We describe a new method for the measurement of molecular mixing ratios called Cross-Band Relative Absorption (CoBRA). The proposed method is based on relative measurements in different molecular bands referenced to a band of O2 with properly selected wavelength combinations providing high level of cancelation in temperature sensitivities. The CoBRA approach is particularly promising for satellite based remote sensing of molecular mixing ratios of the atmospheric trace gases. Very low temperature sensitivities and the potential of achieving close weighting function matching for the measurement and reference wavelengths are the main advantages of the method. The effectiveness of CoBRA approach is demonstrated for the retrieval of CO2 mixing ratios (XCO2) with application to the ASCENDS mission.
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To address the needs in monitoring and analysis of the effects of increasing atmospheric concentration of greenhouse gases, several missions are being planned for the space lidar based mixing ratio measurements of molecules such as CO2, CH4, N2O etc., which rely upon the use of the integrated path differential absorption (IPDA) methods [1–3]. One of such satellite based lidar missions recommended by the NRC decadal survey as an important atmospheric science mission is the Active Sensing of CO2 Emissions Over Nights Days and Seasons (ASCENDS). ASCENDS is aimed at the measurement of CO2 column averaged mixing ratios (XCO2) with an unprecedented accuracy of 0.3% or better .
Previous studies indicated a large number of instrumental and spectroscopic factors significantly limiting the accuracy of the IPDA satellite mixing ratio retrievals [1, 2, 4]. Among these factors are the temperature and water vapor spectroscopic interferences. The IPDA techniques currently investigated for space trace greenhouse gas sensing provide measurements of integrated path total absorption values. The information about the absorption vertical distribution has to be derived from the measured integrated path optical depth (IPOD) values. Vertical distribution of absorption is determined by fitting of measured IPOD data to the calculation results of transmission simulation codes with known temperature, pressure and humidity profiles as a function of altitude for the corresponding time and location along the satellite measurement path. Such atmospheric profiles for the IPDA technique retrievals are usually derived from the Numerical Weather Prediction Models (NWP) and are only known with a finite precision resulting in uncertainties in the derived mixing ratios . If it was possible to ensure that the normalized absorption distribution as a function of altitude, which is characterized by the shapes of the weighting functions, was close for the measurement (such as in the CO2 band) and reference (such as an O2 band used for the pressure determination) channels, it could be possible to significantly reduce precision requirements on the atmospheric NWP models data or completely eliminate its need by enabling self-sufficient column averaged mixing ratio measurements.
In this paper we describe a new approach based on cross-band matching of spectral lines which results in significant reduction of temperature sensitivities compared to the traditional IPDA implementations. The method also facilitates weighting functions matching optimization. The proposed approach is demonstrated with application to the ASCENDS mission for the measurements of the CO2 mixing ratios (XCO2). Our results suggest that further refinements of the cross-band technique may provide a way for self-sufficient atmospheric molecular mixing ratio measurements requiring little or no NWP corrections for the column-averaged mixing ratios determination.
2. Cross-band relative absorption technique
One of the approaches used to derive the atmospheric molecular mixing ratios is by performing two independent measurements: one to determine the concentration of a molecule of interest (such as CO2, CH4 etc.), and the second one to obtain the total density of molecules.
For convenience, we call the wavelength used for the measurement of the gas of interest the “measurement” wavelength and the one providing information about the total pressure or molecular number density as the “reference” wavelength.
The total density may be determined by measuring the concentration of oxygen (such as in the A-Band or 1.26-1.27 µm bands) or other well-mixed atmospheric molecule having concentration directly proportional to the atmospheric total pressure. These two measurements are then combined to obtain the mixing ratio.
Figure 1 further illustrates this approach by comparing the IPDA method with one proposed cross-band relative absorption (CoBRA) technique. As can be seen from Fig. 1(a), the IPDA approach is based on two independent measurements in the molecular (measurement) and oxygen (reference) bands with a combination of on- and off- line wavelengths used in each band to determine the corresponding measurement (,) and reference (,) optical depths. Their corresponding differential optical depths and may then be used to determine the mixing ratio X as illustrated in Fig. 1(a). In this approach the optimizations related to temperature sensitivity and water vapor interferences for the measurement and reference bands are usually carried out independently.
In contrast to the traditional IPDA approach described in Fig. 1(a), the proposed CoBRA technique relies on combined analysis of both measurement and reference spectral bands to establish measurement and reference lines having similar spectral characteristics and identify wavelength combinations in the measurement and reference channels providing the best reduction in interferences including those due to the temperature variations. This concept is illustrated in Fig. 1(b). The absolute optical depth values and at the measurement and reference wavelengths are combined for further determination of the atmospheric molecular mixing ratios. As can be seen in Fig. 1(b), to better illustrate the CoBRA concept no off-line wavelengths are explicitly used, instead correction terms Am and Ar are included for the measurement and reference channels to provide the missing attenuation components due to water vapor, aerosols etc.. These correction terns may be obtained by a variety of additional measurement methods some of which will be suggested later in the article.
Our initial results suggest that the introduction of the CoBRA technique has significant implications for improvements in the mixing ratio measurement accuracies and provides ways for potential simplification of the data retrieval methods and system components. The key advantages of the new technique include the reduction of the temperature sensitivity, especially for excitation regions shifted away from spectral line centers, and close matching of the measurement and reference weighting functions. Due to the large number of cross-band wavelength matching combinations with reduced temperature induced errors, the method further allows proper selection of excitation wavelengths to also achieve minimizations of the water vapor absorption contributions. The reduction of temperature and water vapor interferences and weighting functions matching relax the requirement on the precision of the NWP models correction data, and with further improvements to the method may provide a path for self-sufficient mixing ratio measurements not requiring NWP corrections. Additionally, flexibility in the selection of the background correction techniques, which may exclude explicit use of the off-line wavelengths, provides a path for system optimizations which may lead to reductions in the complexity and cost of the measurement setup.
3. Application of CoBRA to the sensing of XCO2 in missions such as ASCENDS
We have carried out semi-empirical validation studies to evaluate the performance of the CoBRA approach  for several molecules. These studies were based on verified spectral databases, atmospheric transmission modeling codes and satellite meteorological data such as HITRAN 2008, Line-by-line radiative transfer model (LBLRTM), and the modern-era retrospective analysis for research and applications (MERRA) [7–9]. The atmospheric parameters for line-by-line calculations were taken from the “inst6_3d_ana_Nv” MERRA data set which provides data on 72 pressure levels grid with a minimum pressure of 0.01 mBar (corresponding to a maximum altitude of ~80 km) on a 360 x 540 latitude / longitude surface grid and 4 data sets per day. To reduce the number of calculations required, the “inst6_3d_ana_Nv “ MERRA dataset was first pre-analyzed to find the frequency of occurrence ni of temperature values around the globe over the annual span of year 2009 within each layer on a temperature grid of 1 Kelvin. Subsequently, transmission calculations were carried out for each temperature/pressure combination within each pressure level with a fixed layer path length of 1 km. Each pressure level was analyzed independently counting from the lowest altitude. The transmission spectra obtained for all temperature / pressure combinations available within each layer were used to establish the errors in optical depth to be expected due to temperature variations.
The CoBRA analysis was performed by considering the ratios of the measurement and reference absolute optical depths () at equivalent temperature and pressure conditions (Ti and Pj) at all possible measurement / reference wavelength combinations ( and ) as shown in Eq. (1). These ratios were used as variables xi for the calculation of weighted mean values (Eq. (2)), the standard deviation s (Eq. (4)) and the coefficient of variation (Eq. (5)) over the span of temperature changes in each layer and every possible measurement / reference wavelength combinations. The standard deviation was calculated using a two-pass algorithm involving separate iterations for the calculation of the mean and the standard deviation values.
where j is the index of the layer counting from the surface, and i is the index of a temperature bin in a given layer j.
where xi is a relative optical depth value at a given combination of the measurement and reference wavelengths, ni is the frequency of occurrence of a temperature value in a given temperature bin corresponding to the calculated optical depth spectrum, K is the number of temperature data bins in a given layer, N is the total number of temperature data points in a layer.
The total path coefficient of variation used to ascertain the total path temperature induced uncertainties was then calculated as a sum of individual layer contributions up to the total M = 72 layers by scaling the individual layer relative coefficients of variation (Eq. (5)) with the corresponding average molecular air density in each layer as shown in Eq (6)-(8). Such adjustment was carried out to take into account the reduction in molecular concentration with increasing altitude and consequently lower contribution to the total relative error for atmospheric layers at higher altitudes. This procedure is previously described in .
where Pj is the pressure within level j, is the averaged layer temperature, and Rd is the specific gas constant for dry air.
Since the MERRA data set used represents assimilations of measured atmospheric data from multiple experimental sources, the relative precision coefficients of variation provided by such simplified approach are representative of what should be expected in an experiment involving annual global satellite observations. It should be noticed that due to the summation of calculated errors over 72 pressure levels, the coefficient of variation obtained using the above approach includes the effects of both changing temperature as well as the total pressure and is also called the relative uncertainty or simply uncertainty in this article.
One of the molecules analyzed included the CO2 molecule with application to the sensing of XCO2 for prospective satellite lidar missions such as ASCENDS. The analysis was carried out under an assumption of the interference free case by only considering the CO2 spectra without water vapor or aerosol interferences . The spectral regions considered in the CO2 and O2 bands were limited by optical depth to a region of 0.1 to 2 which represents a slightly expanded optical depth span previously determined as having optimum values for space lidar applications [11, 12]. The top threshold of 2 was also dictated by the maximum absorption values in the 1.57µ band of CO2. To ensure the absolute optical depths are within the desired range, a comparison with independently generated total 80km vertical path transmission spectra for a US Standard atmospheric profile in both 1.57 CO2 and 1.26-1.27 O2 spectral bands was done during calculations.
Due to the low atmospheric concentration of the molecules studied (such as CO2, CH4 etc.) and proximity of their self- and pressure-broadening coefficients it was possible to keep molecular concentration constant in simulations without introducing significant errors . This was done to eliminate interferences with the temperature sensitivity analysis by considering the fact that the changing concentration only results in changed absorption intensity without affecting the Voigt spectral line shape. The concentrations of CO2 and O2 were kept at 400ppm and 2.09*105 ppm respectively. The transmission calculations were performed with a resolution of 0.001 cm−1 using the LBLRTM program employing the Voigt lineshape profile .
the cross-band matching of the 1.57µm CO2 and 1.26-1.27 µm O2 bands showing point distribution of the combinations of wavelengths resulting in relative optical depth uncertainty values of 0.3% or lower. We are operating in the optical depth units for convenience due to the direct proportionality between the optical depth and the corresponding molecular column density along the optical path length . As can be seen, there is a considerable number of measurement and reference wavelength combinations resulting in significant reductions in temperature sensitivities. The star pattern observed is attributed to both cross-matching of the spectral lines as well as to the presence of the low temperature sensitivity regions in the CO2 and O2 bands.
Figure 3(b) further shows the point distribution values of the relative optical depth uncertainties as a function of measurement wavelength in the 1.57µm CO2 band with a total CO2 optical depth spectrum for 80km path shown in Fig. 3(a). The uncertainty point distribution in Fig. 3(b) includes all possible O2 band reference wavelength combinations as shown in Fig. 2(c) for each of the CO2 spectrum measurement wavelengths shown in Fig. 2(b) and 3(a). A magnified sub-portion of Fig. 3(b) in the vicinity of 6360 cm−1 is shown in Fig. 3(c). As can be seen, each point corresponds to a single combination of a measurement and reference wavelength with uncertainty levels as low as 0.1% achievable for selected wavelength pairs.
To better illustrate the cross-band matching of individual spectral lines, Fig. 4 shows magnified portions of the distribution plotted in Fig. 2(a) for two sample lines in the 1.57 µm CO2 and 1.26-1.27 µm O2 bands. In particular, Fig. 4(b) shows all possible O2 reference line locations providing uncertainty of 0.3% or lower if combined with the CO2 line shown in Fig. 4(a). As can be seen, there are several cross-band matching possibilities covering different regions of the O2 band leading to the 0.3% or better accuracy limits. In a similar way, Fig. 4(d) illustrates the same cross-matching distribution of a single reference O2 line shown in Fig. 4(c) over the entire measurement CO2 band. As can be seen, at a given accuracy limit of 0.3% close matching resulting in low temperature sensitivities is achieved almost along the entire line shapes for several CO2 lines with partial compensation for other lines in their vicinity.
Figure 5 presents cross-band matching when a single spectral line is used both within the measurement and the reference bands. This example is for matching of sample CO2 and O2 spectral lines previously shown in Fig. 4(a) and 4(c).
Plots 5c and 5f are the corresponding point distributions of the relative optical depth uncertainties under 0.3% for all possible measurement and reference wavelength combinations within the CO2 and O2 lines shown in Fig. 5(a) and 5(d). Figure 5(b) and 5(e) show the uncertainty point distributions for the entire set of reference or measurement wavelengths respectively. As can be seen, cross-band matching with an accuracy of under 0.3% is achieved almost along the entire spectral CO2 and O2 lines selected.in the example. The discreetness of the point distribution in Fig. 5(b) and 5(e) is attributed to the uncertainty values grid with a step of 0.01% used in calculations.
The comparison of the results shown in Fig. 5 with those of Fig. 2 and 3 further suggests that the two sample lines of CO2 and O2 selected in the examples of Fig. 4 and 5 do not represent the best combination for achieving the lowest reductions in temperature sensitivities and that better cancelation levels are possible for several other lines and spectral regions.
4. Weighting functions matching, water vapor and other interferences
Out earlier results only considered the magnitude of temperature induced errors for each layer and the total path without analyzing the consistency of the measurement and reference optical depth ratios xi with increasing altitude. As mentioned previously, it is desirable for the CoBRA technique that the weighting functions selected for the measurements of CO2 and O2 had closely matching shapes as a function of altitude to ensure the consistency of the measurement and reference absorption for varying atmospheric conditions.
The CoBRA approach is based on matching of lines with similar spectral characteristics, therefore their shapes evolve similarly as the atmospheric parameters are changed. Such line matching, as well as the need in positioning the measurement and reference wavelengths in spectral regions having similar half-width relative distances from the line center to achieve better temperature compensation, provides a potential way for achieving weighting functions with close matching shapes in the measurement and reference channels. This ensures close correspondence in the altitude sensitivity at both wavelengths in the cross-matched bands used regardless of the atmospheric conditions.
Figure 6(a) and 6(b) illustrates the altitude distribution of the individual layer mean optical depth ratios and the coefficients of variation (calculated using Eq. (2)-(5) as described previously) for a pair of measurement and reference wavenumbers of 6364.855 and 7822.172 cm−1 respectively. This sample wavelength pair was selected because it was identified previously as providing high degree of temperature compensation with the total path relative optical depth uncertainty of 0.19%. The layer coefficients of variation values as a function of layer number are shown in Fig. 6(b) indicating a high level of temperature compensation for the selected pair of wavelengths leading to 0.19% total path accuracy previously calculated using Eq. (6)-(8). As can be seen from Fig. 6(a) and 6(b), the separate layer mean optical depth ratios and coefficients of variation remain about the same up to layers 25 - 30 corresponding to the pressure in the range of ~400-200 hPa and an approximate altitude of 7-12 km . The normalized air density distribution used to scale the error contribution with altitude is presented in Fig. 7(c) for comparison. The high linearity of the parameters at lower altitudes for the selected low temperature sensitive wavelength combination suggests the possibility that the high temperature cancelation regions identified previously may also exhibit the best weighting functions matching for the measurement and reference wavelengths.
A requirement for the measurement and reference weighting functions matching is the stability of the optical depth ratio at the measurement and reference wavelengths with increasing altitude under the assumption of constant concentrations of CO2 and O2. In an ideal weighting function matching situation, such ratio would remain the same for all altitude levels. To establish the performance of the CoBRA approach in terms of weighting function matching for the measurement and reference wavelengths in the bands of CO2 and O2 considered in this study, we used the mean optical depth ratio values previously calculated for each layer (Eq. (2)). These separate layer values were combined and analyzed using Eq. (9)-(12) to establish the variability of average optical depth ratios for all pressure layers. As can be seen, Eq. (9)-(12) are based on Eq. (2)-(5) with a modification introduced to take into account the reduction in air density with altitude. In particular, the weighting factors ni in Eq. (2)-(5) were substituted with the average molecular air density for each layer, and the total number of samples N replaced with the sum of over all layers. The resultant coefficient of variation used as a weighting functions matching parameter was calculated as in Eq. (5) by using the standard deviation s (Eq. (12)) and the mean value (Eq. (11)).
where are the mean optical depth ratio values calculated previously using Eq. (2), is the weighted mean of the layer mean optical depth ratios, M = 72 is the number of layers, and is the average molecular air density calculated using Eq. (6).
The calculation results for such weighting functions matching parameter over the entire bands of CO2 an O2 are presented in Fig. 7 showing distributions for points with the total uncertainty of less than 2.5%. Plots in Fig. 7(b) and 7(c) include all reference wavelengths.
As can be seen from Fig. 7(a), there is a significant number of cross-band wavelength combinations leading to close matching of the CO2 and O2 optical depth ratios distribution with altitude. By comparing Fig. 2(a) with Fig. 7(a) as well as Fig. 3(b) and 3(c) with Fig. 7(b) and 7(c) respectively one can see that the regions with wavelength combinations providing low temperature sensitivities also provide close weighting function matching. This result suggests that if water vapor interferences can also be compensated, it may be possible to implement a column averaged mixing ratio measurement approach requiring little or no external corrections for varying atmospheric conditions. The abundance of wavelength combinations providing significant reductions in temperature sensitivities suggests that it may be further possible to significantly minimize water vapor interferences by properly selecting measurement wavelengths. It is anticipated that such method may be capable of delivering the accuracy desired in the projected missions such as ASCENDS for column averaged mixing ratio determinations.
It should be noted that due to a number of simplifications and averaging in the calculation approach used, the accuracy parameter introduced to ascertain the preservation of the optical depth ratio with altitude (Eq. (9)-(12)) is not sufficient to provide conclusive quantitative information about the weighting function matching at different wavelengths. In particular it does not account for the optical depth variation distribution in individual layers. However it is sufficient to show that the wavelength pairs providing the lowest temperature sensitivity also allow achieving the best weighting functions matching levels. Further studies are needed to quantitatively establish the capabilities of CoBRA in terms of the maximum achievable proximity of the measurement a reference weighting functions.
We are currently in the process of extending our simulation approach to further investigate the weighting functions matching and establish excitation wavelengths favorable for the reduction of the water vapor interference effects.
5. CoBRA and classical integrated path differential absorption (IPDA) methods
The traditional IPDA method, which usually relies on the selection of on- and off- line wavelengths within the same spectral line, does not provide the possibility of as high temperature sensitivity compensation as CoBRA due to the need in maintaining at least a minimum absorption difference between the optical depth values at the on- and off- line wavelengths resulting in significant spectral distances between the two wavelengths on the scale of a single spectral line thus leading to higher temperature induced errors.
To illustrate the difference in performance of the traditional single spectral line IPDA approach and the CoBRA method we have carried out IPDA and CoBRA simulations for the 6364.922 cm−1 line of CO2. The IPDA calculation was performed by considering the on- and off- line wavelength optical depth differences as variables for all possible wavelength combinations. To be consistent with the previous CoBRA simulations a requirement was imposed on the IPDA differential optical values to be 0.1 or higher. Since the threshold differential optical depth condition is verified by a comparison with an independently generated total optical depth spectrum as described previously, the calculation approach used results in occasional negative differential values in calculations for selected layer, temperature and on/off wavelength pairs. Such data points with negative components provide erroneous results and have been excluded from the analysis.
The results of the calculations are presented in Fig. 8. The spectrum in Fig. 8(a) is the point distribution plot of coefficients of variation as a function of on-line wavelength for all possible on- and off-line combinations. The data in Fig. 8(a) was obtained by using the same spectral range of 6364.722 – 6365.122 cm−1 for both on- and off-line wavelengths to remain within the same spectral line. The solid shape of the Fig. 8(a) distribution is due to the high density of the data points. The corresponding point distribution for the CoBRA method over the same measurement line spectral range shown in Fig. 8(b) includes all possible reference O2 band combinations in the spectral range of 7780-8000 cm−1. The discreteness of the points in the plots is related to the fineness of the calculation wavenumber and the coefficient of variation grids.
As can be seen, the performance of the CoBRA approach is about 2 times better at the line center compared to IPDA. Additionally, as the measurement line is shifted away from the line center the CoBRA temperature sensitivity remains under about 0.3% whereas the temperature induced uncertainty in the IPDA case is gradually increasing resulting in uncertainties up to about 2 - 7%
As mentioned previously, CoBRA requires compensations for the presence of additional background attenuation components due to water vapor, aerosols and other interferences. One possible way to provide such additional compensation information may be by combining the advantages of CoBRA and the differential absorption methods. Such combined approach may allow eliminating the interferences while still maintaining a high level of temperature sensitivity elimination. One suggested way of achieving this is by introducing additional off-line wavelengths in the cross-bands as follows:
As can be seen, this formula corresponds to the pure IPDA case depicted in Fig. 1(a). As such, in this case the difference between the pure IPDA approach and that combined with the CoBRA method is related to the cross-band optimization of the selected measurement and reference wavelengths to minimize the temperature interferences in addition to the use of the IPDA approach off-line wavelengths to correct for additional attenuation factors and interferences (such as water vapor, aerosols etc.). Validation studies are being conducted to verify if such combined approach is capable of delivering the same level of temperature insensitivity as the pure CoBRA method.
In general, the additional compensation for the interferences due to water vapor, aerosols etc. may be achieved in alternative ways by using different combinations of the CoBRA and the differential absorption methods involving either the use of supplementary off-line wavelengths for the measurement and reference wavelengths or by introducing completely independent additional measurements providing the missing information needed for corrections. This additional flexibility in selecting background correction methods may provide a way for cost reductions of the measurement setup.
6. Summary and conclusions
We have suggested a new technique based on cross-band matching of different molecular bands referenced to a band of O2 for the measurements of atmospheric molecular mixing ratios. The advantages of the technique are up to ~10 times reductions in temperature sensitivity compared to the conventional IPDA methodology. In contrast to the traditional IPDA approaches where the temperature induced uncertainties are increased when the measurement wavelength is moved away from the spectral line center, the CoBRA technique preserves low levels of temperature sensitivity for different spectral line measurement locations. This result is very important as it provides a way of minimizing temperature sensitivities in the spectral line regions favoring maximum low troposphere sensitivities required for the measurements of sources and sinks of greenhouse molecules such as CO2. Additionally, the traditional IPDA method is focused only on using lines within the regions of minimum temperature sensitivities in each of the measurement and reference bands. The CoBRA method relies on spectral lines matching making it possible to achieve relatively low temperature sensitivity levels even for spectral regions which exhibit high temperature sensitivity levels if considered independently.
Due to the fact that the CoBRA is based on close-matching of the measurement and reference lines, it also holds potential for close matching of the measurement and reference weighting functions. This would enable consistent mixing ratio measurements at all altitudes resulting in simultaneous automatic weighting function adjustments to the changing atmospheric parameters in both measurement and reference lines. Our results suggest that with proper selection of measurement and reference wavelength combinations, including the temperature sensitivity, water vapor, and weighting function optimizations, the new method may provide a way for self-sufficient measurements of atmospheric column-averaged molecular mixing ratios without corrections based on the data from Numerical Weather Prediction models. Such self-sufficient measurement technique holds promise for the simplifications of the data retrieval methods. Additional studies are under way to supplement the CoBRA analysis with the water vapor interferences studies to also quantify and minimize the effects of water vapor absorption.
The example analysis presented in this paper was carried out for the 1.26-1.27 micron O2 band taken as a reference. We are also investigating the suitability of the A-Band for the CoBRA technique . Additionally, in some lidar applications, the nitrogen (N2) gas is used as a reference instead of O2 in atmospheric mixing ratio measurements since the concentration of N2 is also proportionate to the atmospheric total pressure. Even though our current study did not involve estimates with the N2 band used as a reference, the CoBRA method is equally applicable for analysis involving the usage of other well-mixed atmospheric reference band molecules such as N2. It is expected that the resulting best achievable accuracies with such alternative references should be comparable to those obtained for the O2 reference band cases.
There are known accuracy restrictions of line-by-line calculations including limitations of the Voigt profile. Additional verification studies are required to establish the performance of the CoBRA approach with advanced lineshape models used and additional attenuation factors such as line-mixing and collision-induced absorption taken into account. Furthermore, the spectral line parameters in the HITRAN database are reported with given uncertainty indexes which are not currently taken into account in our simulations assuming “true line data”. To further improve the accuracy of our predictions, it is planned to further include the HITRAN line uncertainties into the results of our error estimate calculations.
We are further exploring and refining this methodology for its application to the mixing ratio measurements of a variety of molecules. Studies are being conducted to improve the accuracy and further verify our initial findings. It is in our plans to include the CoBRA analysis modules into the lidar modeling framework previously developed by our group .
This study was supported by the Earth Science Technology Office (ESTO), and the NASA Postdoctoral Program (NPP) administered by Oak Ridge Associated Universities.
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