Journal of Geophysical Research: Atmospheres

Retrieval of large volcanic SO2 columns from the Aura Ozone Monitoring Instrument: Comparison and limitations

Authors


Abstract

[1] To improve global measurements of atmospheric sulfur dioxide (SO2), we have developed a new technique, called the linear fit (LF) algorithm, which uses the radiance measurements from the Ozone Monitoring Instrument (OMI) at a few discrete ultraviolet wavelengths to derive SO2, ozone, and effective reflectivity simultaneously. We have also developed a sliding median residual correction method for removing both the along- and cross-track biases from the retrieval results. The achieved internal consistencies among the LF-retrieved geophysical parameters clearly demonstrate the success of this technique. Comparison with the results from the Band Residual Difference technique has also illustrated the drastic improvements of this new technique at high SO2 loading conditions. We have constructed an error equation and derived the averaging kernel to characterize the LF retrieval and understand its limitations. Detailed error analysis has focused on the impacts of the SO2 column amounts and their vertical distributions on the retrieval results. The LF algorithm is robust and fast; therefore it is suitable for near real-time application in aviation hazards and volcanic eruption warnings. Very large SO2 loadings (>100 DU) require an off-line iterative solution of the LF equations to reduce the retrieval errors. Both the LF and sliding median techniques are very general so that they can be applied to measurements from other backscattered ultraviolet instruments, including the series of Total Ozone Mapping Spectrometer (TOMS) missions, thereby offering the capability to update the TOMS long-term record to maintain consistency with its OMI extension.

1. Introduction

[2] Major contributions to sulfur dioxide (SO2) in the atmosphere come from both anthropogenic activities and natural phenomena, which include combustion of fossil fuels, smelting of ores, burning of biomass, oxidation of dimethylsulphate (DMS) over oceans, and degassing and eruptions of volcanoes. The change in the abundance of atmospheric SO2 and its spatial and temporal distribution can have significant impacts on the environment and climate. Remote sensing instruments measuring solar backscattered ultraviolet (BUV) radiation on board satellite platforms have played critical role in monitoring and quantifying these SO2 emissions. The most notable of these instruments was the Total Ozone Mapping Spectrometer (TOMS) [Krueger, 1983; McPeters et al., 1998], which provided a unique and near-continuous long-term (from 1978 to 2006) data record of volcanic SO2 [Krueger et al., 2000; Carn et al., 2003; A. J. Krueger et al., El Chichon: The genesis of volcanic sulfur dioxide monitoring from space, submitted to Journal of Volcanology and Geothermal Research, 2007] and ash [Krotkov et al., 1997, 1999a, 1999b; Seftor et al., 1997] emissions. The Dutch-Finnish Ozone Monitoring Instrument (OMI) [Levelt et al., 2006], launched on the EOS/Aura platform in July 2004, is continuing and expanding these records that are invaluable to both atmospheric scientists and volcanologists [Krotkov et al., 2006, 2007; Carn et al., 2007a, 2007b]. OMI data are also of considerable value for aviation safety through near real-time processing for the detection of volcanic SO2 and ash clouds.

[3] OMI has combined the hyperspectral measurements similar to those made by the Global Ozone Monitoring Experiment (GOME) [Burrows et al., 1999] and the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) [Bovensmann et al., 1999] with improved viewing capabilities, including daily contiguous global coverage with a high spatial resolution not achieved by any of its predecessors. OMI accomplishes this by the use of two-dimensional charge coupled device (CCD) detectors to measure backscattered radiances in spectral and spatial dimensions simultaneously, covering ultraviolet (UV) (270–365 nm) and visible (365–500 nm) ranges at high spectral sampling and resolution with a swath width of 2600 km at a nadir spatial resolution of 13 km × 24 km. Having all these advanced characteristics, OMI provides an unprecedented measurement sensitivity to a number of atmospheric trace gases, including SO2, which is the subject of the current study.

[4] Over the years a number of algorithms have been developed for retrieval of SO2 from BUV measurements in various parts of the spectral region between 310 and 340 nm. Like ozone, SO2 has significant absorption structures in this region (see Figure 1). The typical vertical column density of SO2 in the atmosphere (mostly in the boundary layer) is too small to have measurable impacts on the BUV radiances. However, localized enhancements of SO2, either from volcanic emissions or anthropogenic pollution, can produce noticeable absorption effects, sometimes comparable to or even exceeding those due to ozone in the atmosphere. The challenge of SO2 retrieval is to distinguish its absorption effects from those of ozone.

Figure 1.

Absorption coefficients (α) of SO2 and O3 and their ratio (ρ), SO2 to O3, as a function of wavelength, indicating that a SO2 molecule can have 4 times stronger absorption than an O3 molecule. The positions indicated by the arrows are the central wavelengths of the OMTO3 bands used in the algorithm. These 10 central wavelengths are 310.80, 311.85, 312.61, 313.20, 314.40, 317.62, 322.42, 331.34, 345.40, and 360.15 nm.

[5] For the series of TOMS instruments, which measured backscattered radiances at six discrete UV wavelength bands, the Krueger-Kerr algorithm [Krueger et al., 1995; Gurevich and Krueger, 1997] was used for the retrieval of its entire record. This algorithm derived ozone and SO2 vertical column amounts from the direct inversion of a set of linear equations between the measurements and absorption and scattering optical thickness at four wavelength bands. It provided reasonable SO2 values for large volcanic clouds, but suffered from unrealistic uncertainty in the background area because the equation was sometimes ill conditioned, leading to a solution that was highly sensitive to measurement noises.

[6] For GOME and SCIAMACHY, the standard Differential Optical Absorption Spectroscopy (DOAS) fitting technique has been applied to the measurements in the 315–327 nm wavelength window to derive slant column amounts of SO2 along the viewing-illumination path [Richter et al., 2006; Thomas et al., 2005; Khokhar et al., 2005; Bramstedt et al., 2004; Eisinger and Burrows, 1998]. These slant columns are then converted into vertical columns using air mass factors (AMF) computed at a single wavelength. Retrievals from GOME and SCIAMACHY have demonstrated that a much improved SO2 detection limit has been achieved by frequent observations of anthropogenic SO2 in heavily polluted regions [Khokhar et al., 2005; Richter et al., 2006]. However the traditional DOAS algorithm, well suited for retrieval of absorbers when they are optically thin, may lose its accuracy if a single-wavelength AMF is used for SO2 when column amounts become large. Recent advances in the DOAS technique, like the empirical AMF approach developed for the OMI DOAS ozone product [Veefkind et al., 2006], could alleviate this problem by accounting for wavelength-dependent effects on the AMF induced by strong SO2 absorption.

[7] For OMI, we have developed a technique called the band residual difference (BRD) algorithm that uses only four wavelength bands in the UV2 (310–365 nm) region [Krotkov et al., 2006]. These bands are centered at the local minima and maxima of the SO2 absorption cross section (see Figure 1) between 310.8 and 314.4 nm. This selection enables the BRD technique to take advantage of the large differential absorption of the three pairs formed by the adjacent bands, thereby maximizing the detection sensitivity to small SO2 column amounts. Doing so, however, makes this technique unsuitable for situations with large SO2 loadings, when the band residual differences of these pairs show nonlinear and nonmonotonic responses to SO2 increments.

[8] In an effort to improve the retrieval of SO2 from BUV measurements, especially for the cases with high SO2 column amounts, we introduce a more generalized technique called the linear fit (LF) algorithm for application to OMI SO2 retrieval. The LF algorithm is based on the spectral fitting technique [Joiner and Bhartia, 1997] developed for ozone retrieval from the full spectral measurements of the Solar Backscattered Ultraviolet (SBUV) instrument. This fitting technique was further developed [Yang et al., 2004] to combine with the TOMS-V8 retrieval [Bhartia and Wellemeyer, 2002; Wellemeyer et al., 2004] and was applied to GOME measurements, and now it is adopted and extended to perform simultaneous retrieval of ozone, SO2, and surface reflectivity using just a few discrete UV bands. Note that a similar algorithm, called the Weighting Function DOAS, has been developed by Buchwitz et al. [2000] and then applied by Coldewey-Egbers et al. [2005] to retrieve total column ozone from GOME measurements.

[9] This paper describes the LF algorithm and provides extensive analysis on the various error sources and their impacts on the SO2 retrieval accuracy. Examples of retrievals from volcanic plumes observed by OMI under various conditions and comparisons with the BRD retrievals are presented. The limitations and future improvements of this technique are discussed.

2. Algorithm Description

2.1. Overview

[10] The BUV radiance measurements Im (normalized to the incoming solar irradiance) relate the geophysical parameters, consisting of vertical columns of ozone (Ω), SO2 (Ξ), surface reflectivity (R), and others, via a radiative transfer model that calculates the top-of-the-atmosphere (TOA) radiances I. Taking the log of the measured and modeled radiances at a single wavelength band, their relation can be expressed as

equation image

where N = −100 log10I, and ɛT = −100 *ɛ, denotes the total error, a combination of measurement and model errors, for the band. N is a dimensionless quantity, usually referred to as N value.

[11] In general, TOA radiances are a function of the vertical profiles of the absorbers, which are ozone and SO2 in our study. However, because of the weak profile shape effects under most observing conditions for wavelengths longer than 310 nm and the nonnegligible uncertainty in measurements by spaceborne instruments, there is usually limited information about the vertical distribution contained in these measurements, precluding detailed profile retrievals. Consequently, it becomes necessary to place constraints on the absorber profiles, as is done in most inverse remote sensing algorithms [Rodgers, 2000]. In our algorithm, these constraints are the a priori ozone and the prescribed SO2 profiles used to specify the relationships between the column amounts and the profiles. Doing so makes it possible to express the TOA radiances as a function of total absorber amounts as written in (1), in which their profiles have become part of the model parameters that are not the subject of retrieval. These and other model parameters, not explicitly expressed in (1), are needed as inputs for TOA radiance calculations and described in next section. In writing (1), we have also made the assumption that a scalar quantity R, which may be dependent on wavelength, can be used to describe reflections from various surfaces (i.e., Lambertian surface approximation).

[12] With these simplifications, the retrieval of the geophysical parameters: Ω, Ξ, and R can be achieved by adjusting them until TOA radiances from the forward model match the measurements at the selected wavelength bands. Given the presence of measurement and model errors, the solution to this retrieval can be expressed mathematically as the minimization of the sum of the squares of the residuals over the selected bands. Residuals are defined as the differences between the measured N values and those calculated using the forward model.

[13] The minimization problem can be further simplified by the linearization of (1). To accomplish this, a reference point, denoted by the initial state vector {Ω0, Ξ0, R0, c1 = 0, c2 = 0}, is chosen to be the initial solution to the retrieval. Equation (1) can then be written as

equation image

where N0 = N0, Ξ0, R0), ΔΩ = Ω − Ω0, ΔΞ = Ξ − Ξ0, and ΔR = RR0. Higher-order terms are absorbed into equation imageT in (2). Here R0 is treated as independent of wavelength, and a low-order polynomial (quadratic in our current implementation, i.e., n = 2, c1 and c2 are the coefficients) is used to account for the wavelength dependence of surface reflectivity. The minimization can now be solved as the linear least square fitting of the residuals (NmN0) for a set of measurements at different wavelength bands by the weighting functions: equation image, equation image, and a equation image modulated polynomial of wavelength λ, with λ0 being the reference wavelength, usually chosen to be the wavelength where R0 is derived.

2.2. Discrete Bands

[14] The retrieval algorithm described above can make use of all the hyperspectral measurements in a wavelength window, or it can select just a few discrete wavelength bands. The main advantage of the large number of measurements over a small subset is that impacts from both systematic and random errors in the measurements can be reduced, thereby improving the quality of the retrieval results. For instance, the instrumental spectral response function and wavelength registration can be improved for hyperspectral measurements by the fitting with an extraterrestrial reference spectrum [e.g., Chance, 1998; Liu et al., 2005]. We have demonstrated that retrieval using hyperspectral GOME measurements yields more precise total ozone than using the TOMS-like discrete bands from the same measurements [Yang et al., 2004]. However, in this study, we focus on the use of the bands selected for the OMI total ozone algorithm (referred to as OMTO3) for OMI SO2 retrieval. These OMTO3 bands, including six that center at the Earth-Probe TOMS wavelengths [McPeters et al., 1998], four that are selected for the BRD algorithm [Krotkov et al., 2006], and two additional bands in the nonabsorbed spectral region, are routinely soft calibrated [Taylor et al., 2004] to improve the quality of OMTO3 results. This set of bands samples the various parts of the SO2 and ozone absorption spectra (see Figure 1), including both strong and weak absorbing regions. Measurements at this set of bands are adequate for SO2 and ozone retrievals, but they are not expected to realize the full potential of the complete spectra from OMI measurements.

2.3. Forward Model

[15] The OMTO3 forward model [Dave, 1964; Bhartia and Wellemeyer, 2002; Caudill et al., 1997], named TOMRAD, is adopted to calculate the TOA radiances at the wavelength bands and the corresponding weighting functions. This vector radiative transfer model accounts for elastic molecular scattering and gaseous absorptions through the inclusion of all orders of scattering [Dave, 1964] and a pseudo-spherical correction [Caudill et al., 1997] for more realistic handling of BUV radiances for off-nadir viewing directions and large solar zenith angles (SZA; up to 88°).

[16] A simplifying assumption is made about surfaces, which are considered opaque and are characterized by a Lambert-equivalent reflectivity (LER), sometimes referred to as effective reflectivity. Furthermore, this LER concept is combined with an independent pixel approximation, referred to as the mixed LER (MLER) approach [Ahmad et al., 2004], to account for the effects of thin or broken clouds, as is commonly done in trace gas retrievals. In the MLER approach, the TOA radiance of a partly cloudy pixel is assumed to be the weighted sum of radiances contributed from the clear and cloudy independent subpixels with fixed reflectivity (usually 0.15 and 0.8). The effective cloud pressures needed by the MLER model are taken from a satellite infrared (IR)-derived climatology data set [Bhartia and Wellemeyer, 2002; Wellemeyer et al., 2004]. Aerosols are not explicitly treated in TOMRAD, but their effects on TOA radiances are partially (except for possible aerosol absorption) accounted for by adjusting and treating the effective reflectivity as a function of wavelength using a second-order polynomial.

[17] In this forward model, the ozone profile is uniquely determined by a specified column amount given the day of year and the location using the TOMS-V8 ozone profile climatology, which consists of a priori profiles for each month varying with latitude and ozone column [Bhartia and Wellemeyer, 2002; Wellemeyer et al., 1997, 2004; McPeters et al., 2007]. The TOMS-V8 temperature climatology is also needed to generate time- and latitudinal-dependent vertical temperature profiles, since the ozone [Daumont et al., 1992; Brion et al., 1993; Malicet et al., 1995] and the SO2 [Bogumil et al., 2003] absorption cross sections used in the model are temperature dependent. The use of ozone and temperature climatology improves the calculations of TOA radiances by taking into account their seasonal and latitudinal variations.

[18] In the UV spectral region, rotational Raman scattering (RRS) [Joiner et al., 1995; Chance and Spurr, 1997; Vountas et al., 1998], which is inelastic and accounts for approximately 4% of total molecular scattering, changes the wavelength of the scattered radiation, leading to the smoothing of its prominent spectral features, such as solar Fraunhofer lines (Ring effect) and atmospheric absorption bands (telluric effect). These RRS effects can have a significant impact on the trace gas retrieval [e.g., Vountas et al., 1998; Coldewey-Egbers et al., 2005] if they are not properly accounted for. In our forward model, the RRS effects are included by correcting the TOMRAD radiances with filling-in factors calculated using the scalar LIDORT-RRS radiative transfer program [Spurr, 2003]. The filling-in factors, defined as the ratio of the radiance component due to inelastic scattering to that of the elastic scattering, are computed under the same atmospheric, surface, and geometrical conditions as those used in TOMRAD, insuring that the dependence of RRS effects on absorber loading, surface reflection, and viewing and illumination geometry are properly included. Note that since RRS is weakly polarizing, the filling-in factors can be accurately computed without including radiation polarization, as demonstrated by Landgraf et al. [2004].

[19] Current knowledge of the typical vertical SO2 distributions for both anthropogenic and natural sources is very limited. The SO2 from industrial air pollution as well as oxidation of natural material is likely to be confined to the planetary boundary layer (PBL), while SO2 from effusive eruptions or degassing of volcanoes is likely to spread within a narrow layer at a height similar to the altitude of the sources, and SO2 from explosive volcanic eruptions can be injected into the upper troposphere or lower stratosphere. Corresponding to these three scenarios, three a priori SO2 profiles, with vertical distribution similar to the standard ozone profiles [Bhartia and Wellemeyer, 2002] in Umkehr layers 0, 1, and 3 respectively, are used in the forward model and weighting function calculations. These a priori SO2 profiles are referred to as prescribed profiles to indicate that they are choices of convenience, and not results based on prior knowledge. An Umkehr layer is defined between two atmospheric pressure levels, Patm/2i and Patm/2i+1, where i is the Umkehr layer number starting from zero and Patm is equal to standard atmospheric pressure (=1013.25 hPa). The altitudes for the base of the first five Umkehr levels are roughly 0.0, 5.5, 10.3, 14.7, and 19.1 km (their precise values depend on the actual atmospheric temperature profile). The retrievals associated with the prescribed SO2 profiles in Umkehr layers 1 and 3 are referred to as 5 KM and 15 KM retrievals respectively.

[20] The TOA radiances that are computed at a spectral resolution much higher than the OMI spectral resolution of about 0.4 nm, are then convolved with the OMI instrument spectral response function [Dobber et al., 2006] to model the instrument measurements. The atmospheric weighting functions, equation image and equation image, are calculated using a finite difference approach. Specifically an atmospheric weighting function is computed as the N value difference between two corresponding a priori profiles that differ by 1 Dobson Unit (DU; 1 DU = 2.69 × 1016 molecules/cm2) in total vertical column. The surface reflectivity weighting function, equation image, is calculated as equation imageequation image, where the partial derivative equation image is computed analytically.

2.4. Linearization Point

[21] In principle, an arbitrary initial guess of the reference state vector can be chosen to start the retrieval process; the final state vector can be obtained by iteration until a convergence criterion is reached. However if the initial guess is too far from the correct solution, the iteration may not converge and no solution is obtained. Therefore it is desirable to choose an initial state close to the true state, so that a final state can be achieved with a minimal number of iterations.

[22] Over most of the globe, SO2 loading is usually close to zero. So it is reasonable to set Ξ0 = 0 DU, and use the operational OMTO3 algorithm to derive total ozone (Ω0) and the wavelength-independent LER (R0) as the initial state for the retrieval. The OMTO3 algorithm accomplishes this by matching the calculated radiances to the measured radiances at a pair of wavelengths (317.5 and 331.2 nm under most conditions, and 331.2 and 360 nm for high ozone and high SZA conditions). Starting with an initial guess of total ozone amount, the longer of the two wavelengths is used to estimate the effective surface reflectivity (or radiative cloud fraction), which is assumed to be the same at the shorter wavelength. Next the shorter wavelength, which is highly sensitive to ozone and SO2 absorption, is used to derive total ozone only. This process is repeated until the derived reflectivity and ozone reach their converged values. Finally this algorithm uses measurements at additional wavelengths for quality control and refinement of its retrieval results in more restricted geophysical situations. For instance, OMTO3 ozone is corrected for wavelength-dependent reflectivity errors in case of aerosol and glint using 360 nm residuals, or it is corrected for ozone profile shape errors at large SZA using 312.5 nm residuals. However, the OMTO3 algorithm does not attempt any correction for absorption by additional trace gases; only heavy SO2 contamination is flagged by examining the residuals at multiple wavelengths [Bhartia and Wellemeyer, 2002].

2.5. Empirical Residual Correction

[23] In the presence of SO2, the residuals calculated using (2) contain wavelength-dependent structure that correlates with the differential SO2 absorption cross sections [Bhartia and Wellemeyer, 2002]. The residuals also have contributions from other error sources, each of which has its own spectral pattern that is superimposed on the SO2 structure, interfering with the SO2 retrievals. To reduce this interference, we find it necessary to perform empirical corrections to the residuals before retrieval of the final state is attempted.

[24] Various methods are used for empirical correction of SO2 retrievals depending on the algorithm. For instance, traditional DOAS algorithm uses the reference sector approach [Khokhar et al., 2005; Richter et al., 2006]. In the BRD algorithm, the OMTO3 residuals are corrected by subtracting its corresponding orbital equatorial averages, calculated after excluding heavily SO2 contaminated pixels [Krotkov et al., 2006]. However, forward modeling errors and instrument calibration errors are not randomly distributed over the globe. Model errors usually correlate with viewing and illumination geometry, cloud patterns, and ozone loading and its profile shape, while measurement errors, such as stray light contaminations, are affected by the scenes being observed. Taking these into consideration, we implement a new scheme, named the sliding median method, for residual correction.

[25] In this correction method, a median residual for a band is calculated for each cross-track position from a sliding group of pixels along the orbit track. This sliding group of pixels, centered on the pixel selected for correction, covers about 30° of latitude in the middle of the sunlit portion of the orbit, but the spatial extent is reduced when the selected pixel is near the terminator to ensure that a roughly equal number of pixels on either side of the selected pixel are included in the sliding group. Bad pixels identified in the linearization step and SO2-contaminated pixels, determined by residuals that are consistent with real SO2 and with slant column SO2 greater than 2 DU (estimated using the BRD method [Krotkov et al., 2006]), are excluded from the sliding group. All band residuals of a pixel are corrected by subtracting the corresponding median residuals,

equation image

where 〈ψi〉 is the sliding median residual of the ith wavelength band for the pixel.

[26] The 30° span of latitude is large enough to encompass sufficient background (minimal SO2 loading) pixels, and at the same time it is small enough that the errors (of both measurement and modeling) do not change significantly within the region. This correction approach essentially forces the local median residuals of the background pixels to equal zero for all the bands. Doing so, the cross-track and latitudinal biases are reduced.

2.6. Linear Fit Algorithm

[27] Given the corrected residual ψi for the ith band, (2) can be rewritten as

equation image

where equation imagei is the remaining error for the ith band after empirical correction, and xj is the jth component of the column vector x = {ΔΩ, ΔΞ, ΔR, c1, c2}, and Kij is an element of the weighting function matrix (K matrix [Rodgers, 2000]), i.e., the jth component of its ith row vector, {equation image, equation image, equation image, (λiλ0) equation image, (λiλ0)2equation image}. The least-square (LS) solution to the set of equations can be written as

equation image

where KT is the transpose matrix of K, which is evaluated at the reference state. G is the gain matrix, defined as (KT · K)−1 · KT, and ψ is the sliding median corrected residual column vector for all the bands. Note that the LS solution (5) assumes equal treatment (weight) for all the band residuals.

[28] Figure 2 shows a typical sample of the K matrix elements, i.e., the weighting functions, which exhibit significant distinct spectral structures. These distinct behaviors in turn facilitate a stable solution to (5), meaning that small errors in measurement and forward modeling do not result in large changes in retrieved values.

Figure 2.

Weighting functions calculated for four vertical columns of SO2: 0, 10, 50, and 100 DU (in Umkehr layer 1). Different weighting functions are represented by different colors. The black curves are equation image, with the units of N value per DU of SO2 increment. The red curves are equation image, with units of N value per DU of O3 increment from 275 DU. The blue curves are equation image, with units of N value for an increase of 0.01 in reflectivity. Corresponding to increasing SO2 amount from 0 to 100 DU, the order of the curves are from top to bottom for equation image and equation image, while the order is reversed for the curves for equation image.

[29] Figure 2 also shows that at short wavelengths (<320 nm) the measurement sensitivity to SO2 change decreases as the SO2 loading increases, i.e., the weighting function equation image becomes smaller with increased SO2 amount. To account for this effect, an iterative procedure is required (especially when SO2 loading is large), with residuals and weighting functions recalculated at each iteration step. The iterative process requires forward modeling for all the bands with various ozone and SO2 loadings at each of steps. Usually these forward radiative transfer calculations are the most computationally intensive part of the retrieval process. To simplify the computation and improve the speed of SO2 retrieval, we introduce the LF algorithm for further approximation by avoiding the iterative process.

[30] The LF algorithm performs its retrieval by selecting those bands whose residuals still respond nearly linearly to the change in SO2 at the initial state (consisting of the OMTO3 total ozone, effective surface reflectivity, and zero SO2 loading). As Figure 2 shows, the weighting functions equation image converge for the various SO2 amounts at longer wavelengths (>320 nm). In other words, measurements at longer wavelengths exhibit a more linear response to SO2 changes. Taking advantage of this behavior, the retrieval is accomplished by solving (5) with the exclusion of residuals in wavelength bands strongly affected by nonlinear SO2 absorption effects. As will be shown in the error analysis section later in this paper, this nonlinear absorption effect causes the LF algorithm to underestimate the SO2 amount. Therefore in practice, this algorithm, implemented for operational SO2 retrieval from OMI, picks as the retrieval result the largest SO2 value derived from the process (started only when SO2 from full band retrieval exceeds 10 DU) of dropping the shortest wavelength bands one at a time from (5) until the band centered at 322.42 nm is reached. As a result the high SO2 retrievals from the LF algorithm are nearly always obtained with the set of measurements that start at this wavelength band.

2.7. Internal Consistency

[31] We have used the LF algorithm to process OMI measurements since its launch in July 2004, and have produced a publicly released OMI SO2 (called OMSO2) data set. This data set contains numerous measurements of volcanic SO2 emissions, ranging from low-level degassing to medium level eruptions. While in general it is very difficult to validate the SO2 column amount retrieved from satellite measurements of a volcanic plume, mainly because of the lack of independent measurements that are comparable to the satellite observations, we nevertheless can examine the internal consistency of the retrieved geophysical parameters as an indirect way to check the validity of our results.

[32] One consistency check is to look at ozone values inside and outside of a volcanic SO2 plume. Because of its emission from point-like sources and the subsequent dispersion and conversion into sulfate aerosols, volcanic SO2 in the atmosphere is in general highly variable in its spatial distribution, containing a higher loading at the center of a fresh volcanic plume, but dropping off quickly toward its edges. In contrast, the actual ozone spatial distribution should behave quite smoothly; total column ozone amounts should remain almost the same inside and outside of the plume. This is particularly true in the tropics, where ozone usually exhibits a lower spatial variability compared to other locations on Earth.

[33] In the LF algorithm, the initial state is derived using the OMTO3 algorithm with the assumption of zero SO2. In the presence of SO2, this initial ozone will be higher than its actual amount. The presence of a larger SO2 loading will yield a larger error in initial guess, simply because the two wavelength OMTO3 algorithm does not attempt to distinguish the effects of more than one absorber, and accounts for them with ozone absorption only. Consequently, the initial guess ozone distribution should show elevated values where significant SO2 loadings are located. However, if the LF algorithm works correctly, the corrected ozone retrieved along with the SO2 should show consistency inside and outside the volcanic plumes. To demonstrate this we show two examples of LF retrieval over volcanic plumes in Figures 3 and 4.

Figure 3.

OMI observations (15 KM retrieval) of the volcanic plume emitted from Soufriere Hills Volcano (Montserrat; 16.72°N, 62.18°W) on 21 May 2006, following a lava dome collapse on the previous day, releasing SO2 that reaches an altitude of 18 km [Carn et al., 2007a]. (a) SO2 column totals, (b) effective reflectivity from LF retrieval, (c) OMTO3 total ozone showing errors over the SO2 cloud, and (d) LF corrected total ozone without errors due to SO2. The maximum SO2 pixel value in Figure 3a is 32.71 DU at −74.40° longitude and 11.42° latitude. The total SO2 mass in the area shown in Figure 3a is 161 kilotons.

Figure 4.

OMI observations (5 KM retrievals) of the volcanic plume from Nyamulagira (DR Congo; 1.41°S, 29.2°E) emitted on 28 November 2006. This volcano, which has a summit elevation about 3 km, erupted on the previous day and we assume its SO2 plume is distributed between 3 and 10 km. The maximum SO2 pixel value in Figure 4a is 167.65 DU at 28.46° longitude and −1.03° latitude. The total SO2 mass in the area shown in Figure 4a is 188 kilotons. See Figure 3 caption for panel definitions.

[34] In Figures 3 and 4, the retrieved SO2 field is shown in Figures 3a and 4a, the LF-derived reflectivity at 331 nm is in Figures 3b and 4b, the initial ozone from OMTO3 is in Figures 3c and 4c, and the corrected ozone from the LF algorithm is shown in Figures 3d and 4d. In Figure 3, the maps are the 15 KM LF results on 21 May 2006, capturing the volcanic cloud from the eruption of Soufriere Hills (Montserrat) volcano on the previous day. The plume from this eruption was injected into the stratosphere, reaching an altitude of about 18 km [Carn et al., 2007a], similar to the SO2 profile assumption made in the 15 KM LF retrieval. In Figure 4, the 5 KM LF results are shown from OMI observations on 28 November 2006 of the volcanic cloud from Nyamulagira (DR Congo).

[35] Both Figures 3c and 4c are the maps for the initial guess ozone for the LF algorithm, showing large elevated ozone values where SO2 loadings are high. Displaying the maps of LF ozone, Figures 3d and 4d clearly demonstrate the success of this algorithm, in that the elevated initial ozone values are greatly reduced (with corrections over 100 DU for some pixels), yielding retrieved ozone values inside the volcanic plumes almost indistinguishable from those outside the plumes.

2.8. Comparison: LF Versus BRD

[36] Both the LF and BRD algorithms use the empirically corrected OMTO3 residuals as input to derive atmospheric SO2 column amount. Though the LF algorithm may select a different subset of residuals, both share the same basic idea that these residuals contain information on atmospheric SO2 absorption that can be converted into vertical columns. The BRD algorithm assumes that SO2 columns are proportional to the magnitudes of differential absorptions as measured by the residual differences between the close bands, while the LF algorithm uses individual residuals in a larger subset and strives to account for other factors (including ozone and reflectivity) that affect the retrieval of SO2 columns. It is useful to compare results for the same event from these two algorithms, so their performance and limitation can be explored.

[37] OMI SO2 maps made from LF and BRD (5 KM) retrievals of the Sierra Negra (Galapagos Islands) volcanic plume on 23 October 2005 are displayed in Figure 5, showing the same spatial extent for both results but very different dynamic ranges in column amount distributions. The LF retrieval (Figure 5a) contains much higher SO2 concentrations in the area immediately adjacent to the volcanic vent (located at 0.83°N, −91.17°W), and the concentrations drop off quickly as this plume is dispersing and being advected southwest. The overall BRD map (see Figure 5b) is quite similar to that of the LF, particularly in the area with low LF SO2 concentrations, but the conspicuous difference is the complete lack of high SO2 concentrations in the BRD map.

Figure 5.

OMI observations of the SO2 plume emitted from Sierra Negra volcano (summit elevation of 1124 m) in the Galapagos Islands on 23 October 2005. (a) 5 KM retrievals from LF algorithm. (b) 5 KM retrievals from BRD algorithm. The maximum SO2 pixel value in Figure 5a is 128.26 DU at −90.88° longitude and −0.37° latitude, while the corresponding BRD SO2 value is 6.4 DU. The total SO2 mass in the area shown in Figure 5a is 344 kilotons, while the total mass shown in Figure 5b is 212 kilotons, i.e., BRD algorithm yields 38% less in total mass than LF retrieval for this case.

[38] To quantify the similarity and the difference, we show in Figure 6 all the values (within the geographic area shown in Figure 5) of ozone corrections (ΔΩ) and BRD SO2 columns (ΞB) plotted against the LF SO2 columns (ΞL). As we have discussed earlier in this paper, the OMTO3 total ozone algorithm accounts for all the absorbers (ozone and SO2) by ozone absorption only. Consequently OMTO3 yields SO2-enhanced ozone values in the volcanic plume; the larger the SO2 loading, the higher the enhancement, therefore the greater the ozone correction by LF algorithm if it works correctly. The results in Figure 6a clearly illustrates this relationship, demonstrated the validity of LF SO2 and ozone results.

Figure 6.

Data points gathered on 23 October 2005 from the geographic area shown in Figure 5 for the eruption cloud from Sierra Negra. (a) Corrections to the OMTO3 total ozone retrievals plotted against the LF column SO2 values. (b) Comparison of BRD and LF 5 KM retrievals for total SO2 amounts less than 10 DU in the dilute region of the plume. (c) BRD SO2 retrievals in the entire volcanic plume compared with LF 5 KM values.

[39] It is expected that the BRD retrieval would yield reasonable results under low SO2 conditions, and indeed Figure 6b shows that BRD results are in good agreement with the LF results for SO2 amounts <10 DU. Linear regression, plotted as the straight line in Figure 6b, shows that BRD SO2 values are about 6% percent higher than the LF values. This is due to the BRD assumption of a lower and narrower vertical SO2 profile than the prescribed profile used in the LF algorithm.

[40] However, the BRD retrieval underestimates SO2 amounts in the presence of large SO2 loadings, as shown in Figure 6c. The underestimation is mainly due to the nonlinear absorption effect associated with the use of a fixed set of wavelength bands in the 310.8–314.4 nm range, where both SO2 and ozone have large absorption cross sections (see Figure 1). Starting from zero, an increase of SO2 amount in the atmosphere manifests itself as a proportional increase in the band residual differences. As the SO2 amount increases beyond this initial range, the nonlinear absorption effect becomes important, noticeably reducing the growth rate of band residual differences, leading to an underestimate of SO2 amounts by the BRD algorithm, as illustrated in Figure 6c in the ΞL range roughly between 20 and 50 DU. As the SO2 amount increases even further, the band residual differences reach their peak and begin to decrease; the consequence of this nonlinear effect is illustrated in Figure 6c in which the BRD values fail to increase beyond 25 DU and severe underestimation follows further SO2 increments. In the extreme case, the SO2 amount is so large that no band residual differences due to SO2 are observed, and the BRD would yield an erroneous SO2 value that is completely independent of the actual SO2 amount.

[41] Besides increasing the impact of the nonlinear effect, the presence of high SO2 loading causes an OMTO3 ozone error, which leads to significant OMTO3 residuals at the BRD wavelength bands. The corresponding band residual differences are not equal to zero because of the nonnegligible differential ozone absorption structures at these bands. This results in an additional BRD SO2 error that is proportional to the ozone error induced band residual differences.

[42] The LF algorithm shifts to a set of longer wavelength bands for SO2 retrieval when the SO2 amount increases beyond a certain threshold, and it performs simultaneous retrievals of ozone and effective reflectivity along with SO2. The first approach reduces the impact of the nonlinear absorption effect and the second approach reduces the SO2 error associated with the ozone error, therefore both approaches extend the valid range of LF retrievals.

3. Error Analysis

3.1. Error Expression

[43] Various error sources, from both model calculations and instrument measurements, contribute to the accuracy of the SO2 column amount retrieved using the LF algorithm. The TOA N value function in (1), for a wavelength band i, is rewritten explicitly with all the dependent parameters and the possible errors, and is expanded with respect to the linearization point,

equation image

where the vector quantities, ω and ξ, are the true vertical profiles for ozone and SO2, while ω0 and ξ0, are the a priori ozone profile and the prescribed SO2 profile, and the differences between the true and assumed profiles are Δω = ωω0 and Δξ = ξξ0. In the forward model, the atmosphere is divided into layers, and the absorber profiles are specified by their vertical layer amounts. The layer sensitivities for SO2 and ozone are respectively defined as Kξi = equation imageimage and Kωi = equation imageimage Ri is the true reflectivity of the wavelength band and this expression of reflectivity is more general than the polynomial characterization of its dependence on wavelength used in (2). The reflectivity sensitivity is kRi = equation imageimage and the difference is ΔR = RiR0. Respectively, equation image and equation image0 refer to the true model parameter values and those used in the linearization, the parameter error is Δequation image = equation imageequation image, and the corresponding parameter sensitivity is kequation imagei = equation imageequation image. These parameters include the atmospheric temperature profiles, the angles that specify illumination and viewing geometry, and the effective cloud pressure, the spectroscopic constants of ozone and SO2, and the parameters that determine the spectral response function of the instrument. ΔNi are the forward model errors such as incomplete accounting for RRS effects and other possible imperfections in the radiative transfer calculations. HTi refers to the higher-order terms that are truncated in the LF algorithm. The last term ɛmi is the total measurement error of the instrument, including the errors in radiometric and wavelength calibration, and the random measurement noise.

[44] Using the definitions of the column vector x and the sliding-median corrected residual ψ, we can rewrite (5) as

equation image

where V0 = {Ω0, Ξ0 = 0, R0, 0, 0} is the column vector of the initial guess derived using the OMTO3 total ozone algorithm, while VL = {ΩL, ΞL, RL, c1, c2} is the column vector derived using the LF algorithm.

[45] To see how the model and measurement errors propagate into the final results, substituting Nm in (7) with (6), (7) can be rewritten as

equation image

We have dropped the label i from the scalar variables in (6) and expressed them as column vectors (written in bold typeface) in (8), with their column dimensions equal to the number of wavelength bands used in the LF algorithm. Similarly, the label i for row vectors in (6) has been dropped and these row vectors have become matrices with their column dimensions equal to the number of wavelength bands.

[46] In general, the true effective reflectivity is a smooth function of wavelength in the UV range, and this function can be described accurately by a low-order polynomial. When the absorber loadings are low, kR contains a small amount of high-frequency structure (see Figure 2), though this increases in magnitude as the absorber loading increases, particularly at wavelengths where the nonlinear effect dominates. However the initial estimate of the effective reflectivity from the OMTO3 algorithm is very good because of the use of a wavelength in the weak absorption region, therefore the reflectivity error ΔR is expected to be very small (at the level of 0.001). Consequently the term kRΔR varies smoothly with wavelength, acting like a high-pass filter that removes the overall bias in the residuals. The remainder of the high-frequency component in this term can be absorbed into the higher-order term HT.

[47] The sliding median equation imageψequation image subtracted from the residuals in (8) essentially cancels those terms that are smooth in their spatial variations. These spatially slow-varying terms include the ozone profile error and some of the model parameter errors such as those due to the use of a climatological temperature profile. Some forward model and systematic measurement errors, which usually do not change drastically from one spatial location to another, are also reduced to nearly zero by this correction scheme. However, highly spatially variable terms, such as those errors induced by the presence of SO2, the random component of the measurement error and the effective cloud pressure error, are largely left intact in this scheme. The SO2-induced errors are the profile shape error and the higher-order term, which becomes important when SO2 loading is high. On the basis of these considerations, (8) is rewritten as follows,

equation image

where the matrix A = G · Kξ is the averaging kernel [e.g., Rodgers, 2000; Eskes and Boersma, 2003]. The remaining error after the sliding median correction is ɛr = Kω · Δω + KR ΔR + kequation image · Δequation image + ΔN + ɛm − 〈ψ〉, and it is essentially equal to the random noise of the measurement, but may also contain errors that do not vary smoothly from one pixel to the next, such as the error caused by using the wrong effective cloud pressure when cloud is present.

[48] The row equation that refers to the SO2 column amount can be extracted from (9), and after subtracting ΞT − Ξ0 from both sides of this row equation it can be rewritten as

equation image

where ΞT is the true SO2 column amount, obtained by the summation of the true SO2 vertical profile ξ. The row vectors, AΞ and GΞ, are extracted from the matrices, A and G, the corresponding rows that are specific to the computation of SO2 amount ΞL. The row vector 1 in (10) contains the value 1 for all its elements; its dot product with a vertical profile (a column vector) yields the total column, i.e., the summation of all the individual layer amounts.

[49] The error expression (10) for SO2 from the LF algorithm relates the vertical column derived from the LF algorithm to the true vertical column, and its first two terms on the right hand side are the direct consequences of the two assumptions made in the LF algorithm. These two assumptions are the linearization of the forward model and the use of prescribed SO2 profiles, which determine the unique vertical distribution given the total column amounts. It is obvious that both of these assumptions could be wrong, since the actual SO2 vertical distribution for an observation is likely to be different from the prescribed one, and nonlinear effects are expected to be significant when SO2 loading is large, leading to errors in retrieval results.

3.2. SO2 Profile Error

[50] Though the values of the averaging kernel as a function of atmospheric pressure level differ from one pixel to the next, depending on the actual geophysical conditions, its functional behavior or shape remains basically unchanged given the same prescribed SO2 profile for the cloud-free pixel. For a cloudy pixel, the shape of the averaging kernel can be altered significantly compared to the cloud free pixel depending on the radiative cloud fraction and the cloud pressure. Figure 7 shows three examples of averaging kernels under typical conditions for the LF algorithm with prescribed profiles used in the operational SO2 retrievals. On the basis of these examples, retrieval errors can be estimated quantitatively given the actual SO2 profiles.

Figure 7.

Examples of the averaging kernel (AΞ) for SO2 retrievals. The red curve is for a cloud-free pixel with a surface reflectivity of 0.1 and a prescribed SO2 profile in Umkehr layer 1. The green curve represents identical conditions to the red curve except that SO2 is distributed in Umkehr layer 3. The blue curve is for the same SO2 profile as the green curve in a partially cloud-covered pixel with a radiative cloud fraction of 33% and a cloud pressure of 892 hPa, indicated by the thin horizontal blue line.

[51] For instance, if the actual SO2 layer is located lower than the uniform SO2 profile in Umkehr layer 1 (∼5–10 km) used in the LF algorithm, the retrieval will underestimate the SO2 column for a cloud-free pixel with low surface reflectivity, retrieving as low as about half of the actual column amount if the actual SO2 is at ground level, i.e., at the bottom of Umkehr layer 0. On the other hand, if the actual SO2 layer is higher than the prescribed SO2 profile, e.g., in Umkehr layers 2 to 6 (i.e., between 15 and 35 km), the LF algorithm will overestimate the SO2 column by 20% at most. However, if the SO2 distribution goes even higher in altitude, say beyond Umkehr layer 7 (>35 km), the 5 KM retrieval will underestimate the SO2 column slightly, usually by no more than a few percent of the actual value.

[52] The errors associated with the 15 KM LF retrieval (with prescribed SO2 profile distributed in Umkehr layer 3) behave differently compared with the 5 KM retrieval. For a cloud-free pixel with 10% ground reflectivity, if the actual SO2 layer is slightly below the prescribed level, i.e., in Umkehr layer 2, the 15 KM retrieval will overestimate the SO2 column by no more than 5%. However if the actual layer is in Umkehr layers 1 or 0, the 15 KM retrieval will underestimate the actual SO2 column, and the lower the actual layer, the larger the error, down to a retrieved column that could be slightly less than half of the actual column. If the actual SO2 is higher than the prescribed profile, e.g., in Umkehr layer 4 or higher, the 15 KM retrieval will also underestimate the SO2 column, usually by no more than 10% of the actual column.

[53] For a cloudy pixel, the error analysis becomes much more complicated, even in the case when the correct cloud top pressure is used in the retrieval. This is in part due to the fact that the MLER model used here is too simple to yield reliable quantitative estimates in the case when the absorber is below or mixing with the cloud. However the MLER model should work well enough when the absorber is above the cloud. In the example shown as the blue curve in Figure 7 for a pixel with 33% radiative cloud fraction, if the actual SO2 is located below the prescribed profile but above the cloud, the 15 KM retrieval will overestimate the column amount by as much as 20%. However if the actual distribution is above the prescribed profile, the 15 KM retrieval will underestimate the SO2 column, usually by no more than 15%.

3.3. Nonlinear Effect Error

[54] As shown earlier in the comparison between LF and BRD (section 2.8), the nonlinear absorption effect causes the underestimation of BRD retrievals when SO2 columns are greater than 10 DU. In this section, we will show that this effect has a similar impact on LF retrievals, but only for much higher SO2 column amounts.

[55] To examine the nonlinear effect error in the LF algorithm, we look at cases in which the prescribed SO2 vertical profile is close to the actual profile. In these cases the term HT in (10) can be estimated if we use only the second-order term (i.e., third-order term and higher are truncated)

equation image

As the SO2 column amount increases, the weighting function equation image becomes smaller, and this behavior is clearly illustrated in Figure 2. This implies that the second derivative, equation image, is negative, and its absolute value gets larger with increasing SO2 absorption. Namely the second derivative has a structure that is anticorrelative with its first derivative (i.e., the SO2 weighting function). Therefore the higher-order term HT behaves much like a negative absorber, and the second term in (10) will yield a negative SO2 column amount. In other words, the LF retrieval underestimates a SO2 column with the linearization of the forward model.

[56] In order to take advantage of the fast computation of the forward model and the simple implementation of algorithm steps, this technique always sets the initial guess of the SO2 column (Ξ0) to be zero. Consequently the term Ξ − Ξ0 can be very large, particularly when the actual vertical column is high, resulting in a significant contribution from the higher-order term, which leads to the underestimation of the actual SO2 column. The algorithm mitigates this problem by dropping the shorter wavelength bands, which are affected more by the nonlinear effect, therefore extending the valid range of LF retrievals. Using an iterative algorithm, which would eliminate the nonlinear effect error as discussed later in this paper, we have estimated the error in the LF algorithm when SO2 loading is high, and found that the LF retrieval can underestimate the SO2 column by as much as 70% (the precise error depends on the geophysical conditions) when the actual column is ∼400 DU because of the linearization of the forward model at zero SO2. However, this error is much less when the SO2 loading is lower and it is at the 20% level when the actual column amount is around 100 DU.

3.4. Cloud Pressure Error

[57] One of the forward model parameters needed for the computation of TOA radiances and the weighting functions in the LF algorithm is the effective cloud pressure (p) associated with the MLER model. A climatological cloud pressure data set derived from IR satellite measurements is used in the currently released OMI SO2 product. In general (but not always) the IR-derived climatological cloud pressures are lower (i.e., cloud is placed at a higher altitude) than the effective cloud pressures that are consistent with the MLER model used in this algorithm, therefore introducing additional errors for cloudy observations.

[58] To analyze the impact of cloud pressure error (Δ p), (10) is rewritten explicitly with the cloud pressure,

equation image

where equation imager* is ɛr less the cloud pressure induced error. Note that the averaging kernel AΞ, the higher-order term HT, and the gain matrix GΞ, are all dependent on the cloud pressure. If the cloud pressure error is not too large, its impact on the retrieval can be estimated with just the third term on the right hand side of (12). The cloud pressure sensitivity equation image contains high-frequency spectral structure (similar to the RRS filling structure), which has certain degree of correlation with the SO2 absorption structure. Given that the cloud pressure errors Δp are mostly positive, the OMI SO2 shows consistent error patterns over clouds, and these patterns contain elevated SO2 values that are mostly less than 1.5 DU for 5 KM retrievals. Note that SO2 emissions from degassing volcanoes are usually in the range of a few DU, this cloud-related SO2 error may interfere with the measurements of these emissions.

[59] When the cloud pressure error is very large, the actual averaging kernel is quite different from its initial estimate, and the higher-order terms become dominant, making this analysis not applicable to these situations. Fortunately, cloud pressures consistent with the MLER model are being retrieved from OMI using approaches based on RRS [Joiner et al., 2004, 2006; Vasilkov et al., 2004] or absorption in the O2 − O2 band near 477 nm [Acarreta et al., 2004]. Using OMI-derived cloud pressures will significantly reduce the cloud pressure errors, resulting in a more accurate SO2 retrieval in our next release of the product.

4. Limitations and Improvements

[60] Both anthropogenic and volcanic emissions contribute to an enormous dynamic variation in atmospheric SO2 concentrations not observed in any other trace gases. The vast SO2 loading range and its uncertainty in vertical distribution, coupled with the interference from ozone absorption, poses a unique challenge for accurate SO2 retrieval.

[61] Previously we have developed the BRD technique [Krotkov et al., 2006], which maximizes the detection sensitivity to small concentrations of SO2 in the planetary boundary layer, but nonlinear effect and ozone-error induced residuals have limited the valid range of BRD retrievals to SO2 vertical columns of about 10 DU.

[62] The LF algorithm described in this paper has greatly extended the valid range of SO2 retrievals by shifting the wavelength bands to the weaker absorption region and by performing simultaneous retrievals of SO2, ozone, and effective reflectivity. However our error analysis has indicated that when SO2 loadings are very large, the nonlinear effect can still lead to severe under estimation of the actual column amounts. This is the main factor that limits the valid range of this algorithm to about 100 DU, with an overall uncertainty of about 20%. Note that the use of longer wavelength bands makes the LF algorithm more susceptible to measurement errors and the errors in the SO2 absorption cross sections, which are less accurate in the longer (>325 nm) wavelength region than those in the shorter (between 310 and 325 nm) wavelength region. Therefore even with the availability of hyperspectral measurements, it may not be practical to avoid dealing with the nonlinear effect by shifting to measurements at even longer wavelengths.

[63] Fortunately we can greatly reduce the impact of this nonlinear effect on the SO2 retrieval by iteration without limitation to the use of longer wavelength bands. All the equations presented in this paper are equally valid and can be used without any modification in the iterative retrieval, which can be implemented as the repeated application of LF algorithm steps, each of which takes the state vector derived at the previous step as its new linearization point, similar to the steps in the modified Krueger-Kerr algorithm [Krueger et al., 2000]. Doing so, Ξ0 would approach the correct value, so that the term (Ξ − Ξ0)n (with n = 2 and higher) would become so small that the higher-order term becomes negligible. We are currently developing and implementing the iterative algorithm, which is expected to be valid over the complete SO2 range.

[64] The error analysis (which would be valid for the iterative algorithm also) of the LF algorithm has found that the prescribed SO2 profiles have significant impacts on the retrieval results depending on the difference between actual and prescribed profiles. The error in SO2 retrieval contributed by this uncertainty in the SO2 vertical distribution is mostly limited to less than 20% if the actual SO2 is not located near the bottom of Umkehr layer 0. To improve the accuracy of SO2 retrieval, it is necessary to have better information on its vertical distribution, either obtained from other sources such as the output from chemistry-transport models or derived from the same BUV measurements. It is possible to perform limited vertical SO2 profile retrievals from the hyperspectral OMI measurements.

5. Conclusions

[65] We have presented the LF algorithm developed for the simultaneous retrievals of vertical columns of SO2, ozone, and effective reflectivity from the OMI BUV measurements of OMI. The sample results have demonstrated the success of this algorithm, with which large elevated ozone values in the volcanic plumes from the total ozone algorithm are greatly reduced so that consistent ozone values are retrieved both inside and outside the plumes.

[66] We have also derived an absolute error expression for retrievals from this algorithm and used it to perform detailed analysis of the various factors that affect the retrieved SO2 columns and provide quantitative estimates of their error contributions. The averaging kernel derived along with the error expression is very useful in understanding the altitude-dependent sensitivity of this algorithm, and provides the necessary information to interpret the retrievals. The averaging kernel is needed in comparisons between in situ profile measurements and satellite retrievals and in application of data assimilation [Rodgers, 2000].

[67] The LF algorithm is very fast when applied to measurements at a small set of discrete wavelengths and produce reasonable estimates of vertical columns for a wide range of conditions. Therefore it is able to provide data needed in aviation and ground hazard management for near real-time monitoring and tracking of volcanic clouds.

[68] The LF algorithm is also very flexible in terms of measurement input; it can be applied to the discrete bands from TOMS, or some optimally selected discrete UV bands from the hyperspectral measurements of GOME, SCIAMACHY or OMI, or it can take advantage of their full spectral measurements in selected wavelength windows. Because of this built-in algorithm flexibility, it is an ideal choice for making a long-term consistent SO2 data record using past (TOMS, GOME), present (OMI, SCIAMACHY, GOME-2), and future (GOME-2, OMPS (Ozone Mapping and Profiler Suite)) BUV measurements from instruments on satellite platforms.

Acknowledgments

[69] The Dutch-Finnish built OMI instrument is part of the NASA EOS Aura satellite payload. The OMI project is managed by the Netherlands Agency for Aerospace Program (NIVR) and the Royal Dutch Meteorological Institute (KNMI). This work was supported in part by NASA under grant NNS06AA05G (NASA volcanic cloud data for aviation hazards) and by the U.S. OMI Science Team. The authors would like to thank the KNMI OMI team for producing L1B radiance data and the U.S. OMI operational team for continuing support.

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