Between 14 April and 25 May, 2010, Eyjafjallajökull volcano in Iceland erupted a large amount of fine grained ash. Dispersion models and satellite data were used to identify the location of the ash cloud, but accurate quantitative forecasts of the concentrations could not be made. By using multispectral satellite measurements from the Spin Enhanced Visible and Infrared Imager (SEVIRI), it is shown that quantitative estimates of the mass loadings (g m−2) can be made with a detection limit ∼0.2 g m−2, every 15 minutes. These data represent the most comprehensive coverage, in space and time, of the Eyjafjallajökull ash and its movement. A new ash concentration chart is proposed that removes the ambiguity inherent in assigning high concentrations to highly negative brightness temperature differences. Validation of satellite ash retrievals against measurements from aircraft, ground-based lidars, and air quality data is presented. The results show a mean bias of −47 μg m−3 and standard deviation of ±154 μg m−3. The satellite ash retrievals are sufficiently accurate for use with dispersion models to constrain ash concentration forecasts. Concentrations in the dense parts of the dispersing ash cloud occasionally exceeded 4 mg m−3 (∼3% of ash-affected pixels), and ash clouds with concentrations >2 mg m−3 covered large parts of European airspace on several occasions (∼50% of ash-affected pixels). The statistical analysis leads naturally to a logarithmic scale for assigning ash concentration limits. We suggest that a better approach is to utilize a dosage and illustrate this using a simple model of ash deposition on jet engines.
 It has been known for many years that volcanic ash is dangerous to commercial jet aircraft [Casadevall, 1994]. Volcanic ash contains micron-size silicate particles that can melt in the hot parts of jet turbine engines. The melt products can adhere to and block the high pressure turbine inlet, restricting airflow, causing partial or complete blockage of combustor fuel nozzles and vane and blade cooling air holes, and can cause engines to stall [Dunn and Wade, 1994; Casadevall et al., 1996; Kim et al., 1993; Miller and Casadevall, 2000; International Civil Aviation Organization (ICAO), 2001]. Little is known about the exact atmospheric concentrations of ash that cause build-up on the jet turbine, but it is believed that concentrations of ∼2 g m−3 have caused engine shut-down [Przedpelski and Casadevall, 1994]. The problem of identifying dangerous concentrations of ash is complicated by the different characteristics of jet engines, by the amount of time spent flying through ash clouds, and possibly by the character of the ash itself (e.g., ash composition, effective particle size and the size and mass distribution of ash in the cloud). Until carefully designed engine performance tests are conducted in realistic volcanic ash cloud conditions, a cautious approach to advising commercial jet operations in airspace affected by volcanic ash seems sensible.
 On 14 April, 2010 ash from Eyjafjallajökull volcano (63°38′N, 19°36′W, 1651 m) in southern Iceland, traveled rapidly across the North Atlantic and North Sea, reaching southern Norway on 15 April and then traveling southwards as a frontal cloud crossing into many European countries, including Denmark, Holland, Germany, Austria, Switzerland, Czech Republic, France, Poland, Hungary, and Russia; the southern part finally being grounded in the northern parts of the Alps. Airspace was closed over Europe for a period of 5 days, resulting in a large disruption to air transport with consequences that burdened the global economy with a financial loss estimated to be €5 bn [Oxford Economics, 2010]. Several other ash cloud episodes occurred during late April and May, the most significant of these between 6 and 18 May, when ash incursions into European airspace caused further closures.
 Airspace closures were based mainly on advice from the London Volcanic Ash Advisory Centre (LVAAC), located at the Met Office in Exeter, UK. The LVAAC makes use of a state-of-the-art Lagrangian particle dispersion model (NAME) [Jones et al., 2007] that has been tested and validated and shown to be sufficiently accurate for the purpose of forecasting the movement of ash clouds for periods of 6–24 hours [Witham et al., 2007]. The model requires as input, an estimate of the eruption source parameters [Mastin et al., 2009] and meteorological wind fields, and uses physical parameterizations of important source and removal processes that affect the concentrations in the dispersing volcanic cloud. Aggregation of ash particles and subsequent enhanced removal is an extremely important process for estimating the atmospheric ash burden [Durant et al., 2009], yet this process is not included in most dispersion models because of its complexity and demand on computation time [Folch et al., 2010]. Without accurate knowledge of the temporal variation of the mass eruption rate at the volcano and removal rate in the atmosphere, it is not possible to provide accurate quantitative forecasts of the ash concentrations arriving in the airspace over Europe. Given the large uncertainties in the eruption source parameters, a cautious approach was taken to estimating ash concentrations from the Eyjafjallajökull volcanic eruption, resulting in criticism by some parts of the European aviation industry of the regulators' decision to advise closure of European airspace. The International Civil Aviation Organization (ICAO) advises that it is unsafe for commercial jet operations in airspace affected by ‘visible’ ash [ICAO, 2001], without quantifying the meaning of ‘visible’ ash. Without a quantitative threshold for ash concentrations, and in the absence of reliable data on the level of ash concentrations that causes engine damage resulting in loss of power, the cautious approach is to restrict air traffic from airspace where the dispersion model has forecast the presence of ash. The basic problems with forecasting concentrations and setting limits for safe aircraft operations can be circumvented by using satellite-derived ash retrievals and it is apparent that without proper quantitative use of these measurements, little progress will be made on the ash/aviation problem.
 Satellite data from polar orbiting and geosynchronous thermal infrared instruments have been used to retrieve ash mass loadings in dispersing volcanic clouds for many years [Prata, 1989; Wen and Rose, 1994; Prata and Grant, 2001; Hillger and Clark, 2002a, 2002b; Watkin, 2003; Pergola et al., 2004; Pavolonis et al., 2006; Pavolonis, 2010, 2011; Gangale et al., 2010; Clarisse et al., 2010]. Other satellite data (e.g., Moderate Resolution Imaging Spectrometer (MODIS) visible data, Multi-imaging Scanning Radiometer (MISR) visible multispectral camera data), are also very useful; a discussion of the use of satellite remote sensing for the ash/aviation hazard is provided by Prata . The SEVIRI data were available at the time of the Eyjafjallajökull eruption and were used by the LVAAC only in a qualitative manner to verify model forecasts and develop ash advisories, but new quantitative algorithms are being developed [see Francis et al., 2011]. The SEVIRI retrievals provide ash column amounts in g m−2 and not concentrations. In order to determine concentrations, an estimate of the thickness of the cloud is required. In this study Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) lidar measurements of cloud base and cloud top are combined with coincident mass loading retrievals from the geosynchronous SEVIRI to obtain estimates of ash concentrations.
 The paper is organized as follows: First, a brief outline of the methodology for determining mass loadings from SEVIRI is given (section 2). The description is brief because the methodology has already been described from theory by Prata , for AVHRR data by Wen and Rose  and for AVHRR and ATSR-2 data by Prata and Grant . Next, the overall picture of the ash mass loadings over Europe is provided, based solely on SEVIRI and includes some useful methods for displaying and presenting the vast amounts of satellite data (section 3). A description of the CALIOP data and its use to determine ash concentrations where possible follows (section 4). Section 5 is on validation, which includes an assessment of the satellite retrievals against ground-based lidar, aircraft measurements, and air quality data. There is a discussion on limits and thresholds which is based on a statistical treatment of the data (section 6). Section 7 summarizes the main conclusions drawn from this work.
2. Estimating Mass Loadings From SEVIRI
 SEVIRI is a 12-channel spin-stabilized imaging radiometer, on board the Meteosat Second Generation (MSG) platform, providing a 70 degree total field of view coverage of the earth's surface and atmosphere, centered at approximately 0 degrees longitude [Schmetz et al., 2002]. Measurements are made from the visible (0.5 μm) to the infrared (13.4 μm) with a spatial resolution of 3 km × 3 km at the sub-satellite point to about 10 km × 10 km at the edges of the scan. Images can be acquired in all channels for the whole of the 70 degree disk every 15 minutes. A sub-region of this disk covering 30°W to 30°E and 40°N to 70°N was selected for analysis which included the geographic area affected by the Eyjafjallajökull volcanic ash. Figure 1 shows the region covered for the analysis of SEVIRI data and the spatial variation of pixel size, up to 90 km2. Note that Iceland is near the limit of coverage of SEVIRI.
 The infrared channels located at central wavelengths of 10.8 μm (T11) and 12.0 μm (T12) were calibrated using coefficients supplied by Eumetsat and the data were geolocated and viewing geometry calculated for use with a water vapor correction. Retrievals of effective particle radius, infrared optical depth and mass loadings for each pixel within the sub-region (see Figure 1) were calculated using the method of Prata and Grant . The method relies on identifying pixels that are affected by volcanic ash by use of the ‘reverse’ absorption effect (i.e., T11-T12) [see Prata, 1989] after applying a correction for water vapor absorption [Yu et al., 2002] that also accounts for the path length traveled by the radiation through the atmosphere. Typically the water vapor correction amounts to ∼−0.5 to −1 K added to the difference between brightness temperatures T11 and T12. A radiative transfer model is used to calculate the brightness temperatures T11, T12 based on an assumed surface temperature Ts and cloud top temperature Tc for a uniform plane-parallel volcanic ash cloud consisting of a distribution of spherical silicate ash particles. Two size distributions are used: the modified-γ and lognormal distributions with a mean effective radius ro and standard deviation rs. Calculations are performed for surface temperatures Ts from 270 K to 305 K in steps of 5 K and cloud top temperatures from 230 K to 270 K in steps of 5 K and infrared optical depths from 0.02 to 7.98 in steps of 0.02. The mean radius of the size distribution is varied in steps of 0.20 μm starting from 1 μm and ending at 32 μm. The standard deviation of the size distribution is maintained at a fixed percentage of the mean radius. Refractive index data for rhyolite, andesite, and basalt (based on the data from Pollack et al. ) were used with a Mie scattering program [Evans, 1988] to calculate the extinction coefficients for the 10.8 and 12.0 μm SEVIRI channels. These calculations generate a very large look-up table which can be interpolated using the water vapor corrected SEVIRI measurements to determine the best fit values for the effective radius and infrared optical depth. The composition of the Eyjafjallajökull ash has been described as a trachyte (M. T. Gudmundsson et al., Ash generation and distribution from the April–May 2010 eruption of Eyjafjallajökull, Iceland, submitted to Journal of Volcanology and Geothermal Research, 2011). Spectral refractive index data are not currently available for this ash composition and so we used andesite. To reduce the number of interpolations required, estimates of the surface and cloud top temperatures are made by searching for the highest and lowest brightness temperatures at 12.0 μm (T12), which are then used as starting values for Ts and Tc, respectively, in the search procedure. The first guesses are provided for the land and sea separately.
 The infrared optical depth τ(λ) is related to the infrared extinction efficiency Qext(λ, r), particle size and size distribution, n(r) by
where L is the geometrical thickness of the cloud, λ is wavelength and r is the particle radius. The concentration C is
where ρ is the density of volcanic ash (taken as 2600 kg m−3) [Neal et al., 1995]. If we assume that the size distribution within each pixel is uniform (i.e., n(r) = 1), with effective radius re, then the pixel mass loading is
The total mass can be calculated by multiplying ml by the area of a pixel, and then summing over all ash-affected pixels. The pixel concentration corresponding to a uniform particle size distribution in a homogenous cloud of thickness L, with effective radius re can be calculated from
Sensitivity analyses by Wen and Rose  and Gu et al.  suggest mass loading errors of 40–50% are probable, due to errors in knowledge of the parameters required in the radiative transfer model, measurement errors (typical NEΔT ≈ 0.1–0.8 K, depending on scene temperature) and on the simplifying assumptions employed (e.g., spherical particles and uniform size distribution). Note that the accuracy of the retrieval is highest where the volcanic cloud is semi-transparent (τ(λ) ≈ 1–3), the cloud is located over the sea (relatively uniform surface temperature, Ts and high emissivity), is dispersed and aged (so that that the size distribution is more likely to be uniform), and the ash particles are fine grained (re ∼ 1–10 μm). Thus there are many circumstances when errors may be much larger. Of critical importance is the ability of the retrieval scheme to identify ash-affected SEVIRI pixels accurately, relying almost entirely on the ‘reverse absorption’ technique [Prata, 1989]. The criterion for identifying an ash-affected pixel may be written
where T11 and T12 are brightness temperatures in two infrared channels, with central wavelengths at 11 μm and 12 μm, respectively, and ΔTcut is a prescribed cut-off temperature difference. If the pixel is misidentified then the mass retrieval could produce very large errors. Therefore a conservative cut-off temperature difference of −0.8 K was used. The trade-off then is that some legitimate ash-affected pixels are likely to be missed. This may seem serious but with the addition of a second test, the likely impact for ash hazard assessment is greatly minimized. The second test is based on an estimate of the optical thickness of the pixel. This test is
where Tlim is a prescribed cloud-top temperature and is set at 230 K, and Tk is the top-of-atmosphere brightness temperature in the SEVIRI 7.3 μm channel. For temperatures that are lower than Tlim, where T11-T12 is < ΔTcut, the cloud is likely to be optically thick ash cloud with high mass loadings. It is instructive to analyse the causes for reaching condition (5) as lower temperature differences (more negative values of T11-T12) do not necessarily suggest more ash.
2.1. Heuristic Model for Ash Concentrations
 A simple model is presented here to demonstrate the important parameters affecting ash retrieval using two-channel infrared data. The model is then used to derive a concentration chart (see section 2.2), which could be used at Volcanic Ash Advisory Centres (VAACs). Prata and Grant  showed that the magnitude of the temperature difference between two infrared channels in the window between 8 and 12 μm depends principally on the microphysics of the particles responsible for the absorption and the optical thickness. A heuristic model based on simplifying assumptions for the radiative transfer is employed to give the following equation for the temperature difference:
Tc and Ts are the cloud top temperature and surface temperature, respectively, and
where k11, k12 are absorption coefficients for channels 11 and 12. Given the four parameters, T11, T12, Tc and Ts it is possible to invert (7) to solve for the effective radius of the ash particles and the optical depth. The absorption coefficients were calculated as extinction efficiencies using a radiative transfer program assuming andesitic spherical ash particles (see Prata  for details). The mass loadings are computed from (3) for channels with central wavelengths at 11 μm and 12 μm.
2.2. The Ash Concentration Chart
 Rather than plot mass loadings, a diagram or chart can be constructed for concentrations by assuming a homogeneous cloud of 1 km thickness. Above a certain cut-off temperature, no retrievals are given and this region is considered “uncertain”. An example of this is illustrated in Figure 2 for an ash cloud with Tc = 220 K and Ts = 290 K. It is clear from this diagram that the most negative pixels are not necessarily caused by the most concentrated ash. Indeed the highest concentrations are found where pixels have nearly zero temperature difference and low 11 μm brightness temperature. These are pixels with the highest optical depth and largest effective particle radius. The diagram also shows that when the temperature difference is close to zero and the 11 μm brightness temperature is high, the ash concentrations are low and hence the error in incorrectly assigning these pixels as ash is of little consequence. On the other hand, serious errors could arise when the temperature difference is close to zero and the 11 μm brightness temperature is low. In this case the ash cloud is optically thick and although mass loading retrievals are difficult or impossible to do, the ash cloud is readily identifiable. The advantage of viewing an ash cloud from an acute angle is also made clear from this diagram because in these cases the optical path is long and thus even when the ash concentration is small, the optical depth is increased, leading to larger negative T11 − T12 values. This is the case for SEVIRI's view of Iceland (see Figure 1). Again we emphasize that large negative T11 − T12 values do not necessarily imply large ash concentrations. The most difficult cases for correct ash identification arise when the ash is mixed with hydrometeors, for example ice particles, super-cooled water droplets or unfrozen cloud water droplets. The effect of these hydrometeors on the pixel brightness temperature is to increase T11 − T12, decreasing the ability to identify ash in the pixel and increasing the error in the mass loading retrieval. According to Figure 2, the error in assuming that a mixed pixel contains 100% ash results in a larger ash concentration retrieval than is actually the case. The ash concentration chart can be generated off-line using prescribed cloud-top and surface temperatures and different cloud thicknesses. It is thus a useful aid for VAACs that need to analyse large quantities of infrared satellite imagery rapidly and so may not have sufficient time or resources to undertake a full radiative transfer calculation and retrieval.
 The error characteristics of ash mass loading retrievals are quite complicated and highly dependent on atmospheric conditions as well as on the nature of the volcanic material erupted (e.g., particle size distribution, existence of hydrometeors, ash composition). In section 5 some limited validation of the SEVIRI retrievals is presented; this is an ongoing exercise and definitive conclusions about the accuracy of these satellite retrievals cannot yet be made.
3. Overview of the Eyjafjallajökull Ash From SEVIRI
3.1. Chronology and Spatial Coverage
 The April–May 2010 eruptive activity at Eyjafjallajökull has been described by Gudmundsson et al. (submitted manuscript, 2011). Figure 3 shows the time series of total mass of fine-grained ash (re < 16 μm) retrieved from SEVIRI data for the period 15 April to 24 May. There are two periods where retrievals were not performed because the ash detection criteria were seldom met and false alarms were larger because of the prevalence of clear skies over land. In these atmospheric conditions, the effect of land surface emissivity is to cause negative temperature differences, unrelated to volcanic ash [Prata et al., 2001]. The mass is restricted to the size range 1 < re < 16 μm, which is a small fraction (<10%) of the total mass erupted, but it does represent the main portion of the mass that is transported by the winds [Rose and Durant, 2009]. Total mass ash loadings exceeded 1 Tg at times and the time series exhibits significant variability, presumably reflecting variability in the output of ash at the volcano, as well as other factors, such as ash residence time.
 According to the SEVIRI satellite ash retrievals, the ash clouds were quite extensive at times and spatially inhomogeneous. Three main episodes are identified: 14–17 April, initial eruptive phase characterized by an initial strong ash emission with little SO2 emission [Thomas and Prata, 2011]; 18 April to 4 May, quiescent episode with only localized emissions, and 5–18 May with stronger ash and SO2 emissions. During both fine-ash producing phases, emissions fluctuated on time-scales as short as the SEVIRI sampling period of 15 minutes, with quite sharp emission maxima. This temporal variability in the source strength is particularly problematic to resolve in modeling the dispersion and transport of ash for accurate forecasting of the ash hazard to aviation [Stohl et al., 2011]. To illustrate the spatial coverage of ash over the region on different days, we computed the fraction of each 0.5° × 0.5° cell that contained ash (by area) and plotted these over the domain of interest. Only mass loadings that exceed a certain value (0.2 g m−2 is used) were included. The widespread areal coverage of the three phases of the Eyjafjallajökull ash emissions is illustrated in Figure 4 for the results between 14 April to 18 May. On each day, the percentage of ash in each cell is quite small (<5%) but the spatial coverage is significant. If the criterion for avoidance of ash was based on its detection (say, by visible sighting or by satellite detection) then large areas of airspace should have been closed to air traffic, according to these results. When a quantitative criterion is applied, for example an ash concentration limit, the areal extent of regions affected by ash is greatly reduced. Of course, this area depends on the exact criterion applied.
 Maps like these were also constructed on a daily basis, where the percentage of ash detected in each cell is plotted. An example for 14 May, when airspace restrictions over the UK were made, is shown in Figure 5. These maps make no distinction between low, medium or high ash loadings but demonstrate the temporal variability of the effects of a fluctuating source coupled with variability in the wind fields.
 The maps may also be used to help verify VAAC advisories to validate forecasts and improve understanding of the effects of variability in eruption source behavior and wind field variability. An obvious use for these maps would be for assessing ensemble forecasts of ash movement [Kristiansen et al., 2012].
3.2. Mass Loadings and Effective Particle Sizes
 The data products from the SEVIRI ash retrievals include estimates of both mass loading and the effective particle radius. Retrievals were derived for each 15 minute time interval over the domain shown in Figure 1 and statistical information computed for the percentage of the total number of pixels detected as ash, the percentage of ash-detected pixels above certain thresholds, the mean and standard deviation and the maximum mass loading detected. The thresholds used are those specified by the European Aviation Safety Agency Report [European Union (EU), 2010], viz. 4 mg m−3 (“black” or “No Fly” zone), between 2 and 4 mg m−3 (“Grey” or first enhanced procedures zone), between 0.2 and 2 mg m−3 (“Red” or second enhanced procedures zone) and up to 0.2 g m−3 (“White” or normal zone with no flight restrictions). Figure 6 shows an example of the graphical product for 12:00 UT on 15 April, 2010. For this product the Gaussian mean mass loading is ∼3.35 g m−2 and the mean effective particle radius is ∼5.6 μm. The maximum mass loading is 5.1 g m−2 and the histogram of the effective particle radii is quite narrow. 17% of the pixels detected as ash have mass loadings that exceed 4 g m−2, if these ash clouds were 1 km deep then the concentrations would exceed 4 mg m−3. A second example is shown in Figure 7a for a later time period when fresh ash was emitted from the volcano, while older ash was being transported southwards. The sub-satellite track of the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite (shown as the blue line on Figure 7a), carrying the CALIOP lidar intersects the ash plume. The CALIOP browse image, redrawn in Figure 7b shows high 532 nm backscatter (>0.02 km−1 sr−1) in a cloud layer situated between ∼4 and 5.5 km, at the same location as the SEVIRI retrievals. Note that the backscatter is remarkably uniform within the cloud, suggesting that, at least on this occasion the ash concentration was uniform. Assuming a mean thickness of 2 km, the suggested concentrations in this part of the plume are 0.5 mg m−3 to 1.5 mg m−3. The effective radius histogram still shows the presence of a peak at 5.6 μm but now there is a secondary peak at around 4.5 μm, presumably due to the winnowing effects of gravitational settling and deposition on the size distribution of the transported ash. About 16% of the ash detected pixels have mass loadings >4 g m−2; and nearly 80% of ash affected pixels (less than 0.5% of all pixels) have mass loadings between 2 and 4 g m−2. The ash cloud also covered a much larger geographical region than on 15 April, but did not cause as much aviation disruption presumably because most of the ash was over the ocean, and not being transported toward continental Europe. Notice that the mass loading histogram does not follow a Gaussian distribution but rather has a long tail toward high mass loadings. This is discussed further in section 6.
 The SEVIRI retrievals were mapped into Google Earth so that mass loadings, effective particle radius, infrared optical depth, longitude and latitude and time could be fused with other information, for example air routes, model output, and other satellite data. Figure 8 shows an example that includes ash mass loadings and flight routes from a London airport, when an ash cloud covered a large part of England on 15 May, 2010 at 02:30 UT. Individual pixels can be selected to provide quantitative estimates with location information. When CALIOP data are included (see section 4) the cloud height, thickness and hence ash concentration can also be determined.
 The ability to generate Google Earth visualizations is especially useful when the volcanic cloud has multiple components, for example SO2 gas and ash, or hydrometeors (ice) and ash particles. Figures 9a and 9b show visualizations with SEVIRI ash retrievals and AIRS SO2 retrievals over Iceland at about the same time. In one case on 13 May, 2010 at 14:00 UT (Figure 9a) the ash and SO2 are collocated while in the second case on 14 May, 2010 at 14:30 UT (Figure 9b) the ash and SO2 have separated and are traveling in different directions. Such observations have important implications for air safety as SO2 may be used as a proxy for ash and is easier to detect [Prata et al., 2010; Thomas and Prata, 2011].
 Effective radius histograms are determined for each image (15 min time interval) by binning in 0.2 μm radius intervals and summing up over all ash-effected pixels. Analysis of these effective radius histograms reveals that the size distribution remained remarkably constant with effective radii predominantly between 4 and 6 μm with a significant tail toward lower sizes developing with time. The mass loading histograms suggest slow removal of mass with time and movement of the peak mass loading toward lower values occurring on time-scales of several days. Figure 10 shows mass loading distributions compiled each day for 14, 18 and 20 May when a large ash cloud traveled southwards into the Atlantic and then eastward toward the Iberian peninsula. There is a broad peak near 3 g m−2 on 14 May that changes to a sharper peak near 1.8 g m−2 on 18 May and finally to less than 1 g m−2 on 20 May. A secondary peak on 18 May might be due to plume enrichment from emissions after 14 May.
4. CALIOP Cloud Thickness and Height
 CALIOP on-board the CALIPSO platform is a space-borne lidar capable of measuring the vertical structure of aerosols and clouds in the atmosphere [Winker et al., 2003] (see http://www-calipso.larc.nasa.gov/products/). It sweeps out a narrow path along the sub-satellite point providing vertically resolved backscatter measurements every 333 m along the track at 532 and 1064 nm. Measurements are made twice daily, but the narrow swath and 705 km sun synchronous orbit results in a repeat cycle of 16 days. The data are temporally sparse but have high vertical resolution (30 m below ∼8.2 km; 60 m between 8.2 and 20 km), and so complement the SEVIRI information well. The performance of the lidar and further details on data reduction and availability are reported by Winker et al. . CALIOP's measurements of the vertical extent of clouds can be combined with the SEVIRI mass loading retrievals to obtain concentrations using equation (4).
 The error in estimating the cloud thickness depends on the density of cloud scatterers as well as on the presence of interfering clouds or aerosols. In the lower troposphere, where the CALIOP vertical resolution is 30 m, cloud thicknesses can be estimated with accuracies of ±100 m after profile averaging (to increase signal-to-noise) for clouds with infrared opacities >1. For thinner clouds during the daytime, signal-to-noise becomes an issue. Details of the use of CALIOP for volcanic ash cloud analyses may be found in the paper by Winker et al. .
 The task of validating SEVIRI retrievals is difficult largely because there are very few independent data available to validate against. There have been no field experiments conducted for this purpose and as far as we know, until recently there have been very few published data for validation of ash mass loading retrievals. However, during the eruptions of Eyjafjallajökull and Grímsvötn (May, 2011) concerted efforts were made to measure the ash clouds using a variety of in situ and optical remote sensing methods. Schumann et al.  report airborne measurements of the Eyjafjallajökull volcanic ash, and data from the UK Facility for Atmospheric Airborne Measurements (FAAM) aircraft are available for several flights [Johnson et al., 2012; Marenco et al., 2011], two of which are through concentrated ash over northern England and the North Sea on 14 and 17 May, 2010. Ansmann et al.  report ground-based lidar measurements from four stations in Europe and determine ash concentration profiles. The CALIOP lidar made many measurements of the ash clouds from Eyjafjallajökull and ash concentrations are reported by Winker et al.  for the 14–20 April episode. Air quality data at the surface are available from stations in southern Norway and at Aberdeen, Scotland that report PM10 concentrations as the ash cloud from Grímsvötn moved over those areas. These data, while still sparse, provide the first data-set that may be used for validation of SEVIRI mass loadings.
 All of the independent data-sets report ash concentrations either as point measurements or as profiles, while the SEVIRI retrievals are mass loadings representing a column amount. To convert the mass loadings to concentrations, information on the vertical structure is required. Reasonable assumptions about the vertical structure can be made to convert the mass loadings into concentrations, as described below.
5.1. CALIOP Measurements
Winker et al.  report the ash concentration retrievals from CALIOP during the 14–20 April Eyjafjallajökulll eruption phase. These are the first such retrievals reported in the open literature and the authors note many assumptions and difficulties associated with the retrievals.
5.2. DLR Falcon Measurements
Schumann et al.  describe a series of aircraft flights into and in the periphery of the Eyjafjallajökull ash clouds and provide details of ash concentration measurements, data reduction procedures, assumptions and caveats. The data we use are in Table 3 of Schumann et al. , where they report a total of 12 measurement cases. Of these, only eight are considered, as four of the cases have mean concentrations that are less than ∼100 μg m−3, which, when multiplied by the cloud layer thickness, give mass loadings that are considered to be below the threshold of the SEVIRI retrievals (∼0.2 g m−2). For two of the eight cases, there are no SEVIRI retrievals, because on 2 May (15:15 UT), the aircraft was flying just off the coast of Iceland where it was cloudy with a reported ash layer top of 3.7 km. We suspect that a combination of the thin, low plume coupled with the large SEVIRI pixel (the location is near the edge of the SEVIRI scan) and cloudiness has rendered a retrieval not possible. The other case on 22 April is over land in the evening (19:10–19:13 UT) when SEVIRI ash detection algorithm misclassifies many pixels as ash due to spectral land surface emissivity effects, and the retrievals are somewhat compromised. Nevertheless, there are 6 coincidences from the DLR Falcon data set that may be used and these span the range of concentrations from ∼0.05 to ∼0.6 mg m−3. These represent the lower end of the ash concentrations that need to be validated and this may be a limitation of using in situ aircraft measurements for validation as safety guarantees that aircraft should avoid higher concentrations.
 SEVIRI retrievals are interpolated in space and averaged in time using the coordinates and time ranges specified in Table 3 of Schumann et al. . Conversion of the mass loadings to concentrations is achieved using the layer top and bottom ash cloud values, also reported in Table 3 of Schumann et al. . We assume an error in the SEVIRI retrievals of ±40% (see section 2) and a similar error for the aircraft data [Schumann et al., 2011]. Results are included in the summary Figure 18, at the end of this section.
5.3. Ground-Based Lidar Measurements
Ansmann et al.  report ground-based Raman backscatter lidar measurements from a site in Cabauw, Holland, and three sites in Germany: Hamburg, Leipzig and Munich. The backscatter data are converted to ash concentration profiles with typical error of about 30% [Ansmann et al., 2010]. Gasteiger et al.  did a thorough analysis of the lidar ash concentration retrieval for an episode on the night of 17 April and report an ash concentration at Maisach (25 km northwest of Munich) of 1.1 mg m−3 with a lower value of 0.65 mg m−3 and an upper value of 1.80 mg m−3. There are good SEVIRI coincidences for 4 of these 5 cases.
Figure 11 shows the SEVIRI retrievals on 16 April at 05:30 UT corresponding to the lidar measurements made at this time in Hamburg by Ansmann et al. .
 Note the high degree of spatial heterogeneity present, demonstrating that the placement of the lidar with respect to the ash cloud is critical to assessing maximum and minimum ash concentrations within the cloud. Timing is also an important factor as the ash cloud moved over the lidar sites within a few hours and hence coincidence with satellite sensors may not be achieved. On this occasion the range of ash concentrations reported by the lidar are three times smaller than the range of ash concentrations observed by SEVIRI over the whole of the ash cloud. This demonstrates a limitation of using ground-based lidars to assess ash concentrations, due to the sparse spatial sampling. A well-placed, highly populated network of Raman (or equivalent) lidars (possibly mobile), operating continuously would be capable of solving this limitation in sampling, but the cost of running such a network would be prohibitive. Instead, it would make good sense to utilize the current lidar systems in tandem with satellite measurements to provide vertically resolved ash clouds with better horizontal and temporal sampling.
 A second example is shown (Figure 12) for an ash cloud as it moved over Munich and covered the lidar site at Maisach (marked by the letter “V” on the plot) [Gasteiger et al., 2011]. Again note that there is considerable spatial heterogeneity and high mass loadings are evident to the north and north-west of the lidar site. The lidar results are also included in the summary Figure 18.
5.4. UK FAAM Measurements
 The Met Office operated the FAAM BAe-146 aircraft on several occasions during the Eyjfjallajökull episode in May, 2010 [Johnson et al., 2012]. The data consist of in situ and remotely sensed particle measurements and are described in the papers by Johnson et al.  and Marenco et al. . An encounter with quite a dense ash cloud (concentrations of ∼5 mg m−3) occurred over northern England on 14 May between 13:50 and 13:55 UT as the aircraft descended from about 8 km to about 6 km. The flight coordinates, times and concentrations were provided by Johnson et al.  and Kristiansen et al.  and 26 concentration values are used for inter comparison with SEVIRI. Figure 13 shows a map of the SEVIRI mass loading and the flight path of the BAe146 (colored dots). The inset plot shows the concentration profile along this track corresponding to the FAAM measurements and the inferred SEVIRI estimates (triangles). The altitude of the flight (blue line with black dots) indicates that the aircraft was descending through the cloud, measuring low concentrations at the top and bottom of the flight path. There is a CALIPSO overpass that intersects the edge of the cloud between 12:52 and 13:05 UT (dashed line on Figure 13), but the overlap is poor and considered unreliable. The overpass 12 hours earlier does intersect the ash cloud well, in three places. Figure 14a shows the ash cloud at 03:30 UT on 14 May (at this time it is further north and west) and the CALIOP browse image, redrawn in Figure 14b, depicts the 532 nm backscatter near this location. The high backscatter values for the features between 60–63°N, 7–10°W and 4–6 km altitude, correspond well with the locations of high SEVIRI mass loadings and it is concluded that these are ash clouds. (The cloud causing high-backscatter south of about 60.2°N is assumed not to be ash because SEVIRI does not detect it as ash). The ash clouds appear to have variable cloud thicknesses ranging from less than 1 to 2 km. Using the altitudes reported by the FAAM aircraft measurements, SEVIRI mass loadings were first interpolated in time and space to the FAAM measurement times and locations, and then converted to concentrations, by using the thickness of the ash cloud inferred from the FAAM's movement through the ash cloud. Although there are some assumptions in making this conversion, the high concentrations and the agreement found between the CALIOP and FAAM vertical structure give some confidence in the process. The concentration profiles agree quite well (inset plot in Figure 13) but the FAAM data suggest more variability and some high values not found in the SEVIRI data. Note that the comparison is being made between the point measurements from the FAAM and a layer-averaged concentration inferred from SEVIRI, so strict agreement should not be expected. A path integrated value (integration along the flight path) is also compared with an averaged, derived SEVIRI concentration using an average CALIOP cloud thickness of ∼1.86 km. As before, SEVIRI errors are assumed to be ±40% and the FAAM data are assumed to have errors of ±20%, although Johnson et al.  suggest the ash concentration retrievals may be in error by a factor 2, they provide no analysis for this. Results are included in Figure 18.
 The FAAM undertook several other flights, but many of these measurements were of concentrations close to, or lower than the detection limit of SEVIRI (∼0.2 g m−2). A flight on the afternoon of 17 May over the sea between eastern England (Suffolk and Norfolk) and Denmark encountered ash concentrations ranging from <0.1 mg m−3 to ∼1 mg m−3. SEVIRI detected this ash cloud but there is no coincident CALIOP overpass so no independent estimate of the cloud thickness is possible and hence the SEVIRI mass loadings cannot be converted to concentrations this way. However, the FAAM flight path included several descents and ascents through the ash cloud. Interrogation of the FAAM data shows that ash concentrations are low at the top of the descent and at the bottom of the ascent, so a reasonable assumption is that the aircraft had traversed the thickness of the ash cloud. Using this assumption, the SEVIRI mass loadings may be converted to concentrations by taking the thickness of the cloud to be the differences between the highest and lowest altitudes reported. The mean and standard deviation of the FAAM data for each of the five transects, and the interpolated SEVIRI values are shown in Table 1. Individual values are included in the summary validation plot (Figure 18). For two of the five flight transects considered, SEVIRI detected no ash. We assume this is because the ash concentrations were below the SEVIRI detection limit. One transect was over land where it is more difficult to perform ash retrievals when the signal is small. The location of the five FAAM tracks is shown Figure 15. The ash concentration profile along the transect (shown in red), which is parallel to the ash concentration gradient is depicted in the inset plot of Figure 15 for the FAAM data (in red) and the SEVIRI inferred concentrations (triangles). Note that a constant cloud thickness has been used for SEVIRI and this is probably the reason why the profiles do not match exactly, but their shapes and means are similar (see Table 1). A second example is shown in Figure 16, where the transect is along the ash cloud gradient. Again there are very noticeable differences between the profiles but the general shapes are similar. For these two tracks and track 1 (analysis not shown) SEVIRI measures higher concentrations than the FAAM. In the case of track 1, the aircraft was flying from east to west and descending from about 6.3 km to about 2.4 km. The SEVIRI transect indicates much higher concentrations at the start of the track and almost the same concentrations as the FAAM at the end of the track. This shows that the assumption of a uniform concentration profile is not valid in the determination of SEVIRI concentrations. Johnson et al.  give mass loadings for these flights as 0.23–0.73 gm−2 [see Johnson et al., 2012, Table 3], which compare well to the SEVIRI range of 0.3–1.0 gm−2 (Figures 15 and 16). It is likely that the differences are due to a combination of measurement sampling (spatial), ash cloud heterogeneity [see also Marenco et al., 2011] and assumptions about the ash cloud thickness. We argue in section 6 that a safety limit expressed in terms of ash concentrations may not be the most appropriate metric for assessing the danger of ash clouds to aviation. It would be worthwhile conducting a better planned validation between aircraft measurements and satellite data. The measurement accuracy of the aircraft data has probably been overestimated in this study; Johnson et al.  suggest a factor of two uncertainty in the derived ash mass concentration, so some of the scatter is also due to FAAM measurement uncertainty. Additionally, the sensitivity to particle size may be different between the aircraft instruments and SEVIRI.
Table 1. Means (μ) and Standard Deviations (σ) for FAAM Ash Concentration Measurements and Corresponding SEVIRI Ash Concentrations Based on Mass Loadings and Cloud Thickness Measurements From FAAMa
Time (hh:mm) (UT)
FAAM μ (mg m−3)
FAAM ±σ (mg m−3)
SEVIRI μ (mg m−3)
SEVIRI ±σ (mg m−3)
Height Range L (km)
For two (tracks 2 and 5) of the five tracks, SEVIRI detected no ash. See Figure 15 for the locations of the tracks.
5.5. Air Quality Data
 There are many air quality stations, mostly at ground level, across Europe that routinely measure PM10, without making any discrimination of particle type. The instruments used can measure low concentrations (<10 μg m−3) at relatively high time resolution (minutes to hourly) and are in continuous operation. In most cases these data cannot be used to validate ash concentrations because they are at ground level, while ash clouds are usually detached from the surface and are vertically constrained. Air quality measurements could not be used to validate Eyjafjallajökull ash concentrations, because the ash cloud did not reach ground-level with measurable concentrations. Since it is vital to validate satellite retrievals and since so few occasions have arisen where validation data are available we have used data from the May, 2011 Grímsvötn eruption to supplement our analyses.
 On 24 May, 2011, ash from the Grímsvötn eruption reached air quality stations in Scotland (Aberdeen) and southern Norway. This ash cloud appeared to be trapped in the boundary layer and was well-mixed. True-color MODIS imagery (not shown) taken at 15:00 UT on 24 May suggests an aerosol cloud below meteorological water clouds and embedded in the boundary layer. As the ash cloud propagated from west to east, air quality stations measured unusually high PM10 values (based on climatologies for the respective stations) that could be traced to the movement of the ash cloud. Figure 17 shows time series of hourly PM10 concentrations at 6 air quality stations. SEVIRI concentrations are overlaid onto these series by assuming that the ash cloud is well-mixed with an average thickness of 3 km, based on radiosonde data and an infrared opaque cloud top temperature. An inferred propagation speed of ∼10 m s−1 agrees well with analysed wind fields for the time and location (shown on Figure 17 as a dashed line). The agreement is poorest at Aberdeen where it is likely that the ash cloud was not entirely confined to the boundary layer and so the assumption of a well-mixed cloud layer may be weak. These air quality data provide a total of six validation points and these are also shown in Figure 18.
 In the case of the Grímsvötn ash cloud it appears that the London VAAC forecast concentrations higher than the SEVIRI and air quality data indicated. The need to consider quantitative satellite retrievals (both for ash and SO2 gas) in developing forecasts was clearly demonstrated by the Grímsvötn episode, during which ash concentrations were wrongly forecast in regions of the atmosphere where only SO2 existed (see: http://www.metoffice.gov.uk/aviation/vaac/vaacuk_vag.html for advisory graphics during the Grímsvötn eruption). The details of the Grímsvötn eruption episode and the repercussions for aviation are provided by A. J. Prata and A. J. Curant (Dispersion of the Eyjafjallajökull volcanic ash over Europe: An appraisal using satellite measurements, manuscript in preparation, 2012), and a way to utilize quantitative satellite measurements with dispersion models has been described in the papers by Eckhardt et al. , Kristiansen et al. [2010, 2012], Stohl et al.  and Seibert et al. .
5.6. Validation Results
 Although there are many uncertainties and assumptions used to develop the validation data-set, it represents the first and, so far, only data-set for validating satellite-derived ash mass loadings. There are 70 values in the data-set derived from 4 different independent measurement systems (two aircraft, a satellite lidar, ground-based lidars and in situ air quality instruments). The inter-comparison was done using concentrations (rather than mass loadings) which means that an estimate of the ash cloud thickness is required and an implicit assumption is made that the ash concentration profile is constant; except in the cases where it was measured (lidars) and then an equivalent cloud thickness was used. Figure 18 shows the results plotted on log-log axes (necessary because of the wide variation in ash concentration). The mean bias (μ) and its standard deviation (σ) between the two data-sets (independent-SEVIRI) was calculated and gave values of: μ = −46.8 μg m−3, σ = ±153.6 μg m−3. The range of values validated extends from 50 μg m−3 to about 5000 μg m−3 and covers the three threshold limits recently suggested for flying near ash clouds [EU, 2010]. The agreement is quite good and clearly shows that satellite retrievals of volcanic ash are able to detect concentrations below 200 μg m−3 and above 4000 μg m−3. SEVIRI appears to measure slightly higher concentrations (∼+50 μg m−3) than the independent measurements, a bias that is most likely due to (unknown) biases in the retrieval scheme. It is also apparent that because of the uncertainties in the satellite and validation data, the high spatial variability of ash clouds and the assumptions used in the retrieval algorithm, having confidence in distinguishing between ash concentrations of 2000 μg m−3 and 4000 μg m−3 is difficult to justify. Much more compelling are the conclusions that SEVIRI retrievals are capable of detecting low ash concentrations, below the 200 μg m−3 threshold, can provide by far the best spatial and temporal picture of propagating ash clouds, and can in most cases unambiguously identify the hazardous component of volcanic clouds: silicate-bearing, fine-ash particles. Coupling these quantitative satellite retrieval products with dispersion model simulations would provide the optimum ash product for aviation.
6. Thresholds and Safety Limits
 The validation analysis supports the notion that SEVIRI ash retrievals are capable of determining mass loading ∼0.2 g m−2 which, if a 1 km cloud thickness is assumed, implies an ash concentration of ∼0.2 mg m−3 the current European lower limit for aviation operations in ash affected airspace. The analyses also suggest that there is little skill in discriminating between limits of 2 mg m−3 and 4 mg m−3 and thus these limits will prove very difficult to specify in practice. But what safety limits can be discriminated, and what limits are appropriate? Clearly the fundamental safety considerations depend on how, and under what conditions ash damages engines. A full suite of ash engine tests is yet to be undertaken. Such tests are likely to lead to some quantitative limits or thresholds for safe operation in ash affected airspace. Using the terminology of a safety limit meaning an ash concentration and supposing that a safety threshold may be a more complex parameter with dependence on factors such as ash concentration, time spent in an ash cloud, and engine operating parameters (e.g., thrust settings, operating temperatures, volume of air passing through the heated sections etc.), it is possible from measurements of ash to make some progress on the problem. We first consider the problem of defining appropriate (measurable) limits and then consider what important parameters should be considered for specifying a dosage threshold.
6.1. Safety Limits
 The statistics of the ash mass loadings retrieved for the Eyjafjallajökull ash clouds (and others, not shown here) suggest that the frequency distributions are not Gaussian. Indeed the large majority of the mass loading frequency distributions studied appear to have a long tail extending toward high mass loadings. The shape of the histograms suggests an exponential type probability density function (PDF) and the Gumbel  function appears to fit the data well. Gumbel distributions arise in extreme value problems for natural phenomena, where the interest is to determine the likelihood of a large flood or other extreme event over a period of time (the return period). The reason why the mass loading histograms appear to follow the Gumbel distribution may be due to the underlying shape of the effective particle radius distribution, which is typically lognormal and also from the retrieval methodology which preferentially selects pixels that are contaminated with the most ash, discarding pixels that fall below some pre-determined value. This has the effect of removing pixels with low mass loadings. The winnowing effect of removing large particles from the size distribution plays a role in reducing the frequency of occurrence of high mass loadings, but this effect is not so apparent in the retrievals because of the lack of sensitivity to particles with effective radii larger than 16 μm or so. It is important to understand the underlying PDF of the mass loading histograms because this determines the appropriate statistical moments to be used. The form of the Gumbel distribution is
m is the variate (mass loading), μo is the mode, and β is a scale factor. The mean (μn) is μo−βγ, the median (μd) is μo−β(ln[−ln(1/2)]) and the standard deviation is , where γ is the Euler-Mascheroni constant. The skewness and kurtosis of the Gumbel PDF are constants. The mass loading histogram for all retrievals on 17 May is shown in Figure 19, using a histogram bin size of 0.1 g m−2. The solid line is the Gumbel distribution with μo = 0.6 g m−2 and β = 1.7. Thus the fitted mode mass loading is 0.6 g m−2, the mean is μn = 1.58 g m−2 and the median is μd = 1.22 g m−2. The Gumbel parameters for the best fit on 15 April are: μo = 0.9 g m−2, β = 1.8, μn = 1.94 g m−2 and μd = 1.56 g m−2. A two component Gumbel distribution is a better fit for the histogram on 15 April (Figure 20), reflecting the fact that there had been continuous ash emission on that day, with ‘new’ and ‘old’ ash present in the atmosphere.
 The probability that the mass loading exceeds some critical value α is
and is called the complementary cumulative distribution function (CCDF) or the survival function. This function may be used to calculate the probability that on a given day there will be an exceedance of the mass loading within the detected ash cloud above some limit, and is shown in Figure 21 for SEVIRI retrievals (dots) and the fitted Gumbel CCDF for the 17 May histogram. Choosing values of 0.2, 2 and 4 g m−2, for 17 May the probabilities are
On 15 April the probabilities are 100%, 48.9% and 3.4%, which are not very different to those on 17 May. These values suggest that within the ash cloud, loadings above 0.2 g m−2 are extremely likely, whereas loadings above 4 g m−2 are very unlikely. Based on this analysis safety limits should be set assuming the ash loadings (and by assumption the ash concentrations) follow extreme value distributions, of the exponential type. Thus there are strong physical and empirical arguments to suggest that the limits should increase on a logarithmic scale (exponential scale), for example, 0.1, 1 and 10 mg m−3, rather than the somewhat arbitrary scale of 0.2, 2 and 4 mg m−3. These logarithmic limits could also be used for forecast concentrations from dispersion models and would have the desirable affect of forecasting restrictions on airspace on a statistical basis.
 In the above argument, we have assumed that the distribution of ash concentrations within a cloud is the same as the distribution of mass loadings. This is obviously true for an ash cloud of uniform thickness, but may not be true for ash clouds with significant vertical structure that varies spatially. The likelihood of more uniform cloud thickness increases with distance from the eruption source and with time since the eruption.
6.2. Dosage Thresholds
 Forecasting regions of airspace with a likelihood of exceedance of some ash concentration limit is desirable as a means for ash avoidance, but there are limitations to this approach and developments and improvements can be made [e.g., Peterson and Dean, 2008]. We propose a simple model for the effect of ash ingestion on jet engines, acknowledging that the problem is complex and requires a suite of engine tests and proper engineering modeling. Let us suppose that the cause of engine failure during flight is due to build-up of material (silicate ash) on the hot parts of the engine, and that the concentration of ash at the inlet to the engine is related to the concentration at the compressor outlet by a magnification factor as described by Kim et al. . Kim et al.  made a series of tests on engines (the “Calspan measurements”) using various dust samples and determined the dust feed rate (F in g s−1)
where V is the volume of air passing through the combustor (m3 s−1), Ψ is the magnification factor (dimensionless) and ρ is the ash concentration (g m−3) at the engine inlet. Kim et al.  derive an expression for the magnification factor, which depends on the compressor ratio; but for the development here, the determination of Ψ is not important. The exact mechanisms causing engine failure are also not under scrutiny here, but we assume that a cause is due to deposition of ash onto parts of the turbine inlet and nozzle guide vanes. The amount of ash deposited depends on exposure time and hence on the airspeed and dimensions of the ash cloud. Thus the mass available for deposition onto the turbine may be written
where υ is the airspeed and d is the distance traveled through the ash cloud. Presumably, Ψ and V can be calculated or are known for particular engine types and operating conditions; then we may define an ash dosage as md and set thresholds appropriately. For example, setting Ψ = 10 (compressor ratios may vary from 5 to 20, depending on engine type), V = 500 m3 s−1 (V can vary from 100 to 1000 m3 s−1), and d = 1000 km hr−1, the ash dosages for various transits through an Eyjafjallajökull ash cloud on 13 May at 04:15 UT (assuming a uniform cloud thickness of 1 km) are calculated and shown in Figure 22. The transects were selected based on the spatial structure of the mass loading and not on air routes. The longest transect is 487 km (B) and the shortest is 37 km (D); both have very similar dosage rates (rate of ash mass intercepted per unit of time) but quite different dosages. The Calspan measurements indicate between 2 g and 34 g of ash was deposited on to the test engine with exposure times of 7–14 minutes and inlet ash concentrations of 100–500 mg m−3. The highest dosage measured shown in Figure 22 is ∼68 g and corresponds to the longest transect. High dosage is also found for transect (A), which although shorter, intersects parts of the cloud with ash mass loadings >4 g m−2. Transect D (d ∼ 37 km) also crosses a region of high mass loading, but because the transit time is small (∼2 minutes) the dosage is low. The dosages and dosage rates depend on many factors, including information concerning the engines and their operating parameters, and on measurements of the ash cloud dimensions and mass loadings. Refinements to this simple model are needed as well as information on engine operating parameters. The dosage threshold suggested here is an improvement over a concentration limit and can in principle be specified from forecast dispersion models using actual or anticipated air routes, as shown by Peterson and Dean .
 The identification and quantification of volcanic ash in the atmosphere by use of infrared satellite measurements has been demonstrated here through the processing of high-temporal resolution geosynchronous measurements from the SEVIRI instrument. The retrieval scheme is able to determine effective particle radii, infrared optical depth and mass loading. It is also possible to determine cloud top height from infrared data. This parameter, while extremely important for the ash/aviation problem, has not been determined here because the skill level using infra-red retrievals is relatively poor compared to CALIOP [Heidinger et al., 2010] and the ultimate aim of our work is to utilize dispersion model simulations, where the winds constrain the vertical dimensions of the ash clouds, in conjunction with satellite data that constrains the ash mass loadings. This can be achieved from a combination of satellite data and dispersion model simulations by use of inversion methods [Eckhardt et al., 2008; Kristiansen et al., 2010, 2012; Stohl et al., 2011], which should provide better constraints on ash cloud vertical structure.
 Validation against independent data and statistical analyses show that the lower mass loading detection limit is ∼0.2 g m−2, with a standard deviation of ±0.05 g m−2, and a skewed frequency distribution of the exponential type, with a tail toward high mass loadings. Synergistic use of two satellite instruments: a high temporal resolution infrared imaging radiometer in geosynchronous orbit and a high vertical resolution lidar in sun synchronous orbit provides the capability to determine volcanic ash concentrations from the mass loading measurements and lidar backscatter. A few independent airborne in situ measurements suggest that concentrations as low as 0.1 mg m−3 can be detected by this method, but the overall correlation between the airborne and satellite-based concentration estimates is poor for concentrations in the lower range (<0.2 mg m−3). The likely reasons for this are the differences in sampling, the heterogeneity of the ash clouds, noise in the data and inadequacies in the infrared retrieval procedure. The mass loading frequency distributions follow the well-known Gumbel distribution (type I extreme value distribution) and by fitting data using this distribution, we conclude that a better scaling for defining safe limits is logarithmic. Another approach to defining safety limits based on dosages is suggested and an example is given showing how time spent in low concentration ash clouds can lead to dosages as high or higher than those for highly concentrated ash clouds which are transited quickly. There is an important message in this result: even in the case where ash concentrations are in the “white zone” (normal operations with no restrictions), concentrations <200 μg m−3 [EU, 2010, paragraph 9] for sufficiently long (several minutes) transits, the ash dosage may reach dangerous levels. The dosage metric needs to be applied with information based on jet engine susceptibility, and is therefore a better approach to aviation safety than crude limits based solely on ash concentrations that are either measured or forecast.
 This retrospective study indicates that on occasions during the Eyjafjallajökull eruption, ash concentrations exceeded 4 mg m−3, typically 3% of ash affected pixels exceeded this limit, and frequently exceeded 2 mg m−3 (up to 50% of ash affected pixels). The use of brightness temperature differences (commonly used at VAACs) for ash quantification, rather than mass loadings can be misleading, as the most negative differences do not always correspond to the highest ash mass loadings. A new ash concentration chart has been introduced that can be used at VAACs to assist in identifying regions of high ash concentration and provide a useful aid to dispersion models that do not currently make use of satellite data directly. The chart can be pre-computed and evaluated for a variety of cloud top heights and underlying surface conditions. The chart could be further developed to allow for varying ash compositions (silicate content), particle size distributions and shapes [Gangale et al., 2010; Clarisse et al., 2010].
 The full spatial extent of the ash from Eyjafjallajökull can be clearly discerned in the SEVIRI retrievals. Sparse measurements of ash from ground-based lidars, from infrequent airborne platforms and from fixed measurement sites must be used with caution, and in conjunction with other data or model outputs in order to properly assess the extent and magnitude of ash clouds. Because of the spatial heterogeneity of the ash, revealed in the SEVIRI retrievals, sole reliance on lidar measurements for monitoring ash clouds and for validating dispersion models may provide misleading conclusions on the concentration and homogeneity of ash in the atmosphere. However, these other types of measurements are vital for independent validation of satellite retrievals.
 At the crucial times when airspace was closed, it seems that ash was horizontally widespread, vertically localized in thin layers of 200–1000 m depth (e.g., ash shown by ground-based lidars and CALIOP) [see Winker et al., 2012], and exceeded 2 mg m−3 in large areas. Thus it is concluded that regulators were justified in adopting a cautious approach to air safety in recommending airspace closures.
 The study also indicates that satellite data and other measurements from ground-based lidars, as well as in situ and remote ground-based and airborne measurements could be used to provide improved strategic and tactical awareness for the ash/aviation problem.
 We are grateful to the three anonymous reviewers whose time and effort spent on reviewing our paper have helped to improve it. The European Space Agency (ESA) and Eumetsat are thanked for assistance with supplying satellite data. The Met Office, DLR and NASA are thanked for allowing us to use data from the FAAM aircraft, the DLR Falcon aircraft and the CALIOP sensor, respectively. EARLINET are thanked for use of the ground-based lidar data. Air quality data are used courtesy of the Norsk Institutt for Luftforskning (NILU). Funding for this research was provided by ESA's envelope program through the Support to Aviation for Volcanic Ash Avoidance (SAVAA) project.