Atmospheric aerosols influence the radiative budget of the earth, and the corresponding forcing depends on the vertical distribution of particle scattering properties (IPCC, 2013; Guan et al., 2010). The ability of the lidar technique to provide estimates of the vertical variability of particle parameters is therefore of current interest in understanding the radiative effects of aerosols. As a demonstration of this, numerous theoretical and experimental studies applying the multiwavelength lidar technique to the analysis of different atmospheric events – such as dust intrusion, forest fire smoke, and volcanic ashes – have been performed (e.g., Tesche et al., 2009; Rolf et al., 2012; David et al., 2013). Profiles of particle parameters can be obtained through the synergy of lidar and sun photometer measurements (Wagner et al., 2013; Lopatin et al., 2013; Granados-Muñoz et al., 2014) or from multiwavelength lidar measurements alone (Ansmann and Müller, 2005; Veselovskii et al., 2013; Müller et al., 1999, 2014). In this last case, particle backscattering (β) and extinction (α) coefficients measured at multiple wavelengths with Raman or high-spectral-resolution lidars (HSRLs) are inverted to particle microphysics (Ansmann and Müller, 2005). The system most often used for such measurements, due to its relative simplicity, is a Raman lidar based on a tripled Nd:YAG laser, which provides three backscattering (355, 532, 1064 nm) and two extinction (355, 532 nm) coefficients. To get this so-called 3β+2α data set, the backscatter signals are measured simultaneously with nitrogen vibrational Raman ones at 387 and 608 nm. While high-signal-to-noise measurements of nitrogen vibrational scattering at 387 nm during both daytime and nighttime have been possible using the narrowband, narrow-field-of-view approach (Whiteman et al, 2007), the use of vibrational Raman scattering at 608 nm has posed certain problems. First of all, the cross section of vibrational Raman scattering is approximately a factor of 1700 lower (considering a stimulating wavelength of 532 nm) compared to the Rayleigh one (Inaba, 1976), which limits the range and temporal resolution of the measurements. Daytime skylight values are also typically higher at 608 than at 387 nm. Another issue related to Raman nitrogen measurements at both 387 and 608 nm is the significant wavelength shift of the nitrogen Raman component with respect to the laser line. As a result, information about the spectral dependence of aerosol extinction is needed when α and β are computed (Ansmann et al., 1992), which can be an additional source of uncertainty. A well-known solution for both of these issues is the use of 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 rare instruments. At the same time, there are numerous existing Raman 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 of 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 exponent. Furthermore, the total cross section of nitrogen pure RR scattering exceeds that of vibrational scattering by approximately a factor 32 for the 337.1 nm laser wavelength, if all rotational lines are integrated (Inaba, 1976).

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., 2004; Di Girolamo 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 narrowband 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 measurements for calculating extinction and backscattering is the temperature dependence of the RR spectra of N2 and O2 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., 1974). The total RR return can be collected by using, for example, double diffraction grating polychromators (e.g., Arshinov et al., 2005; Kim and Cha, 2007), though measuring all Stokes and anti-Stokes lines with equal efficiency is technologically difficult and the spectral bandwidth of such a RR channel would be quite large. Temperature-independent RR signals can be also obtained by isolating in separate channels the lines which possess opposite temperature sensitivity for atmospheric temperature profiling and combining those separate signals into a balanced sum (Behrendt et al., 2002; Di Giloramo et al., 2006). Still both of these approaches are quite complicated to be used for upgrading existing multiwavelength systems.

The alternate approach considered in this paper is to select a portion of the RR spectrum characterized by 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. Selection of the RR lines is done by use of a wide-band interference filter which transmits the desired portion of the RR spectrum. Centering the filter transmission band near the temperature-insensitive RR lines decreases the temperature sensitivity of the RR scattering cross section to a level appropriate for tropospheric measurements. We should mention that with such an approach the edge of the interference filter transmission band is located close to the laser line, so blocking the elastic scattering component from penetrating into the RR channel is technologically more demanding compared to the measurements of vibrational scattering. However, the present state of optical coatings technology allows for the manufacturing of interference filters with high transmission and blocking characteristics adequate for this task.

This paper is structured as follows: in Sect. 2 we consider the general expressions for the computation of α and β. 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 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) that the effects related to the temperature dependence of pure-rotational and vibrational-rotational Raman scattering should be taken into account 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 heights corresponding to full geometrical overlap the power of elastic (PL) and Raman (PR) backscatter signals received from distance z can be calculated as PL(z)=1z2KLβLaer(z)+βLmol(z)⋅exp⁡-2∫0zαLaer(z′)+αLmol(z′)dz′,PR(z)=1z2KRFR(T(z))σLmolN(z)⋅exp⁡-∫0zαLaer(z′)+αRaer(z′)+αLmol(z′)+αRmol(z′)dz′. KL,R are range-independent system parameters, indices “aer” and “mol” here correspond to the aerosol and molecular components of backscattering and extinction coefficients, and indices “L” and “R” correspond to the laser and Raman component wavelengths λL, λR. Here, in order to generalize the notation, we use σLmol to refer to the sum of Cabannes, rotational and vibrational Raman contributions to the molecular differential cross section. The specific measurement (e.g., Rayleigh, rotational or vibrational Raman) is then determined by the channel bandpass characteristics as given in FR(T) below. N(z) is the molecular number density. The temperature-dependent factor FR(T(z)) is introduced in the same way as was done in Whiteman (2003a): FR(T)=∫ΔλdσLmol(λ,T)dλξR(λ)dλσLmol. Here ξR(λ) is the spectral transmission of the Raman channel, selecting the vibrational-rotational or pure-rotational part of the spectrum. The temperature-dependent factor can in principle be introduced also for the molecular backscattering in the equation for PL(z) shown in Eq. (1). However for the receivers with narrowband interference filters centered at the laser wavelength, this effect can generally be neglected except for the case of very light aerosol loading (Whiteman, 2003a). Here we consider cases with higher loadings that are suitable for microphysical inversions and neglect this effect.

The particle backscattering and extinction coefficients can be calculated from Eqs. (1) and (2) as βLaer(z)=-βLmol(z)+βLmol(z0)⋅PR(z0)PL(z)N(z)FR(z)PL(z0)PR(z)N(z0)FR(z0)⋅exp⁡∫z0zαLaer1-λLλRA+αLmol-αRmoldz′,αLaer(z)=ddzln⁡N(z)PR(z)⋅z2+ddzln⁡FR(z)-αLmol(z)-αRmol(z)1+λRλLA. The reference height z0 is usually chosen in the free troposphere where βLaer(z0)≪βLmol(z0). To account for the spectral dependence of extinction coefficient the Ångström exponent A is used: αaer(λL)αaer(λR)=λRλLA. For further consideration it is convenient to introduce the effective Raman backscattering cross section: σReff=∫ΔλdσLmol(λ,T)dλξR(λ)dλ. Then the ratio FR(z)FR(z0)=σReff(z)σReff(z0) is the ratio of effective cross sections at height z and z0, characterized by temperatures T and T0, respectively. For vibrational Raman scattering the deviation of the ratio FR(z)FR(z0) from 1 can be neglected, as can the contribution provided by the term ddzln⁡FR(z) in Eq. (5; Whiteman, 2003a). However for pure-rotational scattering, when only a part of the RR spectra is selected, the temperature (and hence height) dependence of FR(z)FR(z0) and ddzln⁡FR(z) can be important. The corresponding effects of these temperature dependencies will be considered in the Sect. 4.

The spectral dependence of particle extinction can be neglected when pure-rotational Raman scattering is used; however for vibrational scattering, which is characterized by a significant wavelength shift of the Raman component, the ambiguity in the choice of the Ångström exponent is an additional source of uncertainty in the βa and αa 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 follows from Eq. (5), the uncertainty in the computation of aerosol extinction εα due to the choice of Ångström exponent depends on the ratio λRλLA, 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 exp⁡∫z0zαL(z′)1-λLλRAdz′=exp⁡D(z)1-λLλRA, where D(z)=∫z0zαL(z′)dz′ is the aerosol optical depth for height interval [z0, z]. Thus the uncertainty εβ of the backscattering coefficient calculation is integrated over distance z0-z. Taking ΔA as the deviation of the Ångström exponent from the “true” value, εβ can be calculated from Eqs. (4) and (6) as εβ=βaer(A+ΔA)-βaer(A)βaer(A)=βtot(A+ΔA)-βtot(A)βtot(A)-βmol=βtot(A)exp⁡DλLλRA1-λLλRΔA-1βtot(A)-βmol=RR-1exp⁡DλLλRA1-λLλRΔA-1. Here βtot=βaer+βmol and R is the scattering ratio βtotβmol. For high aerosol loading, when βLaer>>βLmol, the ratio RR-1≈1 and εβ rises quickly with increasing optical depth D and ΔA. However in the UV and visible spectral ranges the magnitude of molecular and aerosol backscattering outside of clouds can be comparable, so the influence of molecular scattering on εβ must be considered. For estimating the uncertainty εβ for different laser wavelengths and aerosol loadings, numerical simulation was performed.

For simulating retrieval of particle backscattering and extinction coefficients from Mie–Raman lidar measurements a particle bimodal size distribution was represented as dn(r)dln⁡(r)=∑i=f, cNi(2π)1/2⋅ln⁡σi⋅exp⁡(ln⁡r-ln⁡r0i)22(ln⁡σi)2. Here Ni is the total particle number of the ith mode, ri describes the mode radius and lnσi is the dispersion. The index i=f and c corresponds to the fine and coarse mode, respectively. For all computations the values r0f=0.1 µm, r0c=1.2 µm and ln⁡σf,c=0.4 were used and the complex refractive index (CRI) was assumed to be the same for both modes. The concentration of particles in the fine mode Nf 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 NfNc=104 the main particle volume is attributed to the fine mode. For the second type (T2) NfNc=103 the total volume of particles in each mode is comparable. And finally, in the distribution T3 with NfNc=102 the coarse mode is predominant. The particle backscattering and extinction coefficients were calculated from the model size distribution using Mie theory (Bohren and Huffmann, 1983). The parameters of the fine and the coarse mode of real aerosols may exhibit strong variability (Dubovik et al., 2002); still the choice of typical values for this simulation permits us to estimate the effect of the spectral dependence of the Ångström exponent on backscattering and extinction calculation.

A Raman lidar based on a tripled Nd:YAG laser can measure the extinction Ångström exponent at 355–532 nm wavelengths (A355-532). However, when nitrogen vibrational Raman backscatters at 387 and 608 nm are used to determine backscattering coefficients at 355 and 532 nm, the Ångström exponents A355-387 and A532-608 are needed, and these may differ from A355-532. Table 1 shows the Ångström exponents A355-532, A355-387, and A532-608 for the size distributions T1–T3 and refractive indices m=1.35-i0.005, 1.45-i0.005, 1.6-i0.005, and 1.6-i0.05. These values of CRI correspond to a variety of particles, such as water aerosol, biomass burning products and desert dust (Dubovik et al., 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 ΔA may exceed 0.5 when A355-532 is used for the computation of both β355 and β532. For particles with a coarse-mode predominance (T3), the spectral dependence of the Ångström exponent is weaker and ΔA< 0.2 when A355-532 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 is strongest for a PSD with a predominance of the fine mode, so the simulation results are presented for the T1 distribution (NfNc= 104). The uncertainty of the backscattering calculation depends on aerosol loading; thus in the simulations different particle concentrations were considered in order to obtain extinction coefficients of αa=0.1, 0.2, and 0.4 km-1 at 355 and 532 nm. The refractive index used was m=1.45-i.005, and corresponding model values of A355-387, A532-608 and A355-532 were taken from Table 1. The backscattering and extinction coefficients for the chosen size distribution together with model molecular scattering were used to generate noise-free synthetic backscatter and nitrogen Raman lidar signals using Eqs. (1) and (2), but neglecting the temperature dependence of backscattering cross section. Then, the values of α and β were back-calculated with Eqs. (4, 5) using Ångström exponents A, which differed from the model values Amod. The systematic uncertainty for backscattering was determined as εβ=βaer(A)-βaer(Amod)βaer(Amod). The systematic uncertainty in extinction was defined similarly.

The results of the simulations for particle extinction are summarized in Table 2, showing εα at 355 and 532 nm for different assumed values of A in range [0, 2.0]. As mentioned, the uncertainty of extinction εα is independent of range or aerosol loading. Interpolating the results in Table 2, we can conclude that it is below 2 % for 355 nm and below 3 % for 532 nm wavelength when A355-532= 1.32 is used in the computations.

In contrast to extinction, the uncertainties εβ depend on range since the differential transmission between Raman and laser wavelengths is involved and errors in this calculation accumulate with range. The height profiles of εβ at 355 nm for the particle extinction coefficients 0.1, 0.2 and 0.4 km-1 are given in Fig. 1 for ΔA=A-Amod=±0.5. For comparison, the same figure also shows results at 532 nm for α= 0.1 and 0.2 km-1. The uncertainty is negligible near the reference height (z0= 4000 m), and it rises with increasing z-z0. At z= 1000 m the uncertainties can be as high as 8 and 10 % at 355 nm for α= 0.1 and 0.2 km-1, respectively, when ΔA=-0.5. For 532 nm these uncertainties are 4 and 6 %, which is approximately a factor of 2 lower than at 355 nm. An increase of extinction up to α= 0.4 km-1 leads to a rapid increase in εβ, and the correct choice of the Ångström exponent becomes more important. Figure 2 illustrates the dependence of εβ(ΔA) at z= 1000 m on different values of extinction coefficient. This dependence is close to linear, so an increase of ΔA from 0.5 to ΔA= 1 doubles the uncertainty when compared with Fig. 1.

The simulations performed here demonstrate that the uncertainty in the choice of the Ångström exponent can be a source of significant bias in the calculation of backscattering calculation when aerosol layers with high optical depth are profiled and that this effect is especially pronounced at 355 nm. In real measurements, the situation can be even more complicated because of the vertical variability of the Ångström exponent. So it is desirable to eliminate the uncertainties related to the assumption of the A value through the use of rotational Raman scattering instead of vibrational scattering, thus decreasing the frequency shift of the inelastically scattered component.

In this section we describe a rather simple approach for implementing a rotational Raman channel in a conventional multiwavelength lidar. The approach is tested at 532 nm laser wavelength.

The simultaneous use of Mie and vibrational Raman nitrogen backscattering signals in lidars has permitted useful retrievals of particle extinction and backscattering coefficients. 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. The absence of such a frequency shift has been one of the advantages of the technologically more complex approach of high-spectral-resolution lidar for the task of measuring aerosols with a sufficient number of wavelengths to support microphysical inversions. As in the HSRL technique, the use of rotational Raman scattering, instead of vibrational scattering, 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 versus the vibrational Raman ones at 608 nm 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 either anti-Stokes or 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 ratio even under daytime conditions. Upgraded this way, the NASA GSFC multiwavelength Raman lidar has demonstrated improved capabilities for α532 measurements, which in turn have improved the inversion of 3β+2α optical data to particle microphysics.

The next step in our plans is to test the use of the RR signal at 355 nm instead of 387 nm due to vibrational scattering. Though quite capable signal strengths can be achieved 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 attractive and will be the focus of future development.