A Differential Optical Absorption Spectroscopy Method for XCO2Retrieval from Ground-Based Fourier Transform Spectrometers Measurements of the Direct Solar Beam

HUO Yanfeng,DUAN Minzheng,TIAN Wenshou,and MIN Qilong

1Key Laboratory for Semi-Arid Climate Change of the Ministry of Education, College of Atmospheric Sciences,Lanzhou University,Lanzhou 730000

2Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 10029

3Wuhan University,Wuhan 430000

4 Atmospheric Science Research Center,State University of New York,Albany,NY 12203,USA

A Differential Optical Absorption Spectroscopy Method for XCO2Retrieval from Ground-Based Fourier Transform Spectrometers Measurements of the Direct Solar Beam

HUO Yanfeng1,2,DUAN Minzheng?2,TIAN Wenshou1,and MIN Qilong3,4

1Key Laboratory for Semi-Arid Climate Change of the Ministry of Education, College of Atmospheric Sciences,Lanzhou University,Lanzhou 730000

2Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 10029

3Wuhan University,Wuhan 430000

4 Atmospheric Science Research Center,State University of New York,Albany,NY 12203,USA

A differential optical absorption spectroscopy(DOAS)-like algorithm is developed to retrieve the column-averaged dryair mole fraction of carbon dioxide from ground-based hyper-spectral measurements of the direct solar beam.Different to the spectral fitting method,which minimizes the difference between the observed and simulated spectra,the ratios of multiple channel-pairs—one weak and one strong absorption channel—are used to retrieve XCO2from measurements of the shortwave infrared(SWIR)band.Based on sensitivity tests,a super channel-pair is carefully selected to reduce the effects of solarlines,water vapor,air temperature,pressure,instrument noise,and frequency shift on retrieval errors.The new algorithm reduces computational cost and the retrievals are less sensitive to temperature and H2O uncertainty than the spectral fitting method.Multi-day Total Carbon Column Observing Network(TCCON)measurements under clear-sky conditions at two sites(Tsukuba and Bremen)are used to derive XCO2for the algorithm evaluation and validation.The DOAS-like results agree very well with those of the TCCON algorithm after correction of an airmass-dependent bias.

CO2Retrieval,ground-based measurement,hyper-spectrum,shortwave infrared band

1.Introduction

Carbon dioxide(CO2)is considered to be the main greenhouse gas causing current global warming(Solomon et al., 2007).However,Easterling and Wehner(2009)reported that records of surface air temperature show no warming trend or even a slight cooling trend,while greenhouse gas levels are still increasing.The disagreement about climate change is mostly due to the lack of long-term records of CO2measurements,especially for large area measurements and CO2sources and sinks(Stephens et al.,2007;Canadell et al., 2010).

It is advantageous to use satellite remote sensing to monitor atmospheric CO2globally.However,at present,only the satellite datasets of column-averaged dry-air mole fraction of CO2(XCO2)from the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography(SCIAMACHY) on board the Environmental Satellite(ENVISAT)(Bovensmann et al.,1999)and the Thermal and Near-infrared Sensor for Carbon Observation–Fourier Transform Spectrometer (TANSO-FTS)on board the Greenhouse Gases Observing Satellite(GOSAT)(Kuze et al.,2009),are used to estimate regional CO2fluxes.Both instruments use the reflected solar radiation in the shortwave infrared(SWIR)spectral region, making them sensitive to the variation of near-surface CO2concentrations.Unfortunately,the low spectral resolution of SCIAMACHY limits the inversion accuracy,with a single retrieval precision of about 2.5 ppm,as compared to ground-based Fourier transform spectrometer(FTS)measurements(Buchwitz et al.,2005;Reuter et al.,2011).The biases and standard deviations of the column-averaged dryair mole fraction of carbon dioxide(XCO2)from the SWIR L2 V02.xx GOSAT retrieval algorithm reach-1.48 and 2.09ppm,respectively(Morino et al.,2011;Yoshida et al.,2011; Yoshida et al.,2013).

Compared with satellite observations of reflected light, ground-based observations of the direct solar beam are less influenced by surface albedo,aerosolsetc.Therefore,groundbased observations can achieve higher accuracy and precision in determining the CO2total column amount.However,at present,the Total Carbon Column Observing Network(TCCON)is the only existing network that retrieves the total column concentration of CO2from ground-based FTS measurements for satellite validation.TCCON achieves a networkwide uncertainty of XCO2of better than 0.8 ppm,with 2σafter correcting for an airmass-dependent bias and calibrating to aircraft vertical profiles(Wunch et al.,2011a,b).

A Chinese satellite for CO2monitoring is planned for launch in 2015(Liu et al.,2013).To validate the satellite retrievals,a surface observation network has been set up to measure the hyper-spectrum of the direct solar beam in the SWIR bands.To derive the total column amount of CO2from these spectral measurements,a retrieval algorithm is needed. In this paper,a new DOAS-like algorithm is developed,in which multiple pairs of CO2absorption ratios(one in the weak CO2absorption channel and one in the strong CO2absorption channel)are used to derive the column CO2.More importantly,both channels in the pair are carefully selected to reduce their sensitivity to the surface pressure,air temperature,water vapor,noise and frequency shift.Compared with the spectral fitting method,DOAS-like retrievals are less sensitive to temperature and H2O uncertainty.

2.Retrieval algorithm

2.1.Physical basis

Ourretrievalalgorithm isbased on the factthatthe photon path lengths within a narrow spectral range are equal.Therefore,the ratio of the channel pair is proportional to XCO2if the surface pressure,temperature profile and water vapor are known.Based on the Lambert–Beer law,a ground-based measurement of the direct solar beam for a fixed wavelength can be expressed as

where Iλis the downward radiance measured at the bottom of the atmosphere for wavelengthλ,Isca,λis the forward scattering contribution in the incident direction,and I0is the incoming solar radiance at the top of the atmosphere.m is the air mass factor.τis the optical depth in the vertical optical path,which can be written as

where the right-hand terms represent optical depth of CO2absorption,water vapor absorption,aerosol extinction,and Rayleigh scattering,respectively.The scattering term of Isca,λin Eq.(1)is negligible due to a very small field of view (FOV)(～2.4 mrad)ofthe spectrometer,particularly forsmall aerosol particles and small aerosol optical depths(Min et al., 2004;Min and Duan,2005;Wunch et al.,2011a).Therefore, the radiance can be simplified as

In a very limited spectral range,the variation ofτaerandτRayacross the spectral range can be ignored.Therefore the ratio of the selected channel pair is insensitive to the loading of aerosol and Rayleigh scattering.Hence,we have

Letting r=Iλ1/Iλ2and r0=I0,λ1/I0,λ2,Eq.(4)can be rewritten as

By taking the logarithm of Eq.(5),we have

The optical depthτCO2is proportional to the total number of molecules of CO2per surface area,which is positively correlated to XCO2if the surface pressure,air temperature and CO2volume mixing ratio(VMR)profile are assumed to be known.Furthermore,only channel pairs with weak H2O absorption interference are selected.Therefore,the difference associated with water vapor is small and can be treated as a correction coefficient.Then,Eq.(6)is simplified as

Through the about pair selection procedure,the retrieval,i.e., Eq.(7),is weakly sensitive to the atmospheric state uncertainty(temperature and water vapor).Nonetheless,the coefficients of a and b are weakly dependent on temperature and water vapor in the atmosphere.To further reduce the error associated with the atmospheric state,we can calculate bothcoefficients with the surface pressure of in-situ measurements collected by automatic meteorological stations and reanalysis/forecasting atmospheric profiles.The profiles can be fixed for multiple measurements within some specific time period because only channels that are independent of temperature and water vapor are used in our retrieval algorithm.To illustrate the feasibility of fixed profiles,several inversions calculated by the different coefficients a and b at 0000,0600 and 1200 UTC are shown in Fig.1.All the errors are less than 0.15 ppm.The DOAS-like algorithm of Eq.(7)only has one unknown parameter.Hence,no iteration is needed.

2.2.Forward model

2.3.Channel selection

The DOAS-like method could reduce computational cost, but the super channel-pair must be carefully selected to reduce the impacts of H2O absorption,the solar Fraunhofer lines,and other factors such as instrument noise,temperature, pressure,frequency shift etc.In our channel-pair,the mean of 430 channels with very weak CO2absorption is regarded as the weak absorption channel in the super channel-pair,which is applied to the following analyses,and the mean of some strong CO2absorption channels is regarded as the strong absorption channel in the super channel-pair,as shown in Fig. 2.The selection of the strong absorption channel in the super channel-pair is presented in the following paragraphs.

The effects of random noise are also analyzed in the strong absorption channel selection to avoid large errors.Figure 3 illustrates the errors due to instrument noise in differently positioned strong CO2absorption channels if only one strong CO2absorption channel is used in XCO2retrieval.It is clearly shown that when the strong CO2absorption channel located at the far wing is used,large errors could be introduced due to the reduced information content of CO2(Fig. 3a);while in the line center,low signal-to-noise ratio(SNR) results in large uncertainty(Fig.3c).

The line strength and absorption coefficients depend on pressure and temperature.For the ultra-high spectral resolution measurements,an inaccurate pressure and temperatureprofile will introduce extra errors in the retrieval of CO2.Figure 4 shows the XCO2errors of each channel for a+1 hPa bias of surface pressure,which is calculated by comparing inversions with and without a 1 hPa change,when the channel is regarded as the only strong CO2absorption channel.In the error calculations,the coefficients a and b are calculated under the surface pressure,while the“measurements”are given under the+1 hPa bias of the surface pressure.Similarly,Fig. 5 shows the XCO2errors for a+1 K shift of the temperature profile.As shown in Fig.4,inversion errors caused by the +1 hPa pressure bias of most channels are positive,except for some channels in the weak absorption area.To reduce theimpact of pressure,only channels with an inversion error of less than 1 ppm are selected to be the component of the strong absorption channels in the super channel-pair.Different from that of pressure,the errordue to the+1 K offset of the temperature profile could be either positive or negative,and it could be minimized by careful channel selection in real retrievals.

Inaccurate wavelength registration is anothersource oferror in retrievals.As shown in Fig.6,the errors in XCO2retrieval due to a frequency shift of 0.003 cm-1could be up to 25 ppm if only one strong CO2absorption channel located on one side of the line center is used.But if strong CO2absorption channels located on both sides of the line center are used, the errors due to the frequency shift tend to be very small,or even zero.

Based on the above sensitivity studies,and the additional removal of the channels with strong H2O absorption and Fraunhofer lines,the final 588 strong CO2absorption channels are used in our retrieval.In order to evaluate the dependence of the DOAS-like method on the atmospheric state uncertainty,one-year prior profiles in Tsukuba,as shown in Fig.7,are used in simulated inversions.The results for both the DOAS-like and spectral fitting methods are listed in Table 1,in which errors of 1 K for the temperature profile,+5%for water vapor,+1 hPa for surface pressure,and 0.001 cm-1for frequency offset are assumed for solar zenith angles(SZAs) at 20?and 70?.For specific atmospheric parameter analysis, both the spectral fitting and DOAS-like method have one unknown state vector.Relatively,the DOAS-like retrievals are less sensitive to the temperature and H2O uncertainties,especially for large SZAs and high H2O amounts.The effects of surface pressure and frequency shift to being slightly better in the spectral fitting method.

3.Case studies and comparisons

To validate the DOAS-like algorithm,TCCON data in Tsukuba,Japan(36.0513?N,140.1215?E)and Bremen,Germany(53.10?N,8.85?E)are used.The spectra at both stations are measured with an FTS(IFS 125HR,Bruker Optics GmbH,Germany).The absorption spectrum is calculated by a Fourier transform of the interferogram,which is formed by beams reflected from a moving mirror and a static mirror. The resolution and sample rate of the FTS are determined bythe maximum optical path differences(MOPDs)and speed of the moving mirror.The MOPDs of the FTS in Tsukuba and Germany are 45.01 and 64.29 cm,respectively.The retrieved XCO2using the DOAS-like method are illustrated in Fig.8 (left panels),and the results of the official TCCON algorithm are also included for comparison.At first sight,the XCO2of the DOAS-like method is smaller than that of the official TCCON algorithm.After comparing the difference between the TCCON and DOAS-like retrievals with the SZA(Fig.8, right panels),we find that the difference is linearly dependent on the SZA(Fig.9).Moreover,the linear relationship does not vary with time and place.For the TCCON results,a postretrieval algorithm is used to correct an airmass-dependent bias based on the assumption that any symmetric variability within a day should be an artifact(Deutscher et al.,2010; Wunch et al.,2011a).Through a simple correction process in which the linear dependency on the SZA is removed,the DOAS-like and TCCON results agree well with each other, as shown in Fig.10.The standard deviation of the difference between the TCCON and DOAS-like methods is less than 0.8 ppm,both in Tsukuba and Bremen(Fig.11).This suggests that the DOAS-like algorithm provides retrievals with similar precision to TCCON.However,the temporal variability of the atmospheric state in Fig.12 limits the possibility of a higher inversion accuracy.Certainly,there could be many other factors for the low values of DOAS-like retrievals.For example,the solar lines provided by Kurucz used in our algorithm are not so good(Yoshida et al.,2013),and the FTS only focuses on the center of the solar disk due to its very small FOV.This inaccurate extra-terrestrial solar spectrum may be a factor for our lower value of XCO2.

Table 1.The XCO2errors due to temperature,water vapor,surface pressure and spectral shift.

4.Conclusions and future directions

A new algorithm using a channel-pair ratio to derive XCO2is presented in this paper.The algorithm is similar to that of the DOAS method.For the purpose of channel selection,the effects of solar lines,water vapor,air temperature,pressure, instrument noise and wavelength registration shift on the retrieval error are analyzed through a series of sensitivity tests. One super channel-pair is used in the retrieval algorithm. FTS measurements at the TCCON stations in Tsukuba and Bremen are used to validate the new algorithm by comparing our results with the official TCCON product.Our XCO2results are lower than those of TCCON with airmass correction.Taking the TCCON data as a reference,our results are further corrected using an SZA-dependent method.After the correction,our corrected results agree well with those of the TCCON products,suggesting that this new algorithm is useful.However,due to insufficient ground measurements, the new retrieval method is validated by observations at only two stations.Clearly,a thorough validation with extensiveobservation is warranted for our DOAS-like algorithm.

Acknowledgements.We greatly appreciate the TCCON stations at Tsukuba and Bremen for providing FTS observation spectra and auxiliary data.We also thank Atmospheric and Environmental Research(AER)for providing the LBLRTM.The research described in this paper was supported by the Strategic Priority Research Program–Climate Change:Carbon Budget and Relevant Issues(Grant No.XDA05040300),and National Natural Science Foundation of China(Grant No.41175028).

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22 September 2014;revised 8 January 2015;accepted 22 January 2015)

?Corresponding author:DUAN Minzheng

Email:dmz@mail.iap.ac.cn