total column, (d) daily means correlation between tropospheric and DMF of total column

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By way of a comparison, a similar test of the bias between the surface CO₂ with uncorrected DMF of tropospheric CO₂ and the total column XCO₂ computed from the MIR (using pressure rather the air column), gives similar biases (6.11 ± 9.70 ppm and 13.51 ± 8.50 ppm, respectively). The correlation coefficient (R) between the uncorrected DMF of tropospheric and surface CO₂ is 0.53 while the surface CO₂ and XCO_2MIR correlations coefficient is R = 0.58. This shows that the a posteriori correction has removed some of the stratospheric influence on the total column products. And the surface concentrations of CO₂ measured by the in-situ instrument are higher than XCO₂ derived from FTIR data at Anmyeondo station, Korea, which is the nearest TCCON site to our site [64]. Also, the averaged difference between the surface concentrations of CO₂ and XCO₂ is 13 ppm at Jungfraujoch site [65].

Further work is planned to produce an SFIT4 derived profile from the NIR spectra where this cross-dependency from the stratosphere can be reduced, combined with the know improvements that remove instrumental and other effects.

5. Conclusion

In this study, we present tropospheric CO₂ columns retrieved by ground-based high resolution FTIR remote sensing measurements. The tropospheric CO₂ concentration were retrieved from mid-infrared solar absorption spectra based on the optimal estimation algorithm, SFIT4.

The negative values for the tropospheric averaging kernels that occur in the stratosphere indicates that stratospheric CO₂ can affect the tropospheric CO₂ variation. To reduce this dependency on stratosphere variations, a posteriori optimization method based on a simple matrix multiplication was used to correct the retrieved profile. The tropospheric averaging kernel is less negative in the stratosphere after the a posteriori optimization, which means the corrected averaging kernel, and hence the CO₂ retrieved profile are much less affected by the stratosphere than the retrieval with the raw averaging kernel. The retrieved error covariances are calculated, and the dominant error sources are spectral and measurement error. The sensitivity of the troposphere partial column is clearly reduced after this correction. The total error slightly decreases from 1.22% to 1.18% after applying the correction in troposphere.

The corrected tropospheric CO₂ column during the period from August 2015 to December 2019 are presented. The tropospheric CO₂ time series shows an obvious annual increase and seasonal variation. The CO₂ annual increase rate is 2.71 ± 0.36 ppm yr^-1. The annual peak of CO₂ always occurs in January, and then decreases to a minimum in August. The mean annual amplitude of CO₂ over the observed period is 18.53 ± 3.07 ppm, and due to temperature variation in different years, the seasonal amplitude for each year has obvious variability.

Further, the observed DMF of tropospheric CO₂ is compared with the smoothed simulation data from GEOS-chem model and XCO₂ observed from near-infrared solar absorption spectra. The tropospheric CO₂ column from GEOS-Chem simulation are in good agreement with the coincident FTIR data, and the correlation coefficient (r) between the two data is 0.89. But the GEOS-chem model underestimates the seasonal amplitude of tropospheric CO₂ column, with the averaged seasonality amplitude of 10.68 ± 0.52 ppm that is only one half of the FTIR seasonal amplitudes. This discrepancy is largely attributed to the fact that the grid cell and timing of model data mismatch to FTIR data and the model inputs have high uncertainties. The annual increase rate of XCO₂ is in good agreement with the DMF of tropospheric CO₂ but the annual seasonal amplitude of XCO₂ is only about 1/3 of DMF of tropospheric CO₂. This is mostly attributed to the seasonal variation of CO₂ being mainly dominated by sources near the surface, therefore this seasonal variability is more clearly captured in the troposphere compared with the total column derived XCO₂

Appendix

The O₂ total column can be used as an indicator to confirm that the FTIR instrument was stable and prove that the year to year variability in the CO₂ drawdown is not related to instrumental problems. The Appendix Fig. 13 presented the time series of O₂ total column. As shown in Fig. 13, the O₂ total column has an obvious seasonal variation that is stable year to year.

 

Fig. 13. The time series of O₂ total column observed from high-resolution FTIR

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The averaging kernel, partial column averaging kernel and the error covariance matrices observed in 03:36 UTC, 23 Jun. 2019(solar zenith angle: 11.72°) are depicted in Fig. 14 and Fig. 15.

 

Fig. 14. The averaging kernel matrix of the CO₂ retrieval at Hefei site (03:36 UTC, 23 Jun. 2019, solar zenith angle: 11.72°). (a): averaging kernel matrix without any correction (blue: tropospheric averaging kernels, red: stratospheric averaging kernels); (b): averaging kernel matrix obtained after applying the a posteriori optimization (blue: tropospheric averaging kernels, red: stratospheric averaging kernels).

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Fig. 15. Comparison of the raw tropospheric partial column averaging kernel (red solid line) and corrected partial column averaging kernel (pink dashed line) in 03:36 UTC, 23 Jun. 2019.

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Funding

National Key Technology R&D Program of China (2019YFC0214702, 2018YFC0213201, 2016YFC0200404, 2017YFC0210002, 2018YFC0213104, 2019YFC0214802); National Natural Science Foundation of China (41775025, 41722501, 91544212, 51778596, 41575021, 41977184); Major Projects of High Resolution Earth Observation Systems of National Science and Technology (05-Y30B01-9001-19/20-3); Strategic Priority Research Program of the Chinese Academy of Sciences (XDA23020301); National Key Project for Causes and Control of Heavy Air Pollution (DQGG0102, DQGG0205); Natural Science Foundation of Guangdong Province (2016A030310115).

Acknowledgements

The processing environment of SFIT4 and some plot programs are provided by National Center for Atmospheric Research (NCAR), Boulder, Colorado, USA. The NDACC networks is acknowledged for supplying the SFIT software and advice.

Disclosures

The authors declare no conflicts of interest.

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