The AIRS instrument is a part of the Afternoon Train A-Train; and is aboard the Aqua satellite in Sun-synchronous orbit at 705 km altitude. The AIRS spectrometer disperses upwelling radiation across highly sensitive detector arrays, which results in 2378 spectral samples (nominal spectral resolution of λ/Δλ=1200). These high-spectral resolution measurements cover three infrared wavebands 3.74–4.61, 6.20–8.22 and 8.8–15.4 µm; and can be used to detect volcanic ash and SO2 . An individual AIRS granule comprises 90×135 pixels (1800 km × 2700 km) with a spatial resolution of 13.5 km × 13.5 km at nadir.

The data products used in the present study are the level 1B geolocated and calibrated radiances version 5.0.23. Only channels suitable for retrievals were used to calculate brightness temperatures (i.e. with L2_ignore flag set to zero; see https://disc.gsfc.nasa.gov/information/documents?title=AIRS_Documentation).

The CALIPSO satellite is also a member of the A-Train and carries the CALIOP instrument as its primary payload . Following closely behind Aqua (∼ 73 s), the space-borne lidar measures elastically backscattered light at 532 and 1064 nm using a three-channel receiver subsystem . The ratio of the backscatter measured at these wavelengths (i.e. the attenuated colour ratio) can be used to infer information about particle size . The 532 nm signal is also split into two linear polarization states, which enable depolarization measurements to distinguish between irregular (e.g. ash, ice, dust) and spherical (e.g. sulfates) particles.

The CALIOP level 1 version 4, 532 nm total attenuated backscatter profiles (L1-Standard-V4–00) were used to generate attenuated backscatter curtain plots. At a given wavelength, λ, the total attenuated backscatter profile, βλ′(r), is related to the particulate and molecular components of backscatter by βλ′(r)=[βm,λ(r)+βp,λ(r)]Tm,λ2(0,r)Te,λ2(0,r)TO3,λ2(0,r), where r is the range from the lidar, βm,λ(r) and βp,λ(r) are the molecular and particulate backscatter profiles, respectively, and Tm,λ2(0,r), Te,λ2(0,r) and TO3,λ2(0,r) are the molecular, effective and ozone two-way transmittance profiles, respectively. We note that the effective two-way transmittance profile, Te,λ2(0,r), is related to the particulate two-way transmittance profile via Te,λ2(0,r)=Tp,λ2η(0,r), where η is defined here as the multiple scattering factor . The vertical resolutions of the level 1 backscatter profiles are altitude dependent and are broken down into five range intervals. For the altitudes ranges shown here (0–20 km), the relevant vertical resolutions are 30  and 60 m for the altitude ranges from -0.5 to 8.2 and 8.2 to 20.2 km, respectively.

Geometric and optical properties of layers were obtained from the level 2 aerosol layer (L2_05kmALay) product version 3. (version 4, level 2 data had not been released at the time of writing.) The vertical resolution was 60 m for all volcanic layer observations as they were within the 8.2–20.2 km altitude range interval. To ensure constrained conditions for the lidar ratio retrieval (i.e. clear air above and below a lofted layer with acceptable SNR), only stratospheric volcanic aerosol layers that had an extinction quality control flag equal to 1, a valid two-way transmittance measurement (i.e. 0<Te2(rt,rb)<1) and a horizontal averaging value of 5 km were included in the analysis. We refer to “valid” lidar ratio retrievals hereafter as having satisfied these criteria. We note that the operational lidar ratio data (Final_532_Lidar_Ratio) were not used because we wanted to adjust the multiple scattering factor (η) in the lidar ratio retrieval presented in Sect. .

The level 2 optical products used in the present analysis are the effective two-way transmittance (Te2(rt,rb)), the integrated attenuated backscatter (γp′), the layer-integrated volume depolarization ratio (δv) and the layer-integrated attenuated colour ratio (χ′). All products are calculated relative to the base (rb) and top (rt) of a given aerosol layer. As in , δv is calculated as δv=∑k=topbaseβ532,⟂′(rk)∑k=topbaseβ532,∥′(rk), where β532,⟂′(r) and β532,∥′(r) are the perpendicular and parallel components of the attenuated backscatter at 532 nm. The perpendicular and parallel components of attenuated backscatter make up the total attenuated backscatter at 532 nm such that β532′(r)=β532,⟂′(r)+β532,∥′(r). The layer-integrated attenuated colour ratio, χ′, is calculated as χ′=∑k=topbaseB1064(rk)∑k=topbaseB532(rk), where, B1064(r) and B532(r) are the total attenuated backscatter coefficients corrected for molecular and ozone transmittance: Bλ(r)=βλ′(r)Tm,λ2(0,r)TO3,λ2(0,r)=[βm,λ(r)+βp,λ(r)]Te,λ2(0,r). In general, the 1064 nm backscattering component will be less than the 532 nm component for small particles, and so the attenuated colour ratio will also be small. Indeed, the attenuated colour ratio is generally greater than 1 for cloud layers and is less than 1 for aerosols . The particulate integrated attenuated backscatter, γp′, is defined as γp′=∫rtrbβp(r)Tp2(rt,r)dr and is approximated using the clear air trapezoid technique in the level 2 layer products . This quantity is used in the lidar ratio retrieval described in Sect. . Finally, the effective two-way transmittance, Te2(rt,rb), is calculated by taking the ratio of the mean attenuated scattering ratio profiles over regions of clear air detected above and below the layer : Te2(rt,rb)=〈Rbelow′(r)〉〈Rabove′(r)〉, where the attenuated scattering ratio profile is defined as R′(r)=β532′(r)/βm,532′(r). We note that only the top layer in a given profile was considered in the present study so that measurements of Te2(rt,rb) were not degraded by signal attenuation introduced by overlying cloud–aerosol layers. For the top layer, the operational retrieval assumes a purely molecular atmosphere (i.e. 〈Rabove′〉=1), and so the effective two-way transmittance is calculated as Te2(rt,rb)=〈Rbelow′〉. The clear air region is defined by the “clear air analysis depth”, which is determined via an iterative process in the CALIPSO level 2 feature detection algorithm . It should also be noted that Te2(rt,rb) can only be calculated at 532 nm as the molecular scattering signal at 1064 nm is too small (∼ 16 times weaker than at 532 nm).

The CALIOP level 2 profile products (L2_05kmAPro) were also used to obtain the normalized, ozone-corrected, total attenuated backscatter coefficient, βN′(r), which is required as input into the lidar ratio retrieval (discussed in Sect. ). The reason for calculating βN′(r) from the level 2 operational products is so that a new value for η, more representative of volcanic ash–sulfates, can be used in the lidar ratio retrieval.

In order to identify sulfate-rich aerosol layers in CALIOP profiles, we assume SO2 is collocated with SO42- and adopt the SO2 index (SI) defined in . The SI is defined as the difference between brightness temperatures measured at 7.1 and 7.3 µm and exploits the strong absorption signature of SO2 at 7.3 µm. It is defined such that positive values indicate the presence of SO2 in the atmosphere; SI=BT(1407.2cm-1)-BT(1371.5cm-1), where BT(ν) is the brightness temperature measured at wavenumber, ν. For detection of volcanic aerosols dominated by ash particles, we use the brightness temperature difference (BTD) algorithm defined in . To be consistent with the terminology used in , the ash BTD algorithm is referred to hereafter as the ash index (AI). The AI is a 12-channel BTD algorithm designed to exploit the reverse absorption signature of volcanic ash from 10.4–11.7 and 8.8–9.2 µm: AI=BT1-BT2+BT3-BT4, where BT1=14[BT(856.44cm-1)+BT(856.75cm-1)+BT(857.06cm-1)+BT(857.37cm-1)],BT2=14[BT(964.25cm-1)+BT(965.04cm-1)+BT(965.44cm-1)+BT(966.24cm-1)],BT3=12[BT(1131.79cm-1)+BT(1133.96cm-1)] and BT4=12[BT(1080.92cm-1)+BT(1082.41cm-1)]. We note that also introduced a temperature threshold (Th) to remove false detections due to variable surface emissivity over land; however, it became clear that CALIOP detections of weak ash layers were removed by this threshold condition, and so it was relaxed for the present study. As with the SI, the AI is defined such that positive values indicate the presence of volcanic ash.

Volcanic ash and sulfate aerosols are identified in CALIOP profiles based on collocated AIRS pixel values of the AI and SI, respectively. The collocation is achieved by calculating the minimum distance between a given CALIOP profile and the centre of each AIRS pixel. For the Puyehue case study, this set of collocated AIRS pixels is scanned for an AI greater than or equal to 1 K and an SI below 1 K. These conditions were set to ensure that the volcanic aerosol layers analysed for the Puyehue case study were dominated by an ash signal and, importantly, did not exhibit an SO2 signal. Similarly, to ensure that observations of volcanic layers for the Kasatochi and Sarychev case studies were dominated by sulfates (and not an ash), the algorithm required an SI greater than or equal to 1 K and an AI below 1 K. We also note that CALIOP profiles located south of 65∘ S were removed from the Puyehue analysis as conditions over Antarctica during the Southern Hemisphere winter (June–July) are conducive to polar stratospheric cloud (PSC) formation .

We develop our lidar ratio retrieval procedure following and use the same notation as and . The elastic backscatter lidar equation for the normalized, ozone-corrected, total attenuated backscatter coefficient can be written as βN′(r)=βm(r)+βp(r)Tm2(rt,r)Te2(rt,r), where Te2(rt,r)=exp⁡-2ηSp∫rtrβp(r′)dr′ and Tm2(rt,r)=exp⁡-2Sm∫rtrβm(r′)dr′. Here Sm and Sp are the molecular and particulate lidar ratios, which are assumed to be constant throughout the aerosol layer. Following , Eq. () leads to the following first-order differential equation: dTe2(rt,r)dr-2ηSpβm(r)Te2(rt,r)=-2ηSpβN′(r)Tm2(rt,r). Solving Eq. () and rearranging for Sp results in the solution of the two-component lidar equation: Sp=1-Te2(rt,rb)Tm2ηSp/Sm(rt,rb)2η∫rtrbβN′(r)Tm2(ηSp/Sm-1)(rt,r)dr. Equation () is essentially Eq. (15) of , but using the notation of , and the multiple scattering factor, η, has been included. Since Eq. () is transcendental, we apply an iterative solution to retrieve Sp . In order to initialize Eq. (), the solution to the single-component lidar equation could be used to calculate an initial estimate of the lidar ratio (Eq. 7 of ). However, for the top-most layer in the atmospheric column, CALIOP measurements can be used to make a reasonable approximation of the particulate component of the integrated attenuated backscatter γp′ (obtained from the level 2 data products), and an initial value of Sp can then be obtained using Sp=1-Te2(rt,rb)2ηγp′. This value is then substituted into Eq. () to calculate a refined estimate of Sp. The refined estimate is then compared with the previous value of Sp, and the iteration continues until consecutive solutions converge to within a threshold of 0.01 % .

As we can use the value of Sp obtained from Eq. () to retrieve the profile of particulate backscatter, βp(r), we are also able to retrieve the layer-integrated particulate depolarization ratio, δp, which is an intrinsic property of the aerosol layer. The value of δp can be derived from the layer-integrated volume depolarization ratio, δv, by adapting the approach of to integrated quantities: δp=γm(δv-δm)+γpδv(1+δm)γm(δm-δv)+γp(1+δm), where γm=∫rtrbβm(r)dr and γp=∫rtrbβp(r)dr. Here the particulate backscatter profile, βp(r), is calculated using the retrieved 532 nm particulate lidar ratio and the numerical integration procedure of . We also define δm as the layer-integrated molecular depolarization ratio. Due to CALIOP's narrow band optical filter, δm is the depolarization ratio at the central Cabannes line, which can be assumed to be a constant; δm≈0.003656 .

We also note that the layer-effective particulate colour ratio, χp, can be retrieved using the two-colour method of . This approach seeks to minimize a non-linear function by simultaneously varying Sp,1064 and χp using the method of non-linear least squares. However, for the case studies considered here, we found that the method was rather insensitive to variations in the 1064 nm particulate lidar ratio, often resulting in non-physical solutions for Sp,1064. We expect that this was due to the relatively weak signals and low optical depths of the volcanic aerosol layers under examination. As these results were inconclusive, and require a more complete treatment of the sources of error, we decided this analysis was outside of the scope of the present analysis and therefore do not report the results here.

Activity at the Aleutian Islands volcano, Kasatochi (52.18∘ N, 175.51∘ W), began over a period from 7 to 8 August 2008 with SO2 detectable in the atmosphere for at least a month . Using the SI, it was found that the Kasatochi signature was detectable in AIRS measurements until 28 August 2008. All of the available nighttime CALIOP and AIRS data from 8 to 28 August covering a geographic region from 30 to 90∘ N to 180∘ W to 180∘ E were included in the present analysis. As seen in Fig. a, the SO2 dispersion was extremely complex, with the SO2 cloud being dispersed into the atmosphere over a period of ∼ 3 weeks until it became well mixed and undetectable by AIRS. In total, 140 valid lidar ratio retrievals were made for the Kasatochi layers. The mean layer-top height and thickness of the Kasatochi layers were 13.69 ± 2.03 and 1.06 ± 0.47 km, respectively. The mean particulate depolarization and attenuated colour ratios were 0.09 ± 0.03 and 0.35 ± 0.07, respectively, indicating observations of aerosol layers optically dominated by sulfates – composed of small, spherical particles. The mean and standard deviation of the lidar ratios for the Kasatochi layers retrieved over a time period from 8 to 28 August were 66 ± 19 sr (median of 60 sr). The lidar ratios (Sp) and colour ratios (χ′) were quite variable with time, making it difficult to infer any clear trends in these parameters. The particulate depolarization ratios (δp) remained largely unchanged during the measurement time period (Fig. d). Figure  shows the respective distributions of the optical properties for each eruption case study. The layer-mean properties are given in Tables and .

Sarychev (48.09∘ N, 153.20∘ E), which is one of the most active volcanoes in the Kuril Islands chain (Russia), began to erupt on 11 June 2009 . AIRS detected an ash and SO2 signature on 12 June; however, CALIOP data was not available from 12 to 14 June 2009. According to surface observations, no more ash or SO2 was seen emanating from the volcano after 24 June, but SO2 was still detectable in the atmosphere . Data for the Sarychev case study were therefore collected from 15 June to 12 July 2009, covering the same geographic region as the Kasatochi case study. Figure b provides an overview of the Sarychev SO2 dispersion. Unlike Kasatochi, the Sarychev SO2 signature initially separated into two distinct SO2 clouds that dispersed toward the east and northwest. The eastward-travelling SO2 cloud remained over the Alaskan peninsula for several days, while the northwestward SO2 cloud travelled south as it crossed back over the volcano. In total, 183 valid lidar ratio retrievals were obtained. The mean optical properties of the Sarychev layers shared many similarities with the Kasatochi layers (Fig. ); however, the Sarychev particulate depolarization ratio exhibited an exponential decrease with time over 3.6 days. A similar decreasing trend was also observed for the attenuated colour ratio. The time evolution of all optical properties are discussed in Sect.  and are shown in Fig. . The mean particulate depolarization ratio was 0.05 ± 0.04, and the mean attenuated colour ratio was 0.32 ± 0.07 (Table ). The mean lidar ratio for the Sarychev layers was 63 ± 14 sr (median of 59 sr), corresponding to a layer-mean height and thickness of 13.80 ± 1.85 and 1.40 ± 0.41 km, respectively (Table ).

The eruptions of the Chilean volcano, Puyehue (40.59∘ S, 72.12∘ W), began on 4 June 2011 and resulted in widespread and far-reaching ash layers that caused flight cancellations in Australia and New Zealand. analysed CALIOP observations of the volcanic aerosols produced by Puyehue and found that the layers were primarily made up of ash particles with sulfates contributing to less than 10 % of the total attenuated backscatter. In the present analysis, we avoid ice-rich layers and identify ash-rich layers using passive infrared detection from collocated AIRS pixels (i.e. AI≥1 K and SI<1K). The CALIPSO analysis presented by also showed that the ash clouds remained near the tropopause as they were driven around the Southern Hemisphere by a strong westerly polar jet. This spatial description of the Puyehue aerosols has been corroborated by several other authors .

CALIOP was switched into safe mode on 4 June and again from 6 to 14 June 2011 (with 46.8 % coverage on 15 June). During this time period the volcanic aerosols made their first circuit around the Southern Hemisphere. The observations included in the present analysis are therefore representative of aged (∼ 2 weeks) ash-rich volcanic aerosol layers. The AIRS observations were analysed over a time period from 16 June to 4 July and a geographical area from 20 to 90∘ S and 180∘ E to 180∘ W (Fig. c). The CALIOP profiles were restricted to latitudes north of or equal to 65∘ S to avoid PSCs (as noted in Sect. ). In total, 374 valid lidar ratio retrievals were applied to CALIOP profiles containing stratospheric aerosol layers. The mean layer-top height and thickness of the Puyehue layers were 12.45 ± 0.81 and 1.82 ± 0.55 km, respectively (Table ). In contrast to the optical properties of the Kasatochi and Sarychev layers, the Puyehue layers exhibited consistently high depolarization ratios (δp = 0.33 ± 0.03; Table ), indicating aerosol layers optically dominated by non-spherical particles over the measurement period. The layer-integrated attenuated colour ratios for the Puyehue case study were also higher (χ′=0.53±0.08; Table ) than the Kasatochi and Sarychev case studies (χ′=0.32–0.35). In general, changes in the Puyehue lidar ratios (Sp mean of 69±13 sr and median of 67 sr) with time were quite similar to the changes in lidar ratio with time for Kasatochi and Sarychev case studies. The lidar ratio distributions for the three case studies were similar in shape and were all positively skewed. We therefore provide both the mean and median lidar ratios (annotated on each histogram of Fig. ).

provide a comprehensive assessment of the version 3.01 CALIOP 532 nm total attenuated backscatter calibration. For nighttime measurements under clear air conditions, the mean relative error was reported to be 2.7±2.1 % when compared against airborne high spectral resolution lidar measurements. One of the main sources of error that is particularly relevant here can arise in the case of an undetected (background) stratospheric aerosol layer. highlighted how this issue would impact the CALIOP calibration region, concluding that undetected aerosols up to 35 km led to an underestimation of the particulate (aerosol) scattering ratio (an average relative error of 6 %), with the effects most pronounced in the tropics (20∘ N–20∘ S). Although the observations presented here are confined to middle–high latitude regions, they directly coincide with ongoing volcanic eruption events, and so we must consider errors introduced by aerosol contamination (which have not been corrected for in the version 3 datasets).

Considering the ∼ 5 % calibration error suggested by and the 6 % aerosol contamination error suggested by , we anticipated a relative error of 10 % in the normalized, attenuated backscatter profile (i.e. ε(βN′)/βN′=10 %).

The CALIOP level 2 aerosol products provide an estimate of the measured two-way transmittance error, which is calculated as the standard deviation of the attenuated scattering ratio in the clear air region below the detected layer . For the case studies considered, the means (and standard deviations) of the two-way transmittance relative errors were 16.04±2.94, 16.69±2.72 and 16.70±3.84 % for Kasatochi, Sarychev and Puyehue, respectively. However, since the operational algorithm assumes pure Rayleigh scattering above the top layer of a given CALIOP profile, it is assumed that there is no attenuation by undetected layers aloft and that all of the attenuation is in the detected layer. In this case the estimate of Te2 will be too low and Sp will be too high. considered the possible influence of volcanic aerosols affecting the two-way transmittance between 8 and 30 km. Based on volcanic stratospheric optical depths from , they estimated a maximum bias in the two-way transmittance of 3 %. Considering the mean transmittance errors for the three case studies (∼ 17 %) and the error introduced by undetected volcanic aerosols (∼ 3 %), a relative error of 20 % in the effective two-way transmittance constraint was assumed (i.e. ε(Te2)/Te2=20 %).

To estimate how the errors in βN′, Te2 and η propagate into errors in Sp a multi-variable functional approach was applied to Eq. () to calculate a perturbation error for each variable. As discussed in the previous sections, βN′ and Te2 were perturbed by 10 and 20 %, respectively, and η was perturbed by 0.05. If any variable was perturbed outside of its physical bounds then it was set to the relevant upper or lower bound. Each perturbation error was then summed in quadrature to calculate the absolute error in the particulate lidar ratio: ε(Sp)=±ε(Sp,βN′)2+ε(Sp,Te2)2+ε(Sp,η)2, where ε(Sp,βN′), ε(Sp,Te2) and ε(Sp,η) represent the three components of error in Sp. The subscripts represent the variable that was perturbed while holding the other two variables constant. Figure  illustrates, for each case study, how each of the three perturbation errors propagated into the error in Sp. The assumed relative errors in βN′ and Te2 translated into mean absolute component errors of ∼ 6 and ∼ 14 sr, respectively, while the assumed error perturbations of 0.05 in η corresponded to errors in Sp of ∼ 3 sr. Overall, the perturbation errors, when summed in quadrature, corresponded to a mean absolute error in Sp of ∼ 15 sr.

As Te2 was considered to be the largest source of error in Sp, we examined how the relative error in the lidar ratio, ε(Sp)/Sp, varied as a function of Te2 (Fig. ). Here we see that the relative error in Sp asymptotes toward ∼ 10 % as Te2 approaches zero and increases exponentially as Te2 approaches unity. In other words, for non-transmissive (optically thick) layers, error in the retrieved value of Sp will be limited by errors in βN′ and η. For highly transmissive (optically thin) layers, error in Te2 will become the dominant source of error in Sp.

Figures – show how the CALIOP–AIRS analysis performed for an individual AIRS granule selected from each case study, illustrating the conditions under which the lidar ratio retrievals are successful and how the volcanic layers correlate with the AI and SI. The times of each of the selected observations (Figs. –) are also indicated on Fig. a–c, which show the overall times series of the aerosol optical properties (Sp, δp and χ′) for each case study. For the Kasatochi and Sarychev layers (Figs.  and , respectively), the lidar ratio is relatively constant throughout the strongly backscattering regions of the stratospheric layers. The AIRS SO2 signals also collocate well with these aerosols, suggesting that they are largely composed of sulfates. The curtain-average value of the lidar ratio for the two sulfate-rich layers are also very similar (Sp‾∼ 53 sr) but lower than the median values of the corresponding lidar ratio distributions (∼ 60 sr; Fig. a and b). The Kasatochi observation corresponds to an aerosol layer that had resided in the stratosphere for ∼ 7 days, whereas the Sarychev observation corresponds to a layer approximately twice the age (∼ 14 days) of the Kasatochi layer. The mean particulate and volume depolarization ratios for the sulfate-rich layers are both relatively low (δp‾, δv‾ ∼ 0.05–0.10), indicating that these layers are dominated by spherical particles. The curtain-mean attenuated colour ratio for the Kasatochi observation (χ′‾ = 0.37; Fig. ) was higher than the Sarychev observation (χ′‾ = 0.33; Fig. ) although both were smaller than the Puyehue observation (χ′‾=0.54; Fig. ), indicating that the sulfate-rich layers were composed of smaller particles than the ash-rich layers.

The Puyehue layers (Fig. ) are quite similar to the sulfate-rich layers in terms of the geometric thickness; however, the curtain-mean particulate depolarization ratio (δp‾ = 0.32), along with the AIRS ash signal, unambiguously identify this layer as being optically dominated by non-spherical ash particles. The variability in the lidar ratio for the Puyehue observation generally increases as features become more tenuous, reflecting an increase in sensitivity in the lidar ratio retrieval for transmissive layers (as discussed in Sect. ). The lidar ratios are also more variable than the sulfate ratios, which may be an indication of greater inhomogeneity in the Puyehue layer observations. The curtain-mean lidar ratios for the Puyehue observation are also quite high ∼ 68 sr, and we note that this may be due to the age of the layers (∼ 17 days; discussed in more detail in Sect. ).

As volcanic aerosol layers evolve and disperse into the atmosphere, their microphysical properties are expected to change with time. The Kasatochi and Puyehue layers were observable for a duration of ∼ 12 days, while the Sarychev observations covered a time period of ∼ 17 days. Figure a–c show that all observations were made more than 3 days after eruption onset. The Kasatochi and Puyehue volcanic aerosols were observed for a similar time period (∼ 12 days); however, for the Puyehue case study, the aerosol layers had resided in the stratosphere for more than 11 days before the measurement period began. The Sarychev case study covered the longest observational time period, providing observations of sulfate-rich aerosols for over 2 weeks. All volcanic aerosol layers were subject to long-range transport across the globe as shown by the spatial distribution of observations plotted in Fig. j–l. The particulate lidar ratios for all three case studies were quite variable with time (Fig. a–c). Over these timescales (1–2 weeks) it is likely that the volcanic aerosol layers are mixing with ambient aerosol, resulting in fluctuations in the lidar ratio with time. Changes in the lidar ratio may also be a result of sampling different parts of an inhomogeneous aerosol cloud.

The Puyehue lidar ratios (65–70 sr) are relatively high in comparison to previously reported volcanic ash lidar ratios 40–60 sr;. In fact, the Puyehue lidar ratios share interesting similarities with long-range transported Saharan desert dust lidar ratios 40–75 sr;. provide two main reasons for high lidar ratios of long-range transported dust particles. The first is an increase in the fine to coarse mode particle ratio due to gravitational settling of coarse mode (diameters >1 µm) particles. The second is a large reduction in backscattering efficiency due to the non-sphericity of the particles. Both explanations are consistent with the Puyehue observations. The ash-rich aerosol layers were observed after 11 days of long-range transport (providing the necessary time for coarse mode particles to fall out), and the layers were also dominated by irregular, highly depolarizing (δp>0.30) particles.

The particulate depolarization ratios of the Puyehue layers were generally higher than the Kasatochi and Sarychev layers (Fig. d–i). report similar depolarization ratios (δp∼0.30) for aged (∼ 27 days), stratospheric (∼ 22 km) volcanic aerosol layers produced by the 1991 Mt Pinatubo eruption. , and report even higher particulate depolarization ratios from 0.35 to 0.40 for Eyjafjallajökull ash observed over Germany; however, these were observations of young (1–3 days old) tropospheric ash layers.

Over the ∼ 2.5 weeks of Sarychev CALIOP observations, δp is seen to decay from 0.27 to 0.03 exponentially with time. A decrease in χ′ is also observed (Fig. h). The decay in δp corresponds to an e-folding time of 3.6 days (dashed line; Fig. e) and may indicate that ash particles were being removed from the atmosphere during the measurement period for the Sarychev case study. Since the Sarychev layers were only analysed if the CALIOP observations were collocated with an AI<1K and SI≥1 K, it is possible that the CALIOP instrument is detecting ash particles with a very weak reverse absorption signature that have not been removed by the AI threshold criterion.

Figure h demonstrates that χ′ also decreased with time over the measurement period. Changes in χ′ can be due to changes in the size, complex refractive index and shape of the aerosols being measured. It is difficult to infer, quantitatively, what the volcanic aerosol particle sizes are without assuming more about the complex refractive index and size distribution of the particles; however, we note that report effective radii of 0.25 µm for the Sarychev aerosols over the Arctic. As the attenuated colour ratio is constructed based on two measurements (532 and 1064 nm attenuated backscatter), we can only use it to infer relative changes in particle size. We speculate that ash particles were present in the initial observations of the CALIOP measurements, and so a combination of the sedimentation (contributing to a reduction in particle size) and sulfate formation (contributing to a change in the imaginary part of the refractive index) led to a decrease in χ′ with time. Overall, the Puyehue colour ratios reported here (χ′ = 0.54 ± 0.07) are in agreement with the values reported by . These colour ratios are at the low end of values reported for the free-tropospheric ash layers produced by Eyjafjallajökull 0.47–0.77;, and, considering the high particulate lidar ratios (Sp∼ 70 sr) and particulate depolarization ratios (δp = 0.33 ± 0.03), these results suggest that the CALIOP observations of the Puyehue aerosol layers are representative of layers dominated by fine mode, ash particles. The Kasatochi (χ′ = 0.35 ± 0.07) and Sarychev (χ′ = 0.32 ± 0.07) colour ratios were, on average, quite similar, but both were lower than those found for the Puyehue case study. This indicates that the Puyehue aerosol layers were composed of particles that were larger than those in the Kasatochi and Sarychev aerosol layers. The Kasatochi and Sarychev colour ratios (χ′ ∼ 0.32–0.35) were also lower than typical colour ratios for desert dust (χ′∼ 0.45; ), while the Puyehue colour ratios (χ′∼ 0.53) were generally higher. Both classes of volcanic aerosols had smaller colour ratios than those CALIOP typically observes for ice (χ′ = 0.7–1.2) and water clouds χ′ = 1–1.4;.

Figure a compares the optical properties of the Kasatochi and Sarychev sulfate-rich aerosols with the Puyehue ash-rich aerosols. When combined, the volume depolarization ratios and attenuated colour ratios emphasize distinctive differences between the two classes of volcanic aerosol. These optical properties are relevant to the new stratospheric aerosol classification scheme that considers δv, χ′ and γp′ . The results of the present analysis support a sub-classification scheme, also suggested by , that categorizes stratospheric sulfate layers having volume depolarization ratios of 0<δv≤0.2 (Fig. a; dashed line). Further classification could potentially be achieved using the colour ratios (e.g. χ′≤0.4 = sulfates, 0.4<χ′≤0.7 = ash). However, based on the aerosol layers under examination here, distinctions between ash-rich and sulfate-rich layers using χ′ are less clear than distinctions made with δv. We point out that our suggested δv threshold of 0.2 has been optimized for the eruption case studies considered here and that a slightly different threshold might be found for a different or larger dataset. For example, found a slightly lower threshold of δv = 0.15 for the cases they examined. We also note that, for the depolarization ratio range 0.075<δv≤0.15, use χ′<0.5 to identify stratospheric smoke. As volcanic aerosols are often composed of a complex mixture of both ash and sulfate, which changes with time, strict classification using a single threshold is challenging. In the case of ambiguous depolarization ratios (δv∼ 0.2), supplementary information from collocated AIRS measurements may provide more insight into the likely composition of stratospheric volcanic aerosol layers.

Figure b shows the relationship between the particulate lidar ratio and the particulate depolarization ratio. As previously noted, the particulate lidar ratios for the Puyehue ash-rich aerosol layers and the sulfate-rich layers of Kasatochi and Sarychev were similar. This would make it difficult to discriminate between a volcanic layer dominated by ash versus a volcanic layer dominated by sulfate using Sp alone. Nevertheless, these lidar ratio retrievals provide important information for distinguishing volcanic aerosols from water (Sp≈ 20 sr) and ice (Sp≈ 25 sr) clouds and could potentially be utilized in new lidar aerosol classification schemes e.g..

In cases where the lidar ratio cannot be retrieved directly, the CALIPSO extinction retrieval relies on a predefined lidar ratio that is associated with a predefined type. Classification of volcanic aerosols into ash-rich and sulfate-rich layers is therefore important as the lidar ratio may change depending on the composition of the layers. The depolarization ratio appears to be the most appropriate parameter for determining whether a stratospheric volcanic layer is sulfate-rich or ash-rich. As we have shown, the lidar ratio varied with time for the case studies presented here, and so the assumption of a constant lidar ratio will likely introduce errors in the retrieval of extinction profiles. Optimum results for a volcanic aerosol optical depth time series could be obtained by following the method presented here and only accepting cases where an extinction retrieval was constrained by an estimate of the two-way transmittance (i.e. extinction quality control flag equal to 1). This would most likely restrict observations to nighttime measurements of layers with optical depths >0.2 (Fig. ). In cases where the two-way transmittance method fails, a predefined lidar ratio would have to be used. One could use the histograms presented in Fig.  to constrain the choice of the lidar ratio. As the histograms for the lidar ratios are positively skewed, the median lidar ratio would be best suited for this approach. For example, 60 sr for sulfate-rich (δv<0.2) and 67 sr for ash-rich (δv>0.2) layers.

In order to facilitate interpretation of the results presented in Sect. , η was held constant for each case study. However, since the “true” value of η for volcanic aerosols is unknown, we provide Sp calculated for a range of different η values in Table . The relationship between η and Sp for the three case studies is also shown in Fig. . As expected from Eq. (), the mean particulate lidar ratio decreased as the assumed multiple scattering factor was increased.

Previously reported values of the lidar ratio (at 532 nm) provide insight into the likely range of Sp for case studies considered here. The reported lidar ratios (at 532 nm) for Kasatochi and Sarychev range from 40 to 65 sr . Although it is difficult to make direct comparisons (due to a lack of coincident observations), these values support a choice of η closer to unity for sulfate-rich aerosols.

To our knowledge there have been no lidar ratio observations reported in the scientific literature for the Puyehue volcanic aerosols. However, ground-based lidar observations were made at Lauder, New Zealand. applied the algorithm to ground-based lidar measurements to derive aerosol (particulate) extinction profiles. They assumed a lidar ratio of 50 sr but noted better agreement with independently derived optical depths when they set Sp to 60 sr. Their initial choice of lidar ratio was based on previous reports of the lidar ratio for the Eyjafjallajökull ash layers. According to Fig. , a lidar ratio of 60 sr corresponds to a multiple scattering factor close to unity.

The impact of multiple scattering on CALIOP measurements can also be indicated by high depolarization ratios. found that effective lidar ratios (S*=ηSp), derived from CALIOP measurements of opaque African dust layers, decrease as the volume depolarization ratio increases, an effect they ascribe to the impact of multiple scattering in denser layers. For layers with optical depths greater than 3, they found that volume depolarization ratios increased from a value of ∼ 0.3, typical for African dust, to ∼ 0.36, while the effective lidar ratios decreased to 30.5 sr from a typical value of 40 sr, implying a multiple scattering factor of ∼ 0.75. For low to moderately dense layers, they found multiple scattering to be negligible. Since the volcanic aerosol layers in this study were generally optically thin (τe<0.8, Fig. ), multiple scattering effects are also expected to be small, consistent with our assumption of η=0.90–0.95 for the ash-rich volcanic layers considered here.