A new optimal estimation algorithm for the retrieval of volcanic ash
properties has been developed for use with the Infrared Atmospheric Sounding
Interferometer (IASI). The retrieval method uses the wave number range
680–1200 cm

Assuming a single infinitely (geometrically) thin ash plume and combining this with the output from the radiative transfer model RTTOV, the retrieval algorithm produces the most probable values for the ash optical depth (AOD), particle effective radius, plume top height, and effective radiating temperature. A comprehensive uncertainty budget is obtained for each pixel. Improvements to the algorithm through the use of different measurement error covariance matrices are explored, comparing the results from a sensitivity study of the retrieval process using covariance matrices trained on either clear-sky or cloudy scenes. The result showed that, due to the smaller variance contained within it, the clear-sky covariance matrix is preferable. However, if the retrieval fails to pass the quality control tests, the cloudy covariance matrix is implemented.

The retrieval algorithm is applied to scenes from the Eyjafjallajökull
eruption in 2010, and the retrieved parameters are compared to ancillary data
sources. The ash optical depth gives a root mean square error (RMSE)
difference of 0.46 when compared to retrievals from the MODerate-resolution Imaging Spectroradiometer (MODIS) instrument
for all pixels and an improved RMSE of 0.2 for low optical depths
(AOD

The detection of volcanic ash and
the retrieval of its properties have become a topic of increasing interest
following the eruption of Eyjafjallajökull in 2010. Volcanoes are
responsible for the emission of large quantities of aerosol particles and
gases – such as H

Presented here is a new optimal estimation algorithm for the retrieval of
volcanic ash properties that has been developed for IASI to take advantage of
its spectral information, which could be further adapted for use with other
hyperspectral satellite instruments. The retrieval method uses the wave number
range 680–1200 cm

In this work the Oxford-RAL Retrieval of Aerosol and Cloud (ORAC) algorithm

In this paper the fundamental instrument used in the analysis is described in
Sect.

IASI, on board the MetOp platforms, is a series of three identical Fourier
transform spectrometers designed primarily to provide data to be assimilated
for use in numerical weather prediction (NWP). The instrument is a Michelson
interferometer covering the mid-infrared (IR) from 645 to 2760 cm

An optimal estimation scheme has been developed to retrieve the properties of
volcanic ash plumes. The method analyses the brightness temperature spectra
from IASI to retrieve the following parameters: ash optical depth (at a
reference wavelength of 550 nm), ash effective radius (

An ash detection method, based upon the trace gas detection method described
by

For a detailed description of optimal estimation see

The retrieval aims to find the most probable state of

In order to find the minimization point of Eq. (

The measurement error covariance matrix,

The elements of the error covariance are calculated using

Given that the error covariance is relative to this mean residual, the input
IASI spectrum to the retrieval must be adjusted to account for this bias.
This produces a new cost function that must be minimized:

The measurement error covariance matrices created using
IASI data from

.

A pictorial form of the assumed scenes for each covariance matrix:

Initially, when selecting the IASI scenes to include in the creation of the
covariance matrix, only scenes from days with no known volcanic activity were
used. However, this produces a covariance with a large variance due to the
large impact the presence of cloud has upon the spectral region chosen for
the retrieval, i.e. any transparent window channels. In cloudy scenes, this
makes the retrieval possible as the variation due to cloud is accounted for
and, because of the large variance, the retrieval is able to converge.
However, for a clear-sky scene, including such large variances allows the
retrieval to appear to converge, albeit with a large uncertainty. Therefore,
separate covariance matrices have been produced using solely either clear-sky
scenes or cloudy scenes, where a cloudy scene is deemed to be where the
window channel brightness temperature differs by more than

It must be noted that there are further error components that are not considered within the current covariance matrices that may be addressed in future work. These are the errors associated with the modelling of the plume, such as assuming a plane-parallel atmosphere, assuming that there is no leakage of radiation from the edges of the plume, assuming that the plume has only a single layer, and assuming the ash particles to be spherical and have a log-normal size distribution of fixed spread.

Due to the computational intensity of the retrieval algorithm the forward
model used to simulate the atmospheric conditions must be chosen to achieve a
practical speed; for this a fast radiative transfer model is needed. The
chosen model to simulate clear-sky radiances (i.e. containing gaseous
absorbers but not cloud or aerosol/ash) is RTTOV

Standard atmospheric profiles are assumed within the forward model, except
for temperature, pressure, altitude, and water vapour. These profiles are
obtained from ECMWF operational forecast data

RTTOV provides the clear-sky top of atmosphere (TOA) radiance along with both
upwelling and downwelling radiances at each altitude level. These can be used
to formulate an overcast TOA radiance that includes a single layer of ash (or
other broadband scatterer), which is assumed to be infinitely thin. Figure

Schematic showing the atmospheric interactions simulated in the radiative transfer forward model.

Ignoring multiple reflections between the layer and the surface, the “ash”
TOA radiance,

An advantage of the optimal estimation framework is it provides a rigorous
estimation of the uncertainty in the retrieved state. The a posteriori
error covariance matrix,

The uncertainties in the retrieved parameters and the DFS available in the retrieval using the clear (first column) and cloudy (second column) covariance matrices, shown as a function of ash optical depth (horizontally) and plume top altitude (vertically). From the top, the rows exhibit the uncertainties in ash optical depth, effective radius, plume top altitude, effective radiating temperature, and available DFS. Any value higher than the colour bar scale is shown hatched.

An uncertainty analysis was performed using synthetic spectra (adding an ash
plume to a reference clear atmosphere) to assess the sensitivity of the
retrieved parameters to variations in the state. In the simulations the ash
optical depth at 550 nm varied between 0.01 and 10, and the plume top
altitude lay between 1000 and 100 mb (

Using the clear covariance gives consistently larger DFS available for all
combinations of parameters, with optically thick plumes at lower altitudes
having nearly 0.5 DFS more than the results using the cloudy covariance. The
impact of this difference in DFS can be seen in the uncertainty in effective
radiating temperature, where the more optically thick plumes have a
significantly larger uncertainty. Interestingly, and perhaps unexpectedly,
the effective radiating temperature uncertainty improves when the ash layer
is at the highest altitudes. This is due to the substantially larger amount
of atmosphere below a plume at 16 km (as opposed to 8 km). This leads
to an increase in the fraction of the total radiance across the window
regions contributed by the atmosphere below the plume and, conversely, a
decrease in the fraction of the total radiance that comes from the emission
of the plume itself. It is also known that discerning ash plumes from
meterological cloud is challenging when the temperature contrast with the
surface is very small

The retrieved altitude uncertainty is typically

For both ash optical depth and effective radius, the associated uncertainties
have a similar pattern and are significantly lower for large values of
optical depth. The smallest uncertainties occur for high-altitude, optically
thick plumes, similar to both plume top height and effective radiating
temperature, as this is where the largest number of DFS is available. In
contrast to the uncertainty in plume top altitude, the estimated
uncertainties decrease as the height of the plume increases, with a maximum
expected uncertainty near the surface. This is most apparent at AOD

The overarching behaviour of the expected uncertainty produced using both the clear and cloudy covariance matrices is the same, with the clear covariance producing consistently smaller uncertainty. It must be noted that this sensitivity study was carried out assuming a clear atmosphere with no clouds (except for the volcanic ash plume), and therefore the clear covariance is expected to perform better due to the smaller variance it contains. If used for a cloudy scene, this smaller variance gives rise to the potential for a retrieval to have a high cost or fail to converge entirely, whereas the larger variance of the cloudy covariance matrix can account for the cloud beneath the plume and produce a better retrieval.

Ideally, the clear covariance matrix would be used for plume scenes where there is no meteorological cloud, and the cloudy covariance matrix would be used for scenes where meteorological cloud is detected. Cloud clearing of this manner is challenging and infeasible. Instead, a criterion is currently applied to the retrieval whereby it must pass a set of quality control tests. These ensure the output is sensible and realistic (e.g. the plume top altitude is not below the surface or the effective radius negative) but also only consider the retrieval a success if it converges within 10 iterations and the normalized cost is below a specified threshold (default is 2). Consequently, the retrieval is first carried out using the clear covariance matrix, and then, if it fails to pass the quality control tests, the retrieval is further carried out using the cloudy covariance matrix. If the retrieval again fails to pass the quality control tests, it is discarded and deemed a failed retrieval.

Example retrieval output from 9 May 2010 during the eruption of Eyjafjallajökull. The left-hand column presents the retrieved parameters: ash optical depth, effective radius, and height. The centre column shows a histogram of the respective retrieved values with the a priori value indicated by the red dotted line, and the right-hand column contains the associated uncertainties for each parameter.

An example of the retrieved plume properties and their associated
uncertainties is shown in Fig.

MODIS instruments reside aboard the
sun-synchronous orbiting NASA Terra (launched May 2002) and NASA Aqua
(launched December 1999) satellites. Terra orbits at a 705 km altitude, with
a period of 98.8 min, an inclination of 98.2

ORAC uses radiances measured
from satellite-based imaging radiometers, including MODIS, to retrieve
aerosol, cloud, volcanic ash, and surface properties. The retrieval algorithm
is based on a long heritage of optimal estimation based on the work of

The ash particles are assumed to be spherical with a log-normal size
distribution, and the size distribution averaged spectral optical properties
(extinction coefficient, single-scattering albedo, and phase function) are
calculated using Mie theory. Since the width of the distribution is not a
retrieval parameter, it must be assumed, and a standard deviation of 2.0 is the
value adopted for the ORAC retrieval. The complex index of refraction must
also be assumed for which we use values measured from Eyjafjallajökull
ash samples

The ash optical properties are further used as input to the plane-parallel
radiative transfer solver DISORT to compute scalar spectral reflection,
transmission, and emission operators used in a “fast” forward model, details
of which are described in

IASI and MODIS have very different fields of view, and, hence, they must be co-located in order for a comparison to be carried out. The number of MODIS retrievals is far greater than that for IASI due to its better spatial resolution along the track. In order to compare the results, the MODIS data are aggregated onto the IASI resolution; i.e. all MODIS pixels within 6 km of the IASI pixel centre are used to formulate the average. Co-location is assumed if the IASI measurements and the MODIS measurements lie within 50 km and 1 h of each other.

A comparison of the AOD at 11

Comparison of AOD at 11

Reasonable correlation,

Immediately following the Eyjafjallajökull eruption in 2010, it became
clear that aircraft measurements (both in situ and remote sounding) were
needed in order to validate the ash dispersion forecasts. Two of the European
aircraft deployed were the UK's BAe-146 FAAM aircraft (

On board the FAAM aircraft were instruments capable of taking in situ and
remotely sounded measurements. The in situ observations come from two
wing-mounted optical particle counters: a passive cavity aerosol spectrometer
probe for particles with size distributions of diameter 0.1–3

The DLR aircraft used the same instruments as the FAAM aircraft; however, the
assumptions made in the calculation of the size distributions were different.
Values for the optical properties (refractive index and shape) of the
particles must be assumed as the response of the detectors is dependent upon
these as well as the size

The parameters observed by aircraft on 17
May 2010 (geometric mean diameter by volume, geometric standard deviation,
and relative weight by mass, taken from

A histogram of the effective radius retrieved in the IASI scenes on 17 May 2010.

The values for the particle effective radius vary due to differing assumptions made in the calculations. The assumed type of size distribution in the retrieval and assumed shape in the aircraft calculations can impact the expected effective radius. The distribution of retrieved effective radius from IASI measurements is consistent with the values from the aircraft measurements, although slightly smaller. This is expected to be due, in part, to the sensitivities of the different instruments to different particle sizes, as well as due to the IASI histogram including the full extent of the plume and, therefore, including regions where the larger particles have been deposited out of the plume.

CALIOP is the primary instrument on board the Cloud-Aerosol Lidar and Infrared
Pathfinder Satellite Observations (CALIPSO) satellite, launched in May 2006.
CALIPSO flies as part of the NASA Afternoon Constellation (A-train) of
satellites in a sun-synchronous orbit with an Equator-crossing time
(ascending) of 13:30 local solar time. With an orbit inclination of
98.2

The results for an overpass of Eyjafjallajökull on 6 May 2010. The derived CALIOP cloud top heights (triangles) and the retrieved IASI plume top altitude (circles) are overplotted onto the CALIOP backscatter.

The results of comparisons between the retrieved IASI altitude and the derived CALIOP plume height for the Eyjafjallajökull eruption on 6 and 11 May 2010.

Given the very differing footprints of IASI and CALIOP, they must be
co-located in order to allow comparison. The frequency of IASI retrievals is
far greater than that for CALIOP; however, CALIOP has far greater spatial
resolution along the track. CALIOP observations of volcanic plumes have been
identified using Spinning Enhanced Visible and Infrared Imager (SEVIRI) false-colour images based on the infrared channels at
8.7, 11, and 12

CALIOP produces atmospheric backscatter profiles for every pixel. However, the quantity required for validation is the cloud top height of the volcanic plume as this is the comparable ash property retrieved from IASI. Initially, the mean backscatter above 15 km is calculated for each CALIOP scene and is subtracted from the total backscatter. This removes any background backscatter, leaving only the backscatter caused by the presence of clouds or the ash plume. For each CALIOP pixel the cumulative backscatter value is calculated descending through the atmosphere and the cloud top height is considered to be at the altitude at which the atmospheric extinction passes a given threshold. For the purpose of this study, and given the manageable number of scenes considered, the threshold value is calculated individually for each scene and chosen to be the value that best matches the CALIOP image.

Due to the narrow swath of the CALIOP instrument, there are only eight coincidences (119 pixels in total) between the two satellite datasets where the CALIOP track intersects with the volcanic plume seen by IASI. This leads to only a few scenes available for comparison. Shown here are examples from the Eyjafjallajökull eruption in April/May 2010.

Figure

Comparisons are not shown for all scenes individually; however, Fig.

The results of comparisons between the retrieved IASI altitude and the derived CALIOP plume height for all scenes during the the Eyjafjallajökull eruption. The different colours indicate different scenes.

The results shown follow the criterion
established in Sect.

A new optimal estimation scheme has been developed for the detection and characterization of volcanic ash plumes using IASI measurements. Pixel-by-pixel estimates are derived for the properties of the volcanic ash: ash optical depth, effective radius, plume top altitude, and effective radiating temperature, with associated uncertainty estimates.

The measurement error covariance matrix is created using difference spectra, which are the residuals between IASI measurements and simulated spectra (calculated using RTTOV with ECMWF operational data). This ensures that all inaccuracies in the radiative transfer modelling of the IASI spectrum, caused by lack of knowledge of the background atmospheric conditions (e.g. atmospheric profiles) or imperfections in the radiative transfer calculation (e.g. spectroscopy), are accounted for within the covariance matrix. Separate covariance matrices have been created using only clear-sky or cloudy scenes, where the latter contains the variance caused by the impact of meteorological cloud. It should be noted that this does not account for errors in the ash optical properties.

A sensitivity study has been carried out using both the clear-sky and cloudy covariance matrices, which showed that the clear covariance consistently produced smaller resultant uncertainty due to the smaller variance it contains. However, this only considers clear-sky synthetic spectra. Therefore, the criterion that is enforced first iterates the retrieval using the clear covariance matrix; then, if the retrieval fails to pass the quality control tests (e.g. convergence), the retrieval is re-run using the cloudy covariance matrix. The uncertainty analysis demonstrates that the uncertainty in AOD, effective radius, and plume top altitude is higher for optically thin plumes, and for AOD and effective radius; this further increases as the plume nears the surface. In contrast to this, the uncertainty on plume top altitude decreases at lower altitudes.

The results of comparisons between the retrieved volcanic ash properties and measurements from other instruments have been shown. The AOD has been show to have good agreement with retrievals carried out using the MODIS instrument on board NASA TERRA. This is especially true at lower AOD (RMSE: 0.15–0.2) with an increase in spread at increasing AOD (RMSE: 0.46). Aircraft campaigns during the Eyjafjallajökull eruption confirm that the retrieved distribution of effective radii from IASI is in line with the aircraft measurements, skewing towards slightly smaller particles due to viewing a larger area of the plume and therefore a slightly different distribution of the ash. Comparing the derived cloud top heights from CALIOP and retrieved IASI plume top heights further illustrates the robustness of the retrieval, with RMSE values consistently less than 2 km. Underestimation of the plume top altitude in optically thick pixels is observed, which is thought to be caused by the physical thickness of the plume, or the existence of multiple layers within the plume, which are not accounted for in the forward model.

Future work will aim to improve the current limitations within the retrieval and examine further ways to fully capture high plumes and account for the presence of cloud within the IASI scenes through the inclusion of another cloud (or ash) layer within the retrieval process (a two-layer forward model) and an improved selection of channels specifically chosen to minimize the impact caused by clouds.

The data shown in this paper for the Eyjafjallajökull eruption can be
made available on request to the author (lucy.ventress@physics.ox.ac.uk). The IASI ash detection algorithm

Roy. G. Grainger and Elisa Carboni were supported by the NERC Centre for Observation and Modelling of Earthquakes, Volcanoes, and Tectonics (COMET). The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement number 606738, APhoRISM project. The authors acknowledge funding from the NERC VANAHEIM project NE/1015592/1 and the NERC SHIVA project NE/J023310/1. This study was funded as part of NERC's support of the National Centre for Earth Observation. The authors would also like to acknowledge F. Marenco for providing additional FAAM aircraft data that, although not shown in this paper, have proved very useful in the study. Edited by: A. Sayer Reviewed by: two anonymous referees