Using Ground-Based High Resolution Fourier Transform Infrared Spectra

High resolution Fourier transform near IR solar spectra are used to estimate the column-averaged dry-air mole fraction (DMF) of CO 2 andCH4 variations in the atmosphere.The preliminary retrieval results for CO2 andCH4 variations in the area ofHefei, China, are presented, and the underlying error sources are also analyzed. Both a forward analysis and an inversion algorithm are included in the retrieval. The forward analysis uses the modeled atmospheric transmittance to line-by-line (LBL) convolute the instrument line shape function. The influences of the temperature, pressure, humidity, and a priori gases are considered in the atmospheric transmittance model.The inversion algorithm is based on the nonlinear iterative and nonlinear least squares spectral fitting, which is used to obtain VCDCO2 and VCDCH4 (which represent vertical column density of CO2 and CH4, resp.). Furthermore, the VCDO2 is also retrieved for converting the VCDs into DMFs. DMFs are final products of data analysis. The inversion results can clearly resolve the tiny variations of CO 2 and CH4 under strong atmospheric background. Spectral fitting residuals for both VCDCO2 and VCDCH4 are less than 0.5%. Finally, CO2 and CH4 diurnal variations are investigated based on a typical observation. About 2 ppm amplitude for DMFCO2 diurnal variations and less than 15 ppb amplitude for DMFCH4 are observed.


Introduction
Greenhouse effect caused by greenhouse gases (GHGs) can produce a series of environmental and economic problems.Recording GHG variations with high precision and accuracy is of great significance for predicting future climate change.Besides, good knowledge of global source and sink of carbon is the prerequisite for global warming control because carbon (except vapor) is the most important component in the GHGs [1].
CO 2 and CH 4 are two important GHGs and carbon compounds, which have been the research hotspots for decades [1,2].To have good knowledge of these two gases, the world has established more than 100 in situ observation sites over the past 30 years [3,4].A large number of GHG researches have been accomplished based on the combination of the in situ observation and global transmission model.In situ observations are mainly focused on the atmospheric boundary layer.The most striking characteristic of in situ observations on the atmospheric boundary layer is its high accuracy.But it is severely affected by the local source and sink and limited in the spatial coverage range [5].Column density measurements can fill these gaps and are less influenced by the atmospheric boundary layer height changes and vertical transport [6].Compared to in situ observation, column density measurements are less affected by temporal and spatial variations and thus make the horizontal gradients of the results more directly related to the underlying regionalscale fluxes [5].The typical high precision tools for column measurements are satellite-based and ground-based Fourier transform spectrometer [7].Currently, satellite-based Fourier transform spectrometer includes GOSAT (Japan), launched  This paper aims to first retrieve CO 2 and CH 4 variations in China using ground-based high resolution Fourier transform infrared spectra.This study can not only provide an evidence for resolving the local source and sink of carbon circle but also facilitate the satellite-based GHG measurements validation.

Instrument Descriptions
The observation laboratory is installed on an island located in the west of Hefei (the capital of Anhui Province) in central and eastern China.It is adjacent to a lake with a longitude of 117 ∘ 10  E, latitude of 31 ∘ 54  N, and altitude of 30 m.The system consists of a high resolution ground-based Fourier transform infrared spectrometer (IFS125HR) and a solar tracker (Tracker-A Solar 547), both of which are purchased from Bruker Company.IFS125HR has 9 scanner compartments, with a maximum resolution of 0.00096 cm −1 , and covers a spectral range of 5∼50,000 cm −1 .The solar tracker is mounted inside a dome controlled by a motor on the building roof (as shown in pictures on the right of Figure 1).A tracking precision of ±0.1 ∘ can be achieved by using the Camtracker mode (a built-in camera continuously adjusts the distance between the sun spot and the field spot).Solar tracker directs the sun light through the roof aperture (as shown in pictures on the left of Figure 1) into the spectrometer.For CO 2 and CH 4 observation, the spectral resolution is set to 0.02 cm −1 and the CaF 2 beam splitter is used [8].We choose InSb as the detector which covers 3900∼15500 cm −1 spectral range and cooled with liquid nitrogen during operation.In order to avoid detector saturation, we select a minimum entrance aperture (0.5 mm) and insert an attenuator (grid metal) in front of the detector.

Spectra Retrieval
Spectra retrieval includes two steps, that is, VCDs retrieval and then DMFs retrieval.We use the GFIT algorithm to retrieve the CO 2 and CH 4 VCDs.GFIT is developed by JPL (Jet Propulsion Laboratory), California Institute of Technology [5,9].It combines nonlinear iteration and nonlinear least squares fitting.It is a standard inversion algorithm for TCCON network.When fitting a spectral range, GFIT attempts to minimize the quantity  2 with respect to the variables , , ,  1 ,  2 , and  3 and other parameters: where   represents the measured spectra,   represents the calculated spectra,  is termed the continuum level,  is termed the continuum tilt,  is the frequency shift, and the various  terms are the scale factors for the different gases and   is the uncertainty in the value of the th element of   ., , ,  1 ,  2 ,  3 , . .., and so forth are important outputs of GFIT.Due to the complexity of modeling the measured spectra   , a forward model   is exploited.It is expressed as where  is the measurement error.Forward model   is commonly termed the convolution of atmospheric transmittance and the instrument line shape function [10,11]: where    is the th element of   ,   top is the atmosphere top layer spectra,  is continuum level,  is continuum tilt,  is frequency drift, and (]  ) represents atmospheric transmittance.When modeling measured spectra, a discrete, line-by-line, multilayer, and multispecies expression for the atmospheric transmittance is applied as expressed by (4) [5].] 0 is the center frequency of a spectral window, ILS(]  , ) is instrument line shape function, and  offset is spectral zero level offset.And the ILS used in GFIT is a nominal ideal ILS that is a numerical convolution of the sinc function with a rectangular function when the instrument is well aligned.The effect of the thermal radiation is ignored due to its negligible influence on the near-infrared spectrum.Solar intensity relative fluctuation threshold is set to 5% for removing the interference of clouds and aerosols.

Model Parameters Determination.
In order to achieve high precision retrieval, longitude, latitude, altitude, a priori profiles, real-time surface temperature, humidity, pressure, wind speed, wind direction, and other meteorological parameters need to be considered in the process of the forward model calculation [12].In addition, the high resolution spectrometer IFS125HR should be calibrated by a low pressure HCl cell regularly because instrument alignment has great influence on the inversion results [10].For the current version of spectra, we did not save the real-time surface temperature, humidity, and pressure parameters, and no HCl cell is available.Thus, in this study, we have to make some assumptions in the model calculation.
(1) Inside the laboratory, the air conditioning is set to a constant value of 24 ∘ , the dehumidifier is set to a constant value of 60%, and the IFS125HR is evacuated while saving the solar spectra.So we assume that the temperature inside the instrument ( inside ) is a constant value of 24 ∘ , the internal pressure ( inside ) is a constant value of 1 mbar, the internal relative humidity ( inside ) is a constant value of 60%, the temperature outside the instrument ( outside ) is a constant value of 24 ∘ , the external pressure ( outside ) is a constant value of 1 standard atmospheric pressure (1024 pa), and the external relative humidity ( outside ) is a constant value of 60%.In addition, a priori profiles for temperature, pressure, and humidity above observation station are based on NCEP (National Center for Environmental Prediction) data [13].A priori profiles for all gases use the American standard atmospheric parameters for the mid-latitude of northern hemisphere.
(2) We already aligned the IFS125HR just before we started to save the spectra, so we assume that the alignment of instrument is well because of the excellent stability of the instrument; that is, the influence of the instrument drift is neglected for all the spectra.
(3) Time correction is done every day before observations, so the saved spectra are consistent with the UTC (Universal Time Coordinated) within ±1-second precision.

VCD Retrieval.
We use the GFIT algorithm to calculate the CO 2 and CH 4 VCDs which finds the best fitting between the calculated spectra and the measured spectra [14].The most important outputs of the GFIT algorithm are scaling factors and their uncertainties as mentioned in (1).A priori profile mole fraction of a gas is multiplied by the scaling factor to yield the retrieved vertical column density [13] where SF gas is the scaling factor for a gas,  apriori gas is the a priori profile of the gas,  is the total molecules number,  represents altitude, and   is the altitude of the first mirror of the solar tracker.

DMF Calculation. Gas column average dry-air mole fraction (DMF) is defined as
Because VCD O 2 in the atmosphere is well known, the total dry-air column can be obtained by using the relationship between VCD O 2 and the total dry-air column [15]: Substituting ( 7) into (6) yields the DMF: The advantages of DMF compared with VCD are as follows: (1) reducing the influence of surface pressure changes and water vapor interference on the inversion results; (2) reducing the systematic error sources which affect both the target gas and O 2 ; (3) improving the inversion precision by minimizing the common scatter [15].

Data Analysis and Discussion
In this study, the direct solar spectra collected between October 6, 2014, and December  of interest (bold font) and interfering gases are also shown in Table 1.We set a fitting residual of <1% to filter out those spectra which do not fulfill the assumptions in Section 3.1.
Figures 2, 3, and 4 are fitting examples for CO 2 , CH 4 , and O 2 , respectively, which are from a spectrum measured at 26.535 ∘ SZA (solar zenith angle) on October 8, 2014.  and   represent calculated spectrum and measured spectrum, respectively.Fitting residuals (  −   ) for CO 2 , CH 4 , and O 2 are 0.2459%, 0.3535%, and 0.3085%, respectively.The fitting residuals are mainly attributed to the unknown structure of spectroscopies and systematic errors, for example, electronic noise, acquisition noise, spectral structure noise, and scanning mirror fluctuation noise.
The time series of retrieved VCD CO 2 and VCD CH 4 are shown in Figures 5 and 6, respectively.Time periods ranging from October 6, 2014, to December

Conclusions and Discussion
CO 2 and CH 4 are important greenhouse gases and carbon compounds.Capturing their variations in the atmosphere is of importance to determine their source or sink information.This study uses high resolution Fourier transform near IR solar spectra to calculate the CO 2 and CH 4 VCDs and DMFs.The preliminary retrieval results for CO 2 and CH 4 variations in the area of Hefei, China, are presented, and the underlying error sources are also analyzed.The results show that tiny variations of CO 2 and CH 4 in the atmosphere can be clearly resolved.The retrieval error is dominated by the deficiencies in the forward model.Future work will concentrate on optimizing the input parameters of the model and calibrate the instrument regularly with HCl cell.We are confident that, with these improvements, this technical will be more than adequate for future climate change forecast and satellitebased column observations validation.

Figure 2 :
Figure 2: CO 2 spectral fitting within 6339 cm −1 window: the spectrum was recorded on October 8, 2014, 0:47 (UTC).Black lines are the measurements, orange lines are the fitted transmittance, and contributions from individual gases are shown in color.Fitting residuals (  −  ) for CO 2 are 0.2459%.

Figure 3 :
Figure 3: CH 4 spectral fitting within 5938 cm −1 window: the spectrum was recorded on October 8, 2014, 0:47 (UTC).Black lines are the measurements, orange lines are the fitted transmittance, and contributions from individual gases are shown in color.Fitting residuals (  −  ) for CH 4 are 0.3535%.

2 Figure 5 :
Figure 5: VCD CO 2 time series ranging from October 6, 2014, to December 1, 2014, which are the average of the retrieval values in 6220 cm −1 and 6339 cm −1 windows.
Figure 4: O 2 spectral fitting within 7885 cm −1 window: the spectrum was recorded on October 8, 2014, 0:47 (UTC).Black lines are the measurements, orange lines are the fitted transmittance, and contributions from individual gases are shown in color.Fitting residuals (  −  ) for O 2 are 0.3085%.
2 , CH 4 , and O 2 gases are retrieved simultaneously.Retrieval window parameters for CO 2 , CH 4 , and O 2 are listed in Table 1.The two central frequencies for CO 2 windows are 6220.00cm −1 and 6339.50 cm −1 , respectively.The final VCD CO 2 is the average of the windows' results.The same treatment is also applied to CH 4 .The target gases

Table 1 :
1, 2014, are presented forFigure 6: VCD CH 4 time series ranging from October 6, 2014, to December 1, 2014, which are the average of the retrieval values in 5938 cm −1 , 6002 cm −1 , and 6076 cm −1 windows.Figure 7: VCD O 2 time series ranging from October 6, 2014, to December 1, 2014, which are the retrieval values in 7885 cm −1 window.Retrieval window parameters for CO 2 , CH4 , and O 2 .and CH 4 .The VCD CO 2 in Figure 5 is the average of the fitted results in 6220 and 6339 windows.The averaged fitting errors for CO 2 are less than 1%.Most VCD CO 2 lies between 8.2 and 8.8 × 10 21 molecules/cm 2 .The VCD CH 4 in Figure 6 is the average of the results in 5938 cm −1 , 6002 cm −1 , and 6076 cm −1 windows.Most VCD CH 4 lies between 3.7 and 4.1 × 10 19 molecules/cm 2 .The averaged fitting errors for CH 4 are also less than 1%. Figure 7 is the VCD O 2 time series retrieved from 7885 cm −1 window with fitting error of <1%.VCDs as shown in Figures 5∼7 are intermediate products of data analysis and so postprocessing procedures Figure 8: DMF CO 2 time series ranging from October 6, 2014, to December 1, 2014, which are calculated according to VCD CO 2 and VCD O 2 .Figure 9: DMF CH 4 time series ranging from October 6, 2014, to December 1, 2014, which are calculated according to VCD CH 4 and VCD O 2 .are not applied to them.Time series of DMF CO 2 and DMF CH 4 , respectively, in Figures 8 and 9 are calculated by the ratio of VCD CO 2 /VCD O 2 and VCD CH 4 /VCD O 2 , respectively.DMFs are final products of the data analysis.Both retrieval errors and precision are improved greatly (with less scatters).In addition, the diurnal variations of DMF CO 2 and DMF CH 4 are investigated based on typical daily measurements.The diurnal variations of both DMF CO 2 and DMF CH 4 are clearly observed, which are shown in Figures 10 and 11, respectively.Precision (1 standard error) for both DMF CO 2 and DMF CH 4 is less than 0.1%.DMF CO 2 concentrates on around 396 ppmv with diurnal variation amplitude of ∼ 2 ppm.DMF CH 4 concentrates on around 1845 ppbv with diurnal variation amplitude of ∼15 ppbv.The peak in DMF CO 2 and DMF CH 4 on October 24, 2014, may be caused by human activities.The observed diurnal variations do not indicate any feature so far, but with the increase of the number of observations we will do further research.
Figure 10: DMF CO 2 time series on October 24, 2014, which are calculated according to VCD CO 2 and VCD O 2 .Figure 11: DMF CH 4 time series on October 24, 2014, which are calculated according to VCD CH 4 and VCD O 2 .