A robust method to detect volcanic ash, using data from the infrared channels of the Spinning Enhanced Visible and Infrared Imager instrument mounted on-board Meteosat Second Generation, is presented. The simultaneous retrieval of quantitative volcanic ash physical properties using a one-dimensional variational analysis framework is also described. These methods are demonstrated using data from the Icelandic Eyjafjallajökull eruption in 2010. Sensitivity experiments are presented which show that the retrieved quantities are strongly dependent on the choice of ash refractive index data used in the retrieval scheme's radiative transfer model. Validation of the retrieved properties is carried out against lidar data, which demonstrate that the retrievals are realistic, and which indicate the most suitable refractive index data sets to use for these cases.
 The London Volcanic Ash Advisory Centre (VAAC), hosted by the U.K. Met Office, has the responsibility to issue volcanic advisories for the Icelandic region to provide guidance to civil aviation as to which areas have high concentrations of volcanic ash. Satellite images can provide a vital overview of the ash coverage and can be used by the forecasters, along with the guidance from numerical model prediction systems such as NAME (Numerical Atmospheric-dispersion Modeling Environment [Jones et al., 2007; Webster et al., 2012], to prepare their advisories. The satellite products can be used to show the current extent of the ash in real time, to validate the forecasts of ash extent and concentration, and to help determine the source parameters of the ash plume which are input to the model.
 Remote sensing is a vital tool in the tracking of hazardous volcanic plumes, with established satellites monitoring techniques existing [e.g., Prata, 1989a, 1989b]. Geosynchronous and polar orbiting satellites have both been used to track volcanic plumes and derive physical properties. Geosynchronous satellites have high-temporal resolution allowing for the plume to be detected and tracked in near real time, and polar orbiters provide high-spectral resolution data allowing physical properties to be retrieved [Wen and Rose, 1994; Prata and Grant, 2001]. Meteosat Second Generation (MSG) with its main payload the Spinning Enhanced Visible and Infrared Imager (SEVIRI) provides high temporal and multispectral data with eight infrared channels, making it a valuable tool for the Volcanic Ash Advisory Centres (VAACs). It has the potential to derive quantitative measurements of volcanic ash plumes in clear areas or above cloud. Until the eruption of the Eyjafjallajökull volcano in 2010 only qualitative indices were derived from the satellite imagery available in the VAAC [Watkin, 2003]. In this paper, we present results for the 2010 Eyjafjallajökull eruption using a new method, applied to the SEVIRI data, to derive quantitative measurements of the volcanic ash plume and discuss the sensitivities of the retrieved physical properties to assumptions made about the volcanic plume.
2. SEVIRI Measurements
 The second Meteosat Second Generation (MSG) satellite (known as Meteosat-9) was launched on 21stDecember 2005, becoming the prime geostationary observational satellite located at 0 degrees longitude in September 2006. The main payload of Meteosat-9 is the SEVIRI imager which has 12 spectral channels and a baseline repeat cycle of 15 min. The spatial resolution at the equator is 3 km for the infrared channels used for volcanic ash monitoring, although this increases as one moves further from the sub-satellite point. The channels used in this study are the three long-wave window channels centered at 8.7, 10.8 and 12.0μm, and the channel in the CO2 absorption band at 13.4 μm.
 Meteosat-9 was used extensively during the 2010 Eyjafjallajökull volcanic eruption, for monitoring of the emitted plume by the London VAAC, and to aid the NAME model initialization and verification.
3. Ash Detection and Retrieval Methods
 This section gives details of the methods used in this study, first for the detection of ash-affected SEVIRI pixels, and second for the retrieval of quantitative physical properties for these pixels.
3.1. Volcanic Ash Detection
 Volcanic ash is a generic term used to describe particulate emissions from volcanic eruptions. The major constituent of volcanic ash is SiO2 which depending on the volcano constitutes more than 50% of the total particulate emissions. The most widely used method of volcanic ash detection takes advantage of the “reverse absorption” of silicate particles relative to ice and water particles [Prata, 1989a] using the channels centered at 10.8 μm and 12.0 μm. This method has been used successfully with SEVIRI data for the detection of volcanic ash from eruptions of Karthala [Prata and Kerkmann, 2007] and Mount Etna [Corradini et al., 2009], and forms the basis of some of the ash detection tests used in the present work. In addition, the 8.7 μm channel is also used in two of the tests. The full detection process consists of five separate steps, which are described briefly below.
 1. Test 1 is a straightforward brightness temperature difference (BTD) test, whereby a pixel is given a definite positive ash detection flag if the observed BTD between the 10.8 μm and 12.0 μm channels is more negative than −2 K, i.e., if:
For simplicity, we have used a constant threshold here (and also for the tests described in items 2 and 3 below), although we recognize that, in general, such thresholds should probably be dependent on the specific viewing geometry. Because this test is intended to provide a definite positive flag (i.e., it cannot be over-ridden by the test described in item 4 below), and is supplemented by additional tests, the value of −2 K used for the threshold is deliberately set to be stricter than that which would normally be used when applying this test in isolation. An example of the result from this first test may be seen inFigure 1b for the 1230 UTC image on 7th May 2010, where all pixels less than this threshold are colored according to their BTD and overlaid on a background gray scale image corresponding to the 10.8 μm brightness temperature. For reference, we also show the corresponding “Dust RGB” image for this case in Figure 1a. In this Red-Green-Blue (RGB) composite image, the 12.0μm minus 10.8 μm BTD is assigned to the red component of the image (with the red intensity increasing as the BTD increases from −4 to +1 K), the 10.8 μm minus 8.7 μm BTD is assigned to the green component (over the range 0 to 15 K, with a gamma enhancement factor of +3.0), and the 10.8 μm brightness temperature is assigned to the blue component (over the range 261 to 289 K). This RGB product, originally developed at EUMETSAT (European Organisation for the Exploitation of Meteorological Satellites), was used extensively at the Met Office during the Eyjafjallajökull eruption period as a qualitative volcanic ash monitoring tool. In Figure 1a, the volcanic ash shows up as the red plume immediately to the south of Iceland, gradually becoming a more orange color over the oceanic areas to the west of the British Isles. Test 1 detects part of the plume immediately to the south of Iceland, and also identifies much of the ash in the 45°–54°N latitude range, but misses much of the intervening ash.
 2. Test 2 is a three-channel BTD, which was developed in-house during the early part of the Eyjafjallajökull eruption. In this test, a pixel is given atentative ash detection flag (see below) if:
The threshold value of +1.5 K was determined by way of subjective comparisons with time-varying loops of the Dust RGB images described above, from the early phases of the eruption. It is recognized that factors such as viewing angle, particle size and, perhaps most importantly, the level of SO2 absorption will all have an effect in determining the optimum threshold to be used for ash detection, and as such, it is not clear at the present time how valid generally is the current value. Figure 1cshows the detection mask resulting from the application of Tests 1 and 2 to the same case as above, where the colored pixels are those which have passed either Test 1 or Test 2. From this, we see that a significantly larger proportion of the ash-contaminated pixels (as determined subjectively fromFigure 1a) are captured by the addition of this second test, which has reinstated some of the pixels not identified as ash by Test 1. However, we also see the introduction of several areas of false alarms, associated mainly with areas of ice cloud. Note that, because Test 2 only applies a tentative ash flag to each pixel, this means that it can be over-ridden by the test described in item 4 below, which addresses these false alarms.
where BT10.8clr and BT12.0clrare the calculated clear-sky brightness temperatures at 10.8μm and 12.0 μm respectively. These thresholds have been chosen so as to maximize the detection of ash in marginal areas, and as such lead to a significant over-prediction in many areas, as seen inFigure 1d, which shows the detection mask resulting from the application of Tests 1 and 3 to the same case as shown previously, and where the colored pixels are those which have passed either Test 1 or Test 3. As in item 2 above, we note that the tentative ash flag supplied by Test 3 is allowed to be over-ridden by the test described in item 4 below, to counter this over-prediction.
 4. Test 4 is used to remove any false-alarms introduced by Tests 2 and 3, and is based on the work described byPavolonis and Sieglaff , using the concept of “β-ratios” as described byPavolonis . In this approach, effective ash cloud emissivities are calculated from the observed radiances at 8.7 μm, 10.8 μm and 12.0 μm, and these are used to construct ratios of effective absorption optical thickness between pairs of channels. For example, the β-ratio for the pair of channels at 8.7μm and 10.8 μm is given by:
with the emissivities being derived from a combination of the measured radiances, the clear-sky and overcast radiances calculated from RTTOV, and an assumed radiative emission height. For the purposes of ash detection, we assume in the current paper that this height is that which corresponds to an NWP model temperature ofBT10.8 − 5 K, where BT10.8 is the observed 10.8 μm channel brightness temperature. We have chosen this height specification, rather than a constant height (for example, the tropopause height), in order to provide more accurate emission-height estimates for the optically thicker areas of ash nearer the source. If detection of the more diffuse areas of ash further downstream were considered to be more important, then it is possible that a somewhat different emission-height specification could provide greater detection sensitivity for these areas (seePavolonis  for a detailed discussion on this topic). Pavolonis and Sieglaff  have shown that simultaneous estimates of β(8.7, 10.8) and β(12.0, 10.8) yield quantitative information on whether individual pixels are affected by volcanic ash. For the present study we have derived our own thresholds for these quantities, based on a subjective analysis of a series of cases from the 2010 eruption period (as in item 2 above), to provide criteria for rejecting pixels which have previously been tentatively flagged as containing volcanic ash. Specifically, if:
where a0 = 4.264, a1 = −5.823, and a2= 2.446, then any tentative ash identification (i.e., by Test 2 and/or Test 3, but not by Test 1) is classed as being a false-alarm, and that pixel has the ash flag removed.Figure 1eis the resulting ash mask derived from a combination of Tests 1, 2, 3 and 4, i.e., pixels flagged by either Tests 1, 2 or 3, and with Test 4 removing, where possible, the false-alarms introduced by Tests 2 and 3. This is seen to be in good qualitative agreement with the areas of ash apparent in the RGB image inFigure 1a.
 5. In practice, we have found it beneficial to apply a final spatial noise-reduction test to remove occasional patches of speckle arising from the application of the above tests. This involves determining for each pixel the number of ash-flagged pixels (from the above tests) in a surrounding 3 × 3 pixel box, and only retaining the ash flag where at least 6 of these 9 pixels have been flagged.Figure 1f shows the ash mask after this test has been applied, and represents the final ash detection product for this example, which is then passed on to the ash retrieval scheme described below.
3.2. Retrieval of Physical Properties
 The retrieval of ash properties uses the SEVIRI wavelengths centered at 10.8 μm, 12.0 μm and 13.4 μm. Use of the 8.7 μm channel has been considered, and is technically feasible, but has not been used for the results presented in this paper because of the potential effects of SO2 absorption, which is significant at this wavelength, but which is difficult to include within the current retrieval framework. The retrieval approach is similar in principle to the scheme developed by Pavolonis and Sieglaff , although the details of how the retrieval scheme is implemented are very different.
 The retrievals are carried out using a one-dimensional variational (1D-Var) analysis, based on the Bayesian optimal estimation techniques described byRodgers . This approach attempts to reach a statistically optimal estimate of the atmospheric state vector, x, consistent with the observations, yob, and any a priori knowledge of the background state, xb, by minimizing the following cost function, J:
where B is the error covariance matrix of the a priori background, y(x) is the vector of radiances calculated from the atmospheric state x, and R is the measurement error covariance matrix, which in this case also includes the effects of errors inherent in the forward (i.e., radiative transfer) model. The superscript T denotes the matrix transpose, and the superscript −1 denotes the matrix inverse. To minimize this cost function, we need to calculate the gradient of equation (6) with respect to the state vector:
where H(x) = ∇xy(x) is known as the Jacobian matrix, the gradient of the calculated radiances with respect to the state vector x. As is common with many nonlinear 1D-Var problems, the analysis code used in this paper utilizes a Levenberg-Marquardt minimization algorithm [Levenberg, 1944; Marquardt, 1963], an iterative technique that is essentially a combination of the gradient descent and Gauss-Newton methods.
 In the current scheme, we assume that x = (pash, L, rash), i.e., the state vector consists of just three elements, the ash layer pressure (pash), the ash column mass loading (L), and the ash size distribution effective radius (rash). Implicit in this method, therefore, are the assumptions that: (1) all other parameters that affect the radiances are known exactly, and therefore are not variables of this problem; (2) there is only one ash layer with a well-defined radiating temperature at pressurepash; and (3) there are no water or ice clouds above, in or below the ash plume. In practice, we tend to assume that the retrieved pash is associated with the pressure at the top of the real ash layer. For thicker layers this is a reasonable assumption, but as the optical thickness decreases, pash will actually tend to correspond to levels somewhat lower down in the ash layer.
 In terms of these three state vector elements, the calculated top-of-atmosphere (TOA) radianceyi(x) in channel i can be written as:
where yiclris the modeled TOA clear-sky radiance in channeli, and yiovc(pash) is the modeled TOA radiance due to overcast (i.e., blackbody) ash cloud at pressure pash. The modeled spectral emissivity εi is given by:
where kabs,i(rash) is a suitable ash mass absorption coefficient (defined as a function of rash) and θ is the satellite zenith angle. The fast radiative transfer code RTTOV is used to calculate yiclr and yiovc(pk) for all channels i and vertical model levels k, again using background profile data from the most recent run of the NAE NWP forecast model. The NWP model’s surface temperature is used as input to these calculations, and the default RTTOV surface emissivity values are applied.
 From equations (8) and (9), it is relatively straightforward to calculate the elements of H(x) to be:
It is important to note that the formulation of radiative transfer as set out in equations (8) and (9), although convenient to use within the current 1D-Var framework alongside the RTTOV calculations, does neglect the effects of scattering, which are often significant in the infrared.Chou et al.  have shown that scattering effects may be approximated by the use of a scaled extinction coefficient , defined as follows:
where ksca is the ash mass scattering coefficient and b is the backscatter fraction, all terms being functions of i and rash. Therefore, the corresponding value of (rash) from equation (13) is used in place of kabs,i(rash) in equations (9) to (12). Values of kabs,i(rash), ksca,i(rash) and bi(rash) are calculated using Mie theory, assuming spherical ash particles. These assumptions are similar to those made in the radiative transfer calculations carried out by Millington et al. , although in that paper the calculations are done within the RTTOV model itself using its own scattering scheme [from Matricardi, 2005], whereas in this paper they are applied to equations (9)–(12)within the 1D-Var retrieval. A lognormal formulation is assumed for the particle size distribution:
where Nd is the total number density, r is the particle radius, r0 is the geometric mean radius and σPSD is the geometric standard deviation of the particle size distribution. In terms of the size distribution's effect on the ash optical properties, the effective radius is the most important parameter, and is calculated using:
However, the optical properties are also sensitive to the shape of the size distribution as governed by the value of σPSD. Therefore, values of are pre-calculated and tabulated as a function ofrash for eight different values of σPSD(1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0). When processing an individual ash-contaminated pixel, a separate state vector solution (pash, L, rash) is obtained for each of these σPSD values in turn, and the final retrieved values are set to the solution with the lowest final cost from these eight. The values have been calculated using a number of different ash refractive index data sets (see Section 4 below).
 We assume that the measurement error covariance matrix R is diagonal:
where σi2 is the combined (observation plus forward model) variance of the measurement error in channel i. The observation errors σE,i2 are derived from published figures (EUMETSAT, SEVIRI radiometric noise, 2011. http://www.eumetsat.int/idcplg?IdcService=GET_FILE&dDocName=PDF_MSG_SEVIRI_RADIOM_NOISE&RevisionSelectionMethod=LatestReleased) for the radiometric noise of the relevant SEVIRI channels. The forward model errors σF,i2must also contain a contribution from the errors in the forecast temperature and humidity profile (which the current method assumes is known perfectly), and have been estimated using statistics derived from long-term monitoring of cloud-free SEVIRI radiance data. The values ofσE,i2, σF,i2 and σi2 used are given in Table 1. Also, a simple bias-correction has been applied to the radiances simulated using the RTTOV model, based on the same long-term monitoring statistics (over oceans), to account for any systematic biases existing between the measured and simulated radiances arising from calibration or radiative transfer model errors.
Table 1. Error Characteristics Assumed for the Measurement Error Covariance Matrixa
Here σE,i2 is the assumed radiometric noise of the observation, σF,i2 is the assumed forward model error, and σi2 is the combined measurement error variance for channel i.
 In defining the background state xb and the background error covariance matrix B, we have to accept that we have very little a priori knowledge to constrain the analysis, other than from the NAME forecasts themselves. The background value of pash is set simply to a constant value of 600 hPa. The background column mass loading L is defined as being the value consistent with 10.8 = 0.5, where 10.8 is the scaled extinction optical thickness at 10.8 μm. The background ash effective radius is set to a constant value of 3.5 μm. B is assumed to be diagonal, with the variances of the three state variables as given in Table 2. These values are set to be large compared with the desired accuracy of the retrieval, indicating that the background term will only be providing a weak constraint on the analyzed state.
Table 2. Error Characteristics Assumed for the Background Error Covariance Matrix
State Variable j
(20 g m−2)2
 Due to the nonlinear nature of the present 1D-Var retrieval, it is desirable to initialize the minimization with as good a first-guess as possible. The first-guess value ofpash is defined to be the NWP model pressure that corresponds to a model temperature of BT10.8 − 10 K, where BT10.8 is the observed 10.8 μm channel brightness temperature. Given the lack of any further independent a priori knowledge in this case (i.e., other than from the NAME predictions themselves), the first-guess values of the other two state vector parameters are simply set to be equal to the background values as described above. We currently avoid using the NAME model output to influence the background/first-guess specification in order to maintain independence between the SEVIRI retrievals and the model predictions.
4. Results and Discussion
 In this section, we present some results from the retrieval scheme during the Eyjafjallajökull eruption period of April/May 2010, together with some sensitivity experiments, and comparisons with CALIPSO and aircraft lidar data for validation of the retrievals.
4.1. Retrieval Examples
 An example of the various imagery products available from the retrieval scheme is shown in Figures 2c to 2f for the SEVIRI image ending at 1900 UTC on 6th May 2010. The Dust RGB image is shown in Figure 2a for comparison, and the detection product described in Section 3.1 above is shown in Figure 2b. For this example, the refractive index data from Pollack et al.  corresponding to andesite have been used to calculate the values of required by the retrieval scheme. Andesite refractive index data have been found to be a suitable approximation for volcanic ash in previous studies [e.g., Wen and Rose, 1994; Prata and Grant, 2001], and are used by default in the present retrieval scheme when used operationally.
 The derived ash heights (converted from pash using the NWP profile data) are shown in Figure 2c, and it is worth noting that the heights in this particular example represent the highest values retrieved during the eruption period, occasionally in excess of 12 km altitude. The corresponding column mass loadings are shown in Figure 2d, and show a range of values, generally of order 1–3 g m−2, but with significant areas of 5 g m−2 or more. The ash effective radius retrievals are shown in Figure 2e, and show a general trend for decreasing size with distance from the source, values being in the range 6–8 μm close to Iceland, and generally falling to the 2–4 μm range south of 58°N. An additional diagnostic image is shown in Figure 2f, which plots the final cost of the 1D-Var solution, as given byequation (6). In this case, the solution is seen to have a relatively low cost (<0.2) generally, although it is apparent that there are patches where the solution cost is significantly higher (>0.5), with many of these higher-cost areas corresponding to the highest ash height retrievals inFigure 2c. These higher-cost areas are indicative of pixels where the 1D-Var scheme has been less able to match closely the measured radiances (and weak a priori constraints) with those calculated from a model ash cloud analysis, and therefore represent areas where the retrieved quantities are perhaps subject to greater uncertainty.
 Some further examples of the retrievals are shown in Figure 3, showing cases from 1215 UTC on 15th April 2010 (near the start of the first ash eruption phase), 1230 UTC on 7th May 2010 (i.e., the same case as shown in Figure 1), and 0800 UTC on 13th May 2010 (toward the end of the second ash eruption period).
4.2. Sensitivity Experiments
 One of the major sources of uncertainty in the retrieval scheme is the choice of ash refractive index data with which to calculate the tabulated values of ext. As noted above, we use the Pollack et al.  andesite data by default operationally, but here we perform a number of comparison studies using different refractive index data sets, in order to assess the sensitivity of the retrievals to this assumption, and to try to determine the optimum data set to use in this case. Figure 4 shows graphs of the scaled mass extinction coefficient ext at the three wavelengths used by the retrieval scheme, plotted as a function of ash effective radius rash, in this case using a value of σPSD = 2.0 in the lognormal size distribution (equation (14)). Also shown in these plots is the ratio ext,10.8/ ext,12.0, as this is a key parameter in determining the sensitivity of the ash retrievals at these wavelengths. As well as the Pollack et al.  andesite data used in Section 4.1 above and plotted in Figure 4a, we also use the Oregon obsidian data from the same paper, shown in Figure 4b, mineral dust data from Balkanski et al. , shown in Figure 4c, and volcanic dust data from Volz  (as tabulated by World Climate Research Programme ), shown in Figure 4d. The Balkanski et al. data have been used extensively by other workers analyzing data from the Eyjafjallajökull 2010 eruption period [e.g., Newman et al., 2012; B. T. Johnson et al., In-situ observations of volcanic ash clouds from the FAAM aircraft during the eruption of Eyjafjallajökull in 2010, submitted toJournal of Geophysical Research, 2012] – in the present study, the data corresponding to 1.5% hematite have been used. The ash density is assumed to be 2.3 g cm−3 for all the Mie calculations carried out in this paper, this figure falling within observed values for erupted ash material [e.g., Sparks et al., 1997] and being the value currently used within the NAME system.
 Although the graphs shown in Figure 4 have broad similarities, there are some significant differences. The Balkanski et al. values for ext are generally lower than for the other three data sets, for example, this behavior contrasting with the Pollack et al. andesite data, which show the largest ext values and a much larger degree of spectral variation, especially for smaller values of rash. It should also be noted that these curves change slightly depending upon the shape of the underlying particle size distribution, as governed by the value of σPSD in equation (14).
 Comparisons of ash retrievals using these four refractive index data sets are shown in Figure 5, for the same 13th May 2010 case as shown in Figures 3c, 3f and 3i above. Figure 5 shows the retrievals made using the Pollack et al. andesite data (Figures 5a, 5e, and 5i), the Pollack et al. obsidian data (Figures 5b, 5f, and 5j), the Balkanski et al. data (Figures 5c, 5g, and 5k), and the Volz data (Figures 5d, 5h, and 5l). The ash height retrievals (Figures 5a–5d) show some significant differences, with the Pollack et al. andesite and Volz data leading to retrievals generally higher than those from the other two data sets. The column mass loading retrievals (Figures 5e–5h) are also seen to vary significantly, with the Volz data leading to the smallest loadings and the Balkanski et al. data leading to the largest. These differences arise partly due to the competing effects of ash height and column loading on the simulated radiances, i.e., a higher ash height retrieval as given, for example, by the Volz data in Figure 5dneeds a correspondingly smaller value of column loading to yield the same top-of-atmosphere radiance. However, the larger values of retrieved column loadings from the Balkanski et al. data are also directly related to the relatively small values of extin this case, in that a greater column loading is therefore required to provide a large-enough value of ash optical thickness to satisfy the observed radiances. To summarize the differing masses derived using these various refractive index assumptions,Table 3 presents the mean, standard deviation and maximum value of the column loadings for this 13th May 2010 case, together with the total retrieved mass, these values being calculated over the area shown in Figure 5.
Table 3. Summary of Ash Mass Retrievals From 0800 UTC on 13th May 2010, for the Area Shown in Figure 5, Using Four Different Assumptions for the Ash Refractive Index Dataa
Figures 5i–5lshow the final costs of the 1D-Var retrievals for the four refractive index data sets. The most striking features of these images are the areas of relatively high cost near the source for the Pollack et al. obsidian and Balkanski et al. data (i.e., the purple areas inFigures 5j and 5k) compared with the other two data sets. Therefore, for these near-source retrievals, it would seem appropriate to have more confidence in the retrievals from the Pollack et al. andesite and Volz refractive index data. However, it is also worth pointing out that this is not always the case, and that there are some small areas further away from the source (e.g., around 66.5°N, 6°W) where it is the Balkanski et al. and Pollack et al. obsidian data that yield the lower final costs. In general, for the April/May 2010 period, we have found that the Pollack et al. andesite and Volz data sets tend to produce retrievals with lower final cost than the other data sets (although we have not attempted to quantify this difference at the present time), and we conclude therefore that more confidence should be placed on the retrievals carried out using these two data sets for the present cases.
4.3. Height Retrieval Validation
 It is important to validate the above retrievals against independent observations where possible. In practice, the most realistic way of doing this is to compare the ash height retrievals with coincident space-borne lidar ash-top height measurements. In this paper, we have used data from the Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) [Hunt et al., 2009] flown on board the Cloud Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) mission [Winker et al., 2009]. For the April/May 2010 period we have identified eight CALIPSO overpasses where the lidar data indicate a reasonably well-defined layer that is identifiable as volcanic ash and where ash is also detectable in the corresponding SEVIRI retrievals. The coincident data have then been averaged into 0.2° latitude bins, and the mean ash heights from the SEVIRI retrievals have been compared with the mean ash-top heights (as calculated from the feature mask) from the CALIOP profiles. For these comparisons, it is important to account for parallax effects in the SEVIRI retrievals due to the high viewing angles. Therefore, the horizontal positions of these retrievals have been corrected, based on the heights retrieved for each pixel, to ensure maximum consistency in the horizontal locations of both data sets. Note that low-level water clouds are frequently apparent in both the CALIOP and SEVIRI data for many of these cases. Restricting our comparisons to only those cases where no underlying clouds existed would have resulted in a data set too small to be meaningful, so we have allowed these extra cases, while remaining mindful of their potentially detrimental effects on the retrieval accuracy. Note also that, because we are comparing with CALIOP ash-top heights, then we are implicitly assuming that the SEVIRI-derived ash heights correspond to the top of each ash layer, whereas it was noted previously that the SEVIRI heights probably corresponded to a level below the top. Although we have not attempted to quantify the size of this effect, it is not considered to be large enough to affect the sense of the following conclusions in any significant way.
 The results of the comparisons are shown in Figure 6for all four of the refractive index data sets used in this study. The error bars in this case represent the standard deviation of the heights in each 0.2° latitude bin, and the different colors correspond to different CALIPSO overpasses. It is clear that use of either the Pollack et al. obsidian or Balkanski et al. data leads to a general under-estimation in ash height. The agreement is good for heights in the range 2–4 km, but diverges for higher ash tops. Although the Pollack et al. andesite and Volz retrievals show a slight over-estimation for the lowest ash heights, agreement is generally seen to be better overall, and in particular for the higher values. This supports the conclusion reached inSection 4.2 that the retrievals derived using the Pollack et al. andesite and Volz refractive index data sets should have higher confidence placed on them for the 2010 Eyjafjallajökull eruption period. This is supported by the findings of Millington et al. , who concluded that, in general, the Pollack et al. andesite data set provided the best agreement when attempting to match measured SEVIRI images with those simulated using radiative transfer calculations based on NAME forecast ash profiles.
 It is less easy to validate the retrieved column mass loading and ash effective radius values in any robust way. Validation of the effective radius is reliant on a relatively small number of in situ samples from aircraft data which are themselves subject to significant uncertainties, and we have therefore not attempted to try this within the present study. It is possible to derive column mass loadings from lidar data (either space-borne or airborne), although again it must be recognized that the lidar measurements are themselves indirect, and reliant on a number of assumptions. B. J. Devenish et al. (Sensitivity analysis of dispersion modeling of volcanic ash from Eyjafjallajökull in May 2010, submitted toJournal of Geophysical Research, 2012) have presented some comparisons for 14th May 2010, which indicate that the SEVIRI retrievals of column loading are somewhat larger than those derived from the airborne lidar measurements of Marenco et al. , although it is possible that contamination from underlying water cloud in this case could have had a significant impact on the accuracy of the SEVIRI retrievals.
Figure 7shows a comparison of column mass loadings from the 17th May 2010, where contamination from other clouds was not an issue. In this case, an area of thin volcanic ash was moving southeastward over the southern North Sea, and downward-pointing airborne lidar measurements, as described byMarenco et al. , were made in this area. The SEVIRI retrievals for the 1430Z image using the Pollack et al. andesite refractive index data are shown in Figure 7, with the lidar data for the 1400Z-1439Z time period over-plotted. For this particular case, because the ash cloud has a low optical thickness, we have changed the threshold inequation (1) from −2 K to −0.7 K in order to detect an area of ash as extensive as that shown in Figure 7. The mass loadings are seen to be in reasonable agreement over the sea, with both data sets showing maximum values of around 0.7–0.8 g m−2 at similar locations. It is also apparent from Figure 7 that, when using a threshold of −0.7 K in equation (1), the current scheme exhibits a detection lower limit corresponding to a mass column loading of around 0.2–0.3 g m−2 in this particular case (where the infrared optical thickness is generally < 0.1), and that the smaller column loadings seen in the aircraft data over northern England are too small to be detectable in the SEVIRI data.
 Qualitatively, at least, the mass column loadings derived using the current scheme appear to be comparable with the values presented by Thomas and Prata , although we have not attempted a detailed side-by-side comparison at this stage. It is hoped that a detailed inter-comparison between this new scheme and others, such as those described by A. J. Prata and A. T. Prata (Eyjafjallajökull volcanic ash concentrations determined from SEVIRI measurements, submitted toJournal of Geophysical Research, 2012) and Pavolonis and Sieglaff , can be carried out in the near future.
 We have developed a scheme to first detect the presence of volcanic ash and then attempt to derive its physical properties, using infrared radiances from SEVIRI. The method has been demonstrated using cases from the Eyjafjallajökull eruption in 2010. The detection of ash is shown to be robust after the application of five separate tests using measured and simulated radiances, with few false alarms. The ash identified by this detection scheme is then passed to the 1D-Var retrieval.
 It has been shown that the retrieved quantities are often strongly dependent on the choice of ash refractive index data set used in the retrieval scheme's radiative transfer model. Using the 1D-Var solution cost as a metric, we have seen that, in general, thePollack et al.  andesite and Volz  volcanic dust refractive index data sets tend to give lower cost solutions, and hence generally produce better agreement with the measurements and a priori constraints than the Pollack et al.  obsidian and Balkanski et al.  mineral dust data sets, although this is not always the case.
 The a priori constraints that we have used are relatively weak, so the analyzed states tend to be driven mainly by the measured radiances. In theory, we could use a priori constraints from the NAME model (e.g., ash-top height, column mass loadings), and increase their weight in the 1D-Var analysis by decreasing the corresponding elements of the background error covariance matrix. We have chosen not to do so in the current paper in order to preserve independence between the retrievals and the model predictions.
 Validation of the ash heights against CALIOP lidar data show reasonable agreement, particularly for the Pollack et al. andesite and Volz refractive index data sets. In some ways, the level of agreement is perhaps better than expected, because low-level water clouds were frequently present in the validation data set, and these might have been expected to reduce the accuracy of the height retrievals. A thorough analysis of the likely errors introduced by these clouds is beyond the scope of the current paper. Nevertheless, the validation results suggest that the ash heights are generally accurate to within 1–2 km for lower-level ash layers (<5 km), with the accuracy decreasing somewhat for higher altitude ash layers, an accuracy of around 3–4 km being more appropriate. Comparisons with coincident lidar data suggest that the retrieved column mass loadings are at least reasonable. We have not attempted here to quantify the likely errors in the retrievals of mass loading or effective radius, other than to reiterate that they are extremely sensitive to the choice of ash refractive index used in the retrieval scheme.
 The SEVIRI retrievals of ash height and total column loading described in this paper are provided operationally every 15 min to the London VAAC forecasters to provide guidance to be used together with the NAME model output and other observational data sets. Studies such as those reported here are increasing the confidence of the value that such satellite products can provide to the forecasters.
 We acknowledge EUMETSAT for the provision of SEVIRI data via EUMETCast, and we would also like to acknowledge NASA's CALIPSO project for making the CALIOP data available via the NASA Langley Research Center, Atmospheric Science Data Center. We thank Franco Marenco for the aircraft lidar data used in Figure 7.