Volcanic eruptions can release large quantities (Tg) of volcanic ash and also gases such as water vapor, carbon dioxide, and sulphur dioxide into the atmosphere [Robock, 2000]. These eruptions can occur in remote locations which are not the focus of regular measurements, and the first indications of such events often come from satellite observations. These satellite measurements are key tools in detecting and tracking both ash and gases from eruptions. Sulphur dioxide (SO2) is often used as an indication of volcanic hazard when using satellite observations [e.g., Carn et al., 2009], under the assumption that ash and SO2 are collocated passive tracers. However, it has been shown that this assumption does not hold in general. This is usually due to the differing densities of ash and SO2 coupled with vertical wind shear causing lateral separation of the ash and gas plumes [e.g., Schneider et al.,1999; Prata and Kerkmann, 2007; Rose et al., 2000; Thomas and Prata, 2011]. While previous work has demonstrated that separation does occur, in this work we introduce a numerical missed ash fraction, defined in section 2, which allows a quantitative assessment of the effectiveness of SO2 as a proxy for ash and its evolution throughout an eruption period. We use the eruptions of Eyjafjallajökull in 2010 and Puyehue in 2011 as case studies, using ash flags derived from the Advanced Along Track Scanning Radiometer (AATSR), the Infrared Atmospheric Sounding Interferometer (IASI) satellite instruments, and an SO2 flag derived from IASI.
 The volcanic ash hazard to aircraft arises from a range of physical damage done by the ash. The most significant of these is that, if ash enters a jet engine, it melts due to the high operating temperatures (the melting point of volcanic ash is ∼1100 K while typical operating temperatures of aircraft engines are ∼1400 K, [Vogel et al., 2011]), and then adheres to moving parts of the turbine, causing them to jam and, potentially, the engine to stall. One of the most famous examples of this, and the one which first brought the danger of ash to the media's attention, was the case in June 1982 of a British Airways Boeing 747-200 that lost power to all four engines mid-flight. It glided for 16 min before the crew managed to restart three of the four engines and make an emergency landing at Jakarta, Indonesia. Following the incident, investigation of the engines revealed significant damage due to volcanic ash from the nearby Mt. Galunggung, which was erupting at the time [ICAO, 2007]. Another similar incident occurred 3 weeks later, and another during the 1989 eruption of Mt. Redoubt, Alaska. These further encounters confirmed that the 1982 British Airways incident was not a one-off event, and that any volcanic ash encounter is likely to have serious consequences [Casadevall, 1994]. Other effects caused by ash encounters include the sandblasting of the windscreen and landing lights, affecting visibility, the blocking of pitot tubes causing flight instruments to show incorrect readings, and interference with the communication systems in the aircraft due to the charged nature of the ash particles [Casadevall and Murray, 2000]. Between the years 1970 and 2000, over 90 aircraft sustained damage as a direct result of flying through clouds of volcanic ash. The danger of the ash is compounded by the fact that it is invisible on aircraft radar and so, particularly at night, there is no way of pilots knowing if they are heading for a hazardous cloud until they reach it and symptoms begin.
 In addition to the potential loss of life and assets, the financial implications of any accident would be severe, as is the cost associated with any prolonged closure of airspace or airports as a result of a volcanic eruption—being able to accurately predict ash cloud movements could therefore bring financial benefits to airlines. According to the International Air Transport Association, during the 2010 eruption of Eyjafjallajökull in Iceland, the closure of airspace over much of Europe caused a loss to the airline industry of an estimated US<DOLLAR/>1.7 billion (The International Air Transport Association press release no. 15, 21 April 2010: http://www.iata.org/pressroom/pr/Pages/2010-04-21-01.aspx).
 Although the immediate negative effects are not as serious as those from ash, SO2, which is also emitted in large amounts from volcanoes, can also have a detrimental effect on aircraft, leading to degradation of parts and hence costly repairs [Vogel et al., 2011]. During 1983–1984, Japan Airlines saw an increase from 1 to 30–40 in replacement cockpit windows due to crazing. This was attributed to acidic conditions in the stratosphere due to long-lived stratospheric sulphuric acid (H2SO4) aerosols from the 1982 eruption of the El Chichón Volcano, Mexico [Bernard and Rose, 1990].
 As well as inconveniences to air travel, SO2 has a negative effect on the environment, mainly through the following reactions:
where M denotes either N2 or O2. The lifetime of SO2 depends strongly on the availability of oxidizing agents, in particular the presence of water vapor, but is typically a few days in the troposphere. The net result is the production of sulphuric acid, which forms sulphate aerosol and, in high concentrations, acid rain [Ward, 2009].
 While ash is the primary concern for air travel, SO2 is, in general, easier to identify and quantify using remote sensing, since there is good sensitivity to absorption by SO2 in both the ultraviolet and infrared regions, meaning there are many different satellite instruments which can be used to detect it. Also, background levels are generally low (less than 1DU, compared to volcanic column amounts >1DU within volcanic plumes over hundreds or thousands of kilometers downwind of an explosive eruption) and as a result, the majority of positive detections will be from volcanic activity [Carn et al., 2009; Zehner, 2012]. Ash detection can be hampered by the presence of overlying ice or water clouds causing the ash to be obscured and, in addition to this, high concentrations of water vapor in clouds can sometimes be flagged as ash, thus causing false positive ash detections. Also, the presence of ice within the ash cloud can affect identification [Clarisse et al., 2010]. Another difficulty with the detection of ash is that sometimes ash clouds do not display sufficient thermal contrast to distinguish them from the underlying terrain and so do not show up in satellite images [Pergola et al.2004].
 At the time of the 2010 eruption of Eyjafjallajökull, the London Volcanic Ash Advisory Centre (LVAAC), which was responsible for determining the areas likely to be affected by ash, did not use quantitative data from satellites for this purpose due to the difficulties in reliably quantifying ash. Instead, it relied upon a sophisticated Lagrangian particle dispersion model in order to predict the trajectories of the ash particles, with satellite images simply being used to verify the results obtained from the dispersion model [Webster et al., 2012]. The significant uncertainties in the model meant that a conservative estimate of the location and concentration of ash had to be taken in order to eliminate the possibility of any aircraft encountering unforecast ash. More quantitative estimates from satellite data are being developed to work alongside the dispersion model to improve ash forecasts [Francis et al., 2012], but the difficulty of determining ash properties from satellite data remains. The use of satellite SO2 products by the VAACs is already well developed, with the Support to Aviation Control Service (SACS) regularly supplying near-real-time SO2 products from a range of UV and infrared satellite sensors [van der A et al., 2010], so being able to reliably use SO2 as a proxy for ash would be advantageous to VAACs. Although there have been several studies comparing ash and SO2 emissions from various volcanic eruptions [Schneider et al., 1999; Prata and Kerkmann, 2007; Rose et al., 2000; Thomas and Prata, 2011], but these have been largely qualitative. In this work we attempt to provide a quantitative measure of the effectiveness of satellite SO2 products as an ash proxy.
1.2 Retrieval Techniques
 The satellite used for the majority of the SO2 and ash detection for the eruptions studied for the purposes of this paper was the Infrared Atmospheric Sounding Interferometer (IASI) on board the EUMETSAT Metop-A satellite. However, for comparison, an ash retrieval was also used from the Advanced Along Track Scanning Radiometer (AATSR), which was stationed on board the now-defunct ENVISAT satellite from 2002 until communication was lost with the satellite in April 2012.
 IASI completes a global scan once every 12 h. The instrument works in the thermal infrared region and uses a Fourier transform spectrometer covering the spectral range 645–2760cm−1(3.62–15.5μm). Its field-of-view consists of four circular pixels, each of diameter 12km at the surface, within a square of 50km × 50km, step-scanned across track in 30 steps, giving a swath of approximately 2000km. Clerbaux et al. present a diagram of the setup in their Figure 1. IASI has been widely used for the detection of SO2, and a brightness temperature index based on channels around the so-called ν3 band centered at 7.3μm [Clarisse et al., 2008] is now included in the SACS system.
 Both the SO2 and ash detection schemes used with IASI in this work rely on the approach described by Walker et al. [2011, 2012]. The scheme makes use of a generalized error covariance that contains not only the instrument noise, but covariance due to interfering trace gases and broadband scatterers (such as aerosols and clouds) that should be unrelated to the required retrieved property. Since these signals are included in the covariance, they need not be retrieved nor their variance taken account of in the forward model of the atmosphere.
 Using the notation of Rodgers , we define the measured spectra, y, as a function of the forward model, F(x,b):
where x is the quantity of interest (either optical depth of volcanic ash or column amount of SO2), bcontains the properties of some background atmospheric state, and ε indicates a vector of errors in F(x,b). The value of x is calculated by linearizing about some fixed value, x0, leading to the following expression:
where K is the Jacobian of ywith respect to x. The least squares estimate of x can be obtained by
The error covariance matrix, Sε, is built up from IASI measurements in the same geographical area and time of year when no volcanic signals are present.
 This approach has the advantage of making use of the high spectral resolution provided by the IASI instrument, while not sacrificing computational speed. The retrieved value of x does, however, rely heavily on the choice of linearization point and so requires independent calibration measurements of x to provide accurate numerical results.
 The ν3 absorption features (at 7.3μm) are used in the SO2 detection scheme [Walker et al., 2012]. This detection scheme is complemented with an SO2 column amount optimal estimation retrieval, which uses both the 8.7μm ν1 and ν2 bands [Carboni et al., 2012]. The latter has the strongest absorption; however, it lies within a strong absorption band for water vapor and as a result is not very sensitive to emission from the lower atmosphere. The 8.7μm band is weaker, but lies in an atmospheric window and so contains a total column SO2 signal. By using both bands, the retrieval has some sensitivity to plume height, as well as a column amount.
 Walker et al.  performed a sensitivity study of this IASI SO2 detection using data from the 2010 Eyjafjallajökull eruption. They found that the detection threshold decreased exponentially with height; plumes that lay below 2 km provided a threshold of 17 DU, but this rapidly improved to 3.3 DU between 2–4 km, 1.3 DU for 4–6 km and reached 0.3 DU for the tropopause cold point. This sensitivity is approximately an order of magnitude better than earlier IASI SO2 flags [Clerbaux et al., 2009; Zehner, 2012] and was able to reliably detect the plume from the earliest explosive stages of the eruption.
 The application of this method to volcanic ash detection with IASI is a more recent development, and the approach taken is similar to that described by Clarisse et al.. In this case the x defined in equation (4) is the volcanic ash optical depth, τ, and a broad region of the IASI spectrum from 7.8–14.7μm is used. The value of τ retrieved strongly depends on the linearization point, τ0 chosen, which limits its usefulness in determining the amount of ash present. However, the method has been found to be a useful ash flag for the presence of ash clouds, as elevated ash amounts are clearly visible above the noise in the retrieved fields.
 AATSR measures radiance in seven different channels ranging from the visible to the thermal infrared. One of the defining features of AATSR is the fact that it takes two images, one of which is a nadir view and the other a forward view at a zenith angle of 55°. This allows the radiance from the surface and the radiance from particles in the atmosphere to be distinguished from each other, since in each view the signal has a different atmospheric path length. Following any particular forward view image, it takes ∼150 s for the satellite to be in a position such that the nadir view samples the same region, and as such the two views are near-simultaneous. The instrument has a swath width of 512km (with 555 pixels across the nadir swath and 371 pixels across the forward swath), and global coverage is achieved every 3–6 days. The spatial resolution of this instrument is better than that of IASI (∼1 km as opposed to ∼12 km), but the small swath width and relatively infrequent coverage of any particular area reduces the number of coincident measurements from AATSR, hence the desire for an IASI ash retrieval. A full description of the AATSR instrument is given by Llewellyn Jones  and Smith et al. .
 The measured radiances were converted into ash heights using the parallax between the two images. The brightness temperature difference between the 10.8μm and the 12μm channels can be used as a rough, qualitative indication of the amount of ash present in each pixel. This brightness temperature difference gives a negative value where ash is present, but a positive value where water vapor or ice (i.e., cloud) is present, as described by Prata  and Wen and Rose . In this work, a pixel was flagged as ash if both of the following conditions were met:
The additional condition on the brightness temperature difference between the 3.7μm and 10.8μm channels is imposed as a means of removing false detections, as high, cold ice cloud can also produce a negative 10.8–12μm brightness temperature difference.
1.2.3 Comparison of Instruments
 Figure 1 shows the spectral optical depth for a 5DU column of SO2, with a Gaussian altitude distribution centered around 15km, and a 1km thick ash plume. The horizontal bars at the top of the plot show the wavelengths covered by IASI and AATSR. From this it can clearly be seen that SO2 has a spectral-line based signature, while the corresponding result for ash is a broadband spectrum. Furthermore, all seven of the AATSR channels are completely clear from the SO2 spectral features, meaning that the AATSR ash retrieval is unlikely to be affected by any SO2 present. The spectral region sampled by IASI, however, encompasses both ash and SO2 features, which suggests that the presence of ash may affect the IASI SO2 retrieval, and vice versa. This is found to be the case where ash concentrations are particularly high, such as very close to volcanoes themselves, and a method to reduce this problem is discussed later in relation to the 2011 eruption of Puyehue.