Use of rotational Raman measurements in multiwavelength aerosol lidar for evaluation of particle backscattering and extinction

Vibrational Raman scattering from nitrogen is commonly used in aerosol lidars for evaluation of particle backscattering (β) and extinction (α) coefficients. However, at mid-visible wavelengths, particularly in the daytime, previous measurements have possessed low signal-to-noise ratio. Also, vibrational scattering is characterized by a significant frequency shift of the Raman component, so for the calculation of α and β information about the extinction Ångström exponent is needed. Simulation results presented in this study demonstrate that ambiguity in the choice of Ångström exponent can be the a significant source of uncertainty in the calculation of backscattering coefficients when optically thick aerosol layers are considered. Both of these issues are addressed by the use of pure-rotational Raman (RR) scattering, which is characterized by a higher cross section compared to nitrogen vibrational scattering, and by a much smaller frequency shift, which essentially removes the sensitivity to changes in the Ångström exponent. We describe a practical implementation of rotational Raman measurements in an existing Mie–Raman lidar to obtain aerosol extinction and backscattering at 532 nm. A 2.3 nm width interference filter was used to select a spectral range characterized by low temperature sensitivity within the anti-Stokes branch of the RR spectrum. Simulations demonstrate that the temperature dependence of the scattering cross section does not exceed 1.5 % in the 230–300 K range, making correction for this dependence quite easy. With this upgrade, the NASA GSFC multiwavelength Raman lidar has demonstrated useful α532 measurements and was used for regular observations. Examples of lidar measurements and inversion of optical data to the particle microphysics are given.

A well-known solution for both of these issues is the use of High Spectral Resolution Lidar (HSRL) (Eloranta, 2005). The recent results provided by the NASA/LaRC airborne lidar demonstrate the possibility of reliable HSRL operation at both 355 and 532 nm (Müller et al., 2014). However such lidars, due to their complexity and cost, are still unique instruments. At the same time, there are numerous existing Raman 5 lidars which can potentially be upgraded to improve on the weak vibrational Raman scattering measurements at 608 nm. One of the ways this can be accomplished is to use pure rotational Raman (RR) scattering instead vibrational scattering. The small spectral separation of the elastic and RR components of the signal implies that aerosol backscatter and extinction can be obtained without information about the Ångström ex-10 ponent. Furthermore, the backscatter cross section of anti-Stokes component of pure RR nitrogen scattering exceeds that of vibrational scattering by approximately a factor of 15-20, when all lines for nitrogen and oxygen are integrated (Fenner, 1973). Pure rotational Raman scattering is widely used in laser remote sensing for the measurement of atmospheric temperature (e.g. Behrendt and Reichardt, 2000;Balin et al., 15 2004;DiGirolamo et al., 2004;Arshinov et al., 2005;Radlach et al., 2008), where the pure RR and elastic signals are generally separated by the use of narrow-band interference filters or diffraction-grating-spectrometers. Rotational Raman scattering can also be used for the particle extinction and backscattering calculation (e.g. Kim and Cha, 2007;Achtert et al., 2013). However, an important consideration in the use of RR mea-20 surements for calculating extinction and backscattering is the temperature dependence of the RR spectra of N 2 and O 2 molecules. This issue in principle can be resolved by using the sum of lidar returns from the Stokes and anti-Stokes branches, which is essentially temperature independent (Penny et al., 1973). However, measuring all Stokes and anti-Stokes lines with equal efficiency is technologically very difficult. The alternate 25 approach considered in this paper is to select a portion of the RR spectrum characterized by a low temperature sensitivity inside one of the spectral branches. Such an approach simplifies the implementation of a RR channel in conventional multiwavelength Raman lidar systems without significant modification of the receiver design. Se- lection of the RR lines is done by use of a wide-band interference filter which transmits the desired portion of the anti-Stokes branch. Centering the filter transmission band near the temperature insensitive lines of the RR spectrum decreases the temperature sensitivity of the RR scattering cross section to a level appropriate for tropospheric measurements.

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This paper is structured as follows: in Sect. 2 we consider general expressions for α and β computation, Sect. 3 presents an analysis of uncertainties related to the choice of the Ångström exponent when nitrogen vibrational Raman measurements are used. Our approach to implementing RR observations and first measurement results are given in Sect. 4. The paper is finished with conclusion. 10 2 Calculation of particle extinction and backscattering from Mie-Raman lidar measurements The possibility of independent calculation of aerosol backscattering and extinction coefficients from simultaneously measured elastic and vibrational Raman backscatters was first demonstrated by Ansmann et al. (1992). Later it was shown (Whiteman, 2003a, b) 15 that the temperature dependence of Raman scattering can be significant when considering measurements of Rayleigh-Mie and Raman lidar. That temperature dependence will be considered later in this paper and a correction for the effects of temperature dependence of rotational Raman scattering will be developed. For this reason, we introduce the temperature dependent lidar equation for Raman scattering here. For the 20 heights corresponding full geometrical overlap the power of elastic (P L ) and Raman (P R ) backscatter received from distance z can be calculated as: K L,R are range independent system parameters, indices "aer" and "mol" here correspond to aerosol and molecular components of backscattering and extinction coefficients, while indices "L" and "R" correspond to laser and Raman component wave- is molecular differential backscattering cross section, which includes Cabannes line together with vibrational and rotational Raman contributions, N(z) is the molecular number density. The temperature dependent factor F R (T (z)) is introduced the same way as it was done in (Whiteman, 2003a): Here ξ R (λ) is the spectral transmittance of Raman channel, selecting vibrationalrotational or pure rotational part of the spectrum. The temperature dependent factor can in principle be introduced also for the molecular backscattering in Eq. (1). However for the receivers with narrowband interference filters centered at laser wavelength, this effect can normally be neglected (Whiteman, 2003a). 15 The particle backscattering and extinction coefficients can be calculated from Eqs. (1) and (2) as The reference height z 0 is usually chosen in the free troposphere where β aer L (z 0 ) β mol L (z 0 ). To account for the spectral dependence of extinction coefficient the Ångström exponent A is used: For further consideration it is convenient to introduce the effective Raman backscattering cross section Then the ratio is the ratio of effective cross sections at height z and z 0 , characterized by temperatures T and T 0 respectively. For vibrational Raman scattering 10 the deviation of ratio F R (z 0 ) from 1 can be neglected as well as contribution provided by term d dz ln F R (z) in Eq. (5) (Whiteman, 2003). However for pure rotational scattering, when only a part of RR spectra is selected, the temperature (and hence height) dependence of The spectral dependence of particle extinction can be neglected when the pure rotational Raman scattering is used, however for vibrational scattering, characterized by significant wave shift of Raman component, ambiguity in the choice of the Ångström ex-5 ponent is an additional source of uncertainty in β a and α a calculations. This uncertainty was considered before for measurements acquired at 351 nm (Whiteman, 2003a, b).
Here we consider the case for the 355 and 532 nm wavelengths of the 3β + 2α lidar system. As it follows from Eq. (5) the uncertainty in the computation of aerosol extinction ε α due to the choice of Ångström exponent depends on the ratio

and for a constant
A this uncertainty is range independent. The effect of the Ångström exponent on the calculation of backscattering coefficient is described by the exponent term in Eq. (4), which for height independent A can be written as 15 Where D(z) = z z 0 α L (z )dz is the aerosol optical depth for height interval [z 0 , z]. Thus the uncertainty ε β of backscattering coefficient calculation is integrated over distance z 0 − z. Taking ∆A as the deviation of the Ångström exponent from the "true" value, ε β can be calculated from Eqs. (4) and (6) as Here β tot = β aer +β mol and R is the scattering ratio β tot β mol . For high aerosol loading, when β aer L β mol L the ratio R R−1 ≈ 1 and ε β rises quickly with increasing optical depth D and ∆A. However in the UV and visible spectral ranges the magnitude of molecular and 5 aerosol backscattering outside of clouds can be comparable, so the influence of molecular scattering on ε β must be considered. For estimating the uncertainty ε β for different laser wavelengths and aerosol loadings, numerical simulation was performed.
In the simulations performed here the particle bimodal size distribution was represented as: Here N i is the total particle number of the i th mode, r i describes the mode radius and ln σ i is the dispersion. The index i = f, c corresponds to the fine and coarse mode, respectively. For all computations the values r 0f = 0.1 µm, r 0c = 1.2 µm and ln σ f, c = 0.4 were used and the complex refractive index (CRI) was assumed to be the same for 15 both modes. The concentration of particles in the find mode N f was kept constant through all simulations, while the concentration in the coarse mode varied. The spectral dependence of the Ångström exponent is influenced by the relative contributions of the fine and the coarse modes (O'Neil et al., 2001), so to evaluate this effect three types of particle size distribution (PSD) were considered. For the first type (T1) with A Raman lidar based on a tripled Nd:YAG laser can measure the extinction Ångström exponent at 355-532 nm wavelengths (A 355-532 ). However, when nitrogen vibrational Raman backscatters at 387 and 608 nm are used to get backscattering coefficients at 5 355 and 532 nm, the Ångström exponents A 355-387 and A 532-608 are needed and these may differ from A 355-532 . Table 1 shows the Ångström exponents A 355-532 , A 355-387 , A 532-608 for the size distributions T1-T3 and refractive indices m = 1.35-i0.005; 1.45-i0.005; 1.6-i0.005; 1.6-i0.05. These values of CRI correspond to variety of particles, such as water aerosol, biomass burning products and desert dust (Dubovik et al., 10 2002). The spectral dependence of the Ångström exponent is the most significant for particles with a fine mode predominance. For the T1 distribution, the uncertainty in the choice of the Ångström exponent ∆A may exceed 0.5 when A 355-532 is used for the computation of both β 355 and β 532 . For particles with a coarse mode predominance (T3), the spectral dependence of the Ångström exponent is weaker and ∆A < 0.2 when 15 A 355-532 is used.
To estimate how sensitive the backscattering coefficient is to the choice of the Ångström exponent, we considered an aerosol layer extending from the ground up to 4000 m with a height independent particle concentration. As mentioned, the spectral dependence of A has the most influence for PSD with a predominant fine mode, so 20 the simulation results are presented for the T1 distribution ( . The uncertainty of the backscattering calculation depends on aerosol loading, so in the simulations different particle concentrations were considered in order to obtain extinction coefficients of α a = 0.
The systematic uncertainty in extinction was defined similarly. The results of the simulations for particle extinction are summarized in Table 2, showing ε α at 355 and 532 nm for different assumed values of A in range [0, 2.0]. As mentioned, the uncertainty of extinction ε α is independent of range or aerosol loading and in our computations it does not exceed 2 % for both wavelengths, when A 355-532 is used.
In contrast to extinction the uncertainties ε β depend on range since the differential transmission between the two Raman wavelengths is involved and errors in this calcu-10 lation accumulate with range. The height profiles of ε β at 355 nm for the particle extinction coefficients 0.1, 0.2 and 0.4 km −1 are given in Fig. 1   In this section we describe the rather simple approach to implement a rotational Raman channel to a conventional multiwavelength lidar. The approach is tested at 532 nm, and implementation of RR channel at 355 nm is in future plans for the system upgrade.

Temperature sensitivity of rotational Raman measurements
In our implementation a part of RR spectrum is selected by the steep edge interference 10 filter. For calculation of effective RR backscattering cross section (σ eff RR ) the integral in Eq. (7) can be replaced by the sum of contributions from individual rotational lines of nitrogen and oxygen. For every Stokes (s) and anti-Stokes (as) line in RR spectrum, resulting from a molecule in state J, the differential backscattering cross section for the sum of components with polarization parallel and perpendicular to polarization of 15 laser beam, can be computed as (Penney et al., 1974;Behrendt and Nakamura, 2002;Adam, 2009): and the frequency shifts are: The rotational energy is approximated as E J = J(J +1)hcB 0 , the values of g(J), I, γ for 5 molecules of nitrogen and oxygen were taken from Behrendt and Nakamura (2002). Figure 3 shows RR the spectra of N 2 and O 2 molecules weighted with corresponding number density fractions in atmosphere for a laser wavelength of 532.12 nm and T = 300 K. The spectrum includes Stokes and anti-Stokes branches and spreads over several nm on both sides of the stimulating laser wavelength. In our implementation, 10 the filter transmitted only portion of the anti-Stokes branch in order to have the possibility to shift the filter transmission band toward shorter wavelengths by filter tilting, if necessary. The effective differential cross section σ eff RR of atmosphere is obtained by summing cross sections σ i J = σ i as (J) of individual RR lines of molecules at respective wavelengths λ i J : The indices i = 1, 2 correspond to N 2 and O 2 molecules, η i are the density fractions of these molecules in atmosphere. The frequency shift of rotational lines with respect to the frequency of the laser radiation is small compared with vibrational scattering, so in practice the spectral depen-20 dence of particle extinction can be neglected. Thus the expressions (Eqs. 4 and 5) for backscattering and extinction coefficient become: β aer (z) = −β mol (z) + β mol (z 0 ) · P R (z 0 )P L (z)N(z)σ eff RR (z) P L (z 0 )P R (z)N(z 0 )σ eff RR (z 0 ) Using notation X (z) = σ eff RR (z) σ eff RR (z 0 ) , the error of β aer computation (ε T β ) due to neglecting the height variation of temperature (X = 1), can be estimated from Eq. (16) as: Here R is the scattering ratio β tot β mol . For β aer β mol the error ε T β becomes X −1 X , while for 5 low aerosol loading there is an enhancement factor R R−1 . The influence of temperature dependence of σ eff RR on extinction calculation (∆α T ) is given by the second term in Eq. (17) This term can be significant in the presence of strong temperature gradients. To quan-10 tify the possible uncertainties in the evaluation of backscattering and extinction coefficients arising from the temperature dependence of σ eff RR , numerical simulation studies were performed. The RR line with least temperature sensitivity is in the vicinity 530.4 nm (J = 9) for O 2 and in vicinity of 530.2 nm (J = 7) for N 2 , so centering the filter transmission band near these values will minimize the sensitivity of σ eff RR to changes 15 in temperature. When choosing filter parameters the desire is to maximize the cross section σ eff RR by including only the strongest rotational lines since unnecessarily wide transmission band will lead to an increase of the sky background noise and an overall decrease in signal to noise under daytime conditions. performed with T varying in the range 230-300 K where the reference temperature T 0 was taken to be T 0 = 300 K. For all intervals the relative change of RR scattering cross does not exceed 3.5 %. The ratios of σ eff RR (T 0 ) to the total cross section of anti-Stokes branch for these three intervals are 0.2, 0.37 and 0.7. Of these intervals, that of 529.2-531.2 nm is the most attractive, as it contains approx-5 imately 70 % of the Raman signal provided by the entire anti-Stokes band and possesses a small temperature dependence (the variation of σ eff RR is below 1.0 %). Based on these considerations, we chose this interval as the target for the interference filter design.
The transmission spectrum of the interference filter used in our experiments, taken from the manufacturer's data sheet (Alluxa, CA, USA), is shown in Fig. 3. The filter has transmission greater than 95 % at the peak with bandwidth of approximately 2.3 nm FWHM. The suppression of the elastic scattering at 532.12 nm is performed with OD > 4. The temperature dependence of X −1 X for this filter is also shown in Fig. 4. To get the effective scattering cross section the filter transmission was convoluted with Raman 15 spectrum in accordance with Eq. (14). The variation of σ eff RR in 230-300 K temperature range does not exceed 1 %. The temperature dependence of particle backscattering coefficient can be accounted by computing X (z) in Eq. (16) on a base of the atmosphere model or radiosonde measurements. Figure 5 shows X (z) computed for the US Standard Atmosphere model up to 10 km height, the reference height is taken at 20 z = 0. The value of X in this height range does not change for more than 1 %, so in many practical cases X = 1 can be used.
The error of the extinction coefficient calculation ∆α T induced by the temperature height variation depends, as it follows from Eq. (17), on the gradient of the temperature profile. To estimate this error we have tested the temperature profiles from the 25 US Standard Atmosphere model and from radiosonde launches performed at Dulles airport, VA in the vicinity of Washington DC. The results of computations are shown in Fig. 6 cubic spline over 7 points was used. For the model temperature profile the decrease of the temperature with height provides a negative contribution to the calculated particle extinction. The error ∆α T varies with height but it is below 0.002 km −1 for the heights up to 10 km. The same figure shows also the results for radiosonde launches on 5 January and 10 July 2013. Corresponding temperature profiles present low-scale oscillations, 5 still for both days ∆α T < 0.002 km −1 . Computations performed for days at different seasons have demonstrated that, in general, temperature variations contribute an error in calculated extinction of less than 2 % for extinction values of 0.1 km −1 and greater.
Using the scattering cross sections provided by Fenner et al. (1973) for 488.0 nm laser line we estimate that the total RR cross section, including both Stokes and anti-Stokes branches of N 2 and O 2 , exceeds that of vibrational nitrogen by approximately a factor of 40. Considering a temperature of 270 K, the filter shown in Fig. 3 transmits approximately 73 % of the total anti-Stokes components for nitrogen and oxygen. We therefore estimate that the scattered power in the RR channel is a factor of 15 higher than that of vibrational nitrogen Raman channel at 608 nm (using a filter trans-15 mission of 70 % for the vibrational channel). Thus, under skylight limited conditions, the RR channel would provide greater signal-to-noise if the width of the filter used for the vibrational Raman measurement is greater than approximately 0.15 nm, which is the case for most implementations of vibrational Raman measurements at 608 nm. The attractiveness of the rotational Raman approach is enhanced by the fact that many PMT 20 detectors normally have higher quantum efficiency at 532 than at 608 nm.

Modification of GSFC Raman lidar system
A description of the NASA/GSFC multiwavelengh Raman lidar is presented in Veselovskii et al. (2013). Our experience in inverting time-series of 3β + 2α measurements to particle microphysical properties has demonstrated that uncertainties of the 25 retrieved parameters are related mainly to the random uncertainty of the α 532 data, which in turn is due to insufficient power of the 608 nm backscatter signal (Veselovskii et al., 2013). This is in agreement with the sensitivity studies performed by Perez-   et al. (2013). To incorporate the RR channel at 530 nm the lidar receiving module was modified as shown in Fig. 7. This optical configuration permitted simultaneous measurements of the vibrational and rotational Raman signals. The spectral components at 608 and 532 nm were separated by a dichroic mirror DM with approximately 95 % being reflected to 608 nm channel. The beamsplitter shown in Fig. 7 then 5 reflected approximately 10 % portion of the 532 signal into the Mie channel with more than 85 % being transmitted into the RR channel. Two RR filters each possessing the characteristics shown in Fig. 3 were used together to provide more than 8 orders of magnitude of rejection of the elastic signal. The Mie 532 nm and RR 530 nm signals were measured by R1924 Hamamatsu PMTs, while in 608 nm channel a Hamamatsu R9880-20 PMT was used. To compare the scattered power in 608 and 530 nm channels, we made two sequential measurements using the same R1924 PMT for both channels. After correction for difference in quantum efficiency of the photocathode at 608 and 530 nm, we estimate the enhancement of scattered power in RR channel compared with the vibrational one to be more than a factor 10. 15 The initial measurements were taken under cloudy conditions to test the blocking of the Mie scattering by the RR filters. Those tests did not reveal any enhancement of the signal measured in the RR channel due to backscatter from the base of the cloud. Figure 8 shows backscattering coefficients at 532 nm calculated from vibrational and rotational Raman signals together with the temperature profile measured by ra-20 diosonde from Dulles airport. The Ångström exponent was chosen as A = 1.0 when the 608 nm signal was used. In the height range 1000-5000 m the temperature changes were within an interval of 25 • and the error in the calculation of the backscattering coefficient due to temperature variation was below 1.0 %. The maximal difference between backscattering profiles was observed in the maximum of scattering layer at approxi-25 mately 1750 m height and did not exceed 2 %.
The extinction profiles for the same day, calculated from vibrational and rotational Raman signals, are shown in Fig. 9. For comparison, the same figure also shows α 355 calculated from the 387 nm Raman signal. This figure clearly demonstrates the im- Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | provement of the extinction calculation when the RR signal at 530 nm is used instead of that of vibrational scattering at 608 nm. After these test measurements were performed, the 608 nm beamsplitter was removed from the receiver to maximize the RR signal at 530 nm and the system was used for regular observations. An example of vertical profiles of 3β +2α measurements 5 made on 1 July 2014 is given in Fig. 10. The measurements were performed during the night time from 01:00-01:30 UTC. Figure 11 shows the lidar ratios at 355 and 532 nm and the extinction Ångström exponent calculated from the optical data averaged in 100 m height bins. The lidar ratio below 2000 m is about 90 sr for both wavelengths, but above 2000 m the lidar ratios gradually decrease. The Ångström exponent rises 10 above 2000 m from 1.2 to 2.3 at 2750 m, indicating that the aerosol layer above 2000 m contains smaller particles.
The 3β + 2α measurements were inverted to the particle microphysical properties using inversion with regularization as described in Veselovskii et al. (2002). Vertical profiles of the effective radius and the real part of the refractive index are shown in 15 Fig. 12. Up to 2000 m the effective radius is about 0.26 µm and above that height it decreases reaching 0.13 µm above 2500 m. Simultaneously with the decrease of r eff , the real part m R increases from 1.37 to approximately 1.50. Thus above 2000 m there is a layer with a different particle type possessing smaller size and higher m R .

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The simultaneous use of Mie and vibrational Raman nitrogen backscattering signals in lidars has permitted useful retrievals of particle extinction and backscattering. However, vibrational Raman measurements are characterized by a significant frequency shift of the return signal from the stimulating one, introducing uncertainties due to the wavelength scaling of particle scattering. This has been one of the advantages of the technologically more complex approach of High Spectral Resolution Lidar (HSRL) to the task of measuring aerosols with a sufficient number of wavelengths to support microphysi- Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | cal inversions. As in the use of HSRL, the use of rotational Raman scattering, instead of vibrational, essentially removes the concern due to wavelength scaling while simultaneously permitting measurements to take advantage of a much larger cross section. For the case of measurements made using the 532 nm stimulating wavelengths, the RR signals at 532 nm are also improved vs. the vibrational Raman ones at 608 nm 5 due to the typically higher quantum efficiency of detectors operating at 532 nm. We have presented a practical approach to implementing rotational Raman measurements in multiwavelength aerosol lidar using sharp edge interference filters to separate the RR and Mie signals. During the design phase of the development, numerical simulations were performed demonstrating that a measurement of aerosol extinction could be made with low temperature dependence using a portion of the either anti-Stokes of Stokes components. This selection also achieved a signal increase of more than a factor or 10 when compared with vibrational nitrogen. In most cases, this permits filters with larger FWHM to be used for the extinction measurement while still increasing the overall signal-to-noise even under daytime conditions. Upgraded this way the 15 NASA/GSFC multi-wavelength Raman lidar has demonstrated improved capabilities for α 532 measurements which in turn has improved the inversion of 3β + 2α optical data to particle microphysics. The next step in our plans is to test the use of RR signal at 355 nm instead of 387 nm due to vibrational scattering. Though quite capable signal strengths can be achieved 20 using vibrational nitrogen signals at 387 nm, the issue of wavelength scaling still remains. The modeling performed here shows that when the aerosol layers with high optical depth are considered errors due to wavelength scaling for Raman vibrational measurements can be larger at 355 nm than at 532 nm. Thus the prospect of achieving 3β + 2α measurements using RR scattering for both extinction measurements is