The altitude of volcanic sulfur dioxide (SO2) plumes determines the transport and atmospheric residence time of derived sulfate aerosol, and hence their impacts on the environment and climate. Knowledge of the altitude of fresh eruption clouds is also very important in aviation safety to avoid flying through ash clouds and for forecasting of plume drift. In this paper, we demonstrate the altitude dependence of the spectral response in the backscattered ultraviolet (BUV) radiance when a SO2 absorption layer is added to an ozone-laden atmosphere. The distinctive spectral response serves as the physical basis for simultaneous SO2 loading and altitude retrievals, which can improve the characterization of volcanic emissions. We accomplish this by extending the recently developed Iterative Spectral Fitting (ISF) algorithm to include effective plume altitude determination when performing simultaneous ozone and SO2 retrievals. The extended ISF algorithm is applied to hyper-spectral Ozone Monitoring Instrument (OMI) measurements of two volcanic eruptions: Sierra Negra in October 2005 and Jebel al Tair in September 2007. The results show for the first time that a wide range of SO2 plume altitudes can be estimated directly from hyper-spectral BUV radiance measurements.
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 Volcanic emissions are a major natural source of sulfur dioxide (SO2) and other trace gases, perturbing atmospheric composition and chemistry, and hence potentially affecting the environment and climate. These effects are primarily due to the conversion of volcanic sulfur-containing gases (mostly SO2 and minor amounts of H2S) to sulfate aerosols [Robock, 2000]. These volcanic impacts are exemplified by the June 1991 Pinatubo (Philippines) eruption, which injected a large amount of SO2 (∼20 Megatons) [Bluth et al., 1992] and ash directly into the stratosphere, up to 35 km above sea level (ASL). While the ash from this eruption fell out of the atmosphere in days, the sulfate aerosol derived from the SO2 persisted in the stratosphere for years, lowered the global surface temperature on average by 0.5°C [McCormick et al., 1995] and produced record lows in global ozone in 1992 [Gleason et al., 1993]. This eruption also illustrates the hazard to aircraft posed by volcanic ash.
 In general the impacts of volcanic emissions increase with the atmospheric loading and residence time of the resulting sulfate aerosol. While the aerosol loading is proportional to the amount of sulfur-containing gases in the volcanic plume, the aerosol residence time is highly dependent on the plume altitude, at which the sulfur-containing gases oxidize to sulfuric acid (H2SO4) that condenses into sulfate aerosol. To evaluate the impacts of volcanic emissions, it is important not only to quantify SO2 abundances but also to determine SO2 injection altitude.
 Nadir-viewing satellite sensors, beginning with the Total Ozone Mapping Spectrometer (TOMS) [Krueger et al., 1995] and followed by other ultraviolet (UV) and infrared (IR) instruments, have long been employed to monitor volcanic SO2 emissions with variable sensitivity and coverage. Until recently all SO2 retrieval algorithms make explicit or implicit assumptions about the SO2 vertical distribution in deriving total columns from these nadir radiances, resulting in errors in the retrieved results when the assumptions are not valid. Recently, two new techniques have been developed to estimate the altitude of SO2 in a volcanic eruption cloud. One is based on the optimal estimation technique applied to hyper-spectral IR measurements that include the SO2 absorption band centered at 7.34 μm from the Infrared Atmospheric Sounding Interferometer (IASI) [Clarisse et al., 2008], and the other is based on inverse trajectory modeling that assigns appropriate SO2 amounts at different altitudes in order to minimize the difference between satellite SO2 column maps and those derived from the trajectory model [Eckhardt et al., 2008]. Both techniques have demonstrated their potential using the September 2007 eruption of Jebel al Tair (Yemen). Satellite BUV measurements in the 305–330 nm wavelength range provide the most sensitive detection of SO2 in the atmosphere, however to date there has been no attempt to obtain vertical information about SO2 plumes (volcanic or otherwise) directly from these measurements, even though they have been used to retrieve vertical profiles of ozone [Bhartia et al., 1996; Liu et al., 2005a]. The averaging kernels of the Linear Fit (LF) algorithm show that SO2 retrievals have significant dependence on the plume altitude [Yang et al., 2007], hinting that this dependence may be exploited for SO2 plume altitude estimation.
 In this paper, we describe the sensitivity of BUV measurements to the altitude at which a SO2 layer is introduced into the atmosphere, and extend the Iterative Spectral Fitting (ISF) algorithm [Yang et al., 2009] to perform simultaneous retrievals of ozone column, SO2 column, and effective SO2 altitude. This extended ISF algorithm is applied to volcanic plumes from two recent eruptions.
2. Ozone Monitoring Instrument
 Flying on NASA's Aura spacecraft since July 2004, the Dutch-Finnish built Ozone Monitoring Instrument (OMI) [Levelt et al., 2006] is a nadir-viewing hyper-spectral imaging spectrometer designed to measure both the backscattered radiance from Earth and the incoming solar irradiance using UV and visible (VIS) channels (full performance ranges 270–365 nm and 366–500 nm, respectively). The Hartley-Huggins bands of ozone and the SO2 absorption band are located and overlap in the range of the UV channel, which is optically separated into UV-1 (270–310 nm) and UV-2 (310–365 nm) sub-channels to reduce stray light below 310 nm. The UV-2 channel has a spectral resolution of ∼0.42 nm, a spectral sampling rate of 0.15 nm/pixel and a spatial resolution of 13 × 24 km2 at nadir; UV-1 has a spectral resolution of ∼0.63 nm, a spectral sampling rate of 0.32 nm/pixel and a nadir spatial resolution of 13 × 48 km2. Essentially the sampling and resolution of UV-1 are equivalent to co-adding four UV-2 pixels, two each in the spectral and spatial (cross-track) dimensions. By combining hyper-spectral capability with its relatively small footprint size and daily global coverage, OMI is providing unique data for improving our understanding of atmospheric composition and chemistry.
3. SO2 Plume Altitude Estimation
 When a thin SO2 layer is introduced into the atmosphere, its altitude determines the proportion of backscattered photons that pass through this absorbing layer after the last scattering toward the sensor. Clearly, the lower the layer in the atmosphere, the more photons are Rayleigh backscattered in the overlying atmosphere, resulting in fewer photons transmitted through the layer, and vice versa. As a result, BUV radiance measurements (e.g., in the OMI UV channel) contain quantitative information about the layer altitude, in addition to information about atmospheric constituents. For an infinitesimal SO2 layer (i.e., both the thickness and column amount, Ξ, approach zero) at an altitude z, the top-of-atmosphere (TOA) BUV radiance at a wavelength (λ) can be expressed analytically as Iz,λ(Ξ) = Iλ(0) exp(−Az,λαz,λΞ) (a similar equation is used as the basis for the DOAS method [Platt, 1994]) according to the Beer-Lambert law, where Iλ(0) is the TOA BUV radiance for the SO2 free atmosphere, αz,λ is the temperature dependent SO2 absorption coefficient  [see Yang et al., 2007, Figure 1], and Az,λ is the ratio of average photon path length (at z) over the layer geometric thickness (this ratio is also called the altitude dependent air mass factor) [Liu et al., 2005b; Eskes and Boersma, 2003] for photons contributing to the TOA BUV radiance. The subscript λ will be dropped from subsequent notation in this paper.
 To illustrate the relative TOA radiance change induced by the changes in a SO2 layer, we derive the corresponding weighting functions (WF), which can be analytically expressed (for the infinitesimal SO2 layer considered above) as kΞ = = −αzAz and kz = = (−αz − Az)Ξ, respectively for the layer column Ξ and layer altitude z. We show the air mass factor Az (Figure 1a, divided by geometric air mass factor Ag), its vertical gradient (Figure 1b, also normalized by Ag), the layer column WF kΞ (Figure 1c), and the layer altitude WF kz (Figure 1d, normalized by the layer column Ξ). A perturbation in the SO2 layer, either in layer column amount or layer altitude, changes the SO2 absorption experienced by the BUV photons, as both WFs contain the term of SO2 absorption coefficient. Therefore both Figures 1c and 1d show the high frequency band structure of the SO2 cross-section (in other words, these two WFs are correlated). However, different physical mechanisms are responsible for the absorption change induced by the different perturbations: a change in layer amount Ξ causes a direct change in the layer absorption optical thickness, so kΞ is proportional to the local air mass factor Az, while a change in layer altitude z induces both a direct change in the number of photons passing through the layer and an indirect change in the layer absorption optical thickness due to the temperature variation with altitude. Since the SO2 cross-section is only weakly temperature dependent, the WF kz is usually dominated by its first term, , which shows that radiance change (in log space) induced by the altitude perturbation is proportional to the vertical gradient of Az. The correlation between the layer column and altitude WFs mentioned above implies that an error in layer altitude z can induce an error in layer column Ξ, and vice versa. However the distinctive wavelength and altitude dependence patterns in Figures 1a and 1b indicate that changes in SO2 amount cause different spectral responses in the BUV radiances to those caused by changes in layer altitude. Therefore BUV radiance measurements can be used to extract these two quantities. Note that the layer altitude WF (Figure 1c) for an unit SO2 layer is much smaller than the corresponding layer column WF (Figure 1d). However the magnitude of the altitude spectral response increases with larger absorption optical thickness of the plume, hence its altitude may be accurately extracted only when there is a significant amount of SO2. The layer column and altitude WFs defined for SO2 also apply to other trace gases, such as BrO, NO2, and HCHO, with αz replaced by the corresponding absorption coefficients. But it is usually difficult to estimate the altitudes of these trace gases due to the small absorption optical thickness in the range 300–330 nm associated with their typically low loadings.
 For lower tropospheric SO2 layers, BUV measurements at wavelengths longer than 310 nm (e.g., in the OMI UV-2 channel) can discriminate altitude because the SO2 altitude sensitivity is strong in the troposphere (<10 km) and peaks in the lower troposphere and boundary layer (see Figures 1b and 1c). To resolve higher altitude (>10 km) SO2 layers, BUV measurements at shorter wavelengths (<310 nm; e.g., in the OMI UV-1 channel) are required. At wavelengths shorter than 300 nm, there is very little column or altitude sensitivity to typical volcanic SO2 clouds (<25 km altitude), although if a volcanic plume reaches very high altitudes (>25 km), measurements at these wavelengths can be used to detect its altitude.
 We have extended the ISF algorithm, which performs simultaneous ozone and SO2 column retrievals [Yang et al., 2009], to include SO2 plume altitude estimation. The extended algorithm derives the SO2 altitude by adjusting it in successive ISF retrievals until the residuals, i.e., differences between measurements and forward model computations, are minimized, since a difference between the assumed and the actual SO2 altitudes produces residuals that can not be well compensated in the 300–330 nm range by adjusting the SO2 column alone. Note that higher SO2 amounts will change the air mass factor shown in Figure 1a, and can further increase the altitude sensitivity. Without using the analytic equations of the TOA radiance and the corresponding WFs derived for an infinitesimal SO2 layer, the extended ISF algorithm employs accurate radiative transfer calculation of the TOA radiance for any given ozone and SO2 columns with the corresponding a priori profiles. Doing so properly accounts for the nonlinear effect by updating the linearization point and WFs at each iteration [Yang et al., 2009].
 The vertical distribution of a volcanic SO2 plume is very different from the typical broad ozone profile and is usually narrowly confined due to its transient source of emission and its dispersion by wind shear. It is not possible to resolve the precise profile of a volcanic plume using BUV measurements, which provide a vertical resolution of about 5–8 km in the stratosphere and about 10 km in the troposphere [Bhartia et al., 1996; Liu et al., 2005a]. Therefore we represent the SO2 plume using a Gaussian profile, characterized by a central altitude and width. The central altitude of the Gaussian derived from the extended ISF retrievals should represent the effective altitude, equivalent to the altitude at the center of SO2 mass when the layer is thin.The precision of the derived effective altitude is higher than the profile vertical resolutions due to the reduction in retrieval dimension. For example, given a 10 Dobson Unit (1 DU = 0.001 atm-cm = 2.69 × 1016 molecules/cm2) SO2 plume and the OMI UV-2 signal-to-noise ratio of ∼1000 [Levelt et al., 2006], the estimated precision of the effective altitude is ∼0.1 km when the plume is located in the troposphere.
4. Case Studies
 We have applied the extended ISF algorithm described above to OMI observations of volcanic plumes from two eruptions, the Sierra Negra eruption (Galàpagos Islands, Ecuador) in October 2005 and the Jebel al Tair eruption (Yemen) in September 2007. These cases were selected because the altitudes of these plumes span a range from the lower troposphere to the stratosphere.
4.1. Sierra Negra Eruption in October 2005
 The Sierra Negra plume resulted from an effusive eruption, characterized by sustained strong gas emissions into the lower troposphere. In a previous paper, we applied the ISF technique to this plume to demonstrate greatly improved quantification of large SO2 columns through proper treatment of non-linear SO2 absorption effects [Yang et al., 2009]. The ISF retrievals can be further improved by simultaneous determination of effective SO2 plume altitude, which can be achieved using the OMI UV-2 measurements alone for this lower tropospheric plume. In Figure 2, we compare the ISF fitting residuals from retrievals with fixed (assumed) and retrieved SO2 plume altitudes for a few pixels along the orbital track for the OMI cross-track position that covers the vent of the volcano (where the largest SO2 column was measured [Yang et al., 2009]). It is clear that higher precision retrievals, as indicated by much smaller fitting errors (ε) computed as the standard deviation of the residuals in the 310.8–333 nm range, are achieved by adjusting the plume central altitude. The smaller fitting errors are mostly a result of better fitting at short wavelengths, though noticeably smaller residuals in the ozone and SO2 fitting window (delimited by the two dashed green lines of Figure 2) also contribute to the reduction in fitting error. The effective plume altitudes determined from the retrievals show that the plume rose gradually along the ascending orbital track from 1.7 km to 4.2 km altitude in a distance slightly over 100 km. These altitudes are consistent with near simultaneous IR observations from the Atmospheric Infrared Sounder (AIRS; on the Aqua satellite in the A-Train), which did not detect any significant SO2 in the same region, indicating that it was located below 5 km altitude where water vapor absorption overwhelms the SO2 absorption [Carn et al., 2005].
4.2. Jebel al Tair Eruption in September 2007
 Jebel al Tair volcano (Yemen) erupted unexpectedly on September 30, 2007 after that afternoon's OMI overpass, injecting gases high into the atmosphere. When OMI made its first observation of this event on October 1, 2007, the plume from the initial explosive eruption had drifted away from the volcano, which continued to erupt effusively and release gases into the lower troposphere. The extended ISF retrievals, depicted as column and altitude maps in Figure 3, reveal a large part of the plume located northeast of Jebel al Tair at about 16 km ASL. Closer to the volcano, the effusive plume is also northeast of the volcano but at altitudes of around 4 km ASL. Note that in this case both OMI UV-1 and UV-2 measurements are used in the extended ISF retrievals. Without the short wavelength measurements (<310 nm, OMI UV-1), it would not be possible to resolve the altitude once the plume reaches the upper troposphere (>10 km), where the longer wavelength measurements (OMI UV-2) have minimal altitude sensitivity (Figure 1b).
 The 16 km plume altitude is near the local tropopause altitude of 15.3 km [Eckhardt et al., 2008], indicating that the explosive eruption injected SO2 into the upper troposphere and lower stratosphere (UTLS), consistent with the IR (IASI) observations and inverse transport modeling. IR sensors (AIRS, IASI) also detected the lower part of the plume northwest of Jebel al Tair, but were unable to detect any SO2 at low altitudes immediately surrounding the volcano, and also missed the part of the plume to the southwest (see figures by Eckhardt et al.  and Clarisse et al. ). In contrast, OMI observed significantly elevated SO2 loadings at altitudes below 3 km in the latter regions, most likely sourced from sustained emissions from the ongoing effusive eruption.
 We have elucidated the different physical mechanisms through which the column content and altitude of a volcanic SO2 plume affects BUV radiances, and showed that BUV radiances in different spectral ranges exhibit different sensitivities to plumes at different altitudes. Based on these findings, we have extended the ISF algorithm to simultaneously retrieve the SO2 column amount in a volcanic plume and its effective altitude from BUV radiance measurements. Applications of this extended ISF algorithm to OMI observations of recent volcanic eruptions demonstrate for the first time that SO2 plume altitudes can be derived directly from satellite BUV measurements. The retrieved SO2 altitudes can distinguish between a plume in the lower troposphere, upper troposphere, or stratosphere, which is crucial for aviation hazard mitigation. The applications of the extended ISF algorithm also show decreased SO2 column errors because the uncertainties in SO2 retrievals introduced by assumed plume altitudes are reduced.
 Future work will investigate the impact of inhomogeneity in the OMI field of view on the retrieved SO2 column and altitude, as this has likely suppressed the retrieved altitudes for some pixels on and near the edge of the plume as shown in Figure 3b. We will also investigate the impact of aerosols, especially volcanic ash, on the plume altitude estimation.
 This work was supported in part by NASA under grant NNS06AA05G (NASA volcanic cloud data for aviation hazards).